Body Language & Banter 85 Learning Swedish with The Two Ronnies Try this experiment on a friend. Tell them you like their shirt using different tones of voice: sarcastic, sincere, amazed. Then see what they understood. You will find it difficult to appear sincere because I have told you to say you like their shirt — unless of course you really do. When you use sarcasm they will find it hard to process your statement. It is revealing how we use the information. Interestingly, a piece of research described in Scientific American shows even insincere flattery is effective. If you want a pay rise from your boss, any form of flattery will do. Vanity appears to override skepticism! Interaction The normal cadence of communication between people includes a great deal of mutual interruption. When a meeting breaks down we often see people begin to say things like, “Please don’t interrupt me” “Do you mind, I was talking,” “Pleeeease, let me finish.’ If the meeting is really getting out of hand, third parties will often step in and tell one to wait for the other. This is where the mechanics of face-to-face interaction fail, as we need to interact in order to communicate effectively. Because we have a lot more time in a face-to-face meeting people can wander ‘off topic. This is an important part of the process of communicating. After all since most phone calls are 2-3 minutes and HOUSE_OVERSIGHT_015775

86 Are the Androids Dreaming Yet? most meetings an hour, there are another 57 minutes to fill! These off topic items bring in social experience and help us form the background context we need to properly communicate. What is Background Context? Alex and Bella are both fans of the British comedy duo, the Two Ronnies, and enjoy their learning Swedish sketch. Bella asks Alex what kind of sandwich he wants for lunch. Alex replies ‘M’ Bella laughs. If you have seen the sketch you will understand the background context to the joke. If not this paragraph might as well have been in Swedish. Take a look at the sketch on YouTube and reread this paragraph... Now you understand. Do I think in English? Most scientists believe we think thoughts using language, but most scientists writing about thought are linguists or psychologists. If you are a dyslexic engineer like me, language is a long way down the processing chain. I think abstractly and then translate those thoughts into words. Some ideas don’t map between languages and often, one language adopts the words of another to fill in the gaps. Some interesting examples are: Zeitgeist German, spirit of the times Schadenfreude German, enjoying others misfortune Chutzpah Hebrew, audacity All of these are fully signed up, card carrying entries in the Oxford English Dictionary. Some languages have fewer distinctions between ideas: truth and law are the same word, ‘torah, in Hebrew. Languages have different tenses and structure. In Chinese all words are one syllable and the script is pictographic rather than phonetic. This is unusual, even Egyptian and linear-B, which look pictographic are mostly phonetic. With single syllable words, Chinese uses voice inflection to change meaning; a rising or falling tone can change the meaning of a word from ‘grey’ to ‘girl’ In many Western languages rising voice inflection is used to indicate a question, as in Australian English or irritation, as in English English. So how do the Chinese show if they are annoyed or want to ask a question? They elongate their words and accentuate the changes in intonation. An argument in Chinese can sound quite alarming to the Western ear, with its percussive monosyllables and extreme inflection changes. This HOUSE_OVERSIGHT_015776

Body Language & Banter 87 degree of inflection is used in English, but only in extreme emotional contexts: A Chinese argument over cold tea can sound like an accusation of murder to a Western ear. Symbolic Communication The earliest recorded permanent human communication is cave painting, dating to 33,000BcE. Written communication emerged in Sumer, the southern part of Mesopotamia (now Iraq), using a script called Cuneiform, written on clay tablets. It was used primarily for accounting. The Sumerians are responsible for our common use of base twelve. Twelve hours in a day, inches in a foot, and notes in the scale; all stem from their civilization. Although not the first to write stories, the Greeks perfected the dramatic forms we use today: poetry, prose and plays. Watch an episode of ‘Law and Order’ and you are seeing a direct descendant of a Greek tragedy, complete with suffering and justice denied. All this permanent thought art is made possible by the translation of ideas into symbols. Scripts and Symbols The world supports a huge variety of scripts split roughly into phonetic, representing the component sound of words, and pictographic, stylized pictures of the ideas. Traditional # se Simplified JF # =} Open Picture Learn Chinese Traditional and Simplified Some scripts have interesting quirks. Ancient Hebrew, although phonetic, is a script where vowels are omitted. Modern Hebrew often leaves them out as well. This means words can be ambiguous and need context to decipher them. A common set of Chinese characters has long been used by Mandarin, Cantonese, and Japanese speakers even though HOUSE_OVERSIGHT_015777

88 Are the Androids Dreaming Yet? their spoken languages are entirely different. The script languages of these people are gradually diverging and might in time become entirely separate languages too. The Chinese government in Beijing has moved to using simplified Chinese for Mandarin speakers, while Hong Kong continues with the traditional form. Japanese has developed many new characters for Latin Hello Reader Japanese WHA TCAITHSIE Russian SypaBcrByH UMTAaTeJIb Greek Teta oag avayyvwotn Hebrew ANNpDVw Arabic {gl Lays Chinese fee: RE ! Chinese ee: FU! simplified Korean c}t] olA} Japanese HEA CAITH IS Linear-a can’t be translated! Linear-b XIFP (best I could do is ‘new wine’) owl Lao avUIWAToIW Hindi eh (hello) Persian 9siilsd aduu Hieroglyphics i= = Ajo k= =| modern ideas, such as computers, that differ from the Chinese, and mixes in a great deal of Katakana, a script allowing the phonetic representation of foreign words. If you walk around these countries their signage looks quite different, although I am told Cantonese speakers can still read HOUSE_OVERSIGHT_015778

Body Language & Banter 89 simplified Chinese. Take a look and normally you will find them to be quite different. Each example in the figure is my best attempt to translate the phrase “Hello Reader” into a script and the corresponding language. Symbols of the World English is one of the most irritating script languages of all. It commonly uses etymological elements, showing the history or origin of the word that has nothing to do with the sound of the word. A word like school has the ‘k sound spelt ‘ch, showing its historical derivation from the Greek, but confusing for pronunciation. English has 53 sounds derived from only 26 letters, so there are plenty of letter combinations, many of which are irregular. Because the language favors historical convention over simplicity, sugar is pronounced “shu-gar” whereas sand is strictly phonetic. As for Leicestershire I'll leave that as a test for the American readers amongst you. If you're British, try Mattapoisett, a town in Massachusetts named in Native American. Yet English is also a ‘lovely’ language. Because of its richness there are often twenty different ways to say something, and a dozen words to choose on any topic. One of my own favorite words is ‘jump% It is phonetic, but also onomatopoeic and even pictographic. Jump both sounds like a jump and looks like a jump. Two scripts that puzzled scholars for many years are Linear-b and Hieroglyphics. Linear-b — found on clay tablets on the Island of Crete - turned out to be a coded form of ancient Greek with some slight quirks, such as dropping the letter ‘s’ from the ends of words. The ‘s is superfluous in most Greek words, and dropping it saved precious clay space! Hieroglyphics was a real puzzle. It looks so like a pictographic language that it fooled many people for centuries. The Rosetta Stone was discovered in 1799 and became the key to their deciphering. This stone had the same edict written out in 3 languages —- Greek, Egyptian and Demotic. The French adventurer Jean-Francois Champollion decoded hieroglyphics in 1822 and although it Jooks pictographic, it was found to be predominantly phonetic. Linear-a, another script found on the Island of Crete has yet to be decoded and remains one of the world’s great- unsolved mysteries. All these different ways to code ideas into symbols present the children of the world a great learning challenge. Because written language is so young, in evolutionary terms, our brains have not had enough time to evolve to master it. Instead words co-opt parts of our brains originally HOUSE_OVERSIGHT_015779

90 Are the Androids Dreaming Yet? evolved for different purposes. As languages differ in their construction they co-opt different bits of the brain. It is possible to see this using brain imaging. Dyslexics - and I am one — have difficulty in translating between the realm of conceptual thought and written script. This translation is subtly different for each language. Chinese speakers use their motor cortex to process characters. Young children write out the characters over and over, to memorize them, so the ‘muscle’ memory is highly involved. French and Spanish children use the audio pathways, as most of their language is phonetic, the motor part of writing is then an add- on and does not process meaning. English children must use portions of their visual cortex to process the meaning of words, as many words have spelling quirks that have nothing to do with the sound of the words. Some studies even suggest a child dyslexic in one language, because, for example, their audio pathway is impaired, might not suffer the condition in another language that relied on a visual or motor skill. Can Objects Communicate? The process of communication has many components, starting with something capable of communicating. Communication usually - perhaps always — is something that occurs between sentient beings. I don't think of my computer as communicating with me, but rather think of it as a medium for communication or a dumb machine. But colloquial language around the subject is a little muddled. We all agree a lighthouse does not communicate, even though it can signal danger, but what do we mean when we say, “That song really spoke to me.” No one believes the song is actually communicating, but some kind of communication was made nonetheless. When we talk of communication do we mean the agent or the message? Stories Humans enjoy communicating; we create works of art, music and literature that transcend simple analysis. The COIN dynamic slide, which we saw earlier detailing the strategic situation in Afghanistan, would probably have been better communicated with a story. Humans, unlike computers, do not cope well with large quantities of unrelated information, and studies of memory and comprehension show we HOUSE_OVERSIGHT_015780

Body Language & Banter 91 benefit from a narrative structure. Let me give you a basic example. One simple trick the human brain uses is chunking. Give yourself a moment to try to learn this string of characters. HALTNTIBMGTATLAMATLOLPOMSGTG TRY TO MEMORIZE THE STRING WITHOUT READING ON Now, if I divide it into chunks, you will see it includes meaningful information. HAL TNT IBM GTA TLA MAT LOL POMS GTG You probably won't recognize all the acronyms unless you are under 10. Even then, you will find memorizing it hard, but if you put the sequence into the context of a story then it is much easier to learn. HAL uses TNT to blow up the IBM building in Grand Theft Auto. “Three Letter Acronyms are annoying, says MAT. I’m Laughing Out Loud; Parents Over My Shoulder. Got To Go. We find it easier to fit new information into existing structures within our brains rather than memorizing by rote. I’ve used quite a bit of modern Internet slang here. You'll find young people recall this information better than older people for whom GTG and POMS are nonsense. If you want to memorize something, experts recommend you imagine bizarre images and relate them to a story pictured in the mind’s eye. Try it and you may very well find you can still remember my sentence in ten years time! Let’s try something else. The following sentences are a little different, yet the recall scores for information in the two are dramatically different: 1. I met an old tramp on 42™ Street wearing a dirty grey rain coat. 2. New York on a cold damp November day; as I cross the street I bump into an old man wearing a dirty grey Macintosh. His shuffling gait suggests some sordid intent. I think nothing of it, but this brief meeting was to change my life. HOUSE_OVERSIGHT_015781

92 Are the Androids Dreaming Yet? The addition of contextual cues allows you to form a mental picture. By withholding some information at the end I have used a dramatic trick to cause your brain to free wheel and imagine what happens next. You are involved in the story. Notice the /Jonger story, with more data in it, is paradoxically more comprehensible and memorable. Ed Tufte makes the point about our ability to process information very forcefully. He believes presentation experts are wrong when they recommend you keep your slides to a few words! He points out the common advice to use only six bullets per slide and six words per bullet comes from a misconception that has blighted a generation of presenters. Studies performed on memory in the 1960s measured unrelated word recall. Six words are all you can remember if the words are meaningless. But if the words have meaning we can comprehend and absorb many pages of data. Hundreds of millions of people throughout the world read a newspaper every morning and can recall the stories throughout the day; the poems, songs and plays we memorize when young are usually long, comprising thousands of words, yet we are able to remember them verbatim for the rest of our lives. When we tell a story, we are trying to draw the reader in so they can to experience our imaginary world and be ‘ir’ the story. When I read a story — perhaps Harry Potter — 1 don't think about the grammar and punctuation, or even the accuracy of character portrayal. I’m transported to a different place. I experience a piece of the reality or ‘imaginality’ the storyteller has created. I can describe the characters, the scene, the sounds and the smells. A good author forms a complete world in our heads corresponding with the world they have in their heads. With more abstract information, comprehension and retention is harder. Often if the information does not hang together in a linear narrative it can be impossible to take in at a single sitting. However, if it forms a story and is well told so you ‘get it, you do not need it repeated. We experience something of this effect when we watch a good movie. “I’ve already seen that one,’ means you have absorbed the whole story in a single sitting. You don’t need to watch it over again to comprehend it. Comedy Finally, when you mix all the elements up, emotional understanding, body language, in-person communication and empathy; you get comedy. Humans ‘do’ comedy from a very young age and it’s vitally important to the fabric of our lives. What purpose comedy serves in communication HOUSE_OVERSIGHT_015782

Body Language & Banter 93 SIIWD CP My XBox is Broken Dead Parrot Sketch The One Ronnie Monty Python Gerald the Gorilla Fork Handles Not the 9 O’Clock News The Two Ronnies Andre Previn Self Defense Against Fruit Morecambe and Wise Monty Python is not clear. In life, telling a joke will make another person smile. This causes people to be happy and happy people release chemicals into their bloodstream which make them healthier. Happy people then tell jokes to others. This circular process improves the well-being of communities and helps bond people together. But why on Earth did comedy evolve to be the mechanism that does this? Comedy may be an important way to avoid an argument when context is unclear. Much of what we say can be taken the wrong way. Simple communication of fact can sound like criticism or challenge, and HOUSE_OVERSIGHT_015783

94 Are the Androids Dreaming Yet? humans are naturally hierarchical — not unlike packs of dogs or beached walruses. Humor allows us to test the response of others to statements, which might otherwise be taken the wrong way. Something said in a ‘jokey’ tone of voice may not generate a negative response, even though the raw content might be quite provocative. “Ah, late again I see...” It is worth taking a look at some great comedy sketches because they bring home the richness of human interaction. Here are some of my favorite links as an antidote to the heavy-duty mathematics I am about to inflict on you. The World’s Funniest Joke Two hunters are out in the woods when one of them collapses. He doesn't seem to be breathing and his eyes are glazed. The other guy whips out his phone and calls the emergency services. He gasps, “My friend is dead! What can I do?” The operator says, “Calm down. I can help. First, let’s make sure he’s dead.” There is a silence, then a gunshot is heard. Back on the phone, the guy says, “OK, now what?” Spike Milligan, from The Goon Show I think comedy is a fitness display. It demonstrates to those around us — particularly of the opposite sex — that we can be creative and use non- computable thought processes, just as dancing is a fitness display of our agility and coordination. When we tell a joke we are showing others we can ‘think outside the box’, a valuable survival skill. At a simple level it has been proven that animals with the ability to behave randomly escape being eaten more often than animals that follow a pattern. Non-computability is the ultimate behavioral randomizer since it is not an algorithm and cannot be copied. The ability to take non-computable thinking to its logical conclusion to create and invent has clearly taken off for humans. Of course, another explanation might be that making people happy is fun. People like to be around other fun people so humor encourages crowds to form. If a saber-toothed tiger attacks you, and you are in a crowd, you're more likely to survive. You only have to outrun one member of the crowd! HOUSE_OVERSIGHT_015784

Chapter 4 THE BRAIN Baby EEG HOUSE_OVERSIGHT_015785

“The brain is a wonderful organ; it starts working the moment you get up in the morning and does not stop until you get into the office.” Robert Frost “The brain looks like nothing more than a bowl of cold porridge.” Alan Turing HOUSE_OVERSIGHT_015786

as looking like a bowl of cold porridge. To get to the porridge you must first cut through the skull, a two-millimeter thick protective layer of bone. The adult human skull has almost no gaps in it, and the only ways into the brain without a bone saw are through the eye sockets or the soft area of bone at the back of the nose. Egyptian mummies had their brains removed through the nose and preserved in a jar for the afterlife! P hysically the human brain is very boring. Alan Turing described it Thinking with Porridge Protecting the brain is very important and the skull does a good job by being a tough, impenetrable barrier. But sometimes this toughness backfires. In 2009, Richard Hammond, one of the presenters of the TV motoring series Top Gear, suffered a crash while testing a land speed record-breaking car. Although he was in a multipoint harness, the crash, at over 200 miles per hour, bounced his helmeted head around the inside of the cockpit and his brain was badly bruised. As you know from experience, when you bruise you get swelling, and the brain is no exception. However, the brain is encased in bone, so this swelling has nowhere to escape. The resulting buildup of pressure is dangerous, causing an interruption of blood supply to the un-bruised parts. Brain damage in such accidents is often fatal; Richard Hammond was very lucky to live through the experience. Surgeons often need to cut into the skull to relieve pressure on the brain, or to gain access to remove tumors. Going through the scalp involves a great deal of blood, but once you have a clean hole in the skull you can peel back the thin membranes, called the meninges, to reveal a wrinkly folded whitish thing that looks a bit like a cauliflower. This is the outer surface of the brain where much of our thinking is done. Unfolded, this surface layer would cover the area of a football field and this intense folding distinguishes the human brain from the brains of simpler animals. Some animals, such as elephants and dolphins, have larger brains than ours, but the area of their folded surface is considerably smaller. It is thought that this efficient folding is key to giving us the ability to think complex thoughts. Analysis of Einstein’s brain held at Princeton University shows it is not particularly massive, but it is strikingly more folded than average, and has a shorter lateral sulcus - the fissure between the front and back HOUSE_OVERSIGHT_015787

98 Are the Androids Dreaming Yet? , ee Einstein’s Brain of the brain. Whether this is related to his highly creative thinking or just random chance is unknown, but it’s an interesting data point in our quest to understand creativity and intelligence. Looking through a microscope, the wrinkly grey matter is composed of 30 trillion neurons; small whitish cells sprouting filaments that wrap around each other like the tentacles of an octopus. The tentacles, and there can be as many as 10,000 per cell, are known as dendrites and spread out to nearly touch other neurons. At the other end of the neuron is a single axon. The gaps between the end of an axon and the next neuron’s dendrites are called synapses, about one-tenth of the width of a human hair and varied in structure. When a nerve ‘fires, an electrical pulse spreads out along the axon to the end and crosses the synapses to other brain cells. This electrical pulse is not like the flow of current in a wire: neurons don't conduct electricity. It is more akin to dominoes falling in a line. Ion gates in the walls of the neuron open, letting potassium ions flow out. As the gates open in one section, the next section is triggered and so on. Thus, electrical signals ripple out along the axon. As the electrical signals cross the synapses they either excite or inhibit the firing of adjacent neurons. There is a lot more structure to a neuron than was once thought. The textbook model is of a sequence of ion sacks stacked end to end rather like plant cells, but neurons have a far more complex structure. Bundles of actin and tubulin form a skeleton in the neuron and the neuron metabolizes ATP to recharge its firing mechanism. Neurons behave far more like small animals than inanimate plant cells. HOUSE_OVERSIGHT_015788

The Brain 99 The wiring of our brain looks a bit like the logic circuits of a computer, and our best guess is the cells in our brain form some kind of computer. The brain cells — a specialized form of nerve cell — connect to the rest of the body via the nerve cells that largely run down our spine. Thoughts trigger action and, in reverse, the nerves in our extremities sense things in the environment and relay information back to the brain. If I think, ‘move my finger’ my finger will move, and if it touches something I will feel the sensation. Interestingly if my finger touches something hot a reflex will kick in. Reflexes work without involving the brain. We don’t have to think, “that hurts” Instead, our finger reflexively pulls away. We may say ouch, but by the time we do, our fingers already moved away from the heat. Nerve cells are much slower than the electronic systems we build with copper and silicon. This speed is quite noticeable and limits the rate we can do certain things. It takes around 0.08 seconds for a nerve impulse to run down to the tips of our fingers, initiate an action and return to give us the sensation of the action. This may sound fast but if you're a tennis player in a rally or a pianist faced with a fast passage, the nerves don't have time to make a full round trip signal before the next action must be initiated. In these instances we need to run on autopilot and there are parts of the body where the nervous system takes action without the brain getting involved. This is particularly the case with things like walking and balance, which must respond fast to changes in ground conditions. The signals just don’t have time — and don’t need — to go all the way up to the top of the body for instructions. Rather like the heat reflex above, the peripheral nervous system can process information locally. After all, brain cells and nerve cells are really all one type of cell. If you have a group of people, you can conduct a fun experiment to show the speed of nerves. Hold hands in a big circle and squeeze the hand of the person next to you. When they feel you squeeze, they should squeeze the next person’s hand and so on. The rate at which people squeeze hands around the circle is limited by the speed at which nerves conduct the signals across our bodies. Imaging the Brain There are several ways to look inside the brain without recourse to a bone saw. The methods are fascinating in their own right, even before we start looking at the results. Each image is generated using a different physical principle. HOUSE_OVERSIGHT_015789

100 Are the Androids Dreaming Yet? X-rays The first Nobel Prize in Physics was awarded to Wilhelm Rontgen in 1901. He had discovered ‘X’ rays; so called because he had no better name for them. X-rays, as they became known, are just light of a very high frequency. Light comes in a variety of colors; at the low end of the frequency scale we see red, higher up blue and, at the top, violet. At this point human eyes give up and cannot see anything higher, so ultraviolet light is invisible to us. Bees, on the other hand, can see a long way into the ultraviolet spectrum and some flowers have beautiful ultraviolet markings that attract bees for pollination. Daylight contains a great deal of ultraviolet light which is wasted on us — other than to tan our skin. But all is not lost. Clever manufacturers put fluorescent dyes into their washing powders which stick to our clothes and convert ultraviolet into visible light, making our T-shirts look brighter as they reflect more visible light than fell on them. You can see this effect most easily in a disco when ultraviolet lights are shone on the dance floor and anyone wearing a newly washed T-shirt will glow bright white. The other common substance that fluoresces strongly on a dance floor is tonic water. Quinine, the active ingredient in tonic water, is a strongly Flowers in Ultraviolet Light HOUSE_OVERSIGHT_015790

The Brain 101 Pit Viper fluorescent substance which converts ultraviolet light down into the visible spectrum. Photoactive dyes have recently become controversial as suggestions have been made that they are unsafe and irritate the skin. Going to discos might not be quite as fun in the future! Thermal Imaging HOUSE_OVERSIGHT_015791

102 Are the Androids Dreaming Yet? At the bottom end of the spectrum is infrared light. Pit vipers have evolved special organs on the sides of their heads to ‘see’ in this spectrum and they use this sense to hunt prey in the dark. I use the word see with some caution. We have no idea what their sensation of ‘heat-sight involves, but their organs are very precise, able to detect things only 0.2 degrees warmer than the background. Infrared cues help several species of snakes, bats and insects locate things in the dark, but the animal that excels at the task, albeit using technology, is mankind. Special cameras allow us to use infrared to see in the dark or detect where our houses lose heat. X-rays are much higher in frequency — about one hundred times that of the ultraviolet light that affects our T-shirts. The high frequency corresponds to a small wavelength that allows the rays to pass through our bodies. Later on in the book we will understand that frequency is not a proper explanation for light, as it is not a wave but rather a particle that obeys the laws of a wave. But for now we will ignore this detail. The first use of X-ray images was to see broken bones. Bones block the rays as they are dense, but the soft parts of our bodies are almost completely transparent to X-rays. We can see the soft tissues if we turn the contrast up, but there are problems when using X-rays to view the brain. Our skull completely encases the brain and however much we turn the contrast up, all we see is bone. The solution to this problem is to perform sophisticated mathematical tricks using a computer to enhance the contrast ratio and make image ‘slices’ through the living head. The slicing technique was invented independently in the 1970s by Sir Godfrey Hounsfield, working for EMI in England, and Allan Cormack, of Tufts University in America, and they shared the 1979 Nobel Prize for Medicine for their work. Legend has it that EMI was making so much money from The Beatles they could fund the enormous development cost of the CAT scanner from the profits; true or not, it’s a great invention. The best way to understand the mathematics is to picture yourself in an episode of ‘CSI, the American television crime drama. An intruder has attacked someone with a knife and there are blood spatters all over the walls of the room. Enter the brilliant pathologist who reconstructs the scene of the crime from the pattern of blood on the wall. She can map the trajectory of the blood spatters and back-calculate that the attacker must have been 5’ 4”, left-handed and wielding a 6” blade. In a CAT scan, our head is hit with billions of rays that bounce and scatter over the walls of the machine. Sensors detect the rays and a mathematical algorithm calculates an image of the body that would produce such a pattern. To HOUSE_OVERSIGHT_015792

The Brain 103 X-ray of Roentgen’s Wife’s Hand simplify things we shine the X-rays onto the head as a narrow slit of light so we only have to do the back calculation in two dimensions. Then we stitch successive slices together in the computer to form a 3D virtual image. Thus, doctors can ‘fly’ through the brain looking at structures such as tumors from all angles. HOUSE_OVERSIGHT_015793

104 Are the Androids Dreaming Yet? There are two problems with X-ray imaging. Even with clever mathematics, the dense bone in the skull blocks the rays so you don't get much contrast, making it hard to distinguish normal brain matter from something like a tumor. But the bigger concern is X-rays are a form of ionizing radiation, and ionizing radiation causes cancer. We are told to wear sun block to protect our skin from ultraviolet light; X-rays are 100 times more potent and can doa great deal of damage. Fortunately, the body repairs itself quite well in the presence of low levels of radiation. The double part of the double helix in our DNA allows a set of proteins in our cells to go around correcting errors when they detect a mismatch between the two strands. But, now and again an X-ray might make an irreparable fault in both copies. If enough of these faults accumulate, they can lead to cancer or, if the errors are in reproductive organs, birth defects. Doctors try to minimize the radiation we receive and give us as few CAT scans as possible during our lifetime, especially when we are young and have not yet had children. MRI X-rays dominated our ability to see into the human body until the mid-1970s when Raymond Damadian came up with the idea of using magnetism. Magnetic fields are not absorbed by bone and present no danger as they do not damage DNA. Ironically, the technique was originally known as Nuclear Magnetic Resonance, ‘NMR, which patients thought must be dangerous because of the word nuclear. The name was Functional MRI: Working Memory HOUSE_OVERSIGHT_015794

The Brain 105 Diffusion Tensor Image changed to the one we use today: Magnetic Resonance Imaging, ‘MRI. The system works by applying a strong magnetic field to your body to excite the hydrogen atoms. Since we are mostly H2O there are plenty of these. Three magnetic fields are used. First, an extremely strong field is applied to the whole body. This causes all the hydrogen atoms in the water and fat to spin in line with the field of the machine. Next a gradient field is applied to the top of your head so it is slightly more magnetized than the bottom of your feet and, finally, a pulse of magnetism is applied to the top of your head. The spinning hydrogen atoms line up a little more when this pulse is applied and then randomize again when it is switched off. As they randomize, they give off energy. The clever part is the gradient field which causes the atoms to give off energy at slightly different times — the top of your head first, your neck a fraction of a HOUSE_OVERSIGHT_015795

106 Are the Androids Dreaming Yet? at . yy Response ws Response ye toFaces | toHouses sug second later, and so on down to your feet. What you see at any one time is a slice through a specific section of the body. You can then build up 3D images from these slices and look at the soft watery tissue rather than the hard bone you can see with an X-ray. MRI scans give detailed images but today there are many more imaging tricks you can play. Give the patient gadolinium to eat — a type of paramagnetic material — and this contrast agent will highlight active parts of the brain. You can ‘see’ which parts are active: the location of emotions such as love, joy and even the effect of smells as the brain experiences things. This is still coarse grained information; it shows only the general area of excitation and it does not tell us what is going on at the nerve level, but the images are fascinating. Another recent development in imaging is the diffusion MRI. If you remember your school physics, molecules travel with a random walk: they diffuse along pathways just as people wander along a corridor. If the corridor is full of people, they are jostled around and make little progress. If the corridor is empty, they move in straight lines. This difference in jostling affects the reading in an MRI and allows you to color code the image according to the rate of motion of water along the pathways. You can therefore ‘see’ the rate at which signals flow in the brain and not only locate thoughts, but also see the links between them. HOUSE_OVERSIGHT_015796

The Brain 107 Functional PET PET The last scan we will look at is functional positron emission tomography, or f-PET. In this machine the scanner detects positrons given off by excited oxygen atoms. As you think, you burn glucose by combining it with oxygen. The parts of the brain that are thinking hard use a great deal of oxygen and this shows up in scans. Again the consecutive slice trick is used to generate a 3D image that allows you to fly through the brain as it works ona problem. There is one problem common to all these methods. X-rays, MRI and PET scans only show us the location of thoughts with an accuracy of a few millimeters. Each pixel in the image contains around 10 million neurons, so we can't see the details of thought. For a scale comparison it HOUSE_OVERSIGHT_015797

108 Are the Androids Dreaming Yet? is like looking at a car factory from space. You can see cars and people going into the factory but you can’t read the owner’s manual. We need to be able to see at least 10 million times more detail than our current technologies allow to see a thought. A Quick Tour Now that we understand how to look inside the brain, let’s take a tour around it. The brain is a highly distributed thinking machine. Some things, such as hearing, are located in specific places while others, like the enjoyment of music, are spread out. Our eyes work as an extension of the brain and use a specialized type of nerve cell. Light falls on the retina and stimulates these cells, causing nerve impulses to run along the optic nerve into the center of the Frontal Lobe em Parietal Lobe : wa Motorfpeech areaff Broca >> emporal Lobe <3 . Pons Medulla obloifeata/@ —eredellum —— The Brain HOUSE_OVERSIGHT_015798

The Brain 109 Input 4 Retinal rods and cones Pulvinar Lateral geniculate body Superior Colliculus Medial geniculate body Cortex of Occipital Lobes Visual Processing System brain. The impulses split and form two distinct paths, one through the cerebral cortex, which gives us the sensation of conscious vision, and the other into the lower brain which provides us with instinctive reactions. The right hand side of your body is connected to the left hemisphere of the brain and vice versa. This means each hand is controlled by the opposite side of the brain. But, your eyes see both your hands. To resolve this conundrum a very complex thing has to happen to the optic nerve in the center of the brain. The optic nerve from each eye splits and crosses over in the middle, so the left side of the left eye and the left side of the right eye goes to the right hand side of the brain and vice versa. This keeps the brain focused on the correct hand. HOUSE_OVERSIGHT_015799

110 Are the Androids Dreaming Yet? Frogs Eyes are Very Sensitive The processing power of the eye is staggering. The human retina has about 120 million rods and 7 million cones, giving it an average resolution of 10,000 by 10,000 pixels. Each rod is sensitive to individual photons but we register light consciously only if we see around 5-7 photons. It is thought frogs can react to single photons because of the chemistry of their eyes and the fact they are cold-blooded, but this is not proven. Some animals, including some frogs and my cat, have a tapetum lucidum. This is a reflective backing to the eye that allows each photon two chances to react with a rod, once on the way in and, if that fails, once on the way out. This is why you can see the eyes of some animals if you shine a light into the forest on a dark night. Cones are less sensitive than rods but give us color perception. In the human eye, there are three types of cone: a red, a green and a blue, giving us trichromatic vision. We see colors because light stimulates more than one types of cell and we infer the color in between. A fourth type of cone is present in some species such as birds, reptiles, and fish. This gives them tetra-chromic vision, allowing them to see into the ultraviolet range. It is speculated some humans might have this ability but so far none has come forward. Some animals lack the ability to see certain colors. Most dogs can't see red, This gives cats a big advantage! Many people wonder if we all see the same color as each other. Is your red the same as mine? The brain’s perception of color is complex. Although the color red is absolute and can be detected by a calibrated sensor, our perception of color is relative. We perceive them in the context HOUSE_OVERSIGHT_015800

The Brain 111 Color is Relative of other colors — not in isolation. The two panels above contain identical blocks of color but they look very different against the background. Check out the website if you have a black and white book. It is an irrelevant question to ask if my red is the same as yours, since my red against one background is not even the same as my red against another. People generally agree on naming colors but not all languages have the eleven specifically named colors of modern English: black, blue, brown, gray, green, orange, pink, purple, red, white, yellow, if you are interested. Ancient Celtic languages, so called ‘grw languages, recognized only four colors and other languages don’t distinguish purple from blue. Color, or at least the naming of color, is a cultural thing. HOUSE_OVERSIGHT_015801

112 Are the Androids Dreaming Yet? The resolution of the eye is not the same across the image. High resolution is concentrated in the center, while lower resolution black and white vision dominates the edge. This peripheral vision helps us detect predators or play football but it is not the focus of our attention. When we focus our attention on something, we turn our eyes to look at it directly. The central part of our eye is called the fovea centralis and is composed of cones. About half our cones are concentrated in this very small section and this gives us immense visual acuity. For a computer display to outperform this section of the eye it would need one billion by Scintillating Dots Optical Hlusion one billion pixels. The fovea centralis is tiny, only two degrees across, so our eyes must dart around the image to take in all the detail. Once the basic information is encoded in our retina and sent down the optic nerve, it goes into a production line process in the visual cortex where all the elements are analyzed. Our brains extract information from the image such as texture, edges and depth perception in specialized portions of the brain. Because of this specialization it is possible to play tricks on the brain with images that are not easy to process. Some we find pleasurable, while others can be a little disturbing. HOUSE_OVERSIGHT_015802

The Brain 113 Penrose Steps Optical Illusions This picture is an illusion that plays with your stereoscopic synthesis. The dots appears to flip between black and white. Other illusions play with depth perception. The Penrose Steps are a type of illusion that tries to build an impossible physical model in our cerebral cortex. The brain sees perspective and depth perception cues, but the resulting shape could never exist. Hearing Unlike sight, hearing is an absolute sense. Our ears capture and focus sound down to the eardrum where a set of small hairs called cilia convert it into electrical impulses. The impulses stimulate cells corresponding to specific pitches. We are born with perfect pitch, yet most of us lose it early on. When I hear Maria Carey sing a top B flat a specific set of neurons located near the ear fires, and if she sings a top ‘A then a different clump of neurons are stimulated. By the time most children come to learn music they have edited out this absolute pitch information. One group of children who do not lose the ability are Chinese pianists. Because Chinese is a tonal language — where the pitch of words affects their meaning — and because HOUSE_OVERSIGHT_015803

114 Are the Androids Dreaming Yet? HESTwo McGurk Effect; Go to the Website and Watch the Linked Video Chinese children tend to learn the piano very young, they don't lose the absolute part of pitch. An astonishing 93% of these children develop and retain perfect pitch throughout their lives. There are many cross connections between the audio and video processing systems. At parties you often can't hear speakers clearly because of the background noise. Watching their lips will help comprehension, but which sense wins if there is conflict between the two? The McGurk effect shows this. To test the effect, go to the website, watch the video and see if you can distinguish when a speaker talking normally and when he is making the mouth movement of another sound. There is a winner. Try it for yourself; check out the link on my website. Once upon a time people imagined the brain was like a camera forming an image of the world, but if this were the case there would be a paradox. Who is looking at the image in our brain to make sense of it? Modern research shows we don’t take a complete picture of the world like a camera but rather parse the image into its constituent parts on the fly. If someone asks, “Which side of the house is the tree on?” your brain parses the question and compares it with the image map in your mind’s eye. What is the image composed of: trees, houses, sky, grass? Your brain manipulates the linguistic question about the relationship of elements and matches it with the visio-spatial understanding of the image, allowing you to answer the question. You might not have to answer HOUSE_OVERSIGHT_015804

The Brain 115 copyright (c) 1999 Daniel]. Simons. All rights reserved. Humans’ Ability to Concentrate the question verbally. If you hit a baseball, no language is involved; you distinguish the ball from the background and perform quite a feat of tracking and calculation to connect it with your bat. Because the brain is editing the scene on the fly to keep within its processing power, the eye only sees what it turns its attention to. Magicians take advantage of this to play amazing tricks on us. Watch the video on the web and then tell me what you see. VISIT THE WEB AND VIEW THE VIDEO TO SEE WHAT HAPPENS SAN FRANCISCO GOLF PERFORMANCE CENTER Tiger Woods Swing HOUSE_OVERSIGHT_015805

You can see just how intensively the brain works on a given problem, throwing away all unnecessary information. The brain contains mirror neurons, a type of brain cell that responds when we see another human do something. These neurons fire as if we were performing the action ourselves even though we are merely witnessing it. It is one of the ways we learn a skill. If] watch Tiger Woods's golf swing, my mirror neurons will fire as if I were practicing his swing. Later when I practice the swing for real, my neurons will have already been partially programmed. This effect is presumably the reason we enjoy watching sports; our mirror neurons allow us to begin acquiring a skill while sitting in an armchair! This is clearly a useful evolutionary trait but you do also need to practice for real! Mirror neurons also fire in response to witnessing emotions. When we see an actor laugh or cry, we experience their emotion as if for real. This helps us empathize with the person we are watching and is part of the reason we enjoy movies and plays. ~ Output Neural Network HOUSE_OVERSIGHT_015806

Thinking “We cannot solve our problems with the same thinking we used when we created them.” Albert Einstein is normal. Mental work takes energy. Scientists estimate the brain consumes 20% of our resting energy; around 12 watts. Physical fitness is important for thinking. If you get out of breath running for a bus, thinking is going to be harder for you. Studies are mixed about whether the additional work involved in solving a difficult problem causes you to use more energy. We certainly see an increase in the flow of glucose to the appropriate part of the brain, but the overall energy use in the brain is quite high in the first place, so it is hard to see the incremental effect. Unlike muscles, which store energy locally as glycogen, brain cells ‘burn’ glucose and oxygen from the blood stream in real time. If scientists detect glucose and oxygen flowing to a part of the brain they know it must be working on a problem. As we know, there are several ways to make glucose and oxygen show up in brain scanners. You can, therefore, inject someone with the right chemical markers, wheel them into a brain scanner, and watch them learn new skills. On a practical level, there is limited space within a scanner and you can't wield a golf club, for example. Julien Doyon, a researcher at the University of Montreal, was recounting this problem to a friend and she suggested knitting. Knitting is a physical activity you learn just like a golf swing or a tennis stroke, with all the initial fumbles and jerky activity, settling down to a fluid learned skill. Most experienced knitters can engage in a full conversation while knitting complex patterns, only needing to break off and concentrate during a pattern change. Luckily, there are ceramic and bamboo knitting E you feel mentally exhausted reading this book, don’t worry. This HOUSE_OVERSIGHT_015807

118 Are the Androids Dreaming Yet? needles which don’t interfere with MRI scanners, and they are small — no golf swing problems here. Studies of knitters show that when they initially learn a skill, several areas of their brain light up, but after a while, the brain activity becomes concentrated in the sensorimotor striatal territory. Glucose, the brain’s power source, is a sugar we get directly from eating sweets or indirectly by digesting starch. Some studies show children do slightly better at school if they eat starchy foods in the morning for breakfast — a bowl of cereal or porridge. When you think and work your brain consumes the glucose in your blood, and blood glucose level drops. If there is a steady source of glucose from the starch digesting in your gut, the glucose is constantly topped up and the level will stay high. If there is no input of glucose from your gut, the body will first get glucose from glycogen in your liver or generate it by converting fat reserves. This takes more work so the body tends to avoid doing so until it absolutely has to. You can function with slightly lower glucose levels but the body will shut down a little. One thing that suffers as a result is the brain’s ability to perform cognitive tasks. A quick and easy way to fix this is to consume some raw glucose and most fridges have a ready supply in the form of sugary drinks. Stories of kids ranning amok, due to sugar highs brought on by too many sweets and sodas, appear to be an urban legend. In tests, parents told their children have had a sugar drink report them to be hyperactive even if they had been given a sugar free drink. ’'m not suggesting you drink lots of sugary drinks — it is bad for your teeth and will make you fat — but the occasional soda is fine. Memory Scientists are just beginning to explore the mechanisms that lay down memory in the brain. There are two main classes of theory. ‘The first believes memory is formed in the large scale wiring of the brain. Neurons connect with other neurons and the number and strength of these connections cause memory. When we learn, new connections are formed. The electrical activity in a given part of the brain triggers the formation of new dendrites. They grow, piloted by tubulin micro-tubes, rather like vines growing in a slow motion nature clip. Once a micro- tube guided filament is close enough to other, a synapse forms. This gross-scale wiring growth is one method of memory formation. Another gross-scale effect is myelination. Myelin is the insulation the body uses on nerves cells, including nerve cells in the brain. It looks a bit like the insulation we used in the 1930s. Before the invention of plastic, strips of waxed canvas were wrapped around wires to provide insulation. Myelin HOUSE_OVERSIGHT_015808

The Brain 119 7 atten, Pry thd Ly oe* * (a1) ea > » ra. wd eb fi; Postsynaptic cell ti. eg ii, we Ci es Sectee@ Synapse has a similar structure. It is a flat protein laid down as a spiral on the outside of nerve cells. The theory is that cell firing causes myelination, which permanently imprints the memory. The alternate class of theory proposes memory is encoded at a much smaller scale. Neurons are quite complex structures in their own right. Inside each neuron is a lattice of proteins, which forms a skeleton. Part of that skeleton provides structural integrity to the neuron, while other elements provide control and motility. It is this control part of the skeleton that people believe might encodememory. A 2012 paper by Travis Craddock and Jack Tuszynski of the University of Alberta, and anesthesiologist Stuart Hameroff of the University of Arizona proposes a protein called CaMKII binds to the cytoskeleton in 32 different configurations, providing a binary data encoding. It is an elegant idea but it also relies on your believing their model for quantum neuron processing which is still highly controversial. If proven, they are my top Nobel Prize tip for this decade! Photographic Memory Until recently conventional wisdom held that true photographic memory was a myth and the few people claiming to have it really used some sort of mnemonic memory technique to selectively memorize things. The HOUSE_OVERSIGHT_015809

120 Are the Androids Dreaming Yet? most famous case was a Russian journalist known as ‘S. He habitually memorized things using association with places. In antiquity this was taught as ‘the method of loci. The unusual thing was his inability to turn the effect off, and he found it as much a curse as a blessing. He was unable to forget useless information and found it hard to interpret complex images, tending to see areas of color and shade rather than objects such as trees, houses and fields. Very recently some people have come forward, six in America and one in the UK, who appear to have genuine photographic memories It is well worth watching the TV documentary The Boy Who Can't Forget to gain a sense of what this is like. These people appear to lack the ability to forget, and this turns our understanding of memory on its head. It seems memory might work the opposite way we thought. We had previously thought we only remember what we pay attention to, but perhaps we must actively forget, and this ability is missing in these subjects. Scientists are studying these people to see if they can understand more about memory. The Aging Brain We can explode a myth and encourage older readers simultaneously. Memory does not deteriorate with age, or at least not until we are very old. Most studies looking at memory deterioration focus on the very old and compare them with the very young. Even then, the differences are small. When people are asked to attempt memory problems there is a mild drop off with age but the results are quite similar. The most likely reason older people don’t remember so well is they don’t believe they can. Perhaps they don’t have as much incentive to remember new information. Why learn someone’s name if you're unlikely to meet them again? Since IQ actually increases with age, don't believe people when they say you are going downhill from the age of 40. You are not! Computer Brains Computers are really quite simple compared with all the evolved baggage we humans carry around. When a computer is presented with instructions, for example, for a program like Excel and a file such as my expenses, it will load everything into memory and ‘run it. The process of running a program is simple. Each instruction is a number. The computer reads the number, looks it up in a table, finds a corresponding number, and writes that down. Essentially that’s all there is to it. From a simple mechanism like this, we get the enormous complexity of a modern HOUSE_OVERSIGHT_015810

The Brain 121 computer. The sophistication is achieved through reading and writing many numbers in parallel, and chaining the steps together so that if you read a particular number it triggers another read/write process, and so on. I’m glossing over some details such as logical functions but, if you know how a modern computer chip is constructed, my description is not far off. Almost all logic today is implemented in tables to achieve the speeds we expect from modern chips. All modern computers are clocked. A small piece of quartz rock has been polished, coated with metal, and wired up to a control circuit in the computer. When you apply voltage to the rock it bends and absorbs energy. When the voltage is taken away it bends back and gives out the energy. This is effectively a pendulum and it can be used to make an accurate clock. I used to design these for a living. Every logic gate in a computer is connected to this clock, and each time the clock ticks the logic gates in a computer compute. Most modern computers are entirely synchronous. The clock rate is set so that the gates in the computer fully recover by the time of the next tick, and every gate is therefore ready in its standard position when the next instruction arrives. The human brain does not have a central clock. Each neuron acts independently — firing regardless of whether the neurons it is adjacent to are ready or not. It is wrong to think of the brain as digital. Each neuron does fire and recover, but it may be triggered again before it fully recovers. This makes for a chaotic and essentially analogue operation. If one neuron fires when a second has only half recovered, then it gets half an effect. Ifthe neuron is 80% recovered, an 80% effect. Neuron recovery time is quite long, perhaps as much as 1/1000" of a second, and they are wired in three dimensions to as many as 10,000 other neurons. It is perfectly possible for a set of neurons to run one ‘program’ when they are rested and a completely different ‘program’ when they are 50% recovered and yet another programs if triggered from different starting locations. I have said ‘program, but arguing a brain runs a ‘prograny is misleading. It is not organized like this. Neural Networks A neural network is our best attempt at a computer model for the human brain. Each neuron is represented by an entry ina table. The entry records all the connections to it, along with the strength of each connection — these are called ‘weights. In some models the connections can be both HOUSE_OVERSIGHT_015811

122 Are the Androids Dreaming Yet? inhibitors and activators like in real synapses. An individual neuron will fire if the sum of all the connections multiplied by the weights reaches a certain pre-determined threshold. A neural network does not run a program in the conventional sense, and must be trained through experience rather like a human brain. The training process allows the weights in the network table to be adjusted to give the correct result. But, unlike the brain, you can read the weights and even save them to a disk. The neural network tables start with random settings. You show the network the letter ‘A’ and adjust the weights in the tables until it gives a positive answer: ‘It’s an A. Repeat the process with the other letters until the network correctly distinguishes them. As you do this a computer algorithm constantly adjusts the weighting tables using a method called ‘back propagation. At the end of the training process you can show the network some new input and see how it does. For example, a letter ‘A that is in a slightly different font to anything in the training set. Trained neural networks can perform complex tasks such as recognizing faces or making clinical diagnoses, and they can be allowed to modify their weighting tables as they work so they learn from experience in a similar way to a human brain. Strong AI proponents believe making a thinking machine is just a matter of building a really large, fast neural network and working out how to train it efficiently. Quantum Brains Conventional wisdom says each brain cell is a single processing unit making an on-off decision — fire, or don't fire - depending on the state of its neighbors. But, Stuart Hameroff, Professor of Anesthesiology at the University of Arizona, thinks neurons are not the fundamental information-processing unit in the brain. He suggests that this accolade should go to tubulin. Tubulin is a small, versatile protein that self- assembles into filaments rather like the way buckyballs - a magnetic children’s toy — can be arranged. There are two types of tubulin molecule: a and B. They slot together and wrap around to form a micro tube about 25nm in diameter. Tubulin micro tubes do several important things in the body. They form the skeleton of neurons and give them structure. They are involved in guiding neurons as they grow towards each other to form new connections, and they also operate in the nucleus of a cell to unzip HOUSE_OVERSIGHT_015812

The Brain 123 Paramecium DNA into its two complementary strands when a cell divides. In single- celled organisms, including paramecium, the ends of the tubes stick out of the body and form the cilia that drive the organism along. The presence of tubulin in complex, single-celled organisms provides a clue that the smallest information processing unit might not be the neuron. Some single cell organisms, such as paramecium, display complex behavior: hunting for prey and escaping danger. This suggests they can process small amounts of information without the need for a matrix of neurons. Since we evolved from these organisms, why wouldn't our brain cells take advantage of this sub-cellular intelligence? The structure of tubulin lends itself to digital processing as the molecules forming the walls have two stable states and can flip between them. We might recognize this as the basis of a binary computer, and cells might have little computers within them. They would not need to process many bits to be useful. Perhaps single-cell organisms developed information processing capabilities in their micro tube structures that allowed them to better survive and, as their nervous systems evolved, they coupled these structures to form the brains we see today. This piece of theory is not too controversial. After all, nerves have wiring within them to carry information to the synapses and it’s likely this wiring is involved in the thinking process. But Hameroff is not finished. He has teamed up with Roger Penrose to bring quantum mechanics into the picture. HOUSE_OVERSIGHT_015813

124 Are the Androids Dreaming Yet? Their reasoning is straightforward but has generated a great deal of controversy. Hameroff observes that anesthetics cause humans to lose consciousness by binding to tubulin, but they do not halt all brain function. He, therefore, concludes our conscious thinking is mediated by tubulin, not the larger scale firing of the neurons. Penrose had been looking for a mechanism in the brain that would explain how brains solve non-computational problems. Together Penrose and Hameroff propose tubulin micro tubes are quantum gravity computers that allow us to think non-computationally and are the seat of consciousness. The ideas are still being worked. Penrose and Hameroff have a difficult task conveying their ideas to the rest of the scientific community. Scientists don’t recognize a need for something that can think non-computably, so they are highly skeptical of a mechanism which performs that sort of thought. The latest development on the Hameroff Penrose model comes in the work of Travis Craddock, now of Nova Southeastern University, Florida, and others. They have written a paper arguing signals propagate according to quantum principles within microtubules through the excitation of thiamin molecules along the length of the tube. They believe these molecules are quantum, entangled in a similar manner to the mechanism recently discovered in photosynthesis. The geometry of these molecules is set out in a similar way to the active areas in chlorophyll and they have a complementary problems to solve. Chlorophyll tries to maximize energy conversion efficiency, while a microtubule tries to minimize the use of energy while propagating signals along a nerve. You might wonder Tubulin Protein HOUSE_OVERSIGHT_015814

The Brain 125 Tubulin where the light comes from since tubulin is housed deep within the neurons inside our brains and shielded from light by our skull. It turns out that the mitochondria which powers our bodies emit photons of UV light as a waste product of their metabolism. The speculation is tubulin harvests this waste energy. Before we argue for this mechanism any further we still need to establish that a non-computational mechanism is needed to allow human thought. In the next chapters, we will look at the nature of knowledge and, in particular, mathematical creativity and the Wiles Paradox. Microtubule Tubulin Quantum Coupling of Tubulin in Microtubule HOUSE_OVERSIGHT_015815

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Chapter 5 KNOWLEDGE Chimpanzee and Typewriter HOUSE_OVERSIGHT_015817

“Theres an infinite number of monkeys outside who want to talk to us about this script for Hamlet they've worked out.” Douglas Adams “I'm not young enough to know everything.” J.M. Barrie “He has Van Gogh’ ear for music.” Billy Wilder HOUSE_OVERSIGHT_015818

ouldan army of monkeys write Hamlet by bashing away randomly on typewriters? Of course, we don't mean this literally. We are asking whether knowledge can be created without understanding. Can a monkey, or perhaps some form of computerized random number generator, accidentally type out the script for Shakespeare's Hamlet or write Tolstoy’s War and Peace? Is knowledge generation simply a numbers game? Leo Tolstoy’s War and Peace is generally assumed to be the longest novel ever written. This is not quite true. Wikipedia reckons the longest novel is a French book, Artamene, with over 2.1 million words. Tolstoy comes in sixteenth, with a mere half million! Written in 1869, War and Peace tells the story of five Russian families during the Napoleonic wars. Originally written in a mixture of Russian and French, and numbering over 500,000 words, it was quickly translated to other languages. The mistress of composer Franz Liszt translated it fully into French, where it expands to 550,000 words. Contrary to popular myth the length of the book drops slightly in German. If you really want to save paper Chinese is best. Because it uses a single symbol per word, the Chinese translation needs only 750,000 characters compared with the 3 million for English. It is wrong to assume this is necessarily more efficient than a phonetic language. Although it might save on paper, it is considerably more laborious to write. Three strokes are required to write ‘war in English whereas the Chinese pictogram requires ten. Computers work with numbers. It is a simple process to translate a book into numbers because books are composed of discrete symbols. All we need do is give each symbol a unique number and record those numbers in digital format. Artistic works involving pictures and sound are more difficult to represent because they are continuous in nature. We have to digitize them first. With music or painting this inevitably means some loss of information as we can’t cut a sound or image into an infinite number of pieces. The modern standard for translating text to numbers is Unicode. Each character is represented by a five-digit number ranging from 1 to 64,000 — two bytes for those of you who know computing. This is War in Chinese HOUSE_OVERSIGHT_015819

130 Are the Androids Dreaming Yet? sufficient to code almost all the world’s symbols, so we can avoid any accusation of being language-ist! Here are some examples of the OF H Q ARASH OK A Ancient Greek, Japanese: Kanji, Katakana, Chinese, and Russia-Cyrillic Symbols characters represented by Unicode. For our discussion, it does not matter which language War and Peace is written in. We just treat the symbols as numbers. I am going assume the English translation which has around 500,000 words; a nice round number. Assuming a generous 10 characters per word, War and Peace is approximately 10-megabytes — that’s about the same size as a music track on iTunes. In practice, the book uses a bit more memory, as there is some overhead for formatting information. My laptop has a 500 Gigabyte hard disk so I could fit half a million copies of War and Peace on it! If we take a look at the contents of the file on my computer the book starts: 8710110810844801141051109910144115111 Can a computer calculate this number? The obvious answer is YES. It is just an integer like 1, 3 or 42. Granted it’s a large number, but the length of the number is simply the length of all the symbols in the book coded into Unicode — about 10 million digits. We have already determined this number can be stored on my hard disk half a million times, so it’s not an unimaginably large number. How long would it take to calculate the number corresponding to War and Peace? The simplest method is to count up starting at 1 then 2, 3, 4, 5, and so on until I try every number. Will this eventually get to the War and Peace number? The answer is yes. Eureka! All of human knowledge is computable. I have written this computation out as a simple computer program below. It says, in plain English, start at zero, go round a loop counting up one at a time and print each number as you go along. i==0; Loop i++ Print i; HOUSE_OVERSIGHT_015820

Knowledge 131 Easy! No, unfortunately. The problem is subtler than it first appears. First it will take a VEEEEERRRY long time. If I counted up from one, I would print out War and Peace eventually but it would take 120 billion, billion, billion, billion, billion... (I would need the entire length of this book to write out all the billions) years! For the physicists amongst you, I would need 10°” years, assuming I could use every atom in the known universe counting in parallel at the plank interval. “The plank interval is the shortest time that can exist in the Universe as a discrete ‘tick. Even going at this speed using with every atom in the known Universe would take 10°° longer than the age of the Universe. This is stupendously long. Remember scientific notation means I have a 1 with 5000 zeroes after it. It is a deceptive notation as something as innocuous as 10'”° is equal to the number of atoms in the known universe. 10° is an absolutely enormous number. If you hear something is going to ‘take until the end of time; we're talking a lot longer than that! You may have spotted that in the process of counting up to the War and Peace number we also count through EVERY book ever written shorter than 500,000 words in all the world’s languages. Interestingly we counted through the Japanese and Chinese translations of War and Peace quite a bit before we reached the English and finally French translations. During the process, we also stepped through countless other wonderful works: proofs of amazing theorems, the complete works of William Shakespeare, and every composition ever written. Sadly, we never knew it. The problem is my program never stopped and told me it had found any of these wonderful things. I would have to sit staring at the screen to spot them. If I was off doing something else — making a cup of tea, taking the kids to school - I would miss all these wonders; the program never tells me if it has succeeded, but quietly prints out War and Peace and carries on. This is really annoying. It’s not a useful machine. What I need is a machine that rings a bell when it finds something interesting so I can break away from what I am doing and take a look. Reading every book it writes in every language and all the nonsense in between would take a ginormous amount of my time. (By-the-way, contrary to statements by school teachers that ginormous is not a word — it is!) I want a computer to come up with War and Peace without me having to do all the work. It’s no help if the machine writes everything down and lets me take a look in my own good time. That only puts off the time when I have to begin reading all the gibberish it produced. Another practical problem is the massive storage required. Just imagine the immense piles of printer HOUSE_OVERSIGHT_015821

132 Are the Androids Dreaming Yet? paper! Stephen Hawking and Jacob Bekenstein have shown space appears to have a limit to the quantity of information it can store. The quantity of information we are looking at here is greater than the storage capacity of the Universe and would collapse space-time to a black hole before I got even a fraction of the way through. Let us try to be a bit cleverer about the task of creating this information. The simplest way to tie the computer down is to run a much stricter program. Ask it to count up from one until you get to a number representing the novel War and Peace and then print it, stop and ring a bell. Loop i++ until i == “War and Peace...”; Print i; ring-bell; This program succeeds! I am triumphant. I have calculated the War and Peace number, and this time I did not miss the event. But, if you consider this a little more deeply I gave the computer the answer! I told it the string “War and Peace...” and it was able to count up, stop, and tell me it reached it. In mathematical terminology, the program is said to have ‘halted’ when it reached the War and Peace number and in computer science speak it is a special purpose program designed to do only this one thing. This program is pointless. First, it would still take a ginormous amount of time to get there and, second, it is trivially the same as running the program: Print War and Peace. i = “War and Peace...”; Print i; It’s just the same as me taking my laptop, finding War and Peace and pressing print. In no way is this equivalent to Leo Tolstoy’s creative effort of writing War and Peace in the first place. What went wrong? I wanted my computer to find an interesting string I did not already know. War and Peace is trivially computable after Leo Tolstoy created it but the question is whether my computer could come up with War and Peace or some similar creative work on its own. Can it create and, more importantly, understand it has created something? We have linked the ideas of creativity and understanding, and this will prove to be the key to the problem. HOUSE_OVERSIGHT_015822

Knowledge 133 The Problem One suggestion put forward by Daniel Dennett is the creative process is a two-part task — generate ideas, then critically assess them. I can, in principle, make a program write out every possible book less than 500,000 words long. Provided I don't store the results this will not collapse the Universe. This just leaves the problem of writing another program to read all the output and ring a bell each time it finds some interesting truth. This second program might be called an appreciation program. Let’s examine this approach. I can write out a very simple program to do this — provided I cheat and ignore the complexity of the term ‘something interesting. In plain English: Count up from one until I get an interesting fact, write it down and stop. Loop i++ until i == (Something Interesting), Print i This generates two problems. We need to make a program that can tell if something is interesting and it will need to be fast because it is going to be handed a huge amount of junk. Clearly I have a process running in my brain that can determine if something is interesting, but it is quite slow. It takes me an appreciable time to open a book, leaf through the pages and declare it either junk or interesting. Leo Tolstoy had a process in his brain that allowed him to create something interesting but I want to prove he did not do this by generating random junk and sifting through it. Let’s look at the mathematics. We know simply counting sequentially through every number would take too much time, but why not generate random numbers and run our critical eye over them? Surely this would give a faster result. Let us try with a short poem. How hard would it be to come across something as simple as a four-line poem using this technique? This poem, by the late Spike Milligan, is only 23 words long, including the title, and I have a powerful computer. Wouldn't it be possible to generate it using a computer? Unfortunately, no. We humans don't have a good head for large numbers and this problem is much harder than it appears. Let’s use playing cards to get a feeling for large numbers. HOUSE_OVERSIGHT_015823

134 Are the Androids Dreaming Yet? A Simple Poem Rain There are holes in the sky Where the rain gets in But they’re ever so small That’s why the rain is thin. Spike Milligan Spike Milligan Coming upon a poem by chance can be likened to the probability of dealing a perfect bridge hand. Shuffle the deck thoroughly and then deal four hands. What is the probability every player will have the ace through king in a single suit? It’s about 1 in 1,000,000,000,000,000 hands. Because lots of people play a lot of bridge around the world, this outcome has been reported quite a few times. The possibility appears within the bounds of human experience. Fifty-two playing cards seems close to the 80 characters that make up this poem and 13 choices of cards is about the same as the 26 letters of the Latin alphabet. Wouldn't we expect poems of this complexity to crop up almost as often? NO. HOUSE_OVERSIGHT_015824

Knowledge 135 The 80 characters of this poem versus the 52 playing cards and the greater choice offered by 26 letters increases the problem geometrically. Taken together the probability of accidentally getting this poem is vastly less than a perfect hand of bridge, 1 in 10@ against the perfect bridge hand of 1 in 10”. That’s the difference between the number of atoms in the known universe and the number of atoms in a jug of water! Numbers get big very quickly when we are looking at the permutation of information. And there is another problem with our bridge analogy. All the bridge players in the world are part of the machine finding the perfect hand. When a human sees a perfect bridge hand they are amazed. It is an event that usually hits the local newspapers and a couple of years ago one reached the national papers in Britain. Each bridge player looks at every hand, they play so there is a huge amount of processing going on during every bridge game. To replicate this for our poem, we would need millions of poetry classes spending hours each evening reading through computer printouts of gibberish. I should also add that sightings of perfect bridge hands are almost certainly hoaxes. The probability of it happening even once would require everyone on Earth to play bridge continuously for a thousand years. It is reported somewhere in the world about two or three times a year. If we are charitable, we might assume people failed to shuffle the deck properly but I suspect some mischief is going on! The numbers don't stack up... You might think the problem is one of improving the efficiency of the filter so humans would only have to examine a smaller number of possibilities. Surely I could improve things by writing a simple program to ban all non-English characters, words and poor grammar; things that don't pass the Microsoft Word grammar checker. This would generate a more manageable number of potential poems. Lewis Carroll shows this does not work; my idea to use a grammar and spelling checker to filter out gibberish just eliminated Jabberwocky, one of the most famous verses in the English language. Take a look at what Microsoft Word thinks of it. HOUSE_OVERSIGHT_015825

136 Are the Androids Dreaming Yet? The Jabberwocky *Twas brillig, and the slithy toves Did gyre and gimble in the wabe; All mimsy were the borogoves, And the mome raths outgrabe. “Beware the Jabberwock, my son! The jaws that bite, the claws that catch! Beware the Jubjub bird, and shun The frumious Bandersnatch!” He took his vorpal sword in hand: Long time the manxome foe he sought— So rested he by the Tumtum tree, And stood awhile in thought. And as in uffish thought he stood, The Jabberwock, with eyes of flame, Came whiffling through the tulgey wood, And burbled as it came! One, two! One, two! and through and through The vorpal blade went snicker-snack! He left it dead, and with its head He went galumphing back. “And hast thou slain the Jabberwock? Come to my arms, my beamish boy! O frabjous day! Callooh! Callay!” He chortled in his joy. Twas brillig, and the slithy toves Did gyre and gimble in the wabe; All mimsy were the borogoves, And the mome raths outgrabe. Lewis Carroll Lewis Carroll’s Jabberwocky HOUSE_OVERSIGHT_015826

Knowledge 137 "Twas brillig, and the slithy toves Did gyre and gimble in the wabe; All mimsy were the borogoves, And the mome raths outgrabe. “Beware the Jabberwock, my son! The jaws that bite, the claws that catch! Beware the Jubjub bird, and shun The frumious Bandersnatch!” He took his vorpal sword in hand: Long time the manxome foe he sought— So rested he by the Tumtum tree, And stood awhile in thought. And as in uffish thought he stood, The Jabberwock, with eyes of flame, Came whiffling through the tulgey wood, And burbled as it came!_ One, two! One, two! and through and through The vorpal blade went snicker-snack! He left it dead, and with its head He went galumphing back. “And hast thou slain the Jabberwock? Come to my arms, my beamish boy! O frabjous day! Callooh! Callay!” He chortled in his joy. Twas brillig, and the slithy toves Did gyre and gimble in the wabe; All mimsy were the borogoves, And the mome raths outgrabe. The Jabberwocky Spell Check Microsoft Verdict on the Poem 39 of the 166 words in the poem are unknown to Word’s spelling checker and this is an optimistic analysis of how the algorithm would fare. Many of the words are in the spelling checker because of the poem: galumphing, for example. Lewis Carroll’s work was sufficiently influential that part of HOUSE_OVERSIGHT_015827

138 Are the Androids Dreaming Yet? the English language was created in this poem. The same goes for much of Shakespeare. If we used a filter method, we would have just deleted most of Shakespeare from the English language! Indeed half the poems in my anthology of English verse are destined for the waste paper basket due to some minor infraction of ‘the rules. If you want something that completely flummoxes my spelling checker here is the Loch Ness Monster Song by Scottish poet Edwin Morgan. I asked a Scottish friend whether Scottish spelling checkers fared any better and he assures me, no. The Loch Ness Monster’s Song Sssnnnwhufffill? Hnwhuffl hhnnwfl hnfl hfl? Gdroblboblhobngbl gbl gl g g g g glbgl. Drublhaflablhaflubhafgabhaflhafl fl fl - gm grawwwww erf grawf awfgm graw gm. Hovoplodok - doplodovok - plovodokot - doplodokosh? Splgraw fok fok splgrafhatchgabrlgabrl fok splfok! Zgra kra gka fok! Grof grawff gahf? GombIl mbl bl - blm plm, blm plm, blm plm, blp Edwin Morgan The Loch Ness Monster HOUSE_OVERSIGHT_015828

Knowledge 139 The foibles of spell checkers have long been a personal pain to me because of my dyslexia. Although I can see the red underlining Microsoft Word kindly inserts so liberally into my text, I can’t easily see the occasions when I use ahomonym. A fine poem illustrating the problem was kindly written by Jerrold H. Zar and published in The Journal of Irreproducible Results. It hangs on the wall behind my computer to remind me to check for these errors. Candidate for a Pullet Surprise By Jerrold H. Zar I have a spelling checker, It came with my PC. It plane lee marks four my revue Miss steaks aye can knot sea. Eye ran this poem threw it, Your sure reel glad two no. Its vary polished in it’s weigh. My checker tolled me sew. A checker is a bless sing, It freeze yew lodes of thyme. It helps me right awl stiles two reed, And aides me when eye rime. Each frays come posed up on my screen Eye trussed too bee a joule. The checker pours or every word Too cheque sum spelling rule. Bee fore a veiling checker’s Hour spelling mite decline, And if we’re lacks oar have a laps, We wood bee maid too wine. Butt now bee cause my spelling Is checked with such grate flare, Their are know fault’s with in my cite, Of nun eye am a wear. HOUSE_OVERSIGHT_015829

140 Are the Androids Dreaming Yet? Now spelling does knot phase me, It does knot bring a tier. My pay purrs awl due glad den With wrapped word’s fare as hear. Too rite with care is quite a feet Of witch won should bee proud, And wee mussed dew the best wee can, Sew flaw’s are knot aloud. Sow ewe can sea why aye dew prays Such soft wear four pea seas, And why eye brake in two averse Buy righting want too pleas. The Search for Knowledge I hope this explanation shows you the simplest model for creativity -— working through every possibility, and examining them all — is doomed to failure. It would take longer than until the end of time to even list all the options, let alone analyze them. You might wonder just how long it is until the end of time? It’s generally assumed there are two possible ends to the Universe, a Big Crunch or heat death. Either way the approximate estimate is our Universe will last somewhere between one and fifty times longer than it has lasted so far. That’s a long time, at least another 15 billion years, but just generating War and Peace would take 5000 orders of magnitude longer than this! More complex models such as a three-step process have been suggested. We could perhaps randomly create information and put it through a mechanical filter to bring it down to a manageable set of options and then give it to an appreciation algorithm to finally decide whether we have created something. The real problem with this model is the filters. If we try to reduce the effort by assembling works only from pre-existing words, we will have filtered away many works we know and love. Gone are Shakespeare, Lewis Carroll, Dylan Thomas and Roald Dahl, shall I go on? Indeed, once upon a time there were no words, every word was coined at some point. The process of creating art is continually creative and mechanical filters can't be applied to things they have not seen before. HOUSE_OVERSIGHT_015830

Knowledge 141 You might argue we could devise a more sophisticated mechanical filter, something that contains an algorithm with an understanding of the rules of language. The problem is both the size of the task and the nature of understanding. If I devised some really good appreciation algorithm which did not delete all the creative words of the English language, it would still have to read and appreciate the huge quantities of input until it hit upon something good. There is no way for any machine to read all this information in the age of our Universe; the numbers are just too large. And there is no way for a machine to understand all the rules of language, they are not written down and constantly evolve. These descriptions should give you an intuitive feel for nature of the creative problem. If you try to deconstruct it into mechanical steps you end up with either a mechanism that needs to be infinitely specified or one that lets through an infinite quantity of nonsense. A human could never sift through all that garbage to find the occasional pearl of wisdom. Until the beginning of the 20" century, most people thought knowledge and creativity must be just a matter of scale. A big enough, fast enough machine should be able to solve any problem. But early in the 1930s two mathematicians — Kurt Godel and Alan Turing — showed knowledge was not so simple. Let me give you a feel for why. Knowing When You Know The essence of creating knowledge, is to know when you have done so. In a sense, counting from one to infinity means I know everything, and merely counting to 50 million creates every piece of significant symbolic knowledge that will ever be written — all the books, plays, mathematical theorems you could possibly want. But, if I were to list all these numbers in an enormous imaginary book it would hardly constitute knowing everything: I would be awash with numbers but not with knowledge. The essential feature of ‘knowing’ is to have a small number of steps that will definitely answer a problem. For example, if I wish to phone someone I can look up their details on my phone. The process will tell me their number in two or three steps. If you tell me the number is somewhere in the phone book this is not knowledge. It could mean I need an infinite number of steps. If I accidentally deleted all the names in my phone - a nightmare scenario — and just had a print out of numbers would I still ‘know’ them? Obviously I would recognize my mother’s number, but most of them would be useless. To know something, I need link the information to what it is for. A number with a name allows me to predict what will HOUSE_OVERSIGHT_015831

142 Are the Androids Dreaming Yet? happen if I make a call. I will have an interesting conversation or pay my gas bill. It’s the same with most numbers. If I have a number that represents the design for a building or a mathematical theorem, these numbers have purpose. If I input these numbers to a computer along with some building design software or a copy of Mathematica they will do something interesting; allowing a construction firm to build a innovative building or a mathematician to check a theorem is sound. It’s a lot harder to prove numbers representing art are functionally useful. A work of art is in some sense not complete — it still needs to go through the process of being appreciated by someone. We could show it to a friend or exhibit it in a gallery but this is un unpredictable process. Van Gogh's paintings were so criticized in his lifetime, many people would have denied them the label art, and Edwin Morgan’s Loch Ness Art or Information Monster poem is almost pure gibberish, but it’s undoubtedly art. Art is a tricky problem but, in practice, most of us agree on what constitutes good and bad art. We will look again at art, in Chapter 10. Classically we assume knowledge is discovered through random chance and iteration. To understand how this might work let’s lay out the world’s information in a way we can visualize. Imagine every piece of discoverable knowledge could be found in an infinitely large library. HOUSE_OVERSIGHT_015832

Knowledge 143 The infinity library would contain every possible symphony, theorem, novel, poem, and play ever written, or to be written. Its sister library next door, the continuum library, would contain all the analogue works of art; painting, sculpture, architecture, physical artifacts and the like. The curators of the two libraries would constantly argue over whose collection was the better. We'll leave them to differ for the moment. The infinity library is interesting enough so let's explore it first. After all, its sister, the continuum library, takes an infinite amount of time just to look at the first room, and we are in a hurry! Although the infinity library is infinite, we are probably only concerned with entries shorter than a million symbols. All the interesting papers, proofs and symphonies I know of are shorter than this. If wanted to include all computer programs, I would still only need to increase it to 100 million symbols. Looking for knowledge is not itself an infinite task. For the sake of clarity, I will ask the infinity librarian to organize the collection. Any book or paper will be sorted according to its title and the contents of its pages, and similar books should be grouped together. I also only want to look at the English section of the library for the moment. I will still have a huge section to look through but at least every work is titled and readable by me. Much of the information will be junk but amongst the sea of rubbish will be islands of useful knowledge. Now, is there a way to find knowledge in this library in an automated fashion? Battleship HOUSE_OVERSIGHT_015833

144 Are the Androids Dreaming Yet? The best analogy I can find to illustrate iterative knowledge discovery is the 1970s family game ‘Battleship. The game consists of two 10 by 10 grids that you plug your ships into. All the ships are linear shapes of a few squares in length. The players cannot see each other's ships and must guess where they are. A very simple way to do this would be to ask your opponent whether they have a ship on the top left square and continue systematically across the board, square by square, until you reach the bottom right hand corner. This would eventually find every ship. If every ship were a piece of knowledge we could discover all the knowledge in the world by simply stepping through the board one cell at a time, but it would take a long time. A better way to play Battleship is to pick a square at random. If you get a hit, explore linearly around the hit. This will efficiently find the rest of the ship. The same might be true for knowledge. We could take random shots, get lucky and move linearly to flesh out our knowledge. Once we had exhausted an area we could take a step away at random and again hope for another hit. This process is exactly the way some people imagine the frontier of knowledge expands. But, it is wrong. The monkey moon shot story explains... ‘I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a monkey on the moon and returning him safely to Earth.” President Monkey The monkey nation is asked to mount a moon shot. After a little time a monkey is asked to report on progress. “I can report, says the monkey, “I have climbed a particularly tall tree on the tallest hill on my island and have made over seven hundred meters progress towards the moon, although this is only 0.0001% of the way there, this has been quick so I believe we are well on the way” You see of course the problem. Progress in many problems is nonlinear. Moving a bit of the way towards the goal does not provide any actual progress: That is the problem with knowledge. It is not linear in structure. You need to take leaps to discover new knowledge. You can not simply look around in the general area. Such leaps are mathematically huge. The chance of making a successful one by pure chance is virtually zero. HOUSE_OVERSIGHT_015834

Knowledge 145 But Cats Can! As chance would have it, as I was writing this book about the impossibility of creating great literary works at random, our new kitten, Jessie, sat on my keyboard - she likes the warmth. To my great embarrassment I have been proven wrong. Here is her first literary work. I managed to capture her on camera a little later that evening, editing a spreadsheet. My brain interprets this string as the cat thanking me for good food. I wonder if you see the same thing? This is just a demonstration of the strength of human pattern detection algorithms and not, sadly, of feline communication. Cats Creation .... KkkkInk gfooooo000fd0------- iitiissssss33331i... APTA ATA. ..... PPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPPPP--OPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPPP PPPPPPPPPPPPPPPPPpPh Jessie, Our Creative Kitten HOUSE_OVERSIGHT_015835

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Chapter 6 KITTENS & GORILLAS Orangutan and Kitten HOUSE_OVERSIGHT_015837

“No kitten that loves fish is unteachable; No kitten without a tail can play with a gorilla; Kittens with whiskers will always love fish; No teachable kitten has green eyes; No kittens have tails unless they have whisters; hence...” Lewis Carroll “Once you eliminate the impossible, whatever remains, however improbably, must be the truth.” Sherlock Holmes, Arthur Conan Doyle HOUSE_OVERSIGHT_015838

Lewis Carroll lectured on mathematics at Oxford University. He wrote several books on logic, illustrated with wonderful problems involving fish, kittens, and gorillas - much less boring than the brown, grass-eating cows of modern textbooks. Kittens and gorillas are not usually in much contact, but I did find one hit on Google, pictured! The words we organize into books, poems and plays are not just a random jumble; they have structure and a logic to them. We group verbs, subjects and objects together to form sentences and, at a larger scale, characters have motivations and relationships: this character loves that character, the valet had the candlestick in the ballroom and could not have stabbed the butler in the kitchen, and so on. We have dictionaries to define words, but to truly understand the information they convey we need to understand the logical rules governing how they can be combined. A s well as giving us Alice, the Jabberwocky, and the Cheshire Cat, Everyday conversation is fragmented and repetitive. Fortunately, now and again, we say something definitive. For example, “This gorilla is brown.” The statement links a property, ‘brownness; to a thing, ‘a gorilla. Logical statements are precise but often need to be put in context. IfI were standing in a forest when I made my statement you must guess I mean the nearest gorilla. The word “This implies nearness, but nearness is not well defined. Better to be precise. “The gorilla I am closest to, measured by line of sight distance is the Pantone shade dark brown? However, if I talked like this all day I would not have many friends. Logical Beginnings The formal study of logic began in 3848c with the publication ofa treatise called the Organon by the Greek philosopher Aristotle. A student of Plato, Aristotle taught many of the famous leaders of his time, including Alexander The Great. Ancient Greece was not some idyllic think tank. If you annoyed the political establishment you might find yourself having to leave town in a hurry. This happened to Aristotle after Plato’s death, and he spent nearly a decade touring Europe. Eventually, he returned to Athens where he published his study on logic. In the Organon, Aristotle examined groups of up to four statements, each containing up to four relationships. For example: All kittens eat fish. Some kittens eat fish. No kittens love gorillas. No gorillas eat kittens - luckily. It is possible to put two statements back to back and infer things. HOUSE_OVERSIGHT_015839

150 Are the Androids Dreaming Yet? mm « I could say, “All gorillas eat leaves.’ “All leaves are green.” Therefore I can infer all gorillas eat some green things. This is a valid inference. It is not correct to say, gorillas eat only green things. There are 256 ways you can arrange four Aristotle statements with four relationships but only 19 valid deductive conclusions can be drawn. The kitten puzzle at the start of the chapter is an example of such a logical puzzle. Can you reach the right conclusion? TRY SOLVING THE KITTEN PUZZLE WITHOUT READING ON Aristotle's syllogisms are only a start. There are many other types of logic. In antiquity, the Stoics developed a different brand of logic based on the idea of larger and smaller. Stoic logic allows us to answer questions of relative size. If a Mini is smaller than an Audi, and an Audi is smaller than a Rolls Royce, then a Mini is smaller than a Rolls Royce. The Stoics pursued their branch of logic until around 180aD when study of this sort died out. It’s not quite clear why. Perhaps the rise of religious power and the onset of the Dark Ages curtailed intellectual inquiry. Even after the Enlightenment began around 1650 it took some time for the discipline of logic to re-emerge. If you want to learn more about syllogistic logic and how to solve Lewis Carroll’s puzzle you should read his book The Game of Logic. The definitive book on the logic of language, in my opinion, is Logic by Wilfrid Hodges. Logic for Computers Western civilization mostly survived on syllogisms and stoic logic for nearly two thousand years before George Boole devised his theory of binary logic in 1847. Boole developed an elegant mathematical system for representing logical statements that allowed simple arithmetical operations to answer logical questions. We now call this system Boolean logic and he gave us the modern convention of using one for true, and zero for false. Computers use his principles all the time. For example, if it is true my bank account shows less than zero, then make it true that someone will send mea letter warning me I am overdrawn. The best way to get your head around Boolean logic is to solve the ancient puzzle of the Two Guards. The puzzle featured in the 1986 movie, The Labyrinth, HOUSE_OVERSIGHT_015840

Kittens & Gorillas 151 starring David Bowie and Jennifer Connelly. If you want to cheat watch the film to see the answer. Here is the puzzle. I'll put the answer on my website. Two guards stand barring your way and behind them are two doors. One guard always speaks the truth, while the other always lies. You are only allowed to ask one question of one of the guards. Your life depends on picking the right question to ask as, based on the answer, you must pick a door. One leads to life, the other to certain death. Is there a question you can ask to ensure you pick the door leading to life? TRY SOLVING THE GUARD PUZZLE Twin Guards - Left door or Right If you are reading this, you picked the correct door and lived. HOUSE_OVERSIGHT_015841

152 Are the Androids Dreaming Yet? Logic for Humans Syllogisms can be used for practical purposes. Take, for example, the following set of statements, “I want a hot drink.” “Coffee and tea are hot drinks.” “I always drink milk with tea” “We have no milk” What drink should I choose? I’m sure you can work it out. This logical problem follows a simple chain and results in me getting the hot drink I like. We use Boolean logic on a day-to-day basis. The simplest form is a checklist. Pilots use checklists all the time; do I have wings, fuel and a copilot? If they are all there, go ahead and fly. Otherwise do not. Mathematically speaking, a checklist is simply the product of the options. If they are all one, then the product is one — in this case we can fly. If any is false — represented by a zero — the product will be zero and we cannot fly. Life is often more complicated and we have many logical tools at our disposal. Let’s take a look at a few, starting with a famous historical one. Benjamin Franklin invented the lightning rod and bifocal glasses, as well as charting the Gulf Stream and all manner of other scientific discoveries. He described his process for decision-making when there are many pros and cons to consider. “. my Way is, to divide half a Sheet of Paper by a Line into two Columns, writing over the one Pro, and over the other Con. Then during three or four Days Consideration I put down under the different Heads short Hints of the different Motives that at different Times occur to me for or against the Measure. When I have thus got them all together in one View, I endeavor to estimate their respective Weights; and where I find two, one on each side, that seem equal, I strike them both out: If I find a Reason pro equal to some two Reasons con, I strike out the three. If I judge some two Reasons con equal to some three Reasons pro, I strike out the five; and thus proceeding I find at length where the Balance lies; and if after a Day or two of farther Consideration nothing new that is of Importance occurs on either side, I come to a Determination accordingly.” Another important piece of logic is reductio ad absurdum. Reduction to the absurd allows us to disprove something because, if it were true, it would lead to an absurd conclusion. An alibi is a familiar form. If I was seen in the pub when the murder occurred in the ballroom of the manor house and you claim I committed the murder, I must have been in two places at once. People can’t be in two places at once — that would be absurd. Conclusion: I am innocent! HOUSE_OVERSIGHT_015842

Kittens & Gorillas 153 Notice I not only prove I am not guilty I also prove the opposite: I am innocent. When a mathematician uses this trick, it is called an indirect proof and works the same way as the alibi. Assume the opposite is true of some theory you want to prove (I am guilty). If it generates a contradiction or paradox (can't be in two places at once) you can deduce the opposite must be true (innocence). Mathematicians use this all the time. It assumes, of course, mathematics is consistent and that true and false are opposites. Some mathematicians argue this is too strong an assumption. Why should we assume consistency and recognize only two logical states, true and false? These mathematicians believe the only way to prove a theorem is with positive argument rather than using the opposite of a negative argument. They don't allow indirect proofs in their mathematical models. This type of mathematics is unsurprisingly called positivism. It’s a pure theory but, unfortunately, if you try to follow it you lose much of our current mathematical knowledge and understanding. Most modern mathematicians think it a historical curiosity, but it does pop up from time to time. Modern mathematics is founded on the axioms that true and false are the opposite of each other and that inconsistency is forbidden within the system. Mathematical proofs submitted to journals are not permitted to contain inconsistencies or result in paradoxes. Paradoxes - When Logic Fails “T would not be a member of any club that would admit me. Groucho Marx Paradoxes occur when a state- ment makes no sense, or results in an internal contradiction as with Groucho Marx’s famous quote. They are widely used in mathematics to implement indi- rect proofs. To do this, we sup- pose something is true, and if it results in a paradox then the Groucho Marx HOUSE_OVERSIGHT_015843

154 Are the Androids Dreaming Yet? thing we thought true must be false and the opposite is true. This is a somewhat circuitous route to prove things, but it is often the only prac- tical way. Two paradoxes we are taught as children are the liar’s paradox and Zenos paradox — also known as the story of the tortoise and hare. The first is a real paradox but the second is a false paradox. The liar’s paradox is just the simple statement: “This sentence is false.” It is a paradox because of the internal inconsistency: We cannot determine if it is a true or false. First assume it is true, but it says it is false, so it is not true. Then try it the other way around. Assume it is false but the sentence states it is false, so it must be true. If that were so it must be false by the first argument and so on ad infinitum. Either way around, the sentence contradicts itself. A paradox. Zenos Paradox, on the other hand, is a false paradox. Here is the story. Once upon a time there was a hare. He was a very arrogant hare and believed he could outrun any animal. A tortoise was walking along the way and the hare jumped out in front of him. “You are so slow,’ said the hare. The tortoise replied, “You may be the fastest hare in the kingdom but I am the most persuasive tortoise. I bet I can persuade you of anything, including that I am faster than you.” “T don't believe you,” said the hare. “OK; said the tortoise, “let me show you. Give me 100 meters head start since you are so fast. Then, we'll both start to run. After 10 seconds you will have run 100 meters and arrived where I used to be, but I will now be ten meters ahead. After another second you will be where I am now, but I will be 1 meter ahead again. So you can never catch me.” The hare pondered for a while but, being a hare of little brain, could not make out the true answer. It is a false paradox. The time intervals are getting shorter. The question for a mathematician is, does the problem converge to a solution. The answer is yes, and I can reframe the problem to see how it is solved. Let’s simply look at who would be ahead after 20 seconds: the hare! HOUSE_OVERSIGHT_015844

Kittens & Gorillas 155 The mathematical reason for it being a false paradox is that some series converge and some do not. If I move progressively closer and closer to something in smaller and smaller time intervals then I may indeed reach it. On the other hand, some series never converge. I will never reach infinity how ever many steps I take. The Barber Paradox Now, for a slightly harder paradox, let’s suppose there is a town with just one barber. In this town, every man keeps himself clean-shaven by either shaving himself or going to the barber; the barber shaves all the men in town who do not shave themselves. All this seems perfectly logical, until we pose the question: who shaves the barber? This question results in a paradox because, according to the statement above, he can either be shaven by himself or the barber, which is he. However, neither of these possibilities is valid! This is because if the barber shaves himself, then the barber must not shave himself and if the barber does not shave himself, then the barber must shave himself. You might think this paradox an oddity but, using this simple idea, Bertrand Russell changed the course of mathematical history and it is the fundamental paradox used to show computers are Turing limited. The Russell Paradox In the late 19 century, mathematicians began to think about the nature of numbers. What is a number? It is certainly not an object we can hold. I can't hold a two, unless it’s the brass number plate, for my front door. And, in that case I am holding one number plate, so I am not holding the idea of two, but rather the idea of one: one brass plate in the shape of a two. The ‘idea’ of a number is to say something about the things I have in my hand: two apples, two oranges and two brass number plates. These are all sets of two things and ‘two’ is the collection of all these sets. In 1890, Gottlob Frege completed his theory of sets. The project had taken him five years. Unfortunately, just before sending the book to the publisher, Bertrand Russell wrote to him and pointed out the following paradox. What about the set of sets that does not contain itself? Think about it... HOUSE_OVERSIGHT_015845

156 Are the Androids Dreaming Yet? It is the barber paradox with the word ‘set’ substituted for ‘barber’ and ‘contains’ rather than ‘shave. But it’s essentially the same logical problem. You might find this rather contrived but mathematicians must have a system totally free from paradox, otherwise there is no certainty. Frege's system was holed below the water line. Eventually, after much further work, a theory of sets was worked out that does not contain the Russell Paradox. It’s called Zermelo-Fraenkel set theory, or ZF for short. It solves the Frege problem by forbidding sets to refer to themselves. It’s a bit like Microsoft Excel’s solution to dividing something by zero. It is simply forbidden and generates an error message. Set theory was fixed and is now the basis of most mathematical thinking. What is Logic for? Logic is the foundation of mathematics. Applying it enables us to make irrefutable statements about things: numbers, lines, planes, equations and the so on — the things you learned at school - and to prove statements about these things beyond any doubt. This is not the ‘reasonable doubt’ hurdle of our law courts, but an absolute measure: No possible doubt whatever. Let’s look at one of the earliest mathematical proofs: Euclid’s proof there are an infinite number of prime numbers. Euclid created this proof in ancient Greece around 300sc — so far back that logic was in its infancy Euclid’s Elements 100AD HOUSE_OVERSIGHT_015846

Kittens & Gorillas 157 and numbers had not yet been properly invented. Euclid used distances rather than numbers for all his proofs but I will use the word ‘number’ in this explanation. First a little revision. A prime number is a number that can only be divided by itself and one, for example three, five, seven, and eleven. All numbers can be split into primes using a couple of tricks. First, all numbers are divisible by a set of primes. Ten is five times two — two primes. We are also fairly sure we can form any number by adding two primes together. This is Goldbach’s Conjecture, set as a question in a letter written to Euler in 1742. It is still unproven! Euclid proved there are an infinite number of primes by using reductio ad absurdum. Imagine we have a complete list of prime numbers — James’ list of primes. It contains every prime number. (This is the setup. We are proposing something we suspect is incorrect and will lead to a paradox or contradiction. When it does, we will have proven the opposite fact. The proof relies on the fact that a number can either be prime or not prime. There is no middle ground.) Let’s make a new number by multiplying all the numbers on my list together and adding one. There are two possibilities: this new number is either prime or not prime. If the number is prime, it is a new prime number that was not on my list and I have disproved the theory. If it is not prime then it must be divisible by two prime numbers already on my list. However, neither of these numbers could have been on my list, because dividing by one of them would give me a remainder of one. Remember I multiplied all prime numbers together and added one. It must, therefore, be a new prime number, which had previously not been on my list. Once again, I disprove the theory. Since both routes fail, James’ list of prime numbers is not complete and, therefore, prime numbers are infinite. Feynman's Proof My favorite piece of logic is Richard Feynman's disproof of the existence of polywater. It’s a strange logical proof bordering on philosophy, but it shows just how far you can take logic. In 1969, an urban legend spread around the world that there was a substance called polywater. It even made it into an episode of Star Trek. Polywater was believed to be a lower energy state of water, more viscous than ordinary water. If this substance did exist, it would be possible to mine the oceans of the world converting water to polywater and HOUSE_OVERSIGHT_015847

158 Are the Androids Dreaming Yet? therefore generate energy. There was a concern that if the right catalyst was accidentally introduced into the oceans they would solidify into polywater thus dooming the human race, or at the very least making water sports impossible! Feynman was consulted and stated, “If there were such a substance as polywater then there would have evolved an animal that eats water and excretes polywater, using the liberated energy as its power source. Since there is no such animal, polywater does not exist? Feynman's proof is an elegant indirect proof coupled with a syllogism. Polywater exists. Polywater is a lower energy form of the high- energy substance called water. Food is a high-energy substance that can be converted to a low energy substance by a process we shall call ‘being good to eat? All things on earth that are good to eat have something that eats them. Polywater is a food and therefore good to eat. Therefore an animal must exist that eats polywater. No such animal exists, so either something in our chain of logic is wrong, or the premise is unsound. Since the chain is sound, the original premise must be wrong: Polywater cannot exist. In short, Feynman’s proof says: if a thing is so, then the inevitable consequence is the evolution of something else, and since that something else does not exist, the original thing cannot be so. QED: disproof by nonexistent consequence. The polywater disproof neatly demonstrates the important elements of Feynman's Evolutionary proof. First, life must be continuously exposed to the thing in question, in this case water. This is clearly so as most life on planet Earth lives in the oceans or is intimately entwined with water. Evolution takes time, so enough time must be allowed for life to evolve. It must be a nearly linear problem so that a solution proceeds in steps where each step is an improvement and no step requires too high a level of mutation or adaption. We can illustrate the boundary between a linear problem and one requiring a step change by describing how triple drug therapy works in the treatment of AIDS. Until triple drug therapy entered the picture progress against AIDS had been a depressing story of drug discovery followed by the almost immediate evolution of the virus to evade the drug. The AIDS virus is a retrovirus with a shell composed of sugar molecules. It is almost trivial for an AIDS virus to mutate these outer markings to look different, even from one day to the next. This is the way the virus continually and nimbly evades our immune system. However, the AIDS virus does have some components that it can’t easily mutate because they are not merely aesthetic, they have a functional purpose. Why not target them? HOUSE_OVERSIGHT_015848

Kittens & Gorillas 159 Unfortunately, it turns out the AIDS virus can even mutate its functional parts, but this is harder. The probability of a successful functional mutation is 1000 times less likely than a simple aesthetic mutation to the sugar coat. Triple drug therapy works by attacking three different functional elements of the virus simultaneously. It is possible for the virus to modify all these functional elements but the likelihood of it doing so is tiny. One mutation alone does not help because the drug cocktail will still target the other two elements and kill the virus. The AIDS virus does not understand that it is facing a triple drug cocktail. It cannot reason like a sentient being and random chance is not sufficient to make the big leap necessary to overcome the cocktail of drugs. Unless you can mutate all three elements at once your time as a virus particle on this planet is over. Most problems we have to solve in this world require more than one simultaneous logical step and these don't happen by chance. HOUSE_OVERSIGHT_015849

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Chapter 7 COMPLEXITY & CHAOS Mandelbrot Set HOUSE_OVERSIGHT_015851

“Life is really simple, but we insist on making it complicated.” Confucius ‘Any darn fool can make something complex; it takes a genius to make something simple.” Pete Seeger HOUSE_OVERSIGHT_015852

fend off boredom he collected all manner of interesting games and puzzles. One day an inventor came to his palace and told the King he had a game of such subtle complexity, yet apparent simplicity, the King would play no other. The King learned the game and soon agreed it was, without doubt, the best of all games. The game was, of course, ‘chess. The King asked the price of this game and the inventor told him it was a mere trifle. The King should give him one grain of rice on the first square of the board, two on the second, four on the third, and so on, doubling each square until he filled the board. The King called his treasurer to honor the bargain and the first bags were brought from the storehouse. The grains were placed on the board in each square but soon there was not enough space and the grains had to be piled on the table next to the board. Soon this, too, was not enough and every table and chair in the hall had to be covered. Even this was not enough and they began to stack whole bags up in the courtyard. When they reached the thirtieth square, the treasurer turned white. He sat and calculated for a while before saying with a trembling voice, “My great ruler, there is not enough rice in all the world to cover this board. The ruler called the inventor and told him he could not honor r here was once a great King who lived in a marvelous palace. To the debt and the inventor should name another price. The King had two beautiful daughters, the first knew she was beautiful and deported herself accordingly, and the second, was bookish and shy, but perhaps more beautiful for this. The inventor asked for the hand of the second daughter and lived happily ever after. In the less favorable version of this story, the King becomes very angry and has the inventor beheaded. I prefer the romantic version. Placing rice on a chessboard and doubling it successively leads to wildly large numbers. Covering it completely requires 18,446,744,073,709,551,615 grains, about four hundred trillion tons and equivalent to one thousand years of worldwide rice production. Like the king, humans do not intuitively grasp the enormity of this problem because we're not good with large numbers. Although the number of grains needed to cover a chess board is very large, it is not hard to calculate. The treasurer is the one who should have lost his head for not being able to do the calculation. The equation is simply two, doubled sixty-four times, less one, 2-1. A pocket calculator can produce this number in a thousandth of a second: it’s just long multiplication. Although calculating this number is quick, it is not always the case. Answers to some problems have short cuts, while others do not. HOUSE_OVERSIGHT_015853

164 Are the Androids Dreaming Yet? Mathematicians have catalogued the universe of problems into classes rather as biologists have catalogued animals into species. Each problem is examined and put into a genus with a name. Sadly the names are not as readable as the Latin names for animals. For example, ‘nlogn’ is the complexity class of most sorting programs, while traversing a maze typically sits in the class NP or P/POLY. Although the classifications look complex the basis of cataloging is simple, a class name signifies the time needed to solve a problem using the best possible algorithm, and the scale this is measured in is ‘Big O° Big O Every problem has a complexity. In mathematics this is expressed using ‘Big O’ notation, where ‘O’ stands for order-of-magnitude. The simplest problems have order 1. If I am working at my computer on a Word document and I press print, the printer will spring to action and print the document. This problem is of flat complexity, notated O(1). It does not matter how large the file is; one click is all I need. I am, of course, assuming sufficient paper in the printer and ink in the cartridges. The next complexity class is a linear problem, O(n). For example, walking to the store to buy a pint of milk. The farther the store, the longer the walk. The time needed to get to the store is directly proportional to the distance: if ] am walking, a single step multiplied by the number of steps required to cover the distance. You might think adding two numbers together is a linear problem — the bigger the number, the harder the problem — but there's a clever trick to speed it up. You can get 10 people to add each column in parallel. They'll need to coordinate when someone ends up with a number larger than ten and has to carry the extra digit but this can be easily solved. A problem gets its classification only once we’ve used the cleverest possible trick to solve it. Most problems we meet in mathematics are somewhere in between flat and linear but there are some that are much harder. The most common hard problem we come across in our daily lives is sorting. Rather than go through a tedious written description, check out the video link on my website. Sorting without using any spare space requires a bubble sort. This is an example of something that needs n squared operations and, since n squared is the simplest example of a polynomial, it is said to be in the polynomial time, or ‘P’ time classification. HOUSE_OVERSIGHT_015854

Complexity & Chaos 165 facebook.com/AlgoRythmics Intercultural Computer Science Education afO) all] af2) af3) a[4) af[S) af6) al7] af8) al9) Created at Sapientia University (in cooperation with "Maros Mivészegyittes") Bubble Sort Ballet The Hardest Problems You probably hope cracking the encryption used to secure the Internet is one of the hardest problems known to man but I’m sorry to tell you it is not. When you use your credit card to buy something from an online shop, your web browser changes from http to https, the ‘s’ stands for secure. The data you send to the Internet is coded using a system developed in 1977 by Ron Rivest, Adi Shamir and Leonard Adleman of MIT, which is why it is called RSA encryption. Any information you send is raised to the power of a very large number - usually around one hundred digits long. Raising something to the power simply means multiplying it by itself that many times. What makes decrypting a message hard is that division is a slow process; it is called ‘long divisiow for a reason. It turns out there is no way to speed it up on a conventional computer so, unless you know the right number to divide by you will have to try every number. It is this that makes decrypting RSA messages hard. Although RSA messages are difficult to decipher, they are nowhere near the hardest problems. That accolade is commonly believed to go to non-deterministic polynomial problems known as ‘NP’ problems. NP problems are easy to describe but fiendishly difficult to solve. Nondeterministic means each time you come to a branch in the problem there is no way to tell which branch is the best to pursue without exploring it all the way to the end. It’s the same as a maze; at each junction in the maze you can decide which path to take, but the junction gives you no HOUSE_OVERSIGHT_015855

166 Are the Androids Dreaming Yet? Maze clue which one will be better. Beware the confusing naming system, ‘N’ stands for nondeterministic in this case, whereas in normal complexity classes ‘n’ stands for number. Sorry. That’s just the way it is. Let me give you an example of one of these NP problems. Let us assume we have one of those complicated recipes from the latest celebrity chef cookbook. If all the ingredients can be bought from one store, making the dish is straightforward, but if they come from different stores, you will have your work cut out. What is the best order to visit them? With 2 shops, it’s trivial. Either order will do. With 3 it is a little harder and with 4 there is quite a bit of choice. This is known as the ‘traveling salesman’ problem because the original formulation described a salesman wishing to find the shortest route between all the cities in which he had customers. The complexity of this problem rises much faster than the Rice and Chess Board problem. Try it for yourself. It doesn’t matter if you imagine you are visiting customers or shops. I have given you a grid to count off distances. Try to solve a problem for 3 cities, 5 and 10. What is the shortest path allowing you to visit each place? HOUSE_OVERSIGHT_015856

Complexity & Chaos 167 TRY THE PUZZLE ON THE WEB Warning: Don’t spend too long on these problems. The reason I warned you not to spend too long is that solving the 50-city problem would take longer than the age of the known universe. NP problems get harder very fast as the number of elements goes up. A 50-city problem is hugely larger than a five-city problem, not just ten times harder. The Clay Mathematics Institute has offered a $1 million prize for anyone who can say whether NP problems are really as hard as they appear. It may be there is a general trick or a series of tricks that allow you to solve any NP problem in a shorter time. If you could do this, the problem would be demoted to P, allowing fast computers to tackle it. No one has yet found a proof of the P=NP problem. At the time of writing several proofs are sitting with the Clay Prize judges but don’t hold your breath. Most people assume there is no solution. If you want to have a crack at the problem let me state it in simple terms. Marplent bo rr H H o Traveling Salesman LS lac oo HOUSE_OVERSIGHT_015857

168 Are the Androids Dreaming Yet? Imagine you wanted to find the center of a maze. Is there a way to speed searching the maze, so you do not have to test every branch? If you can provide a mathematical proof that there is or is not, you win the prize. Places Game While it is commonly assumed NP problems are the hardest, this is not the case. There are quite a few that are harder still. One such is called a PSPACE problem. It’s quite difficult to explain but luckily many of you will have played a form of it on long car trips when you were a child: My family calls it The Places Game. I will pick a place —- “London; and you must then pick another place, say, ‘New York, that starts with the letter my place ends with. Pll then pick ‘Canterbury’ and my kids will laugh at my dyslexia and I'll have to switch to ‘Kansas’ and so on. Once you use a place you can’t use it again. The mathematical question is to predict who will win given each player has a finite list of places they know? It turns out this type of problem is even harder to solve than an NP problem. This is because on each turn a player gets to pick any name from their list. With the traveling salesman problem, there is only one ‘player’ — the salesman - so we can write out a route and check it. In the Places Game there is no single route through the game because, after I pick my favorite town ‘London; you can pick any place beginning with ‘N’ I have to anticipate an enormous table of possible paths through the game. The table takes huge physical space — which is where PSPACE gets its name. Remember I’m just playing the simplest mathematical games with bits of paper and discrete ideas. I haven't strayed into the quantum world yet. That brings with it a whole new level of complexity to explore. Complexity is such a diverse subject that Scott Aaronson of MIT has created a web site called the complexity zoo to catalogue all the different ‘species. It is much to complex to reproduce here but let me provide a sketch. The Complexity Hierarchy My table below represents the hierarchical complexity of knowledge. We start off with the problems both humans and computers find easy, then rapidly move onto problems that even the fastest machines find difficult: a perfect game of chess or predicting the weather. Above these computable problems are the non-computable ones which no computer HOUSE_OVERSIGHT_015858

Complexity & Chaos running any algorithm can solve, and then there are the free will problems: how do we pick a problem in the first place? How do inventors come up with problems no one had ever thought to solve in the first place, such as the invention of the Rubik’s Cube? 169 Problem Flat nlogn Linear Logarithmic Exponential P Near NP NP-non-complete NP-Complete, tractable Chaotic NP-Complete, Quantum NP-Complete, intractable PSPACE Non-computable Non-deterministic, Non-time divisible, Non- computable Impossible Known Unknowns Unknown Unknowns Erné Rubik's Cube Example Print File (for Human) Searching a list Finding the lowest number in a list Long Multiplication Long Division Most Algorithms Factor Prime Number Perfect Game of Chess Travelling Salesman, SAT Weather Modeling a Quantum Process Busy Beaver, Towers of Hanoi Graph Problems, Places Game Creativity, Finding Fermat Theorem for a Turing machine, Tiling the plane with Penrose Triangles Free will Halting problem for a Turing Machine, some mathematical theorems such as the Continuum Hypothesis in ZF+AC (Hilberts Ist). Travelling faster than the speed of light. Understanding the American tax code. I know that I don’t know either way. I have not thought to ask that question yet. Inventing the Rubik's Cube HOUSE_OVERSIGHT_015859

Butterfly “Does the flap of a butterflys wings in Brazil set off a tornado in Texas?” Philip Merilees, improving on Edward Lorenz HOUSE_OVERSIGHT_015860

Chaos in 1987 with the publication of James Gleick’s book Chaos. It’s Cm is the twin of complexity. It burst into the public psyche not a difficult concept to grasp. Complex systems can be formed using simple rules, and very small changes in starting conditions can profoundly affect future events. I experience this if I miss my train to work in the morning: 30 seconds either way will change the whole pattern of my day, the people I meet and the level of stress I experience. I’m sure you can think of similar experiences. Henri Poincaré, a French mathematician, first studied the effect back in 1880. Poincaré was trying to solve an old mathematical problem called the Three Body Problem originally set by Isaac Newton. Take the Earth, Mars and the Sun. These three bodies orbit each other, or strictly speaking a point in space somewhere between them. Is there an equation that will tell you where the bodies will be in, say, 100 years’ time? The answer is surprising, no. The three bodies will orbit in a non-repeating way. There is no analytical short cut, no equation that will predict where they will be Poincaré HOUSE_OVERSIGHT_015861

172 Are the Androids Dreaming Yet? at some point in the future. The only way to know is to build a perfect model of the system and see what happens. Poincaré won a valuable prize for his proof from the King of Bavaria. You can see some amazingly complex orbits plotted below. Remember these are still deterministic and predictable — after all, they were calculated with a computer — they are just chaotic. Four Body Problem Butterflies and Sliding Doors After Poincaré, the field of chaos remained fairly quiet until Edward Lorenz began studying weather patterns using computers in the 1960s. The story goes, one day his computer was misbehaving and he had to re- key some data into the machine. Rather than using eight decimal places he used only six to save time, and was amazed when the results of his program came out completely different. Dropping the seventh and eighth decimal place represents a change of only one part in a million, yet the patterns of weather predicted by the computer were completely altered. HOUSE_OVERSIGHT_015862

Complexity & Chaos 173 Lorenz went on to study the effect and created a new branch of mathematics. His quote about the beat of a butterfly wing creating tornados has entered the public psyche and is central to the plot of numerous Hollywood movies. One of his functions —- known as the Lorenz Attractor — nicely illustrates the nature of chaos. A very simple equation plots the beautiful, apparently three-dimensional, non-repeating shape. Chaosville Chaos, taken to its logical conclusion could explain our Universe. Stephen Wolfram in A New Kind of Science, makes the argument that simple rules could explain the extraordinary complexity we see in our Universe. He applies rules to elements in a two-dimensional grid programmed on the computer which form ‘cellular automaton’ that function a little like simple animals, generating all manner of complex shapes and behaviors. The inspiration for this approach is almost certainly Conway’s Game of Life developed by John Conway in the 1960’s. In his computer game, animals and machines seem to appear on the screen but in truth they derive from the most simple set of rules. You can check out the website to see a live version of Conway’s Game of Life. It’s a lot of fun. Wolfram’s Strange Attractor HOUSE_OVERSIGHT_015863

174 Are the Androids Dreaming Yet? thesis is that we could all be living in one of these games. Perhaps our Universe is a form of Mandelbrot diagram - albeit a 3D version with stars and planets. If you look at the picture of a nebula and compare it to the Mandelbrot set, you can see how this is a tempting conclusion. In the Game of Life the rules are simple yet the behavior simulates little animals being created and destroyed. Of course, there are no actual animals. The things you see on the screen, ‘gliders’ ‘walkers, and ‘cannons, just hang together accidentally. But, Wolfram considers these little digital creatures are animals. He argues our Universe is just like the Game of Life: A set of simple rules leading to complex behavior. If we are Nebula HOUSE_OVERSIGHT_015864

Complexity & Chaos 175 prepared to call ourselves animals, so should the little creatures which emerge within the game. We simply emerged in a similar but slightly more complex game. This proposal would mean our Universe is entirely deterministic, our lives the result of a gigantic computer program that we live within and form part of. Chaos might make it impossible to predict the future without running the program and watching what happened, but the results would be inevitable, set in motion at the dawn of time. There is no place for free will in such a Universe, no place for reason. The world would simply be. But a strange idea will come to our aid to show us the limits of computation and allow us to question whether we live in a predetermined world. This idea is Aleph 1 - something larger than infinity. And it is infinity we will explore next. ~ Lube ee te 1. ty* @ * @ aVh ow” rm a a . a er ™ alt oly en . ia he ath, ii hs 2s Conway's Game of Life HOUSE_OVERSIGHT_015865

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Chapter 8 HOUSE_OVERSIGHT_015867

‘All infinities are equal, but some are more equal than others.” George Orwell, paraphrase “Only two things are infinite, the universe and human stupidity, and I’m not sure about the former” Albert Einstein “God gave us the integers, all else is the work of man.” Kronecker HOUSE_OVERSIGHT_015868

ealth warning! The man who discovered infinity had a mental breakdown. This subject may tax your brain. Georg Cantor didn’t really ‘discover’ infinity but he was the first mathematician to put it on a firm theoretical footing. In the late 19" century, most mathematicians thought infinity was a curious idea with no proper place in mathematics. They treated Cantor's attempts to make it into a real mathematical object with contempt. This affected Cantor’s morale and caused him to suffer several bouts of deep depression, retreating to a sanatorium from time to time. Infinity is a difficult idea to grasp but it is vital to our study of information. It behaves counter-intuitively but is not impossible to grasp. The reason it is important is that information can always be translated into numbers and numbers go on to infinity. If you want to know all about information, you must understand infinite numbers. History Indian scholars began studying infinity in the 4 Century BC. It turns up naturally in all manner of places. In geometry, parallel lines extend forever in either direction without ever meeting. To define a parallel line you must contemplate infinity. In arithmetic, even if you pick the largest number you can imagine, there is always a larger one; just add one. In the physical world if you look up at the night sky it appears to go on forever. Again you have infinity. Historically there were two interpretations of infinity. The first, favored by Plato, was a journey. When you embark upon a journey, you can always take another step. Infinity is the idea of ‘one more’ or never- ending. It can never be reached. The second definition is more radical. Infinity is a thing, a number so bigyou could not imagine anything bigger, but it is one number. Plato thought this second definition tantamount to madness. Today we embrace this madness and go a whole lot further. Let me show you how. Ifinfinity were a number, you should be able to perform mathematics with it; add it, multiply it, and even raise it to a power. This is not as radical as it might first seem. Until comparatively recently, zero was not accepted as a number - if you consider recent to be one thousand years! Nowadays it is. At the end of the first millennium Indian scholars found, against their intuition, that you can use zero as a number without generating contradictions. Take addition. I can have zero cakes, add one, and I have one cake, add another, and have two cakes and so on. In this way, HOUSE_OVERSIGHT_015869

180 Are the Androids Dreaming Yet? the number zero behaves just like any other counting number. It also works with multiplication. If I have zero lots of 4 cakes, I have no cakes. Zero times four is zero, so multiplication with zero works. There is one embarrassing exception, if I divide by zero I seem to get infinity. When I was a child this was a definition for infinity, but nowadays mathematicians simply forbid the operation. Division by zero is not allowed and if you try it on your computer, you will get the not terribly useful, #DIV/0! Error. That’s progress I guess! Zero had been tamed. What about infinity? Cantor showed that while you could think of infinity as a number, it might not be just one number. He proposed there are many infinities. In fact, there are a greater than infinite number of them! He did this through a rigorous analysis of a new branch of mathematics called set theory. Set theory is now the cornerstone of modern mathematics, but it was treated with suspicion in Cantor's time. Rather than embrace the new thinking, many mathematicians ridiculed it; Poincaré wrote that Cantor’s ideas were a grave disease infecting the discipline of mathematics! This seems odd given our modern propensity to embrace innovation, but the tone of science back then was different: innovation was not necessarily considered a good thing. At the turn of the 20" century, scientists were on a mission to tidy things up. Lord Kelvin announced in 1890 that mankind had discovered everything there was to know and the role of future scientists was simply to catalogue and observe the consequences of these laws, and to improve the accuracy of measurement. The last thing scientists wanted was a completely new set of numbers that behaved in strange ways. Cantor was upsetting the apple cart, but he was in good company. Just a few miles away in Berlin, a young Albert Einstein was beginning to study physics in his spare time. Those studies would culminate in his four papers of 1905, two on Quantum Mechanics and two on Relativity, ushering in the modern age of physics. How to Count To understand infinity you need to count in a particular way. You’re probably used to counting with numbers. You count apples: one, two, three, and say, “I have three apples.” You can do the same with oranges. If you have three apples and three oranges, the totals are the same and you can declare you have the same number of fruits. This is the first way to count. HOUSE_OVERSIGHT_015870

00 181 But there is a second way of counting. Take your apples and put each next to an orange. If they match up, you can easily see they are equal in number. “Look,” I say, “I have the same number of apples as oranges.” This method is more primitive and does not require the concept of numbers, but it is very useful. If ’m a shepherd I can hold a set of counters in a bag, one for each sheep. To ensure all my flock are gathered in for the night I drop one counter into the bag as each sheep enters the enclosure. I don't need to give the counters number names. The Munduruku tribe, from the Amazon rainforest, have no concept of number names beyond five. Their counting system simply goes one, two, three, four, five, many. Yet this second way of counting allows them to function successfully, deciding whether two groups of things have the same number of elements, even if there are more than five of them. For example, if they need to determine if they have enough spears for a hunt, each person simply stands next to their spear. If everyone has one, they're ready. If not, then the empty handed Munduruku simply make one. No need for pesky numbers or mathematics lessons. This second way of counting is particularly useful when tackling infinity because we are not sure what infinity is. Treating it the same way the Munduruku treat the number ‘many’ is the safest thing to do. The first question we would like to answer is whether all infinite things are the same. iil i Spears and Hunters HOUSE_OVERSIGHT_015871

182 Are the Androids Dreaming Yet? We know from our childhood that infinity plus one is still infinity. Is there anything we can do to make infinity bigger? Perhaps multiplying infinity by infinity will do the trick. Infinity times infinity can be visualized as a square with edges of infinite length. We can show that this square is the same size as a one- dimensional infinity through a clever trick — the zigzag method. Mark the infinity square into a grid. Start in the corner square, go across, diagonally down, then across, diagonally up, and so on. I'll draw you a picture. We visit every square in our grid using a single line. We can then lay down our infinite zigzag line next to the infinite line of one of the edges. The lines are the same length as they are both infinitely long! So infinity, times infinity, can be matched to infinity, they are the same. Cantor thought this a very strange result and wrote to a fellow mathematician, Dedekind, “Je le vois, mais je ne le crois pas!”, “I see it, but I don't believe it!” If you are struggling with this, don’t worry. We just jumped forward to quite a complex concept. Let’s take it more slowly. One way to get a better grip on infinity is through the stories of David Hilbert and the Infinity Hotel. Infinity for Dummies Hilbert’s Hotel is a mythical building with an infinite number of rooms. Other than this strange feature it is a regular hotel complete with minibar, dodgy TV, and slightly mad manager. The rooms are numbered sequential starting at one, then two, three, four, and so on. The hotel allows you to play a series of mathematical games to see how infinity behaves. Are there the same number of minibars as there are rooms? That's easy. I said every room has a minibar. We can use the matching technique to match minibars with rooms. Go to the first room. There is a number on the door and a minibar inside. The same goes for room 2 and 3 and this goes on forever. I’ve just proven two infinite things are the same - rooms and bars, but I still have not shown you why the zigzag line is the same length as the edge line. When you first explain infinity to a child they immediately ask “What's infinity plus one.” A particularly smart kid I met, Dermot, asked, “What's infinity plus three?” Hilbert’s Hotel allows us to answer this problem in a way we can visualize. HOUSE_OVERSIGHT_015872

vhylbyyy | | tt tt VAVAVAVA A MY YI | i tt tt tt tt tT Traversing an Infinite Plane with a Line The infinite hotel is full. A man comes to the front desk and asks for a room. The hotel manager says, “I’m terribly sorry, but we are full... But I may be able to help you. Let me think” He ponders for a moment and then says, “OK - I’ve found you a room? He calls the people in room 1 and asks them to move into room 2. He calls the people in room 2 and explains that due to a double booking they must move out of their room to let the people from room | in. But it’s OK; they can move into room 3. Everyone moves up a room and the new guest gets the checks into the now vacant room I. This is a little harder to understand. We did not have a perfect one- to-one match as with the rooms and mini-bars. We had a mismatch of guests to rooms. But, we were able to show it is possible to re-establish a one-to-one match by doing something to every guest, having them move up a room. There is no problem with the last guest because it is an infinite hotel, there is no last guest! Another way to visualize the problem is to ask ever hunter to pass their spear to the right in the picture below. HOUSE_OVERSIGHT_015873

184 Are the Androids Dreaming Yet? Hunter with Spears Provided there are an infinite number of hunters there is always someone to hand the spear to and the person at the front of the line now has space for another spear. You can probably see how to answer Dermot’s question. The hotel manager calls the guest in the first room and asks him to move 3 rooms up rather than one. He then calls the remaining guests and tells them the same thing. Thus, he has managed to fit three more people into the infinite hotel. Infinity plus 3 is infinity. You may worry that it takes the manager an infinite time to call all the rooms, but it’s OK; he lives infinitely long so it all works out. What about fitting an infinite number of new guests into the already full hotel? Surely then we will get stuck. No, Hilbert’s Hotel can fit an infinite number of extra guests. Here’s the trick: ask all the people currently in the hotel to move to the room with double the number they are currently in — 1 goes to 2, 2 goes to 4, 3 goes to 6, and so on. Now all the odd numbers are empty and you can fit an infinite number of people into the empty odd rooms. Infinity plus infinity is infinity. Voila. HOUSE_OVERSIGHT_015874