Epstein Secrets

more complex than they first appear. They are infinite, yet there are different infinities, and they have meaning. The smallpox example above and the Turing numbers we will discover shortly suggest numbers do have meaning independent of culture and language. The next two chapters will show us what happens

away their secrets. The Enigma machine was an elegant compromise between a truly unbreakable code and a simple cipher. Unfortunately for the Germans, Turing was on the side of the Allies. In the 1930s almost all mathematics, accounting, and code-breaking were performed by humans using pencil and paper. I

tubulin molecules can flip between two states, propagating a ripple along the tube wall. The scale is small enough for quantum effects to matter, and Hameroff suggests quantum error correction keeps the ripples from decohering too fast. Because the processing is happening at a molecular level rather than at

is also, interestingly, the protein that unzips the double helix when a cell divides, and so plays a fundamental role in our evolution. Penrose and Hameroff suggest these tubes form the true processing element in our brains. The walls of the tubes are formed of successive alpha and beta tubulin molecules.

in non-computable thought. It is his ‘machines’ we will look at next. Penrose-Hameroff Machines, aka Brains Roger Penrose of Oxford University and Stuart Hameroff of the University of Arizona have proposed a very different way to understand the workings of the brain. They focus on the much smaller scale structu

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

sdom 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 sugges

e 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

. 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 Dream

take c to denote algorithmic information measured on some reference Turing machine, and F(X) to denote what appears on the second tape of a two-tape Turing machine ¢ time-steps after placing X on its first tape. Other more naturalistic computational models are also possible here and are discussed extensi

ssible to make AGI on digital computers. While we suspect this is correct, we must note that it isn’t proven. It might be that — as Penrose [Pen96], Hameroff [Mam87] and others have argued — we need quantum computers or quantum gravity computers to make AGI. However, there is no evidence of this at this st

sists of the wealthiest nodes and links. Figures 3.3 and 3.4 illustrate the existence and flow of attentional focus in OpenCog. On the other hand, in Hameroff’s recent model of the brain [Ham10], the brain’s moving bubble of attention is achieved through dendro-dendritic connections and the emergent dendrit

ake c to denote algorithmic information measured on some reference Turing machine, and F(X) to denote what appears on the second tape of a two-tape Turing machine t time-steps after placing X on its first tape. Other more naturalistic computational models are also possible here and are discussed extens

sts of the wealthiest nodes and links. Figures 3.3 and 3.4 illustrate the existence and flow of attentional focus in OpenCog. On the other hand, in Hameroff's recent model of the brain 'Hamill], the brain's moving bubble of attention is achieved through dendro-dendritic connections and the emergent dendr