Sock Theory vs. String Theory: "When Einstein Walked with Gödel - Excursions to the Edge of Thought" by Jim Holt

My contribution to Holt’s Edge of Thoughts in the form of an article too:

An unauthorised and short version of physics.

How did scientists first deduce that the universe had hidden dimensions, dimensions that are curled up so tight we can't see them? Until recently SOCK THEORY was the ruling paradigm. It was thought that Theodor Kaluza and Oscar Klein deduced the existence of at least one additional dimension from well known tendency of socks to disappear and then re-appear in unlikely places. How else to explain the mysterious behaviour of hosiery? Latterly a new paradigm, STRING THEORY, has superseded sock theory. Leave a length of string or anything long, thin and flexible lying undisturbed for even a day and you will find it has somehow got itself tied into knots. This can only be explained if we assume at least one additional dimension. String theory also gave birth to QUANTUM FIELD THEORY. Richard Feynman found that if you stored several discreet pieces of string in a cupboard for an hour or so they would become inextricably entangled. Feynman realised that given half a chance everything would get ENTANGLED with everything else. String theory also gave rise to superstring theory which in turn morphed into the theory of branes. If you've read this far you're probably a P-BRANE.

Quantum theory is flawed and quantum proponents are in denial. String theory is in crisis (it has recently been described as dangerous nonsense). The Copenhagen interpretation is under attack (by recent experiments - even though this not allowed by Copenhagen). Neutrinos don't actually exist (did your Neutrino lose it's flavour on the bedpost overnight?).

LOOP QUANTUM GRAVITY RULES! Determinism rules OK!

NB (not part of the article above): The references to one of Gödel's Incompleteness theorems in Holt’s first article suggest a slight misunderstanding of the meaning of Godel's work. What Gödel showed was not that the axioms of mathematics must be taken on faith (this insight is much older and relatively harmless) but something more subtle. Gödel showed that in any reasonably powerful mathematics, there must be perfectly legal statements which cannot be proven within the framework of that system, but will require additional axioms to plug the gap. And that this more powerful system will in turn necessarily include legal statements that cannot be demonstrated to be true or false without resort to still more new axioms, and so on... In other words, that no systems of mathematics along the lines of the Principia of Whitehead and Russell can ever be self contained. Yet another way of saying this is that the mathematical backbone of thought is a convention or a construct, not a pure, freestanding Platonic ideal. This was a startling insight, because prior to this discovery it had been assumed by all who are equipped to assume such things (e.g., Hilbert, Russell, etc) that a proof of the completeness of mathematics would be positive, not negative. Mathematicians are Platonists in their souls - it's profoundly disturbing to find out that the universe is not Platonic. Turing's and Church's related insight (the discovery of well-formed problems which no computer program can solve) was even more unsettling and of far greater practical significance. (The strategy of reducing a new problem to the halting problem, and thereby demonstrating it to be unsolvable is routine even for undergraduates, and applies to a universe of problems that come up frequently in practical applications, which undecidability does not.) Godel's theorem is simply the formal-logic manifestation of the same drubbing that Einstein, Plank, Heisenberg, Turing, Darwin, Freud, Wittgenstein, Lyell, et al, gave in other fields to our formerly rather poetical understanding of the nature of knowing.

Gödel's incompleteness proof shows that axioms, formulated in the artificial language of Peano arithmetic (the five Peano's axioms that is), could not be reducible to logic. They required supplementing with other branches of mathematics such as set theory. Effectively that requirements for completeness and consistences in any logical system were violated - hence the need for supplementing logic with other constructs.

The Nature of Consciousness: "Are the Androids Dreaming Yet? - Amazing Brain. Human Communication, Creativity & Free Will" by James Tagg

Disclaimer: I received a reader's copy of this book from NetGalley in exchange for my honest review. All opinions expressed are my own, and no monetary compensation was received for this review.

(The book was published on Jan, 2015; review written 10/05/2015)

“What is the physics that underlies human understanding?”

“Humans need around 10,000 hours of practice to become proficient at a skill. (“The Talent Code” by Daniel Coyle, but referenced by Tagg)

(my own 1991-battered copy of Penrose’s book)

I still remember the feeling I’d when I first read Penrose’s “The Emperor’s New Mind” for the first time in 1991. I’d just finished college. I was full of myself. After reading Penrose I came down to earth in a big way. My education was severely lacking in several “departments”. The impression this book had on me was so great that I still have it at home. I was perusing it after finishing Tagg’s book. 

I hadn’t “touched” Penrose’s book in a long time, but what still remains with me was his take on the nature of consciousness. Chapter 9 (“Real Brains and Model Brains”) to be exact, is full of my annotations. This particular chapter was so mind-boggling that I remember I couldn’t stop thinking about it. After re-reading this chapter in its entirety, and particularly the two main sections of it: “Where is the seat of consciousness?” and “Is there a Role for Quantum Mechanics in Brain Activity?”, and after more than 20 years, some of the assertions made at the time were as bit as polemic then as they are now, but I’m not so flabbergasted by Penrose’s theory of quantum consciousness of the brain as I was at the time. There are some serious flaws in it. 

Quantum theories of consciousness have to deal with the same difficulties as neural or computational theories. Quantum effects have some outstanding properties (e.g., non-determinism and non-locality: “I [ ] argue all human creativity is noncomputational; art, communication, understanding – all are based on non-algorithmic principles.” in Tagg’s words), and it’s only natural to hypothesize that these properties may have something to do with the explanation of cognitive functions, such as random choice, and this hypothesis cannot be ruled out a priori. But when it comes to the explanation of experience, quantum processes are in the same boat as any other. The question of why these processes should give rise to experience is entirely unanswered. No theory I’ve read so far is able to explain this, namely Orch-OR (Orchestrated Objective Reduction by Penrose and Hameroff). 

Even admitting that Quantum Mechanics is somehow at the core of the theme, I still have trouble explaining how does the wave function stays together to go into an afterlife... When dealing with subjects mathematic-oriented, Penrose is always quite solid. Unfortunately when he delves into stuff outside of his field of expertise (like the "quantum nature of consciousness") than one needs to become aware of the less-than-fully-concocted nature of his ideas. Tagg is also a very strong proponent of this view: “Excluding exotic quantum effects, the main difference between computer and human brains is their processing architecture. Brains use slow, asynchronous logic to process information rather than the fast, synchronous type used in modern day computers.”

I’m still very fond of some of Penrose’s nutty ideas (and now Tagg’s). And because they’re nutty one can't automatically dismiss what he says just because the word "quantum" shows up. We still need evidence to corroborate his ideas.

Penrose's assertion that we are not bound by Godel's incompleteness theorems also seems very nutty at best. Tagg as Penrose did before him, bought into the so-called "libertarian free will", though I still haven’t seen any kind of evidence supporting its existence. This has led to claims, such as the assertion that photons registering in vision aren't absorbed by the retina, but unbind in the microtubules in the neurons of the brain… Evidence, that’s what we need! In this respect Orch-OR is still in the realm of pseudoscience. Whether the inner workings of neuronal processes in the brain are enhanced by quantum effects or not, I fail to see how this resolves the free will issue, as it still seems to require some external non-deterministic influence to determine each choice. 

I still haven't read a good argument why the neural networks of the brain are not sufficient to handle it without macro-scale quantum effects. By chapter two of Tagg’s book it was clear that he supported this notion as well, which was not a good omen to start with. Still, I persevered. At the end I felt the book had some interesting titbits, namely the chapters dealing with Computer Science (e.g., “Turing’s Machine”, “The Machine”, “Silver Bullets Can’t Be Fired”, “Hyper-Computing”), the chapter on how to bash Powerpoint (“Power corrupts, Powerpoint corrupts absolutely” – Ed Tufte), and Math (“The Game of Mathematics” dealing with Godel's Incompleteness Theorem and Turing’s undecidable Theorem; Tagg makes a very clear explanation on how Turing proved that Hilbert's Entscheidungsproblem was unsolvable shattering Hilbert's dream in consequence). 

Bottom-line: Stating that quantum vibrations in microtubules have anything to do with consciousness is hocus-pocus. It's interesting as an idea, and it's also worth exploring, and frankly I think it would be very cool if it was true. But extraordinary claims require extraordinary evidence, not just something casually related. Despite my misgivings I’m glad I persevered. Tagg‘s Computer Science book, albeit biased for the role of Quantum Mechanics in our consciousness, made for a very interesting reading.

On a side note, if it’s later proved that quantum theory has any kind of effect on the brain at a cellular or even on a molecular level, I will print out this review and eat it. Promise.