I'm reading Douglas Hofstadter's Gödel, Escher, Bach right now and it's probably one of the best books I've ever read. It lays down the true foundations of Mathematics and introduces you to formal systems in a really accessible and insanely interesting way. The whole book is an argument on how to explain human consciousness using the idea of a "Strange Loop," which is a fundamental concept in Mathematics (and is beautifully reflected in Escher's and Bach's work).

I created this account shortly after a psychotic break. It's still close to my heart. I try to keep these thoughts in quarantine, because they are difficult to express coherently. BUT SINCE YOU ASKED:

Emptiness, vacuum, the Void, not-self, ego death, Zero, O, 0, circularity, contradiction, falsehood, true paradox, null. Striving to be something disconnected from my subjectivity, while knowing that my experience cannot be anything other than subjective. The clearness achieved by meditation. Living in the present without fear of the future nor regret of the past. Return code 0 indicates success. The wheel is the root, superuser, all-powerful within one system. Wheel of the dharma, spinning, eternal. Root of the Tree of Life, Sephirot. Infinite loops correspond to contradiction.

Infinite stairs are UNACCEPTABLE.

Contradiction powers computation; computation powers the mind but not the soul. We cannot think without contradiction, but we cannot be conscious with only thinking.

Followers of Boolean Logic are taught wrong, Truth is beyond comprehension to those without a four-valued logic encompassing paradox and the void.

Is this thing true? Is it false? Both? Neither?

Sense and nonsense. A paradox can make sense, but eludes capture by binary truth. A nonsensical statement has no reference, can be neither true nor false, but it may still reflect Truth.

The ineffable is located in the Mind of God, truths unknowable. Gödel taught us.

Very interesting, TAA. I wonder if you have read Gödel, Escher, Bach, by Douglas Hofstadter. In particular, I am thinking about a section where he discusses the emergence of a mind in an ant colony where the ants work as social units similar to neurons. If you haven't read GEB, I highly suggest it. Hofstadter has laid a lot of groundwork in this area of intelligence as an phenomenon that emerges from parts lesser than (and arguably independent from) the whole.

But, that leads to a question I have. IMO intelligence is in the eye of the beholder, and from a certain perspective, we could say that a Global Brain already exists. I wonder what measures you might use for calculating the evolution (or emergence) of a GB, and in what framework does the Global Intelligence operate? Also, to what extent will the GB depend upon our higher intelligence, and to what extent will it exist independently of us?

Also, you mention that we might be able to predict the evolution of the GB. Does this include a singularity scenario?

Finally, I'm not sure I agree that only crystals exhibit non-living, non-random behavior. I think by that measure you could say that all objects exhibit non-random behavior in their gravitational interactions. You could probably extend that to the atomic forces, quantum systems, rivers, etc. There are lots of non-living processes where entropy is reduced within the observed system, but increased overall.

> I am interested to know why you believe that the arrow of time is superstition.

There is telltale evidence in both Number and Quantum Mechanics. The necessary work regarding latter has already been done, but most physicists reject the thought out of hand because of the said superstition. Surely, information flows from both past and future and the fact of wave function collapse is witness to it. Even when some, such as Roger Penrose, do consider it, they are circumspect for obvious reasons.

At some point, God Willing, the task of an elaboration of the nature of the former may be accomplished, or at least a measure of progress made, should yours truly become sufficiently motivated. For now consider (the fanciful notion that) the patterns of standing waves of the bounded electron are faithfully represented by "mere" Natural numbers. And would it interest you to know that the phenomena of the incidence, too, can be shown in what is to date asserted as the "chaotic" and "mysterious" Prime Numbers?

While I maintain my own personal confidence in the veracity of this matter -- based on above and certain experiences -- it would surprise me should an attempt at conveying inner perception, regardless of heroic effort to touch the asymptote that forever bars one from communicating in full, would suffice to convince you and cause you to abandon your firm faith in the construct. Certainly, if global the construct rents itself asunder in places to maintain the facade of completion -- here I refer to the singularities -- then what chance do I, a mere mortal, have to succeed in rendering the matter in full in objective form?

   I don't see any reason why we should have less confidence
   in this kind of perception, i.e., in mathematical intuition,
   than in the sense perception, which induces us to build up
   physical theories and to expect that future sense perceptions
   will agree with them, and, moreover, to believe that a 
   question not decidable now has meaning and may be decided
   in the future.  The set-theoretical paradoxes are hardly any
   more troublesome for mathematicians than deceptions of the 
   senses are for the physicist. […] Evidently the "given" 
   underlying mathematics is closely related to the abstract
   elements contained in our empirical ideas.  It by no means
   follows, however, that the data of this second kind, because
   they can not be associated with actions of certain things 
   upon our sense organs, are something subjective, as Kant
   asserted.  Rather, they, too, may represent an aspect of 
   objective reality, but as opposed to the sensations, their
   presence in us may be due to another kind of relationship
   between ourselves and reality.  

   [Kurt Gödel, What is Cantor's Continuum Problem?]


        How the world is, is completely indifferent for what 
        is higher. 

        God does not reveal himself in the world.	

        ...

   Whereof one cannot speak, thereof one must be silent.

   [Ludwig Wittgenstein - Tractatus Logico-Philosophicus]

I worked in a hardware store in Cambridge MA, partied very hard, and enrolled at the Harvard Extension School, taking a classes on James Joyce, Playwriting, Chemistry, and Neurobiology. I don't think I completed the last two. I walked out of my Neurobiology lab final because I was about as prepared for it as you likely are at this moment.

I finished up the hiatus with a road trip across the US on which I read Broca's Brain and Gödel, Escher, Bach. The time was transformative for me. It wasn't until some time after I re-enrolled that I started making what I consider to be progress, but without that break, I wouldn't be where I am at today.

I think the important thing for me, was that I knew all along that it was a temporary detour, and that it wasn't a lifestyle that I wanted to settle into. That was a freeing aspect of it.

I only read his Gödel, Escher, Bach (often referred simply as GEB). His style can be annoying, conjunctions are one of the more apparent traits. [And,] if GEB intrigued you, leaf through but don't buy into the hype: Hofstadter's true accomplishment is inspiring countless people to talk about aspects of GEB with half the vocab and tenth of pretentiousness.

I have started Gödel, Escher, Bach three times now. I've yet to make it all the way though. I hate books that are supposedly fantastic, must-reads but can't hold my attention for more than a few days. It feels like the horribly naggy ex-girlfriend of failure.

what a neuron itself does is calculate whether to pass a signal forward or not. How it does this is, in a very oversimplified way, add up the inputs from the neurons that input into it and, if the sum of those inputs are over a certain threshold, pass the signal on.

As Hofstadter put it (in Gödel, Escher, Bach: An Eternal Golden Braid):

In any case, it is simple addition which rules the lowest level of the mind. To paraphrase Descartes' famous remark, "I think, therefore I sum" (from the Latin Cogito, ergo am).

Totally depends. Gödel, Escher, Bach took me at least a good six months; Zen and the art of Motorcycle Maintenance took a few weeks.

OK don't be mad, but what sort of breakthroughs can still be made in Mathematics for someone to earn a Nobel prize equivalent?

Most people name the Fields Medal as the math-equivalent of a Nobel prize.

In recent history, there was a lot of work figuring out the math required to get string theory to work. There's also a bunch of big unsolved problems in a few different veins of mathematics. A famous one to computer people is P != NP, which would prove the complexity and consequent intractability of many problems. There's stuff related to predicting prime number which always makes cryptography nerds perk their ears up.

In another vein, there's Gödel's incompleteness theorems which say that it is impossible to prove that system of logic underlying all of mathematics is consistent, using that same system of logic. So on the more philosophical end of the spectrum, there are people studying other systems of logic to extend the domain of what is provable and what we know for certain about what we have proven.