...

.. to desire a thing so much that one is paralyzed by the very possibility of it being unattainable...

Silly details about numbers

The ancient Greeks found numbers fascinating in an unprecedented way (or so Morris Kline's Mathematics for the Nonmathematician informs me). Rather than adopting the more practical attitude of the Egyptians and Mesopotamians toward numbers, the Greeks recognized a conceptual beauty in the ability use the self-same methods on any possible collection of objects. That is to say, abstraction, and the universality thereof.

To assign a single, unique label to every quantity, and then to perform mental operations upon them which, amazingly, correctly modeled comparable situations in reality--astonishing. And I do mean that without irony.

Take a pie or any appropriately divisible object. Cut it into halves, then cut each half into thirds. We take it for granted today that the answer may be computed easily through a mechanical procedure: (1 * 1/2) * 1/3 = 1/6. This is to say that, without having made any cuts or further measurements, we already know with certainty what size the smaller pieces will be! (Or the size that they will approximate, because it is not an ideal world.)

But this is a fantastic discovery, for by beginning from only a few known facts, we discover what must be the case for physical objects after manipulating them--all without having left our armchairs.

Another Note Regarding Content

I've realized I still want to keep this blog alive, or at least in a feeble state of existence that approximates life. Unfortunately, for whatever reason, I don't have the interest or motivation to write out posts with the thought and research I'd originally planned. In fact, at this time (judging from my last post), I can't even assemble together posts that reach a definitive point backed by argument, or that are structured in a coherent manner.

But hey, then, why not just go with that? Basically, I am now relaxing the standards for my posts (wait, what? I had standards before?). Until further notice, Doubt Rests shall be a repository for half-formed thoughts, quotes, or whatever vaguely interesting factoids I come across. Don't expect explanation or justification for everything I write (although if you ask nicely I might elaborate), and certainly don't expect fully developed ideas. The contents will likely be of a more personal nature than previously. All will be fragmentary, but fragments put forth in the hope that failed attempts to progress are better than none at all.

And maybe someone, somewhere, some time might find a fragment here which fits well into his/her own thoughts.

Fallibility

Quantum mechanics tells us that the universe operates in very, very unusual ways. It is natural to want to dismiss some of the interpretations of QM (such as that natural laws are inherently probabilistic) as problems with our understanding, not as genuine features of reality. This is essentially a knee-jerk reaction to the oddness of QM and how it does not "mesh" with our everyday understanding of the world. However, science also informs us that we are the products of many years of evolution--and this evolution process equipped us to deal with one thing, and one thing only: survival. Our senses and reasoning faculties were not "designed" to help us humans apprehend truths about the world; rather, they were selected to enable humans qua systems to manipulate information in such a way that the systems preserve and replicate themselves. Luckily, knowing the truth--or approximating it--proved beneficial to the survival of these systems (these information processing patterns).

In simpler terms, more proto-humans who were able to correctly judge that there really is a savage tiger hiding in the grass over there successfully passed on their genes than those who hallucinated constantly. Or than those who had no knowledge whatsoever, who were not able to act on their knowledge, who had faulty reasoning processes, whatever.

Thus evolution tells us.

Unfortunately, to say "there really is a tiger over there" and leave it at that drastically oversimplifies the state of human existence. Because really, we don't know that there is or is not a tiger over there. All we know is that some collection of sights, sounds, scents, or inferences has caused us to believe that something over there can cause damage to us if we do not act accordingly. (Assume it's a hungry tiger and that we are defenseless in a savanna.) We may think to ourselves "There is a tiger," and we may believe "There is a tiger," and there is probably even a sense in which it is true that there is a tiger. But what we call a tiger is a convenient abstraction--a shorthand tag which bundles together a collection of concepts, memories, and/or feelings. So too, presumably, with our notion of existence--we have a certain understanding of what it means for something "to be" and "to be there." and we predicate this notion upon the abstraction "tiger."

[Edit as of 04-05-2009: I should mention that yes, Kant (and other philosophers) claim that existence is not a predicate. I do recognize that it's a contested notion and I disagree with the mainstream opinion; but I shan't defend it now.]

"Well, what of it?" I hear you say. "You're not telling us anything that the pioneering philosophers of the 17th-18th century didn't when they first speculated about our psychological workings; and you're barely even consistent with today's psychological theories."

Fair enough. But, if we can suppose that the tenets of natural selection are true, then we should firmly keep in mind that our knowledge...

....Something...

This post is dissolving into incoherency. And as usual I don't have the patience to fix it. I shouldn't even post it. But whatever.

Fancy

[Please forgive this amateur flight of fanciful, mystical indulgence. This comes from a diary entry I wrote over the summer. I decided I needed to post it somewhere. I can't say I believe these sentiments, but I have sometimes taken comfort in them.]

Maybe I am starting to feel... that somewhere, somehow, in a realm outside of conceivability, our essences intermingle. And our essences love each other, they love each other so much that it almost tears them apart, yet simultaneously unites them all the more gloriously for it. Our essences love and understand why all this tragedy is necessary, why the struggle is necessary for growth, why all is truly joy and not sorrow. Our beings love each other because they created each other, because they dreamed themselves into being, and they chose each other out of all the other possible existences because this way was right. We love each other eternally, devoutly, devotedly, passionately, irrepressibly.

We love each other and are each other. We love each other because we are each other--because of that sympathetic resonance from one core to another--a unification in rhythm that reveals our inherent, underlying unity. Our oneness.

... You and I are one, just as everything else is one. Yet somehow you are special, and I am special, and our love is special.

So we play this game--because it is the unmasking, the revealing, the unraveling, the development, the exploration, the uncertainty, the discovery--these things give us more meaning than jumping straight toward the answer.

Because It's So True

A quote from www.friesian.com:

In the Twentieth Century, philosophy was like a confused and clumsy person who repeatedly tries to commit suicide, but keeps failing, though with the addition of debilitating damage at each attempt.

Mrrem

Yeah, so this blog is suffering from a definite lack of attention.

I don't have any particularly meaningful, worked-out content to post now, so I'll just mention some of the things I've been thinking about lately.

I recently started learning about Alonzo Church's lambda calculus (via Penrose's The Emperor's New Mind), and I'm very impressed. It's so cool that logicians were able to construct systems like this (and like Turing's work) before the advent of computers – indeed, these logical systems led directly to and facilitated the advent of computers. They start from such simplicity, but possess incredible power.

The lambda calculus reminds me of the programming language LISP (unsurprisingly, of course, since LISP was based on this very calculus), and reading about it makes me want to get back into programming again. I dabbled with Haskell a bit at the start of this summer, and I found it oddly fascinating. There is something quite elegant about these functional* languages that more practical languages (C/C++, Python, Perl) don't quite capture.

* Apparently only certain variants of LISP (like Scheme) are fully functional, but anyway.


Still, it is difficult for me to remain interested in these things for their own sake. I think I would need some kind of projects to work toward if I were to take up programming again seriously. Ah, motivation, that state which so often eludes me...

There are so many things I would love to learn, but somehow actually sitting down and doing the work required bores me terribly. Sometimes it doesn't; sometimes I go through brief periods where I feel a great deal of enthusiasm toward some subject (say, Wittgenstein's Tractatus, or some aspect of symbolic logic), but then I end up dropping it again, feeling utterly bored with it for months.

I would like to have a very extensive knowledge of mathematics, physics, philosophy, logic, computer science, linguistics, music, and (select aspects of) history. It would be swell to know Greek, Latin, German, and French. It is so difficult to care about, though; sometimes my mind just seems to shut off, and whatever I'm currently trying to study becomes excruciatingly dull; suddenly I can't remember why I wanted to learn about it in the first place. I value knowledge generally, but to actually feel something for it, to care – somehow that is different from merely saying "I value it"?