On Fri, Feb 28, 2014 at 3:25 PM, Robert Hansen <email@example.com> wrote:
> > > That doesn't make the relationship between computers and mathematics any > less amazing or less beautiful. The way I feel is this... >
You like to express yourself based on "the way I feel" and this has been a topic between us; your tendency to "navel gaze" and use "private language" (which, as you put it, helps you "see in the dark" -- even as it may leave your prose indecipherable and obscure, another one-off).
> Mathematics is abstract. Sure, we can apply it to model natural phenomena, > but its true beauty, and all of its logic and self revealing truth, still > lie in that abstract imaginary land in our heads.
There are other religions, than this one to which you cling.
<belief_system type = "philosophical">
Consider that those forms which actually have physical reality have passed some tests that imaginary stuff does not have to: laws of physics, laws of economy.
One could say that actually extant "stuff" is the higher value, as it has the integrity to actually enter the stage of space and time, whereas anything imaginary, such as a dimensionless point, is in comparison "lame", precisely *because* it's missing the one essential ingredient that makes something most respectable: existence.
Because it's a world of suffering, disease, decay, a lot of the time, we seek refuge in our minds in the imaginary, and posit an eternal existence free of these phenomena. We attempt an escape to the "Platonic realm".
In order to believe an escape is possible, we glorify what's "in our heads" as "more real than real". The Platonists / NeoPlatonists are called "realists" for this reason.
But maybe we should just call them "naively hopeful" and/or "misguided" at best?
> But in one rare instance it actually manifested itself, and its logic, and > its truth and and its beauty in our physical world.
I might say "as" our physical world; not "in". The physical world itself is the actually manifest consequence of a metaphysical "way that it is". Geometry begets Geography. In the beginning was Logos and all that.
We're well inside conventional Western Civ with such thinking, though perhaps with a different terminology.
Terminology does not "hold still" much as we'd like our words to be "heavy stones" of high inertia, in the trajectories *we* set for them -- talking linguistics as ballistics, and mostly missing moving targets (but it's the aim / intention that counts?).
> Mathematics begot the machine. So it's no wonder that after loving math > all through high school, I was smitten the first time I saw the machine. > > Thinking of Charles Babbage.
But before him, a lot of people really believed an automaton could play chess, well enough to beat Napoleon (yes, The Turk).
As one sees from Hollywood movies today, the public imagination tends to be far out ahead of the actual science, with leading lights in their fields sometimes piggy-backing on these public mis-perceptions.
The classic stereotypical case is a billionaire who thinks major life extension technology is mere millions away. Science needs his money, and indeed, what good will it be to him all too soon?
You could say he's a benefactor, a donor, "for the wrong reasons" (he actually believes he might live to reach 200), but if the money is spent wisely (dubious) it could be a shot in the arm for other projects.
> After that though, I wouldn't call much of what I do with the machine that > mathematics made, mathematics. And that includes even the majority of my > deepest dives and thoughts about programming and AI. Only when it > approaches fundamental truths, like the papers you have shown, do I call it > mathematics. And I have done some of that, in college. And I do some of > that in AI. > > Bob Hansen >
Some of us don't conceive of mathematics coming from a place of pure imaginary in-the-head beauty but rather from the loud and dusty marketplace of camel traders and ideas, from everyday commerce and interaction.
Computation comes from the fact that nature is always computing, with molecules, with photons. It's 'computation' that's ongoing, that's the verb in this picture.
So "to compute with a computer" is not to invent some "new thing" but to provide new energy pathways for that which has always relied on computation: the universe, a computer. "Com put" means "to put together" (as in photosynthesis).
You might argue that mathematics is oh so much more than "mere computation", but having defined neither one nor the other, we're in the realm the logical positivists would call "music" (pleasant nonsense, syllables that sound sensical but mislead in that regard).
Is chess a mathematics? It has a notation. It has a goal.
Are all games a kind of mathematics?
Is living and breathing a kind of computation?
These terms have not been nailed down, so the best answer is: no one knows, nor must we expect everyone to converge to some "answer" (such convergence to one terminology is "not in the cards" I'd say).