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Posts Tagged ‘logic’

GEB: Class Begins Today

January 17th, 2012 No comments

Here’s something I didn’t see coming. Remember the MIT Open Courseware class on Gödel, Escher, Bach I discovered and wrote about a month ago? Well, that day I submitted it to /r/cogsci on Reddit to bring it to the attention of some people I thought might appreciate it. I expected it to generate little interest, since it wasn’t formal cognitive science narrowly construed, such as a link to an article about cogsci research. Well, I was wrong.

That link became one of the most upvoted submissions to /r/cogsci in recent memory, and generated tremendous interest. Someone cross-posted to /r/philosophy. Around this time I submitted it to Wubel, where it became the featured submission for a few weeks. Then a redditor announced he was going to lead an online scheduled reading of the book with anyone who was interested. His home for this reading, /r/geb, mushroomed from 4 members to over 2700. Big class!

It looks like I launched a kind of online GEB movement. Quite a response to nothing more than free course materials for a beautiful but very intellectually challenging book! I’m happy to see it. Class starts today.

Lessons of Gödel, Escher, Bach

December 21st, 2011 2 comments

How cool is this. MIT Open Courseware offers a class called Gödel, Escher, Bach: A Mental Space Odyssey. It is an entire course geared around Douglas Hofstadter’s book Gödel, Escher, Bach.

This is one of the greatest books I’ve ever read; it’s a true masterpiece. I first encountered it in high school. Ostensibly it’s a gorgeous web interconnecting art, mathematics and music, but that’s actually instrumental to the book’s true purpose. Quoth Wikipedia:

Hofstadter has emphasized that GEB is not about mathematics, art, and music but rather about how cognition and thinking emerge from well-hidden neurological mechanisms.

And now MIT offers a free class geared around this book, using it as a kind of textbook, bracketed with a syllabus and class notes in PDF. All this for free. Wow. Props to the instructors, Justin Curry and Curran Kelleher, and to MIT for providing this to the world gratis.

Quasicrystals Are Chaotic

September 12th, 2009 No comments

Thus I do declare. Why?

A quasicrystal.

A quasicrystal. These things were first created in a lab in 1984.

First, a quasicrystal is something that…

  • is orderly; it exhibits perfect translational symmetry (i.e. it can be divided by straight lines into a sequence of identical figures).
  • is aperiodic (i.e. not defined by a unit cell that repeats itself over and over) and is therefore irregular. Which is why it is radically different from ordinary crystal.
  • is produced by crystallization, which is very sensitive to initial conditions (i.e., it can grow in wildly different ways with only tiny changes in how it starts).

And something is a chaotic system if it…

  • is orderly; not random, but it looks random.
  • is aperiodic.
  • has sensitive dependence on initial conditions.

So there you go. And apparently, I’m not alone in thinking so either.

Dreamspace

January 15th, 2009 No comments

Of late I’ve been thinking of dreams. For me it’s at least a mental space of internal perception where anything is possible (and certainly much more). Dream is as close as you can get to pure creativity. It’s a wonder that we get to do this at all, and how peculiar it happens only while we sleep. It suggests something very interesting is happening while we’re out.

credit: unknown

In a dream, one has godlike powers. Not just of creativity or absolute control, but also the ability to pass right through the absolute boundary separating the possible from pure impossibility. And without even slowing down, like a neutrino through a stone wall. Once I dreamed that I was still living in an apartment I used to have in St. Louis. Yet at the same time it was my bedroom in the house where I grew up. It was not confused. It really was both, simultaneously, and I existed in both places, and they were a unity, and I was both myself as an adult and as a teenager. It was a clear violation of the principle of non-contradiction, yet there it was. It worked. When I woke up and remembered the dream, I was astonished.

Dreamspace is introspective, even when it is just the world recapitulated, because it is your world, no one else’s. Some dreams seem to carry such intensity and profundity, such an overload of meaning, that it’s as if you have accessed transcendent substance in some sense, that your mental fabric is, only briefly, of material too subtle and fine to be of this world. And yet, there you are. You haven’t left the natural world, but you’ve accessed some wellspring of meaning and symbol and even ritual deep within yourself. I’m completely dissatisfied with the two English words I know of to describe this experience: spiritual, religious. I think it is hypernatural, not supernatural. To be connected to the natural world–the cosmos, the totality of all being–not just rationally, but entirely. To be this way isn’t to go beyond the world; it is to be utterly of the world, and not off somewhere else.

What do dreams mean? I’ve stopped asking why. Why-questions are semantically vapid in dreamspace. It’s like asking why a tree. It need be nothing other than purposeless beauty, unharnessed to a causal story. On the other hand, maybe it’s part of being consciously aware.

Sometimes the dreams are lucid. This is a very special experience. I am aware that what I experience is not the waking world of objects–things thrown in my way–but a world of unitary subject–me and other things within myself, in a way. Though I am aware, the me-world is not consciously constructed. If it were, I would understand the mechanics, and I don’t. I do see that it’s a kind of reciprocity between my conscious cognizance of the dream experience and some subconscious process within me generating that-which-is-cognizable. There’s the me acting in the movie and the invisible me directing it. In lucid dreams, one is actor/director, though the relation is inverted: the actor commands the director. Somehow this presentation of dreamspace has exceptional vivacity, and rather than seeming somehow abstract or sensually attenuated, the experience is just as strong as anything I perceive while awake. These dreams are rare and never last long as I’d like. Once I realize what’s going on, I get excited, and then wake up.

I’m curious why evolution equipped us with this counterintuitive capability. Or does it have survival value? All the explanations I’ve read seem to me to be just-so stories, made up, as if with a shrug, starting with “I don’t know, maybe it’s because…” Dreamspace begs for scientific and introspective exploration.

Least is Most

January 6th, 2009 No comments

I encountered something interesting this morning. But first, a little background. In the pursuit of my philosophy degree I took an introductory logic class. In it we examined and worked with deductive logic, such as this:

If someone has a Y chromosome, he is a man.

Aristotle has a Y chromosome.

Therefore, Aristotle is a man.

This form of logic is called modus ponens, “mode that affirms by affirming.” It’s the simplest kind of syllogistic reasoning you can have. Intuitive, really.

Now, compare that with a Taoist “syllogism” I encountered this morning, of similar form:

More than enough is too much.

Too much is less.

Therefore, least is most.

Looks something like modus ponens, doesn’t it? Hardly workable, though, in the logical tradition I was taught. There is no tool of formal logic I’m aware of that can generate that conclusion from those premises.

Yet the wisdom of this poem-syllogism isn’t really that hard to unpack. Having too much of something is worse than having just enough of it, of course. Otherwise, it wouldn’t be too much! And having the worse of two things is to have the lesser of the two. So the advice here is to go with the least you need–that is, enough–and that way you get the most benefit (let’s say).

For example, think of food. If you have too much, it may spoil before you eat it or make you fat if you do. Keeping it to what you really need is optimal.

So I began to wonder. Could one develop a system of formal logic that would permit expression of such logical structures? The logical “confusion” stems from the poetically essential ambiguity of what is being described as “more,” “enough,” “least,” and so on. That’s where modus ponens fails. So I wonder a logic that can work with such ambiguity would look like. It would be much less of a straightjacket.

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