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Friday, September 28, 2012

Testing the limits of your imagination: Part 2

In this post I invite my readers to test the limits of their imagination. As I said in Part 1,
In Part 1 I tried to determine the maximum number of sides that you can visualize a polygon as having. This time, I want you to test something different: imagined motion.

Experiment 1:
Visualize a disc (or a square; whichever proves to be easier). To help you to keep track of the motion, imagine it as half white and half black, or as having black and white stripes or dots. Now imagine the figure rotating about its center, at a relatively slow pace--say about half a rotation per second. After a few seconds, imagine it rotating once per second. Now repeat his process, gradually increasing the number of rotations  per second. I predict that at some point you will no longer be able to "keep track" of the motion. What I would like to know is how many rotations per second you can  visualize before you lose track of the motion.

Experiment 2:
Now, I want you to imagine a system consisting of two discs, one about two to three times as big as the other, with the larger one at the center.  Now visualize the smaller disc orbiting the larger one, much like planet orbiting a star (as the system would be viewed from "above", i.e., not "edge on"). Start by imagining the smaller disc orbiting at one half a revolution per second. As in Experiment 1, gradually increase the number of revolutions per second step by step: How many orbits per second you can  visualize before you lose track of the motion?

Thanks for your cooperation!

Wednesday, September 26, 2012

A past philosopher toasts a potential president

I had a most interesting dream last night (well, not really, but let's pretend). I was at a university I'd never seen before, but somehow I knew where I was going. Walking through the Humanities building, I noticed that some people looked vaguely familiar, though hard to place. Passing one of the doors, which was ajar, I heard the voice of Mitt Romney. It turned out that a professor was playing a clip of Romney's acceptance speech from last night. The professor, apparently trying to explain his views on  one's knowledge of one's own mental states to his students, paused the video and resumed his lecture: "Now imagine yourself saying, 'But I know how bored I am!', and banging your head against your desk to prove it..." Immediately I began to suspect something. I made my way to the lounge, where a party was to be held. The faces of those who were there were mostly glum. The results from last night were clearly not what they had expected; or, at any rate, not what they had  hoped for. I overheard one professor say to another that it looked like he lost his bet with professor Voltaire that this was the best of all possible worlds. I'm still not sure if he was joking or not, but my suspicion was correct: Many of the faculty were great philosophers from the past! At that point I saw someone dressed in a monk's robes stand up and clear his throat. The room became silent, and everyone turned to face him. I don't know how I knew it--again, this was a dream--but it must have been St. Anselm. "I propose a toast to our president elect!", he said. I remember his words vividly:

Obama had his problems, as it is plain to see,
but they pale beside those that face our new president, Romney.
It would not be a slander, if it can be believed, 
to define poor Mitt as he than which none blander can be conceived.
He hasn't got a lot of charm, or personality,
nor has he very much respect for folks like you and me.
He worries little about the poor, who have a "safety net",
and worries less about those whose votes he thought he could not get.
"If only I were Latino", he joked, "I'd be assured to win"
--tragically, Mitt failed to see, he should be liked for being him. 
So let us all drink to his health, and wish him lots of luck;
he'll need it most four years from now, when his only term is up!

At that point everyone in the room laughed and cheered. It turned out to be a good dream after all.

Friday, September 07, 2012

A Brief Sketch of Kant’s Critical Philosophy

Over at Scholardarity I've posted A Brief Sketch of Kant’s Critical Philosophy in Scholardarity Student’s subsection Open Source Study Notes. Here's an excerpt:

Metaphysical knowledge can be either dogmatic or critical. Dogmatic metaphysics seeks to know things as they are in themselves. Critical metaphysics, which Kant calls “Critique”, only gives us knowledge of things as they must appear to us, and hence of the necessary features of all possible experience. Dogmatic metaphysics would have to meet two requirements which are inconsistent in Kant’s system. First, it would have to be synthetic a priori. It could not be analytic a priori, for then it could not give us new knowledge. Neither could it be synthetic a posteriori, for then it could tell us no more than natural science does. Second, it would have to go beyond the bounds of all possible experience; otherwise, it would not be distinct from mathematics and geometry, which, while also synthetic a priori, are limited to possible experience. This limitation is what makes them possible, for as we said above, they are “built into” space and time as forms of our sensibility. Anything which can appear to us must be subject to our forms of sensibility, and so mathematics and geometry must hold of all appearances. But since dogmatic metaphysics is supposed to apply to things which cannot appear to us, we cannot know a priori what they are like, for they are not subject to the only conditions under which experience, and hence synthetic a priori knowledge, is possible. In consequence, metaphysical knowledge of a dogmatic sort is impossible. Now we can see the source of Kant’s distaste for dogmatic metaphysics: It poses questions which it cannot answer.