I used to be convinced that mathematical objects are in some sense real. That numbers have an existence independent of humans knowledge of them. Recently, in a Wittgensteinian turn, I’ve come to the realization that the question “are numbers real” is a bad one.
The heart of the problem is that the question is ambiguous. Math is a set of models that attempt to describe phenomena we observe in reality. Those models are obviously invented. We didn’t discover them carved into a rock somewhere. The phenomena in the world they are describing are obviously discovered. So the answer to the (badly phrased) question is both. “Numbers” are a feature of a model humans invented to describe a physical phenomena. The physical phenomena that numbers model is something humans discovered in the world. The only way we have access to those things is through the intermediary that is our models. But this introduces a new problem.
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Logic, Mathematics, Metaphysics
Time travel has been a trope of Science Fiction since its inception as a genre. Perhaps the most famous is H. G. Wells “The Time Machine,” which gives us brief glimpses of the future at several points. The idea is certainly seductive. Who wouldn’t want to be able to whiz off to the future to view the progress humanity has made, or travel to the past and witness historic events?
But whether or not time travel is possible is still an open debate among physicists. In this post I want to discuss some of the paradoxes that would seem to result if time travel is possible, as well as an interesting algorithm for solving NP problems using a time machine.
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Computer Science, Metaphysics, Musings, Philosophy
At a philosophical discussion last night, we read “Jipi and the Paranoid Chip” by Neal Stephenson (Which, I just noticed, was posted to reddit 9 days ago, and got 1 up vote and 1 down vote. WTF?). If you’ve never read anything by him, I suggest you stop right this moment, go out and buy Cryptonomicon, Snowcrash and the Baroque Cycle, and do nothing until you’ve read them all.
The story is about a piece of software that was evolved to be indistinguishable from a paranoid schizophrenic. In the course of discussing the plot, someone asked if the paranoid schizophrenic chip would pass the Turing Test, with their inclination being no, it couldn’t.
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Computer Science, Metaphysics, Philosophy
Reading this XKCD comic brings to mind something I’ve thought about off and on for a while now. Doing a quick google search brings up nothing on the subject, so here is a small attempt to at least sketch out the domain of a question/answer.
I think that some people don’t accept the (what I believe to be) self evident proposition that reality must be consistent.
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Metaphysics, Musings