A lot of bits have been spilled talking about the singularity, but I very often find myself with the impression that some of the contributors are talking at cross currents. So in this paper, I would like to lay out several conceptions of what the singularity is, starting with something that’s fairly uncontroversial, and progressing towards conceptions that cause some to go apoplectic. I do not wish to defend any one in particular, but rather layout three different conceptions of the event.
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Philosophy
Note: This is based off of a discussion I recently lead titled “Science vs. Bayes.” Portions of this were inspired by Overcoming Bias.
Some believe that science is facing a crisis. I don’t mean those who argue that we are approaching “the end of science.” I mean that some physicists are disturbed that those damn kids believe in kooky, untestable theories like String Theory, which isn’t science. Or that some people believe in the Many Worlds interpretation of quantum mechanics rather than the Copenhagen interpretation. To these scientists, the acid test is falsification: is there some way of making a prediction with the theory that can be demonstrated to be wrong? If it cannot be falsified, it is not a scientific theory.
Others argue in response that while falsification is definitely important to science, it is not the end all, be all of it. Other factors must be taken into account when considering what theory to adopt to explain a given phenomena. Sometimes these people are called Bayesians, named for their use of Bayesian Inference, which depends on using Bayes theorem to calculate the probability of a theory being true given a set of other probabilities.
I’d like to argue here that the supposed differences between Bayesians and Scientists are actually non-existent, and that the Bastian’s are simply making explicit certain actions scientists take in the course of doing science.
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Bayes, Musings, Philosophy, Science
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
Or, You Can’t Know What You Don’t Know You Can’t Know.
This is an interesting result from modal logic that I will try to sketch here. The upshot of the result, depending on which side of a divide you fall into, is either that there are some truths that are logically impossible to know, or that every truth is already known by someone.
The dividing line in this case is whether you are a realist or anti-realist. The realists posit that there is an external reality that has certain definite properties. The anti-realist deny that such an external reality exists (or, in some cases, that we can have access to it). I’ll get more into this distinction after I sketch the proof. If you find logic boring, feel free to skip the proof and scroll to the end for a brief discussion on the implications of this result.
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Logic, 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
The paradox of the heap, also known as the Sorities Paradox (from the Greek word for heap), is a paradox revolving around the problem of vagueness.
In its classical formulation, the paradox is expressed as follows:
One grain of sand is not a heap.
If one grain of sand is not a heap, adding one grain of sand will not make it a heap.
So two grains of sand are not a heap.
So three grains of sand do not make a heap.
…
X grains of sand do not make a heap.
Therefore, 10,000 grains of sand do not make a heap.
The form of this argument boils down to:
X grains of sand are not a heap.
If X grains of sand are not a heap, adding 1 grain of sand will not make it a heap.
(Some arbitrary large number of grains of sand) do not make a heap.
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Computer Science, Evolution, Musings, Philosophy, Vagueness