### a failure of vision.

To the average tyro, it is a simple matter to devise philosophical questions which are unanswerable. "Can god create a rock so large that he can't pick it up" comes to mind. I don't believe such a question is even worth answering, becuse there are so many failures of descriptive language contained in it that it is as close to a nonsense statement as you can assemble. Within this, I find myself wondering about translation and translatability, and I am reminded of the old saw about the Eskimo language having such-and-such many words for the concept of "snow", and that the English language fails when trying to understand the Eskimo mind for snow.

But I don't buy that anymore

I have also taken to pondering some of the concepts around infentesimals and infinites. The ancient Greek and Arabic philosophers had no concept of the mathematics of the calculus, which is based upon some very interesting applications of the concept of infinites and infintesimals. For instance, Zeno's paradox (the impossibility of motion) relies on a complete failure to understand limits and infintesimals. Zeno's paradox is just an ordinary equation to the likes of Leibniz. In the course of reading Popper last night, totally unrelated to the text at hand but also discussing the ideas of sets and infinite sets, I was imagining two circles (see drawing). The first (inner) circle is of arbitrary diameter, say 1. The next circle is infintesimally larger, say 1.0...1. The two circles touch at one side, and therefore are infintesimally apart at the other side (0.0...1). But btween the two circles, going around from the far side to the near side, are a series of infintesimally smaller distances. My question is not how one can compare the relative size of two infintesimally small numbers, for instance, to prove that say, the distance between the two at 30 degrees is smaller than at 120 degrees from where they touch. I know (analytically) that it can be proven (even if by gedankenexperiment), even through there is no empirical difference between the two infintesimals A real picture of the scenario I described would look like a single circle at any level of magnification. My concern is of the failure of the vast majority of well-educated individuals to understand concepts such as infintesimals and other unexperiencable entities. Further, they will often offer mathematical conveniences (such as imaginary numbers such as √-1, also know as

For the creation of an imaginary or unobservable entity to be useful in a theory, the consequence of usage of an imaginary or unobservable entity (such as the use of imaginary values for magnetic spin in quantum mechanics) must forbid the existence of certain results in real 'observation'. The failure to observe potential falsifiers over time increases the practical utility of a theory. Popper (building on the work of others) envisions a continuum between tautology and paradox, where a theory can be neither, but lies somewhere between the two. He argues that the most useful theories lie closest to paradox, because the most easily disproved theory, which despite that, holds up to experimental test, is the most useful. Any statement which cannot be disproved (tautology/ metaphysical statement) is not useful because it is not informative, it does not separate or differentiate between what is possible and what is unlikely.

My problem with popularization of things such as Quantum Mechanics lies in the difference between random bullshitting and actual use of the theory. QM is highly useful both as a tool of philosophy and science, but because it is difficult, it is too easy to bullshit over failures to understand given parts of the theory. Complexity is not an excuse to get lazy, but a challenge to be more rigorous. I frequently have to remind myself of this. Just because alternate universes or infinite realities are possible, doesn't make them useful. If there is use in discussing the existence of parallel universes, there must exist a theory to explain why that universe allows, or more importantly, forbids certain realities in this universe. If it is as tautological as "a million monkeys on a million typewriters", the speculation has gotten us no closer to the original Klingon.

But I don't buy that anymore

**( Collapse )**I have also taken to pondering some of the concepts around infentesimals and infinites. The ancient Greek and Arabic philosophers had no concept of the mathematics of the calculus, which is based upon some very interesting applications of the concept of infinites and infintesimals. For instance, Zeno's paradox (the impossibility of motion) relies on a complete failure to understand limits and infintesimals. Zeno's paradox is just an ordinary equation to the likes of Leibniz. In the course of reading Popper last night, totally unrelated to the text at hand but also discussing the ideas of sets and infinite sets, I was imagining two circles (see drawing). The first (inner) circle is of arbitrary diameter, say 1. The next circle is infintesimally larger, say 1.0...1. The two circles touch at one side, and therefore are infintesimally apart at the other side (0.0...1). But btween the two circles, going around from the far side to the near side, are a series of infintesimally smaller distances. My question is not how one can compare the relative size of two infintesimally small numbers, for instance, to prove that say, the distance between the two at 30 degrees is smaller than at 120 degrees from where they touch. I know (analytically) that it can be proven (even if by gedankenexperiment), even through there is no empirical difference between the two infintesimals A real picture of the scenario I described would look like a single circle at any level of magnification. My concern is of the failure of the vast majority of well-educated individuals to understand concepts such as infintesimals and other unexperiencable entities. Further, they will often offer mathematical conveniences (such as imaginary numbers such as √-1, also know as

*i*) as proof or evidence of parallel universes or infinite realities. This is sloppy thinking.For the creation of an imaginary or unobservable entity to be useful in a theory, the consequence of usage of an imaginary or unobservable entity (such as the use of imaginary values for magnetic spin in quantum mechanics) must forbid the existence of certain results in real 'observation'. The failure to observe potential falsifiers over time increases the practical utility of a theory. Popper (building on the work of others) envisions a continuum between tautology and paradox, where a theory can be neither, but lies somewhere between the two. He argues that the most useful theories lie closest to paradox, because the most easily disproved theory, which despite that, holds up to experimental test, is the most useful. Any statement which cannot be disproved (tautology/ metaphysical statement) is not useful because it is not informative, it does not separate or differentiate between what is possible and what is unlikely.

My problem with popularization of things such as Quantum Mechanics lies in the difference between random bullshitting and actual use of the theory. QM is highly useful both as a tool of philosophy and science, but because it is difficult, it is too easy to bullshit over failures to understand given parts of the theory. Complexity is not an excuse to get lazy, but a challenge to be more rigorous. I frequently have to remind myself of this. Just because alternate universes or infinite realities are possible, doesn't make them useful. If there is use in discussing the existence of parallel universes, there must exist a theory to explain why that universe allows, or more importantly, forbids certain realities in this universe. If it is as tautological as "a million monkeys on a million typewriters", the speculation has gotten us no closer to the original Klingon.