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Tag Archives: Leopold Kronecker

Yes, this is a math post, but don’t run off too quickly. I’ll keep it as simple as possible (but no simpler), and I’ll do all the actual math so you can just ride along and watch. What I’m about here is laying the groundwork to explain a fun fact about the Mandelbrot.

This post is kind of an origin story. It seeks to explain why something rather mind-bending — the so-called *“imaginary numbers”* — are actually vital members of the mathematical family despite being based on what seems an impossibility.

The truth is, math would be a bit stuck without them.

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17 Comments | tags: complex numbers, complex plane, fun with numbers, imaginary unit, integers, Leopold Kronecker, natural numbers, numbers, rational numbers, real numbers | posted in Math

Oh, no! Not *math* again!

Among those who try to imagine alien first contact, many believe that mathematics will be the basis of initial communication. This is based on the perceived *universality* and *inevitability* of mathematics. They see math as so fundamental any intelligence must not only discover it, but must discover the same things we’ve discovered.

There is even a belief that math is more real than the physical universe, that it may be the actual basis of reality. The other end of that spectrum is a belief that mathematics is an invented game of symbol manipulation with no deep meaning.

So today: the idea that math is *universal* and *inevitable*.

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41 Comments | tags: alien math, cardinal numbers, cardinality, counting, counting numbers, first contact, Leopold Kronecker, math origins, math theory, mathematics, natural numbers, numbers, Philosophy of Math, rational numbers, real numbers, Theory of Mathematics | posted in Math, Opinion

One of the things I mentioned in my recent *Material Disbelief* post was that, if you accept everything physics has discovered in the last 100 years or so — and if you believe in philosophical materialism — you are faced with the very strong possibility that all of reality is some sort of simulation or machine process.

Not only does all the evidence, as well as some basic logic, seem to point in that direction, but as a model of reality it provides easy answers to many of the conundrums of modern physics (e.g. Einstein’s “spooky action at a distance” and some basic questions regarding the Big Bang).

Today I want to lay out the details of the arguments for this.

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28 Comments | tags: Albert Einstein, Bell's Theorem, DisneyQuest, DNA, EPR paper, Leopold Kronecker, materialism, metaphysics, Philosophical materialism, physicalism, reality, simulations, virtual reality, Zeno's paradoxes | posted in Physics

We’re still motoring through numeric waters, but hang in there; the shore is just ahead. This is the last math theory post… for now. I do have one more up my sleeve, but that one is more of an overly long (and very technical) comment in reply to a post I read years ago. If I do write that one, it’ll be mainly to record the effort of trying to figure out the right answer.

This post picks up where I left off last time and talks more about the difference between numeric *values* and how we *represent* those values. Some of the groundwork for this discussion I’ve already written about in the L26 post and its followup L27 Details post. I’ll skip fairly lightly over that ground here.

Essentially, this post is about how we “spell” numbers.

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1 Comment | tags: base 10, base 2, base 8, Frederik Pohl, Heechee, irrational numbers, Leopold Kronecker, natural numbers, number bases, number names, numbers, pi, prime numbers, rational numbers | posted in Math, Sideband