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Non-Simple Arithmetic
The Intelligent Design folk tell you that complexity requires a designer. The Richard Dawkins crowd tell you that complexity must evolve from simplicity. I claim they’re both wrong, because the natural...
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Jellyfish Math
Is mathematics invented or discovered? In my experience, applied scientists often think of mathematics as a human invention, while actual mathematicians (with a few notable exceptions) feel sure that...
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Real Numbers
Yesterday we started a conversation about whether mathematics is invented or discovered. Today I’ll give you my three best arguments for “discovered”. And to focus the discussion, I’ll talk not about...
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Just the Facts
During our brief intermission last week, commenters chose to revisit the question of whether arithmetic is invented or discovered—a topic we’d discussed here and here. This reminded me that I’ve been...
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Basic Arithmetic: On What There Is
This is an extremely elementary post about numbers. (“Numbers” means the natural numbers 0,1,2 and so forth.) It is a sort of sequel to my three recent posts on basic arithmetic, which are here, here...
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The Grand Design
To understand the universe at the deepest level, we need to know not only how the universe behaves, but why. Why is there something rather than nothing? Why do we exist? Why this particular set of...
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The Mathematical Universe
Some quick words about the mathematical universe, which is the theme of the first chapter of The Big Questions: 1. A “mathematical object” consists of abstract entities (that is, “things” with no...
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Rock On
I don’t trust rocks. Rocks keep fooling me. They sit there looking all solid until you examine them more carefully and find out they’re mostly empty space, with a smattering of charged particles here...
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That Does Not Compute
Stanley Tennenbaum was an itinerant mathematician with, for much of his adult life, no fixed address and no permanent source of income. Sometimes he slept on park benches. He didn’t have a lot of...
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The Number Devil
In the comments section of Bob Murphy’s blog, I was asked (in effect) why I insist on the objective reality of the natural numbers (that is, the counting numbers 0,1,2,3…) but not of, say, the real...
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Simple as ABC
The (really really) big news in the math world today is that Shin Mochizuki has (plausibly) claimed to have solved the ABC problem, which in turn suffices to settle many of the most vexing outstanding...
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WWCT? (What Would Copernicus Think?)
In The Big Questions, I argued that math is all there is: The Universe we live in is a mathematical object and is no more or less “real” than any other mathematical object. Thus, for example, the Godel...
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Accounting for Numbers
Over at Less Wrong, the estimable Eliezer Yudkowsky attempts to account for the meaning of statements in arithmetic and the ontological status of numbers. I started to post a comment, but it got long...
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Many Many Worlds
Max Tegmark is a professor of physics at MIT, a major force in the development of modern cosmology, a lively expositor, and the force behind what he calls the Mathematical Universe Hypothesis — a...
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Truth, Provability and the Fabric of the Universe
Here is my talk to the University of Rochester’s Society of Undergraduate Math Students on “Truth, Provability and the Fabric of the Universe”. The audience was great, and except for a couple of slips...
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Flashback
Last week, I posted video of my talk to the undergraduate math students on truth, provability and the fabric of the universe — and heard from several readers who requested that I post it in a non-flash...
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Aha!
Christmas week seems like a good time to share this video of my talk on “Truth, Provability and the Fabric of the Universe” delivered in March, 2018 in Madison, Wisconsin. The venue was the Free...
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Where I’ve Been
Video of my recent talk to the Philadelphia Association for Critical Thinking (topic: Why is There Something Instead of Nothing?”) is now available here. Click here to comment or read others’ comments.
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Where to Find Me
I don’t always enjoy being interviewed, but I do always enjoy being interviewed by the thoughtful and provocative (in the best way!) Bob Murphy. You’ll see why if you listen to the latest episode of...
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Math, the Universe, and Ethan Siegel
Ethan Siegel, writing in Forbes, concludes that No, the Universe is Not Purely Mathematical in Nature. His argument, unless I’ve badly misunderstood him, is that many purely mathematical models of the...
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