Support my writing at Ko-FiOld Books and the Passage of Time
I've been working my way through my reading list, and it's really interesting to see how quickly some books age. Right now I'm reading The Art of the Steal and Enlightenment 2.0, and both books had fascinating failures to predict that I wanted to comment on.Read Post
A Fictional History of Numbers, Part 4: Imagination, Complexity, and the Fundamental Theorem of Algebra
We continue our exploration of what numbers are, and where mathematicians keep finding weird ones. In the first three parts we extended the natural numbers in two ways: algebraically and analytically. Those approaches gave overlapping but distinct sets of numbers. This week we combine them to get the complex numbers, and see some hints of why the complex numbers are so useful—and so frustrating.Read Post
A Fictional History of Numbers, Part 3: Computability, Reality, and Leaving Well Enough Alone.
This week we continue our exploration of what numbers are, and where mathematicians keep finding weird ones. Last time we defined the real numbers, but it took a lot of work. Now we'll see how truly strange they are. They're so strange that it's tempting to avoid them and stick with something simpler.But the real numbers do a much better job of describing modeling the parts of the world we care about. Their weirdness is exactly what we need to guarantee that a bunch of "obvious" claims are actually true. And we'll end by seeing why we could stick to the computable numbers instead—but we shouldn't bother.