Open Thread June 2010, Part 4

Will_Newsome

This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.

This thread brought to you by quantum immortality.

This thread is for the discussion of Less Wrong topics that have not appeared in recent posts. If a discussion gets unwieldy, celebrate by turning it into a top-level post.

This thread brought to you by quantum immortality.

Most people don't need to understand evolution. Maybe we should distinguish between "harmful to self", "harmful to society", and "harmful to a democratic society".

If you can't do math at a fairly advanced level - at least having competence with information theory, probability, statistics, and calculus - you can't understand the world beyond what's visible on its (metaphorical) surface.

I've got a tangential question: what math, if learned by more people, would give the biggest improvement in understanding for the effort put into learning it?

Take calculus, for example. It's great stuff if you want to talk about rates of change, or understand anything involving physics. There's the benefit; how about the cost? Most people who learn it have a very hard time doing so, and they're already well above average in mathematical ability. So, the benefit mostly relates to understanding physics, and the cost is fairly high for most people.

Compare thi... (read more)

2Will_Newsome16y

I'd like this to be true, as I want the time I spend learning math in the future to be as useful as you say, but I seem to have come rather far by knowing the superficial version of a lot of things. Knowing the actual math from something like PT:LOS would be great, and I plan on reaching at least that level in the Bayesian conspiracy, but I can currently talk about things like quantum physics and UDT and speed priors and turn this into changes in expected anticipation. I don't know what Kolmogorov complexity is, really, in a strictly formal from-the-axioms sense, nor Solomonoff induction, but I reference it or things related to it about 10 times a day in conversations at SIAI house, and people who know a lot more than I do mostly don't laugh at my postulations. Perhaps you mean a deeper level of understanding? I'd like to achieve that, but my current level seems to be doing me well. Perhaps I'm an outlier. (I flunked out of high school calculus and 'Algebra 2' and haven't learned any math since. I know the Wikipedia/Scholarpedia versions of a whole bunch of things, including information theory, computer science, algorithmic probability, set theory, etc., but I gloss over the fancy Greek letters and weird symbols and pretend I know the terms anyway.)

8JoshuaZ16y

While as a mathematician I find that claim touching, I can't really agree with it. To use the example that was one of the starting points of this conversation, how much math do you need to understand evolution? Sure, if you want to really understand the modern synthesis in detail you need math. And if you want to make specific predictions about what will happen to allele frequencies you'll need math. But in those cases it is very basic probability and maybe a tiny bit of calculus (and even then, more often than not you can use the formulas without actually knowing why they work beyond a very rough idea). Similar remarks apply to other areas. I don't need a deep understanding of any of those subjects to have a basic idea about atoms, although again I will need some of them if I want to actually make useful predictions (say for Brownian motion). Similarly, I don't need any of those subjects to understand the Keplerian model of orbits, and I'll only need one of those four (calculus) if I want to make more precise estimations for orbits (using Newtonian laws). The amount of actual math needed to understand the physical world is pretty minimal unless one is doing hard core physics or chemistry.