meanerelk

270

It is too easy to come up with a just so story like this. How would you rephrase it to make it testable?

Here is a counterstory:

Children have a survival need to learn only well-tested knowledge; they cannot afford to waste their precious developmental years believing wrong ideas. Adults, however, have already survived their juvenile years, and so they are presumably more fit. Furthermore, once an adult successfully reproduces, natural selection no longer cares about them; neither senescence nor gullibility affect an adult's fitness. Therefore, we should expect children to be skeptical and adults to be gullible.

130

The quantum physics textbooks I read were happy to define linear operator-ness in great gory detail, but they never actually came out and said, "This is not something physically happening to the wavefunction. We are just using this math trick to extract an average value."

I think is is a common problem for many mathematical conventions in physics.

The same thing happened be me in high school physics. I was confused by the torque vector, and I spent an entire year thinking that *somehow* rotation causes a force perpendicular to the plane of motion. I just could not visualize what the heck was going on.

Finally I realized the direction of the torque vector is an arbitrary convenience. My teacher and textbook both neglected to explain **why** it works like that.

The "why's" are important!

70

I'm an artist, and believe that any two given individuals will not share an identical color perception.

Being an artist has nothing to do with the accuracy of this belief.

I've always had issues with infinity and transcendental numbers. For instance, pi is said to be transcendental as it cannot be expressed as the ratio of two integers; yet, in a sense, is the ratio of two numbers - the circumference over the diameter.

There are two problems here. First, *irrational* numbers are the ones that cannot be expressed as a fraction of integers. Transendentals are defined as numbers that are not algebraic. All transcendental numbers are irrational, but the converse does not hold.

Second, pi is **defined** as the ratio of circumference to diameter, true. This would only be a contradiction if both the circumference and diameter could be integers at the same time, which is impossible.

This got me to thinking about numbers as mere concepts. Numbers that we count on our fingers and toes have a greater "reality" than such oddballs as radical two and i, yet those oddballs seem to me much more useful.

You are confused about what numbers actually are. Some classes of numbers are useful for certain tasks, but there is no sense in which one class is more 'real' than another. I recommend *Mathematics, Queen & Servant of Science* by Eric Temple Bell for a wonderful overview of mathematics. Chapter 2, "Mathematical Truth", is relevent to this discussion. Also, see *Godel, Escher, Bach*, Chapter 11: "Meaning and Form in Mathematics".

I am looking forward to the API. I am much more likely to continually use Beeminder if it can be automatically updated or, failing that, updated easily from a mobile device. The site is actually OK (not great) to navigate with a phone, but typing updates is not that easy.

Thanks for the hard work. Beeminder looks like a great tool.