I had an ultimate fallback for high school physics. Start putting stuff in likely equations where the units work out to the desired answer. That always worked, save for two or three occasions. Unfortunately, once I figured that out, that let me be lazy and kept me from learning as well as I should have.

When Wolfram Alpha starts solving word problems, time to start worrying. Not about machines rebelling, but about cheating in grade school math classes.

> Start putting stuff in likely equations where the units work out to the desired answer.

Working physicists call this 'dimensional analysis' and it's pretty much the foundational skill of theoretical physics.

How true is this? Isn't dimensional analysis basically one kind of bookkeeping like Haskell's type checking?

What makes it particularly important in theoretical physics? Is it "foundational" because equations become unintuitive?

With known equations, then yes, dimensional analysis is essentially just a form of bookkeeping that helps you verify your math as you go.

But once you get into using quantum field theory to study new systems, the standard approach is to concoct a conservation of energy equation by summing terms, where each term is a combination of the system's variables with units of energy.

From there, you can discretize the coordinates and predict the existence of various particles (or pseudo-particles, depending on what kind of system you're describing) and their dynamics.

Thanks, but...

my guess is nobody will really get what you mean until they actually try to learn QFT, huh. I'll revisit your comment in a few years.

"When Wolfram Alpha starts solving word problems..."

http://www.cs.utexas.edu/users/novak/cgi/physdemo.cgi

It's no Wolfram|Alpha, but it solves word problems fairly well.

Unfortunately both this and Alpha are trivial to confuse:

  What is the area of a circle with radius "2x"

yields 3.1415926535897931 * 2x^2 which is obviously incorrect. Alpha on the other hand doesn't give a result unless simplified to

  area of a circle with radius (2x)

where it gives a nonsensical display alongside the fact that 4pi is about 12.5664.

It may give you the wrong answer, but it makes it hard to be led astray:

  Evaluated area = pi * radius^2  giving AREA = 3.1415926535897931 * 2x^2

That description makes it obvious that a pair of parentheses are the only thing lacking.

I've run into some weird bugs trying to perform calculations in Wolfram|Alpha. For example, I cannot come up with any query for the general question "human height vs Empire State Building" that works, even though the separate queries "height Empire State Building" and "height average male" return answers with units of length.

Don't take this the wrong way -- I know where you're coming from, and it's natural to push the boundaries, especially for a hacker. But let's stop to appreciate how hilarious this comment looks to someone who majored in physics in the era just before the web. It's like eavesdropping on the gods as they complain about the quality of this year's batch of ambrosia.

You own a machine that returns a meaningful number for "height Empire State Building" and "height average male". In less than a second. And which will perform floating-point division for you, at the press of a few keys. And you're vaguely unhappy because you can't do it all in one step!

Now I know how Hans Bethe (acknowledged grandmaster of the slide rule, who routinely computed logarithms in his head) must have felt when he heard the young grad students comparing the features on their scientific calculators.

I wonder if tools like Wolfram Alpha will eventually succeed in doing for Fermi problems what Google did for Trivial Pursuit: Turning an activity that was formerly regarded as a touchstone of intelligence into a typing exercise. Estimating the number of piano tuners in Chicago will be a lot less impressive when you can just type "piano tuners in Chicago" into a text box and get the answer back to within a decimal place.

Fortunately, right now typing "piano tuners in Chicago" into Alpha just makes Javascript crash in Safari, so I guess we humans can sleep soundly for a while longer. ;)

Adding "average" helps it parse the question.

height Empire State Building divided by average height human

= 235

height Empire State Building divided by height human

Fails

Neat.

a billion light years / average height human * (1/9) furlong / age universe = 1.01 c (speed of light)

Very neat.

I was pretty sure I tried every permutation of the words "average," "height," and "human," but I guess I didn't. Bravo.

It comes roughly close with something like "empire state building height + average human height" but yeah, that's quite odd.

Edit: And hitting "Show details" for a breakdown.