All of Captain_Obvious's Comments + Replies

Is Humanism A Religion-Substitute?

Space shuttles weren't present in our era of evolutionary adaptedness, neither was science.

OK, but neither was anything like our modern forms of religion. Just because you don't have something to fit a given hole doesn't mean the hole couldn't exist (and of course I'm kidding about the specifics of the shuttle-launch-shaped-hole)

Besides, while "modern" science wasn't present, the overall goal (trying to understand the world we find ourselves in) certainly was. Lacking anything like modern science, people had to "fill in the hole" (in th... (read more)

Is Humanism A Religion-Substitute?

How do we know that the religionists don't have a "space-shuttle-launch"-shaped hole in /their/ heads?

Geez, it almost makes you wonder if maybe religion might be a substitute for science...

Beautiful Math

Back in high school I discovered this by accident (yes, I was really bored!). I suppose it's nothing new, but it turns out that this works for more than simple squares and cubes:

Given any sequence of numbers, keep finding differences of differences until you hit a constant; the number of iterations needed is the maximum exponent in the formula that produced the numbers. That is, this works even if there are other terms, regardless of whether any or all terms have coefficients other than 1.

0AnthonyC10y
So did I! And in general the nth order finite differences of nth powers will be n factorial.
-1dlthomas10y
Your procedure (though not necessarily your result) breaks for e^x
0Technoguyrob10y
This is obvious after you learn calculus. The "nth difference" corresponds to nth derivative (a sequence just looks at integer points of a real-valued function), so clearly a polynomial of degree n has constant nth derivative. It would be even more accurate to say that an nth antiderivative of a constant is precisely a degree n polynomial.