Category Archives: Math

Q: Is it possible to write a big number using a small number? Is there a limit to how much information can be compressed?

Physicist: Although there are tricks that work in very specific circumstances, in general when you “encode” any string of digits using fewer digits, you lose some information.  That means that when you want to reverse the operation and “decode” what … Continue reading

Posted in -- By the Physicist, Combinatorics, Computer Science, Entropy/Information, Math | 8 Comments

Q: How can I set up a random gift exchange that’s different from year to year?

The original question was: I’ve got a large family and we do a yearly gift exchange one person to one person. And I’d like to make a algorithm or something to do random selection without repeating for some time. And … Continue reading

Posted in -- By the Physicist, Combinatorics, Experiments, Math | 2 Comments

Q: How does “1+2+3+4+5+… = -1/12” make any sense?

Physicist: When wondering across the vast plains of the internet, you may have come across this bizarre fact, that , and immediately wondered: Why isn’t it infinity?  How can it be a fraction?  Wait… it’s negative? An unfortunate conclusion may … Continue reading

Posted in -- By the Physicist, Equations, Math, Number Theory | 14 Comments

Q: What determines the size of the bright spot when you focus sunlight with a lens?

Physicist: This question really appeals to my ten-year-old self.  If you’ve never tried to burn something with a lens, collect three pairs of sunglasses, a magnifying lens, and something you dislike.  On a bright day, put on all three pairs … Continue reading

Posted in -- By the Physicist, Equations, Geometry, Math, Physics | Leave a comment

Q: Why are numerical methods necessary? If we can’t get exact solutions, then how do we know when our approximate solutions are any good?

Physicist: When a problem can be solved exactly and in less time than forever, then it is “analytically solvable”.  For example, “Jack has 2 apples and Jill has 3 apples, how many apples do they have together?” is analytically solvable.  … Continue reading

Posted in -- By the Physicist, Computer Science, Equations, Math | 11 Comments

Q: How can something be “proven” in science or math?

The original question was: … it confuses me that abstract concepts, such as Banach-Tarski, and other concepts in pure mathematics and theoretical physics, can be considered to have been “proven”.  Is it not the case that one can only prove … Continue reading

Posted in -- By the Physicist, Conventions, Math, Philosophical | 7 Comments