Category Archives: Math

Q: Can planes (sheets) be tied in knots in higher dimensions the way lines (strings) can be tied in knots in 3 dimensions?

Physicist: Yes! Mathematicians are pretty good at talking about things in spaces with any number of dimensions.  Sometimes that math is fairly easy and even intuitive.  For example, a line has 2 sides (ends), a square has 4 sides, a … Continue reading

Posted in -- By the Physicist, Geometry, Math | 8 Comments

Q: When you write a fraction with a prime denominator in decimal form it repeats every p-1 digits. Why?

The original question was: How come the length of the repetend for some fractions (e.g. having a prime number p as a denominator) is equal to p-1? Physicist: The question is about the fact that if you type a fraction … Continue reading

Posted in -- By the Physicist, Math, Number Theory | 6 Comments

Q: Is there such a thing as half a derivative?

The original question was: Another one of those questions of the type “does this make sense”.  You have first derivatives and second derivatives.  f'(x), f”(x) or sometimes dy/dx and d^2y/dx^2. Is there any sensible definition of a something like a “half” … Continue reading

Posted in -- By the Physicist, Conventions, Equations, Math | 13 Comments

Q: After the heat death of the universe will anything ever happen again?

Physicist: If you wait forever, then you might see something happen.  But the more practical answer is: no. The universe does a lot of stuff (for example, whatever you did today), but literally everything that ever happens increases entropy.  In … Continue reading

Posted in -- By the Physicist, Entropy/Information, Physics | 22 Comments

Q: Quaternions and Octonions: what?

Physicist: The most straightforward way to stumble across quaternions is to sit around thinking about complex numbers, where we have “i” which is the square root of -1 and stands for “imaginary number”.  If you have i, then you have … Continue reading

Posted in -- By the Physicist, Logic, Math | 9 Comments

Q: How do I know my windmill is on straight?

The original question was: I got quite the challenge from my father in law. The problem is well defined, but I’m having difficulties finding a meaningful answer. The reason why he asked me is because I’m an engineering student and … Continue reading

Posted in -- By the Physicist, Engineering, Equations, Geometry, Math | 4 Comments