Category Archives: Math

Q: Since it involves limits, is calculus always an approximation?

Physicist: Nope!  Calculus is exact.  For those of you unfamiliar with calculus, what follows is day 1. In order to find the slope of a curve at a particular point requires limits, which always feel a little incomplete.  When taking … Continue reading

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

Q: If a long hot streak is less likely than a short hot streak, then doesn’t that mean that the chance of success drops the more successes there are?

One of the original questions was:  I understand “gambler’s fallacy” where it is mistaken to assume that if something happens more frequently during a period then it will be less frequently in the future.  Example:  If I flip a coin … Continue reading

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

Q: Where do the rules for “significant figures” come from?

Physicist: When you’re doing math with numbers that aren’t known exactly, it’s necessary to keep track of both the number itself and the amount of error that number carries.  Sometimes this is made very explicit.  You may for example see … Continue reading

Posted in -- By the Physicist, Conventions, Equations, Math | 1 Comment

Q: Is there a formula for finding primes? Do primes follow a pattern?

Physicist: Primes are, for many purposes, basically random.  It’s not easy to “find the next prime” or determine if a given number is prime, but there are tricks.  Which trick depends on the size of the number.  Some of the … Continue reading

Posted in -- By the Physicist, Math, Number Theory | 10 Comments

Q: If the number of ancestors you have doubles with each generation going back, you quickly get to a number bigger than the population of Earth. Does that mean we’re all a little inbred?

Physicist: In a word: yes.  But it’s not a problem in large populations. The original questioner pointed out that in the age of Charlemagne (more or less when everybody’s 40-greats grandfolk were living) the world population was between 200 and … Continue reading

Posted in -- By the Physicist, Biology, Evolution, Probability | 8 Comments

Q: How do you define the derivatives of the Heaviside, Sign, Absolute Value, and Delta functions? How do they relate to one another?

Physicist: These are four standard reference functions.  In the same way that there are named mathematical constants, like π or e, there are named mathematical functions.  These are among the more famous (after the spotlight hogging trig functions). The absolute value … Continue reading

Posted in -- By the Physicist, Equations, Math | 3 Comments