# Category Archives: Conventions

## 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

## 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

Physicist: Because calculus. When you first start doing trigonometry the choice between radians, degrees, turns, or hexacontades is a matter of personal preference.  Most people use degrees because most other people use degrees (and other people seem pretty on the … Continue reading

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

## Q: Where do the weird rules for rational numbers come from? (Dealing with fractions)

The original question was:  Why is it when we multiply fractions we multiply the numerators across  and the denominators across?  Whereas when we divide we don’t do the same?  Who came up with these rules and why do they work … Continue reading

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

## Q: How are imaginary exponents defined?

The original question was: How do you do xi (x to the i power), and how on Earth was it developed?  There isn’t really anything to base xi on from previous rules of exponents as it is a completely new … Continue reading

Posted in -- By the Physicist, Conventions, Equations, Math | 36 Comments