Category Archives: Math

Q: In base ten 1=0.999…, but what about in other bases? What about in base 1?

Physicist: Yup! The “0.999… thing” has been done before, but here’s the idea.  When we write 0.9, 0.99, 0.999, 0.9999, etc. we’re writing a sequence of numbers that gets closer and closer to 1.  Specifically, if there are N 9’s, … Continue reading

Posted in -- By the Physicist, Math | 5 Comments

Q: How many samples do you need to take to know how big a set is?

The Original Question Was: I have machine … and when I press a button, it shows me one object that it selects randomly. There are enough objects that simply pressing the button until I no longer see new objects is … Continue reading

Posted in -- By the Physicist, Combinatorics, Math, Probability | 3 Comments

Q: How do we know that everyone has a common anecestor? How do we know that someone alive today will someday be a common ancestor to everyone?

The original question was: From biology and genetics we know that any group of living organisms had a mitochondrial most recent common ancestor (mitochondrial Eve): a female organism who lived in the past such that all organisms in this group … Continue reading

Posted in -- By the Physicist, Biology, Evolution, Probability | 3 Comments

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 | 8 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