Mathematics

i really hated pi day when i was an academic. it seemed like it only really began to catch on after 2000. drove me crazy. now i am one degree removed. it's silly to focus on pi. i have identified more interesting constants in my published work.

Edward Evans

TREE(3) day

12:19 AM

Some pi trivia. 22/7 is an ok approximation, but it's even better if you subtract 0.04%. That is, (22/7)(1-4/10000). Of course, 355/113 is much better, but that denominator isn't much fun when you're doing mental arithmetic.

when i'm doing what, now? :)

i was on a call the other day where three people spent about ten minutes computing the volume of a very small chamber. the stumbling block seemed to be once you've cubed everything, you're getting thousands of cubic meters, which aren't liters. i remained silent and hoped that nobody remembered my background. it was a success.

i may have opened this window and chatted about something else while it was playing itself out.

I must admit that my mental arithmetic skills aren't as sharp as they were a few decades ago. But I still like to do some stuff mentally, to keep those brain circuits functional.

and when i say about ten minutes, i mean, at least ten minutes. it was a long time. i floated the possibility of suggesting that people compute a volume offline, but abandoned it because i was one of five or six conference participants and didn't want to disrupt the flow of the meeting.

i think i have only gotten better with mental arithmetic over time, but i still suck.

i did a finance interview where they asked me to estimate the number of gallons of gas sold in the US in a day. my estimate was right, to the number of digits. they didn't hire me anyway. it's all a game.

One good thing about going to school during the era of slide rules & log tables: you got pretty good at keeping track of powers of 10.

i did mention this. i said "we all agree it's 1.32 times something and we just need to pin down the power of 10." it was ignored.

12:29 AM

I'm slightly disappointed that I got no responses to this:

Mar 8 at 20:46, by PM 2Ring

Quick Fermi problem: What's the square root of the ocean? That is, what volume is $v$, such that $n$ is the number of molecules of water in $v$ and $n^2$ is the number of water molecules in the ocean, IOW, the volume of the ocean is $nv$.

also it's not going to be a large power of 10, or a small power of 10. same as when i used to go to the grocery store and buy apples, i know if i buy five apples it's not going to be $25 or $0.50.

i hate fermi problems. they take me back to finance interviews, which i generally performed well in until the non-fermi part of the interview. and finance guys are d*cks anyway.

and by guys i do mean guys. i did not have a single female interviewer.

@leslietownes Exactly. Kids who depend on calculators don't seem to see the benefit in doing rough estimates just to make sure you haven't screwed up a decimal place somewhere.

it's really that simple. i'm not buying a new car for $2000 or $200,000. i might buy a car for $20,000.

oh, mathjax, where would i be without you.

geocalc33

$ ds^2=c^2dt^2-dx^2-dy^2-dz^2 $ anybody know how to write this in null coordinates?

\\$

12:33 AM

geocalc, no time travelling. we go positive t only. none of this goofy business.

@PM2Ring 5 mL

or a teaspoon

one of my officemates in grad school was notoriously bad at practical math. to the point where he had a collection agency going after him for missed cell phone payments. another officemate, completely useless at practical calculation, off by powers of a thousand. but she could spot errors in arguments. she had a superhuman ability.

@AkivaWeinberger Very good. I think it's closer to 8 mL, but the water volume I used includes all the water in the atmosphere, and groundwater in the crust. And it's probably a fair bit more if we include the water "dissolved" in the mantle.

Yeah I'll take it as being within the margin of error

@geocalc33 Mr Wiki knows.

Light-cone coordinates

In special relativity, light-cone coordinates is a special coordinate system where two of the coordinates, x+ and x− are null coordinates and all the other coordinates are spatial. Call them x ⊥ {\displaystyle x_{\perp }} . Assume we are working with a (d,1) Lorentzian signature. Instead of the standard coordinate system (using Einstein notation) d s 2 = − d t...

12:39 AM

1-2 tsp

@AkivaWeinberger Sure. If you're within an order of magnitude or two, you're fine.

Another way to phrase your question is, what's the geometric mean of the oceans and a molecule of water

$\sqrt{ab}$

Yep

We had a similar sort of question recently on Astronomy.SE. If you could bring all of the stars from the Milky Way together into one giant ball, without changing their density, how big would that ball be. There's somewhere between 100 & 400 billion stars in the galaxy.

geocalc33

$\delta_{ij}dx^idx^j$ what does this expression mean?

it would seem to not care about the quantity unless i = j, in which case it does care. maybe an integral involving coordinates labeled with superscripts.

Q: How big would the Milky Way be if all the stars were emptied into one sphere?

12:49 AM

1

Neglecting the fact that this ball of gas would just collapse on itself - I'm curious if there's an agreed-upon measurement that takes into account the volume of all the ~100 billion stars to predict the diameter of a milky way where all the gas is in one orb. If not, is it safe to just use the v...

milky-way

the sun is a mass of incandescent gas. some wise sage said that