5 ms·

I really like to put it this way: "Of the several professional mathematicians I have known, only one of them could calculate a 15% tip in her head." Now, mind

by drostie 15y ago

I really like to put it this way: "Of the several professional mathematicians I have known, only one of them could calculate a 15% tip in her head." Now, mind you, all of them know that, in order to get the right overall tip, every person can just calculate the tip on what they themselves ordered and pay that -- and it will magically sum to the right value. They might also know that if you had to tip self-consistently -- that is, if you also had to pay a 15% tip on your tip, and a 15% tip on your tip on your tip, and so on, that this process converges and is essentially the same as just paying an effective tip. (They might even be able to tell you that the effective tip is 15%/0.85, if they're still reasonably young.) Those are the sorts of things they're good at. I know some who will talk your ears off about the convergence of an involution series in a noncommutative algebra and the problems of just finding a nice notation which makes the problem not look ugly, because the idea is really just so simple once you skip past the messy derivation to the intuitive result. Computing the actual tip? Not so much. Heck, that effective tip? That's 3/17ths, if you really churn the mental gears! Who has time to divide 3 by 17?! That's what I have a calculator for. Except, well, I didn't bring a calculator because we never use them -- but that's what the computer in my office is for.

vacri 15y ago
I really don't understand your point. Calculating a 15% tip is monstrously simple to do in your head. When I visited the US, I was able to do it from the first meal onward, for meals solo or alone. Dropping the last digit and adding half again is so brain-numbingly simple, though I must admit I did dine at one stage with some native college students who pulled out a calculator to figure out their part of the tip. It's not clear in what you're writing if you mean "when presented with a bill, how much to tip" or "given the final payment, how much of it was tip", or something else.
- drostie 15y ago
  I mean "when presented with a bill, how much to tip." It's just not the sort of thing which mathematicians are ever expected to do. There is no math journal where you can publish the tips you calculated. It's not their job, there are no theorems to be proven there, etc., etc. (You're actually doing it a little more complicated than it has to be because it sounds like you're spending a little memory remembering the number you took 10% of. Take half, add it to the original, which is presumably still right in front of you, then drop the digit after.) I learned a lot of mental calculation because my background is in applied physics, where you're expected to reason about the size of things etc. (A good example question might be, "how far do you think an air molecule can go before it bumps into another air molecule?") So, just for example, to convert Celsius to Fahrenheit you multiply by 2, subtract 10%, and add 32. It is exact. So 25°C → 50 → 45 → 77°F. To convert Fahrenheit to Celsius you subtract 32, divide by 2, add 10%, then add 1% if you really feel like it; it is approximate. So 52°F → 20 → 10 → 11 → 11.11°C. Those sorts of things I will do in my head when people give me a number in one or the other temperature. Tipping is especially nice when compared to the fact that in New York State there is an 8% sales tax which is not added to any of the prices on stuff at the store -- calculate a tip and halve it. [Naive reasonings on air: small upper bounds can be given by the fact that it has to travel easily through the small passageways in your inner ear, but my favorite calculation is to take (kinematic viscosity) / (speed of sound), both of which are things that an applied physics geek should roughly know.]
- jinfiesto 15y ago
  Alternatively, doubling the tax usually works fine. At least in places where the tax is 7.5%.
ckpwong 15y ago
I don't know about you, and your mathematics education background, but by the time I took my various math classes in university (I was in faculty of math), the higher level the classes, the less often I see numbers. People seem to associate "mathematicians" with "wizardry in arithmetics," but even before I finish undergrad, I understand "1 + 1" doesn't necessarily have to be 2. That's how mathematicians think (at least those who are interested in rings, fields, etc). That stupid 15% tip? It's child's play and has long since been delegated to calculators.

by drostie 15y ago

vacri 15y ago

I really don't understand your point. Calculating a 15% tip is monstrously simple to do in your head. When I visited the US, I was able to do it from the first meal onward, for meals solo or alone. Dropping the last digit and adding half again is so brain-numbingly simple, though I must admit I did dine at one stage with some native college students who pulled out a calculator to figure out their part of the tip. It's not clear in what you're writing if you mean "when presented with a bill, how much to tip" or "given the final payment, how much of it was tip", or something else.

drostie 15y ago
I mean "when presented with a bill, how much to tip." It's just not the sort of thing which mathematicians are ever expected to do. There is no math journal where you can publish the tips you calculated. It's not their job, there are no theorems to be proven there, etc., etc. (You're actually doing it a little more complicated than it has to be because it sounds like you're spending a little memory remembering the number you took 10% of. Take half, add it to the original, which is presumably still right in front of you, then drop the digit after.) I learned a lot of mental calculation because my background is in applied physics, where you're expected to reason about the size of things etc. (A good example question might be, "how far do you think an air molecule can go before it bumps into another air molecule?") So, just for example, to convert Celsius to Fahrenheit you multiply by 2, subtract 10%, and add 32. It is exact. So 25°C → 50 → 45 → 77°F. To convert Fahrenheit to Celsius you subtract 32, divide by 2, add 10%, then add 1% if you really feel like it; it is approximate. So 52°F → 20 → 10 → 11 → 11.11°C. Those sorts of things I will do in my head when people give me a number in one or the other temperature. Tipping is especially nice when compared to the fact that in New York State there is an 8% sales tax which is not added to any of the prices on stuff at the store -- calculate a tip and halve it. [Naive reasonings on air: small upper bounds can be given by the fact that it has to travel easily through the small passageways in your inner ear, but my favorite calculation is to take (kinematic viscosity) / (speed of sound), both of which are things that an applied physics geek should roughly know.]
jinfiesto 15y ago
Alternatively, doubling the tax usually works fine. At least in places where the tax is 7.5%.

ckpwong 15y ago

I don't know about you, and your mathematics education background, but by the time I took my various math classes in university (I was in faculty of math), the higher level the classes, the less often I see numbers. People seem to associate "mathematicians" with "wizardry in arithmetics," but even before I finish undergrad, I understand "1 + 1" doesn't necessarily have to be 2. That's how mathematicians think (at least those who are interested in rings, fields, etc). That stupid 15% tip? It's child's play and has long since been delegated to calculators.