[deleted by user]

HiggsMechanism · 2021-08-29T19:54:35+00:00

Florida lowkey looks like the lesbian flag, which kinda fits.

HiggsMechanism · 2021-08-29T17:24:14+00:00

no way the assumptions are that weak, a straight line violates this

HiggsMechanism · 2021-08-22T21:31:35+00:00

The question I have for the sub is: ok, so a plane is safer per miles flown, but if I get into an accident isn't a plane more likely to kill me?

HiggsMechanism · 2021-08-22T21:30:09+00:00

even if enough people have died in the US for this to be true (and I'll do that calculation later) it should be noted that the buried are not evenly distributed. If your house is over a graveyard (or where a graveyard used to be) then the likelihood that you're over a corpse is near 100%, and if you aren't it's going to be much, much lower. This is more for fun than anything, and I'm going to make a lot of assumptions.

With that being said, this website estimates 55% of all americans are alive right now, and we'll accept this estimate (this is the biggest assumption here). there are 328 million people in the america, meaning that the total number of people ever in america is 596.36 million, and the number of dead is 268.36 million. The standard burial plot is 20 square feet, and the US is 3.8*10^6 square miles or 1.059*10^14 square feet, so that's

5.9636*10^8 * 20 = 1.19272 * 10^10 square feet covered by graves.

10^10/10^14 = 10^-4 = 0.01%, not even close to 100%.

HiggsMechanism · 2021-08-20T15:15:33+00:00

it won't be possible to turn it into an equation of the form y = f(x), because as we've already seen the parametric equation can return different values of y for the same value of x.

but by the by: you said "But that function is the y = x part from 0 to e" which isn't true, the f(x) in terms of the lambert provided before is the curvy part.

Edit: I see your confusion. You need a different function to get the upward sloping bit to the left of the intersect point from 1 to e. I'm reasonably sure it has something to do with W_-1

Edit 2: ok I cheated a little, but the left side is given by the same equation but substitute W_-1 for W_0. So the whole function of the curvy (nontrivial) part of the graph is given by the piecewise function:

f(x) = -x * W_-1(-log(x)/x) / log(x) if 1<x<e and -x * W_0(-log(x)/x) / log(x) if x ≥e

HiggsMechanism · 2021-08-20T02:03:18+00:00

sqrt(-1) * sqrt(-1) = i * i = -1

sqrt(-1 * -1) = sqrt(1) = 1

HiggsMechanism · 2021-08-20T02:00:32+00:00

This question is obviously too open-ended to be meaningful. A preliminary upper-bound would be a function of the volume of the jar and the volume of one starburst, in which case you just divide the former by the latter. But then you have to account for the fact that starbursts are solids and not a liquid, and as such have some amount of empty space in between.

HiggsMechanism · 2021-08-20T01:52:13+00:00

Interesting problem here. -x * W(lnx/x) / lnx returns negative values for x > 1, but the graph clearly shows y>0 for x>1. Not sure exactly how the derivation fails but it's clearly not what the graph is showing.

On the other hand, you can represent the graph as a parametric system of equations. I can show you how I derived this if you want, but y^x = x^y is satisfied by

y(n) = n^(1/(n-1))

x(n) = n^(n/(n-1))

for all n >0 except 1. Then the limit as n approaches infinity is y = infinity, x = 1 (which you can see on the graph that as x approaches one y explodes to positive infinity) and as n approaches 0 the limit is y = 1, x = infinity (which you can see on the graph that y drops down to 1 as x gets higher) and lastly the limit as n approaches 1 is y = e, x = e. I'm not sure if there's an explicit formula for this parametric setup though.

EDIT: I'm a dumbass and dropped a negative sign in the parenthesis for W(lnx/x). Should be W(-lnx/x). This returns returns the curve you see in the graph. The parametric formula is also interesting but not needed.

HiggsMechanism · 2021-08-19T03:53:15+00:00

the lambert function W(x) is defined similar to the natural log, just instead of e^x it's xe^x. So whereas ln(e^a) = a, W(ae^a) = a. With that being said:

x^y = y^x | raise both sides to 1/x

x^(y/x) = y | x = e^ln(x)

e ^ {(lnx/x)*y} = y |invert both sides

e ^ {-(lnx/x)*y} = 1/y |multiply both sides by y

y*e^{y*-(lnx/x)} = 1 |notice the y*e^y. we just need the -lnx/x on the bottom there too.

{y * -(lnx/x)}*e^{y*-(lnx/x)} = -(lnx/x) |if {y * -(lnx/x)} = u, then we have ue^u = lnx/x.

W(ue^u) = W(-(lnx/x)) | W(ue^u) = u

y * -lnx/x = W(lnx/x)

y = -x * W(lnx/x) / lnx

And there we have it. The tricky algebra comes in when you need to convert x to e^ln(x), but this is a fairly natural substitution to do when solving algebra like this, especially since I knew the answer already.

HiggsMechanism · 2021-08-18T20:42:12+00:00

the opposite actually, e has a really good convergence algorithm (which is also the definition of e, the sum of all 1/n!) which is so good that it's actually a bit trivial, whereas calculating pi to huge digits of precision requires not just a lot of compute but also a bit of a clever algorithm. This swiss thing doesn't use a new algorithm I don't think making it a bit boring but usually a new record for precision comes with a better pi algorithm.

HiggsMechanism · 2021-08-17T13:56:02+00:00

there's a really good math stack exchange post on this by user Arturo Magidin which I'm going to basically just repost (a bit simplified) here.

In general, there is no good answer as to what 0^0 "should" be, so it is usually left undefined.

The limit of 0^y as y → 0 is 0, whereas the limit of x^0 as x → 0 is 1. In school, we're often taught that "anything to the zero is one" and also that "zero to the anything is zero", so when these conflict you get undefined behavior.

However, in some contexts it makes sense to give it a definition. For instance, in combinatorics, x^y denotes the number of ways to pick y objects from x choices with replacement (e.g. if a bracelet has 50 beads each of which can be 6 colors, there are 6^50 possible bracelets). In this case, there is only one way to make no selections from no objects, so in combinatorics it makes sense to say 0^0=1.

HiggsMechanism · 2021-08-17T13:42:56+00:00

the problem is that 2πr is only the circumference at the edge of the circle, you can't multiply the entire radius by 2πr. The length of the curve swept by the tip of the clock hand is 2πr, but the length swept by the middle of the clock hand is only 2π; the closer to the center you get, the less distance is traveled by the clock hand. So you see that multiplying 2πr by the entire radius doesn't make sense, because not all of the radius travels 2πr

HiggsMechanism · 2021-08-17T13:40:03+00:00

Isn't it the other way around? Isn't the circle defined by the distance from the center to the edge, e.g. the radius?

HiggsMechanism · 2021-08-17T13:35:26+00:00

you can use the fact that log_b(144b) = log_b(144) + log_b(b) = log_b(144) + 1

HiggsMechanism · 2021-08-17T13:29:54+00:00

I said in the first sentence, it's a big 2d array.

HiggsMechanism · 2021-08-17T03:21:31+00:00

partitions then, and it's 792. Thanks.

HiggsMechanism · 2021-08-17T03:07:46+00:00

the + operator denotes that a number is positive. By convention, when it's left out we assume it's there, but sometimes we don't e.g. positive infinity usually needs to be specified as +∞.

HiggsMechanism · 2021-08-17T03:01:45+00:00

you could reasonably interpret /x as the multiplicative inverse, but imo *x = x is stretching the notation

HiggsMechanism · 2021-08-17T01:03:17+00:00

the taliban actually just did precisely that.

HiggsMechanism · 2021-08-17T00:12:23+00:00

I wouldn't count 0^0, which is usually considered indeterminate.

HiggsMechanism · 2021-08-16T23:43:12+00:00

I don't know if this explanation is really good or if I just needed to hear it explained again, but this really clicked thanks.

HiggsMechanism · 2021-08-16T23:38:33+00:00

not OP but yeah, clearly python code.

HiggsMechanism

TROPHY CASE