Let's discuss Mathematics

[Atticus]

First you calculate the multiplicator:

2.61 years/month= 952 days/30 days= 31.8 (about)

So one real day corresponds to 31.8 days in his life. Then 116 days is 31.8 * 116 ... ans so on.

BTW, doesn't "rewind" mean that his life is going backwards?

[PlutonianEmpire]

Originally Posted by Atticus

First you calculate the multiplicator:

2.61 years/month= 952 days/30 days= 31.8 (about)

So one real day corresponds to 31.8 days in his life. Then 116 days is 31.8 * 116 ... ans so on.

BTW, doesn't "rewind" mean that his life is going backwards?

Yes. But his body ages normally. Meaning, that the rewind is enough so that December 21st, 2012 is the equivalant of him being born, indicating he will die by whatever the voodoo witch wanted him to die by.

I figured out that "31.8 * 116" should actually be "116 / 31.8", which would be about 3.6478 days.

Anyways, thanks.

[PlutonianEmpire]

Google has failed me. Wolfram Alpha has failed me. EVERYTHING has failed me.

I've been looking for the past bleeping hour for an easy calculation for the roche limits of celestial objects, to no avail, and at this point, I am way beyond pissed off.

So I've come here as a last resort. My request is simple.

Can someone translate the formula for celestial roche limits into a single line of code-ish text, with info on which numbers go where? (Preferrably I'd be able to copypasta into Win 7's Calculator.) The images on Wikipedia (for example) containing the formulas are too confusing.

Example (the formula for calculating the semi-major axis of a given planet):

semi-major axis = (perihelion + aphelion) /2

[LulThyme]

What exactly is confusing about the Wikipedia formulas?

To be really honest, I do think everybody's time would be spent more productively if you tried to learn how to parse such formulas. Especially in the long run, you wouldn't have to ask again for every new formula (teach a man to fish and all that..) .

As far as I can tell, the formulas on Wikipedia only have the four basic operations plus exponentiation, so you only need to understand a bit of notation and order of operations, it should not be too hard and you can come and ask here for help I suppose.

[Mise]

I looked on wiki for "Roche limit" and here is the first formula in that page:



Which is d = R*(2*p_M/p_m)^(1/3) if you're typing it into a computer. (I'm using p's instead of rho's.)

[Chairman Meow]

Originally Posted by meromorph

Mathematica stores symbolic expressions as nested functions. For example, 1 + 2 Pi would be stored as:

Plus[1, Times[2, Pi]]

Expressions with rational powers like 4 + 2 sqrt(5) expand to:

Plus[1, Times[2, Power[5, Rational[1,2] ] ] ]

Nested functions can be visualized as trees, f[a,b] becomes a parent node f with two child nodes a and b.



Interesting. In mathematica, constants like Pi are kept as symbols but have an attribute marking that they can be evaluated to a number, and the tests 4 > Pi and 4.0 > Pi both return true. Mathematica uses dynamic typing, so if an expression combines symbols and floating-point like 2 + 2.0 then the result is output as floating-point 4.0 instead of returning a type error.

One thing you have to watch out for in Mathematica if you use the Units and PhysicalConstants packages is that Mathematica treats pi as a unit rather than part of the number. This means if you try to strip the units off a physical constant by taking the first part (e.g. VacuumPermittivity[[1]]), then you can end up with a number that's off by a factor of pi. I've been bitten by that bug in the past...

[peter grimes]

Originally Posted by Mise

I looked on wiki for "Roche limit" and here is the first formula in that page:



Which is d = R*(2*p_M/p_m)^(1/3) if you're typing it into a computer. (I'm using p's instead of rho's.)

I don't have any mathematical proficiency (nor do I know anything about windows 7 calculator's interface) yet I was able to enter this formula into a couple different calculators on my phone with results congruent to 8 significant figures.

I used the same values for a variable in each iteration.

Maybe W7Calc has some quirks that are really strange??

[Lord Chambers]

For those of you who know a few quantitative methods and statistics, where did you learn? I'm curious if anyone is partially self-taught and what resources he or she used. Any websites or podcasts you use to enhance your understanding?

[Mise]

"Numerical Recipes" is good to have as a reference, but most of the stuff I learnt was at university or on the job.

[sanabas]

Originally Posted by Lord Chambers

For those of you who know a few quantitative methods and statistics, where did you learn? I'm curious if anyone is partially self-taught and what resources he or she used. Any websites or podcasts you use to enhance your understanding?

http://mathworld.wolfram.com/ plus a few texts I have lying around, plus whatever else google might send me to. Or in some cases, housemates were struggling with their uni stuff, so I grabbed their textbooks/lecture notes, and taught myself enough of what they were doing to be able to help them. Plus there's always the fun option of deriving formulae & things yourself.

[Atticus]

Does anyone here know any proof other than the four colour problem, which has used computers as an aid?

[sanabas]

I know of proofs of why something was wrong that used computers to find a counter-example. Think it's earlier in this thread somewhere. Do they count for what you're looking for?

[uppi]

Originally Posted by Atticus

Does anyone here know any proof other than the four colour problem, which has used computers as an aid?

http://en.wikipedia.org/wiki/Compute...puter_programs

[Atticus]

Thanks Uppi!

And Sanabas, I'm not sure, first I thought definitely no, whereas I thought about finding simple counterexample. Then I thought to clarify that counterexamples suffice if they aren't produced by mere raw power. Then I thought everything done by computer is produced by that. Then I thought that raw power can at least in theory add up to artificial reasoning.

The thing is, I read an article by John Horgan, a science reporter, who said that computers are increasingly used in maths to prove theorems. I think that's at least misleading, since they aren't used significantly (that I would know). Horgan has also some trouble with himself because he goes at the AI too in the same article, and so he claims that maths is done more and more by computers and that there are and probably will not be AIs that are any good.

[PlutonianEmpire]

How do I calculate the Semi-Major Axis of an orbit from just the perihelion, and eccentricity?

[Petek]

Atticus,

Perhaps Horgan was referring to automated theorem proving.

[Leoreth]

Originally Posted by PlutonianEmpire

How do I calculate the Semi-Major Axis of an orbit from just the perihelion, and eccentricity?

If a is the semi-major axis, e the eccentricity and p the perihelion, and f the distance from the center of the ellipse to one of its foci (i.e. the gravitational center of the orbit), then p = f+a.

The equation for eccentricity is e = f/a <=> f = e*a.

Plugging that into the perihelion term gives p = e*a+a <=> p = (e+1)*a <=> a = p/(e+1).

[del62]

Does anyone know of any web-sites that will give a good understanding of fourier theory.

[Atticus]

I don't know anything in the web, but found once the start of this book enlightening.

It's not probably worth of the 85 dollars they are selling it for, but if you can borrow it or something like that, read the introduction.

I didn't read the book more though. A sad thing about it was that they used Riemann integral rather than Lebesgue, which makes things a bit harder. I suppose (but am not sure) that Lebesgue integral is a must if you're going to study Fourier analysis from the maths point of view. Physics and such do probably with less.

[dutchfire]

I used the same book as Atticus. I think it's a useful book for a theoretical mathematician but not so much for an applied mathematician/physicist. I don't know if there are any particularly good books for physicists, most of them learn Fourier theory from their quantum mechanics courses.