## Search found 526 matches

- Mon Jul 20, 2015 2:19 am UTC
- Forum: Science
- Topic: Pluto down, next stop...interstellar?
- Replies:
**30** - Views:
**5818**

### Re: Pluto down, next stop...interstellar?

How would planets create interference? I know Jupiter produces radio waves but their wavelength isn't anywhere near 10 km. And if the planets in the destination system do produce radiowaves at that wavelength, we can examine it and pick a different frequency beforehand. If it's really neccessary, wi...

- Sun Jul 19, 2015 6:14 pm UTC
- Forum: Science
- Topic: Pluto down, next stop...interstellar?
- Replies:
**30** - Views:
**5818**

### Re: Pluto down, next stop...interstellar?

cant we just send signals as radio waves, or anything not in the center of the blackbody spectrum. the spectral radiance of a 5790K blackbody is 1.4E-100 W/m^2/sr/m at 10km wavelength, so we shouldn't get any interference from the stars at 4 lightyears and with a 1kW transmitter, the aercibo telesco...

- Sun Jul 19, 2015 12:55 am UTC
- Forum: Mathematics
- Topic: sum and product of natural number
- Replies:
**9** - Views:
**2765**

### Re: sum and product of natural number

I understand it a bit more now -- though thinking about it hurts my brain. I was hoping to compute the pair as a function of the number of times the mathematicians ask each other but that seems out of the question now.

- Sun Jul 19, 2015 12:40 am UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3681**

### Re: N-Body Simulation questions

I tried it out, and it seems to work ok. But I'm still not seeing filaments. The uniform grid seems to collapse, forming some geometric patterns (probably because of the barnes-hut quadtree). Then, large areas of high and low density temporarily appear before the simulation reverts to a more chaotic...

- Fri Jul 17, 2015 11:42 pm UTC
- Forum: Mathematics
- Topic: sum and product of natural number
- Replies:
**9** - Views:
**2765**

### sum and product of natural number

I was reading this post: https://mathoverflow.net/questions/9754/magic-trick-based-on-deep-mathematics/31656#31656 But I'm a bit confused what the apparent "strategy" is. Can anyone explain how the mathematicians can figure out what number it is? I think it may be related to another puzzle...

- Fri Jul 17, 2015 12:56 pm UTC
- Forum: Science
- Topic: Puzzling artifacts and reasonable reasoning
- Replies:
**79** - Views:
**13875**

### Re: Puzzling artifacts and reasonable reasoning

While there may not be another ratio within 1% of the stones, it is relatively likely that the mass of stones were altered after creation by around 10% from erosion or some human activity, meaning any explanatory ratio off by up to 10% is good enough.

- Wed Jul 15, 2015 12:39 pm UTC
- Forum: Science
- Topic: Puzzling artifacts and reasonable reasoning
- Replies:
**79** - Views:
**13875**

### Re: Puzzling artifacts and reasonable reasoning

But you can assign odds to whether time-travel/FTL are possible and it makes sense to assign odds to whether they exist after that. If a rich man had amnesia and forgot how he acquired his wealth, he might reason winning the lottery was highly unlikely, therefore he probably didn't win the lottery. ...

- Tue Jul 14, 2015 10:02 pm UTC
- Forum: Science
- Topic: Puzzling artifacts and reasonable reasoning
- Replies:
**79** - Views:
**13875**

### Re: Puzzling artifacts and reasonable reasoning

Whoever was weighing the stones must have been hallucinating (if that doesn't fall under the hoax category).

- Tue Jul 14, 2015 1:08 pm UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3681**

### Re: Equation for repulsive forces in N-body simulation?

thanks! By the way, a bit off-topic, but would you happen to have any idea on what would be a good initial starting condition? I've read that a lot of large scale simulations use actual cosmological data, but if I just wanted to place the particles, how should I? I was thinking the mass of the parti...

- Tue Jul 14, 2015 12:52 pm UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3681**

### Re: Equation for repulsive forces in N-body simulation?

Just for fun, I'm trying to simulate the large scale structure of the universe by placing a bunch of particles and hoping they collapse into filaments and clusters and such. I wanted a repulsive force both to prevent everything from clumping together and to prevent force from going to infinity as ra...

- Sun Jul 12, 2015 3:22 am UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3681**

### Re: Equation for repulsive forces in N-body simulation?

Thank you. Just to be clear, u is the speed of the stellar wind?

- Sat Jul 11, 2015 7:00 pm UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3681**

### N-Body Simulation questions

I'm trying to model an N-body system, and in addition to gravity, I want to have a force which models the repulsive forces of stellar wind, star formation, and other phenomenon. Hopefully something of the form F(m1, m2, distance). I tried using PV = nRT to solve for T, then using Stefan-Boltzmann, b...

- Thu Jul 09, 2015 12:15 pm UTC
- Forum: Mathematics
- Topic: variance of weighed sum of random variables
- Replies:
**7** - Views:
**2162**

### Re: variance of weighed sum of random variables

Thanks, that's the word I was looking for, and http://stats.stackexchange.com/a/16609 gives a nice expression for it.

- Thu Jul 09, 2015 3:40 am UTC
- Forum: Mathematics
- Topic: variance of weighed sum of random variables
- Replies:
**7** - Views:
**2162**

### Re: variance of weighed sum of random variables

I just realized what I really needed wasn't what I thought I was looking for here. What I actually want is the variance of the weighed average of two probability mass functions X and Y. In other words, the variance of the probability mass function Z = aX+bY, given a+b = 1. I'm not exactly sure what ...

- Wed Jul 08, 2015 11:04 pm UTC
- Forum: Mathematics
- Topic: Prove that 25+8*(n!)) is not square
- Replies:
**10** - Views:
**3293**

### Re: Prove that 25+8*(n!)) is not square

Somewhat related to this https://en.wikipedia.org/wiki/Brocard%27s_problem

I tested up to n = 20000 without finding any squares

I tested up to n = 20000 without finding any squares

- Tue Jul 07, 2015 10:01 pm UTC
- Forum: Mathematics
- Topic: Wanted: Elegant proof of sin(x)/x limit
- Replies:
**49** - Views:
**8223**

### Re: Wanted: Elegant proof of sin(x)/x limit

If you can use area of circle = pi r^2, then you can show the area of a sector as a ratio of the circle area: pi r^2 * (theta/2pi) = theta r^2 /2

- Mon Jul 06, 2015 9:45 pm UTC
- Forum: Mathematics
- Topic: variance of weighed sum of random variables
- Replies:
**7** - Views:
**2162**

### Re: variance of weighed sum of random variables

let sum = 2*A = A + A if variances linearly add var(sum) = var(A) + var(A) = 2*var(A) but if weights scale standard deviation std(sum) = std(A) + std(A) = 2*std(A) var(sum) = sqrt(std(sum)) = sqrt(2)*sqrt(std(A)) = sqrt(2)*var(A) this is a contradiction though edit: whoops i see where i messed up no...

- Mon Jul 06, 2015 5:09 pm UTC
- Forum: Mathematics
- Topic: variance of weighed sum of random variables
- Replies:
**7** - Views:
**2162**

### variance of weighed sum of random variables

how do i find the variance of a weighed sum of random variables? http://stats.stackexchange.com/questions/5392/variance-of-two-weighted-random-variables the question in this link suggests it's the sum of the (w_i*std_i)^2 given that correlation is 0 the first answer suggests it's the square of the s...

- Sun Jul 05, 2015 2:23 pm UTC
- Forum: Mathematics
- Topic: Mancala game and factorization of big numbers
- Replies:
**7** - Views:
**1573**

### Re: Mancala game and factorization of big numbers

Dixon's factorization algorithm factorizes in O(exp(2*sqrt(2)*log(n)*log(log(n)))) compared to at least O(sqrt(2

Äsymptotically, 2*sqrt(2)*log(n)*log(log(n)) < n*log(2)/2

^{n})) = O(2^{n/2}) = O(exp(n*log(2)/2)) for this.Äsymptotically, 2*sqrt(2)*log(n)*log(log(n)) < n*log(2)/2

- Tue Jun 30, 2015 11:43 pm UTC
- Forum: Mathematics
- Topic: Attrition population model and Laplace transform
- Replies:
**1** - Views:
**1290**

### Attrition population model and Laplace transform

I was trying to come up with a population model for attrition today. Each member of the population has a risk of death per unit of time, so that you have a distribution A(r,t) which describes the distribution of the population across the axis of risk at a certain time t. Then dA/dt = -rA, by seperat...

- Mon Jun 22, 2015 5:37 pm UTC
- Forum: Mathematics
- Topic: A Diophantine equation related to happy bases
- Replies:
**3** - Views:
**1458**

### Re: A Diophantine equation related to happy bases

by https://en.m.wikipedia.org/wiki/Fermat's_theorem_on_sums_of_two_squares we know any counter example has b^2+1 = 1 mod 4. by http://mathworld.wolfram.com/SumofSquaresFunction.html we know the number of ways we can write a 1 mod 4 prime as a sum of squares is 1, and since 1+b^2 works, there are no ...

- Mon Jun 15, 2015 1:40 pm UTC
- Forum: Mathematics
- Topic: standard deviation on number of events.
- Replies:
**15** - Views:
**3117**

### Re: standard deviation on number of events.

with some algebra i think you can find it for e > u. let e be epsilon, t be time (20), u be mu. t/(u+e) = t/u + [ - t/u + t/(u+e) ] = t/u + [tu - t (u+e)]/(ue+u^2) = t/u - te/(u^2+ue) so std = ts/(u^2 + us) where s is the original std. which is remarkably similar to the other answer, ts/u^2, other t...

- Sat Jun 13, 2015 5:01 pm UTC
- Forum: Mathematics
- Topic: standard deviation on number of events.
- Replies:
**15** - Views:
**3117**

### Re: standard deviation on number of events.

Yes, that's what I was looking for -- thank you.

edit: what happens if i have a large standard deviation making ε > μ

this makes (20/μ)*(1- ε/μ + (ε/μ)2 - ...) diverge and you end with ???

edit: what happens if i have a large standard deviation making ε > μ

this makes (20/μ)*(1- ε/μ + (ε/μ)2 - ...) diverge and you end with ???

- Sat Jun 13, 2015 3:21 pm UTC
- Forum: Mathematics
- Topic: standard deviation on number of events.
- Replies:
**15** - Views:
**3117**

### Re: standard deviation on number of events.

Yes, that's what I was looking for -- thank you.

- Sat Jun 13, 2015 1:09 am UTC
- Forum: Mathematics
- Topic: Numbers representable by successive exponentiation
- Replies:
**13** - Views:
**1928**

### Re: Numbers representable by successive exponentiation

On a tangential note, would it be impossible to do much better than just a decimal system from an information theory standpoint? You might as well do (10*n1+n2)*10^(10*n3+n4) and now you can have, within a magnitude of 1E57 10*10^55 11*10^55 ... 99*10^56 10*10^57 which is certainly a lot more accuracy

- Sat Jun 13, 2015 12:36 am UTC
- Forum: Mathematics
- Topic: standard deviation on number of events.
- Replies:
**15** - Views:
**3117**

### Re: standard deviation on number of events.

I'm not sure I understand.

I understand vaguely/intuitively why the standard deviation of the harmonic mean would help -- but once I have it, what do I do with it?

I understand vaguely/intuitively why the standard deviation of the harmonic mean would help -- but once I have it, what do I do with it?

- Fri Jun 12, 2015 3:03 am UTC
- Forum: Mathematics
- Topic: standard deviation on number of events.
- Replies:
**15** - Views:
**3117**

### Re: standard deviation on number of events.

I'm afraid I wasn't making myself clear enough. If I knew the times between the events had a mean of say, 5 and a standard deviation of 3, then the standard error of the mean would tell me that the average of the times between nine events would have a deviation of 3/sqrt(9) = 1. But I want to know, ...

- Thu Jun 11, 2015 6:49 pm UTC
- Forum: Mathematics
- Topic: standard deviation on number of events.
- Replies:
**15** - Views:
**3117**

### standard deviation on number of events.

Given the times of a series of events, I can find the distribution of the amount of time elapsed between each event. Given this, I can predict the mean number of events which will happen in a certain time-frame -- but how can I find the standard deviation of that prediction? I'm not sure how to appr...

- Mon Jun 01, 2015 8:42 pm UTC
- Forum: Mathematics
- Topic: Finding result of calc with upto 14 digits exponent
- Replies:
**4** - Views:
**1802**

### Re: Finding result of calc with upto 14 digits exponent

I'm not familiar with mathematica but given that there's 39 trillion digits in the product, you would need a lot of memory or drive space for that. I doubt it's possible to do the computation in any reasonable amount of time.

- Mon Jun 01, 2015 10:46 am UTC
- Forum: Mathematics
- Topic: Stubborn bettor
- Replies:
**99** - Views:
**10987**

### Re: Stubborn bettor

Do you mean 490? I'm pretty sure the chance of losing $490 is 2%. You keep betting until you have $10 or go broke so there's no chance of reaching $9, 8, 7, or so on. The only outcomes are -$490 or +$10.

- Sat May 30, 2015 9:25 pm UTC
- Forum: Mathematics
- Topic: Stubborn bettor
- Replies:
**99** - Views:
**10987**

### Re: Stubborn bettor

shouldn't he overshoot $10 at least some of the time, making k > 490?

- Sat May 30, 2015 1:36 pm UTC
- Forum: Mathematics
- Topic: Stubborn bettor
- Replies:
**99** - Views:
**10987**

### Re: Stubborn bettor

what do you mean by "rebets his current wins"?

- Tue May 26, 2015 12:48 am UTC
- Forum: Mathematics
- Topic: Statistics question: Quantifying sample bias?
- Replies:
**3** - Views:
**1329**

### Re: Statistics question: Quantifying sample bias?

It doesn't really make sense without N. If you flip a coin once and get 100%/0% instead of the expected 50%/50% it's not very surprising. But if you flip it a thousand times and get 100%/0% something is going on. If you just want some arbitrary threshold, play around with random N values and pick on...

- Sun May 24, 2015 8:15 pm UTC
- Forum: Mathematics
- Topic: Statistics question: Quantifying sample bias?
- Replies:
**3** - Views:
**1329**

### Re: Statistics question: Quantifying sample bias?

How about a chi-squared test ? For example: suppose in a sample size of 1000 we expect 0.1%/99.9% (1 and 999) and find 1%/90% (10 and 990). Then our chi-squared statistic is (1-10)²/1+(999-990)²/999 = 81.081. We have 1 degree of freedom so P(X² >= 81.081) ~= 0, thus it is significant. With the 51/49...

- Sat May 16, 2015 2:44 am UTC
- Forum: Mathematics
- Topic: Cutting and rearranging a half-colored square
- Replies:
**28** - Views:
**3846**

### Re: Cutting and rearranging a half-colored square

I don't think I understand along which axis you are cutting? Are the cuts perpendicular to the x-axis? Could you draw a picture of the first two iterations?

- Mon May 11, 2015 10:38 pm UTC
- Forum: Science
- Topic: reducing joules to elementary units
- Replies:
**5** - Views:
**1315**

### Re: reducing joules to elementary units

The fact that a formula for calculating a particular value has a coefficient, is totally unrelated to what the units are doing. Sure, changing from one system of units to another often involves an extra conversion factor, but going from kilograms * meters^2/seconds^2 to joules does not (or has conv...

- Mon May 11, 2015 11:54 am UTC
- Forum: Science
- Topic: reducing joules to elementary units
- Replies:
**5** - Views:
**1315**

### Re: reducing joules to elementary units

I'm not sure i understand. What's the difference between kg * m^2/s^2 and 1 kg * m^2/s^2?

- Mon May 11, 2015 2:35 am UTC
- Forum: Science
- Topic: reducing joules to elementary units
- Replies:
**5** - Views:
**1315**

### reducing joules to elementary units

kinetic energy is 1/2 mass * velocity^2, or 1/2 kilograms * meters^2/seconds^2

wolfram alpha agrees: http://www.wolframalpha.com/input/?i=kg ... +in+joules

except... where did the 1/2 term go? what happened to the coefficient?

wolfram alpha agrees: http://www.wolframalpha.com/input/?i=kg ... +in+joules

except... where did the 1/2 term go? what happened to the coefficient?

- Mon May 04, 2015 12:00 am UTC
- Forum: Mathematics
- Topic: Can anyone solve this probability problem?
- Replies:
**15** - Views:
**2734**

### Re: Can anyone solve this probability problem?

to be clear, the k crucibles are created each with an k-sided dice if the prime dice rolls k?

- Sat May 02, 2015 1:29 pm UTC
- Forum: Mathematics
- Topic: Dice Probabilities in any order.
- Replies:
**7** - Views:
**1543**

### Re: Dice Probabilities in any order.

yes, P(aabbcc) is the same as P(dfefde)