## Search found 527 matches

- Thu Nov 26, 2015 6:38 am UTC
- Forum: Science
- Topic: convert bits to J/K -- and more entropy mischief
- Replies:
**14** - Views:
**3192**

### Re: convert bits to J/K -- and more entropy mischief

Ah, where does that number come from?

- Wed Nov 25, 2015 6:36 am UTC
- Forum: Science
- Topic: convert bits to J/K -- and more entropy mischief
- Replies:
**14** - Views:
**3192**

### Re: convert bits to J/K -- and more entropy mischief

What I'm looking for is the conversion rates between information entropy (bits) and thermodynamic entropy (J/K)

H = log_b W, but that H is in bits. How do I get that to Joules / Kelvin?

H = log_b W, but that H is in bits. How do I get that to Joules / Kelvin?

- Tue Nov 24, 2015 5:22 am UTC
- Forum: Science
- Topic: convert bits to J/K -- and more entropy mischief
- Replies:
**14** - Views:
**3192**

### convert bits to J/K -- and more entropy mischief

Supposedly, thermodynamic and information entropy are related. I want to find the conversion rate between them. The wikipedia page gives two formulas S = k_b ln W H = log_b M the first for thermodynamic and the second for information entropy how do i compare between the two? also, if you multiply bo...

- Mon Nov 23, 2015 7:23 pm UTC
- Forum: Computer Science
- Topic: Could a machine optimize language source code?
- Replies:
**10** - Views:
**8369**

### Re: Could a machine optimize language source code?

Just wanted to add that a quantum computer wouldn't simply be able to just test "all possible" things at once -- that would be a nondeterministic machine (almost). It's still unknown if the two models are equivalent, but it is suspected that NP complete problems cannot be solved by a quant...

- Sat Nov 21, 2015 5:27 pm UTC
- Forum: Science
- Topic: GR, the SM, SUSY, ST, and QM -- some general questions
- Replies:
**5** - Views:
**1895**

### Re: GR, the SM, SUSY, ST, and QM -- some general questions

Great answers -- this really unconfuses everything in my mind for me, thanks!

- Sat Nov 21, 2015 4:18 am UTC
- Forum: Science
- Topic: GR, the SM, SUSY, ST, and QM -- some general questions
- Replies:
**5** - Views:
**1895**

### GR, the SM, SUSY, ST, and QM -- some general questions

I only have a very vague grasp of how all of these areas of physics overlap with each other, and I'd like to clear that up. I've heard of the standard model of particle physics, but how does that relate to supersymmetry, string theory, and quantum mechanics? I'm also aware that a lot of physics is d...

- Mon Oct 26, 2015 1:57 pm UTC
- Forum: Logic Puzzles
- Topic: "Shoot for the moon. If you miss, you may hit a star."
- Replies:
**8** - Views:
**4588**

### Re: "Shoot for the moon. If you miss, you may hit a star."

Well there's still a chance they'll hit a star that way They could possibly be launched into heliocentric orbit by a slingshot though -- and after that, maybe a chance encounter with a star during the Milky-way Andromeda collision in the future will result in either 1. object hitting the star direct...

- Mon Oct 26, 2015 5:08 am UTC
- Forum: Logic Puzzles
- Topic: "Shoot for the moon. If you miss, you may hit a star."
- Replies:
**8** - Views:
**4588**

### "Shoot for the moon. If you miss, you may hit a star."

This is not so much a logic puzzle as a fermi problem but hopefully it's ok. The quote in title (and many, many variants) claims one who shoots for the moon may hit a star. Find the probability of this. In other words, compute Pr[hit a star | shoot for the moon and miss] Given that the quote leaves ...

- Sun Oct 18, 2015 10:04 pm UTC
- Forum: Mathematics
- Topic: Coin Bias Problem
- Replies:
**1** - Views:
**1493**

### Re: Coin Bias Problem

Bayes' formula is P(A|B) = P(A)*P(B|A)/P(B) B is the event that more tails then heads comes up Let x be the bias: the probability that the coin lands on tails A is the event that the coin is biased towards tails Notice that PDF(x|A) is 2 from 1/2 to 1 and 0 elsewhere P(A) = 1/2, since x is uniformly...

- Sun Oct 18, 2015 8:00 pm UTC
- Forum: Mathematics
- Topic: Intuition for dual of a linear program
- Replies:
**1** - Views:
**2093**

### Intuition for dual of a linear program

In general, I understand the constraints of an LP as giving a lower bound on the objective function. Then the dual raises this lower bound as high as possible, which is conveniently gives the minimum value. http://www.cs.columbia.edu/coms6998-3/lpprimer.pdf This pdf gives a seven step plan for findi...

- Thu Oct 15, 2015 8:25 pm UTC
- Forum: Mathematics
- Topic: Little conjecture
- Replies:
**6** - Views:
**2043**

### Re: Little conjecture

Without using the fact that it has only one zero, the probability that it is composite is 1-2/ln(n) by prime number theorem, which gets pretty close to 1 when n = 2 p -1 is large Since all your 2 p -2 k -1 > 2 p-1 , the probability that each of your 2 p -2 k -1 is composite is about the same: (1-2/(...

- Thu Oct 08, 2015 4:04 pm UTC
- Forum: Science
- Topic: Nuclear explosion powerplant
- Replies:
**31** - Views:
**6069**

### Re: Nuclear explosion powerplant

might the radiation cause the tomatoes to be mutant tomatoes?

- Thu Oct 01, 2015 3:46 pm UTC
- Forum: Mathematics
- Topic: Axioms and multiplication?
- Replies:
**18** - Views:
**3552**

### Axioms and multiplication?

I am aware of only two sets of axioms in popular use, which are ZFC and Peano. ZFC operates on sets and Peano on natural numbers. Is there a set of axioms on real numbers? I'm asking because this page seems to make a bold claim that multiplication isn't repeated addition http://www.maa.org/external_...

- Tue Sep 29, 2015 6:45 pm UTC
- Forum: Mathematics
- Topic: Theoretical problem about traveler salesman
- Replies:
**6** - Views:
**2024**

### Re: Theoretical problem about traveler salesman

If your algorithm always runs in polynomial time, it does not work. Suppose your algorithm runs in polynomial time given G and cost C. To solve TSP(H,K) in polynomial time, feed H and K into your algorithm. Suppose the answer to TSP(H,K) is yes (there does exist such a path)...

- Mon Sep 28, 2015 8:51 pm UTC
- Forum: Mathematics
- Topic: Theoretical problem about traveler salesman
- Replies:
**6** - Views:
**2024**

### Re: Theoretical problem about traveler salesman

My intuition tells me this problem is still NP hard but I'm not completely convinced yet. Notzeb's algorithm gives you a TSP PTAS, but i'm not sure if it's possible to select your guesses so that you'll find the optimal solution in polynomial time. Jaap mentions subset sum but I don't think exactly ...

- Thu Sep 24, 2015 1:10 am UTC
- Forum: Science
- Topic: Nuclear explosion powerplant
- Replies:
**31** - Views:
**6069**

### Re: Nuclear explosion powerplant

Hmm, it seems, unless i'm mistaken, that geothermal plants are only limited by how fast they can generate energy from the heat difference. This means the lake idea won't be very useful. I'm not sure how I would convert a nuclear blast to plasma for the MHD. I still have the containment problem, and ...

- Wed Sep 23, 2015 3:56 pm UTC
- Forum: Science
- Topic: Nuclear explosion powerplant
- Replies:
**31** - Views:
**6069**

### Re: Nuclear explosion powerplant

1. I was kind of hoping the plug would relieve the pressure, saving the chamber 3. Yes, but luckily a 7 meter radius cable out of 2800 Maraging steel will withstand the 400 GN of gravitational force 4. Actually I went with a radius of 100 because I was afraid with anything larger, I wouldn't get any...

- Wed Sep 23, 2015 2:08 pm UTC
- Forum: Science
- Topic: Nuclear explosion powerplant
- Replies:
**31** - Views:
**6069**

### Nuclear explosion powerplant

You have an unlimited supply of thermonuclear weapons, each with a cost of $1 million and with a yield of 1 MT (~4E15 J). Disregarding safety concerns and public outcry, design a powerplant which detonates the bomb and generates electricity. The powerplant should be both economical, and extract a re...

- Fri Sep 18, 2015 3:51 pm UTC
- Forum: Mathematics
- Topic: Bayes theorem applied to sports betting
- Replies:
**6** - Views:
**2524**

### Re: Bayes theorem applied to sports betting

So what you're looking for is the probability distribution of how defective the cars are. Bayes' Theorem: P(H|E) = P(H)*P(E|H)/P(E) In this case H is continuous and E is discrete, so when I say P(H) and P(H|E) that's really a PDF. P(H) is your prior -- your guess on how defective the cars are. Say t...

- Fri Sep 18, 2015 1:04 pm UTC
- Forum: Mathematics
- Topic: Bayes theorem applied to sports betting
- Replies:
**6** - Views:
**2524**

### Re: Bayes theorem applied to sports betting

what you need, which is missing, is the probability that those cars are defective, and the probability that a defective car can win a race, and how certain you are on those previous two items.

- Mon Sep 14, 2015 1:52 pm UTC
- Forum: Science
- Topic: space fountain energy fermi estimation
- Replies:
**14** - Views:
**3396**

### Re: space fountain energy fermi estimation

according to wikipedia, on the rising side of the pellet stream, a series of devices are used to extract energy and slow down the pellets. on the falling side, that energy is used to accelerate the particles downward. this setup exerts the upward forces necessary to keep the tower up. the tower can'...

- Sun Sep 13, 2015 7:21 pm UTC
- Forum: Science
- Topic: space fountain energy fermi estimation
- Replies:
**14** - Views:
**3396**

### Re: space fountain energy fermi estimation

one thing that concerns me is that the 1 percent figure is just when the flywheel is spinning. whereas the roundtrip energy efficiency is more like 90% with 10% loss. and since the fountain is constantly converting between kinetic and potential energy, it seems like the second scenario is the better...

- Fri Sep 11, 2015 8:40 pm UTC
- Forum: Science
- Topic: space fountain energy fermi estimation
- Replies:
**14** - Views:
**3396**

### Re: space fountain energy fermi estimation

i'm no upper-atmospherologist but that sounds like placing an awful amount of trust in the constant stability of the wind

- Fri Sep 11, 2015 5:34 pm UTC
- Forum: Science
- Topic: space fountain energy fermi estimation
- Replies:
**14** - Views:
**3396**

### Re: space fountain energy fermi estimation

It would only be the same if you had a turbine below collecting wind energy from the helicopter and blowing air back up and the helicopter was able to run on the electricity generated by that upward stream

A helicopter with frictionless bearings cannot stay up indefinitely. This will.

A helicopter with frictionless bearings cannot stay up indefinitely. This will.

- Fri Sep 11, 2015 3:48 pm UTC
- Forum: Science
- Topic: space fountain energy fermi estimation
- Replies:
**14** - Views:
**3396**

### space fountain energy fermi estimation

The design for a space fountain looks like it could be applied to constructing extremely tall skyscrapers. I'm looking for a fermi estimation to how many watts it would take to support a skyscraper weighing m kilograms. There are two main sources of energy loss 1. Drag between particles and air in t...

- Fri Sep 11, 2015 4:41 am UTC
- Forum: Mathematics
- Topic: I don't seem to understand my own brain teaser, please help!
- Replies:
**22** - Views:
**5023**

### Re: I don't seem to understand my own brain teaser, please h

the average case was, when you said, "There is a 55% chance of heads, which will double your remaining earthly time, and a 45% chance of tails, which will reduce your remaining earthly time by 70%." This means that for every flip there is a 55%/45% chance of heads versus tails; and that a...

- Fri Sep 11, 2015 1:52 am UTC
- Forum: Mathematics
- Topic: I don't seem to understand my own brain teaser, please help!
- Replies:
**22** - Views:
**5023**

### Re: I don't seem to understand my own brain teaser, please h

The expected value is still 10*(1.235)^1000 days. However, this is made up of a very small chance of living a very long time, and a very large chance of living a very short time. Wait, isn't this wrong? If I win 55 times and lose 45 times I end up behind. Isn't the only valid way to do this with lo...

- Thu Aug 13, 2015 3:18 pm UTC
- Forum: Mathematics
- Topic: maximization on a function with constraints
- Replies:
**4** - Views:
**1541**

### Re: maximization on a function with constraints

I'm confused by this sentence. The first half defines g as a derivative of f, then the second half looks like a new and different definition of g? Also, f(1, q) is a constant if q is a constant, so I'm not sure how you would maximize it. g is a derivative on f, but f(x,t) isn't fixed for t != 0 yet...

- Wed Aug 12, 2015 6:30 pm UTC
- Forum: Mathematics
- Topic: maximization on a function with constraints
- Replies:
**4** - Views:
**1541**

### maximization on a function with constraints

I'm given a function f(x,0) which is f(x,t) at t = 0, and T(x,t) Both of these functions map the [0,1] x R+ to R+ How can I find g(x,t) = d/dt f(x,t) which maximizes f(1,q), for a constant q in R+? Also subject to the constraint that for all t, f(1,t) = ∫ 0 1 g(x,t)/T(x,t) dx I'm not sure if it matt...

- Mon Aug 10, 2015 3:37 pm UTC
- Forum: Mathematics
- Topic: Powertrains
- Replies:
**2** - Views:
**4252**

### Re: Powertrains

yeah if you take that definition of indestructible then 2534 is, but the book specifically mentions the two numbers as fixed points, which 2534 would not be. also reduce doesn't necessarily mean to reduce in size in general, mathematically speaking. you can say P(2534) reduces to 2592 in the same wa...

- Fri Aug 07, 2015 4:48 am UTC
- Forum: Science
- Topic: A million years
- Replies:
**59** - Views:
**8939**

### Re: A million years

Slightly off topic, but would you happen to know how temperature corresponds to intensity or power? http://www.setileague.org/photos/miscpix/waterhol.gif this image seems to suggest that the CMB has an intensity of around 3K, but from what I know, doesn't temperature just specific a specific black b...

- Thu Aug 06, 2015 3:16 pm UTC
- Forum: Science
- Topic: A million years
- Replies:
**59** - Views:
**8939**

### Re: A million years

sure, i just wasnt sure if it might get drowned out by other sources like cmb or exoplanets' magnetospheres or blocked by objects in space. As i said before, it would be nice if there was data somewhere on the "brightness" of space in all frequencies of em

- Thu Aug 06, 2015 2:47 am UTC
- Forum: Science
- Topic: A million years
- Replies:
**59** - Views:
**8939**

### Re: A million years

well then, with an alternate angle of attack, why not launch a new probe every few years to act as relay stations. the planets might not be aligned properly, making probe launch tricky, but that's nothing that can't solved with brute force. OR, just wait a million years, and when the probe has info ...

- Wed Aug 05, 2015 4:10 pm UTC
- Forum: Science
- Topic: A million years
- Replies:
**59** - Views:
**8939**

### Re: A million years

if not elf radiowaves, how about gamma rays. Takes about 1E20 times more energy but if you increase telescope area to 1E9 sq km, you get a manageable 1E7J/photon

- Tue Aug 04, 2015 11:36 pm UTC
- Forum: Science
- Topic: A million years
- Replies:
**59** - Views:
**8939**

### Re: A million years

I haven't been able to find any data on this but are there any EM spectrum wavelengths that just don't appear at all from natural sources? If there is such a frequency, sending just one photon back should be enough to transmit data. For example, ELF radio waves have energy on the order of 1E-32 joul...

- Wed Jul 29, 2015 2:16 am UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3772**

### Re: N-Body Simulation questions

I implemented metric expansion and also leapfrog integration. For some reason, the simulations with leapfrog integration seem to collapse much slowly.When I add metric expansion (linear expansion from 5E23 m to 1E24 m), barely any clusters have time to form. However, when I computed the error in the...

- Thu Jul 23, 2015 11:54 am UTC
- Forum: Science
- Topic: A million years
- Replies:
**59** - Views:
**8939**

### Re: A million years

10^12 kilometers is a fraction of a light-year -- it's nowhere near enough to get to any star. The communication at 10^12 kilometers should be easy -- we could probably do it now. Communication at tens of light-years is harder, but we can simply wait a million years for the technology to get there b...

- Wed Jul 22, 2015 11:32 pm UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3772**

### Re: N-Body Simulation questions

If it's necessary I can try a run with 16384 or 65536 particles. I looked up the zel'dovich approximation and the math seems to be a bit beyond me. By power spectrum do you mean the distribution of the magnitudes of the displacements? Can it be described as a normal/poisson/gamma distribution? Curre...

- Wed Jul 22, 2015 1:14 pm UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3772**

### Re: N-Body Simulation questions

I was actually trying to find the equation for the repulsive/radiation force, but ended up only implementing plummer softening. Since radiation drops off proportional to distance squared, I reasoned modeling it would be equivalent to weakening the gravitational constant a little. Plus, as icicletast...

- Tue Jul 21, 2015 9:28 pm UTC
- Forum: Science
- Topic: N-Body Simulation questions
- Replies:
**19** - Views:
**3772**

### Re: N-Body Simulation questions

Actually it turned out to be a pretty severe bug in my Barnes Hut implementation which I've fixed. :oops: Here's the corrected simulation , covering just 15 billion years Here's frame four hundred . There's definitely clusters and voids, but I'm not sure about the filaments. With a bit of creative l...