## Search found 497 matches

- Mon Jul 07, 2008 2:55 pm UTC
- Forum: Mathematics
- Topic: how many smooth functions are there?
- Replies:
**24** - Views:
**2897**

### Re: how many smooth functions are there?

Unfortunately, to do that you have to choose an ordering for each of those countable sets. That the sets are countable means the collections of bijections with the naturals are nonempty, but you need an element of the product of all those collections to use your argument.

- Mon Jun 30, 2008 2:13 pm UTC
- Forum: Mathematics
- Topic: Your Axiom of Choice is SILLY
- Replies:
**60** - Views:
**8654**

### Re: Your Axiom of Choice is SILLY

Another way to state Choice is that products of nonempty sets are nonempty. That seems pretty intuitive to me.

- Tue Jun 24, 2008 1:02 pm UTC
- Forum: Science
- Topic: Superluminal velocities
- Replies:
**14** - Views:
**2004**

### Re: Superluminal velocities

Sure. But how do you plan to obtain a material with n<1?

- Tue Jun 24, 2008 12:54 pm UTC
- Forum: Mathematics
- Topic: Irrational indices
- Replies:
**12** - Views:
**2882**

### Re: Irrational indices

For nonnegative x and real a, you can also define x a by first defining rational exponents (the way you've done), and then extending the definition to be continuous. In other words, x^a := \displaystyle\lim_{n\to\infty} \left(x^{\displaystyle p_n/q_n}\right) where p_n/q_n\to a as n\to \infty...

- Mon Jun 23, 2008 3:33 pm UTC
- Forum: Science
- Topic: Superluminal velocities
- Replies:
**14** - Views:
**2004**

### Re: Superluminal velocities

Note that the "getting light to go faster" paragraph you quoted is riddled with "citation needed" notices - I wouldn't take it without a grain of salt. On the other hand, you're absolutely correct in inferring that slowing down light does not change the "speed limit" im...

- Thu Jun 19, 2008 2:50 pm UTC
- Forum: Science
- Topic: Black body
- Replies:
**11** - Views:
**2396**

### Re: Black body

It isn't the total amount of light that reflects; it's the percentage. If you shine a ridiculously bright light at the sun, most of it will still be absorbed and re-emitted as (approximate) blackbody radiation, and only a small proportion will be reflected.

- Wed Jun 18, 2008 5:38 pm UTC
- Forum: Science
- Topic: Twin paradox: a question
- Replies:
**18** - Views:
**4399**

### Re: Twin paradox: a question

The signal would arrive as if it were being fast-forwarded - if your television is capable of understanding the sped-up signal, then you'll also be watching the program in fast-forward. This fast-forwarding is really the same phenomenon as the blueshift. As for the accelerating twin in my exposition...

- Wed Jun 18, 2008 2:00 pm UTC
- Forum: Science
- Topic: Twin paradox: a question
- Replies:
**18** - Views:
**4399**

### Re: Twin paradox: a question

Would you mind showing us how special relativity handles the twin paradox from the reference frame of the accelerating twin? Sure. Let's suppose we're in flat 1+1 Minkowski space, and that one twin's worldline is given by (t,x)=(0,\tau) , i.e. the twin is at rest in some chosen coor...

- Tue Jun 17, 2008 10:21 pm UTC
- Forum: Science
- Topic: Twin paradox: a question
- Replies:
**18** - Views:
**4399**

### Re: Twin paradox: a question

the tein paradox cant be fully described using special relativity, you need general relativity. as stated above, the real trickery happens when the traveling twin TURNS AROUND (i.e. accelerates) if he just kept rocketing off and never came home, it is indeterminate which is older and which is young...

- Tue Jun 17, 2008 6:17 pm UTC
- Forum: Science
- Topic: Miscellaneous Science Questions
- Replies:
**2949** - Views:
**710167**

### Re: Common Questions

The reason faster-than-light communication is believed to be impossible is that, if such a consistent method of communication existed, special relativity tells us that we would be able to use this method to communicate back in time as well, and this opens up all kinds of paradoxes.

- Tue Jun 17, 2008 9:16 am UTC
- Forum: Language/Linguistics
- Topic: "Natural Selection" - Compound noun or adjective+noun?
- Replies:
**10** - Views:
**3193**

### Re: "Natural Selection" - Compound noun or adjective+noun?

I'd vote for "naturally deselected" as well. Would anyone say "natural selected"? I would. Ok, so it isn't just "naturally deselected" that sounds odd to you. If you're not willing to put "naturally deselected", "undergo natural deselection" seems l...

- Mon Jun 16, 2008 10:44 pm UTC
- Forum: Language/Linguistics
- Topic: "Natural Selection" - Compound noun or adjective+noun?
- Replies:
**10** - Views:
**3193**

### Re: "Natural Selection" - Compound noun or adjective+noun?

I'd vote for "naturally deselected" as well. Would anyone say "natural selected"?

- Mon Jun 16, 2008 1:59 pm UTC
- Forum: Mathematics
- Topic: Is there an equation for ANY function?
- Replies:
**47** - Views:
**6638**

### Re: Is there an equation for ANY function?

Yeah, I really don't think the IFT helps at all here. Essentially, the IFT says under certain conditions "the vertical line test doesn't fail around here", i.e. "there's a bit of function that matches a part of this graph." Since we're already assuming that the graph is a graph o...

- Sat Jun 14, 2008 3:20 pm UTC
- Forum: Science
- Topic: I don't understand antimatter
- Replies:
**32** - Views:
**4048**

### Re: I don't understand antimatter

If antiparticles go backwards in time, wouldn't they obey a backwards 2LoT, et cetera? Explain this Clarissa! Yes, they would. However, the "backwards" second law is the same as the forwards one. In other words, the second law states that as time moves forward, entropy tends to increase. ...

- Wed Jun 11, 2008 5:00 pm UTC
- Forum: Mathematics
- Topic: Infinite Dimensional Hypersphere
- Replies:
**26** - Views:
**3028**

### Re: Infinite Dimensional Hypersphere

Yeyui: It is the function you gave, which is a metric on the space of points where it (exists and) is finite. In particular, it's a metric on the "hyperball" we're considering.

- Wed Jun 11, 2008 12:36 am UTC
- Forum: Science
- Topic: A question about the consequences of relativity.
- Replies:
**21** - Views:
**3792**

### Re: A question about the consequences of relativity.

A proton, or a positron, or a W+, or 500 protons and 499 electrons. There isn't anything really special about gamma rays that causes them to be emitted by evaporating black holes, it's just our word for energetic photons. Other particles are bound to be mixed in, but possibly in smaller quantities a...

- Tue Jun 10, 2008 11:32 am UTC
- Forum: Language/Linguistics
- Topic: Little editing/grammar mistakes that drive you up the wall
- Replies:
**784** - Views:
**109477**

### Re: Little editing/grammar mistakes that drive you up the wall

Depends if they're wearing thick gloves. Otherwise, that sentence and ones like it drive me madly.Is anyone else driven MAD by "I feel badly"?

- Tue Jun 10, 2008 11:21 am UTC
- Forum: Science
- Topic: A question about the consequences of relativity.
- Replies:
**21** - Views:
**3792**

### Re: A question about the consequences of relativity.

1) Not as such. If you have a proton traveling at high speed, you can always boost to its rest frame, in which it won't seem to be moving at all. (You can think of it this way: The relevant qualities of a particle are its energy and momentum, and any relativistic quantity that depends on the energy ...

- Tue Jun 10, 2008 2:47 am UTC
- Forum: Movies and TV Shows
- Topic: Doctor Whom
- Replies:
**4990** - Views:
**749850**

### Re: Doctor Who

I still don't get it. Died "originally"? Here's how I see it, in chronological order: ⋅ Old Doctor arrives from the future with the knowledge that River will die and how to "save" her. ⋅ Old Doctor takes River on a date, gives her the sonic screwdrive...

- Tue Jun 10, 2008 2:34 am UTC
- Forum: Movies and TV Shows
- Topic: Doctor Whom
- Replies:
**4990** - Views:
**749850**

### Re: Doctor Who

I don't get

**Spoiler:**

- Mon Jun 09, 2008 11:33 pm UTC
- Forum: Mathematics
- Topic: Infinite Dimensional Hypersphere
- Replies:
**26** - Views:
**3028**

### Re: Infinite Dimensional Hypersphere

Nevertheless, it is a metric on the set of all sequences of real numbers for which the series converges (called [imath]\ell^2[/imath]). Since we're only concerning ourselves with those sequences for which the series converges to a value at most one, we're fine.

- Mon Jun 09, 2008 11:27 pm UTC
- Forum: Language/Linguistics
- Topic: Little editing/grammar mistakes that drive you up the wall
- Replies:
**784** - Views:
**109477**

### Re: Little editing/grammar mistakes that drive you up the wall

I can't tell whether you're being serious, this post and my earlier one both contain comma splices.

- Mon Jun 09, 2008 11:24 pm UTC
- Forum: Science
- Topic: A question about the consequences of relativity.
- Replies:
**21** - Views:
**3792**

### Re: A question about the consequences of relativity.

I think saying that the mass of an object increases when you speed up is a bad way to look at it. The rest mass stays the same. However, in your equations a factor gamma shows up. This causes the extra inertia. For example, instead of E=mc^2 you should write E=\gamma mc^2 , where \gamma = 1/\sqrt&#...

- Mon Jun 09, 2008 8:15 pm UTC
- Forum: Language/Linguistics
- Topic: Little editing/grammar mistakes that drive you up the wall
- Replies:
**784** - Views:
**109477**

### Re: Little editing/grammar mistakes that drive you up the wall

No, a comma splice is the name for two independent clauses joined by a comma, it is jarring and should be avoided.

- Sun Jun 08, 2008 4:27 pm UTC
- Forum: Mathematics
- Topic: Your Axiom of Choice is SILLY
- Replies:
**60** - Views:
**8654**

### Re: Your Axiom of Choice is SILLY

If there were attempted proofs of it, it wouldn't be called an axiom would it? Seriously though, it's been shown that if the other axioms of set theory are consistent, then it's impossible to prove the axiom of choice from them. (And also impossible to disprove it.) Your attempt does illustrate an i...

- Sat Jun 07, 2008 11:12 am UTC
- Forum: Science
- Topic: Question regarding compton scattering
- Replies:
**7** - Views:
**1335**

### Re: Question regarding compton scattering

It sounds like you're drawing some incorrect conclusions from the photoelectric effect. I'll recap, and show how Compton scattering doesn't contradict it. In the photoelectric effect, you shine light on metal and electrons come off, observing the following: 1. Below a certain critical frequency, no ...

- Fri Jun 06, 2008 11:20 pm UTC
- Forum: Mathematics
- Topic: joint probability question.
- Replies:
**2** - Views:
**1081**

### Re: joint probability question.

No, the domains don't have to be the same. Let f be a probability density function on XxY. Then if f(x,y) factors as g(x)h(y), you can pick out g(x) as g(x)=\int f(x,y)\ dy , and similarly h(y), so f(x,y) factors iff f(x,y) = \left(\int f(x,y')\ dy'\right&...

- Fri Jun 06, 2008 7:22 pm UTC
- Forum: Mathematics
- Topic: Braid groups
- Replies:
**4** - Views:
**1232**

### Re: Braid groups

I think the idea is that B

_{n}is generated by the s_{i}'s, so there's at most one homomorphism from B_{n}to G sending s_{i}to A_{i}. The conditions listed on the A_{i}'s ensure that a homomorphism exists, so it's also unique.- Fri Jun 06, 2008 7:14 pm UTC
- Forum: Language/Linguistics
- Topic: "Mappamondo" in English?
- Replies:
**17** - Views:
**5538**

### Re: "Mappamondo" in English?

That sounds like the kind of atlas I'm used to seeing. If I heard "globe" in the context of maps, I'd surely think of something like the image you posted, even though in general a globe is just a spherical object.

- Fri Jun 06, 2008 10:57 am UTC
- Forum: Science
- Topic: Telling Matter from Antimatter
- Replies:
**6** - Views:
**1719**

### Re: Telling Matter from Antimatter

It's a famous theorem of quantum field theory that any (sufficiently realistic) quantum field theory must have CPT symmetry; that is, if you 1. Flip all the charges in the universe (C), 2. Undergo parity reversal (P, reflection across a mirror/space inversion), and 3. Reverse the direction of time (...

- Tue Jun 03, 2008 9:31 pm UTC
- Forum: Movies and TV Shows
- Topic: Doctor Whom
- Replies:
**4990** - Views:
**749850**

### Re: Doctor Who

I can somewhat identify with them - I think it's disrespectful to ignore someone's last wishes, and in this case that translates to the hearing of their last words. However, I agree that it's one of the creepiest things I've ever seen, and I can also identify with the one guy (was it proper Dave?) w...

- Tue Jun 03, 2008 6:28 pm UTC
- Forum: Movies and TV Shows
- Topic: Doctor Whom
- Replies:
**4990** - Views:
**749850**

### Re: Doctor Who

I got the impression that the data ghosts were a well-understood but unpleasant side-effect of the technology. (I think it was likened to the last draft in your mental outbox.) I'm sure it would be easy to get rid of, but I don't think people would want to do so. Like Prof. Song said, it's the least...

- Mon Jun 02, 2008 10:05 am UTC
- Forum: Language/Linguistics
- Topic: Linguistic survey
- Replies:
**56** - Views:
**6797**

### Re: Linguistic survey

a. You / You guys (regardless of gender)

b. Firefly

c. Dust bunnies

d. Goose-bumps

e. TP-ing

f. A paper bag.

b. Firefly

c. Dust bunnies

d. Goose-bumps

e. TP-ing

f. A paper bag.

- Sun Jun 01, 2008 2:45 pm UTC
- Forum: General
- Topic: Sleep-time holodeck experiences
- Replies:
**3404** - Views:
**764365**

### Re: What were your dreams last night?

I've had third-person dreams as well as first-person dreams. I've had dreams where it's both at once, too (which is weird). I don't remember what I dreamt last night, but I remember thinking when I woke up that it wasn't anything noteworthy.

- Sat May 31, 2008 9:00 pm UTC
- Forum: Forum Games
- Topic: Repeat the last word of the last post you made.
- Replies:
**139** - Views:
**16517**

### Re: latex Q

You can use \left. and \right| together to get a vertical line that matches the size of whatever's between them. For example: \left.\frac{dy}{dx}\right|_{x=0} comes from \left.\frac{dy}{dx}\right|_{x=0} If you want to make the vertical line a specific height, but there isn't something that size for ...

- Sat May 31, 2008 7:08 pm UTC
- Forum: Mathematics
- Topic: A most mysterious of numbers
- Replies:
**33** - Views:
**5577**

### Re: A most mysterious of numbers

e^(-e^(-e^(...x) spits out another mysterious number, I think. This can be written as W(1), where W is the Lambert W function . I wonder if any other of these "mysterious numbers" can be expressed with W, especially since sin and cos can be written as linear combinations of complex expone...

- Sat May 31, 2008 4:05 pm UTC
- Forum: Movies and TV Shows
- Topic: LOST
- Replies:
**454** - Views:
**37774**

### Re: LOST

Continuity error: at the start, they said there was enough C4 to blow up an aircraft carrier. Yet the actual explosion didn't even engulf that poky little freighter. Yeah, I noticed that too. I figure maybe there was modeling clay mixed in with the C4 to make it look more dangerous to anyone wh...

- Fri May 30, 2008 11:11 am UTC
- Forum: Mathematics
- Topic: poor e
- Replies:
**40** - Views:
**5173**

### Re: poor e

Radian measurement of angles arises anytime calculus is invoked. Just as base e is natural for logs and exponentials in calculus, radians (defined by measuring the arc length along the circumference of a circle in terms of its radius) are the "natural" angle measurement. Okay, but a harmo...

- Wed May 28, 2008 1:08 pm UTC
- Forum: Logic Puzzles
- Topic: Complete the sequence...
- Replies:
**4** - Views:
**1700**

### Re: Complete the sequence...

Here's how I got to it: I said, okay, if we subtract 1 from each term we get 0, 0, 0, 0, 41. I know of a quartic that vanishes at 0, 1, 2, and 3, namely n(n-1)(n-2)(n-3) . But I want the fourth term to be 41, not 24, so multiply by 41/24 and you get 41n(n-1)(n-2&#...