Search found 190 matches

Mon Mar 30, 2009 5:15 pm UTC
Forum: Science
Topic: Global Warming Fail.
Replies: 22
Views: 3170

Re: Global Warming Fail.

Launch the excess sea-water into the sun.
Fri Mar 20, 2009 8:24 pm UTC
Forum: Mathematics
Topic: Alternative definitions of the derivative
Replies: 15
Views: 2255

Re: Alternative definitions of the derivative

Distributions are a generalization of functions that let you do more things with them. For example, the "derivative" of the Heaviside step function is the Dirac delta function. Distributions are defined in terms of their integrals. So, even though the delta function carries an "infini...
Mon Mar 09, 2009 6:39 pm UTC
Forum: Mathematics
Topic: Graph: F(x)=x^∞
Replies: 25
Views: 3286

Re: Graph: F(x)=x^∞

∞ is not an integer and therefore even and odd don't really make sense for it. Compare: Is 3.5 even or odd? pi? \sqrt 2? Neither even nor odd works for ∞ if you try to use naive infinite math on it, either. ∞ + ∞ = ∞, so ∞ must be even. But, ∞ + 1 = ∞, so ∞ must be odd. It just doesn't work. So the ...
Thu Feb 26, 2009 7:22 pm UTC
Forum: Science
Topic: Kelvin double bridge?
Replies: 2
Views: 1172

Re: Kelvin double bridge?

My guess, and I know almost nothing about circuits, is that the leftmost path is the original circuit, so you don't exactly "need" it, but you are probably not going to remove it either.
Fri Feb 13, 2009 5:47 pm UTC
Forum: Science
Topic: Neutrinos and the expansion of the Universe.
Replies: 11
Views: 1087

Re: Neutrinos and the expansion of the Universe.

I think what you're saying is, given a fixed density for the universe, any additional mass must increase the size of the universe. I think we have calculated the size of the universe independently of its mass or density. In fact, our calculation of the universes size was too large to account for its...
Tue Feb 10, 2009 1:10 pm UTC
Forum: Mafia
Topic: The Gojoe Memorial Mafia Discussion Thread
Replies: 32852
Views: 2614572

Re: Forum-Mafia Discussion/Recruitment/Gojoe canNEVER be trusted

I will gladly fill in for anyone who needs a replacement.
Tue Feb 10, 2009 1:05 pm UTC
Forum: Science
Topic: Charged Black Hole
Replies: 27
Views: 3208

Re: Charged Black Hole

Remember that in relativity, different observers can have different notions of time. Part of the reason that black holes are confusing is that different observers have very different notions of time. If a particle falls into a black hole, an observer far away from the black hole would calculate it a...
Sun Feb 08, 2009 6:51 pm UTC
Forum: Science
Topic: Charged Black Hole
Replies: 27
Views: 3208

Re: Charged Black Hole

There would be an electromagnetic field around the black hole, outside the event horizon.
Sat Feb 07, 2009 6:18 am UTC
Forum: Movies and TV Shows
Topic: Look around you
Replies: 5
Views: 1272

Look around you

Look around you is a very amusing show. It takes the form of one of those old science shows, but the science is completely bogus. The bell isn't broken. In fact it's in perfect working order. It's just that when bumcivilian is produced, it has the effect of sucking up all the sound in the vicinity. ...
Fri Feb 06, 2009 5:43 pm UTC
Forum: Mathematics
Topic: How does the cartesian product relate to other products?
Replies: 30
Views: 3047

Re: How does the cartesian product relate to other products?

In Nathaniel's definition of a matrix, a 3x3 matrix is just a list of 9 real numbers, so it can be defined as a function with takes as input one of the nine positions of the matrix and takes as output whichever element of the matrix is in that position. Linear algebra takes advantage of the fact tha...
Fri Feb 06, 2009 6:02 am UTC
Forum: Mathematics
Topic: How does the cartesian product relate to other products?
Replies: 30
Views: 3047

Re: How does the cartesian product relate to other products?

The identity matrix in three dimensions can be defined either as I: m:{1,2,3}x n:{1,2,3} -> r:R where r=1 if m=n and r=0 if m=/=n or as the function I: x:R3 -> y:R3 where y=x. Both are valid and useful depending on what aspect of matrices you're studying.
Fri Feb 06, 2009 5:03 am UTC
Forum: Mathematics
Topic: How does the cartesian product relate to other products?
Replies: 30
Views: 3047

Re: How does the cartesian product relate to other products?

That's a horrible way to define a matrix. It's a fine way to define a matrix, depending on your context. In particular, if you want to deal with higher-dimensional matrices, then that's a very good definition to use, since you can just slap on d cartesian products, where d is the dimension you want...
Thu Feb 05, 2009 1:46 pm UTC
Forum: Forum Games
Topic: Post next in this thread and
Replies: 80
Views: 7149

Re: Post next in this thread and

Can it be hugz tiem nao?

The next person to post in this thread will divide by zero.
Sat Jan 31, 2009 9:40 pm UTC
Forum: Mathematics
Topic: Stacked Hypercube Vertex Convex Hull Boundary Minimization
Replies: 6
Views: 750

Re: Stacked Hypercube Vertex Convex Hull Boundary Minimization

For example, if n=2 and h=4 you assign:
(0,0) -> 1
(1,0) -> 2
(0,1) -> 3
(1,1) -> 4

The level set for 2 goes from (0,0.5) to (1,0). so r is [imath]\sqrt 5 / 2[/imath].

This is the minimal arrangement.
Fri Jan 30, 2009 7:01 pm UTC
Forum: Mathematics
Topic: Stacked Hypercube Vertex Convex Hull Boundary Minimization
Replies: 6
Views: 750

Re: Stacked Hypercube Vertex Convex Hull Boundary Minimization

Choose h vertices from a n-dimensional hypercube. Assign each point a "Temperature" T from 1 to h, without replacement. The temperature varies linearly between the points. Minimize the size of all the isothermal surfaces.
Fri Jan 30, 2009 6:26 pm UTC
Forum: Mathematics
Topic: The continuous elevator
Replies: 15
Views: 2055

Re: The continuous elevator

In other words, he's saying a restaurant where two people each wait 30min (30 2 +30 2 =1800) is better than one where one person waits 5min and another waits 45min (5 2 +45 2 =2050). I think the a good solution would be to create a potential function P(x|y,t) for each dot that depends on where and w...
Thu Jan 22, 2009 7:25 pm UTC
Forum: Mathematics
Topic: Argh... what am I not seeing? (homework problem)
Replies: 14
Views: 2044

Re: Argh... what am I not seeing? (homework problem)

Sorry, I meant ex [imath]\neq[/imath] -3.
Thu Jan 22, 2009 7:02 pm UTC
Forum: Mathematics
Topic: Argh... what am I not seeing? (homework problem)
Replies: 14
Views: 2044

Re: Argh... what am I not seeing? (homework problem)

ln(x) [imath]\neq[/imath] -3 for any x
Thu Jan 22, 2009 6:56 pm UTC
Forum: Logic Puzzles
Topic: Gravity, Acceleration, or Centrifugal Force?
Replies: 19
Views: 3266

Re: Gravity, Acceleration, or Centrifugal Force?

Never mind that all three of those cases are gravity.
Tue Jan 20, 2009 4:58 am UTC
Forum: Science
Topic: Freezing Water
Replies: 18
Views: 1758

Re: Freezing Water

You could try insulating either the cage, the bottle, or the metal spout. If you occasionally shake the bottle, that should stop the bottom from freezing first.
Tue Jan 20, 2009 4:14 am UTC
Forum: Logic Puzzles
Topic: Outsmarting the Genie
Replies: 257
Views: 25916

Re: Outsmarting the Genie

I wish for whatever would be best for me.
Tue Jan 20, 2009 4:02 am UTC
Forum: Logic Puzzles
Topic: Cutting The Cake
Replies: 14
Views: 2646

Re: Cutting The Cake

Consider all the intersection points of the cake. Consider the partition of these intersections such that two points are in the same partition if they are connected by a cut. Before cutting, there are 122 partition sets: one for all the boundary points, and one for each interior point. Consider maki...
Wed Jan 14, 2009 7:25 pm UTC
Forum: Mathematics
Topic: Beginner Stuff
Replies: 23
Views: 2443

Re: Beginner Stuff

There is nothing wrong with repeating elements in a set. Writing "A={(9,0), (8,2), (7,3), (8,2)}" means "(9,0) is in A, (8,2) is in A, (7,3) is in A, and (8,2) is in A." Sure, it's redundant, but I wouldn't go so far as to call it wrong. More relevant to the OP's question, though...
Sun Jan 11, 2009 5:37 pm UTC
Forum: Science
Topic: Pair Production
Replies: 6
Views: 1183

Re: Pair Production

http://en.wikipedia.org/wiki/Pair_production

According to wikipedia, pair production can't occur from a single photon, but it has more to do with conservation laws than antiparticles.
Tue Jan 06, 2009 7:52 am UTC
Forum: Logic Puzzles
Topic: Tarot
Replies: 18
Views: 2153

Re: Tarot

I would ask 'Will I receive the bottom card from the deck before the top card?', proving that the fortune teller is inaccurate.
Wed Dec 24, 2008 1:00 am UTC
Forum: Mathematics
Topic: Fractals, baby! Vote now!
Replies: 45
Views: 8488

Re: Fractals, baby! Vote now!

The coastline of Britain is a fractal. It has a fractal dimension of 1.25. Granted, it may not be an exact fractal as the coastline itself is poorly defined at smaller scales, but it is statistically self-similar at all larger scales.
Thu Dec 18, 2008 2:12 am UTC
Forum: Logic Puzzles
Topic: Slot machines
Replies: 9
Views: 2089

Slot machines

A casino has two types of slot machines available: a nickel machine which takes 5 cent bets and pays out 40 cents every 1 in 10 games, and a quarter machine which takes 25 cent bets and pays out 225 cents every 1 in 10 games. As a casino owner, which machine should you install more of? As a player, ...
Tue Dec 16, 2008 6:05 am UTC
Forum: Science
Topic: Downwind faster than the wind
Replies: 262
Views: 32697

Re: Downwind faster than the wind

It is important to be very careful about which frame of reference you are in. Also, you seem to be disregarding contributions to kinetic energy and momentum from the ground. In the ground frame, the propeller takes energy from the air, and gives it to the vehicle. In the air speed frame, the vehicle...
Thu Oct 30, 2008 4:32 pm UTC
Forum: Logic Puzzles
Topic: Quantitative Analysis riddle
Replies: 13
Views: 2126

Re: Quantitative Analysis riddle

since P(+) must be nonzero (otherwise he could not have gotten a positive test) Just because something happens doesn't mean its probability is non-zero. We should take P(+)=0. Then Bayes Theorem gives P(G|+)=P(+|G)P(G)/P(+)=0/0. Or, to rewrite: P(G|+)P(+)=P(+|G)P(G)=0. This is satisfied for any pro...
Thu Oct 30, 2008 4:14 pm UTC
Forum: Logic Puzzles
Topic: 2 simultaneous chess games (simple solution)
Replies: 20
Views: 4198

Re: 2 simultaneous chess games (simple solution)

Perhaps she has a strategy for Chess that proves either a win for white or a win for black. By playing her strategy perfectly, she guarantees at least one win (assuming she plays white in one game and black in the other).
Thu Aug 07, 2008 4:33 pm UTC
Forum: Language/Linguistics
Topic: What is a "climax"? (In literary terms.)
Replies: 11
Views: 4030

Re: What is a "climax"? (In literary terms.)

The climax is the point of greatest tension in the story. It is usually followed immediately by the resolution. It is not usually found in the middle of the story.
Sat May 17, 2008 7:11 pm UTC
Forum: General
Topic: Writing Badly (you can too!)
Replies: 40
Views: 9687

Re: Writing Badly (you can too!)

I recall "Half-Life: Full-Life Consequences" as a particularly poorly written example of awful fan fiction.
Sat Mar 29, 2008 6:23 pm UTC
Forum: Logic Puzzles
Topic: Pi litres
Replies: 17
Views: 3601

Re: Pi litres

If you have a string, you can wrap it around the cylinder to get the length 2πR. Then draw it across the cylinder to get the length 2R. Use those two length to construct a right triangle with base 4R and height πR. Use that triangle and the height of the cylinder to construct the length (π/4)H. Fill...
Fri Mar 28, 2008 12:43 pm UTC
Forum: Mathematics
Topic: Exponents using only addition and subtraction
Replies: 9
Views: 2214

Re: Exponents using only addition and subtraction

There's always Taylor polynomials. I think most calculators use Taylor polynomials or some variant to calculate trigonometric functions. The Taylor polynomial for that function is 1 + [ln2(x-69)/12]1/2! + [ln2(x-69)/12]2/3! +[ln2(x-69)/12]3/4! + . . .

It should converge rather quickly.
Sat Mar 15, 2008 8:26 pm UTC
Forum: Mathematics
Topic: Pi, Monkeys, and Shakespeare
Replies: 27
Views: 3357

Re: Pi, Monkeys, and Shakespeare

The usual definition of "natural" or "unnatural" sequences or sets is to imagine a computer program (in some programming language) that would print the result. Or you could use a natural language like English. For example, "110100000101110" falls into the category "...
Wed Mar 12, 2008 6:32 am UTC
Forum: Religious Wars
Topic: Which of Valve's creative guns doyou want?
Replies: 120
Views: 20360

Re: Which of Valve's creative guns doyou want?

Well, the storage cube would have to be large enough to accommodate a portal, which would make it too big to fit through a portal. Even if you had a rectangular shape, it would just get stuck partway through the portal. You're not imaginative enough. Pop one on a piece of plywood and the other on t...
Wed Mar 12, 2008 5:49 am UTC
Forum: Forum Games
Topic: Haiku.
Replies: 316
Views: 39010

Re: Haiku.

Oh, pentameter
You are so full of iambs
but not in haiku.
Wed Mar 12, 2008 5:46 am UTC
Forum: Logic Puzzles
Topic: Can you pick out what's wrong here?
Replies: 9
Views: 2980

Re: Can you pick out what's wrong here?

Would this be a good place to post similar puzzles? My favorite was always:

2πi = ln(e2πi)=ln(1)=0
Wed Mar 12, 2008 1:11 am UTC
Forum: Logic Puzzles
Topic: Can you pick out what's wrong here?
Replies: 9
Views: 2980

Re: Can you pick out what's wrong here?

Well, precisely which step is wrong depends on your definition of the square root. Step 2 is wrong because the square root is multi-valued. If you have a single-valued square root with an appropriate branch cut, then step 3 is no longer correct. Steps 1, 4 and 5 are always correct with standard def...
Tue Mar 11, 2008 3:20 am UTC
Forum: Religious Wars
Topic: Which of Valve's creative guns doyou want?
Replies: 120
Views: 20360

Re: Which of Valve's creative guns doyou want?

Here's a thought experiment: suppose portals could be attached to weighted storage cubes and that they didn't disappear when the surface moved. What would happen if you put a portalled cube through a portal on the wall? Well, the storage cube would have to be large enough to accommodate a portal, w...