Search found 6289 matches

by skeptical scientist
Mon Aug 19, 2013 3:31 am UTC
Forum: Mathematics
Topic: When will $1 be the smallest denomination?
Replies: 51
Views: 10334

Re: When will $1 be the smallest denomination?

As an American, the quarter seems like the most functional coin in terms of being common in circulation but still valuable enough that I'm happy to have a dresser covered in them. It's the only coin I would actually mind getting rid of. Also, there are a lot of machines out there which only accept ...
by skeptical scientist
Sat Aug 17, 2013 3:20 pm UTC
Forum: Science
Topic: There is only one* model consistent with CPT Symmetry
Replies: 129
Views: 39039

Re: There is only one* model consistent with CPT Symmetry

Each operator, C, P and T implies a pair of states. There are many such pairs. No, each operator is a function mapping states of the universe to states. For example C is the function s -> s C . The only thing "binary" about it is the fact that C(C(s)) = s for every state s. In other words...
by skeptical scientist
Fri Aug 16, 2013 2:59 pm UTC
Forum: Mathematics
Topic: When will $1 be the smallest denomination?
Replies: 51
Views: 10334

Re: When will $1 be the smallest denomination?

We still have products going out to the tenth of a cent. You mean gas? The 10th of a cent thing is the same sort of window-dressing as the .99 thing, although I suppose it tells you that the gas companies think that extra 1c per gallon is significant. I'm not sure why gas stations do that when nobo...
by skeptical scientist
Fri Aug 16, 2013 6:35 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9979
Views: 1975709

Re: Coding: Fleeting Thoughts

jareds wrote:Edit: To be clear, I'm not claiming that the average-case run-time of comparison-sorting n strings of length k is O(n k log n), just that it isn't O(n log n). It's probably something like O(n log(n) min(k, log n)).

Yeah, that's true. I think it's exactly O(n log(n) min(k, log n)).
by skeptical scientist
Thu Aug 15, 2013 1:30 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9979
Views: 1975709

Re: Coding: Fleeting Thoughts

jareds wrote:Say we are sorting n strings of length k. A comparison sort will perform O(n log n) comparisons of cost O(k), for a running time of O(n k log n).

Comparing strings of length k is worst-case O(k), but average-case O(1) as long as your strings are somewhat random.
by skeptical scientist
Wed Aug 14, 2013 1:51 am UTC
Forum: Mathematics
Topic: When will $1 be the smallest denomination?
Replies: 51
Views: 10334

Re: When will $1 be the smallest denomination?

Pennies are currently not worth carrying, but they're still around (possibly because of the political power of Illinois?). Just sayin', inflation is not the only thing that determines whether a unit of currency is discontinued.
by skeptical scientist
Tue Aug 13, 2013 5:21 am UTC
Forum: Mathematics
Topic: Volume of pyramids, and showing it
Replies: 3
Views: 2197

Re: Volume of pyramids, and showing it

It's triangular pyramids like these that I'm having a harder time with. I could just pick some dimensions, solve the triangles, and then make them with a protractor, but it probably wouldn't come out very pretty. Step 1: construct a triangular prism out of card, without attaching the sides (or atta...
by skeptical scientist
Tue Aug 13, 2013 1:36 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9979
Views: 1975709

Re: Coding: Fleeting Thoughts

Snark, why did you come up with a "linear time" algorithm, when you could just as easily have sorted in "constant time"? Surely constant time is better. * * * Xanthir, that is a rather hilarious sorting algorithm. (This is actually linear-time in the maximum value in the array. I...
by skeptical scientist
Mon Aug 12, 2013 2:58 pm UTC
Forum: Science
Topic: There is only one* model consistent with CPT Symmetry
Replies: 129
Views: 39039

Re: There is only one* model consistent with CPT Symmetry

I have not at any point suggested that symmetry/invariance is part of the proof. It doesn't matter if it's part of the proof, it's part of your conclusion. (Unless you want to claim that "There is only one model consistent with CPT Symmetry" isn't one of your conclusions.) We've shown tha...
by skeptical scientist
Mon Aug 12, 2013 12:24 am UTC
Forum: Mathematics
Topic: Colors format conversion
Replies: 6
Views: 2600

Re: Colors format conversion

P(5/12, 2/12, 5/12) = L(1, 1/2, 1) How did you get this? By assuming the formula that a 1:1 mix of P(a,b,c) and P(a',b',c') gives P((a+a')/2, (b+b')/2, (c+c')/2), and the same formula also works for L. But this contradicts the idea that a 1:1 mix of L(1,0,0) (cyan) and L(0,0,1) (yellow) gives L(1,0...
by skeptical scientist
Sun Aug 11, 2013 6:55 pm UTC
Forum: News & Articles
Topic: New malaria vaccine shows promise
Replies: 2
Views: 1474

New malaria vaccine shows promise

A new kind of malaria vaccine that mimics the effects of mosquito bites has shown early promise by offering 100 percent protection to a dozen human volunteers, researchers said Thursday. Maryland-based Sanaria's PfSPZ vaccine contains live parasites and is complicated to make because it requires sc...
by skeptical scientist
Sun Aug 11, 2013 5:28 pm UTC
Forum: Mathematics
Topic: Colors format conversion
Replies: 6
Views: 2600

Re: Colors format conversion

So I guess you want P(a,b,c) = L(a/m,b/m,c/m) when a+b+c = 1 and m = max(a,b,c)? And P(a,b,c) = L(a,b,c) when only one of a,b,c is nonzero? A natural way to generalize those two constraints would be P(a,b,c) = L(a/k,b/k,c/k) where k = max(a,b,c)/(a+b+c). The inverse transformation would then be L(a,...
by skeptical scientist
Sun Aug 11, 2013 4:33 pm UTC
Forum: Science
Topic: There is only one* model consistent with CPT Symmetry
Replies: 129
Views: 39039

Re: There is only one* model consistent with CPT Symmetry

What I am (attempting) to show is that based solely on the information that charge, parity and time each has 2 possible states, there is only one possible model for the universe. Later it will be interesting to look at a specific instance of that model. ORLY? You then go on to talk about symmetry. ...
by skeptical scientist
Sun Aug 11, 2013 3:39 pm UTC
Forum: Mathematics
Topic: Colors format conversion
Replies: 6
Views: 2600

Re: Colors format conversion

I defined a second color format by expressing it from pigments: P (c, m, y) where c is the percentage of cyan pigment m is the percentage of magenta pigment y is the percentage of pigment yellow The difference with the first format is the sum of the percentages does not exceed 1. I'm not quite sure...
by skeptical scientist
Fri Aug 09, 2013 3:51 pm UTC
Forum: Mathematics
Topic: Group theory II
Replies: 46
Views: 13622

Re: Group theory II

Note: I already know about the undecidability of the word problem, and of the fact that there are uncountably many 2-generator groups, I'm just working through a few relatively simple cases. As you point out, there are no general, effective methods to do this. One thing which may work in particular...
by skeptical scientist
Thu Aug 08, 2013 3:18 pm UTC
Forum: Logic Puzzles
Topic: A board game based on ´symmetry´
Replies: 15
Views: 8940

Re: A board game based on ´symmetry´

Every time I try to make a move, a Koala tells me something went terribly wrong. I would also really like to know how I could find out what complexity class this game is in. (its probably not as complex as for example Go, but still). Perhaps any of you are knowledgable in the field of complexity the...
by skeptical scientist
Thu Aug 08, 2013 3:10 pm UTC
Forum: Mathematics
Topic: Some questions about "truth" in formal logic
Replies: 14
Views: 5249

Re: Some questions about "truth" in formal logic

Is there a formal way to talk about semantics in the same way that we can talk about (and quantify etc) languages? Yes. Model theory is essentially formalized semantics. ~(P^~P) is an example of a contradiction. T is consistent if it does not prove any contradictions. We hope that our favorite logi...
by skeptical scientist
Tue Aug 06, 2013 1:11 am UTC
Forum: Science
Topic: Is a previous spacefaring species on Earth possible?
Replies: 102
Views: 32203

Re: Is a previous spacefaring species on Earth possible?

Are you asking about a spacefaring species that evolved, gained technology for spaceflight, used it, and then disappeared leaving no evidence that we have found? I would say that's impossible, for the reasons other have said. Or are you just asking about a spacefaring species that evolved on another...
by skeptical scientist
Mon Aug 05, 2013 2:49 pm UTC
Forum: Mathematics
Topic: How to prove the uniqueness of solutions for this problem ?
Replies: 6
Views: 2707

Re: How to prove the uniqueness of solutions for this proble

I believe the minimal counterexample is (1,1), (1,2), (2,1), (1,3), (3,1).
by skeptical scientist
Fri Aug 02, 2013 3:52 am UTC
Forum: Science
Topic: How did we figure out the Earth's mass?
Replies: 28
Views: 10541

Re: How did we figure out the Earth's mass?

Eratosthenes experiment is pretty trivial to do. If you're on a new planet, exploring and mapping your new environs is going to be a pretty high priority. Once you've mapped a few hundred miles and computed latitudes, you're done.
by skeptical scientist
Fri Aug 02, 2013 2:57 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9979
Views: 1975709

Re: Coding: Fleeting Thoughts

Memoization seems like it's mostly only useful in the case when it's being applied to a recursive function which is likely to call itself multiple times with the same argument. The classic example of this is the recursive fibonacci algorithm: def fib(n): if n < 2: return n return fib(n-1)+fib(n-2) I...
by skeptical scientist
Thu Aug 01, 2013 3:29 pm UTC
Forum: Mathematics
Topic: "Oh no! We forgot how to say... math... stuff!"
Replies: 294
Views: 91732

Re: "Oh no! We forgot how to say... math... stuff!"

Emm... yeah. Spell check is my fiend. Lack of the associative property means having to use as many brackets as the binary case> Lack of commutative property means ambiguity about which operation is the "inverse" Yes, but if you just talk about "left-inverse" and "right-inve...
by skeptical scientist
Thu Aug 01, 2013 3:23 pm UTC
Forum: Science
Topic: How did we figure out the Earth's mass?
Replies: 28
Views: 10541

Re: How did we figure out the Earth's mass?

Just from Wikipedia, Earth's mass came first experimentally, in the Cavendish Experiment mentioned earlier, but apparently for the purpose of determining the Earth's density. (The experimental setup would have determined the mass directly, since it was based on comparing the gravitational force of ...
by skeptical scientist
Thu Aug 01, 2013 3:10 pm UTC
Forum: Science
Topic: Runner on a Treadmill
Replies: 46
Views: 14274

Re: Runner on a Treadmill

Lack of oxygen is not the only danger of being in a vacuum, and probably isn't even the worst. See Wikipedia . Few effects can kick in over a period of less than 15 seconds. Bolt takes 10.4 seconds to run 100m. The low pressure outside the body causing rapid de-oxygenation of the blood (hypoxia) is...
by skeptical scientist
Thu Aug 01, 2013 2:30 pm UTC
Forum: Science
Topic: Runner on a Treadmill
Replies: 46
Views: 14274

Re: Runner on a Treadmill

As long as we keep friction... And he might actually perform not that bad, it took him a little bit less than 10s, and he although it would affect his performance, holding his breath that long is very possible, even when running. Lack of oxygen is not the only danger of being in a vacuum, and proba...
by skeptical scientist
Thu Aug 01, 2013 2:25 pm UTC
Forum: Science
Topic: How did we figure out the Earth's mass?
Replies: 28
Views: 10541

Re: How did we figure out the Earth's mass?

Once you know G the measuring the mass of the earth becomes trivial. The hard part is figuring out G. As far as I know, there is no way to figure out the mass of the earth independent from G. We know the volume of the Earth and the approximate composition, which is enough to compute the mass. DId w...
by skeptical scientist
Thu Aug 01, 2013 2:17 pm UTC
Forum: Mathematics
Topic: "Oh no! We forgot how to say... math... stuff!"
Replies: 294
Views: 91732

Re: "Oh no! We forgot how to say... math... stuff!"

PM 2Ring wrote:Communicative? I presume you mean "commutative".

...or possibly associative, which seems the more important property here.
by skeptical scientist
Thu Aug 01, 2013 2:59 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9979
Views: 1975709

Re: Coding: Fleeting Thoughts

Dynamic programming in python how-to:
  • Step 1: write a recursive function
  • Step 2: @memoize it
  • Step 3: profit
by skeptical scientist
Thu Aug 01, 2013 2:51 am UTC
Forum: Mathematics
Topic: Trying to find a way to describe this "set" of numbers
Replies: 24
Views: 7133

Re: Trying to find a way to describe this "set" of numbers

That's very similar to the definition dudiobugtron and I were playing with. If you want to define addition and multiplication to both have those properties I don't think it's possible to also get distributivity.
by skeptical scientist
Wed Jul 31, 2013 5:36 am UTC
Forum: Mathematics
Topic: Trying to find a way to describe this "set" of numbers
Replies: 24
Views: 7133

Re: Trying to find a way to describe this "set" of numbers

So does yours, though; Not necessarily. It could be, depending on the structure of C under *, but it could be false. Yours is necessarily true if A<B always holds. A > B iff (B * C = A or C * B = A for some C) or (for some D, A > D and B * C = D or C * B = D for some C) This has the same problem. I...
by skeptical scientist
Wed Jul 31, 2013 1:10 am UTC
Forum: Mathematics
Topic: Trying to find a way to describe this "set" of numbers
Replies: 24
Views: 7133

Re: Trying to find a way to describe this "set" of numbers

Anyway, I think you could re-write your Axiom 2 in a 'recursive' way, like this: A > B iff (B * C = A or C * B = A for some C) or (A > D and D > B for some D). I thought of that, but unfortunately it's not logically equivalent. It's not? I'm interested in seeing a counter-example, since I can't thi...
by skeptical scientist
Wed Jul 31, 2013 1:09 am UTC
Forum: Mathematics
Topic: Some questions about "truth" in formal logic
Replies: 14
Views: 5249

Re: Some questions about "truth" in formal logic

Is that assumption something above and beyond ~(P^~P)? (I'm familiar with the principle of proof by contradiction) ~(P^~P) is an example of a contradiction. T is consistent if it does not prove any contradictions. We hope that our favorite logical systems (such as Peano Arithmetic or ZFC) are consi...
by skeptical scientist
Tue Jul 30, 2013 2:43 pm UTC
Forum: Mathematics
Topic: How to convince a friend the equivalence of infinite sets
Replies: 32
Views: 8145

Re: How to convince a friend the equivalence of infinite set

So it simply requires the assertion that there exists an infinite set that does not permit a choice function? (i.e. ¬C) No. Countable choice is sufficient to imply that every infinite set is Dedekind-infinite, and ZF+CC+¬C is consistent. The existence of an infinite set, no infinite subset of which...
by skeptical scientist
Tue Jul 30, 2013 2:30 pm UTC
Forum: Mathematics
Topic: Trying to find a way to describe this "set" of numbers
Replies: 24
Views: 7133

Re: Trying to find a way to describe this "set" of numbers

I was trying to set up a situation where A * B = C, but A * B * D != C * D, which is pretty non-sensical. I think this was sort of what the OP was going for, so I don't think my axioms (or your better, modified axioms) fit the OP's purpose. Yeah, if you want A * B = C, but (A * B) * D ≠ C * D, you'...
by skeptical scientist
Tue Jul 30, 2013 6:07 am UTC
Forum: Science
Topic: Runner on a Treadmill
Replies: 46
Views: 14274

Re: Runner on a Treadmill

Goemon wrote:And I've got to wonder how much faster he could achieve 100m without the air resistance...

We should totally make him run the 100 meters in hard vacuum and compare.
by skeptical scientist
Tue Jul 30, 2013 6:06 am UTC
Forum: Mathematics
Topic: Help with proof (or not) in symmetry
Replies: 11
Views: 4355

Re: Help with proof (or not) in symmetry

We say a transformation F is a symmetry of D if F fixes all realisations in R . That is, a symmetry of D is a transformation F in G which acts trivially on R (clearly this occurs if and only if each of the components of F acts trivially on the corresponding state set). This doesn't seem quite right...
by skeptical scientist
Tue Jul 30, 2013 2:54 am UTC
Forum: Mathematics
Topic: Trying to find a way to describe this "set" of numbers
Replies: 24
Views: 7133

Re: Trying to find a way to describe this "set" of numbers

I just took a look at your axioms again, and noticed that in axiom 1) you insist that m=n. This is inconsistent with axiom 3, because A * B = C for some A, B, and C, but 2≠1. Here's a modified version of your axioms (rewritten to avoid offending my aesthetics) which is consistent: 1') If A * B = C *...
by skeptical scientist
Tue Jul 30, 2013 2:23 am UTC
Forum: Mathematics
Topic: How to convince a friend the equivalence of infinite sets
Replies: 32
Views: 8145

Re: How to convince a friend the equivalence of infinite set

Run an injection both ways, and then simple logic leads you to the fact that there must be *a* bijection of some kind. What simple logic? It is somewhat tricky to actually construct a bijection here. You seem to be implicitly assuming that sizes of infinite sets are totally ordered, but this is by ...
by skeptical scientist
Mon Jul 29, 2013 3:04 pm UTC
Forum: Mathematics
Topic: Trying to find a way to describe this "set" of numbers
Replies: 24
Views: 7133

Re: Trying to find a way to describe this "set" of numbers

Now, it's apparent that * can't be associative ... A 1 * A 2 * ... * A n Please don't write multiple applications of a non-associative operation like this. You're confusing the hell out of me. I thought I found a contradiction in your axioms. Then I remembered * was not supposed to be associative. ...
by skeptical scientist
Mon Jul 29, 2013 2:45 pm UTC
Forum: Mathematics
Topic: Help with proof (or not) in symmetry
Replies: 11
Views: 4355

Re: Help with proof (or not) in symmetry

Okay, you're still not being precise enough in your definitions. I still don't know what you are talking about. A satisfactory definition should be precise enough for someone to start formulating and proving theorems about whatever it is you are talking about. I don't know what any of your terms mea...

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