Search found 1427 matches

by Macbi
Sun Dec 09, 2012 10:28 am UTC
Forum: Logic Puzzles
Topic: Squish the bug
Replies: 20
Views: 5039

Re: Squish the bug

What if the bug follows an arithmetic progression with arbitrary real parameters, at each step always choosing the integer closest to the value of the progression? Can we still always squish it? Example: The AP starts on 3.6 and has a difference of 2.4, so it goes 3.6, 6, 8.4, 10.8, 13.2, ... So the...
by Macbi
Sat Aug 18, 2012 12:05 pm UTC
Forum: Logic Puzzles
Topic: Coin tossing game
Replies: 6
Views: 4198

Re: Coin tossing game

There's only 8 possible sequences of three coinflips, so it would probably be easiest to check that the trick works for each of them each of them. You only really need to check half; for example if I know that HHT beats HTH then I also know that TTH beats THT, because I've just swapped heads and tai...
by Macbi
Mon Jul 16, 2012 6:19 pm UTC
Forum: Mathematics
Topic: "Oh no! We forgot how to say... math... stuff!"
Replies: 294
Views: 87685

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

Adopt the convention of only writing down expressions that are equal to zero (if you want to mention some other expression then you can put it in quote marks). Then redefine "=" as a very low precedence subtraction sign. Then we could just write e i pi +1, for example. Moving stuff from on...
by Macbi
Sat Jul 14, 2012 1:17 am UTC
Forum: Mathematics
Topic: Help understanding lower bound on pi(n)
Replies: 1
Views: 1009

Help understanding lower bound on pi(n)

I'm trying to understand a proof that we got in lectures of the fact that pi(x)>=x/(8log 2 (x)), where pi(x) is the number of primes less than or equal to x. The proof we got was this (Using (n)C(r) to denote n choose r): (2n+2)C(n+1) <= 4((2n)C(n)) so we can pick n with x/4 <= (2n)C(n) < =x Then pi...
by Macbi
Mon Apr 23, 2012 12:08 pm UTC
Forum: Mathematics
Topic: Need to confirm my thinking on a probability problem
Replies: 5
Views: 1384

Re: Need to confirm my thinking on a probability problem

Hi this is a homework problem, so I am not looking for an answer. Just want to confirm my thinking is right, because this seems too simple. We are given \xi is a random variable following the standard normal distribution. Find E\left( {\xi |{\xi ^2}} \right) . It seem given {{\xi ^2}}>0 we ...
by Macbi
Fri Feb 24, 2012 5:34 pm UTC
Forum: Books
Topic: Harry Potter and the Methods of Rationality
Replies: 1036
Views: 372045

Re: Harry Potter and the Methods of Rationality

"Bahl's Stupefaction," Moody said, naming an extremely addictive narcotic with interesting side effects on people with Slytherin tendencies; Moody had once seen an addicted Dark Wizard go to ridiculous lengths to get a victim to lay hands on a certain exact portkey, instead of just having...
by Macbi
Sun Feb 05, 2012 5:58 pm UTC
Forum: Logic Puzzles
Topic: Making Waves
Replies: 29
Views: 6806

Re: Making Waves

Spoiler:
1)Take the posterboard and wrap it around a cylindrical thing like the paint roller.
2)Saw through it at an angle with the circular saw.
3)Unroll it.
4)Use the pencil to trace the edge of the sine wave template you've just made.
by Macbi
Mon Jan 09, 2012 10:35 am UTC
Forum: Logic Puzzles
Topic: The Mysterious Coin
Replies: 34
Views: 11414

Re: The Mysterious Coin

by Macbi
Wed Dec 14, 2011 2:57 pm UTC
Forum: Logic Puzzles
Topic: math problem - driving me crazy
Replies: 31
Views: 6821

Re: math problem - driving me crazy

Kick wrote:Yes, W|A has the 100th digit as being 4, but is that not just the 100th digit and not the 100th digit after the decimal place?

EDIT: I am no mathematician, I just use W|A a lot...

Ah, yes. That was my mistake.
by Macbi
Tue Dec 13, 2011 12:40 pm UTC
Forum: Mathematics
Topic: "Likelihood" used to describe existence or historical fact
Replies: 9
Views: 3380

Re: "Likelihood" used to describe existence or historical fa

My impression is that Bayesians are happy to use the word 'probability' to represent their knowledge or belief in something - the probability can then be updated if they get more information. For frequentists the the probability of something is not dependent on their knowledge or belief, but they t...
by Macbi
Mon Dec 12, 2011 4:47 pm UTC
Forum: Logic Puzzles
Topic: math problem - driving me crazy
Replies: 31
Views: 6821

Re: math problem - driving me crazy

Xias thanks a lot! I'm at work right now but i will definitively try that path when ill get home. Hint: Look at (\sqrt{7}+\sqrt{5})^n + (\sqrt{7}-\sqrt{5})^n. I tried going in that path... but that only gave me results when n was even (then the expression is an integer)... m...
by Macbi
Sun Dec 11, 2011 11:51 pm UTC
Forum: Logic Puzzles
Topic: math problem - driving me crazy
Replies: 31
Views: 6821

Re: math problem - driving me crazy

Hint:

Spoiler:
Look at[math](\sqrt{7}+\sqrt{5})^n + (\sqrt{7}-\sqrt{5})^n.[/math]
by Macbi
Mon Nov 28, 2011 2:59 pm UTC
Forum: Mathematics
Topic: Cambridge "senior wranglers" -good stories? career paths?
Replies: 4
Views: 4607

Re: Cambridge "senior wranglers" -good stories? career paths

My brother graduated there in 2007 and says there was fierce competition for who would be the SW. No-one in the top 5 who had a chance of being no.1 discussed his working methods with anyone else, in or out of the top 5. Even at Cambridge, undergraduate mathematics just isn't hard enough for studen...
by Macbi
Mon Nov 21, 2011 6:45 pm UTC
Forum: Coding
Topic: AutoHotKey!
Replies: 11
Views: 2367

Re: AutoHotKey!

I use it to suppress the caps lock key, since I never use it.
by Macbi
Sat Nov 19, 2011 11:47 am UTC
Forum: Science
Topic: Well, this could change things (neutrinos)
Replies: 289
Views: 39558

Re: Well, this could change things (neutrinos)

Bumping with these articles about some new results: http://www.science20.com/quantum_diaries_survivor/opera_confirms_neutrinos_travel_faster_light-84763 http://www.interactions.org/cms/?pid=1031226 And the pre-print for those so inclined: http://arxiv.org/abs/1109.4897v2 From the first link: It is ...
by Macbi
Fri Nov 11, 2011 3:26 pm UTC
Forum: Logic Puzzles
Topic: Surface area of an island
Replies: 26
Views: 5946

Re: Area of circles

We had a thread on this a while back...

Here it is!

EDIT: Also, I was being a total n00b in that thread. :oops:
by Macbi
Thu Oct 27, 2011 4:34 pm UTC
Forum: Science
Topic: "The only instance where mass and weight are different."
Replies: 42
Views: 7177

Re: "The only instance where mass and weight are different."

dainbramage wrote: Oh, and she always pronounced de Broglie as "de-bro-glee".
Aww... dammit. How is it supposed to be pronounced?
by Macbi
Wed Oct 26, 2011 4:48 pm UTC
Forum: Mathematics
Topic: "Oh no! We forgot how to say... math... stuff!"
Replies: 294
Views: 87685

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

Open, closed, clopen, and ajar.
by Macbi
Wed Oct 19, 2011 6:52 pm UTC
Forum: Logic Puzzles
Topic: Solve this! (A mathemagical game.)
Replies: 62
Views: 10120

Re: Solve this! (A mathemagical game.)

Good, now I'll ask Jaap's questions with all the implied restrictions included: Divide the closed unit circle into finitely many congruent pieces that may overlap on boundaries only, such that the boundary of the circle is not evenly split among the pieces, or show that such a division is impossibl...
by Macbi
Mon Oct 10, 2011 6:29 pm UTC
Forum: Logic Puzzles
Topic: Solve this! (A mathemagical game.)
Replies: 62
Views: 10120

Re: Solve this! (A mathemagical game.)

ibgdude wrote:narcissitic means that an expression can be created from its digits... and concatenation.
Aha, trivial!
(Seriously, I have no idea.)
by Macbi
Sun Oct 09, 2011 9:39 pm UTC
Forum: Science
Topic: Wait, can free will exist?
Replies: 247
Views: 23865

Re: Wait, can free will exist?

Macbi, I don't know you so well on these forums. Just tell me that you read the previous page and that this post was a joke given the context of the immediately preceding ridiculously-prolonged discussion. I think I've communicated badly. I won't bother trying to explain better, I don't care that m...
by Macbi
Sun Oct 09, 2011 8:04 pm UTC
Forum: Science
Topic: Wait, can free will exist?
Replies: 247
Views: 23865

Re: Wait, can free will exist?

New question: Some people say the universe is deterministic, some say it is random, some say there is free will, some say that it is a mixture of the three. Now, you may argue that some of these options don't make sense, that free will is an illusion caused by the way our brain evaluates choices. Bu...
by Macbi
Fri Oct 07, 2011 6:47 pm UTC
Forum: Science
Topic: is it possible to hit a bowling pin and not knock it over?
Replies: 8
Views: 2453

Re: is it possible to hit a bowling pin and not knock it ove

The friends that I bowl with claim that it is possible and that they have witnessed it. I say that they cannot possibly discern an inch or so of space from 60 feet away and that it is just the wind from the ball that is shaking the pin. They're not lying. This happens all the time, and the pins can...
by Macbi
Wed Oct 05, 2011 7:31 pm UTC
Forum: Science
Topic: Does randomness exist ?
Replies: 48
Views: 6250

Re: Does randomness exist ?

Bell's theorem and the subsequent experiments as performed by Aspect suggest at the very least that a hidden variable theory for the universe can exist, however, such a theory cannot be local. So either the universe is truly random (i.e. not determined by a hidden variable theory) with the possibil...
by Macbi
Mon Oct 03, 2011 9:16 am UTC
Forum: Logic Puzzles
Topic: Solve this! (A mathemagical game.)
Replies: 62
Views: 10120

Re: Solve this! (A mathemagical game.)

...For i = 2,..., m and j = 2,..., n (i.e. all entries that are neither in the first row nor first column), we choose x ij to be arbitrary integers. Oh, duh! It just occurred to me: If we're choosing "arbitrarily", why not just choose x ij = 0 for i = 2,..., m and j = 2,..., n...
by Macbi
Sun Oct 02, 2011 12:00 am UTC
Forum: Logic Puzzles
Topic: Solve this! (A mathemagical game.)
Replies: 62
Views: 10120

Re: Solve this! (A mathemagical game.)

If I have a rectangular grid of real numbers, each row and column adding to an integer, can I always make a grid of integers with the rows and columns each having the same total as before?
by Macbi
Sat Oct 01, 2011 11:57 pm UTC
Forum: Science
Topic: Well, this could change things (neutrinos)
Replies: 289
Views: 39558

Re: Well, this could change things (neutrinos)

To be totally clear, they send no photons from CERN to Gran Sasso, they just measure the distance (using clever GPS tricks) and then dived by the already calculated value of c.
by Macbi
Fri Sep 30, 2011 9:32 pm UTC
Forum: Science
Topic: Miscellaneous Science Questions
Replies: 2870
Views: 638698

Re: RELATIVITY QUESTIONS! (and other common queries)

howdy, So I just read the wikipedia page on "the speed of gravity" and there is one part which perplexes me. It is the fact that gravitational field always points towards the "instant" position of the emitter (as opposed to the light delayed position). Why? I had always thought ...
by Macbi
Thu Sep 29, 2011 12:03 am UTC
Forum: Logic Puzzles
Topic: Solve this! (A mathemagical game.)
Replies: 62
Views: 10120

Re: Solve this! (A mathemagical game.)

I don’t know what it’s called, but the problem I see is an algorithm has finitely many instructions which produce (up to) countably many steps during execution. The method described requires continuously-many steps.


Yup.
by Macbi
Wed Sep 28, 2011 10:46 pm UTC
Forum: Logic Puzzles
Topic: Solve this! (A mathemagical game.)
Replies: 62
Views: 10120

Re: Solve this! (A mathemagical game.)

When two people want to share a cake equally, one strategy is for the first person to cut the cake in two and the second person to choose who gets which piece. How can three people split a cake in a manner that all three agree is fair, without measuring anything? No Banach-Tarskiing allowed. There ...
by Macbi
Sun Sep 25, 2011 11:19 pm UTC
Forum: Mathematics
Topic: euler's number
Replies: 16
Views: 3338

Re: euler's number

Now that the OP has figured out his solution, can someone be kind enough to write out a full proof of the limit? I have just started learning proofs and feel like it would be instructive to see (and I already tried working it out on my own but got nowhere). My method written out in full: We use the...
by Macbi
Sun Sep 25, 2011 5:51 pm UTC
Forum: Science
Topic: Looking for material on Electrodynamics
Replies: 16
Views: 3248

Re: Looking for material on Electrodynamics

Here are some notes that I used when doing Vector Calculus at Cambridge U.K. They were made by a student the previous year, and are hig quality.

http://dl.dropbox.com/u/41824698/VC.pdf
by Macbi
Sun Sep 25, 2011 5:45 pm UTC
Forum: Mathematics
Topic: euler's number
Replies: 16
Views: 3338

Re: euler's number

jaap's needs the limit as n-> infty = limit as n->-infty. That's not clear to me, though it is true. otoh, macbi has a pretty clear path if you take the log. Or even just multiply out: (1-1/n 2 ) n = 1 - (1/n)(stuff) Where "stuff" is an alternating series that must always come out between...
by Macbi
Sat Sep 24, 2011 11:35 pm UTC
Forum: Science
Topic: How Does A Bike Work?
Replies: 20
Views: 4140

Re: How Does A Bike Work?

I think it's something to do with how the shaft from the handle bars to the front wheel goes at a forward angle. This (for some reason I don't understand) means that when the bike goes forward it corrects itself. If the shaft was tilted backward instead I think you'd fall of straight away. EDIT: pox...
by Macbi
Sat Sep 24, 2011 10:21 pm UTC
Forum: Mathematics
Topic: euler's number
Replies: 16
Views: 3338

Re: euler's number

Yeah, don't use my idea. jaap's is cool.

EDIT: My idea works fine, as it turns out.
by Macbi
Sat Sep 24, 2011 6:58 pm UTC
Forum: Mathematics
Topic: euler's number
Replies: 16
Views: 3338

Re: euler's number

Maybe show that (1-(1/n))n * (1+(1/n))n goes to one? I have no idea if that's the best way to do it.
by Macbi
Sat Sep 24, 2011 6:20 pm UTC
Forum: Mathematics
Topic: easy way to integrate (x^2)*(cos x)^3
Replies: 7
Views: 4996

Re: easy way to integrate (x^2)*(cos x)^3

Blatm wrote:Try writing [imath]\cos x[/imath] as [imath]\frac{e^{ix} + e^{-ix}}{2}[/imath].


Does that help? You've still got to bash a bunch of things by parts, and then you've got to smush it all back into trig functions once you've reached the end.
by Macbi
Sat Sep 24, 2011 5:56 pm UTC
Forum: Mathematics
Topic: easy way to integrate (x^2)*(cos x)^3
Replies: 7
Views: 4996

Re: easy way to integrate (x^2)*(cos x)^3

Don't think so. :(

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