Search found 671 matches

by notzeb
Fri May 01, 2015 8:26 am UTC
Forum: Mathematics
Topic: Greatest Mathematician of all time?
Replies: 65
Views: 20267

Re: Greatest Mathematician of all time?

Fermat: invented analytic geometry, the method of using derivatives to minimize/maximize functions, the principle of least time, proof by infinite descent, the theory of Pell equations, etc., all in his spare time and without any help from anyone else. Little known fact: Fermat is the only mathemati...
by notzeb
Tue Apr 28, 2015 10:50 pm UTC
Forum: Mathematics
Topic: Term for this concept
Replies: 8
Views: 1874

Re: Term for this concept

"Maximal element (under containment)" works, if you throw out the word "set" after it. "Union" works, if you interpret union as in the axiom of union. "Base 2 logarithm" seems to be what you really want, but I don't think anyone calls it that.
by notzeb
Tue Apr 07, 2015 10:52 pm UTC
Forum: General
Topic: Hifaleetin' thoughts
Replies: 90225
Views: 9345901

Re: Inspirations

I have failed, on a daily basis over the last ten years, to buy a mountain.
by notzeb
Sun Apr 05, 2015 5:04 pm UTC
Forum: Serious Business
Topic: Trolley Problem
Replies: 349
Views: 125646

Re: Trolly Problem

Distance also matters a bit. I don't think I would kill the person next to me to save every living creature in Andromeda, even with perfect information about outcomes, unless I had a plausible method for travelling to Andromeda within my lifetime. Hmm, let's give the original question a whirl: Origi...
by notzeb
Wed Mar 25, 2015 1:50 am UTC
Forum: Religious Wars
Topic: Sorting small arrays: Algorithm fight!
Replies: 16
Views: 9962

Re: Sorting small arrays: Algorithm fight!

I didn't see Bogosort among the options... am disappoint. (Also, since Bogosort was designed with large arrays in mind, clearly the thing to do is to first pad your small array into a large array before passing it to Bogosort.)
by notzeb
Fri Mar 13, 2015 10:28 am UTC
Forum: Mathematics
Topic: Graph Theory definition question
Replies: 6
Views: 1917

Re: Graph Theory definition question

A) I haven't heard of this before, but there are lots of random combinatorial definitions I've never seen. B) Definitely minimal - there is no point in trying to maximize this quantity. It really doesn't matter for what they are doing though - you could allow graphs to have "multiple widths&quo...
by notzeb
Wed Mar 11, 2015 2:39 am UTC
Forum: Mathematics
Topic: Forming New Polynomials using properties of roots
Replies: 5
Views: 1745

Re: Forming New Polynomials using properties of roots

What happens if you just try it? Pick a value for p, find the roots (approximately is good enough), build the polynomial with those roots squared, and see what it matches? It's by no means a proof that either answer is correct, but it'll work to show that one of the answers is wrong... Fun side pro...
by notzeb
Thu Feb 26, 2015 6:01 am UTC
Forum: Books
Topic: Harry Potter and the Methods of Rationality
Replies: 1036
Views: 414003

Re: Harry Potter and the Methods of Rationality

On the beginning of 112: "Right now my theory is that Quirrelmort's plan somehow hinges on Harry betraying him." Called it! BAM Speculation about the next chapter: It's a long shot, but what about Priori Incantatem? In fact, Voldemort may have left Harry with his wand just so they ...
by notzeb
Tue Feb 24, 2015 6:24 am UTC
Forum: Books
Topic: Harry Potter and the Methods of Rationality
Replies: 1036
Views: 414003

Re: Harry Potter and the Methods of Rationality

About the words on the mirror: Yudkowsky was making a joke about "understanding" or "explaining" things via concepts which are meaningless and have no testable relationship to anything concrete. Once one has formed such a nonsense explanation ("False Comprehension"&...
by notzeb
Sun Feb 22, 2015 7:21 am UTC
Forum: Books
Topic: Harry Potter and the Methods of Rationality
Replies: 1036
Views: 414003

Re: Harry Potter and the Methods of Rationality

Harry Potter towards the end of chapter 108: " Have you tried... not being a monster? " Also, wow, double meaning (guess which meaning I didn't notice until just now): It was possible that Harry was the only person in the world against whom Professor Quirrell wouldn't be able to use a ...
by notzeb
Sat Feb 21, 2015 3:35 am UTC
Forum: Books
Topic: Harry Potter and the Methods of Rationality
Replies: 1036
Views: 414003

Re: Harry Potter and the Methods of Rationality

I caught the fake time travel message as soon as it was handed to Harry. Bit of a "what the hell, hero?" moment there. Right now my theory is that Quirrelmort's plan somehow hinges on Harry betraying him. There has been way too much foreshadowing involving bargains and dark rituals......
by notzeb
Thu Feb 12, 2015 9:28 pm UTC
Forum: Mathematics
Topic: Math: Fleeting Thoughts
Replies: 434
Views: 161216

Re: Math: Fleeting Thoughts

You could probably also get away with calling it composition (in analogy with the semigroup of functions from a set to itself).
by notzeb
Thu Jan 08, 2015 6:50 am UTC
Forum: Computer Science
Topic: Mind Blowing Algorithms
Replies: 76
Views: 29537

Re: Mind Blowing Algorithms

Hashlife algorithm
LLL lattice basis reduction algorithm
Ellipsoid method
Gröbner basis (Buchberger's algorithm)
Cylindrical Algebraic Decomposition
by notzeb
Tue Dec 23, 2014 8:03 pm UTC
Forum: Mathematics
Topic: A seemingly simple geometry problem
Replies: 12
Views: 4119

Re: A seemingly simple geometry problem

If c and d are equal, then the quadrilateral is cyclic, so the left ? would be equal to a and the right ? would be equal to b. Otherwise, you usually have to resort to trigonometry or special triangles (the trigonometric Ceva formula can be adapted to solve this type of problem).
by notzeb
Fri Nov 21, 2014 3:20 am UTC
Forum: Mathematics
Topic: [Resolved] Proving some inequalities
Replies: 2
Views: 1692

Re: Proving some inequalities

For the first one, try multiplying the left hand side by (a 4 (b+c) + b 4 (c+a) + c 4 (a+b)) and using Cauchy Schwarz. Then you will need to prove that 2(a 3 + b 3 + c 3 )(a 2 + b 2 + c 2 ) ≥ 3(a 4 (b+c) + b 4 (c+a) + c 4 (a+b)), which follows immediately from the identity a 5 - 3a 4 b + 2a 3 b 2 + ...
by notzeb
Mon Nov 10, 2014 9:15 am UTC
Forum: Mathematics
Topic: What is the future of Mathematic and mathematicians?
Replies: 10
Views: 4486

Re: What is the future of Mathematic and mathematicians?

The GIT is a theorem about logical systems, not computing platforms. And here I thought Geometric Invariant Theory was some sort of study of the invariant elements of a graded polynomial ring under the action of a reductive group... On topic: Scientists have estimated that only 10% of a computer's ...
by notzeb
Sat Sep 27, 2014 6:47 am UTC
Forum: Logic Puzzles
Topic: Emulating a die roll with a weighted coin
Replies: 7
Views: 3461

Re: Emulating a die roll with a weighted coin

Some what shockingly, the easier problem of trying to extract an unbiased coinflip from a biased coin with unknown bias in the fewest expected flips has been proven to have no optimal solution. Check out this paper: http://projecteuclid.org/euclid.aop/1176993384 . (More precisely, they show that an ...
by notzeb
Sun Sep 14, 2014 12:18 am UTC
Forum: Mathematics
Topic: Assumptions in Math (Calculus) word problems
Replies: 254
Views: 45854

Re: Assumptions in Math (Calculus) word problems

Let's do a practice word problem and just talk about assumptions: Two ants are at a common point at time t=0, the first ant starts crawling along a straight line at the rate of 4 ft/min. Two minutes later, the second ant starts crawling in a direction perpendicular to that of the first, at a rate o...
by notzeb
Mon Sep 08, 2014 8:08 am UTC
Forum: Logic Puzzles
Topic: Prisoners and their enemies
Replies: 21
Views: 7556

Re: Prisoners and their enemies

Any maximal cut solves the problem...
by notzeb
Sun Aug 24, 2014 1:19 pm UTC
Forum: Mathematics
Topic: n1*n3 = (n2*n2)-1 - Is there a theorem for this or a proof?
Replies: 5
Views: 2641

Re: n1*n3 = (n2*n2)-1 - Is there a theorem for this or a pro

This trick does have a name - it's the difference of squares trick, in the special case where one of the squares is 1. Lots of people use similar tricks to do things like quickly square numbers ending in 5 (e.g. 45 2 = 40*50 + 5 2 = 2025). It's also the trick that is used to solve the general quadra...
by notzeb
Sun Aug 24, 2014 1:04 pm UTC
Forum: Mathematics
Topic: Assumptions in Math (Calculus) word problems
Replies: 254
Views: 45854

Re: Assumptions in Math (Calculus) word problems

@Forest Goose, there are two "good" ways to think about this. Using context Using "purpose" Which amount to be the same. One persons said the course is supposed to teach math rather than critical thinking about the balloon's analogy. So I suppose in the end, you do have to think...
by notzeb
Sat Aug 09, 2014 8:08 am UTC
Forum: Mathematics
Topic: questions from algebra (inverse functions)
Replies: 25
Views: 4868

Re: questions from algebra (inverse functions)

So I ask again, how are you defining the cardinals? A cardinal is an ordinal which is not equipotent with any smaller ordinal. By the well ordering principle, for every set there is a minimal ordinal which is equipotent to it, this is its cardinality (of course, if you don't have the axiom of choic...
by notzeb
Fri Aug 08, 2014 11:05 pm UTC
Forum: Science
Topic: EMDrive and other reactionless propulsion claims
Replies: 71
Views: 16771

Re: EMDrive and other reactionless propulsion claims

Yeah, you're moving the geometric center of the box but not its center of gravity, so you're not doing any work. Even if you were, the reaction force would push the box back to its initial position, so the total displacement (and thus work) would end up being zero. Aren't there patters of movement ...
by notzeb
Sat Jul 26, 2014 9:37 pm UTC
Forum: Mathematics
Topic: Is it possible for a math obsession to be unhealthy
Replies: 54
Views: 14538

Re: Is it possible for a math obsession to be unhealthy

Orlando, Florida There's your problem right there. Nothing good can come of living in Florida. Have you considered running away from home and moving to a state that doesn't suck? (Full disclosure: I used to live in Miami) If you are curious about what the rest of math looks like and unwilling to ru...
by notzeb
Sat Jul 26, 2014 3:50 am UTC
Forum: Mathematics
Topic: Is it possible for a math obsession to be unhealthy
Replies: 54
Views: 14538

Re: Is it possible for a math obsession to be unhealthy

find that as long as you remember to eat at least once every two days there is no real danger to your health. Sigh... Thinking that being able to at least solely care for yourself is a sufficient bar for being 'healthy' is pretty narcissistic, and a pretty low bar. Sorry, I meant "as long as y...
by notzeb
Sat Jul 26, 2014 2:51 am UTC
Forum: Mathematics
Topic: Is it possible for a math obsession to be unhealthy
Replies: 54
Views: 14538

Re: Is it possible for a math obsession to be unhealthy

If you were truly obsessed with mathematics, you wouldn't be posting on this forum. You would be hanging out in the mathematical library of your local university until closing time, finding a place to work out your ideas for solving whichever problems interested you, or discussing ideas with friends...
by notzeb
Wed Jun 04, 2014 7:12 am UTC
Forum: Logic Puzzles
Topic: Meta-Puzzles
Replies: 6
Views: 4136

Re: Meta-Puzzles

The first thing that came to mind was this.
by notzeb
Wed May 07, 2014 1:50 am UTC
Forum: Logic Puzzles
Topic: The Blindfolded Poem and the Left Arrow Key
Replies: 14
Views: 6881

Re: The Blindfolded Poem and the Left Arrow Key

(Disclaimer: I don't know how difficult this puzzle is.) In general: very hard. Any given letter in the encrypted text can have any position in the original text, and the distance between two letters that are next to each other in the original text can be as big as the whole text. A decryption that...
by notzeb
Thu Feb 20, 2014 3:58 am UTC
Forum: Forum Games
Topic: *almost* the best superpower in the world
Replies: 703
Views: 100036

Re: *almost* the best superpower in the world

So can any virus or bacteria that infects you. Superbugs for everyone!

I can't be harmed by anything which I do not see.
by notzeb
Sun Feb 16, 2014 12:57 pm UTC
Forum: Forum Games
Topic: *almost* the best superpower in the world
Replies: 703
Views: 100036

Re: *almost* the best superpower in the world

You live in a dystopian future where books have been outlawed.

I can see the true nature of reality.
by notzeb
Tue Feb 11, 2014 1:26 pm UTC
Forum: Logic Puzzles
Topic: The philosopher, the most intelligent man and the fish
Replies: 44
Views: 12714

Re: The philosopher, the most intelligent man and the fish

"Is P equal to NP?" "I don't know." "Are you absolutely certain that you are the most intelligent man?" "No." At that moment, the philosopher understood Steve . Edit: An alternative solution that I suddenly like better: "Can you lip-read?" Steve,...
by notzeb
Sun Feb 09, 2014 10:57 am UTC
Forum: Mathematics
Topic: formal logic and similar topics
Replies: 8
Views: 2942

Re: formal logic and similar topics

Marker's "Model Theory" is the textbook I used in undergraduate. It's decent.
by notzeb
Sun Feb 09, 2014 6:36 am UTC
Forum: Mathematics
Topic: One divided by Zero (1/0)
Replies: 44
Views: 8286

Re: One divided by Zero (1/0)

A set S is well ordered by the operator < iff ∀ x ≠ y ∈ S , x < y or x > y . The projective line does not satisfy that definition for any operator; therefore, it is not well-ordered. It can't be partially well-ordered or kinda well-ordered, because there ain't no such thing. What are they teaching ...
by notzeb
Sat Feb 08, 2014 5:47 am UTC
Forum: Mathematics
Topic: One divided by Zero (1/0)
Replies: 44
Views: 8286

Re: One divided by Zero (1/0)

The OP might be interested in the real (or even complex) projective line. This can be thought of as the set of ordinary real numbers together with infinity, where infinity and -infinity are both treated as the same number (so if you were to draw this version of the number line, you would draw it as ...
by notzeb
Sat Jan 25, 2014 6:14 am UTC
Forum: Books
Topic: Worm : Parahuman Web Serial - Comic Booky
Replies: 20
Views: 24058

Re: Worm : Parahuman Web Serial - Comic Booky

Not entirely. Joker - at least in his more modern incarnations - is far more of a personal mark against a symbol than he is a roving agent of chaos. Why else would he continue to stay in Gotham if not specifically to spite Batman? Jack lacks that obsession. Really, he's got more in common with ...
by notzeb
Fri Jan 03, 2014 8:23 pm UTC
Forum: Mathematics
Topic: Strange constant. Apparently useless.
Replies: 33
Views: 9314

Re: Strange constant. Apparently useless.

According to the Inverse Symbolic Calculator, there isn't any simple relationship with other constants.
by notzeb
Thu Dec 26, 2013 12:01 am UTC
Forum: Mathematics
Topic: Is it possible to prove that something is unprovable?
Replies: 24
Views: 7596

Re: Is it possible to prove that something is unprovable?

I feel the need to point out that if ZFC (or whichever axiom system you like best) is inconsistent, then every statement can be proved. Since we can't prove ZFC is consistent (unless it isn't consistent), the only way we could prove that a statement is unprovable is to either find an inconsistency i...
by notzeb
Thu Dec 12, 2013 2:17 am UTC
Forum: Language/Linguistics
Topic: What does "immortal" mean?
Replies: 11
Views: 8740

Re: What does "immortal" mean?

I define it the second way: possible to live forever, but not guaranteed. After all, anything can be killed if you try hard enough. (I'm looking at you, Worm.)
by notzeb
Sat Nov 16, 2013 2:51 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1240: "Quantum Mechanics"
Replies: 201
Views: 46248

Re: 1240: "Quantum Mechanics"

This thread becomes infinitely more entertaining when you realize that all but two of the posters are cleverly coded chatbots.
Spoiler:
I hope you two find each other.
by notzeb
Thu Sep 05, 2013 10:32 am UTC
Forum: Mathematics
Topic: Any usefulness of this metric?
Replies: 6
Views: 4364

Re: Any usefulness of this metric?

snowyowl wrote:
notzeb wrote:It's also useful if you want to put a metric on a countable product of metric spaces.

I don't think I follow. Could you give me the metric on ℝ?
Sure. The distance between (a0, a1, ...) and (b0, b1, ...) will be defined as the sum over all i of 2-i * |ai-bi|/(1+|ai-bi|).

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