Search found 532 matches

by letterX
Wed Jul 29, 2015 6:52 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9990
Views: 1999583

Re: Coding: Fleeting Thoughts

Lastly, it took me a day to find out matlab does have a function to get the magnitude of a vector: norm . It was neither length nor size and magnitude doesn't exist at all. Nor do normalize or unit exist for normalizing a vector. :cry: So, it used to mystify me why matlab doesn't have a normalize f...
by letterX
Sat Mar 14, 2015 9:31 pm UTC
Forum: Mathematics
Topic: Graph Theory definition question
Replies: 6
Views: 1879

Re: Graph Theory definition question

So, your worry about slightly-non-standard names for the concept is correct -- this concept is usually called the treewidth of a graph: http://en.wikipedia.org/wiki/Treewidth . It turns out that there are several equivalent definitions, and the unfortunate thing is that none of them is particularly ...
by letterX
Sat Jan 17, 2015 5:38 am UTC
Forum: Science
Topic: "connecting" the earth and the moon
Replies: 24
Views: 6041

Re: "connecting" the earth and the moon

Pfah! Moving the moon is too hard. Let's instead slow down the earth so that the moon's current orbit is now geosynchronous. Nobody will notice the difference, right?
by letterX
Fri Dec 26, 2014 4:11 am UTC
Forum: Computer Science
Topic: how to communicate under heavy targeted surveillance
Replies: 13
Views: 8437

Re: how to communicate under heavy targeted surveillance

You can set up quantum cryptosystems that cannot be eavesdropped on without being detected. You still have the issue of key exchange though Wrong! Quantum crypto has no key exchange issue. What you do need to set up is a qubit transfer channel, though. Once you have that, you can exchange a key in ...
by letterX
Thu Nov 27, 2014 5:28 pm UTC
Forum: Mathematics
Topic: Clarification on definition of category
Replies: 6
Views: 2598

Re: Clarification on definition of category

Sorry, I did misspeak. Let's call this putative "category" C (it's not actually a category, but that's what we're trying to show). It has only one object A. So when I said "identity element" I meant "the identity map for the only object". There are lots of possible ways...
by letterX
Thu Nov 27, 2014 4:09 pm UTC
Forum: Mathematics
Topic: Clarification on definition of category
Replies: 6
Views: 2598

Re: Clarification on definition of category

Another concrete example: You can think of any group as a category with only one "object". Note that this is not the same as considering the category of groups, Group. We're just looking at one group, maybe let's pick a very simple one, Z_2. How can we make this a category? Well, we have o...
by letterX
Sun Nov 09, 2014 11:40 pm UTC
Forum: Computer Science
Topic: Choosing the best quiz team
Replies: 8
Views: 4295

Re: Choosing the best quiz team

Covering problem sounds about right. You have n people, which gives you n different sets S, where S_i is the set of questions that person i got correct. You want to pick 3 of these sets to cover as many questions as possible. Set cover is NP-hard so there isn't a general algorithm to solve it, but t...
by letterX
Sun Nov 09, 2014 11:30 pm UTC
Forum: Science
Topic: Can protons be extracted from an acid solution?
Replies: 26
Views: 5418

Re: Can protons be extracted from an acid solution?

If you had all the protons from 1L of water in a sphere, you'd have about 53MC of charge in a sphere 6.2cm in radius, for a total electrostatic potential energy of 2.4e28 J, or 6 trillion megatons of TNT. For comparison, that's only 4 orders of magnitude less than the gravitational binding energy o...
by letterX
Thu Oct 23, 2014 4:57 am UTC
Forum: Mathematics
Topic: How many ways can you prove x + 1/x >= 2?
Replies: 23
Views: 16495

Re: How many ways can you prove x + 1/x >= 2?

x + 1/x is convex. The derivative at x = 1 is 1 - 1 = 0, and 1 + 1/1 = 2, so since convex curves lie above any tangent line, x + 1/x >= 2. Have been doing lots of convex optimization recently, so was my first thought.

Pretty sure that counts as different than all prior proofs.
by letterX
Tue Jul 22, 2014 1:36 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9990
Views: 1999583

Re: Coding: Fleeting Thoughts

For keeping packages synchronized between machines, have you considered Vundle ? That should reduce your problem to keep your .vimrc synchronized between machines (since packages then are specified in your .vimrc with vundle). I haven't actually tried using it across machines, but I do use it for pa...
by letterX
Wed Jul 16, 2014 6:28 pm UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9990
Views: 1999583

Re: Coding: Fleeting Thoughts

Ahh, got it. So, not in-place like an in-place sort. The extra allocated memory ends up being 2x the amount of memory you started with anyways, which ends up being not bad.
by letterX
Wed Jul 16, 2014 3:24 pm UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9990
Views: 1999583

Re: Coding: Fleeting Thoughts

So, the code claims to be an in-place FFT, but from looking at the documentation for valarray, the lines: CArray even = x[std::slice(0, N/2, 2)]; CArray odd = x[std::slice(1, N/2, 2)]; seem to create a copy of the data? Maybe I just misunderstand valarray and slices, though.
by letterX
Sat Mar 08, 2014 9:47 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9990
Views: 1999583

Re: Coding: Fleeting Thoughts

ahammel wrote:Bladow! New keyboard

My! That is a very *vim* keyboard!
by letterX
Sat Mar 01, 2014 7:21 pm UTC
Forum: Fictional Science
Topic: How close can two planets' surfaces get?
Replies: 15
Views: 11057

Re: How close can two planets' surfaces get?

Well yes, but the problem with the 6-foot distance is really that two realistic planets would become too-tidally-locked, in that tidal forces would rip them apart.
by letterX
Sat Mar 01, 2014 6:36 pm UTC
Forum: Fictional Science
Topic: How close can two planets' surfaces get?
Replies: 15
Views: 11057

Re: How close can two planets' surfaces get?

speising wrote:and they certainly couldn't be both tidally locked to each other. for that to work, they'd need to be in geosynchronous orbits.

Actually, Pluto and Charon are both tidally locked to each other. So that on its own isn't impossible.
by letterX
Sat Mar 01, 2014 5:37 pm UTC
Forum: Fictional Science
Topic: How close can two planets' surfaces get?
Replies: 15
Views: 11057

Re: How close can two planets' surfaces get?

Because of the Roche Limit, if the planets are each held together by their own self-gravity, they cannot be this close together. As for rigid planets, I suspect you'd need unobtanium, but I'm not sure how to do the math on that.
by letterX
Tue Feb 25, 2014 4:26 pm UTC
Forum: Mathematics
Topic: Generality of polynomial approximation
Replies: 7
Views: 2465

Re: Generality of polynomial approximation

EDIT: I just realized a problem with my counter-example. f(0) = g(0), but the OP stated f(x) > g(x) on the interval. It may be possible to salvage this, but I'm not sure. The mutual restrictions of min(f-g) does not exist, f > g, and f and g continuous on a close interval are difficult to hit I thi...
by letterX
Tue Feb 18, 2014 3:32 pm UTC
Forum: Science
Topic: Boiling in the greenhouse
Replies: 19
Views: 4037

Re: Boiling in the greenhouse

Yeah, if you re-condense the water, then you get a solar still, which is a pretty handy piece of equipment to have if you're stuck in the wilderness.
by letterX
Tue Feb 11, 2014 4:11 pm UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9990
Views: 1999583

Re: Coding: Fleeting Thoughts

\Why is this allowed? What is the point of const if you can just cast it away like that? Because C-style casts regularly break the type system and you shouldn't use them? There's also const_cast, which does the same thing, but is easier to grep for and specifically alerts anyone reading the code to...
by letterX
Tue Feb 11, 2014 6:22 am UTC
Forum: Mathematics
Topic: almost homework, a system in 3 unknowns
Replies: 11
Views: 3183

Re: almost homework, a system in 3 unknowns

But it's not rational and some luck is needed to find it Or, like, use the cubic formula . Or find it numerically by, e.g., Newton's method. Not sure what "luck" has to do with it, unless you're picking real numbers randomly and seeing if they're roots. If so, "good luck" with t...
by letterX
Mon Feb 03, 2014 3:18 pm UTC
Forum: Mathematics
Topic: How should I approach this optimization problem
Replies: 16
Views: 3250

Re: How should I approach this optimization problem

Yup, sorry about the -2 lambda, that was a mistake. Anyways, Lagrange multipliers are great for turning constrained optimization problems into unconstrained ones. This ends up being most useful in situations where unconstrained optimization is easy (i.e., where you can apply calculus without too muc...
by letterX
Mon Feb 03, 2014 5:14 am UTC
Forum: Mathematics
Topic: How should I approach this optimization problem
Replies: 16
Views: 3250

Re: How should I approach this optimization problem

Ok, so the first thing to know how to do is unconstrained optimization: For one variable, you probably already know that the global optimum is going to either occur at a critical point (a place where the derivative is equal to zero) or at +/- infinity. So the way you optimize a function of one varia...
by letterX
Sun Jan 26, 2014 11:09 pm UTC
Forum: Mathematics
Topic: Need help understanding the usual topology on R
Replies: 23
Views: 5646

Re: Need help understanding the usual topology on R

That is the "definitional if" (possibly not the real word for it), which is actually an if and only if. So, both the things you just said have to hold. It's a bit of a quirk of mathematical prose that we often say "We define x to be a foo if bar happens" which really means x is a...
by letterX
Sat Jan 25, 2014 8:22 am UTC
Forum: Science
Topic: Vacuum particles and gravity
Replies: 6
Views: 2270

Re: Vacuum particles and gravity

Energy density also exerts gravity in General Relativity, so there's no difference between a certain amount of background energy (in the form of, e.g. photons) vs. a virtual particle pair, in terms of the gravity it exerts. For your second question, the virtual particle pairs that we usually talk ab...
by letterX
Fri Nov 01, 2013 6:35 am UTC
Forum: Coding
Topic: Coding: Fleeting Thoughts
Replies: 9990
Views: 1999583

Re: Coding: Fleeting Thoughts

Is it wrong that I wrote my first set of real unit tests the other day, whilst completing a pre-interview programming screen? Is it wrong that the first time I actually worked with any code that utilised inheritance was at an interview? I think you're doing well. I didn't do either of those things ...
by letterX
Mon Oct 28, 2013 11:31 pm UTC
Forum: Fictional Science
Topic: Dual world engineering
Replies: 33
Views: 9783

Re: Dual world engineering

Huh. Somewhere, I'd picked up the intuition that if the effective gravity (actual gravity + centrifugal force) was higher in one location and lower in another, then mass would move around so that they were the same both places. But it occurs to me that that's an argument by way of "getting for...
by letterX
Mon Oct 28, 2013 5:37 pm UTC
Forum: Fictional Science
Topic: Dual world engineering
Replies: 33
Views: 9783

Re: Dual world engineering

No, the deformation actually exaggerates the effect slightly. Huh. Somewhere, I'd picked up the intuition that if the effective gravity (actual gravity + centrifugal force) was higher in one location and lower in another, then mass would move around so that they were the same both places. But it oc...
by letterX
Sun Oct 27, 2013 8:51 pm UTC
Forum: Fictional Science
Topic: Dual world engineering
Replies: 33
Views: 9783

Re: Dual world engineering

That's not how tidal forces work. Remember you are in freefall around the other planet. You are not heavier on the back side of the planet, because of the pull of the other planet. You are lighter because its pull is less and your orbit radius is greater. You would be the heaviest ninety degrees fr...
by letterX
Sat Oct 26, 2013 1:22 am UTC
Forum: Mathematics
Topic: n sided polygon, n < 3
Replies: 35
Views: 6712

Re: n sided polygon, n < 3

mike-l wrote:
gmalivuk wrote:When did "poly" stop meaning "many"?

Polynomials anyone?

You mean the thing which is a sum of many monomials?
by letterX
Sat Oct 12, 2013 2:27 am UTC
Forum: Mathematics
Topic: Is this ambiguous? Is it fallacious?
Replies: 92
Views: 19212

Re: Is this ambiguous? Is it fallacious?

That's exactly what I mean by isomorphic, and you've got me dead to rights. Dunno how I missed that one. Perhaps we better rename mine the "Schrollini minimal commuting Z2 x Z2 faithful action group," or the "SMCZ2xZ2FAG" for short. They're both Z2xZ2 faithful group actions, so ...
by letterX
Fri Oct 11, 2013 11:09 pm UTC
Forum: Mathematics
Topic: Is this ambiguous? Is it fallacious?
Replies: 92
Views: 19212

Re: Is this ambiguous? Is it fallacious?

By the way, your definition of a system <S, X, Y> where X,Y are distinct involutions on S is known in Algebra as a " Group action ". More specifically, the functions {identity, X, Y, XY} are a group (they're the group Z_2 x Z_2), and a group action is a homomorphism G -> Perm(S), where Per...
by letterX
Wed Oct 09, 2013 3:59 am UTC
Forum: Mathematics
Topic: Is this ambiguous? Is it fallacious?
Replies: 92
Views: 19212

Re: Is this ambiguous? Is it fallacious?

Mathematically a binary system can be specified by a non-trivial instance of a function X where X(X(s 1 )) = s 1 . In such a system X(s 1 ) = s 2 , X(s 2 ) = s 1 . That is, when the operator is such that X(X(s 1 )) = s 1 the operator relates a pair of states {s 1 , s 2 } by providing a function tha...
by letterX
Wed Sep 18, 2013 1:53 pm UTC
Forum: Science
Topic: Earth as a column
Replies: 56
Views: 13491

Re: Earth as a column

Define an imaginary sphere with Earth's radius at the center of gravity of your object. If your object is completely contained within that sphere, it will have the same gravity as if it was uniformly distributed, regardless of what it actually looks like. This is only true if you end up with a sphe...
by letterX
Fri Sep 13, 2013 4:00 am UTC
Forum: Science
Topic: Could a dryer randomly fold clothing? (ongoing debate)
Replies: 13
Views: 8769

Re: Could a dryer randomly fold clothing? (ongoing debate)

So, this actually just happened to me! Or rather, one shirt out of an entire load ended up correctly folded (the rest of the load was the usual jumble). This is probably largely confirmation bias because I was already primed to look for folded laundry after the dryer, but it puts an upper bound for ...
by letterX
Wed Aug 21, 2013 9:09 am UTC
Forum: Science
Topic: There is only one* model consistent with CPT Symmetry
Replies: 129
Views: 39283

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

Man, I really thought this thread would be done by now. But, since it isn't, here's my complete, consistent axiomatization of a universe which is CPT symmetric which is clearly not our own: 1) There is nothing. 2) Nothing ever happens. 3) There are no charges (see 1 and 2...) This axiomatization is ...
by letterX
Sat Aug 10, 2013 8:45 am UTC
Forum: Science
Topic: There is only one* model consistent with CPT Symmetry
Replies: 129
Views: 39283

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

The following seems to be the meat of your argument: Objects that are constrained to only 2 possible states are binary objects. If we represent a binary object as b then a group of 3 binary objects can be represented as {b, b, b}. Given that all binary objects are equivalent then there is only one d...
by letterX
Tue Aug 06, 2013 8:11 am UTC
Forum: Computer Science
Topic: How prone are plagiarism-detection tools to false-positives?
Replies: 7
Views: 9349

Re: How prone are plagiarism-detection tools to false-positi

Having been on the using-end of these tools, my impression is that they generally allow a fairly high false-positive rate for a low false-negative rate, so that the tool can report all plausible cases of plagarism to the instructor. Then, it's up to the human to decide if the (much smaller pool of) ...
by letterX
Sun Jul 14, 2013 9:40 am UTC
Forum: Mathematics
Topic: Calculating a progressively more complicated battle
Replies: 6
Views: 1940

Re: Calculating a progressively more complicated battle

Honestly just doing lots of simulated, repeated trials is going to give you the most accurate answers with the least effort. Many of these problems can probably be worked out by hand, but the time to do so is much greater than just writing a few lines of code and running 10 million trials. Though, s...
by letterX
Fri Jun 28, 2013 4:48 am UTC
Forum: Mathematics
Topic: Calculus Question (Existence of a Function)
Replies: 7
Views: 3075

Re: Calculus Question (Existence of a Function)

What do you mean by: (exponential functions don't count as f(x) doesn't span R in that case) Do you mean that e^x doesn't cut it because the limit as x goes to -inf is 0? If that's your only problem, how can you modify e^x to get something that goes to -inf, but still looks basically the same as far...
by letterX
Sun Jun 23, 2013 10:50 am UTC
Forum: Computer Science
Topic: Building a foundation for CS/machine learning
Replies: 4
Views: 5707

Re: Building a foundation for CS/machine learning

Well, "not directly relevant to CS and machine learning" isn't strictly true. However, if you remember the following fact, you'll know basically everything Calculus has to say about machine learning (and... really this is pretty much the only part of Calculus that any CS ever uses): If you...

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