Search found 222 matches

by lightvector
Thu Aug 31, 2017 1:49 am UTC
Forum: Mathematics
Topic: Possible "Spot it!"-like decks
Replies: 30
Views: 3248

Re: Possible "Spot it!"-like decks

morriswalters - Yeah, I think you misinterpreted things originally but hopefully that's cleared up now. There is some finite set of symbols. Each card in the deck is an unordered set of D of those symbols. Every symbol is a member of an equal number of cards as every other symbol. Every pair of card...
by lightvector
Tue Aug 29, 2017 2:48 am UTC
Forum: Mathematics
Topic: Possible "Spot it!"-like decks
Replies: 30
Views: 3248

Possible "Spot it!"-like decks

Just for fun - this is a possibly-hard math puzzle inspired by the following game: https://boardgamegeek.com/boardgame/63268/spot-it You have a deck of cards. Every card has exactly 8 different symbols on it, and for every pair of cards there is exactly one symbol that they have in common. Additiona...
by lightvector
Sat Apr 29, 2017 6:39 pm UTC
Forum: Mathematics
Topic: Prime numbers
Replies: 30
Views: 4023

Re: Prime numbers

To clarify what gmalivuk said in case there's a misunderstanding of what "size" means - normally when people talk about complexity theory, they're talking about something's running time relative to the number of *bits* or *digits* in the input. So if your algorithm takes 10 times longer fo...
by lightvector
Wed Jan 11, 2017 1:38 pm UTC
Forum: Mathematics
Topic: Mathematics of p-hacking: random walks and significance
Replies: 2
Views: 1618

Re: Mathematics of p-hacking: random walks and significance

If the underlying process is exactly zero mean or fair with respect to what you're testing (i.e. fair coin flips), then stumbling into significance will almost surely happen if you are allowed to keep going arbitrarily long, and a multiplicative decrease in number of runs that have not yet hit signi...
by lightvector
Sun Dec 25, 2016 4:22 pm UTC
Forum: Religious Wars
Topic: 1/xy
Replies: 12
Views: 6007

Re: 1/xy

I also tend to be a fan of "infix division has strictly lower precedence than multiplication" rather than having equal precedence. I think it's a better convention, and I use it a lot when scribbling to myself on paper or doing back-of-the-envelope math. It even fits that acronym that peop...
by lightvector
Sat Nov 26, 2016 10:29 pm UTC
Forum: Science
Topic: Does eating food measurably affect body temperature?
Replies: 7
Views: 2257

Re: Does eating food measurably affect body temperature?

This might be more related to skin temperature and/or perceptual heat-loss rate rather than body temperature (particularly core temperature), but in the winter I commonly notice a significant drop in how "cold" I feel outside and how rapidly or easily my fingers become cold versus staying ...
by lightvector
Wed Oct 12, 2016 5:09 am UTC
Forum: Mathematics
Topic: Factorization using modular arithmetic
Replies: 41
Views: 7357

Re: Factorization using modular arithmetic

Thank you very much for taking time to analyze my method. So if I understood your main criticism of my method all depends on how to solve a quadratic congruence. You said (I`m quoting you : "Agreed, if we find X such that: X^2+2*17796*X-24049 = 0 mod 2656631477" if I find a way to solve t...
by lightvector
Mon Oct 10, 2016 4:09 am UTC
Forum: Mathematics
Topic: Factorization using modular arithmetic
Replies: 41
Views: 7357

Re: Factorization using modular arithmetic

Here is the procedure for n= 2656631477 As I do ti using Excel and trying to explain what I have in mind it take me time to avoid keyboard mistakes. Here are the first steps with quoting my self (for n=1633) Let us factorize n=1633 using modular arithmetic. A number with 10 digits was given to me :...
by lightvector
Wed Oct 05, 2016 4:45 am UTC
Forum: Mathematics
Topic: Factorization using modular arithmetic
Replies: 41
Views: 7357

Re: Factorization using modular arithmetic

Here's a slightly larger number, but one that still should be well within Excel's ability to handle, if indeed you've found something that scales well enough asymptotically to break RSA. It's the product of two primes, and it's a large enough number that if you can successfully apply your method, it...
by lightvector
Sat May 28, 2016 4:07 am UTC
Forum: Science
Topic: Which planet?
Replies: 28
Views: 4432

Re: Which planet?

I wonder what Google says. 8-) Approximate number of results that Google reported when I did a search on each thing just now: Searched for "<PLANETNAME>": Earth: About 1,080,000,000 results Mars: About 826,000,000 results Mercury: About 282,000,000 results Venus: About 198,000,000 results ...
by lightvector
Tue Feb 02, 2016 6:56 am UTC
Forum: Mathematics
Topic: Screensaver-inspired Lego dropping
Replies: 0
Views: 2669

Screensaver-inspired Lego dropping

This was inspired by watching a screensaver of falling Lego blocks. At the moment this problem seems well out-of-my-league though to solve precisely. I'm curious if anyone has any thoughts as to an analytic approach that might work, or knows about existing results on a problem like this or theorems ...
by lightvector
Sun Jan 17, 2016 2:13 am UTC
Forum: Mathematics
Topic: Help Illustrating Large Numbers
Replies: 5
Views: 1733

Re: Help Illustrating Large Numbers

Less likely than correctly guessing a single atom randomly chosen from the entire mass of the Earth in a single try. Twice. And then winning Powerball right after that. (To give some further intuition - if you gathered one water molecule for every human alive on Earth into a clump, and gathered a nu...
by lightvector
Wed Jan 06, 2016 5:57 am UTC
Forum: Science
Topic: What's up with avocados?
Replies: 22
Views: 3209

What's up with avocados?

Avocados seem pretty weird to me as fruits* go. In particular: 1. Why are they so fatty when so few other fruits that I've heard of have any significant fat content? (Maybe olives are one of the few others?) 2. Why are they not also very sweet? Basically, what are the major underlying mechanisms beh...
by lightvector
Mon Dec 14, 2015 6:02 am UTC
Forum: Logic Puzzles
Topic: The Two Oracles - a statistics problem
Replies: 74
Views: 10198

Re: The Two Oracles - a statistics problem

ThirdParty is definitely right here (as are a few others who posted earlier pointing out the same thing). I also independently came up with the same conclusion prior to reading through the thread. The probability that represents your posterior belief/confidence can be anywhere at all from 0% to 100%...
by lightvector
Mon Dec 07, 2015 7:18 am UTC
Forum: Coding
Topic: Context-switching/"soft threads" in scripting languages?
Replies: 10
Views: 3033

Re: Context-switching/"soft threads" in scripting languages?

Another approach if you don't have "yield" in the language but you do have functions as first class. Then if the syntactical properties of your language allow you to omit enough of the delimiters, you can do something like this: def doThingA() { walk b.x, b.y after 15 { walk c.x, c.y after...
by lightvector
Sat Nov 28, 2015 7:05 pm UTC
Forum: Mathematics
Topic: Integer Factorization of large semiprimes
Replies: 6
Views: 3745

Re: Integer Factorization of large semiprimes

I found this page fairly readable to learn how the predecessor to the GNFS factoring algorithm worked, and which is now the second fastest general method. https://en.wikipedia.org/wiki/Quadratic_sieve I poked into the linked Github page, and am a little skeptical of the A* search formulation for the...
by lightvector
Sun Nov 22, 2015 7:53 am UTC
Forum: Mathematics
Topic: Least numbers discarded when dealing cards
Replies: 30
Views: 5202

Re: Least numbers discarded when dealing cards

Here's an alternate method that is much more flexible than some of the ways other people have presented above. It actually allows us to throw away no entropy at all in the long run! The basic idea is that we use the the random digits 0-9 to generate a random real number by generating its decimal exp...
by lightvector
Sun Jul 19, 2015 3:30 am UTC
Forum: Computer Science
Topic: Deliberately bad algorithms
Replies: 120
Views: 33545

Re: Deliberately bad algorithms

My favorite example from this thread so far, is: For a maximum balance of simplicity and inefficiency: sort(list): if length(list) < 2: return list else: if head(list) <= minimum(tail(list)): return head(list) followed by sort(tail(list)) else: return sort(tail(list) followed by head(list)) minimum...
by lightvector
Sat Jul 04, 2015 3:31 am UTC
Forum: Computer Science
Topic: In-brain PRNG
Replies: 8
Views: 5408

Re: In-brain PRNG

Something that I've actually done in the past to generate ok-quality non-external-predictable entropy via brain is to generate "random" 5-digit numbers and take them modulo 7 or 13, or similar. I don't think it quite fits in to being doable in just a few seconds for most people (and defini...
by lightvector
Tue Feb 10, 2015 1:36 pm UTC
Forum: Mathematics
Topic: 10% x5 != 50%?
Replies: 17
Views: 3530

Re: 10% x5 != 50%?

It becomes more obvious when you consider the case of "50% x 2 vs 100%". If you flip a fair coin twice, is it guaranteed (i.e. 100%) to come up heads at least once? Obviously not, you could get two tails. But isn't it 50% the first flip and 50% the second flip, and 50% + 50% = 100%? Well, ...
by lightvector
Sun Feb 08, 2015 3:34 pm UTC
Forum: Mathematics
Topic: How do axioms specify a new system vs continuing an old one?
Replies: 81
Views: 7864

Re: How do axioms specify a new system vs continuing an old

So - technically you are right - we can take any statements in the given language and call them axioms. But we shouldn't expect to form a consistent system when we mix true and false statements (with respect to system A). As a rule, we would only expect to have consistent systems when we choose all...
by lightvector
Tue Oct 14, 2014 5:00 am UTC
Forum: Mathematics
Topic: Mildly interesting number theory question
Replies: 6
Views: 2404

Re: Mildly interesting number theory question

Here's an attempt at an argument. This one also assumes am+bn hits all integers, and any single step is not too complicated, but it's not trivial either. It might be the same as the existing proof you mentioned you had. I'll use x and y instead of m and n, since I think it's more common to s...
by lightvector
Sat Sep 27, 2014 5:07 am UTC
Forum: Logic Puzzles
Topic: Emulating a die roll with a weighted coin
Replies: 7
Views: 2864

Re: Emulating a die roll with a weighted coin

Your idea sounds good to me. I haven't thought about it enough, so there might be an altogether different approach that's cleaner and better, but we can take the approach of iteratively improving on your idea to get better strategies by... By just going nuts extracting die rolls out of the entropy t...
by lightvector
Thu Sep 25, 2014 4:35 am UTC
Forum: Science
Topic: Bell's Inequality Experiments Question
Replies: 4
Views: 2313

Re: Bell's Inequality Experiments Question

Here's an interesting article that explains how quantum mechanics can allow two cooperating players to win a certain game ("CHSH game") with strictly greater probability than would be allowed by classical mechanics, assuming no FTL communication. Plus a wacky theoretical application of thi...
by lightvector
Sat Sep 13, 2014 5:22 pm UTC
Forum: Computer Science
Topic: a little rng
Replies: 9
Views: 5918

Re: a little rng

Trying to design a PRNG can be a good learning experience. But actually using one that you've designed yourself for any real application is quite a bad idea. There are a variety of problems you can run into - whether it's having certain initial seed values lead into cycles with very short periods, o...
by lightvector
Sat Aug 30, 2014 2:27 am UTC
Forum: Science
Topic: FTL communication and time travel
Replies: 51
Views: 12225

Re: FTL communication and time travel

I don't understand why this argument is still happening. It sounds like people are just talking past each other because they're using the word "relativity" differently, and not actually disagreeing on anything of actual substance. 1) If by "relativity", you mean "the princip...
by lightvector
Sat Jun 28, 2014 2:44 am UTC
Forum: Computer Science
Topic: alpha-beta pruning seems counterintuitive
Replies: 3
Views: 3362

Re: alpha-beta pruning seems counterintuitive

Consider a game: There are several bags each containing various items. Your goal is to obtain the most valuable item that you can. Your opponent is trying to make you end up with the least valuable item that he can. The rules are that you may inspect the contents of the bags first. Then, you must ch...
by lightvector
Sat Jun 14, 2014 10:44 pm UTC
Forum: Mathematics
Topic: Vectors without components
Replies: 19
Views: 4071

Re: Vectors without components

That's a nice proof. A lot of the basic implications of the axiom of choice become completely obvious when stated using well-ordering and transfinite induction, so much so that I'd say that well-ordering and transfinite induction are usually the "right" way to conceptualize the axiom of ch...
by lightvector
Fri Apr 18, 2014 6:13 pm UTC
Forum: Mathematics
Topic: Estimators for attendance.
Replies: 3
Views: 1954

Re: Estimators for attendance.

Your second and third options are actually the same. In general, you want something of the form y + (S-y-n) * p, where p is your best guess or estimate of the proportion of people who have not RSVPed who will end up deciding to come. Your first option is this with p = 1/2, and your second option is ...
by lightvector
Sat Mar 22, 2014 7:52 pm UTC
Forum: Mathematics
Topic: Axiomatic mathematics has no foundation
Replies: 158
Views: 30093

Re: Axiomatic mathematics has no foundation

Treatid, you're still not understanding. Everyone already agrees with the main point of your thesis (although not all the supporting details). The apparent disagreement is because you are using words like "axiom" to mean something different than what everyone else means when they say "...
by lightvector
Sat Mar 15, 2014 5:02 pm UTC
Forum: Mathematics
Topic: Axiomatic mathematics has no foundation
Replies: 158
Views: 30093

Re: Axiomatic mathematics has no foundation

@Treatid: I think you fundamentally misunderstand the purpose of mathematical axioms. They're not intended to define some sort of ground-level absolute knowledge from which all else springs forth. They're not intended as assertions that you have to assume are "true" in some platonic sense ...
by lightvector
Tue Jan 28, 2014 2:28 am UTC
Forum: Individual XKCD Comic Threads
Topic: 1322: Winter
Replies: 125
Views: 24504

Re: 1322: Winter

Sometimes using different words is part of the fun... Finally, here you are. At the delcot of tondam, where doshes deave. But the doshery lutt is crenned with glauds. Glauds! How rorm it would be to pell back to the bewl and distunk them, distunk the whole delcot, let the drokes discren them. But yo...
by lightvector
Tue Jan 14, 2014 5:56 am UTC
Forum: Mathematics
Topic: Understanding Fast-Growing Functions
Replies: 6
Views: 3164

Re: Understanding Fast-Growing Functions

Why, for example, haven't we gone to D 6 (99)? Or D 5 (100), or D D(99) (99)? What if I were to define a function E(k), where E(k) = D M (k), and M = D D...(k) (k), where we iterate D(k) D(k) times over, and in turn, iterate that process D(k) times over? One thing to note when deali...
by lightvector
Sun Dec 01, 2013 11:50 pm UTC
Forum: Mathematics
Topic: P vs NP is independent of the axioms of ZFC
Replies: 26
Views: 5771

Re: P vs NP is independent of the axioms of ZFC

Treatid, it's okay for different encodings of the same problem to differ as to whether they are in P or not. That's because P is not defined as a set of problems. P is defined as a set of problems-with-specific-encodings. If it turns out that one encoding of a problem is in P, and a different encodi...
by lightvector
Fri Nov 29, 2013 4:40 am UTC
Forum: Mathematics
Topic: P vs NP is independent of the axioms of ZFC
Replies: 26
Views: 5771

Re: P vs NP is independent of the axioms of ZFC

Imagine if I claimed that I had a new theory of gravity, and in an attempt to explain this theory I proceeded to talk about ice cream, and about popular flavors of ice cream, and about the optimal temperature to store ice cream, and about how to make ice cream, and so on, except that every time I wo...
by lightvector
Thu Nov 28, 2013 4:41 am UTC
Forum: Mathematics
Topic: P vs NP is independent of the axioms of ZFC
Replies: 26
Views: 5771

Re: P vs NP is independent of the axioms of ZFC

I don't see where you've provided your definitions of "P" and "NP", but based on your post I'm pretty sure they have nothing to do with what everyone else means when they talk about "P" and "NP". Can you provide a precise definition of what you are referring t...
by lightvector
Sun Oct 20, 2013 3:54 pm UTC
Forum: Science
Topic: Lower bound for Earthlike planet
Replies: 40
Views: 5625

Re: Lower bound for Earthlike planet

Surface gravity should scale as M/r^2, where M is the planet mass and r is the radius. Escape velocity should go as the square root of the necessary kinetic energy for escape, which, integrating, scales as M/r. So you can increase the escape velocity pretty much arbitrarily while holding the surface...
by lightvector
Sun Sep 15, 2013 12:56 am UTC
Forum: Mathematics
Topic: mean of geometric distribution: *intuitive* reason
Replies: 14
Views: 4149

Re: mean of geometric distribution: *intuitive* reason

This might be less intuitive, depending on how your intuition works. But you can also observe that the average needed is the same as 1 plus 5/6 of the average needed (you always need at least 1 roll, then 5/6 of the time you're back where you started). So 1/6th of the average is 1, so the average is...
by lightvector
Fri May 17, 2013 1:41 am UTC
Forum: Science
Topic: D-Wave Quantum Computer
Replies: 5
Views: 3312

Re: D-Wave Quantum Computer

Yeah, n quantum bits are very likely NOT equivalent to 2^n classical bits. You commonly hear that the latter can simulate the former, but all that shows is that (n quantum bits) <= (2^n classical bits) in "computational power". It certainly doesn't let you conclude that they're equal, any ...

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