32 ms·
Ask YC: What is your favourite paradox?
Mine has to be Olber's Paradox which asks 'Why is it dark at night?' Possible answers to this question are profound: the universe is of finite size or has a finite age.
- martianpenguin 19y agohttp://en.wikipedia.org/wiki/Paradoxical_combinator http://en.wikipedia.org/wiki/Paradoxical_combinator
- mercurio 19y agoRussell's paradox. http://en.wikipedia.org/wiki/Russell's_paradox http://en.wikipedia.org/wiki/Russell's_paradox
- mixmax 19y agogirls
- kirubakaran 19y agoIf they are a paradox to you, my hero who scored with a porn star, I don't know what to say :-)
- mixmax 19y agoYou have a good memory ;-)
- mrtron 19y agoIf that is your hero definition, what is your superhero definition?
- kirubakaran 19y agomixmax wearing underwear over his pants, duh
- ghiotion 19y agoZeno's paradox, which proves that motion is an illusion: http://en.wikipedia.org/wiki/Zeno's_paradoxes http://en.wikipedia.org/wiki/Zeno's_paradoxes Those ancient Greeks knew their shit.
- mattmaroon 19y agoIn that same article you linked it explains why those paradoxes don't prove shit.
- webwright 19y agoI'll second Zeno. Sooo applicable to software development. I love it so much, I wrote a blog post about it.
- kalid 19y agoLove Zeno's paradoxes. And apparently they aren't fully resolved today -- is the universe quantized? Is spacetime really continuous, or is that an unrealistic mathematical abstraction?
- hobbs 19y agoZeno is still my favorite. To summarize in modern terms: in order for a particle to move 1 inch, it must first move 1/2 inch. Before it can move 1/2 inch, it must move 1/4 inch. Before it can move 1/4 inch, it must move 1/8 inch. And so on. The paradox is, if a particle has to traverse an infinite number of infinitely small spaces before it can move even one inch, how is it possible that it can move at all? Some mathematicians pull out calculus to "disprove" the paradox, but to me it disproves nothing. For example, you can show, mathematically, that sum( 1/(2^N) ) = 1 as N goes from 1 to infinity. The problem is that you have to go to infinity before it will sum to 1. If space is infinitely divisible and a particle has to traverse an infinite number of subspaces in order to move just a nanometer, I still don't see how it's possible that it could move at all.
- TheWama 19y agoI have a love/hate relationship with Condorcet's paradox (http://en.wikipedia.org/wiki/Condorcet's_paradox http://en.wikipedia.org/wiki/Condorcet's_paradox): love: it illustrates a fundamental limitation of democratic processes hate: it's the main reason the IMO best known voting method (http://en.wikipedia.org/wiki/Condorcet_method http://en.wikipedia.org/wiki/Condorcet_method) is difficult to explain/advocate for...
- doubleplus 19y agoThe 20 Eye: http://www.zappos.com/images/725/7257495/5089-291353-d.jpg http://www.zappos.com/images/725/7257495/5089-291353-d.jpg
- eru 19y ago?
- wallflower 19y ago"Do as I say and not as I do."
- Zeromus 19y agoI didn't have one, but thanks to this article I'll be wasting the next few days reading this: http://en.wikipedia.org/wiki/List_of_paradoxes http://en.wikipedia.org/wiki/List_of_paradoxes
- corroded 19y agoyou didn't have to drag us in with you T_T thanks to you i'll be also reading that list along with all the ones that everyone posted here XD
- eru 19y agoJust to make you procrastinate even more: http://en.wikipedia.org/wiki/List_of_cognitive_biases http://en.wikipedia.org/wiki/List_of_cognitive_biases
- aswanson 19y agoExistence.
- mnemonicsloth 19y agoIt's not really paradoxical [1], but I've always thought Gabriel's Horn was pretty cool. It's a (non-fractal) object with finite volume and infinite surface area. http://en.wikipedia.org/wiki/Gabriel%27s_Horn http://en.wikipedia.org/wiki/Gabriel%27s_Horn
- wallflower 19y agoReminds me of Klein's bottle
- tlrobinson 19y agoFinite volume and infinite surface area, eh? For example, volume grows as the cube of linear dimension, but surface area only as the square. So as animals get bigger they have trouble radiating heat. http://www.paulgraham.com/ycombinator.html http://www.paulgraham.com/ycombinator.html Perhaps large animals should make themselves into the shape of Gabriel's Horn. Of course then they'll radiate too much heat.
- mercurio 19y agoI read the wiki article and it turns out the horn uses precisely that dimensional difference in a very clever way. The radius varies as 1/x along the x-axis, so the volume grows as 1/x^2 while the surface area grows as 1/x. This means the growth rate of volume goes to zero much faster than that of the surface area. As a result the volume integral converges, while the surface area diverges.
- __ 19y agoThe one I like least.
- mercurio 19y agoNot to rain on your parade, but your statement is a lie and not a paradox.
- __ 19y agoThat could be said of many so-called paradoxes. I think it has as much claim to "paradox" as the interesting number paradox.
- mercurio 19y agoYes, the interesting number paradox is particularly weak. But even it has an argument that seems puzzling initially, and has a much stronger version (called the Berry paradox, that has deep connections to Godel's incompleteness theorems). The statement "My favorite paradox is the one I like least" has nothing paradoxical about it. It can easily be deduced to be false. Its just a contradiction, like saying "This sentence is true and false". Compare that to "This sentence is false" which is a paradox.
- __ 19y agoThat statement is false if you're using Merriam-Webster's definition of "lie" ("to make an untrue statement with intent to deceive"). I wrote that with intent to amuse and not with intent to deceive.
- mercurio 19y agoThat's the definition of lie as a verb. I used lie as a noun. I hope you didn't think I was accusing you of lying. All I meant was that the statement was technically a lie, so the humor fell a little flat.
- dfranke 19y agoThe hangman paradox: http://en.wikipedia.org/wiki/Unexpected_hanging_paradox http://en.wikipedia.org/wiki/Unexpected_hanging_paradox
- yters 19y agoCurry's paradox is cool: "If this sentence is true, then Santa Claus exists." http://plato.stanford.edu/entries/curry-paradox/ http://plato.stanford.edu/entries/curry-paradox/
- mercurio 19y agoThis one is particularly cool, as on the face of it, the sentence just seems totally harmless. You think "well the sentence is not true and Santa Claus doesn't exist" and there's no hint of paradox.
- manny 19y agoBanach-Tarski paradox: http://en.wikipedia.org/wiki/Banach–Tarski_paradox http://en.wikipedia.org/wiki/Banach–Tarski_paradox This has always blown my mind. From Wikipedia: "The Banach–Tarski paradox is a theorem in set theoretic geometry which states that a solid ball in 3-dimensional space can be split into several non-overlapping pieces, which can then be put back together in a different way to yield two identical copies of the original ball." Trippy.
- tel 19y agoYou can also deconstruct and rebuild that ball into another one of infinite size, I believe. I'm not sure if you can do infinite off the top of my head, but I'm certain of at least arbitrary. Pretty much everything that involves abusing the Axiom of Choice ends up trippy and fun.
- mnemonicsloth 19y agoMy favorite quote about the Axiom of Choice[1]: "The Axiom of Choice is obviously true, the Well-Ordering Principle is obviously false, and who can tell about Zorn's Lemma?" Of course, AOC, WOP, and ZL are all logically equivalent. [1] Possibly the nerdiest thought my brain has ever formed; this site makes me very happy.
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- nagoff 19y agoLeading to one of my co-worker's favourite jokes, Q: What's an anagram of "Banach-Tarski" A: "Banach-Tarski Banach-Tarski"
- neilk 19y agoI'd really like someone to explain Banach-Tarski to me in some way that I can sort of understand. I understand it has to do with AOC, which seems totally reasonable, and then I'm lost. Also, I have trouble with "incrementally" understanding this. I can understand that the limit of 1/n (n->INF) is 0, because even with large finite numbers we're getting close to 0, but no matter how many times I cut up an orange I detect no Banach-Tarski strangeness.
- paulgb 19y agoI find Hilbert's Paradox is handy when thinking about infinity. http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_Hotel http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_...
- yelsgib 19y agohttp://en.wikipedia.org/wiki/Prisoners_and_hats_puzzle#Countably_Infinite-Hat_Variant http://en.wikipedia.org/wiki/Prisoners_and_hats_puzzle#Count... "In fact, even if we allow an uncountable number of different colors for the hats, the axiom of choice provides a solution that guarantees that only finitely many prisoners must die." This is by far the craziest result coming out of AOC.
- eru 19y agoThe Axiom of Choice saves lives!
- joseakle 19y agoIs "Don't listen to me." a paradox?
- eru 19y agoNo. I read it and followed your instructions. It's not even a contradiction when written down.
- simanyay 19y agoGrandfather paradox: http://en.wikipedia.org/wiki/Grandfather_paradox http://en.wikipedia.org/wiki/Grandfather_paradox
- tlrobinson 19y agoSchrödinger's cat
- bayareaguy 19y agoIt's not a paradox by itself, but the Heisenburg uncertainty principle leads to a lot of unintuitive things too.
- dkokelley 19y agoThis is a false sentence.
- bootload 19y agopython ~ http://www.paulgraham.com/pypar.html http://www.paulgraham.com/pypar.html
- RNlR 19y agoDemocracy or mob-intelligence
- ovi256 19y agoMine: People cannot completely disagree: or, we will always agree about at least one fact. Proof: Let's say we do not agree about anything. After thoroughly exploring our belief space and noticing this, we will have to agree that we do not agree on anything. So there you have it, a common belief. BTW, I am looking for prior art on this one. Any philosophy students around? I think it is related to Russel's Paradox. Any help in elucidating this would be apreciated. Hey, we could co-author the publication :-P
- eru 19y agoI can always refuse to argue with you and punch you instead.
- coffeeaddicted 19y agoThe Fermi paradox - "where are they?" http://en.wikipedia.org/wiki/Fermi_paradox http://en.wikipedia.org/wiki/Fermi_paradox After all, besides the importance to us, the earth is still a rather small dot in this universe and I really like to know what's happening out there. I have some hope that we can answer that paradox some day and maybe we will even get the first hints to that within my lifetime.
- michaelneale 19y agoI think they are still listening to our internets and getting confused as to why we have a global network which seems to exist (at least 60% exist) so we can offer ourselves genital enlargements. And perhaps wonder why we have "heating stations" all over the planet, when we really have a lack of energy.
- wlievens 19y agoPeople often say the problem is the vast distances in space. I think they're wrong: a few thousand years is probably enough to colonize hundreds of worlds with generation ships. The main problem is the vast distance in time. An inhabitable planet may exist 20 light years from here, but odds are it is hundreds of millions of years behind or ahead of us in terms of evolution. The eery thing about the Fermi paradox is that it may spell doom for our own longevity.
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- michaelneale 19y ago'fer me ?
- anewaccountname 19y agoActually, Olber's Paradox can also be answered by assuming the Universe is fractally distributed.