Ask YC: What is your favourite paradox?

https://news.ycombinator.com/item?id=133727

by moog • 18 years ago

30 65 18 years ago

news.ycombinator.com

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• 18 years ago

http://en.wikipedia.org/wiki/Paradoxical_combinator

mercurio6• 18 years ago

Russell's paradox.

http://en.wikipedia.org/wiki/Russell's_paradox

imgabe• 18 years ago

Mine too! It's also the inspiration for my favorite math joke: Consider the set of all sets that have never been considered...Wait, nevermind, they're gone!

jsmcgd• 18 years ago

Mine too too. It makes logic not look so logical anymore.

mixmax2• 18 years ago

girls

kirubakaran2• 18 years ago

If they are a paradox to you, my hero who scored with a porn star, I don't know what to say :-)

mixmax2• 18 years ago

You have a good memory ;-)

mrtron• 18 years ago

If that is your hero definition, what is your superhero definition?

ghiotion2• 18 years ago

Zeno's paradox, which proves that motion is an illusion:

http://en.wikipedia.org/wiki/Zeno's_paradoxes

Those ancient Greeks knew their shit.

mattmaroon• 18 years ago

In that same article you linked it explains why those paradoxes don't prove shit.

ghiotion2• 18 years ago

True. Perhaps I should have put quotes around proves. Still, I remember what a big impact Zeno had on me as a young philosophy student.

webwright• 18 years ago

I'll second Zeno.

Sooo applicable to software development. I love it so much, I wrote a blog post about it.

kalid• 18 years ago

Love 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• 18 years ago

Zeno 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.

anewaccountname2• 18 years ago

Time is very similar to space; what you are saying is like saying you don't see how it take up any space at all.

maw• 18 years ago

Zeno's paradox (deliberately?) confuses a thing — motion — with its measurement. You can always measure something with higher resolution, but so what?

TheWama• 18 years ago

I have a love/hate relationship with 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) is difficult to explain/advocate for...

eru7• 18 years ago

Yes, the Condorcet vote is nice. But for practical purposes I've settled with approval voting as a favorite since it is easy to understand and can not be gamed.

wlievens2• 18 years ago

Slightly related: Arrow's Theorem

doubleplus• 18 years ago

The 20 Eye: http://www.zappos.com/images/725/7257495/5089-291353-d.jpg

eru7• 18 years ago

wallflower2• 18 years ago

"Do as I say and not as I do."

Zeromus• 18 years ago

I 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

corroded• 18 years ago

you 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

eru7• 18 years ago

Just to make you procrastinate even more:

http://en.wikipedia.org/wiki/List_of_cognitive_biases

aswanson• 18 years ago

Existence.

mnemonicsloth2• 18 years ago

It'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

wallflower2• 18 years ago

Reminds me of Klein's bottle

tlrobinson2• 18 years ago

Finite 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

Perhaps large animals should make themselves into the shape of Gabriel's Horn.

Of course then they'll radiate too much heat.

mercurio6• 18 years ago

I 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.

__3• 18 years ago

The one I like least.

mercurio6• 18 years ago

Not to rain on your parade, but your statement is a lie and not a paradox.

__3• 18 years ago

That could be said of many so-called paradoxes. I think it has as much claim to "paradox" as the interesting number paradox.

__3• 18 years ago

That 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.

dfranke• 18 years ago

The hangman paradox: http://en.wikipedia.org/wiki/Unexpected_hanging_paradox

yters• 18 years ago

Curry's paradox is cool:

"If this sentence is true, then Santa Claus exists."

http://plato.stanford.edu/entries/curry-paradox/

mercurio6• 18 years ago

This 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• 18 years ago

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.

tel2• 18 years ago

You 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.

mnemonicsloth2• 18 years ago

My 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.

nagoff• 18 years ago

Leading to one of my co-worker's favourite jokes, Q: What's an anagram of "Banach-Tarski" A: "Banach-Tarski Banach-Tarski"

neilk• 18 years ago

I'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.

tel2• 18 years ago

I honestly have a difficult time understanding the AC paradoxes, too. I recognize that it's totally necessary for many things (i.e. multidimensional integrals) and when it's consistent with a logical conclusion I have little trouble "seeing" it. Otherwise, though, not so much.

I think it's interesting to see the connection between the AC and the Law of Excluded Middle which also causes paradoxical issues from time to time.

http://en.wikipedia.org/wiki/Axiom_of_choice#Law_of_the_excl...

paulgb• 18 years ago

I find Hilbert's Paradox is handy when thinking about infinity.

http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_...

yelsgib• 18 years ago

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.

eru7• 18 years ago

The Axiom of Choice saves lives!

joseakle• 18 years ago

Is "Don't listen to me." a paradox?

eru7• 18 years ago

No. I read it and followed your instructions. It's not even a contradiction when written down.

simanyay• 18 years ago

Grandfather paradox: http://en.wikipedia.org/wiki/Grandfather_paradox

tlrobinson2• 18 years ago

Schrödinger's cat

bayareaguy• 18 years ago

It's not a paradox by itself, but the Heisenburg uncertainty principle leads to a lot of unintuitive things too.

dkokelley• 18 years ago

This is a false sentence.

bootload• 18 years ago

python ~ http://www.paulgraham.com/pypar.html

RNlR• 18 years ago

Democracy or mob-intelligence

ovi256• 18 years ago

Mine: 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

eru7• 18 years ago

I can always refuse to argue with you and punch you instead.

coffeeaddicted• 18 years ago

The Fermi paradox - "where are they?" 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.

michaelneale2• 18 years ago

I 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.

wlievens2• 18 years ago

People 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.

michaelneale2• 18 years ago

'fer me ?

anewaccountname2• 18 years ago

Actually, Olber's Paradox can also be answered by assuming the Universe is fractally distributed.

Ask YC: What is your favourite paradox?

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