Hacker News Board Hacker News, browsed like a classic message board
Live data from Hacker News

Conterintuitive facts in mathematics, CS, and physics

axisofordinary.substack.com

Post reply on HN
Print view View original

131–140 of 335 posts

Re: Conterintuitive facts in mathematics, CS, and physics

#131

Post by eru »

p1necone wrote: post #101
p1necone wrote: post #91

Earlier quoted context omitted.

You're being overly pedantic (and I would argue actually incorrect). Kilograms and pounds are both referred to as "weight" in general conversation and nobody is going to be confused by this. Go to any supermarket in a country that uses the metric system, potatoes will be sold by the kilogram - it's the natural way to phrase this outside of America. In a physics context the definition of kilogram might be specifically…

Although the more I think about this the more I think the difference between technical and colloquial is actually that "weight" in colloquial use refers to mass, because force is not commonly relevant.

Yes, in colloquial use weight refers to mass _most_ of the time. But can also refer to inertia or mass. Or be used metaphorically.

Re: Conterintuitive facts in mathematics, CS, and physics

#132

Post by ffhhj »

d_burfoot wrote: post #114

Here is one of my favorites. Take a light source and shine it at a filter that is polarized up/down that is in front of a filter that is polarized left/right. None of the light will get through: the first filter removes all of the L/R components of the light, and the second filter removes all the remaining light. Now add a third filter, between the two, which is polarized at 45 degrees. Now some of the light goes thr…

For me this is as surprising as the double slit experiment, but much easier to reproduce.

Re: Conterintuitive facts in mathematics, CS, and physics

#133

Post by ameetgaitonde »

pishpash wrote: post #27
rumpelstilz18 wrote: post #7

Earlier quoted context omitted.

> Knowing just slightly more about the value of your car than a potential buyer can make it impossible to sell it > This means that the owner of a carefully maintained, never-abused, good used car will be unable to get a high enough price to make selling that car worthwhile. Both statements are a wrong understanding of the phenomenon. The market collapses because the transactions happen outside of the market. Somethi…

Under this model, if the transaction of quality goods happened anywhere, some buyer reached information symmetry. But among the assumptions in the article is that sellers have no alternate market (they just "leave", whatever that means) and there is no credible way to provide information on the quality of goods. But then how do buyers know to lower their prices with what's left in the market? There're a lot of unreas…

I really don't like how the OP phrased this one, because it's about more than knowing the value of your car.

This paper was published in 1970, but it demonstrated how markets can fail, as well as a method of correcting that failure. Imagine the following scenario:

There's a used car market of private sellers that is comprised of a mixture of peaches (good) and lemons (bad). To keep it simple, let's assume we're just talking about one model of car.

Additionally, there's no way to identify which car is a lemon, but it's known that they're worth much less than a peach because of the much higher cost of maintenance.

If you have a market where the above conditions exist (only seller knows if car is lemon/peach, and a mixture of lemons/peaches), you'd potentially end up with a market failure.

This is because sellers of peaches can't get the price they want for their car, whereas sellers of lemons can profit over the expected value of theirs.

The problem with assuming that lemons would be removed from the market is that any buyer of a lemon would want to sell it once they've realized what they purchased, putting it back on the market. This effect compounds to where a greater percentage of cars being sold on the market are lemons, further depressing the price and removing peaches from the market.

Akerlof's solution to fix the market was to introduce warranties. Owners of peaches would be willing to offer warranties, because they trusted the quality of the cars they were selling. Eventually, buyers would see the lack of a warranty as the indication of a car being a lemon, forcing the sellers of lemons to either offer a warranty or lower their asking price below the market price of the vehicle.

His work applied to the function of other markets, like insurance (older people are the costliest for health insurance companies) and employment markets (Certain classes of people have difficulty finding a job despite similar skills), as well as the institutions that have formed (Medicare, professional licensing) to improve the functioning of these markets.

Re: Conterintuitive facts in mathematics, CS, and physics

#134

Post by moralestapia »

yongjik wrote: post #118
moralestapia wrote: post #115

Earlier quoted context omitted.

It's mean to be a thought experiment but some people (like Veritasium) can't get around this simple realization. Like, "I wonder what could be happening inside of a black hole?" "Oh we would never know, because if we send a camera it would break. Also suppose we MaaaAaAKKeee aa cCAaaMeerra with ThE STROooonngGEEstt Material In the UUunniveersssee, so it wouldn't break, you would find that there's no wifi in there so…

(Disclaimer: I am not a physicist.) I think it's actually a pretty reasonable description? Sounds like it's a paradox because we assume a rigid body, but nothing in real life is a perfect rigid body. So the situation simply becomes a bunch of particles following circular orbits. If you measure distance along one direction (while constantly accelerating in relativistic speed) you get one number; if you measure distanc…

The example you give and its answer follows a line of reasoning that leads you to an interesting conclusion, that's the point of thought experiments.

What I was saying is more akin to answering your example with:

"Oh no you can't! There's not enough steel on Earth to build such thing and even if you had it, it would require an EEeEeeenOOOOrrrMMMoooUUUusss amount of energy to put in place ;)."

That would be quite a moronic interpretation of the problem that completely misses the goal of said thought experiment, which is, well, to make you think.

Re: Conterintuitive facts in mathematics, CS, and physics

#135

Post by istjohn »

caf wrote: post #124
robocat wrote: post #121

Earlier quoted context omitted.

- a chair with four even legs placed on any undulating continuous surface can always be rotated such that all four legs touch the ground at once.

Do the legs have to be even?

Yes. Imagine a chair with one pair of diagonally opposite legs very long and the other pair of legs very short. On even a flat surface it is impossible to touch all four legs to the floor simultaneously.

Re: Conterintuitive facts in mathematics, CS, and physics

#136

Post by tshaddox »

wodenokoto wrote: post #32
dwohnitmok wrote: post #12

29 is not correct as stated and falls prey to logical errors. Hamkins presents a formal take on it here: https://mathoverflow.net/questions/44102/is-the-analysis-as-... His conclusion (which I agree with) is > The claims made in both in your question and the Wikipedia page on the existence of non-definable numbers and objects, are simply unwarranted. For all you know, our set-theoretic universe is pointwise definable…

It’s also terribly phrased. > The vast majority of real numbers can't be described. But it is impossible to give a single example. If we accept the first sentence and assume the second refers to indescribable numbers, then isn’t it obvious that we have no examples of things we cannot describe? If the second sentence refers to real numbers in general I can give one example or two.

How could you give an example? The example you give would be a description of a number.

Re: Conterintuitive facts in mathematics, CS, and physics

#137

Post by sib »

pessimizer wrote: post #61
6gvONxR4sf7o wrote: post #11

> 16. If you let a 100g strawberry that is 99% water by mass dehydrate such that the water now accounts for 98% of the total mass then its new mass is 50g: https://en.wikipedia.org/wiki/Potato_paradox I really like this one. It's a perfect combo of intuitive from one perspective and mind bending from another. > 18. A one-in-billion event will happen 8 times a month: https://gwern.net/Littlewood This one, on the other…

> > 16. If you let a 100g strawberry that is 99% water by mass dehydrate such that the water now accounts for 98% of the total mass then its new mass is 50g: https://en.wikipedia.org/wiki/Potato_paradox >I really like this one. It's a perfect combo of intuitive from one perspective and mind bending from another. Comes up a lot lately because of vaccine effectiveness e.g. 95% is twice as effective as 90%.

It's probably more intuitive if you say that it's "half as ineffective"

Re: Conterintuitive facts in mathematics, CS, and physics

#138

Post by geoduck14 »

charcircuit wrote: post #58

>It is possible to compute over encrypted data without access to the secret key I don't think this is counterintuitive for most people. The most basic encryption scheme that everyone knows is the Caesar cipher. It's easy to see that shifts of the cipher text will cause shifts in the plain text.

>It is possible to compute over encrypted data without access to the secret key

This is counter intuitive to me. For one, I don't consider the Caesar Cipher to be an encryption scheme that I would actually use for data.

In addition, when I want to "compute" data, I want to do things like identify sentiment analysis in free form text or identify key themes in a paragraph - and I'm not sure this actually IS possible with data that is encrypted

Re: Conterintuitive facts in mathematics, CS, and physics

#139

Post by istjohn »

londgine wrote: post #105
adenadel wrote: post #98

Earlier quoted context omitted.

Hm, I'm not so sure that just because the definition of a bijection is technical that it is not intuitive. I'll start an enumeration of the rationals 1 1/3 2 1/4 3 1/5 ... If you can prove that you can do this, is that really so non-colloquial? It is certainly what we mean by "as many" for all finite sets, so what is wrong with doing this for infinitely many sets?

If every whole positive number is a fraction, but not every fraction is a whole positive number, then colloquially, I wouldn't define them as having "as many" elements as each other. Now, if you want to say they have the same cardinality (and you define cardinality as existing a bijection), then I would agree fully.

What's worse, there are an infinite number of fractions that equal each whole number.

Re: Conterintuitive facts in mathematics, CS, and physics

#140

Post by charcircuit »

geoduck14 wrote: post #138
charcircuit wrote: post #58

>It is possible to compute over encrypted data without access to the secret key I don't think this is counterintuitive for most people. The most basic encryption scheme that everyone knows is the Caesar cipher. It's easy to see that shifts of the cipher text will cause shifts in the plain text.

>It is possible to compute over encrypted data without access to the secret key This is counter intuitive to me. For one, I don't consider the Caesar Cipher to be an encryption scheme that I would actually use for data. In addition, when I want to "compute" data, I want to do things like identify sentiment analysis in free form text or identify key themes in a paragraph - and I'm not sure this actually IS possible wi…

Maybe a simpler example would be doing a not operation on a ciphertext for a one time pad? When you decrypt it you will get the plain text with all of the bits flipped.

Doing computations on cipher text is very limited which is why it's not very efficient to do complicated operations.

Post reply on HN