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Conterintuitive facts in mathematics, CS, and physics

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Re: Conterintuitive facts in mathematics, CS, and physics

#41

Post by tharkun__ »

lotsofpulp wrote: post #35
version_five wrote: post #33

Earlier quoted context omitted.

From what I remember from intro physics, we distinguished between pounds and pounds force, the latter having the 32ft/s^2 multiplied in. And wikipedia seems to agree with me, see pound (mass) vs pound (force).

Oh wow, learning a lot today. I was taught in the US that pounds are a measure of force, and that is how it was always used in physics problems.

As a European I learned in metric. When I first learned pounds, it was as the imperial system's equivalent of grams and a conversion factor was given. Force in physics class was taught in Newtons (kg*m/s^2).

Re: Conterintuitive facts in mathematics, CS, and physics

#42

Post by mrestko »

Causality1 wrote: post #16

Considering spacetime, matter, and energy are all quantized, why is something like Gabriel's Horn significant? I don't see how it has any more relation to reality than phrases like "negative surface area" would. Also, it's patently absurd someone would include Fitch's Paradox, a piece of philosophy, on a list of "counterintuitive facts."

I don't think we know that spacetime is quantized.

Re: Conterintuitive facts in mathematics, CS, and physics

#43

Post by tharkun__ »

mint2 wrote: post #22
lotsofpulp wrote: post #14

Earlier quoted context omitted.

> https://en.wikipedia.org/wiki/Potato_paradox The Wikipedia link above says: > Fred brings home 100 kg of potatoes, which (being purely mathematical potatoes) consist of 99% water. He then leaves them outside overnight so that they consist of 98% water. What is their new weight? The surprising answer is 50 kg. It annoys me when mass is used interchangeably with force (weight), so I went to the Wikipedia source, and…

I really don’t like that example because it makes no sense. In no logical circumstance could the potatoes dehydrate so quickly when left out over a single night.

And they also don't consist of 99% water. That is why they called them "purely mathematical potatoes" and they could've chosen any type of fruit or vegetable. Heck, I'm just waiting for a car analogy now!

Brake fluid anyone?

Re: Conterintuitive facts in mathematics, CS, and physics

#44

Post by kadoban »

MatteoFrigo wrote: post #19

The list is missing one of the most astonishing discoveries of all time: if you reflect the universe in a mirror, you can tell whether you are in our universe or in the mirror because the laws of physics are different in the mirror. See https://en.wikipedia.org/wiki/Wu_experiment

Really like that one, especially because it's just so ... random. All the other forces just don't work that way, but the Weak force does, wtf.

Re: Conterintuitive facts in mathematics, CS, and physics

#45

Post by pdonis »

Causality1 wrote: post #16

Considering spacetime, matter, and energy are all quantized, why is something like Gabriel's Horn significant? I don't see how it has any more relation to reality than phrases like "negative surface area" would. Also, it's patently absurd someone would include Fitch's Paradox, a piece of philosophy, on a list of "counterintuitive facts."

> Considering spacetime, matter, and energy are all quantized

First, we don't know that spacetime is quantized; that's a plausible speculation but we have no theory of quantum gravity.

Second, "quantized" is not the same as "discrete". A free particle in quantum theory is "quantized" but the spectrum of all of its observables is continuous.

Re: Conterintuitive facts in mathematics, CS, and physics

#46

Post by [deleted] »

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…

[deleted]

Re: Conterintuitive facts in mathematics, CS, and physics

#47

Post by kadoban »

t8e56vd4ih wrote: post #29
niccl wrote: post #26

Missing one that still makes no sense to me: The Ramanujan Summation: 1 + 2 + 3 + ⋯ + ∞ = -1/12 https://en.wikipedia.org/wiki/1_+_2_+_3_+_4_+_%E2%8B%AF

what? that's incredible ...

Literally incredible, because it's not. It's just really awful notation. It's really more like F(1+2+3+...) = -1/12 for a certain F (pedantically it's not a function I don't think, but whatever).

Re: Conterintuitive facts in mathematics, CS, and physics

#48

Post by GPerson »

I didn’t see this one listed, and thought it was pretty cool when I studied it in a course a few years ago:

https://en.m.wikipedia.org/wiki/Skolem's_paradox

“ Skolem's paradox is that every countable axiomatisation of set theory in first-order logic, if it is consistent, has a model that is countable. This appears contradictory because it is possible to prove, from those same axioms, a sentence that intuitively says (or that precisely says in the standard model of the theory) that there exist sets that are not countable.”

“ Skolem went on to explain why there was no contradiction. In the context of a specific model of set theory, the term "set" does not refer to an arbitrary set, but only to a set that is actually included in the model. The definition of countability requires that a certain one-to-one correspondence, which is itself a set, must exist. Thus it is possible to recognise that a particular set u is countable, but not countable in a particular model of set theory, because there is no set in the model that gives a one-to-one correspondence between u and the natural numbers in that model.”

Re: Conterintuitive facts in mathematics, CS, and physics

#49

Post by pishpash »

IainIreland wrote: post #24
pishpash wrote: post #20

The most counterintuitive fact, er... fib is this nugget: "0% selected the right answer on this SAT question: Circle A has 1/3 the radius of circle B, and circle A rolls one trip around circle B. How many times will circle A revolve in total?" You know how hard it is to get 100% of the people to do something? Don't insult our intelligence like that, or of SAT test takers in general.

The correct answer was not provided as a multiple choice option, which means by definition that 0% of test takers selected it.

All right, that's certainly counterintuitive...

Re: Conterintuitive facts in mathematics, CS, and physics

#50

Post by caf »

clon wrote: post #23
hodgesrm wrote: post #13

> 0% selected the right answer on this SAT question: Circle A has 1/3 the radius of circle B, and circle A rolls one trip around circle B. How many times will circle A revolve in total? That's fun. I of course immediately selected 3 which means I could have a bright career in test preparation ahead of me.

It was implied that the correct answer is 4.

Similarly, if you set out in a boat and circumnavigate the world in an easterly direction, ticking off a day on your calender every sunset, when you arrive back at your setting-off point your calendar will be one day ahead of everyone else.
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