> The Earth makes 366.25 rotations around its axis per year
Isn't it 365.25?
Conterintuitive facts in mathematics, CS, and physics
211–220 of 335 posts
Re: Conterintuitive facts in mathematics, CS, and physics
#212Earlier quoted context omitted.
(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 mo…
The difference there is, I think, that the pragmatic argument of "not enough steel" doesn't prove the non-existence; while the argument about "there are no truly rigid bodies" does.
I haven't seen that Veritasium video, but it sounds like it makes the exact same point. It's not that we haven't found a material that's rigid enough; it's that a rigid disk is counter-factual to begin with, even in non-relativistic conditions.
Re: Conterintuitive facts in mathematics, CS, and physics
#213Re: Conterintuitive facts in mathematics, CS, and physics
#214> 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…
> 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…
When I buy potatoes I am interested to buy 10 kg mass of potatoes, not the amount or potatoes of which has a gravity force of 98,1N. On mars you need to eat 10 kg of potatoes a week, not the amount of which has 98,1N gravity force.
The scales in the supermarket on earth automatically convert the weight into mass for my convenience by applying a constant factor of 1/9,81.
I am hardly far away enough from earth that the constant changed, so I did not need to distinguish between the two measures so far. When carrying the potatoes home I just use the mass of 10 kg as a proxy for the force I need.
And to determine the increased breaking distance of my car, I need to know the mass again.
Re: Conterintuitive facts in mathematics, CS, and physics
#215Earlier quoted context omitted.
I'd deny that our objects do not live in a real space. Spacetime is real-valued. The issue isn't the reals, but that "solid object" isn't defined properly, ie., the sets under question don't have well-defined volumes. As soon as you fix that problem, via measure theory, the paradox resolves. You dont need to ditch real numbers.
> Spacetime is real-valued There's really no evidence for this, as far as we know the real numbers are a pure mathematical invention and don't have any physicality. Even if you want to say that spacetime is dense (i.e. infinitely divisible), there's an infinite number of fields like that, the real numbers are just a convenient superset. There's no evidence that spacetime is dense either, and many practical ways in wh…
That is correct and should be highlighted more.
In a way the real numbers are a model (or maybe a 'language') to describe physical phenomena. They work exceptionally well at that, but they are not backed by evidence and do come with (theoretical) limitations.
This bachelor's thesis is a good starting point [1], search for 'finite precision physics' or 'intuitionistic math/physics'.
Re: Conterintuitive facts in mathematics, CS, and physics
#216I needed a half cup of something for a recipe and only found the 1/3 cup measure. Then it occurred to me that a third and a half (of a third) is equal to a half.
So simple but somehow doesn't feel right.
Re: Conterintuitive facts in mathematics, CS, and physics
#217> There are as many whole positive numbers as all fractions According to a specific non-colloquial definition of "as many".
My sister and I used to figure out who had more candy at halloween by lining up the pieces next to each other. The concept of bijection might be more intuitive than counting itself.
For all we know it's significantly older than counting. Pebbles representing bijections to wares like sheep (called calculi like in calculus) occur earlier than counting marks and much earlier than anything resembling numbers.
There are still today human tribes that don't count at all.
Re: Conterintuitive facts in mathematics, CS, and physics
#218Earlier quoted context omitted.
So what happens to a star inside a "perfect" Dyson sphere?
The same thing that happens to a star not in a Dyson sphere. It slowly radiates energy away and in the process contracts and heats up. In fact when the Earth was initially forming the Sun was only about 70% as bright as it is today. (How liquid water could form under those conditions is still something of a mystery: https://en.wikipedia.org/wiki/Faint_young_Sun_paradox )
I really wish we would have a class K or M star as they would have a far higher life expectancy. The theorized instability in form of solar flares would probably be an acceptable compromise.
Perhaps we could just use a straw to give our sun a liposuction.
Re: Conterintuitive facts in mathematics, CS, and physics
#219> The Earth makes 366.25 rotations around its axis per year Isn't it 365.25?
Here's a nice image that explains the difference between a solar day (meaning the time it takes until the sun is at the same azimuth again) and the sidereal day (meaning the time it takes for earth to rotate around it's axis once): https://qph.fs.quoracdn.net/main-qimg-ab0d69361311b4f15b0064...
Re: Conterintuitive facts in mathematics, CS, and physics
#220Earlier quoted context omitted.
> Spacetime is real-valued There's really no evidence for this, as far as we know the real numbers are a pure mathematical invention and don't have any physicality. Even if you want to say that spacetime is dense (i.e. infinitely divisible), there's an infinite number of fields like that, the real numbers are just a convenient superset. There's no evidence that spacetime is dense either, and many practical ways in wh…
That is correct and should be highlighted more. In a way the real numbers are a model (or maybe a 'language') to describe physical phenomena. They work exceptionally well at that, but they are not backed by evidence and do come with (theoretical) limitations. This bachelor's thesis is a good starting point [1], search for 'finite precision physics' or 'intuitionistic math/physics'. [1] https://www.math.ru.nl/~landsma…
Well this is a popular idea imported from comptuer science, but there's absolutely no evidence for it -- and plenty against.
Eg., QM is only linear in infinitely-dimensional real-spaces, etc.
Essentially of a physics uses real spaces indispensably. There is no evidence whatsoever that this is dispensible; other than the fever dreams of discrete mathematicians.