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Conterintuitive facts in mathematics, CS, and physics

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Re: Conterintuitive facts in mathematics, CS, and physics

#191

Post by Kwantuum »

raldi wrote: post #181
nwallin wrote: post #161

> 17. At any given moment on the earth's surface, there exist 2 antipodal points (on exactly opposite sides of the earth) with the same temperature and barometric pressure: youtube.com/watch?v=cchIr1OXc8E This is not necessarily true. They say a picture is worth 1000 words: https://media.deseretdigital.com/file/5894488349 Regardomg Gabriel's Horn and Banach-Tarski, the paradox is described as a trumpet, or a ball, ma…

I don't get what thought that picture is supposed to provoke.

The earth has "holes" and as such the proof of that statement for a sphere does not apply to the earth.

Re: Conterintuitive facts in mathematics, CS, and physics

#192

Post by zarzavat »

mjburgess wrote: post #179
ncmncm wrote: post #150

Number 19 is a clinker. Banach-Tarski applies only to objects in real-number space, but there are no such objects. For that to work, objects have to be infinitely divisible, but all of our objects are made out of atoms. Real-numbered space is a good enough approximation to our experience that we hardly ever encounter a model failure like this one.

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 which it is not, as an obvious upper bound if you took all the energy in the observable universe to make one photon, it would still have a finite wavelength.

Re: Conterintuitive facts in mathematics, CS, and physics

#193

Post by bloak »

campital wrote: post #87

How is 27 counterintuitive? > Let alpha = 0.110001000000000000000001000..., where the 1's occur in the n! place, for each n. Then alpha is transcendental. (Calculus, 4th edition by Michael Spivak) Nearly all infinite sums involving factorial are transcendental.

I agree. Probably most people who know what "transcendental" means would guess that the number described is transcendental.

However, only a small proportion of people who know what "transcendental" means are capable of proving that any number is transcendental.

Re: Conterintuitive facts in mathematics, CS, and physics

#195

Post by bongoman37 »

caf wrote: post #50
clon wrote: post #23

Earlier quoted context omitted.

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.

Wasn't this a major plot point in Around the World in 80 Days?

Re: Conterintuitive facts in mathematics, CS, and physics

#196

Post by jiggawatts »

amelius wrote: post #189
jiggawatts wrote: post #157

Earlier quoted context omitted.

It makes more sense if you think of the polariser sheets as fences with vertical bars, and light like a string going through between two bars and being wiggled. If the direction of the waves in the string are at right-angles to the slit, the wave can't propagate through the bars. If the wave is at an angle, then some of the wave gets through, with a maximum of 100% when the wave wiggles up and down in the same direct…

Can you explain the double slit experiment with this approach?

Not really, the waves in the double slit experiment travel through vacuum (or air), not through a solid like with polariser sheets.

Re: Conterintuitive facts in mathematics, CS, and physics

#197

Post by curiousgal »

nighthawk454 wrote: post #68
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…

Yes, it doesn't explicitly state the rate or distribution of events. But it is a good reminder of what happens when your whatevers/second are pretty high - see the famous "One in a million is next Tuesday" [1]. "Rare" is soon if you roll the dice fast enough. Any time your service has a high TPS, your API gets a lot of calls, a button in your app gets pressed a lot, ... this applies. Critically, "a lot" is defined re…

> And I’ve seen some absolute doozies in my time – race conditions on MP machines where a non interlocked increment occurred (one variant of Michael Grier’s “i = i + 1” bug)

I could not find any info about that bug, anyone got a link or a source?

Re: Conterintuitive facts in mathematics, CS, and physics

#198

Post by _Microft »

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…

You can do that 'continuously' by inserting many layers of slightly rotated polarizers to rotate the polarization plane by an arbitrary angle.

An applied example of this are liquid crystal screens. Molecules take the role of the polarizers there. The rotation angle depends on an applied electric field and when you sandwich a layer of crystals between polarizers, you almost have a screen:

https://www.britannica.com/technology/twisted-nematic-cell

Re: Conterintuitive facts in mathematics, CS, and physics

#199

Post by elcomet »

analog31 wrote: post #107

>>> 18. A one-in-billion event will happen 8 times a month: https://gwern.net/Littlewood This is certainly counterintuitive, given that one-in-a-billion and 8 per month have different units of measure.

The implicit information is that there is one-in-billion chance that this event happens to someone in a given month.

Re: Conterintuitive facts in mathematics, CS, and physics

#200

Post by Aerroon »

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 is something video games taught me, particularly Path of Exile. In PoE resistance are a flat multiplier to incoming damage. Eg monster does 100 damage per attack and you have 60% resistance then you take 40 damage.

The interesting thing is that the higher your resistances the more effective each additional percentage point of resistance is.

Let's say a monster does 100 damage per attack.

If you have 0% resistance and increase it to 5%, then your incoming damage went from 100 to 95. You take 5% less damage than before.

If you have 75% resistance and increase it to 80%, then your incoming damage went from 25 to 20. You take 20% less damage than before.

It is pretty unintuitive until you realize that you need to focus on the remainder rather than the other part.

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