They list homomorphic encryption as the first fact, but has anyone created a truly complete HE implementation yet? My impression is that there are a lot of great theories and experiments in the field, but nobody has really created a practical standard for it. I'd love to be proven wrong though, it's a fascinating field.
Conterintuitive facts in mathematics, CS, and physics
51–60 of 335 posts
Re: Conterintuitive facts in mathematics, CS, and physics
#52Someone asked about #4 then deleted after I typed the response, so here it is.. :) It's queuing theory in general, related to "utilization". The utilization curve is always shaped the same; 50% utilization always doubles waiting time, and the curve is practically vertical when you get to 99% utilization. That's what explains the difference - 5.8 customers per hour, for a throughput of 6 per hour, shoves the efficienc…
What really throws people for a loop is the wait time after queuing starts. People expect the wait time to drop once arrivals return to normal, but there just isn't capacity to catch up.
In the real world, except at the DMV, people give up and shorten the queue (or don't join it to begin with), causing the arrival rate to go below nominal allowing the workers to catch up. In must-have or automated situations they see the full consequences of under-provisioning.
Re: Conterintuitive facts in mathematics, CS, and physics
#53Earlier 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.
I think there is some weird dual usage that makes them either mass or weight depending on the context. For example, torque is in ft•lbs or N•m so the pounds there are lbs force.
Though checking wikipedia again, it actually specifies that torque is measured in as lbf•ft. I take that to mean that 1 ft•lb is the torque of 1/2 oz (1/32 of an lb) at 1 foot. I expect that's a test question almost everyone would get wrong, myself included.
Re: Conterintuitive facts in mathematics, CS, and physics
#54a couple more: - at any time while stirring a cup of coffee, there will be a point on the top that is right where it started. (if we pretend coffee stirring is 2-dimensional, Brouwer's Fixed Point theorem) - a drunk man will eventually make it home, unless he can fly. in which case he only has a 34% chance. (if we assume the man is walking/flying on a grid, Pólya's recurrence theorem)
Huh, I wonder if there's any relationship to the Hairy Ball theorem. They appear to describe similar situations, but on different dimensions.
Re: Conterintuitive facts in mathematics, CS, and physics
#55Missing 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
If you don't use the regular definitions of how things are defined, you can get surprising results. If I define + as -, it might be surprising if I said 1 + 1 = 0.
Re: Conterintuitive facts in mathematics, CS, and physics
#56So, are there any popular or commercial games that make use of intransitive/non-transitive dice? That seems like it would be fun to break out with friends over.
Re: Conterintuitive facts in mathematics, CS, and physics
#57Earlier quoted context omitted.
In this situation, the mass and weight are proportional and irrelevant to the problem. Other than proper respect of units, why would it really matter? I would agree that using mass+kg would remain correct and be less unusual, but it doesn't matter a lot.
It does not matter, it is just a pet peeve of mine. Might be due psychological trauma from when I was a kid and arguing with an older cousin about how pounds and kilograms are not units of the same thing, and the older cousin "winning" the argument in the eyes of the elders because the cousin was quite a few years older than me and considered to be smart in school.
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Re: Conterintuitive facts in mathematics, CS, and physics
#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.
Re: Conterintuitive facts in mathematics, CS, and physics
#59My favorite paradox in physics: what happens when you spin a disk at relativistic speed? The circumference should contract, since it's parallel to the direction of motion, but the radius is perpendicular, and thus should not contract. https://en.wikipedia.org/wiki/Ehrenfest_paradox
I believe Veritasium covered this: spinning at relativistic speeds generates centripetal forces that overcome the nuclear force. There is no material you can use to test this paradox, and there can be no such material because your device would atomize - or worse - in the attempt.
Effectively there are g-forces so high that you end up with subatomic particles.
Re: Conterintuitive facts in mathematics, CS, and physics
#60> 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…
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