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Conterintuitive facts in mathematics, CS, and physics

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Re: Conterintuitive facts in mathematics, CS, and physics

#261

Post by adrian_b »

jacobolus wrote: post #257
adrian_b wrote: post #184

Earlier quoted context omitted.

Actually in the past "weight" or the Latin "pondus" (=> pound) always referred correctly to what is now named "mass". When someone mentioned "weight" just in a qualitative way, as a burden, they might have thought at the force that presses someone down, but whenever they referred to weight in a quantitative way, they referred to the weight as measured with a weighing scale, which gives the ratio between the mass of t…

> Actually in the past "weight" [...] always referred correctly to what is now named "mass". That’s the same thing I just said. Why add “actually” in front? Yes, weight was historically measured with balance scales. I guess I should have been clearer that the term “mass” as used in physics only dates from 3 centuries ago (from Newton), and did not historically mean weight in Latin. (Mass comes from Latin via French f…

You are right, I have misunderstood what you have said, because it indeed looked like if "mass" would have been some traditional word having anything to do in any language with what are now called "weight" and "mass" instead of a recent post-Newton word choice for naming one of the 2 quantities, while keeping the old names for the other.

I still think that the choice of which of the 2 should get a new name was bad, because the traditional quantitative meaning almost always referred to what is now called "mass"(with extremely few exceptions such when somebody would be described as so strong as to be able to lift a certain weight).

Re: Conterintuitive facts in mathematics, CS, and physics

#262

Post by goohle »

cycomanic wrote: post #173
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

It is a great discover I agree, it might not quite fit in the list because it's not so counterintuitive for someone not into particle physics though. There are actually many examples of things working different for the mirror image, e.g. many medical/chemical compounds work differently based on chirality. The topic of chirality is fascinating, one of the big puzzles in nature is for example why it so strongly prefers…

Maybe nature prefer right-handedness just because it started in North hemisphere.

Re: Conterintuitive facts in mathematics, CS, and physics

#263

Post by Scharkenberg »

yodelshady wrote: post #253
Aerroon wrote: post #200

Earlier quoted context omitted.

#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…

A similar but not quite the same mechanic is fuel economy. Let's say you have two vehicles, both doing 10,000 miles per year. One gets 10 mpg and the other 50. Would you rather upgrade the 10 mpg vehicle to 13 mpg, or the 50 mpg to 100 mpg? Not only should you pick the former - you should pick the former even if you could upgrade the 50 mpg vehicle to run on nothing .

Yes, the fuel savings in the former case are larger than the initial fuel consumption in the latter case, but is it really unintuitive in practice? What I mean is that we generally pay for fuel per volume, not per mileage. Now, I am not sure about others, but I would always base my decision based on the money I'd save over a period of time, which in this case would require considering each vehicle's actual fuel consumption over that period of time.

Re: Conterintuitive facts in mathematics, CS, and physics

#264

Post by dartharva »

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.

I'm confused, I also immediately came to 3 when I read this question. Is that wrong? What's the correct answer?

Re: Conterintuitive facts in mathematics, CS, and physics

#265

Post by dartharva »

TMWNN wrote: post #141
geogra4 wrote: post #100

>Two 12 Inch Pizzas have less Pizza than one 18 inch pizza Love this one. Always go for the biggest pizza you can

No. While two 12" pizzas have more pizza than one 18" pizza, it's possible for the two 12" pizzas to be a better value. If the total price of the two 12" pizzas is $7.20, for example, they are a better value than the 18" pizza once the price of the 18" pizza is greater than $8.10. More generally, the two 12" pizzas are a better value if the 18" pizza's price is higher than 112.5% of the two 12" pizzas' total price.

But that's almost never the case.

Re: Conterintuitive facts in mathematics, CS, and physics

#267

Post by hinkley »

Joker_vD wrote: post #260
yongjik wrote: post #118

Earlier 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…

It's one of the reason I dislike physical terms that has words like "ideal" or "perfect" as their part. They subliminally suggest that their properties and behaviours are the "true" ones while the real material things are their imperfect counterparts whose imperfections you can sometime disregard. Of course, it's exactly the opposite: it's those "ideal" concepts are imperfect approximations of the real things, omitti…

Hence the “perfectly spherical cow” joke.

Re: Conterintuitive facts in mathematics, CS, and physics

#268

Post by behnamoh »

d_burfoot wrote: post #117

Surprising fact about the sun: it actually produces less heat per unit volume than a compost pile - this makes sense when you consider that fusion events are very rare. The reason the sun is so hot is that it has an enormous ratio of volume to surface area. Heat emission due to radiative cooling is proportional to the surface area, but heat creation due to fusion is proportional to the volume.

It's so humbling to think about how huge the Sun is, and then, how small it is compared to the really big giants in the universe.

Re: Conterintuitive facts in mathematics, CS, and physics

#269

Post by Loughla »

FabHK wrote: post #251
d_burfoot wrote: post #117

Surprising fact about the sun: it actually produces less heat per unit volume than a compost pile - this makes sense when you consider that fusion events are very rare. The reason the sun is so hot is that it has an enormous ratio of volume to surface area. Heat emission due to radiative cooling is proportional to the surface area, but heat creation due to fusion is proportional to the volume.

Conclusion: to solve all our energy problems, we just need a sufficiently large compost pile.

I mean, yeah. But at some point the pile will become large enough to collapse in on itself from gravity and start fusion, I would imagine.

So, according to Cornell[don't know how to do a citation], "1,000 BTU per hour per ton" is a good heat capture rate from manure compost. Then, according to something called 'alternative energy geek' "the earth receives 82 million quads of Btu energy from the sun each year. A "quad" is one quadrillion British Thermal Units (BTUs) of energy."

So, to recreate that, we would need. Um. One massive shitload of compost to recreate that.

Citations: https://smallfarms.cornell.edu/2012/10/compost-power/ http://www.alternative-energy-geek.com/solar-energy-per-squa...

Re: Conterintuitive facts in mathematics, CS, and physics

#270

Post by CJefferson »

ColinWright wrote: post #246
CJefferson wrote: post #182

Earlier quoted context omitted.

I agree. Also, until you get super technical, it isn't really any different to "if you take the natural numbers, and split them into odd and even, you get two copies of the natural numbers".

I disagree ... the "two copies of the natural numbers" is sorta fine, except that they're more "spread out" so it's not at all surprising. The surprising thing about BT is that the "pieces" are "moved around" ... there's no expansion or contraction. Yes, the natural number thing helps to understand that simply counting things doesn't help, but the "rigid motion" aspect of BT takes it further.

True, that is the subtle bit -- but I think most people misunderstand (I'm not saying you are!), and don't realise you can always split an infinity into two -- this is just about splitting a sphere into some 'point clouds' such that you can cleverly stitch them back together into the same original space. In particular, the 'cutting' really makes no real-world sense (at least, as far as I can understand).
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