Smart People Share Senseless Ideas That Can Be Proven Mathematically
Math was never really my strong suit, but I do understand that some stuff just needs numbers to make sense. Not sure what I'm talking about? Leave it to Reddit to explain it way better than I ever could. One Reddit user asked:
What are some things that make no sense but can be proven mathematically?
I'm still not 100% sure of the math that goes into explaining why one pizza might be more pizza than two pizzas or why straws don't work in the moon - but I feel like if SpaceForce is going to be able to do SpaceLunch these are just bits of knowledge we all need to have. Prepare to have your mind blown by stuff that makes little-to-no sense in the real world, but math says is perfectly normal.
The Perfect Sphere
The Banach-Tarski paradox is a nice example of something that exists because of mathematical objects that have no correspondence in reality. If you have a mathematical perfect sphere and cut it in ways that are only possible in mathematics (single points do not exist in reality), you can rearrange it to get two spheres. And that is just one example of what messing with infinity can give you.
The great Polish sci-fi writer Stanislaw Lem in his book "Summa Technologiae" wrote that mathematics is like a mad tailor, making all possible sorts of clothes. Some of them fit humans, some fit trees or octopi, some fit creature that exist but we haven't met yet; and some just don't fit anything in our universe. Mathematics makes theories that seemingly have no point in physical reality; that might be so, or it might be that we just haven't discovered a way to apply them. Number theory was thought to be useless until cryptography came along.
The Monty Hall problem's solution doesn't make sense until you start adding tens or even hundreds of doors.
Here's my attempt:
3 doors: 1 goat, 1 car, 1 nothing. Your chances are 1/3 to choose the car, yes? There are still 3 doors.
3 doors, goat is shown. 2 unknowns. There are still 3 doors- your original probability DOES NOT CHANGE because of this. It's still 1/3 chance. This is the part where I got stuck before. There are still 3 doors, your chances are 1/3.
Acting on the information though by swapping ADDS the 1/3 chance by knowing it has a goat behind it will ADD the probability together. 1/3 and 1/3 together. Making 2/3. The important part is acting on the information. However, if you had no outside knowledge, aka if your friend comes after a door is opened, his chances are 1/2 because he doesn't know. By opening a door for you, the dude 'adds value' to the door that isn't chosen by you but not to the one chosen by you originally.
So another way of thinking of it is NO MATTER WHAT choice you had made originally, you had 1/3 chance of winning. What's left is 2/3 right? If you abandon your original choice and jump ship to the other pool, your chance doubles.
How Much Rope?
The old rope-around-the-earth trick.
Imagine you have enough rope to go all the way around the earth's equator (ignoring mountains, etc). Now assume that you'd like to have that rope be 1 meter off the ground all the way around the earth. How much rope would you have to add?
A New Deck Of Cards
If you take a deck of new cards and shuffle it, chances are good that's the first time that sequence has ever existed on earth. 52! Is a long number.
No Straws On The Moon
This is less math and more physics, but straws don't work if they're taller than a very certain height - and they don't work at all on the moon. In order for liquid to flow through a straw, the inside of your mouth needs to be at a lower pressure than the outside air. If there is no outside air (like, say, on the moon for example) your mouth can't be at any lower pressure.
One 18" pizza is more pizza than two 12" pizzas. One 17" pizza is almost exactly two 12" pizzas by area. However, the two 12" pizzas will still have about 30% more crust than the 17" pizza. So if you're going stuffed crust, go small.
When I was in uni, we had a calculus temp/sub prove that the temperature here and a spot exactly on the opposite side of the earth, are the same.
If I recall correctly, he took 2 classes to write it on many many chalkboards. We were mostly in awe of his handwriting, and later found out he was allowed to turn in his thesis in handwriting, rather than typewritten. Before anyone questions, his thesis was not what he burned our time with.
It is the Borsuk-Ulam theorem in topology: for a continuous mapping of a sphere onto a plane, there will be two points which were antipodal on the sphere and are the same point on the plane. In fact, we can pick two continuous variables here: say, temperature and atmospheric pressure. Then it is a mapping between the Earth's surface and a temperature-pressure plane, so there will be two antipodes that have the same temperature and atmospheric pressure.
The birthday paradox.
Get 23 (randomly chosen) people in a room. It is decently likely that 2 of the 23 people share the same birthday (discounting year).
I am a mathematics graduate, I understand the mathematics, yet there's still a part of my brain that is thrown by this logic!
For anyone intrested: the idea is how many times you compare 2 peoples birthday or, in other words, how many unique parings of birthdays you have. The first person has 22 people to compare their birthday to, 2nd one has 21, therefore you have 22+21+20....+1=253 unique parings. Chances of a pair to be identical is 1/365 (disregarding leap years):
(1-1/365)^253=0.4995 or about 50%
The Speed Of Light
Light moves at the same speed for everyone.
If you're moving away from the light, or moving towards it, doesn't make a difference, it's still travelling the same speed for you
Gambler's fallacy - patterns of independent events do not dictate future results. I know it is true but still fall for it.
When a fair roulette table lands on black 10 times in a row it is just so tempting to keep putting money on red.