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Concerning the dartboard, I'd say the probability that the dart hits a specific point is not 0. But since the point is infinitely small, so is the chance to hit it. So the probability is not 0, but it approaches 0. Boom, no more paradox.

can someone explain what that triangle that appears in the beginning of the video means? I still don’t understand. what is scale up by 2?

Ok, it looks like Cantor's Diagonal Argumen and Thomsons Lamp are wrongly explained there. For the first one seems like a logic step is skipped at the end and for second one, as described, lamb will be off (because you grouped actions instead of independent ones). Didn't watched further, just downvoted.

Guinea pigs are pretty round and I’ve been able to comb them pretty smooth

/\/\/\ this is the only complexity i need know

Assume a spherical cow.

I swear I try very hard to understand this s*%+ but my brain refuses to maths, no matter what. I'll just go lock myself in a dark room and play with my feces now... :/

kissing numbers are usually called coordination numbers in material science, which is also where the body-centered and face-centered structures come from.

Damn , feb 2 is my actual birthday

I was at gathering of about a dozen people and there were three of us, me and two others (this was not planned) had the same birthday (Nov 2). One of them was born on the same day as I. The other was several years younger than us. How is that for a coincidence?

I don’t understand how the convex solid packing problem isn’t proven Any slight angle in the shape means less area taken by the lower solid, which can fit the solid on top of it’s slight angle Meaning the shape with the largest angles is the worst at packing, and circles have 180 degree angles and thus no even slightly obtuse angle You can’t go above 180 degrees because it isn’t convex anymore

Wouldn't the concept of a supertask itself be a paradox since it's a task repeated an infinite number of times in a finite amount of time?

Here's a way of thinking about Gabriel's Horn that ought to make your eyes bug out. If you tip the Horn upward and pour in 3.14 m^3 of paint, that paint will completely fill the inside of the Horn, but cannot coat the inside surface.

Hotel paradox isnt a paradox, just put guests in negative numbers room, they are vacant. but for real, its stupid af

Feb 2 is my birthday

The tesseract one is the hardest thing to understand in my life☠️☠️☠️

why did the voice change for simpson’s paradox wtf

00:00 Sierpiński triangle is not defined the way it's presented. It's defined as connecting middle points creating an internatl triangle. You even do this in 00:17 . If you want to be consistent, your triangle shouldn't be "divided" but rescaled and multiplied as previously in the video.

Thomson's lamp reminds me of calculating average values - in average, every person, who has two arms, has more arms than the average person, because there are (for sure) more persons missing limbs than having extra one's.

I feel like there’s an interesting discussion to be had about whether Ulam’s packing conjecture can be disproven using a non-convex solid which is constructed out of convex solids. (Picture the silhouette of a venn diagram or an hourglass)

If we take the lamp on/off one literally while considering the constant speed of light, then having the light half on would be a measurable result if the light is turning on and off at as the rate at which it is alternating between on and off is at the speed of light, at which point, it can no longer be turned on or off any faster. So we'd see a dimmed light, as though it were half on. Phenomena we can observe and measure at least seems to have some finite limitations like the plank length, and the speed of light. Gravity was a constant according to Newton's observations, until we could model it as a curvature in space and time caused by mass thanks to relativity. We don't even have a fundamental explanation as to "why" mass curves space and time. Gravity still isn't fully understood. Numbers, and models and math are all abstract. The reality may be indefinite; a bunch of larger or smaller infinities, and so I'm inclined to think that math and physics are always going to be shy of total consistency.

Gabriel's horny does not have finite colume. Pi is irrational number!

8:07 spongebob

7:38 div.E= rho/r ( in which rho is density and r is distance of point charge) isn't it?

except people play darts and it can be won ^^

The first paradox is outright wrong... Try convince 1 guest to move rooms is hard enough - now they convincing AN INFINITE NUMBER. Not going to happen. 100% unrealistic and unworkable.

The lamp, after 2 minutes of furious switching, will find itself broken

If you consider the quadratic x^2 - (pi+e)x+ex=(x-e)*(x-pi). then you immediately get that pi+e and pi*e cannot both be algebraic, since they would be coefficients to a quadratic with transcendental roots. Similarly, if a and b are both trancendental, then at least one of a+b and ab must also be.

Came into this video thinking I was relatively smart, came out confused and rethinking my life choices

11:24 tringle

The answer to the art/arrow one is that you don't use the size of the point on the dartboard, you use the side of the tip of the dart or arrow which is not infinitely small. So what is the chance the tip will cover the area of the dartboard that contains that infinitely small point.

These are either horribly explained or simply nonsensical

this might effect the hotel prices... and the trivago reviews

We are even further from solving the "Worms lost in a forest" problem

i think that the "solution" of the paradox number 7 is wrong, the expected value is always going to be just 1 dollar. in the zeroth flip, following the same logic of every flip, the expected value is 1, for the first flip, you hace a 50 percent chance of having 2 dollars an 50 for having 0 dollars giving you a expected value of 1 dollar. You can go on and it will always going to be the same expected value. The onlypart you are missunderstanding is that the money of the previous flip does not stack with the nekt flip, so no matter how far you go, if you flip the coin one more time you are playing a different game with the expected value of one, but since you already went that far, you already won 2^n wich is more than one, so you don´t want to try again, so the fair price would be 1 dollar one game. I already saw this "paradox" explained wrong, please stop with this game

Taylor Swift’s kissing number:

I would not use the word approximate for the current best estimate for the square packing problem. I would say "less than or equal to" as in this is an upper bound on the solution, but it's unproven that a better packing does not exist.

All sophistry

4:55 did you see that in the bottom left corner 9:57 its 0 not 2

I LOVE that you just hit the road running and started the vid w/o intro. Thanks for respecting our time.

Please please please do statistics videos!! Im a psych student and want to learn more from you ahout cool statistics things

perelman is legend.

you had a mistake with gabriel's horn. the point of it is, it has finite volume, but if you calculate its surface area it goes to infinity. so you have a shape with infinite surface area enclosing a finite volume, which is very counter-intuitive

wow these are all just kinda stupid aren't they. "🤓umm suppose this literally impossible scenario I just conceptualized" and nobody can find a solution? wow gee I wonder why. if you wanna find a solution to an impossible made up scenario, then you just make up an impossible solution don't you. hotel has infinite rooms? no such hotel can exist, even if you build it in the void space, you'd never finish building it until the gravity of the hotel makes it collapse in on itself. and it's fully occupied yet a novel client just walked in asking for a room? guess the number of people in this scenario is a greater infinity than the infinity of the hotels rooms. the fact that it's fully occupied and then they just move every resident one room over implies you built a new room in the time it took to move everyone, which is entirely possible as every resident doesn't have to move at the same time, you effectively have more time the more residents you have. I solved your riddle. do I get a reward?

Lots of German names here today.

feels like each one can have a 6-15min video of their own too

Hungary mentioned

Infinity exists only in the imagination.

For the little wood experiment what if you put 1 ball back in for every 10 you take out.

You missed one of my favorite infinity paradoxes. I don’t know the exact name of it but I’ll call it “The Arrow Paradox” Numbers can go infinitely up, we all know that. But there’s also infinitely smaller because you can always keep cutting something in half. If you shoot an arrow at a target, it will have to keep traveling across what is essentially an infinite distance because you can always cut an inch into half an inch and half an inch into a quarter inch and so on and so forth. Therefore, the arrow should theoretically never be able to reach its target because it would have to travel across an infinite amount of space.