6 minutes of Fascinating Math

Math can sometimes be fascinating.

[HelloIAmAnExist]

Newcombs paradox is a really interesting problem. Here's my solution to it:
The way I understand it, the argument for choosing A+B is based on game theory (not the channel lol) and the idea that whatever is in B doesn't matter, because you might as well take an extra 1, 000 dollars. The reason that's incorrect, is because you're assuming there's 4 options (0 dollars, 1k dollars, 1M dollars, and 1, 001k dollars) when there's only really 2 (1k or 1M) because assuming that the predictor is perfect means you can't make a decision that "tricks" it. Technically, you can't change the past, and what the predictor put in each box. But practically, you sort of can. If you choose B, then you get 1M. Not 1M/0, because that implies that there's random chance in this completely deterministic problem. Likewise, if you choose A+B, there's only 1 possible result you can get, which is 1k. You can't get 1M from the B box, because that would mean the predictor was wrong, which he can't be.

I think this kind of resembles the idea of a superposition which is pretty neat. Also the concept of free will being an illusion. I really like this problem.

I'm not sure if I managed to explain myself the way it's explained in my head, but this is what I view as the objectively correct answer. If anyone thinks something different I'd be glad to argue in the replies.

Edit: ok, I think I found a better way to put it:
The flaw with the reasoning of: "well I took the 1M and I got it, but I know for certain that A had an extra 1k, so why didn't I just take that as well?" is the idea that you could have chosen differently and gotten the same result with B because it was predetermined what the box had. It's like the A box has a sensor that automatically removes everything in the B box, even though it's seemingly just a free 1k. It didn't have an actual sensor, but it might as well had had one, because the A box is pretty much a trap. B's contents are what I like to call "yet to be predetermined". You can't actively change the past, but the people in the past act differently based on the future, which is your present.

Yeah wow this is really hard to put into words

Did anyone understand a single thing I said

[TheOne_]

hold on why is this channel SO UNDERRATED

[LaugeHeiberg]

On the first one, an interesting observation:
Take 4+5+6 = 7+8
If you take out the first number, 4, and then split it evenly to the other numbers, 5 and 6, you get whats on the other side, 7+8.

Another (barebones) example:

16+17+18+19+20 = 21+22+23+24

16/4 = 4

(17+4)+(18+4)+(19+4)+(20+4) = 21+22+23+24

21+22+23+24 = 21+22+23+24

[OrbitTheSun]

If I open box B and it is empty, I open box A and get at least $1000. Predictor was right that I would open two boxes. If box B contains $1 million, I don't open box A, so the predictor is correct again.

[dheerendrayadav]

3:04 the explanation to this:
Sum of first n odd numbers in n², so the fraction will become n²/((2n)²-n²) which is n²/3n² thats why it always results in 1/3

[Smallpriest]

The problem with the last question is that "reliable predictor" is vague and not clearly explained.
The difference in answers just depends on how someone interprets what "reliable predictor" means to them.
This is yet another example of a question being more of a language problem than a math problem

[Faroshkas]

I simply love this video, and I don't think word can describe how much. This is the first time I've seen a math video structured like this before, and it's fascinating. Thank you for this!

[pepefrogic]

Undulating squares and cubes are easy to completely list. It is not that only 4 have been found and one cube, it is that only 4 EXIST (in base 10) and that is fairly easy to prove/check (modular arithmetic mod say)

[gm_construct__betaexplor]

i love it when luigi explains math to me for 6 minutes

[The_Commandblock]

its a shame that this only has 270 views

[NbNgMOD]

Fun fact, on TI30xs calculator 69! Is the biggest factorial before overflow error and 70! Is the least amount of characters needed for overflow error

[kikivoorburg]

The way I see it, Newcomb’s paradox is just a malformed question regarding free will.

If free will exists, then there is no such thing as an “accurate predictor”. Maybe a very-nearly-accurate one, but never a perfectly accurate one because someone could just _choose_ not to follow its prediction. In that case we have 4 options (ignoring the “take only A” answer, which is funny but rather obviously never the best)
- Predictor guesses taking both and you take both => $1000.
- Predictor guessed taking both and you take only B => $0.
- Predictor guesses taking only B and you take both => $1001000.
- Predictor guesses taking only B and you take only B =>

Notice how out of these 4 cases, it’s always better to take both boxes regardless of what the predictor guessed. Hence why that’s some people’s “obvious” answer.

By contrast, let’s take the predictor being 100% accurate as a definite truth, thereby requiring free will to be false. In that case we have only two options (again ignoring “take only A”):
- You take only B => $1M
- You take both => $1000
We don’t even need to mention the predictor because it’s always right and so only your action is relevant. In this case there’s no good answer to “what do you do?” because if free will is a myth, you don’t know what you do until it happens. The best you can say is “I hope I take only B” because that would mean $1M.

So, the paradox is actually the incompatibility between determinism and free will. If you lean to the side of free will being real, you should take both. If you lean to the side of determinism, you should hope you take only B.

What would I do in a real situation? Well, depends on context. I don’t believe in free will, but also know that we (humanity) definitely do not have a 100% accurate predictor. So if a human came to me with this situation, I’d take both boxes knowing the predictor isn’t flawless. If, however, I was somehow given this prompt in a context where it’s plausible that there is a 100% accurate predictor, I’d only take B. I don’t expect to ever be in the latter situation, so devoid of context I’d take both.

TL;DR:
Free will is incompatible with a perfect predictor. IRL we don’t have perfect predictors, so it’s best to just take both unless there’s a good reason to think the predictor involved is perfect (in which case you better hope you take only B!)

Edit: fixed ‘a “accurate predictor”’ to ‘an “accurate predictor”’.

[chrisg]

1:32 "This is a regular pentagon with one thousand sides" Gosh

[joinfortherapy]

the voice is so soothing, i can use this as sleeping music

[ricsix.]

Great video! The bloopers are also funny like "a regular pentagon with 1000 sides"

[Birch-zp]

For undulating numbers, isn’t it exclusive to base 10. If you worked in binary you would have way more and hexadecimal way less and it wouldn’t be the same numbers as in base 10. As such what is the correlation between undulating numbers and their base

[The-EJ-Factor]

2:24 only 4 discovered? Or was it proven there can’t be another factorion

[tzbq]

for some reason i took the time and calculated the first one, and for any length of n the first sequence will start in (n-1)^2

[Swagpion]

0:51 another fun fact about 11. When you square a string of 1s, you get a number which goes up, and then goes down, and it goes up to the number equal to the number of 1s you started with (if it goes above your base, you have to carry over the extra bits). So 1111^2=1234321

[Velu]

I really hope this will get more recognition in the future