this post was submitted on 03 Aug 2023
196 points (95.0% liked)

No Stupid Questions

35893 readers
1289 users here now

No such thing. Ask away!

!nostupidquestions is a community dedicated to being helpful and answering each others' questions on various topics.

The rules for posting and commenting, besides the rules defined here for lemmy.world, are as follows:

Rules (interactive)

Rule 1- All posts must be legitimate questions. All post titles must include a question.

All posts must be legitimate questions, and all post titles must include a question. Questions that are joke or trolling questions, memes, song lyrics as title, etc. are not allowed here. See Rule 6 for all exceptions.

Rule 2- Your question subject cannot be illegal or NSFW material.

Your question subject cannot be illegal or NSFW material. You will be warned first, banned second.

Rule 3- Do not seek mental, medical and professional help here.

Do not seek mental, medical and professional help here. Breaking this rule will not get you or your post removed, but it will put you at risk, and possibly in danger.

Rule 4- No self promotion or upvote-farming of any kind.

That's it.

Rule 5- No baiting or sealioning or promoting an agenda.

Questions which, instead of being of an innocuous nature, are specifically intended (based on reports and in the opinion of our crack moderation team) to bait users into ideological wars on charged political topics will be removed and the authors warned - or banned - depending on severity.

Rule 6- Regarding META posts and joke questions.

Provided it is about the community itself, you may post non-question posts using the [META] tag on your post title.

On fridays, you are allowed to post meme and troll questions, on the condition that it's in text format only, and conforms with our other rules. These posts MUST include the [NSQ Friday] tag in their title.

If you post a serious question on friday and are looking only for legitimate answers, then please include the [Serious] tag on your post. Irrelevant replies will then be removed by moderators.

Rule 7- You can't intentionally annoy, mock, or harass other members.

If you intentionally annoy, mock, harass, or discriminate against any individual member, you will be removed.

Likewise, if you are a member, sympathiser or a resemblant of a movement that is known to largely hate, mock, discriminate against, and/or want to take lives of a group of people, and you were provably vocal about your hate, then you will be banned on sight.

Rule 8- All comments should try to stay relevant to their parent content.

Rule 9- Reposts from other platforms are not allowed.

Let everyone have their own content.

Rule 10- Majority of bots aren't allowed to participate here.

Credits

Our breathtaking icon was bestowed upon us by @Cevilia!

The greatest banner of all time: by @TheOneWithTheHair!

founded 1 year ago
MODERATORS
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
[email protected]
196
What are the most mindblowing things in mathematics? (lemmy.world)
submitted 1 year ago* (last edited 1 year ago) by [email protected] to c/[email protected]
83 comments fedilink hide all child comments
 

What concepts or facts do you know from math that is mind blowing, awesome, or simply fascinating?

Here are some I would like to share:

  • Gödel's incompleteness theorems: There are some problems in math so difficult that it can never be solved no matter how much time you put into it.
  • Halting problem: It is impossible to write a program that can figure out whether or not any input program loops forever or finishes running. (Undecidablity)

The Busy Beaver function

Now this is the mind blowing one. What is the largest non-infinite number you know? Graham's Number? TREE(3)? TREE(TREE(3))? This one will beat it easily.

  • The Busy Beaver function produces the fastest growing number that is theoretically possible. These numbers are so large we don't even know if you can compute the function to get the value even with an infinitely powerful PC.
  • In fact, just the mere act of being able to compute the value would mean solving the hardest problems in mathematics.
  • Σ(1) = 1
  • Σ(4) = 13
  • Σ(6) > 10^10^10^10^10^10^10^10^10^10^10^10^10^10^10 (10s are stacked on each other)
  • Σ(17) > Graham's Number
  • Σ(27) If you can compute this function the Goldbach conjecture is false.
  • Σ(744) If you can compute this function the Riemann hypothesis is false.

Sources:

you are viewing a single comment's thread
view the rest of the comments
[–] [email protected] 5 points 1 year ago* (last edited 1 year ago)

Let's name the goats Alice and Bob. You pick at random between Alice, Bob, and the Car, each with 1/3 chance. Let's examine each case.

  • Case 1: You picked Alice. Monty eliminates Bob. Switching wins. (1/3)

  • Case 2: You picked Bob. Monty eliminates Alice. Switching wins. (1/3)

  • Case 3: You picked the Car. Monty eliminates either Alice or Bob. You don't know which, but it doesn't matter-- switching loses. (1/3)

It comes down to the fact that Monty always eliminates a goat, which is why there is only one possibility in each of these (equally probable) cases.

From another point of view: Monty revealing a goat does not provide us any new information, because we know in advance that he must always do so. Hence our original odds of picking correctly (p=1/3) cannot change.

In the variant "Monty Fall" problem, where Monty opens a random door, we perform the same analysis:

  • Case 1: You picked Alice. (1/3)
    • Case 1a: Monty eliminates Bob. Switching wins. (1/2 of case 1, 1/6 overall)
    • Case 1b: Monty eliminates the Car. Game over. (1/2 of case 1, 1/6 overall)
  • Case 2: You picked Bob. (1/3)
    • Case 2a: Monty eliminates Alice. Switching wins. (1/2 of case 2, 1/6 overall)
    • Case 2b: Monty eliminates the Car. Game over. (1/2 of case 2, 1/6 overall)
  • Case 3: You picked the Car. (1/3)
    • Case 3a: Monty eliminates Alice. Switching loses. (1/2 of case 3, 1/6 overall)
    • Case 3b: Monty eliminates Bob. Switching loses. (1/2 of case 3, 1/6 overall)

As you can see, there is now a chance that Monty reveals the car resulting in an instant game over-- a 1/3 chance, to be exact. If Monty just so happens to reveal a goat, we instantly know that cases 1b and 2b are impossible. (In this variant, Monty revealing a goat reveals new information!) Of the remaining (still equally probable!) cases, switching wins half the time.