Weird Science

[Einherjar86]

This is the best thing I will ever see in my lifetime:

https://www.stuff.co.nz/environment...r-species-keeps-old-heads-wears-them-as-a-hat

Fuckin' kinda fetishistic shit is this? Jesus.

This Carnivorous Plant Evolved to Also Be a Rodent Toilet

Think the link might have been copied wrong...?

 

[Bloopy]

Think the link might have been copied wrong...?

Oops, fixed.

 

[Einherjar86]

Gives a whole new meaning to the phrase “eat shit.”

 

[Einherjar86]

The Simple Math Problem We Still Can’t Solve

This problem is simply stated, easily understood, and all too inviting. Just pick a number, any number: If the number is even, cut it in half; if it’s odd, triple it and add 1. Take that new number and repeat the process, again and again. If you keep this up, you’ll eventually get stuck in a loop. At least, that’s what we think will happen.

Take 10 for example: 10 is even, so we cut it in half to get 5. Since 5 is odd, we triple it and add 1. Now we have 16, which is even, so we halve it to get 8, then halve that to get 4, then halve it again to get 2, and once more to get 1. Since 1 is odd, we triple it and add 1. Now we’re back at 4, and we know where this goes: 4 goes to 2 which goes to 1 which goes to 4, and so on. We’re stuck in a loop.

Or try 11: It’s odd, so we triple it and add 1. Now we have 34, which is even, so we halve it to get 17, triple that and add 1 to get 52, halve that to get 26 and again to get 13, triple that and add 1 to get 40, halve that to get 20, then 10, then 5, triple that and add 1 to get 16, and halve that to get 8, then 4, 2 and 1. And we’re stuck in the loop again.

The infamous Collatz conjecture says that if you start with any positive integer, you’ll always end up in this loop. And you’ll probably ignore my warning about trying to solve it: It just seems too simple and too orderly to resist understanding. In fact, it would be hard to find a mathematician who hasn’t played around with this problem.

Yeah, I wasted about fifteen minutes today playing around with this. Needless to say, I didn't find the magic number.

 

[rms]

Are you aware of term NP complete?

 

[Einherjar86]

Oh yeah, that shit’s fascinating. There’s a mediocre movie about it—I think it’s called Traveling Salesman.

 

[Baroque]

The Simple Math Problem We Still Can’t Solve



Yeah, I wasted about fifteen minutes today playing around with this. Needless to say, I didn't find the magic number.

It sometimes helps to look at these types of unsolved problems oppositely. Suppose that the conjecture is true. We also know that every power of 2 will collapse to 1 and that pattern by using those rules. If it is true that if we apply those rules to every prime number it will result that pattern, then it’s also true that every prime number will eventually reach a power of 2 from those rules. Then oppositely, we will also be able to generate every prime number using the inverse of those rules starting from the powers of 2. The inverse of the rules are subtract 1 and divide by 3, or double it and do the same.

Since there is no polynomial function in one variable (the starting number) that can generate all the prime numbers (proven by Euler), we have no way of proving the contrapositive of this conjecture. Therefore since the contrapositive of the conjecture is unprovable, the conjecture is unprovable.

Go ahead and publish me now?

What’s interesting to me is that, if the conjecture is true, we have a piecewise polynomial function which does generate all the primes.

 

[Bloopy]

How about starting a mathematics thread on here?

I was surprised when I realised the Riemann hypothesis (another famous unsolved problem) was much easier to understand for a relative layman like me than I'd once thought. I did study discrete math to 3rd year level at university as part of an IT degree, but by the 3rd year it was like flapping my way through a language I don't speak.

 

[Baroque]

I got a master’s in math.. but I went back and got another master’s in statistics. I’m more interested in solving real world problems now. These are like playing with toys, it’s fun but Mostly meaningless. Being able to generate primes would be interesting to cryptography, however I believe this method would be too slow to be of any practical use without quantum computing.

 

[Einherjar86]

How about starting a mathematics thread on here?

I'm down with people posting math shit here. I get most of my science/math "news" from Quanta anyway, and they have a whole category for math.

It sometimes helps to look at these types of unsolved problems oppositely. Suppose that the conjecture is true. We also know that every power of 2 will collapse to 1 and that pattern by using those rules. If it is true that if we apply those rules to every prime number it will result that pattern, then it’s also true that every prime number will eventually reach a power of 2 from those rules. Then oppositely, we will also be able to generate every prime number using the inverse of those rules starting from the powers of 2. The inverse of the rules are subtract 1 and divide by 3, or double it and do the same.

Since there is no polynomial function in one variable (the starting number) that can generate all the prime numbers (proven by Euler), we have no way of proving the contrapositive of this conjecture. Therefore since the contrapositive of the conjecture is unprovable, the conjecture is unprovable.

Go ahead and publish me now?

What’s interesting to me is that, if the conjecture is true, we have a piecewise polynomial function which does generate all the primes.

 

[rms]

I just don't get why anyone is wasting time with that conjecture lol I don't even see how disproving it is at all intriguing. Wasted enough time to check 2^68! Lol

 

[Einherjar86]

It sometimes helps to look at these types of unsolved problems oppositely. Suppose that the conjecture is true. We also know that every power of 2 will collapse to 1 and that pattern by using those rules. If it is true that if we apply those rules to every prime number it will result that pattern, then it’s also true that every prime number will eventually reach a power of 2 from those rules. Then oppositely, we will also be able to generate every prime number using the inverse of those rules starting from the powers of 2. The inverse of the rules are subtract 1 and divide by 3, or double it and do the same.

Since there is no polynomial function in one variable (the starting number) that can generate all the prime numbers (proven by Euler), we have no way of proving the contrapositive of this conjecture. Therefore since the contrapositive of the conjecture is unprovable, the conjecture is unprovable.

Go ahead and publish me now?

What’s interesting to me is that, if the conjecture is true, we have a piecewise polynomial function which does generate all the primes.

Sorry to double quote, but I'm curious: how do mathematicians come up with these "problems" in the first place? I'm sure it isn't a randomly assigned function. So how does one arrive at "if even, divide by two; if odd, multiply by three and add one"?

 

[Baroque]

I just don't get why anyone is wasting time with that conjecture lol I don't even see how disproving it is at all intriguing. Wasted enough time to check 2^68! Lol

There’s a difference between disproving and proving unprovable. It still might be true. As for wasting time, isn’t that everything we do on this forum? I spent about 30 minutes thinking about it after working 2 jobs, big deal. It’s a pet topic of mine showing certain unsolved problems are unprovable. In any case showing it’s unprovable results in what you’re saying, why should anyone continue to try proving the conjecture since we won’t be able to prove it correct, pending some major revelation such as Euler being disproven, or some other new discovery about primes

 

[Baroque]

Sorry to double quote, but I'm curious: how do mathematicians come up with these "problems" in the first place? I'm sure it isn't a randomly assigned function. So how does one arrive at "if even, divide by two; if odd, multiply by three and add one"?

Mathematicians get bored and try all kinds of things looking to make a name for themselves. But my suspicion (which led to my response) is that it began as a search for a prime generating function, and then instead became a search for the inverse of a prime generating function (which they deemed might be easier) and went from there. It could also be based on some obscure number theory rule that I’ve forgotten or haven’t seen.

 

[rms]

There’s a difference between disproving and proving unprovable. It still might be true. As for wasting time, isn’t that everything we do on this forum? I spent about 30 minutes thinking about it after working 2 jobs, big deal. It’s a pet topic of mine showing certain unsolved problems are unprovable. In any case showing it’s unprovable results in what you’re saying, why should anyone continue to try proving the conjecture since we won’t be able to prove it correct, pending some major revelation such as Euler being disproven, or some other new discovery about primes

Wasn't suggesting you were wasting time, but there are various spinoffs and similarly named "solutions" , but I struggle with understanding a use case for this theory, if it's deemed not true in a very few cases. Maybe it's just a problem used in college courses , not sure

 

[Bloopy]

Timekeeping Theory Combines Quantum Clocks and Einstein’s Relativity

Quantum mechanics allows for a clock to move as if it were simultaneously traveling at two different speeds. New research finds that this leads to a correction in atomic clocks known as “quantum time dilation.”

 

[CiG]

Scientists discover 500 metre-tall skyscraper coral reef at Australia's Great Barrier Reef. The detached reef, taller than the Empire State Building, was discovered at the northern end of the Great Barrier Reef off Cape York in Queensland.

Spoiler: Full 'remotely operated vehicle' SuBastian's 4 hour live stream

 

[Einherjar86]

Shit, that is fucking cool.

https://www.quantamagazine.org/the-black-hole-information-paradox-comes-to-an-end-20201029/

So, wtf happens when black holes become cosmic geisers?

They have found additional semiclassical effects — new gravitational configurations that Einstein’s theory permits, but that Hawking did not include. Muted at first, these effects come to dominate when the black hole gets to be extremely old. The hole transforms from a hermit kingdom to a vigorously open system. Not only does information spill out, anything new that falls in is regurgitated almost immediately. The revised semiclassical theory has yet to explain how exactly the information gets out, but such has been the pace of discovery in the past two years that theorists already have hints of the escape mechanism.

 

[rms]

https://www.syracuse.com/news/2020/...a-meteor-explodes-above-syracuse-in-2020.html

Not weird but cool

 

[Einherjar86]

Read about that. Wild.