best clips

[scarface]

Tonight, new videos are available on the forum.



The Blue Hole in Dahab, Egypt. It is one of many of these blue holes around the globe, but this one is considered to be by far the most dangerous.
https://www.youtube.com/watch?v=RM_SH1Heo_E



The Mystery of Flight 823
https://www.youtube.com/watch?v=SFktPRJ48T0



The true Story of The Raft of The Medusa
https://www.youtube.com/watch?v=mNYBddD0Z-I



Ohio's 1986 Balloonfest
https://www.youtube.com/watch?v=_XV6Jz3Xg18

[scarface]

Tonight, new videos are available for the users of the forum.


What Really Happens When A Fly Lands On Your Food?
https://www.youtube.com/watch?v=8kJS9LfdSPM



The most dangerous dive site in Texas
https://www.youtube.com/watch?v=FzJISTmGWLQ



What was in the box?
https://www.youtube.com/watch?v=Jnh_MiPuhyQ



Exploring Vorkuta - a Russian town in Arctic
https://www.youtube.com/watch?v=2i3aS6T6Nng

[scarface]

Tonight, new videos are available for the users of the forum.


Lost Worlds: the Forgotten Creatures of Prehistory
https://www.youtube.com/watch?v=AX7DDrDvC1U



Can water solve a maze?
https://www.youtube.com/watch?v=81ebWToAnvA



Sonic the Hedgehog 3 Retrospective (& Knuckles)
https://www.youtube.com/watch?v=Cp5D6QgL-nU



Found Footage
https://www.youtube.com/watch?v=sKLhP2aGXEg

[scarface]

Today, new videos are available for the users of the forum.

Maybe some of you were awarded the Field medal. In this case, it won't be a problem for you to solve the Collatz conjecture. Nobody has been able to solve it...so far.
The Collatz conjecture is one of the most famous unsolved problems in mathematics. The conjecture asks whether repeating two simple arithmetic operations will eventually transform every positive integer into 1. It concerns sequences of integers in which each term is obtained from the previous term as follows: if the previous term is even, the next term is one half of the previous term. If the previous term is odd, the next term is 3 times the previous term plus 1. The conjecture is that these sequences always reach 1.
If you can show that in every 3x+1 sequence, there is a number that is smaller than the original seed, then you have proven the Collatz conjecture.
https://www.youtube.com/watch?v=094y1Z2wpJg



In November 2016, a stash of hidden documents is discovered in a closet, in France. The papers are written in German and dated April 1945. Among the drawings, telegrams, letters, military orders... Those papers were sent to an international expert on German records. It turns out those documents all came from the Fuhrer-Bunker and paint a vivid and dismal picture of what happened in this concrete dungeon.
An exceptional documentary for humbert and Vasudev.
https://www.youtube.com/watch?v=qGD6P3Oafd0



The true story of the Dybbuk box
https://www.youtube.com/watch?v=iYKWQxEGvSk



Beware of Venus flytraps
https://www.youtube.com/watch?v=O7eQKSf0LmY

[humbert]

There's something I don't understand about the Collatz conjecture. In the beginning it says that all even numbers end up in the 4-2-1 loop. When they ran 27 as a test, it went all crazy but eventually ended up in the 4-2-1 loop too. So which is it? Only even numbers or all of them?

[scarface]

There's something I don't understand about the Collatz conjecture. In the beginning it says that all even numbers end up in the 4-2-1 loop. When they ran 27 as a test, it went all crazy but eventually ended up in the 4-2-1 loop too. So which is it? Only even numbers or all of them?

Hi humbert,
In fact the conjecture says that any positive number (odd or even) will eventually end up in the four two one loop. So this applies to all numbers.

For example with 17:
17→52→26→13→40→20→10→5→16→8→4→2→1

[humbert]

Hey Scarface. Do you totally understand the Collatz conjecture? If so, I thought maybe you could explain at least 2 things I don't fully understand.

At 4:40 into the video, he explains the curve can be better understood by using log(1,465,018). Where did he get that number? I played the video several times and I'm not seeing where 1,465,018 came from or how he applies it. The calculator says log(1,465,018) = 6.16584 - so what?

On the bar graph with percentages, are these the percentage of starting numbers in the numbers in the entire sequence? For example, in the example you gave for 17 (17→52→26→13→40→20→10→5→16→8→4→2→1)  1 is the leading number 5 times, 2 is leading number 3 times, and so on? Is this what he means?

I'm doing exactly what those mathematicians told us not to do. This is truly fascinating. It's hard to believe every number tested up to 2⁶⁸ and ever one ends up in the 4-2-1 loop.

[scarface]

At 4:40 into the video, he explains the curve can be better understood by using log(1,465,018). Where did he get that number? I played the video several times and I'm not seeing where 1,465,018 came from or how he applies it. The calculator says log(1,465,018) = 6.16584 - so what?

the Collatz conjecture says:
f(x) = x/2 if x is even
f(x) = (3x+1) if x is odd
let's call the new function x→u(x).
For a big number u(x) can climb rapidly, so The video uses y=ln(u(x)) to smooth the curve so that one can see the pattern of the curve.
ln(1,465,018) means that for u(x)=1465018, y=6. For u(x)=1 (end of the loop), y=ln(1)=0.

On the bar graph with percentages, are these the percentage of starting numbers in the numbers in the entire sequence? For example, in the example you gave for 17 (17→52→26→13→40→20→10→5→16→8→4→2→1)  1 is the leading number 5 times, 2 is leading number 3 times, and so on? Is this what he means?

I'm doing exactly what those mathematicians told us not to do. This is truly fascinating. It's hard to believe every number tested up to 2⁶⁸ and ever one ends up in the 4-2-1 loop.

17(3x17+1)→52(52/2)→26→13→40→20→10→5→16→8→4→2→1 is the sequence for 17, there is no "leading number".

[humbert]

the Collatz conjecture says:
f(x) = x/2 if x is even
f(x) = (3x+1) if x is odd
let's call the new function x→u(x).
For a big number u(x) can climb rapidly, so The video uses y=ln(u(x)) to smooth the curve so that one can see the pattern of the curve.
ln(1,465,018) means that for u(x)=1465018, y=6. For u(x)=1 (end of the loop), y=ln(1)=0.

I used to be good in math but it's been a while and I'm a little rusty. Let's take a look at this.

The 2 initial function [f(x) = x/2] for even and [g(x) = (3x+1)] for is the general idea. That part is clear.

You lost me when you say "big number", and I don't understand what you mean by x→u(x).

I also don't understand how he came up with 1,465,018. Finally, you're using ln (natural logarithm). I could swear the video says log. As you know, they're not the same.

If you can help explain this to an idiot like me, I'd appreciate it. 

[scarface]

the Collatz conjecture says:
f(x) = x/2 if x is even
f(x) = (3x+1) if x is odd
let's call the new function x→u(x).
For a big number u(x) can climb rapidly, so The video uses y=ln(u(x)) to smooth the curve so that one can see the pattern of the curve.
ln(1,465,018) means that for u(x)=1465018, y=6. For u(x)=1 (end of the loop), y=ln(1)=0.

I used to be good in math but it's been a while and I'm a little rusty. Let's take a look at this.

The 2 initial function [f(x) = x/2] for even and [g(x) = (3x+1)] for is the general idea. That part is clear.

You lost me when you say "big number", and I don't understand what you mean by x→u(x).

I also don't understand how he came up with 1,465,018. Finally, you're using ln (natural logarithm). I could swear the video says log. As you know, they're not the same.

If you can help explain this to an idiot like me, I'd appreciate it. 

x→u(x) was just a mean for me to define the function f used for the Collatz conjecture.
It is defined as follows:
f(n) = n/2 if n=0 (mod 2), 3n+1 if n=1 (mod 2)

As for ln, that's right I said ln (natural logarithm). ln and log are not the same, but it's the same thing (up to a multiplicative constant): log(x)=ln(x)/ln(10). So the function log(x) and ln(x) have the same pattern, it doesn't matter whether they are using one or the other.