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[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.

[scarface]

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


How An Infinite Hotel Ran Out Of Room
https://www.youtube.com/watch?v=OxGsU8oIWjY



Nice, clean, albeit a bit small, this apartment could suit the needs of humbert or shadow.97.
https://www.youtube.com/watch?v=mw7oX1F1IKI&t=193s



HAKIMAKLI - DING DONG
https://www.youtube.com/watch?v=uLaloMHIZ2M



The crypto utopia
https://www.youtube.com/watch?v=B7vg-FbYSlc

[humbert]

How An Infinite Hotel Ran Out Of Room

As a kid I always asked myself this question: on the number line which has more numbers? The entire line or just all positive numbers? You'd think the entire line would be the answer. The problem with this is that both of these are infinite.  ∞ = ∞ If the entire number line has more numbers than the other then there is no infinity.

Right?

Nice, clean, albeit a bit small, this apartment could suit the needs of humbert or shadow.97.

I believe you showed us this video before. I think I said that even if some rich guy gave you this apartment as a gift, there is no way you [indefinite] could afford to live there. Maintenance fees to the condominium association and property taxes would eat you alive. I can't even begin to think about other expenses. And of course, being way at the top and looking down those windows makes me dizzy.

If it were possible I'd move to a place with a cold forest with mountains as far away from the sea as possible.

[scarface]

How An Infinite Hotel Ran Out Of Room

As a kid I always asked myself this question: on the number line which has more numbers? The entire line or just all positive numbers? You'd think the entire line would be the answer. The problem with this is that both of these are infinite.  ∞ = ∞ If the entire number line has more numbers than the other then there is no infinity.

Right?

I don't know, I'm going to let another user of the forum answer this question.

Nice, clean, albeit a bit small, this apartment could suit the needs of humbert or shadow.97.

I believe you showed us this video before. I think I said that even if some rich guy gave you this apartment as a gift, there is no way you [indefinite] could afford to live there. Maintenance fees to the condominium association and property taxes would eat you alive. I can't even begin to think about other expenses. And of course, being way at the top and looking down those windows makes me dizzy.

If it were possible I'd move to a place with a cold forest with mountains as far away from the sea as possible.

That's right, I already posted this video before. I like this one because the music fits in well with the grandiose atmosphere of the place.
It seems you are into heavy intellectual stuff, next time, I'll put appropriate videos.

[scarface]

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


Spain - Water scarcity in a vacation paradise
https://www.youtube.com/watch?v=CftCns18rn4

On the Costa Blanca, the small fishing village of Benidorm has given way to a forest of hotel-buildings, marked by mass tourism.
Maybe Hubert and shadow97 have been there. During a trip to Alicante, in 2002, I've been to Benidorm.


Jeddah Tower: How to Finish the World's Tallest Building
https://www.youtube.com/watch?v=L6E-VjbOVEs



If Maher and Vasudev look at this little animal, they must be dazzled by its simplicity and beauty. But if we study the morphology of this specimen, we can figure out that it's pretty fat.
In this video, you are going to discover the effect of such fatness on one's sleep.
https://www.youtube.com/watch?v=A7waJga9Zdk



Why modern sandwich bread is different from 'real' bread
https://www.youtube.com/watch?v=i3sP2jwG9jc

[humbert]

It seems you are into heavy intellectual stuff, next time, I'll put appropriate videos.

The subject is fascinating. Sadly for the most part it's out of my league. I only wish I were a little smarter so I could discuss these subjects at length.

Spain - Water scarcity in a vacation paradise

Desalination is the only option. Google images for maps of desalination plants all over the world and you'll see there are tons of them, especially in Europe. Of course they're expensive, but if you factor in the fact that you'll NEVER run out of water it becomes well worth it. If someone as a better option, I'm listening.

Jeddah Tower: How to Finish the World's Tallest Building

I'm not too clear exactly what they were going to do with the Jeddah Tower if they managed to finish it. I do have an observation. In the video they used the Burj Kalifa and the Empire State Bldg as points of comparison. Somewhere I heard that probably as much as the upper 3rd of the Burj Kalifa is nothing more that unused structures put the for no other reason than to make it the world's tallest building. After a little bit of Googling, here's what I see:

Empire state building: 102 Floors on 380 meters. Spire and antennas on 63 meters for a total of 443.

Burj Kalifa: 160 floors. Assuming the floors on both buildings are approximately the same height, using rule of 3 then (380x160)/102 ≈ 596 meters. 828-596= 132 meters of unusable garbage whose only purpose is to make it the tallest building in the world? What have you done?

Back to my original question: if the Jeddah Tower had been build to completion, how much of it is usable? Based on this information it's clear no human will ever get anywhere near 1000 meters.

[scarface]

Back to my original question: if the Jeddah Tower had been build to completion, how much of it is usable? Based on this information it's clear no human will ever get anywhere near 1000 meters.

I think the project is not meant to build a useful tower, its purpose is to build the highest tower in the world. Currently, this tower is located in Dubai. The Burj Khalifa has helped to promote Dubai as a center of innovation and progress, and it has attracted international attention to the city.
It's even present in video games: https://www.youtube.com/watch?v=SCDpWm5MYZM
For the Saudis, Mecca is already an important place, but Jeddah not so much, hence the project.

[scarface]

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


The Exploding Whale Incident
https://www.youtube.com/watch?v=Na_zKbN2VJw



India: Sikkim - A Green New World
The Indian state of Sikkim has banned pesticides completely, allowing only organic farming. The results: healthy food and healthy soils.
https://www.youtube.com/watch?v=dBcmlXb_sPQ



Is moldy food really that dangerous?
https://www.youtube.com/watch?v=NgduUAu8s3g



A Math Puzzle
https://www.youtube.com/watch?v=2yeEmqUfI6U

[scarface]

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


In a previous video, humbert expressed his concerns about the Jeddah Tower. But it seems work resumes on the world's tallest skyscraper
https://www.youtube.com/watch?v=fHpW1CStT8I



Concorde: Myth and Tragedy
https://www.youtube.com/watch?v=Ewd-4cAjNME



They were very thirsty. They wanted to drink beers. That's why, on November 8-9, 1923, the Fuhrer and his National Socialist Party colleagues stormed into a beer hall in Munich. Some specialists talk about this unusual event in this video.
https://www.youtube.com/watch?v=SU0-50Y47fc