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I love Graham's Number...particularly because it can be notated. The step from 3 [3 arrows] 3 to 3 [4 arrows] 3 blows my mind...and then g1 to g2 where the number of arrows is g1 is just mind-bending when you consider how the numbers escalate by just adding one arrow. After that all meaning is lost. And then TREE(3) is bigger than Graham's Number in a way that is unimaginable. Fun fact about 3 [3 arrows] 3 is if each 3 was around 2cm high, the power tower (7.6 trillion 3s) would reach the sun...

You are a great orator

But what if we replace the cubes with some other 3d shapes with more vertices

I think I want to start investing Graham now. What are the stock prices?

Great video. I have seen other videos about Grahams number but I found your video to be best

Should do a comparison between Graham Number to Tree(3), such as Graham number the size of an atom while Tree(3) is the size of the observable universe etc!

@Parasmunt

Жыл бұрын

The comparison would be wrong. G(2) itself minus one arrow is zero effectively compared to G2 fully calculated with that arrow. Never mind Tree. The G function does not grow off the number arguments (3) it expands the power of the expansion.

@asparkdeity8717

8 ай бұрын

Nothing physical can compare Tree(3) to Grahams Number, even at just numbers as “tiny” as 10^122, all sense of physicality is lost

@niko_hand589

7 ай бұрын

There is no possible way to display a smooth transition to show the scale of those numbers. The magnitude of the difference between the two render the smaller number to be about 0 in comparison. And i am not overstating this. There is no way. You cannot have a comparison where you, for example, zoom out like most universe scale comparison videos. Even if you double the speed at which you zoom out every second, half a second, nanosecond, planck time etc... Even if you multiply the zoom-out speed by the biggest number you can imagine in your head every nanosecond you will not even be close to representing the scale of those numbers in a video.

@daniel.sandberg.5298

7 ай бұрын

D you have any remote understanding of how unimaniably large grahams number is? TREE is not conceivable in any inventable scale so basically the only way to notate those mathematical absurdities is to build those extremely powerful exponentiations that completely obliterate everything we can applicate in terms of powerups considering the power of powers are finite but uncomputable. And that is only for grahams number. TREE doesnt have a notation because its a notation in such level it makes the other powers completely utterly useless no matter how unprioritized we conceive worth in the concept.

@TheZapper42

3 ай бұрын

Graham's number is effectively zero compared to TREE(3). Graham's number is only at the linear omega level in the fast growing hierarchy. TREE(3) is bigger than the gamma level.

🤔 It sounds like Graham number is Goku's current power level from Dragon Ball Z Super. Lol

@ghettoghost2657

7 ай бұрын

Facts

@daniel.sandberg.5298

2 ай бұрын

Each exponent males the number bigger in a certain pattern. After a couple of steps you cant visualize it. Those arent numbers to us as they are too big. It is beyond comprehension.

Grahams number is g(64). Had a drunk talk about mathematics with a friend who knew Graham's number is big but had no idea how big it really was. I told him if you put the a number on every atom in the observable universe it will still be less than 1%. Then I added If you put the amount of digit of every atom in the observable universe into each atom in the observable universe it will still be less than 1% of Grahams number. He couldn't & didn't believe me.

You didn't mention the lower bound.

The real trick to understand the concept or I might say to know that you have understood the concept is that "You can not understand it" Literally if it could be understood it wouldn't be big. And if you think you have understood it then you basically haven't.

@MABfan11

6 ай бұрын

i mean, for a Googologist, the number is quite small and comprehensible

@russellcurtis6334

3 күн бұрын

If anyone did actually understand it as it truly is, we’d know he was telling the truth because his brain would collapse into a black hole. If not, he hasn’t.

So they know the last 500 digits now? When I was in school they only knew like the last 7 digits lol

@NorbertKasko

20 күн бұрын

They know the last 4 million. You can download it. There is a link on Wikipedia.

as a Googologist, i find Graham's Number to be quite small and comprehensible

@nocktv6559

Ай бұрын

cool

@NorbertKasko

20 күн бұрын

Comprehensible?! No it's not. If you think it's comprehensible you don't understand it.

@MABfan11

20 күн бұрын

@@NorbertKasko Bowers' Exploding Array Function can reach Graham's Number without even stretching its legs

@NorbertKasko

20 күн бұрын

@@MABfan11 That doesn't make Graham's number "small and comprehensible". 1000000000000000000 is small and comprehensible or a Googol maybe. A number which we don't even know how many digits it has or we have no idea how tall the power tower representation would be is not comprehensible by any means.

@MABfan11

20 күн бұрын

@@NorbertKasko in Googology, we deal with far bigger numbers, Graham's Number is on the lower end of the scale when it comes to numbers in Googology

If this number is from a genuine mathematical problem, then what is the real-world application of this problem?

@dm9910

Жыл бұрын

The specific problem it answers is very abstract, very academic, and not directly relevant to any real world problem. However, it's part of a larger field in mathematics called graph theory, which is essentially the study of networks, which has lots of real world applications. For example, you can make a graph with nodes representing cities and connections representing transport links, and use graph theory to predict how it would change if you added an extra lane to a motorway, or a railway between two cities. The particular question that gives rise to Graham's number involves higher-dimensional cubes. Since we live in a world with only 3 spatial dimensions, that might seem pretty useless. But dimensions don't have to be spatial, they can be anything really as long as they're independently variable (like how spatial dimensions are perpendicular to each other). If you wanted to know the best way of taking a free throw in basketball, you could make a scatter plot of velocity vs angle of release, with each dot representing a success or a fail. You could then find a region in that graph which corresponds to the highest rate of success. In other words, the optimal region is a 2D shape where the two dimensions are an angle and a velocity. To make the model more accurate, we can factor in a couple more variables like height of release and spin, and now the optimal region is a 4D shape, which is harder to intuitively visualize but is equally valid. This sort of trick of modelling systems using dimensions is used all the time in fields like big data and machine learning. The Graham's number problem is part of a branch of graph theory called Ramsey theory, that asks how big a structure has to be before it *must* have some property. For example: with at least 366 people in a group, at least 1 pair of people must share the same birthday. For more complex problems it gets much more abstract and theoretical and not easy to apply to the real world, but it could potentially be used for things like analysing social structures. For example you could have a graph representing a group of people, with the connections representing each possible relationship, with the red/blue colourings representing any binary property of the relationship such as whether they're friends or not.

@mubarakvodel5763

8 ай бұрын

Thank you for your excellent and comprehensive elaboration. You gave great examples for comprehension.

When you double it, it doesn't really change. That's how big Graham's number is.