The Insane Ackermann Function

Researchers proved that navigating certain systems of vectors is among the most complex computational problems and involves a function called the Ackermann function. Find out how an easy-sounding problem yields numbers too big for our universe.

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@QuantaScienceChannel

#math #computerscience

[tjrh]

New favourite word unlocked: quinquagintillion

[OutsiderLabs]

Ackerman has only one function: to pwn titans

[nunkatsu]

"Ackermann function"
"Colossal number"
Aot mentioned

[solarsystem]

pov: you've been inventing your sorting algorithms and ended up with complexity of A(n) ☠️

[not_mukul]

zeke won't enjoy studying this function

[KasparOne]

in the 50's scientists once attempted to calculate A[5], but the piece of paper on which the calculations were performed quickly turned into a black hole

[Pining_for_the_fjords]

In other words, the Ackerman function would be useful for describing the weight of your mum.

[jean-joseftolosa]

You've def earned it for summoning a titanic fandom.

[keshavvelayudhannair]

And after tetration (for 4)
You get pentation (for 5)
Pentation is just a tower of tetration
Tetration of tetration
Tetration 5 times is pentation of five
It is represented by a 5 with a small five on its left side bottom (5 with ⁵ at bottom left)

[Misteribel]

Its main use was to demonstrate a total computable function that is not primitively recursive. The original has three arguments. You essentially showed A(n, n, n) here, where all arguments are equal.

[ReginaldCarey]

What is A[pi]? What would the analytic continuation look like?

[luckycandy]

It's actually very simple and beautiful idea, suppose you give me a list of functions f_n(x) with x natural, each growing faster than the one before. Now I could apply the diagonal n -> f_n(n) Which grows faster than each f_n.

To get Ackermann you just choose some functions f_n, there are variations, the one I learnt was f_1(x)=2x and we get f_(n+1)(x) by iterating f_n(f_n(...f_n(1))...) x times, so that f_2(x)=2^x, f_3(x)=2^2^...^2 x times etc.

Hope you have a wonderful day😊

[tahmeedmansib]

Ah yes, the Ackermann function, the mathematical attempt to scale Levi's power level.

[Domo]

You got this completely wrong. This has nothing to do with the Ackerman function, except that both grow fast.

The Ackerman function is a recursive function with 3 arguments. And it grows even faster and takes much longer to compute.

[PhilipSportel]

I drove past Qinquagintillion on my way to Muskoka

[jotarokujo]

Didn't know Mikasa was this good at math

[The_Engineerr]

''This escalated quickly''

[carultch]

Ackermann Function with Graham's number as both of the parameters.

[leslieviljoen]

I'm glad we know how many atoms there are in the universe, I would have thought that would be impossible to know.

[theguywhodoes]

I can't wait to see 3b1b make an analytic continuation video about the Ackerman function.