How can you apply this to investing?

randomness with repeating recurrent recombination and variation on a theme

What about BB(n) × 2^n

this is too big brain for 3am me

I think the reverse is even more crazy. Any task can be simplified to be within this busy beaver bound. Meaning we have an upper limit on all possible computations (well, we are essentially doing that anyway). But if you for example increase your tape alphabet beyond binary.... It can always be done in binary.

Excellent presentation. As I understand it though, the method only works on highly overdetermined linear equation systems. You can't use it on a square matrix with full rank.

Do we know the state table of the turing machine that halts if goldbachs conjetute is false, if so where can i find it?

wonderfully explained, had to watch it twice but I'm glad I did.

Wonderful

You are a legend.

nice gpt2 paper reference with the Dr Jorge Perez text I see you. I remember showing that generated text to my friend in 2019 to show how crazy AI was getting -- how little we knew then lmao

i thought you were going to say f(n) = n ? with n DASHES

function approaching infinity? Nah function reaching infinity

12:55 dude has a green screen to make a black background? Why not just use a black background?

In practice, Ax=b eqns are solved using gradient descent, where each gradient step is O(nm). How does this compare to NLA?

A lot of people will intuitively ask "Why not?" when hearing there is no general solution for the Halting Problem. A good way to think about it is that it is always possible to make a state table and input so that the output of any hypothetical "decider" function is wrong. As in, the function says it halts while we can prove it doesn't - or vice versa.

very intresting but had to skip through so much. video should be structured like 'skip to x if you dont need linear algebra explained' e.t.c.

I’ve seen probably a dozen videos on busy beaver, and I still don’t know if bb numbers are incomputable because computing them is impossible, or just infeasible. It certainly seems that every possible n is finite, even if we’d never be able to calculate it, even if we pooled all the universe’s resources to the task. People seem to equate the idea that we will certainly never find the answer, to the question being theoretically unsolvable.

The future of linear algebra isn't random, but it's certainly evolving and influenced by various factors such as technological advancements, mathematical discoveries, and emerging applications. Linear algebra is a fundamental branch of mathematics with widespread applications across many fields, including physics, engineering, computer science, economics, and more. As technology continues to advance, we may see new algorithms, techniques, and applications of linear algebra emerging. For example, in the field of artificial intelligence and machine learning, linear algebra plays a crucial role in developing algorithms for tasks like image and speech recognition, natural language processing, and recommendation systems. As these fields progress, there may be new developments in linear algebra tailored to these specific applications. Moreover, interdisciplinary research often leads to innovations in linear algebra. For instance, the intersection of mathematics and biology might result in the development of new mathematical models that rely heavily on linear algebra to describe biological systems. So while the future of linear algebra isn't predetermined, it's shaped by the ongoing progress in various fields and the evolving needs of society.

Amazing video. Had me hooked from start to finish. You gained a new subscriber

I didnt find the link

So a matrix is a data itself that can be sampled?

I thought the factorial function was wild. I probably have to update that opinion.

Ive found a bigger number. Its just BB(googol) +1

thanks man, this is very good and clear

I love how Volker Strassen did things so different from each other.

You should consider a quantum computer which uses yes , no , and maybe. I think it would change your entire video.

and what happens when u use irrational or imaginary numbers?

Hallelujah! Finally got a simple explanation of what Importance Sampling is! Thanks a ton!

Sensodyne Repair <3

I think you made the best numerical linear algebra in the world, we really need more content like this. Keep up the good work.

you've GOT to post more, this stuff is amazing, im still in high school but learning about so-called 'mature' processes which become completely revolutionised really inspires me, thanks for this :)

Why finding busy beaver of n when you can search for primes in the range 2^90million to 2^150 million

This was SSSOOOOOO much easier to understand than the wikipedia page! Thank you!

Perfect intro. Please share more of the available methods over finding q(x)!

I rewatched the video because i don't remember any details. then i afterwards realized that there isn't one to begin with... I'll watch the lectures next.

🎉

You should know, i have always been quite bad at math, and this video was surprisingly not impossible to follow! Very well done

Really superb presentation!

Thanks!

Hey thanks so much for the video. I have a question. I am not sure if it is appropriate to ask here. But Thanks in advance for reading this :) Q: I have multiple observations of the heart pressure traces. Can it be fitted to a single Gaussian Process to capture the uncertainty among multiple observations. I mean I need it to be fitted to a single GP. Are there any libraries in python or R that could handle that. Thank you :)

"And if you aren't, you're probably doing something wrong." So very very true. Don't roll your own NLA code. You won't get it right and it certainly won't be faster. The corollary is "If you're inverting a matrix, you're probably doing something wrong." But that's a different problem I have to solve with newbies.

Fantastic video, well done! I'm watching for path tracing rather than ML :)