8 ms·
TREE vs. Graham’s Number [video]
- nils-m-holm 7y agoI love numberphile, but I cannot watch a single episode, because all the zooming and panning while someone writes on a sheet of paper makes me motion sick in no time. WHY? How does this improve the quality of the video?
- baalimago 7y agoIt's action-math. Not meant for teaching, but for showcasing math to the general public. The general public wants action cams and cute animations.
- spacehome 7y agoNumberphile isn't that great if you're already interested in math. They talk a lot about math words, but they hardly ever do any math. 3Blue1Brown is where the good math is.
- gonzus 7y agoA shout out to Mathologer too.
- robinhouston 7y agoIt isn’t a great way to learn the details, but it’s a great way to learn about topics you might not have come across. This video is about the hierarchy of fast-growing functions indexed by ordinals, and it includes enough details for a competent mathematician to be able to work out the rigorous general definition. For someone unfamiliar with the topic, it’s an enjoyable and low-effort way to learn enough about it to recognise whether it’s interesting enough to learn about properly. There are several examples of cutting-edge mathematical work having been directly inspired by numberphile videos, most recently the work of Andrew Booker and Drew Sutherland on expressing integers as sums of three cubes. 3blue1brown concentrates on giving clear, elegant, rigorous explanations of established subjects. So perhaps ironically, despite being typically more rigorous, I don’t know any examples of it inspiring new mathematical research.
- 333c 7y ago> There are several examples of cutting-edge mathematical work having been directly inspired by numberphile videos, most recently the work of Andrew Booker and Drew Sutherland on expressing integers as sums of three cubes. I don't know if this is why you made this comment or not, but Brady Haran (creator of Numberphile) gave a talk on this exact topic a week ago today at the MSRI in Berkeley.
- robinhouston 7y agoOh, interesting! I knew Brady Haran had given a talk at MSRI, but I didn’t know what the talk was about. Was it filmed?
- 333c 7y agoI don't know if it was filmed. I was there but I didn't record it.
- nerevarthelame 7y agoDon't insult them because they discuss topics at a more basic level than you prefer. There's always going to be higher levels (e.g., youtuber A < youtuber B < reading a text book < taking a university course < getting a degree < conducting novel research < conducting novel research published in journal A < journal B < journal C), which may be better suited for different audiences. Landing in one versus the other doesn't make you (or the instructors) better or worse. It's silly to say that the one you happen to prefer is where "good math" is.
- x3n0ph3n3 7y agoI really need a video on transfinite cardinals and ordinals beyond Aleph_0 and Epsilon_0. The VSauce video [1] on the topic only made me more curious with an elusive tree diagram displaying a few, and PBS Infinite Series [2] [3] just barely touched it. The mention of the Veblen hierarchies really piqued my interest, but much of what I've found on them has been a bit too dense for me. 1. https://www.youtube.com/watch?v=SrU9YDoXE88 https://www.youtube.com/watch?v=SrU9YDoXE88 2. https://www.youtube.com/watch?v=uWwUpEY4c8o https://www.youtube.com/watch?v=uWwUpEY4c8o 3. https://www.youtube.com/watch?v=oBOZ2WroiVY https://www.youtube.com/watch?v=oBOZ2WroiVY
- gosub 7y agohttps://www.youtube.com/watch?v=QXliQvd1vW0&list=PL3A50BB9C34AB36B3 https://www.youtube.com/watch?v=QXliQvd1vW0&list=PL3A50BB9C3... enjoy!
- pas 7y agoWait wait. Transfinite induction uses ordinals ( https://en.wikipedia.org/wiki/Large_countable_ordinal https://en.wikipedia.org/wiki/Large_countable_ordinal ) To get large cardinals (beyond ZFC) you need large cardinal axioms. ( https://en.wikipedia.org/wiki/List_of_large_cardinal_properties https://en.wikipedia.org/wiki/List_of_large_cardinal_propert... )
- Eliezer 7y agoTREE(Graham's Number) is just comically inefficient Googology. It makes me wince just to look at. Graham's Number isn't even on the same plane of existence as TREE. You'd just use TREE(TREE(3)) if you wanted to move up in the world. Somebody needs to tell them about the fast-growing hierarchy and how Graham's Number lives around \omega+1 while TREE hangs out with the small Veblen ordinal.
- wodenokoto 7y agoI have absolutely no idea what you are trying to say. The video is mostly about asking which series, TREE or Graham, grows quicker and how we can show it. It does this by starting out asking, which is bigger, TREE(G(64)) or G(TREE(64)). I fail to see how that is comically inefficient or how introducing TREE(TREE(3)) is what they should have done instead. >Somebody needs to tell them about the fast-growing hierarchy and how Graham's Number lives around \omega+1 while TREE hangs out with the small Veblen ordinal. Somebody should watch the video before speaking out about what the video should contain.
- chii 7y agothough the video actually didn't say why TREE grows faster than the epsilon function.
- wodenokoto 7y agoThat’s actually a fair point, they don’t explain why TREE grows faster than anything in the f-series. The argument for where in the f-series Graham’s series lies is also a bit hand-wavy.
- chii 7y ago> where in the f-series Graham’s series lies that is actually explained - fω+1(n) is grahams, because of the way grahams defines as iterated versions of up-arrows.
- pas 7y ago
- IanCal 7y agoThere's lots of things about Graham's number, but because I love the style I thought I'd add in here Wait But Whys "from 1 to Graham's number": https://waitbutwhy.com/2014/11/from-1-to-1000000.html https://waitbutwhy.com/2014/11/from-1-to-1000000.html https://waitbutwhy.com/2014/11/1000000-grahams-number.html https://waitbutwhy.com/2014/11/1000000-grahams-number.html
- umvi 7y agoLet t(n, i) be a function where n is the number of recursive TREE calls and i is an integer. So t(1,3) = TREE(3) t(2,3) = TREE(TREE(3)) etc. Now you can do: t(TREE(3), 3) or t(t(t(t(t(t(t(t(t(TREE(3),3),3),3),3...)
- contravariant 7y agoThe way TREE grows it's very much possible that all these are inferior to simply f(n) = TREE(n+1).
- x3n0ph3n3 7y agoUnlikely since we are piping the output of TREE back into TREE, which is much larger than n+1.
- hidroto 7y agohttps://oeis.org/A028444 https://oeis.org/A028444 would grow faster right? does it make sense to compare the growth rates of non-computable functions?