Very underrated video. I can‘t believe this only has 60 views. Great work, keep it up!

@mostly_mental

2 жыл бұрын

I'm glad you liked it. Thanks for watching!

Among all the videos on yt, this is the only one that helped me understand surreal numbers. Thank you!

@mostly_mental

Жыл бұрын

I'm glad you liked it. Thanks for watching!

@elijahberegovsky8957

Жыл бұрын

Same thing! Like, I knew what they are, but I had no idea of their connection to Hackenbush!

Incredible video! I got really interested in surreal numbers a few years ago and kind of forgot all about them. This is a really great introduction and gets the point across pretty well. RIP John Conway, he really liked to have fun with mathematics and studied some oddball stuff and was a very kind person in general.

@mostly_mental

Жыл бұрын

Conway is pretty much my mathematical role model. He had a major impact on basically every field of math I'm into. I was lucky enough to meet him once, and it was plain to see just how much he loved to play around with cool ideas and to share that joy with everyone around him.

I can't pretend to understand surreal numbers (yet), but this video has at least shown me where the idea of two sets came from, and why the left set must be

I highlighted the need to see this video on the Wikiversity article "Surreal number" and will attempt to include a link to this video on the Wikipedia article with the same name. Nothing on any of these wikis come close to explaining surreal numbers this well.

@mostly_mental

2 ай бұрын

I'm glad you liked it, and I appreciate the enthusiasm, but I'd rather not be directly linked in those articles. Maybe just add a section summarizing the connection to Hackenbush?

@guyvan1000

2 ай бұрын

@@mostly_mental I will be happy to oblige. Just to be clear, you want me to remove the links from Wikipedia or Wikiversity out to this KZread video? I will wait until you verify that this is you wish (because I have no idea why you don't want the link). I control the Wikiversity page, so deleting that link there will be no problem. I will also delete the link I made at Wikipedia, but I can't guarantee that a Wikipedia editor won't reinsert it. I think I will just quietly revert my Wikipedia edit without comment. If I say anything it will draw attention to what they may decide is a good link from Wikipedia to this KZread video.

@mostly_mental

2 ай бұрын

@@guyvan1000 Thank you. I'm not a primary source on the topic, so I'm a bit uncomfortable being listed as a reference. Besides, everything I know comes from the books I mentioned at the end, which are both already listed on the Wikipedia page.

@guyvan1000

2 ай бұрын

@@mostly_mental There is a difference between an external link and a primary source on Wikipedia, but I am not well enough versed in Wikipedia rules to know if a link out of the Wikipedia page is proper. Wikiversity has entirely different standards (one might say no standards...) I would like to include a link from Wikiversity to your video, but won't do it without your permission.

@mostly_mental

2 ай бұрын

@@guyvan1000 I think I'm okay with a link on Wikiversity, so long as the math is the primary focus and not the video.

Excellent visual representative of Surreal Number system!

@mostly_mental

Жыл бұрын

I'm glad you liked it. Thanks for watching!

Hm... what about an edge that can only be cut by the color it's most connected to? AKA blue if, say, two blues and one red are touching it and both/neither can when the same number are touching

@mostly_mental

Жыл бұрын

That's an interesting idea. I filled a page in my notebook with test positions, and it looks like we get the same values as in red-blue-green hackenbush (so a mix of the surreals and nimbers). That makes sense to me, since these new edges act like something between red/blue and green edges, but I don't have a rigorous proof. Great question!

Just turned in. Find it strange to be ending on hackenbush so I’m curious where you started

@mostly_mental

Ай бұрын

I started with impartial games and the nimbers (which I find more interesting than the surreals). If you're curious, you can check out the rest of the series here: kzread.info/head/PLH5zdqQODdBiGrWszPScMO2Dvp0Ix_vpV

@6:30 "it's tedious to find -25/32" No. It is easy... formula = A hackenbush number is determined from the order of colored segments extending from its base. The first and similarly colored subsequent segments have a value of one. Subsequent digits have half the value of their predicesor. The sign of a value is positive for blue segments, while reds are negative. The sum of these signed values is the value of a hackenbush drawing. How to find -25/32 from drawing: order of video example from base = red, blue, red, red, blue, blue signed values = -1 +1/2 -1/4 -1/8 +1/16 +1/32 sum = -25/32 result = calculation is not tedious Also: Video is good. Credit to author

@mostly_mental

Жыл бұрын

Yeah, that's the general pattern I was hinting at from the exercise at 6:20. What I meant was "it's tedious to find with the balancing act we've been using so far."

13:55 could it be that the rational functions aren't contained in the surreal numbers (up to isomorphism) because they don't form an ordered field. Or am i missing something?

@mostly_mental

Жыл бұрын

The rational functions don't have a natural order, but we can impose an order on them. Pick any transcendental number, alpha, and say f < g if f(alpha) < g(alpha). That will give us an ordering. So there's a subfield of the surreals isomorphic to the rational functions (in fact, uncountably many of them).

@Djake3tooth

Жыл бұрын

@@mostly_mental and what is the cardinality of the surreals?

@mostly_mental

Жыл бұрын

@@Djake3tooth The surreals are actually too large to fit into a set (they're a proper class), so cardinality isn't defined.

🤯

I like this more than the p-adic numbers

@mostly_mental

11 ай бұрын

Yeah, the surreals are great. But my favorite number system is still the nimbers.

@codatheseus5060

11 ай бұрын

@@mostly_mental I enjoy the dual complex quaternions the most