HN Theater @HNTheaterMonth

I also love the idea that computation (ie rule/recipe-following) is fundamental to nature/reality, but I don't think it's pure-maths that is the bedrock.

Pure maths (as a tendency, not strictly) focuses on formal systems that are on the consistent end of the spectrum (as those are the ones that can be used to build more maths on top of). Nature probably doesn't (or needn't) have this restriction/tendency! Formally consistent might be higher performing in many cases (more stable over long time-spans, like dna), but it is not the end of the story as to what is ultimately possible in rule-following systems! Any sense of determinism demands this, even if the system makes its own rules as the universe/reality - the ultimate all, with nothing outside of it - must. Whether this fully gives way to a properly random (like an oracle of rand) system at the quantum level is still an open question.

It is possible to expand ones view of nature/ultimate-reality to include other rule-systems (such as including inconsistent or entirely 'complete' systems.) This can have more coverage (completeness) of any particular model, or even be totally incomplete and inconsistent! These 'degenerate' (according to maths) formal systems might sometimes be the ones that happen to work in nature/reality. Once you do this extension, now you're talking about computation, admitting a broader class of rule-following than pure maths. You can argue that the two are equivalent because sure, anything can be translated between them - i'm more talking about tendencies here. The computational universe includes lots of formal systems that are abhorrent or impractical to mathematical understanding, so mathematicians avoid them, but nonetheless they are still rule-following! Nature/evolution probably uses/finds those rules where they are the best performing solution (through its exploration of possibilities).

As to 'optimal end-states', I'm afraid you've lost me there. I gave up teleology (the idea that the universe or nature or evolution have any obvious goals) a long time ago, how could anything like that (high level) feed-in to reality? There is no hint of this in all of science. What self-organises and self-replicates is what persists. This self-support might even reach down into physics!

To me, religion is nearly the opposite to all of this: An explanatory system that says explanation-of-reality='fixed string' with no update method available. Very incomplete (unless ridiculously long, which current examples of religion are not) and inconsistent: The fixed string might assign True and False at once, or neither - to new knowledge that falls outside the original scope of its meaning.

So no, I don't think that this pi-result suggests that religion and science have a commonality here. Pi is awesome (even though very constructible) and we should probably expect to find it [0], especially in places like this (pure QM) that involve geometry.

[0] https://youtu.be/HEfHFsfGXjs

Reminds me how you can compute pi in a hilariously inefficient yet very interesting way with a physics engine by counting collision of 3 blocks bouncing with one another: https://youtu.be/HEfHFsfGXjs

Reminds me of this:

https://youtu.be/HEfHFsfGXjs

This is a time someone must cite 3Blue1Brown: [(183) The most unexpected answer to a counting puzzle - YouTube](https://www.youtube.com/watch?v=HEfHFsfGXjs)

This is the second video in a series, first video: https://www.youtube.com/watch?v=HEfHFsfGXjs

⬐ edh649

The explanation video: https://www.youtube.com/watch?v=jsYwFizhncE

⬐ earthicus

An interesting response to the explanation video from u/functor7 on reddit:

https://www.reddit.com/r/math/comments/ahz8k3/so_why_do_coll...

⬐ PuffinBlue

This is kind of a plea for help - how can I learn maths 'via' geometry?

I just can't get my head around 'numbers'. I can't seem to really visualise them or understand what they are. I know this sounds weird. With language or abstract things like 'problems' I can almost see them in my head. I can analyse a problem and all it's flows of cause and effect in a visual way. That's literally what happens in my head.

But with numbers I can't understand them at a basic level. Like - what are they? How do I visualise them?

When it comes to geometry it's almost like it's the 'language' of my brain, how I think, in terms of shape and form and translation and dimension.

I'll give you an example. I learnt Pythagoras theorem aged about 13 or something. But didn't truly understand it until I was about 20 something when I saw a diagram showing graphically the squares of the sides like this[0].

I really need to start at the absolute beginning, like build of a whole foundation of what maths is based on geometry. Does that even exist?

This might not be possible, but if I can even get started it would be great.

[0] https://mysteriesexplored.files.wordpress.com/2011/08/pythag...

⬐ PinkMilkshake

I think I know what you are getting at. You may have something like dyscalculia[1], but I'm not a doctor.

There are several mental models used for picturing numbers. I think the most popular is the number line [2]. Common Core uses this in a clever way. I've never found it useful personally.

I suspect some people might see numbers as purely symbolic and perform purely symbolic operations. When the symbol 2 and the symbol 3 have the operation 'add' applied, it yields the symbol 5. Or something.

I think I mostly visualize the numbers as a quantity of solid objects. So I think of 3 as 3 things. This has limitations. I can break objects apart but how do you visualize 3.767? So some of it is intuitive.

There is evidence that the human mind can only encode exact quantities up to four [3], after that they use an estimate. [4] So maybe your situation is the norm. What I mean is, sometimes it can feel like everyone else has 'got it' and you're the one lacking, when in reality everyone is just as bad.

[1] https://en.wikipedia.org/wiki/Dyscalculia [2] https://en.wikipedia.org/wiki/Number_line [3] https://en.wikipedia.org/wiki/Parallel_individuation_system [4] https://en.wikipedia.org/wiki/Approximate_number_system

⬐ abecedarius

Just one suggestion, but https://www.euclidea.xyz/ is a great place to start. Visual Group Theory sounds appropriate too: https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/0...

⬐ brianpgordon

I think this is a better image for the Pythagorean theorem:

https://i.imgur.com/UxZ3fQR.png

⬐ empath75

Have you watched the khan academy videos? He leans on geometry and visual intuition quite a lot.

⬐ earthicus

If you managed to survive high school algebra, you might be able to 'redo' your basic math education with a geometric bent from Stillwell's book 'Numbers and Geometry', which teaches the classical link between the two subjects that has been eliminated from elementary education to some extent. However, the kind of intuition he presents is still semi-abstract - it's not a super duper picture heavy book - but I think it's about as close to what you're asking for as you are likely to find.

https://www.amazon.com/Numbers-Geometry-Undergraduate-Texts-...

⬐ jhrmnn

Geometric proofs of problems that do not seem to be geometric are the most satisfying in my experience.

⬐ ColinWright

I wrote about this nearly four years ago:

https://aperiodical.com/2015/03/%cf%80-phase-space-and-bounc...

It doesn't have nifty visualisations, but the (mythical) interested reader might find this a useful complement to the video and explanation provided there.

Edit: Thought so - I did submit my write-up at the time:

https://news.ycombinator.com/item?id=9202913

⬐ jsweojtj

Your links to the original paper are broken in that writeup.

⬐ ColinWright

Bother.

Thanks for the catch, I'll get onto the hosts and get them to fix them.

Cheers.

⬐ ColinWright

And for completeness - now fixed. Thanks again.

⬐ qualsiasi

I wrote a small Java program to verify the collision count, just because I was bored and laying on the sofa:

> https://github.com/Qualsiasi85/collision-pi

warning: code is a mess - and may have all sorts of nasty bugs, but after all this has been done for fun and doesn't need to be "enterprisey" :)

I do like this kind of videos, they tickle my fantasy and keep alive my passion in programming (that is slowly dying because of work! :) )

⬐ Outermeasure_A

There was an ACM problem a few years ago where it was asked to count the collisions. We implemented the simulation and noticed the digits of PI but we didn't actually proven the fact. Got AC.

⬐ Aardwolf

Nice, but I miss the more fundamental series of 3Blue1Brown like "the essence of linear algebra" series, the "essence of calculus" series, and the unfinished "deep learning" series from more than a year ago

Shame that this awesome visualization method he uses isn't used more for more fundamental concepts to learn from the ground up rather than specific puzzles like lately, I learned a lot from the "essence" series!

⬐ empath75

The solution he posted is about using phase spaces, not really about this problem in particular.

⬐ ragebol

> Shame that this awesome visualization method he uses isn't used more ...

The animation engine is on GitHub so you can make your own: https://github.com/3b1b/manim

⬐ kowdermeister

I think the are in the works, but it's just a guess. There's a subreddit for fans, you might post your wish list :)

https://www.reddit.com/r/3Blue1Brown/

⬐ Aardwolf

By the way, I don't want to sound unhappy about the videos, the answer for sure is interesting indeed, I totally don't want to say it's bad content at all, it's awesome in every way, graphics, audio, explanation, ... :D

⬐ thanatropism

The essence of linear algebra is vector spaces and linear transformations. It's not entirely impossible (although probably way more difficult) to learn it without reference to Euclidean spaces and geometric reasoning.

Should be called "The intuition for linear algebra". But heck, the whole reason we have and teach the mathematical method is that intuition either breaks down in interesting cases (e.g. stochastic integrais versus "an area under a curve" integrals) or limits you (linear algebra in function spaces, etc).

It's a nitpick. I love 3b1b.

⬐ cordonbleu

we should probably make an attempt to distance the term gravity from our model of the universe. when a mass is in motion an inertial wave is created, this is an inertial reference frame, the frame dragging that occurs is a set of harmonics, that are nodes in the hyperbolic field structure of spacetime. these nodes correspond to dividends of Pi, thus any inertial phenomenon "spirals down hyperbolicly" into subspace to become heat [quantum field pertuberance]

⬐ 3blues1brown

3blue1brown’s voice is like nails on a chalkboard. Hearing it for more than half a minute is tedious, hearing it more than once is regrettable.

⬐ kylnew

I understand maybe 30% of 3blue1brown’s videos, mostly due to his excellent visualizations, but he really gets me excited for math in a way I’ve not experienced before. How does he make such awesome visualizations? Does anyone know what tools are being used?

⬐ danra

A few tools, detailed in his FAQ page. https://www.3blue1brown.com/faq/

⬐ nradk

He has written a python library called "manim" for his visualizations https://github.com/3b1b/manim

⬐ chrisdsaldivar

He built a python library for his visualizations called manim available on his github [1].

[1] https://github.com/3b1b/manim