5 ms·

A most unexpected answer to a counting puzzle [video]

155 points by espeed 8y ago

cordonbleu 8y ago
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]
edh649 8y ago
The explanation video: https://www.youtube.com/watch?v=jsYwFizhncE https://www.youtube.com/watch?v=jsYwFizhncE
jhrmnn 8y ago
Geometric proofs of problems that do not seem to be geometric are the most satisfying in my experience.
Aardwolf 8y ago
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!
- kowdermeister 8y ago
  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/ https://www.reddit.com/r/3Blue1Brown/
- thanatropism 8y ago
  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.
- ragebol 8y ago
  > 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 https://github.com/3b1b/manim
- empath75 8y ago
  The solution he posted is about using phase spaces, not really about this problem in particular.
- Aardwolf 8y ago
  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
earthicus 8y ago
An interesting response to the explanation video from u/functor7 on reddit: https://www.reddit.com/r/math/comments/ahz8k3/so_why_do_colliding_blocks_compute_pi/eekeglk/ https://www.reddit.com/r/math/comments/ahz8k3/so_why_do_coll...
kylnew 8y ago
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 8y ago
  A few tools, detailed in his FAQ page. https://www.3blue1brown.com/faq/ https://www.3blue1brown.com/faq/
- chrisdsaldivar 8y ago
  He built a python library for his visualizations called manim available on his github [1]. [1] https://github.com/3b1b/manim https://github.com/3b1b/manim
- nradk 8y ago
  He has written a python library called "manim" for his visualizations https://github.com/3b1b/manim https://github.com/3b1b/manim
qualsiasi 8y ago
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 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! :) )
ColinWright 8y ago
I wrote about this nearly four years ago: https://aperiodical.com/2015/03/%cf%80-phase-space-and-bouncing-billiard-balls/ 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 https://news.ycombinator.com/item?id=9202913
- jsweojtj 8y ago
  Your links to the original paper are broken in that writeup.
  - ColinWright 8y ago
    Bother. Thanks for the catch, I'll get onto the hosts and get them to fix them. Cheers.
    - ColinWright 8y ago
      And for completeness - now fixed. Thanks again.
PuffinBlue 8y ago
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/pythagoreantheorem.png https://mysteriesexplored.files.wordpress.com/2011/08/pythag...
- earthicus 8y ago
  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-Mathematics/dp/0387982892 https://www.amazon.com/Numbers-Geometry-Undergraduate-Texts-...
- abecedarius 8y ago
  Just one suggestion, but https://www.euclidea.xyz/ 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/088385757X https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/0...
- empath75 8y ago
3blues1brown 8y ago
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.
Outermeasure_A 8y ago
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.

155 points by espeed 8y ago

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]

edh649 8y ago

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

jhrmnn 8y ago

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

Aardwolf 8y ago

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!

kowdermeister 8y ago
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/ https://www.reddit.com/r/3Blue1Brown/
thanatropism 8y ago
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.
ragebol 8y ago
> 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 https://github.com/3b1b/manim
empath75 8y ago
The solution he posted is about using phase spaces, not really about this problem in particular.
Aardwolf 8y ago
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

earthicus 8y ago

An interesting response to the explanation video from u/functor7 on reddit: https://www.reddit.com/r/math/comments/ahz8k3/so_why_do_colliding_blocks_compute_pi/eekeglk/ https://www.reddit.com/r/math/comments/ahz8k3/so_why_do_coll...

kylnew 8y ago

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 8y ago
A few tools, detailed in his FAQ page. https://www.3blue1brown.com/faq/ https://www.3blue1brown.com/faq/
chrisdsaldivar 8y ago
He built a python library for his visualizations called manim available on his github [1]. [1] https://github.com/3b1b/manim https://github.com/3b1b/manim
nradk 8y ago
He has written a python library called "manim" for his visualizations https://github.com/3b1b/manim https://github.com/3b1b/manim

qualsiasi 8y ago

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 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! :) )

ColinWright 8y ago

I wrote about this nearly four years ago: https://aperiodical.com/2015/03/%cf%80-phase-space-and-bouncing-billiard-balls/ 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 https://news.ycombinator.com/item?id=9202913

jsweojtj 8y ago
Your links to the original paper are broken in that writeup.
- ColinWright 8y ago
  Bother. Thanks for the catch, I'll get onto the hosts and get them to fix them. Cheers.
  - ColinWright 8y ago
    And for completeness - now fixed. Thanks again.

PuffinBlue 8y ago

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/pythagoreantheorem.png https://mysteriesexplored.files.wordpress.com/2011/08/pythag...

earthicus 8y ago
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-Mathematics/dp/0387982892 https://www.amazon.com/Numbers-Geometry-Undergraduate-Texts-...
abecedarius 8y ago
Just one suggestion, but https://www.euclidea.xyz/ 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/088385757X https://www.amazon.com/Visual-Group-Theory-Problem-Book/dp/0...
empath75 8y ago

3blues1brown 8y ago

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.

Outermeasure_A 8y ago

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.