I've been making diagrams like this for some time, but I've never found a good way to differentiate the large primes, I don't like how they all end up looking the same
That's very interesting how you and Jacob came up with the same idea! Yeah in my program you'll notice any prime above 40 looks the same. Maybe when a prime gets higher than 7, you could split it into multiple shapes that add to that prime?
@@motherisape I coded it with Javascript using a library called P5JS. If you're interested, Daniel Schiffman (Coding train) has lots of excellent TH-cam tutorials on coding with P5JS. If you're interested specifically in how my program works, here's how you can look at the source code: 1. Open the website and press F12. This opens the developer window. 2. Click on the >> button at the top and select "Sources". 3. Click on the file that says "sketch.js" . That's where all my code is. 4. Click and drag the developer window to make it bigger so you can see the code more easily. Hope this helps
@@Ikebot Thank you for taking the time demonstrating how we can make the world a better place and I'm not talking about the coding specifically rather more generally taking the time and effort to help another in providing the response that you did. 💞
In terms of efficiency, I agree. I think the value of this system is it's a neat reminder that we can think about and depict numbers in ways other than abstract base-ten symbols. It certainly wouldn't be practical for every day use though
It would be great if you could assign LFO's with rate, upper and lower range, tempo sync, and different waveforms, for each px value, and if they can remain through number changes.
Hmm I'm not sure if I understand your idea but it sounds intriguing. Are you suggesting using low frequency oscillators to make, like a color gradient?
problem is it's non abelian. each non prime will have (n! - a correction term for possible overlap) different representations which may look entirely different (where n is the amount of numbers in it's prime factorization). cool looking though
Are you referring to how the primes could be reordered so the shapes have a different hierarchy? If so, you'll be happy to know that my new version (which is linked in the pinned comment) allows you to reorder the terms by dragging the factors around. It also has other features like mobile support and different render modes
Ok. Nice. But multiplication is comutative so this 3 lines on each vertex of a triangle must be somehow isomorphic to two triangles connected by a line, etc.
This is a good question and I wish I had time to talk about it in my one minute video! These diagrams are good for illustrating prime decomposition. I think they are also a useful way to visualize multiplication with more than two products, especially how it's commutative (for example, for 15, you could draw a triangle with a pentagon at each point or a pentagon with a triangle at each point).
I hadn't thought to do that, that's a great idea. I don't know much about 4d but I have seen a brilliant tesseract simulator by someone who uses the same JavaScript library that I do: openprocessing.org/sketch/205544/
It's actually pretty interesting. He should be about 24 now. According to the Genius of Autism Wiki: "He is currently a doctoral student at the Perimeter Institute for Advanced Theoretical Physics (specializing in Quantum Foundations and Quantum Gravity)"
@@Ikebot Thanks for putting up new link - I was curious to see this. I do see what David Oman says below about large primes all looking the same. Not sure how to address that in an interesting way - the numbers are prime, after all. ;)
This is according to the Genius of Autism wiki which might be outdated but I'm not sure: "He is currently a doctoral student at the Perimeter Institute for Advanced Theoretical Physics (specializing in Quantum Foundations and Quantum Gravity)."
Well, this is actually the definition of a side. It is not complicated or innovative at all. Triangle, three-line, three points, pentagon 5 lines 5 points, hexagon, etc., consider each point as a number and connect it with a line. 😐
hey can I please get your email , I should check your TH-cam email this is brilliant ❤❤ I saw his Ted tall few hours ago only just checked your description 😬
Ah, the Ted Talk. So that's where all these views are coming from... Yes feel free to send me an email, I love emails: ikebot33@protonmail.com Thank you for the compliment
UPDATE: I've made a new and improved version that now works on mobile!
th-cam.com/video/XH9-f3pKiBE/w-d-xo.html
If you enjoyed this, please consider liking the video to help make me eligible for the Veritasium contest! Thank you.
Nice work
Basically prime number polygons and then you combine them to form composite numbers
Yes! Prime decomposition.
Incredible.
you are amazing!! wonderful idea!! thank you so much!!
amazing! thank you for the program!
I've been making diagrams like this for some time, but I've never found a good way to differentiate the large primes, I don't like how they all end up looking the same
That's very interesting how you and Jacob came up with the same idea! Yeah in my program you'll notice any prime above 40 looks the same. Maybe when a prime gets higher than 7, you could split it into multiple shapes that add to that prime?
@@Ikebot how you made that program
@@motherisape I coded it with Javascript using a library called P5JS. If you're interested, Daniel Schiffman (Coding train) has lots of excellent TH-cam tutorials on coding with P5JS. If you're interested specifically in how my program works, here's how you can look at the source code:
1. Open the website and press F12. This opens the developer window.
2. Click on the >> button at the top and select "Sources".
3. Click on the file that says "sketch.js" . That's where all my code is.
4. Click and drag the developer window to make it bigger so you can see the code more easily.
Hope this helps
@@Ikebot thanks 😊
@@Ikebot Thank you for taking the time demonstrating how we can make the world a better place and I'm not talking about the coding specifically rather more generally taking the time and effort to help another in providing the response that you did. 💞
This is ingenious.
Amazing video!
GO JACOB!!!!!
this is so epic dude
Awesome
Amazing
Imo the most efficient way to think about numbers is their decimal representation in normal or scientific notation
In terms of efficiency, I agree. I think the value of this system is it's a neat reminder that we can think about and depict numbers in ways other than abstract base-ten symbols. It certainly wouldn't be practical for every day use though
Mind blown
It would be great if you could assign LFO's with rate, upper and lower range, tempo sync, and different waveforms, for each px value, and if they can remain through number changes.
Hmm I'm not sure if I understand your idea but it sounds intriguing. Are you suggesting using low frequency oscillators to make, like a color gradient?
Ohh do you mean LFOs that change each shape's size? That would be cool to sync it up with music
@@Ikebot You could, but I mean the values you call "px".
@@Ikebot Yes, I think it would reveal new structures/patterns/relationships to play around with different rates for each size and so forth.
this is called geometry
Does it have any advantages over the regular decimal number system?
problem is it's non abelian. each non prime will have (n! - a correction term for possible overlap) different representations which may look entirely different (where n is the amount of numbers in it's prime factorization). cool looking though
Are you referring to how the primes could be reordered so the shapes have a different hierarchy? If so, you'll be happy to know that my new version (which is linked in the pinned comment) allows you to reorder the terms by dragging the factors around. It also has other features like mobile support and different render modes
Ok. Nice. But multiplication is comutative so this 3 lines on each vertex of a triangle must be somehow isomorphic to two triangles connected by a line, etc.
Yes! That's why in the new version of my program, you can reorder the terms to change thr hierarchy of shapes (see the pinned comment)
I want my minute back.
:(
What are some use cases? They sort of look nice, like viruses.
This is a good question and I wish I had time to talk about it in my one minute video! These diagrams are good for illustrating prime decomposition. I think they are also a useful way to visualize multiplication with more than two products, especially how it's commutative (for example, for 15, you could draw a triangle with a pentagon at each point or a pentagon with a triangle at each point).
so it's a way to visualise prime factorization I guess?
Yes
Thinking of numbers in 2 dimensions, fascinating. Now do this in 3 dimensions. How about 4D ?
I hadn't thought to do that, that's a great idea. I don't know much about 4d but I have seen a brilliant tesseract simulator by someone who uses the same JavaScript library that I do: openprocessing.org/sketch/205544/
what is he doing now
It's actually pretty interesting. He should be about 24 now. According to the Genius of Autism Wiki:
"He is currently a doctoral student at the Perimeter Institute for Advanced Theoretical Physics (specializing in Quantum Foundations and Quantum Gravity)"
reminds me of touch points
Interesting, I've not heard of touch points before. I can see the similarity
Hey I can't get to your website there is a problem
Hmm, is it this link that doesn't work for you? bit.do/jacobdiagram
Or is it this link to my website? ikebot108.weebly.com/
Interesting how prime numbers are all polygons.
Website doesn't seem to load?
Sorry about that, the bit.do website is down right now, so I've updated the description to have a working link
@@Ikebot Thanks for putting up new link - I was curious to see this. I do see what David Oman says below about large primes all looking the same. Not sure how to address that in an interesting way - the numbers are prime, after all. ;)
Right, but where is he now? I can't find his name on anything.
This is according to the Genius of Autism wiki which might be outdated but I'm not sure:
"He is currently a doctoral student at the Perimeter Institute for Advanced Theoretical Physics (specializing in Quantum Foundations and Quantum Gravity)."
Well, this is actually the definition of a side. It is not complicated or innovative at all. Triangle, three-line, three points, pentagon 5 lines 5 points, hexagon, etc., consider each point as a number and connect it with a line. 😐
hey can I please get your email , I should check your TH-cam email
this is brilliant ❤❤
I saw his Ted tall few hours ago only
just checked your description 😬
Ah, the Ted Talk. So that's where all these views are coming from...
Yes feel free to send me an email, I love emails: ikebot33@protonmail.com
Thank you for the compliment