Mathologer - 2022-02-19
Today, a long overdue foray into the realm of VORTEX MATHEMATICS :) 00:00 Intro 04:16 The vortex 08:10 The maths of remainders and digital roots 13:25 Demystifying the vortex 16:30 A matter of base. The 8 fingered Tesla. 19:21 Explanation why the digital root is the remainder on division by 9 24:01 Tristan's challenge 24:44 The magic of modular multiplication maths 25:19 Intuition for multiplier - 1 petals 28:23 Thank You! Coding competition: My wish list for the modular times table diagram app: -Being able to color line segments according to length. -Indication of the "direction" of multiplication. 1x2 = 2 and so there should really be a little arrow from 1 to 2 not just a simple connection :) -different loops in different colors. ... Here is the prize, a copy of my and Marty's new book. https://bookstore.ams.org/mbk-141/ That early Mathologer video featuring the modular times tables Times Tables, Mandelbrot and the Heart of Mathematics https://youtu.be/qhbuKbxJsk8 A really nice article about various ways to generate the cardioid by Dave Richeson https://divisbyzero.com/2018/04/02/i-heart-cardioids/ Nice debunking/demystifying article about vortex math by "Professor Puzzler" https://www.theproblemsite.com/vortex/ For a growing pile of implementation of modular times table diagrams see my comment pinned to the top of the comment section of this video. Simon Plouffe's website http://plouffe.fr/Simon%20Plouffe.htm Articles by him relevant to this video can be found in this directory http://plouffe.fr/Inverseofprimes/ See in particular the files The shape of b^n mod p.pdf La forme de bn mod p.pdf What I am talking about in this video is really just the tip of a bizarre mathematical iceberg that most mathematically minded people are completely unaware of. Have a look at this presentation by Marko Rodin on vortex math (beware serious nutty and at the same time truely beautifully presented numerology ahead :) A LOT more than is usually reported on in popular YouTube videos. https://sciencetosagemagazine.com/vbm-vortex-based-mathematics-with-marko-rodin/ In turn this iceberg is just another tip of an even bigger iceberg of mainly wishful thinking. Have a look: https://sciencetosagemagazine.com/category/library/ Today's music: Aftershocks by Ardie Son Enjoy! Burkard
In school whenever I noticed patterns such as these divisibility tests, my teachers discouraged me from pursuing them because they themselves were not sure if they'd always hold and were concerned they'd lead me astray. Another example that I recall is my noticing that each power of two is equal to one more than the sum of the lesser powers of two. That's well-established and taken for granted in computer science, yet was unknown to my teachers and regarded with skepticism. I remember also my mom pleading with my teachers to stop counting my work wrong for my daring to use techniques I developed myself from having explored the mathematical foundations of the rote mechanisms they taught. I understand that the pressures on elementary school math teachers drive them to stick with safe techniques, but for them to feel threatened by a student privately moving beyond that is frankly an indictment of the whole system of education.
What a damn shame... Here in France, a lot of school teachers are just "failed researchers" - uni students who wanted to get into academia but just weren't good enough. So we end up with quite a few unmotivated teachers who just rotely follow the program, without much passion at all. I wish the schoolteacher career were seen with more prestige, so that more qualified people would sign up.
You are so right! I myself am a math teacher teaching in advanced (higher level) classes. I share the same experience like you.
I see so many students being discouraged because they had incompetent teachers in middle school killing all the fun one can have with math. I always try to encourage my students to "explore" a topic, not just feeding them subjects.
I myself had a bad experience when I was a high school student. My math teacher once kicked me out of the class, because I presented him an alternative solution to a problem. He simply couldnt stand this, didnt let me prove my solution. Turned out I was right and he never apologized later. How pathetic! But this never discouraged me. It had the opposite effect. Otherwise I never would have studied math at university later :)
I was lucky to have the mother I did (herself a teacher, though not of math) and many fine books at home (including math books). Also getting into computer programming at a very young age gave me an appreciation for math and its applications not shared by my fellow students or even my teachers. Thus I was able to tough it out.
You noticed these patterns, but did you prove that they hold? Without some explanation for why it works you can't say for sure that it will work in a given problem.
"each power of two is equal to one more than the sum of the lesser powers of two" adding 1 would make it an odd number. Makes no sense. Did you mean "two more"?
[edit] Now I see that you start with 2^0, and it makes sense.
Can you imagine what Tesla could be capable of today with our tech 🧠
It’s his tech
Tesla would be dead in modern times. Death by suicide. 7 shots in the back.
@Shaun Grondanot the battery based technology
@Vanja Menadzerjajajaja. So true.
Wow, I could listen to you all day! If I had had you for a math teacher in high school for a semester or two, I would have majored in mathematics in university! I hope you are teaching young people somewhere. Thank you!!
Math is the language used to understand everything that exists from subatomic particles to the universe itself! Your love of math is beautiful. Please continue sharing your enthusiasm for math and sharing your ability to break down items into their various pieces and parts, and of course, the fun you have in combining those things then in various ways.
🥰🥰🥰 get well everybody
um maths is a numeric philosophy that can only tell you anything about the model, rather than reality itself.
@The Time Island thats what you think
@Arthur W thats what i philosophise! it is also technically true. Math can only prove its own internal models, never reality.
absolutely loved your video! I think the vortex is still very special even though it works in all kinds of base systems. Surely the fact the vortex remains strong in all counting systems adds to its beauty and power. It's maybe just only about 9 in the base 10 system
That was my exact thought... the "shape" holds up. I never heard of this vortex stuff until tonight. I think it's very "special" and even "cute" :)
It certainly is the Continuum Transfunctioner!
In my younger days in school because of the overcrowding in public schools I got moved around in math class so I never was able to get a full grasp of algebra but I find this type of math absolutely fascinating what you are demonstrating very intriguing
I didnt learn nothing in school ... To busy day dreaming and chasing chicks , skipping class , ect.
Buy a set of Cuisenaire rods and they will help by making algebraic equations physical in a lovely way.
@ghetto cowboy your username represents you well lol.
@Shoshana1610 please, where can I learn more about this? I have a son who needs help in math and I would absolutely be so grateful for any tips that would help.
Edit: I just googled them to see that they can be purchased easily but how on Earth do you learn really well with them? Any advice at all is appreciated more than you could fathom.
Just another piece of evidence in the case against maths in schools when, in my case, all the beauty I innately felt from numbers, especially those in the nine times table were systematically removed from my consciousness by the dumbing down effect of schooling. As a 68 year old, I am now reliving and rediscovering my childhood love for mathematics which underpins my understanding of sacred geometry, frequency and cymatics. Thank you for this fabulous video ;-) Don't stop making videos like this, I beg you!
yes patterns are not what the elite want you to see . . . . . some of us see patterns without trying . sacred geometry and mystery schools .
Scared geometry is embedded in our dna is a great video and quote
I have to agree some of us see patterns without even trying
I dropped a healthy amount of acid one night and in the morning the dew on the grass was reflecting in the early light. they were all connected forming a blanket over the earth and it was the flower of life pattern. The feeling was intense, i wanted to cry but it was because it felt so beautiful and the level of understanding felt so intimate.
I've been watching your videos for years and only today realized that I have your book! Q.E.D.: Beauty in Mathematical Proof. My mother gave it to me for Christmas maybe 10 years ago and I enjoyed my first read through immensely. Now I peruse it from time to time, it really is a gem! If you like the Mathologer videos I thoroughly recommend the book!
Crazy I had that book too from wooden books.
I recognized those beautiful patterns.
Small universe
I was taught divisibility using the digital root sometime in 5th-6th grade. I was taught how to check that the result of a multiplication is correct by using the same principle of DR(a x b) in third grade actually. We had a great teacher.
I find this beyond interesting as a child, and up until my late 30's, I would walk and count by 3's with multiplication, division, adding and subtracting depending on my step cadence.
Super cool as always. This looks pretty accessible. I hope to find time to look into Seymour's explanation. Thanks!
I found this very interesting. I don't know if it was noticed or not, or previously mentioned, but when you did the example of 527=14 and then add the 1 and 4, you get 5...if you take that 14 and subtract the 5 it equals 9. Same for the 2 number example. Maybe I missed something and this is already explained lol.
You didn't miss anything. Rather you saw what's hidden in plain sight.
Looks like I unknowingly introduced this to myself and my wife and daughters with a little game we used to play while travelling. We would add up the numbers on license plates and see who came up with the "digital root" the quickest, even though we didn't know that was the term to use. We saw very quickly that any combination of numbers that add up to 9 could be eliminated so 572 would be 5 without going through the process of adding. Later, as 3 or 4 number plates lost its challenge, we included letters. The letters "I" and "R" could automatically be eliminated since they corresponded to the number 9 and 18 respectively. This expanded the challenge because you had to figure out the numbers corresponding to the letters. As you played the game this became more intuitive when you could eliminate combinations of letters that added up to 9 for elimination. Example GSP562 would be 1. One of my daughters got so good at it that within seconds she could get the digital root of signs with just letters such as names of towns or short sentences.
fascinating sounds like you are all natural at decoding
Ask yourself are you right handed left handed what are your daughters you have two daughters Plus Sons they will give you up for the sons.
wow. an incredible game. we kearn and see patterns so quickly.
Wow!
What a brilliant game? I’ll have to keep this in mind when we pile in the van for our next trek.
As a regular watcher of the Numberphile and Sixty Symbols channels, (both excellent, in my opinion), this sort of thing seems to pop up all over the place in math and get expressed in various ways in physical reality. This is a nice exploration of this particular instance. Now that I have discovered your channel, I will add it to my "interesting math channels" subscriptions. Thanks!
It would be interesting to apply vortex math to the patterns that occur from the different frequencies of sound. That would integrate visual and audible. I wonder if a 3-D printer would be able to do a large vortex.
Check out Robert Edward Grant's videos. The work he's doing and what he's discovered will blow your mind. Look into Sacred Geometry with Russell Carlson too. Alan Green's Bard Code will make mush of what is left of your brain, lol!!
I cannot even rap my brain around that concept. I can kind of imagine it but just a sound in a room could be diagramed as it bounced off the walls but it would soon be so many lines that it would become black space? Not even factoring in frequencies. Now take that outdoors and do the same. It would bounce off houses, buildings, cars, mountains, trees and anything else in it's path. If done higher up, it would go so far up and I am not even sure if space could pick up a sound outside the atmosphere as NASA was saying as there is no gravity beyond a certain point and the sound would then bounce back to Earth. Would kind of make you think that if NASA picked up on a sound that it would probably be one of our own sounds bouncing back at some point. Lol Scanning would in the form of an image but when there is no gravity, can the sound even travel and without the sound travelling, how can we scan it? Another planet I don't think would be able to pick up on a sound from Earth. The planet would have to specifically come across Earth, move in to our atmosphere to hear anything otherwise it would be like a solid mass from afar. Your comment really made me think, something I have not ever done as a kid and probably should have. Thanks for commenting.
We had those division tricks in my school in 90s. All math teachers we had this time were post-USSR ones. In Poland these days kids do not have this in main course and I have to help my kids on my own.
I hope AI like ChatGPT will invent and adapt the very best math learning programme individually based on every child progress (exactly what I do at home with kids and every level programmers at work)
this is something I've not been exposed to before. I'm 68 so I'm a product of what I learned before around 1973. however, to use your vernacular, as soon as you started talking about the number nine I was saying to myself, all that really is is b - 1. I was a COBOL programmer for a few decades I'm familiar with base 8 and base 16. some of the other programmers I worked with used to call me a bit fiddler. in fact, I remember learning about using different bases way back in 1963 in summer school at my grade school. it was very confusing at first.
but the bottom line for me even from the beginning of this video was that what it's really showing is just how fascinating the relationship with numbers is, rather than any kind of a key to the universe.
but as you pointed out later, that the universe is based on mathematics. heck, even music is based on mathematics.
I've been adding numbers to get the digital root my whole life and NEVER knew it had a name or that it was an actual math process, I feel so validated by this video 🖤
Usually i am doing it with time
modular mathematics makes it basically pointless, so except for divisibility tests its sort of useless
You shouldn't need a video to validate yourself
You, sir, are brilliant. I’ve never seen something so complex, presented in such a simple way, that was so incredibly easy to follow. Please don’t ever stop making these videos. They, and you, are terrific. Thank you.
I agree! Unfortunately, or not, now I'm going to theorize and write proofs that freak people out, and that never ends well...but it's so fun!!!
he is just copying and pasting every other video out there.
He’s just copying every other single video that talks about 369z
@Cecily Schneider epic, show me them lol
@SURFER BY BLOOD isn't every other video the ones saying they're the secret to the universe?
I LOVE THIS. I have been terrified of maths but I now sit in wonder. ❤️🙏
Fantastic, thank you so much! I wonder if you can connect these cycles/attractors to sounds and resonance, harmonics in music, and different bases to different tunings (like Pythagorean)? Beautiful
Glad to find someone who had the same conclusion on vortex math as me, then expanded it so much farther.
Highest I've gone is base 12 and x6.
Definitely will be using this for the game I'm working on, as you've simplified it into 2 units, which is far simpler than what I was planning!
My math skills are far beneath the level of this video as I've never gotten past basic math (a + b = c). I do appreciate the explanations and it's both kind of sad to see a bit of mystery leaving the world and interesting to see how numbers work and how patterns emerge
What an amazing video! Thank you so much for your teaching.
I was taught the concept in elementary school, under the name “casting out nines”. Sadly, it was presented as a trick or technique, without real explanation, which I had to discover for myself. So much is lost when mathematics is taught as a bag of techniques without the underlying beautiful patterns!
@JoelNeely, I fully agree to your comment. I was also taught this at elementary school, for a later confusion as follows: Since these divisibility rules are Base-10 dependant, I had thought for many years that the divisibility of a number with another was Base dependant, and that perhaps on another base those same numbers were "conmensurable". A gross mistake that hindred developing intuition on numbers theory.
I loved the explanation where Prof. Burkard decomposes a base 10 number in: a (9+1) + b (99+1) + c (999+1) ... seen it that way is so straightforward !
my grandfather taught me "casting out nines" about 50 years ago. he used it to verify this hand calculations (pre-calculator) (+ - * /). it is a way to find single digit errors, however it has a weakness, it cannot detect the error of having a zero instead of a nine (and vice versa) . Also, it is only for numbers expressed in base ten.
@Mark Larsen Yes, the single-digit issue is shared by many check-digit schemes used to protect "numbers" from transcription errors. (I used the scare quotes because these "numbers"—such as account "numbers"—are really just identifiers made up of digits, not intended for use in numeric calculation.) Such schemes were especially important before computer networks were so pervasive, and data were captured and coped by hand. There are other kinds of errors—such as transposing adjacent digits—to which a simple digit-sum check digit is blind. That's why some check-digit schemes also applied weights to the individual digit positions.
I was also taught "casting out nines" in high school back in the 90s. My math teacher was great, but didn't have significant post-high school math education, and didn't know any of the deeper meaning behind anything. So the only application she knew for "casting out nines" was what it said in our textbook (error checking), and everybody hated it because we were lazy high school kids who were prone to saying stuff like "in the real world I'll just use a calculator".
While it's easy to be amused or annoyed at some of these silly viral math things that miss the forest for the trees, I feel like there's something very important we need to learn from them about how to engage with people about math and education in general.
I'm a math teacher, and, believe me, we would love to teach the real explanations alongside the techniques. Unfortunately, we simply do not have the time, and we have to prioritize. The techniques are more useful for getting students to pass the tests, and the tests determine our ratings as teachers. Additionally, we are training for the workforce, so the technique and ability to get the correct answer is pragmatically more important than understanding the correct answer. Knowing your bridge will stand up is more important than knowing why it stands up. Proper dieting is essential to good nutrition even if you don't know the chemistry or biology involved.
At my school, I've got 45 minutes a day for 187 days to teach students everything in Algebra. That 187 days does not account for student holidays (at least 14 days), bad weather days (at least 3), and the many interruptions caused by events such as Pep Rallies, ACT-testing, SAT-testing, MAP-testing, emergency drills, professional learning conferences, etc. I would estimate that I only have about 113 hours (two full 8-hour-day weeks) with my students over the course of the entire year. Can you imagine learning EVERYTHING there is to know about Algebra if you were given only given 8 hours a day for 14 days? It's simply not feasible. Especially if you're sharing the instructor with 150 peers.
9:46 I remember figuring this out after teacher taught us the usual divisibilty rule for 9 and I shared it with the class. The teacher praised me for pointing it out and it made the topic a little simple for the whole class!
This is a well made and informative video. I am not a mathematician, but was still able to understand most of it.
First time I heard about Nicola Tesla thinking that 3 6 and 9 were key to the universe, the first thing that came to my mind was, "Wouldn't those numbers be completely different if we didn't use base 10?"
This looks like its using base 9..?
It does not use 0 therefore seemingly has no origin point.. Repeats itself
@Frater Niram you didnt watch the whole video
Yes of course, but regardless of the base system, these same patterns will emerge. Do you think the electromagnetic fields function only because we choose a base 10 system, or maybe, just maybe, a different mathematics system would still create a version of maxwell equations.
@HRNThe way mathematical equations like those in physics work are not dependent on the base used to display the numbers.
@K1naku5ana3R1ka Math is a tool to measure reality, nothing more, nothing less. We give properties to objects and phenomena around us based on systems we invented in our heads to comprehend reality. Like we use words to describe situations and feeling we use math to describe our universe.
Hi, I’ve been looking all over the ‘net, libraries etc. and written text is so slim on the ground! I recall being amazed, when as 9 yr kid, finding the symmetry of the 9X table. Then as time wore on, through school and on, I stumbled across Teslas’ Vortex diagram. Watching this video has opened my eyes to more patterns!!
The advances cardioid curve at the start looks in a diffrent perspective, like a dark tunnel that goes on forever. Also like a black hole. The lines create a grid of curvature like a tunnel, possibly meaning that the infinity symbol serves its purpose too. Two point, shown on a 2D plane, connected though, reflect a "infinite" symbol correspondingly. Maybe an eye opener to believe that there really will always be something new to explore.
I am from Austria and we never learned that the number, which remains actually is the remainder (9:45). When I learned about modular arithmetic in math Olympiad, I guessed that fact to be true while doing an example. Not even my highly invested teacher was sure, whether the solution was right. Infuriating, that you do not learn these deeper truths about mathematics at school.
depends on your school. we were thought about that.
we were also given homework to come up with divisibility tests for other numbers like 7 and 11.
@DSDS SPP Dude is your teacher Flammable Maths? I think he talked about giving his students that exact homework. I'm just asking because I don't think that is going to be a common task to give to students.
@Samuel Mahler Out of curiosity what's the answer?
@Samuel Mahler no, it's from years ago back in high school. it might have been a textbook question, it's not hard to figure out if you know modular arithmetic which was a part of our curriculum.
we certainly did have very passionate maths teachers though.
Oh cool. I programmed a visualizer for these diagrams with different moduli a while back in unity. But only for the multiplier of 2. Turns out i only needed to make 2 another variable and i could produce a whole bunch of new diagrams :D Thank you!
This is actually great math if you are searching for a logo for your slipknot tribute band lol.
Math explains patterns in science and nature. There's arguments that other types of phenomenon can be described by dimensions not comprehendible to us in the ones available to us. Great video!
Man this is mind-blowing. Is this the key to the universe? It certainly seems so.
WOW! I've always been better with something other than math, but that was a great tip! Thank you brother!
We were taught casting out nines which was basically mod 9 arithmetic. It made it easy to check the addition of a long list of numbers.
I have always been intimidated by math. But this video has been eye opening. For the first time in my life I am interested in math. It was engaging and made me want to know more.
I suck at match and got lost halfway thru vudeo
Yes, math can be intimidating but also beautiful when observed with an open mind.
For me too
In the great words of Billy Mays.. 😆
Same with me Katherine. Astonishing vid.
Excellent video that includes the rest of the story.
This might be unrelated but Curt Doolittle’s Propertarianism includes a claim the temporal universe boils down to a rather simple algorithm tied to the triangle (ternary logic), where everything is based in the number three. In said triangle are points A and B represent opposing interests( male/female for example) where C indicates successful cooperation within a stable environment (mass). I’ve been learning more but have much yet to go. Love to hear your thoughts, thanks!
A beautiful universe, with beautiful symmetry! It seems this would correlate with crystalline matrices, too
Heard about this thanks to marco rodin and his coil tech, i used to think reverse engineering this pattern from vedic myths was "a bit nuts" BUT I now understand it is more akin to using the uh shape, as a base (like binary, base 10, others) worth looking into for sure
Bardzo Ciekawe Informacje.
Ciekaw jestem, czy zmieniając perspektywę wynik byłby tak samo zadowalający.
Co by było, stosując Systemy zamiast dziesiętnego (10), to " ósemkowy (8)" " dziewiątkowy (9) " " dwunastkowy (12)" " piętnastkowy (15)" " sześćdziesiętny (60)" Pozdrawiam
Your failure to follow the very obvious line of reasoning created an instant subscriber over here. I like your style and look forward to learning more with you. Great video!
I’m terrible at math but have always been interested in mathematical concepts. At the start of this video I pondered “maybe 9 is special simply because we base our integers on 10”. I felt so vindicated when you proved that the diagram works with any other base minus 1.
Base 10 is expressible as base-9 plus null (0). That's why everything seems to revolve around 9 in base 10.
I discovered the digital root 9 thing, then introduced it to my math class 😀 well impressed the teacher - never went any further 🤔
These petals and colors remind me of the petals that are represented in the 7 chakra system and when you added colors it even resembled what I was feeling even more. Thank you for your explanation.
Same. I think they’re somehow linked.
27:38 shows 8 not 7. The point of this presentation is to dispel your ridiculous mystical notions.
When joining cell coils together you gain an extra Volt on both sides giving a 9 the rule of 3 is not always dominant as much as 4.5 is in my Generators.
You blow my mind open in a good way with each of your videos—thank you !
Loved this. Thank you for covering Nikola's vortex.
I really appreciate the fact that you spend time watching other YouTube videos, in addition to creating your own. This is what makes Mathologer not merely “yet another maths channel”, but something of higher value; your videos don’t just provide yet another explanation of the same thing, but provide further explanation in context of existing explanation attempts. Love it!
Mathologer - 2022-02-19
(updated 2 April 2022) Thank you to all of you who contributed a modular times table app. All the apps I am aware of are listed below. The winner of the draw is Mathis Aaserud. Congratulation!
Here are a few implementation contributed by viewers so far. Look at these first:
Adam Abrams: https://theadamabrams.com/modularmultiplication
Ed Collen: https://vortex-rho.vercel.app/
Andrew “Ash Mystic” Herman: https://codepen.io/hippiefuturist/full/NrvqgZ (check out the preset animations on this one. Also check out his fractal tree generator https://codepen.io/hippiefuturist/full/KRromj )
Man Hin Li: https://mandelbrot.vercel.app
Liam Applebe: https://tiusic.com/vortex.html
Owen Bechtel: https://owenbechtel.com/games/times-tables/
William Ward: https://scratch.mit.edu/projects/647469837/
Артём Маевский: https://tinyurl.com/yc8danxx
Baxi: https://baxi-codes.github.io/mathologer-vortex/
Marc Donis: https://madc0w.github.io/cardioid/
Rafael Castro Couto: https://codepen.io/rafaelcastrocouto/pen/KKyoKWm
Laurent Bucher: https://anceps.net/modularTimesTables.html
Hannes Wendt: htts://math.wendt.sbs/vertex
Hugo Cardoza: Code in p5js https://editor.p5js.org/hugomosh/sketches/1Sg1NxqI7
john Schoeman: https://www.doodles.camp/#/doodles/modular-times-table
Banjamin Elo: https://bnelo12.github.io/vortex-math/
Joe Lucette: https://jluqu.github.io/modmult.html
Federico Marotta: https://federico-marotta.shinyapps.io/tesla_vortex
T3CHN01200: https://victorsohier.github.io/
Tom DeRensis: https://github.com/tderensis/ModularTimesTableJavascript
Ehsan Kia: https://ehsankia.com/cjs/vortex
Jayson Vivet: https://www.geogebra.org/m/cufneprj
Tyler Wolfe-Adam: https://mathologer-vortex-app.herokuapp.com/
Andrea Coletta: https://mathologer-modular-time-table.lm.r.appspot.com/app
Mathis Aaserud: https://sirkular.ispaceyourtube.com/
Justin Kirk: https://intern-jck.github.io/vortex-math/
Jarred Branch: no online version
Álvaro Silva: https://mathlogervortexalvaro.web.app/
Rafael Castro Couto: https://codepen.io/rafaelcastrocouto/pen/KKyoKWm
planck_cst: https://www.jerpint.io/blog/mathologer-challenge/
Anton Shcherbinin: https://ch.ant-on.net/modulo/moire?p=1009&m=303
Cristian Merighi: https://js.pacem.it/2d/vortex
Krischna-Gabriel Schulz: no online version
András Kirisics: https://kiri-mathologer-vortex.web.app/
relikd: https://relikd.github.io/Vortex-Math/
Eclectic Gamer: https://youtu.be/n_YLB0ncbpI (Video on using Blender and Geometry nodes to make these diagrams)
Some existing implementations of the modular times table diagrams:
Aymeric Ramiere: http://www.aymericramiere.com/others_modular.html
Steve Phelps: https://www.geogebra.org/m/z8wrdret#material/dqKkQEv7
I did this a while ago: http://www.qedcat.com/cardioid.cdf
Marcus Metzler: https://github.com/drmocm/Modulo-graphics
Start of a wish list for the modular times table diagram coding competition:
-Being able to color line segments according to length.
-Being able to highlight different loops in different colors.
-Indication of the "direction" of multiplication. 1x2 = 2 and so there should really be a little arrow from 1 to 2 not just a simple connection :)
...
Tridiv Sharma - 2022-02-19
@Mathologer I need your help, I've learnt all the basic integration techniques (By parts, Partial Fractions, Trig Sub, U-sub, Chain Rule) and I cannot find any more integration techniques to learn, can you please give me some more, all the websites say that you will learn more but I cannot find any more.
3D4U - 2022-02-19
Zero doesn't exist in the natural world - it's a man-made construction. There is never 'nothing' in the universe - never. There is no 'zero' in reality. The digital root of 10 doesn't exist in the natural world, only in the world of man. That is to say that whatever mathematics governs the natural world it does so without the use of a 'zero'.
Can we devise a base9 system that does not use a zero?
I'm no expert in this - just a curious layman - but I did do some thinking on this. Could we not begin counting at 11? The first iteration and the first 'number'? The first "one" so to speak? One One or 11. Then we'd have the first "two" so 12 would be next - 13, 14, 15, 16, 17, 18 and then ,19 - the first "nine". Then we would go to 21 - the second "one" and so on totally eliminating the use of a zero. I understand that multiplication and division become very difficult without the use of a zero so I assume that more complicated mathematical functions also become very difficult. I also assume that this is the reason we invented "zero" in the first place - to make is easier to calculate - is this right? Is there any other purpose for the zero? I don't know. I am simply curious as to whether or not we can do mathematics without the zero.
And I think that if we could do this that doing this vortex math in such a system would yield different results. As I said, I'm no expert and could be talking out of my ear but I do think that the mathematics we use and the mathematics of the natural world are not the same and that perhaps using the maths that governs the natural world might yield interesting results.
Niels Korpel - 2022-02-19
@3D4U what number of lions live on mars?
* Is that a question about the natural world?
* What is the answer to that question?
* Is this an example of 'zero'?
My answers:
* I would say so.
* Zero, given what i think i know about mars.
* I would say so.
What are yours?
Very Potato - 2022-02-19
@3D4U
So base 9 but formatted differently.
11->10 (base 10 “9”)
12->11
13->12
…
19->18
21->20
22->21
Pretty sure what you have invented is just base 9 but with all 0s replaced with 1s, 1s replaced with 2s, 2s replaced with 3s, all the way up to 8s which are replaced with 9s.
I could create a mathematical system where every digit is indicated with a color and that would be functionally the same as one which used digits.
Very Potato - 2022-02-19
@3D4U
Also, how would you express 1-1? That was most likely the reason 0 was invented.
0 means “nothing”, and that’s why it is something.