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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.

bookstore.ams.org/mbk-141/

That early Mathologer video featuring the modular times tables

Times Tables, Mandelbrot and the Heart of Mathematics

• Times Tables, Man...

A really nice article about various ways to generate the cardioid by Dave Richeson

divisbyzero.com/2018/04/02/i-...

Nice debunking/demystifying article about vortex math by "Professor Puzzler"

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

plouffe.fr/Simon%20Plouffe.htm

Articles by him relevant to this video can be found in this directory

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 KZbin videos.

sciencetosagemagazine.com/vbm...

In turn this iceberg is just another tip of an even bigger iceberg of mainly wishful thinking. Have a look: sciencetosagemagazine.com/cat...

Today's music: Aftershocks by Ardie Son

Enjoy!

Burkard

Ever heard of Viktor Schauberger?

@3D4U So no money means zero money.

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.

@Tim Spiker I teach in NB Canada. I actually do not teach music, but I totally agree with you.

@Ryan Gardiner This is true in very rare cases like private schools or maybe in a few countries. This is not true for every where in the world. There's a lot that needs to be done still. But I see you're a music teacher. If you're teaching music at Elementary. Music is great for at the same time teaching mathematics, I'm a producer myself. Musical mathematical patterns are a lot more in line with the world and problem solving due to their reoccurrence in nature and the universe itself.

I am an elementary school teacher. Thankfully the education system has evolved significantly since we were in school. Mathematics is taught to encourage deeper understanding. Students are encouraged to explore their own strategies and to think about their thinking.

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.

For me to mate I left school at 15 thinking I was a bad arse.he has got me

@Steve Thea It was amazing to watch, but he starting spitting numbers and I started smoking weed lol. Those 2 things didn't mix.

Same with me Katherine. Astonishing vid.

In the great words of Billy Mays.. 😆

For me too

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.

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

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?"

@Frater Niram you didnt watch the whole video

This looks like its using base 9..? It does not use 0 therefore seemingly has no origin point.. Repeats itself

I apologize for being 10 months late, you did quite a good job of illustrating a math concept that I am not familiar with at all but almost instantly it was understandable due to you being a great illustrator.

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!

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 have to agree some of us see patterns without even trying

Scared geometry is embedded in our dna is a great video and quote

yes patterns are not what the elite want you to see . . . . . some of us see patterns without trying . sacred geometry and mystery schools .

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

It certainly is the Continuum Transfunctioner!

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" :)

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!

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!

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!!

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.

@SURFER BY BLOOD isn't every other video the ones saying they're the secret to the universe?

@Cecily Schneider epic, show me them lol

He’s just copying every other single video that talks about 369z

he is just copying and pasting every other video out there.

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!!!

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

@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.

@ghetto cowboy your username represents you well lol.

Buy a set of Cuisenaire rods and they will help by making algebraic equations physical in a lovely way.

I didnt learn nothing in school ... To busy day dreaming and chasing chicks , skipping class , ect.

It’s nice to know new people are trying to understand a new topic of math I remember when I came across this when mark Rodin was first starting off when we where still trying to work out coils and the potential of the math! And we’re constantly learning new things!

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.

Thank you. Very concise and humorous! I was taught this as part of a "bag of tricks" to speed through math tests in elementary school in post-WW2 Britain. Mental arithmetic was highly prized. I hope you do keep up your excellent videos beyond your 100th birthday. I mean, what's special about 100?

A beautiful universe, with beautiful symmetry! It seems this would correlate with crystalline matrices, too

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.

@Steve Thea left handed

@Ole Rocker what's LH?

That's actually really cool. I don't do the math part. When I see license plates, I try to make a phrase or sentence, using the each letter as the root of a different word. It's great for training a quick mind and the imagination. Your family must be fairly amazing at doing mathematics in your heads like that. I'm going to try this out now too. Lol Thanks for the new game to play friend!

@Ole Rocker interesting. will keep in mind when prospecting future dates.

@John Zucced My wife and I are the oldest of our siblings and the only LH of the families, both children and parents.

I LOVE THIS. I have been terrified of maths but I now sit in wonder. ❤️🙏

I'm fascinated by all this. I have to watch it multiple times. I have no clue what this is used for. I only use basic math in my work. I ♥️ all these videos. Great job explaining 👏

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.

I'm not a math teacher, but I am a math adjunct teacher: I teach physics. I do teach the rule "add up the digits to see if it is divisible by 3 (repeat for 9)" rule. If you could make a video of "things they ought to teach in school" I promise I will teach all of them. Thanks, Steve

I was thought both for 3 and 9 the rule is similar. That would mean the system can be setup in base of 1 2 3 which is just a triangle. Doubling between 1 and 2 as the repeated sequence. An alien duck with 3 toes maybe?

I believe humanities savoir is outside the realm of physics

From your perspective as a physics teacher, have you ever considered the possibility that the physics paradime being taught could be an unnecessarily complicated way of modeling the universe? Could some of the most prolific engineers in history have been aware of a greatly simplified model which can be used to explain everything, including that which your existing paradime has no answers for?

I love this .

Crazy thing i found out just right now. After watching this video. I calculated the numbers of my actual birthday, i calculated every singular digit and its crazy how it end up with a 9. Whats even more crazy is my spirit number is 9.

I was not taught the divisibility by 9 test in school. But my father did teach that and many other mathematical concepts to me when I was very young. (Mid 1960's) He used a book called The Calculator's Cunning which used number theory to teach people how to perform complex math in their heads. I still have the book. Edit: Here's the book information for those who asked. CALCULATOR'S CUNNING The Art of Quick Reckoning Karl Menninger Translated from the Tenth, Revised, German Edition by E. J. F. PRIMROSE Forward by Martin Gardner BASIC BOOKS, INC., PUBLISHERS New York First published in the German language by Vandenhoeck & Ruprecht, Gottingen, under the title, Rechenkniffe: lustiges und vorteilhaftes Rechnen Tenth, revised edition 1961 English translation copyright 1964 by G. Bell and Sons Ltd. Library of Congress Catalog Card Number: 65-19543 Printed in the United States of America

@Bee Page fantastic!

Thanks just bought the book!

Thanks for the recommendation.

@bawa tabetando check my edited comment for the book's information.

@Jack Richards 60 is only days away for me, but I too enjoy learning. This long-hand square root process also allowed me a chance to think of my dad, which is always a good thing. Good luck on your search for the book, check out my edited comment for more details.

4 minutes in and i must say your presention skills are impressive. Keep up

I figured this out in high school when I learned about hexadecimal system and ASCII Tables. What I have always wondered is how much we are not easily able to identify in relationships between math and nature because we’re using the wrong base?

That's the root of the lie. Use of a wrong base to hide the real truth.

@Ken Shultz Specify, there is no monolithic overall body for organized religion. What do you mean?

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.

Just a few observations on this.It's a great explanation. The higher powers make wonderful mandala effect.Starting the the count from the incalculable 0 would also prove the fallacy (try plotting this in base 2). And as a cheeky finish the cardioid is a great mathematical way of drawing butts :D

Try doing the 2x, 5/ in base 12 and see if the trick still holds.

A true Vortex must have a center thats void of matter and having matter trying to enter but at the event horizon the matter will relax like a parachute opening up leaving more space void of matter in its center, that how the vortex is able to grow and the positive and negative ions are reformed with the matter that resides outside of the void.

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)

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!

my nephew is a math wiz (his college major) and helped his younger brother understand math at a higher level.

I was taught multiples of nine using your hands. 9 x 4, bringing down your forth finger, you get 36. I thought that was pretty neat.

Exactly why I hated math and seriously struggled in school, but watch videos like this for fun and totally understand it. You can't just tell me "this does this, that's just the way it is" it'll never stick in my head. I need to know WHY that numbers do what they do, and teachers NEVER give that explanation. Tbh I wouldn't be surprised if most genuinely don't KNOW the answer

Amazing video thanks for explaining this and finally making sense of it

The vortex is a representation of a photon. It's a packet of energy that folds back in on itself. Inside that vortex time stands still.

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.

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.

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

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.

I'm also from Austria, and we learned the digital root ("Neunerrest") and even modular arithmetics. But that was nearly 50 years ago.

@Armament Armed Arm Ancient Sumeria, the 1st civilization

@Christian Dauz Surely you can pick a better civilization than that.

I wish a Time-traveler went back and Industrialized the Roman Republic

The main reason people don't teach these rules in high school is that they are never actually used for anything. We also don't teach how to compute products with a slide rule. (That said, I _did_ learn how to find products using log tables in high school, which I thought was bizarre.) Divisibility rules _are_ useful in primary school when learning to reduce fractions, and that's where I learned the rules for divisibility by 2, 3, and 5. Of course, if you think about it, these rules also give you the remainder if you divide by that number. Like, the divisibility rule for 5 says that if a number ends in a 0 or 5, then it is divisible by 5. I think most students realize pretty quickly that if a number ends in 1 or 6, it is one more than a multiple of 5, and if it ends in 2 or 7, it is two more, etc. This works for 3 in the same way. Although the divisibility rule itself is less obvious (that a number is divisible by 3 iff its digital root is 3, 6, or 9), the corollary still is. If 51 is a multiple of 3 (cause it's digital root is 6), then 52 must be one more than a multiple of 3, and 53 must be two more. That's basically all that's going on here. If you take a class on number theory, this basic idea comes up in more general form pretty quickly. But there are like fifty things I wish I had learned in high school math, and this barely even makes the list. There's just too much math to teach.

The digital root is fun with 11 as well. 10 is congruent to -1 mod 11 so you just add the even digits, subtract the odd digits of a base 10 number, then you get an easy analog for "11" digital roots.

Great explanation of the mathematics behind this. Would appreciate a video adding some physics into the story, e g. explaining the same thing starting with a base frequency (1) and observing its harmonics (doubling, i.e. mul. by powers of 2). Then thinking about resonant frequencies (like in the story where soldiers marching on a bridge in a resonant freq. amplifying the vibration destroy it). How do 3/6/9 fit into such a perspective? Would they help with more efficient vibration amplification using resonant frequencies than the other numbers. What if the base frequency is the frequency of the Earth (or make base its third, so Earth frequency is number 3)? No idea whether any of it would make sense, just curious to have an expert cover the topic...

When you find the frequency of the earth, see if it can be a tool for healing on a rapid scale. We are all from the earth, when we separate ourselves from the frequency we get sick. Reconnecting with the frequency heals, and some light frequencies have been used for the rapid healing process.

If you map that sequence order (1,2,4,8,7,5) to an inline-6 engine : 1 4 7 8 5 2 (piston number) or a V6 engine : 1 8 4 5 7 2 I think you get the optimal firing order of each cylinder.

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.

I personally was not taught these math tricks in the 1970"s in grade school. Deliberately. I am thankful for it. We learned to do problems the long way and then without paper. We learned to visualize number patterns like the 2 and 5 trick in a base 10 system. My classmates and I were faster than any calculator and always right. In 4th grade We wrote a 0x0 to 15x15 multilocation tables or division tables, including the table itself and filled it in in under 30 seconds. We at the time thought our teachers were mean but they were very correct. I rarely used a calculator until I got into long complex math and calculus. But my son was taught these tricks in the late 1990's. I tried to discourage them. He was am excellent student but had trouble visualizing complex problems and doing math in his head. I never let him use a calculator even when his teachers would. They are nice but have limited practical use. These tricks happen in a even numbered base system like base 10 (0-9). But all bases should have similar tricks in any repeating number system. They are not keys to the universe since math is am man made construct. Thank you for clarifying that. Those other similar videos are all just hype.

I the 1950's I was taught to check math problems by something the teacher called "casting out nines." I didnt know why it worked but was intrigued by it. 60 years later I stubble across the answer.

I was in grade school in the 60's in NY and was taught the same thing and they also called it "casting out nines". Later in life when we were using printing calculators and you had to "double tape" every bank deposit, if your two results were different and the difference was divisible by nine, you knew you had a transposition error.

Divisible by 9 errors in accounting are many times a transposing error ..eg writing 187 instead of 178 ..the difference is 9( 187 -178)..back in the days of adding up columns of numbers w a calculator .

@Karel I had forgotten about it until I read your post, but in accounting some similar process was used.

Don't have the answer but one of my finance managers used to use the technique to check the added up data from his spreadsheets.

@Beżål Elle tell me too!

I always thought that when looking at these diagrams, there wasn’t anything mystical about them, but that they are of our own making based on our counting system. This video confirmed what I thought was true in a well articulated and easy to understand format. Thank you!!

Totally off topic, but if your user icon was meant to mess with people you totally got me! I have a dog so I have dog hair all over the house. Your icon looks exactly like a short dog hair stuck to my laptop screen. I tried to wipe it off with my finger then it started moving up and down as the screen scrolled. I was so confused for a few seconds😆😆😆

Yeah I was wondering if this work when counting in other bases, other than base 10. Probably not. But it’s still interesting. I think there’s something to learn there. Patterns are patterns.

I have seen the „multiply 2/modulus many digits“ pattern before, just in front of me. And yes at that point in time, it was my whole universe. 😊

This is a well made and informative video. I am not a mathematician, but was still able to understand most of it.

WOW! I've always been better with something other than math, but that was a great tip! Thank you brother!

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

I really appreciate the fact that you spend time watching other KZbin 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!

Bu kadar bilgiye rağmen, daha iyi bilen bizi de bilgilendirsin demeniz. Bu konunun daha çok bilgi barındırdığını çağrıştırıyor. Ve sizin anlatımınız çok iyi senin gibi öğretmenim olsaydı benim için matematik ve hayat çok farklı olabililirdi.

Most of what you talked about that made sense to me, despite being unfamiliar. But at the begining of the video my first thought was that all of it would change if we did math in base 12 or something. That made me wonder how the base number would effect Benford's law.

Loved this. Thank you for covering Nikola's vortex.

I don't know anything about mathematics but you explained all this very well. Thank you!

This reminds me of the circle of 5ths in music theory. I know music is mathematical in some way so now I have to begin my journey to learn how these two concepts are connected 🤔

Harmonising frequencies are just fractions or multiples of a key. All Harmonising notes that make a cord share a mathematical correlation to the key, fractions. That's the basics of it. Take the highest frequency note in the cord, and all the lower frequency harmonising notes that make that cord will have frequencies that equal fractions of the highest frequency note.

The more we investigate & learn, the more it jells.

Way, way back in the early 1980's, I had to make a choice between continuing Math or Art studies, for my final 2 years of high school. I chose my artistry and have always kept a little candle burning for my love of numbers and equations. I have to tell you, I watched as I am interested in Tesla and was curious of the vortex diagrams you might display. Now I musts thank you as I am SO EXCITED by what you have shared, despite being in my late 50s, I am going to return to study math. So, thank you, thank you for inspiring me!

@Rick the Swift that is the art of fooling yourself to be happy. I can enjoy that tho...

@Gustavo Neves I'm guessing you are perhaps stumped, so I'll present it another way. You say "there is a pattern in everything", but still, you don't realize the simple art of not allowing for a pattern to exist, nor the beauty of breaking the common rule that a pattern must somehow always exist. The origins of art is simply to appreciate, that which had a beginning with or without a preceding pattern, as well as an end, which likewise never required a preceding pattern. I hope that makes some sense, friend.

@Gustavo Neves "For some reason you seem to think that these things compete..." No. I simply disagreed with your first opinion that art comes from mathematics. That was entirely a projection on your part. It sounds like now you are admitting that mathematics actually comes from art when you say "mathematics is a form of art", but somehow you still wish to be right. I can't argue with your two competing views when one is correct.

@Rick the Swift Just because you don't see a pattern, it does not mean it is not there. There is ALWAYS a pattern in everything. The question is if we can understand it already or not. Mathematics in itself is a form of art. The great minds in both areas were always people that thought out of the box. And always combining patterns in ways unexpected. For some reason you seem to think that these things compete...

@Gustavo Neves Respectfully, I disagree with part of your comment. Math CAN be a basis for art, but doesn't have to be, and in fact art can easily stand alone, without any knowable form of math involved. I too, like the OP decided where I would focus my talents, between art and math, and likewise, I chose art. Art, is a basic foundation of humanity, and likely a basic foundation to many other creatures as well. Let's not bring Darwinism into the equation just yet, but suppose a group of creatures who were quite ape-like in many aspects, had a special ape within the group- one who just seemed a little brighter than the rest from an early age, and even showing considerably more learning ability than even the wisest of the elder apes. And suppose too that one day the apes come back from hunting/gathering to find a rather large splat of condor poop just above their heads on the face of a large rock they slept under. All of the apes see the bright splat of poop and some are wondering what caused it, while others already recognize it as being poop from a large bird. Now, imagine our special ape walking up to the poop splat, pointing at it, the pointing at one of the other apes, immediately recognizing a resemblance. Other apes in the group can't quite make the correlation, so what does our special ape do? He picks up a stick, and dips into some mud or wet ashes, and attempts to replicate on the rock what he sees in the bird poop, only he replicates it with the intent on highlighting certain features which will help others realize he is painting a portrait of an apes face. Of course as someone who understands math, you could argue the special ape was calculating angles and mathematical patterns, but I as an artist I understand the special ape merely simply saw one thing, and had the courage to imagine it was something else other than what he knew the material to actually be. To fake something, or fool someone. I could also argue that the most important part of what the special ape was doing was completely void of math, and indeed it only had to do with the desire to be a part of something bigger, to live in the moment of true inspiration, or to lavish in one's own egotistical self. I think that too often people who latch onto math as their " key to the universe" often miss out on what true art and beauty really means. Yes, much of our music and visual art is filled with mathematical concepts, but they don't always lie at the heart- they are at times simply tools to help the artist express deep emotions and ideas. Yet some of the most beautiful music is often complete silence, and with no calculable time patterns. Just as often the most beautiful and artful part of a motion picture, or a theatrical production may be complete blackness, where any concept of math would be completely out of place, and merely a projection of someone who willfully desires for it to be there. In the end, it may in fact turn out that art is at the very foundation of mathematics as we discover that many mathematical formulas turn out to be mere illusions created by clever con-artists who meant to mislead or persuade others.

What an amazing video! Thank you so much for your teaching.

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.

"Casting Out Nines", was taught in Amish schools, at least as late as the 1990's). My dad was taught "Casting Out Nines", when he was in school in about the 1920's & 1930's. I used "Casting Out Nines", for speed math in college after I broke my $200 calculator, in 1974. I am as amazed now as I was then ...

Well done, thank you. Your time and effort is much appreciated. 👍😃

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

I think this is the kindest, most conscientious debunking of mathematical mysticism I've ever seen. I love this channel so much lol

He didn’t debunk anything

@eternal conciousness spark bro sorry, talk like what? I'd love to discuss the content in the video, I think I'm just missing some context

why do you people talk like that

So what did Tesla mean when he said that then? Was it just an elaborate troll? Do you think Tesla would say something like that with nothing behind it?

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!

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!

A truly intellectual video, thank you

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!

I discovered the digital root 9 thing, then introduced it to my math class 😀 well impressed the teacher - never went any further 🤔

I wasn't even taught the divisibility test, let alone the remainder function! This is really cool!

I like this. Thank you.

Xx seeds see some pics of your face and a few other things I need to get. Wizarding is growing to be the best thing to manage my heart and soul and body and mind and heart. Tuesdays bring about students whose sense of humour and the rest of the week and then prop up that way I can make sure you have your phone on you. Irresolute forward strategy can mitigate the first time such difficult and virtually nothing is going on with my order. The Earth would be hollow if they were going through it and let me up at the end of night around the house and we can eat at the pool your grandma thought you were going to be at.

@Jay Travis I know that I shouldn't laugh, but damn if you weren't spot on with the "phys. Ed majors" teaching math classes". It's very true. And you've got math teachers at the high school level acting like robots in order to get through the course so the teacher can enjoy her summer break.

@Daniel Davies i am within the annoying olympus.... hard to see 1 year ahead

3 has always been the most wonderful number to me. Sounds cheesy, but School House Rocks "3 is a magic number" opened my eyes to it as a child.

Love it… so simple but so complex

7:20 I think that if you did this in base 9, then multiples of 8 would have the same property of digital roots summing to 8.

Really nice video, explain a lot the maths involve in the mysticism world around Tesla. Now can be nice to comparate which kind of Multiplier and Modulus apear more in the Nature cycles, in the earth events and also the stars movement. May we can start to predict next events.

i'm falling more and more in love with math. thank you

Division by 7 always produces 142857. Spare key to the Universe, if you lost the master copy

@William Chamberlain until the guy by the name of “jan Misali” comes over and shouts “SEXIMAL”

@ValkyRiver wellllllll.. if god(s) made people, and people have ten-ish fingers to count on ....

We used that method in Cabalastic procedures

142857. Add them up and you will get 27. 2+7=9 once again

The correct order is 124875 be careful.

You sir are a modern day legend, if only math was taught like this in schools.

Just after a few minutes in after seeing the digital roots and how they describe the vortex I'm wondering what would happen in an alternate number system and how the pattern would represent itself there in say duodecimal.

You blow my mind open in a good way with each of your videos-thank you !

I've been watching beginning piano lessons. I believe I just saw the circle numbers there, too. Amazing how numbers and frequency (I almost said "music") are what; equal? Are we held together as humans by frequency?

Yes, the circles with numbers on the Music Theory charts have a very similar structure to all this logic in Mathematics. It is what we refer to as the Trivium (Rhetoric, Mathematics, and Logic) graduating us into the Quadravium (which includes Music, Astronomy, and two other sciences the Greeks taught in their curriculum, I forget off the top of my head).

Before watching this video, I have also thought of these numbers and agree that they are very key. But the study of physics is important to know why. :)

I recognized the divisibility pattern around 3's and 9's as a child doing the times tables as explained in the video. I later briefly brought up recognizing the pattern in college during Algebra II (comes in handy doing factors) and seemed to surprise everyone in the room. Didn't know other people like "junk" math. 😆

Vortex and fractal dimensions/structures are all really intriguing. This here is just the tip of the iceberg so to speak. Total geek food, and I can eat it all day.

Math, Light, Water and Sound are simply fascinating to me.

Love this and am not at all ashamed to say that you, legit, snagged me with that t-shirt. Brilliant on so many levels.

Mind Blowing information, love this explanations and love the giggles.... thanks for making it easy to understand.

Can you do a video that shows universal (divine) mathematical relationships in 3 dimensional shapes like spheres, cones, and tetrahedrons? How might that be related to TesIa's numerology?

I first ran into this bit of math, and realized that it wasn't limited to the number nine whenever in electronics and computer science classes I had to deal with numbers in base systems other than 10. it appeared with the last numeral of the sequence; 9 in base 10, F in base 16, 7 in base 8, 255 in base 256 and so on, I realized that it wasn't that 9 was so magical, than that it was an effect of whatever integer numbering system was being used, the last numeral in that system held prevalence in exactly the same way. That being said, 3 being a prime, and 6 being the product of the first two primes does present some interesting components, regardless of the numbering system. I have found in electronics, pi and e have more prevalence, though usually expressed as fractions or products of such, especially in AC theory. Kinda hard to integrate either into integer number systems however, not being integral

@infinidimensional infinities You hit the nail on the head. The specific relationship to 9 in geometry, related to spacial properties and manifolds concerning electrical dynamism, isn't scaled to other vortex base sets.

i think you are too dismissive of the nine phenomena, as it relates to vortexes, and torus dynamics of electricity. but that's ok. no worries, no hurries.

@Nicholas Leclerc Not a whole number integer?

"not being integral" ? What do you mean by that ?

Yeah, that was rather trivial for a mathematician (or serious student of mathematics), being a 1st semester question in a homework.

I remember learning to see if the sum of the numbers works out to be divisible by 3.

Those are literally my favorite three numbers, for personal reasons, but that is very interesting.

Strangest thing! I had stumbled upon i1 3 6 9 patterns in numbers I was tracking, expanding a 2-d matrix. I still have the notes on my notepad now through 16 iterations. And then this video shows up in my youtube queue.

The vortex is just the formula for calculating counter frequencies. It's really interesting what vibrations can do...

Great video - not just for the math (which I enjoyed) but the music at the end. Who wrote that? It's gorgeous!

I remember learning this in 1st grade. She said it was a short cut and I assumed it was being taught to everyone. I remember taking longer than other students to learn long division because I couldn’t find a reason I should use it since I could do the problems in my head using these techniques. I didn’t t know it was rarely taught until you said it.

@Justin Dickerson if the math leads to the correct answer than there it is easy enough to scribe down the major steps in the equation, but ya too many people cheat so cleverness adds an extra step of having to show the steps.

@Justin Dickerson: I ended up dropping out of school because I kept falling Algebra because I'd get the answer right without showing my work. It's amazing how these teachers would rather assume that I'm cheating as opposed to asking me a question that isn't on the test and seeing if I could do it in my head.... Public schools... I swear.

@Anne Gallagher it’s eye opening how destructive a single bad teacher can be, had a similar experience learning algebra.

@Justin Dickerson I was accused of cheating too after an Engineering math, exam, also before that, when I tried to teach another student I couldn't explain how I did it. I wanted to study maths all my life but my teacher said she taught the same maths each year - I need a teacher who loves teaching or I 'freeze'.

Would it also be true that it’s impossible to yield a sequence which corresponds to an irrational number (non repeating decimal) given an input pattern with regularity (algorithmic input; in this case multiplying the output by a fixed number?

Does magnetics follow the patterns? I failed calculus but while in mechanical cad design did several years of dimensional tolerance stack studies at Bosch in Farmington Hills , Michigan. Enjoyed it!

I only know a little bit of this complicated math because my dad taught me to add up my age every year. Freaks me out that our birthdays and year are divisible by 5, I always wanted to remove myself from getting too deep into the study of mathematics for how complicated it is to the detriment of looking at pretty flowers in nature.

Again very interesting, some excellent mathematical debunking. I believe I have learned in primary school in the 1980's (I'm that old ☹️) to use the 'negenproef' (Dutch-flemish)to find the remainder ( If this was the question at all btw).

Okay, let me see if I got this straight. "For a prime number p, the finite field zed p has the cyclic multiplicative group effect." I love it.

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.

What I'm upset about is that this was not tought to me in school. This stuff is rudimentary to our very existence and of mathematics and could have made highschool a lot easier than it was not only for me but for everyone.

There is a method of checking addition, subtraction, multiplication, and division using this sum of the digits called casting out nines. Your explanation almost made me understand it. I'll listen again.

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