(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: theadamabrams.com/modularmultiplication Ed Collen: vortex-rho.vercel.app/ Andrew “Ash Mystic” Herman: codepen.io/hippiefuturist/full/NrvqgZ (check out the preset animations on this one. Also check out his fractal tree generator codepen.io/hippiefuturist/full/KRromj ) Man Hin Li: mandelbrot.vercel.app Liam Applebe: tiusic.com/vortex.html Owen Bechtel: owenbechtel.com/games/times-tables/ William Ward: scratch.mit.edu/projects/647469837/ Артём Маевский: tinyurl.com/yc8danxx Baxi: baxi-codes.github.io/mathologer-vortex/ Marc Donis: madc0w.github.io/cardioid/ Rafael Castro Couto: codepen.io/rafaelcastrocouto/pen/KKyoKWm Laurent Bucher: anceps.net/modularTimesTables.html Hannes Wendt: htts://math.wendt.sbs/vertex Hugo Cardoza: Code in p5js editor.p5js.org/hugomosh/sketches/1Sg1NxqI7 john Schoeman: www.doodles.camp/#/doodles/modular-times-table Banjamin Elo: bnelo12.github.io/vortex-math/ Joe Lucette: jluqu.github.io/modmult.html Federico Marotta: federico-marotta.shinyapps.io/tesla_vortex T3CHN01200: victorsohier.github.io/ Tom DeRensis: github.com/tderensis/ModularTimesTableJavascript Ehsan Kia: ehsankia.com/cjs/vortex Jayson Vivet: www.geogebra.org/m/cufneprj Tyler Wolfe-Adam: mathologer-vortex-app.herokuapp.com/ Andrea Coletta: mathologer-modular-time-table.lm.r.appspot.com/app Mathis Aaserud: sirkular.ispaceyourtube.com/ Justin Kirk: intern-jck.github.io/vortex-math/ Jarred Branch: no online version Álvaro Silva: mathlogervortexalvaro.web.app/ Rafael Castro Couto: codepen.io/rafaelcastrocouto/pen/KKyoKWm planck_cst: www.jerpint.io/blog/mathologer-challenge/ Anton Shcherbinin: ch.ant-on.net/modulo/moire?p=1009&m=303 Cristian Merighi: js.pacem.it/2d/vortex Krischna-Gabriel Schulz: no online version András Kirisics: kiri-mathologer-vortex.web.app/ relikd: relikd.github.io/Vortex-Math/ Eclectic Gamer: th-cam.com/video/n_YLB0ncbpI/w-d-xo.html (Video on using Blender and Geometry nodes to make these diagrams) Some existing implementations of the modular times table diagrams: Aymeric Ramiere: www.aymericramiere.com/others_modular.html Steve Phelps: www.geogebra.org/m/z8wrdret#material/dqKkQEv7 I did this a while ago: www.qedcat.com/cardioid.cdf Marcus Metzler: 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 :) ...
@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.
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.
@@alflud 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?
@@alflud 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.
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.
I am just a little younger than you, but I hated math in school because every teacher was so dry and boring, I love numbers now, where were all the people like you back then that could have spurred my curiosity much earlier in life. I love when you show your true passions and giggle about it.
When I was in school my math teachers would get together in the halls to play golf. I don't know where your math teachers came from, but mine must have busted outta tha looney bin at some point. :)
9:23 I'm a high-school maths teacher. I have taught that dumbed-down divisibility-by-9 test without going into digital-roots and the remainder property. I shall never do it again. Props to your deliciously made videos.
My maths skills have always been lacking but I find this absolutely fascinating. Just learning about digital roots, the shortcuts for dividing by nine and finding the remainders is blowing my tiny mind. I’ll probably have to watch it a few times. Yep, definitely have to watch it a few times.
math is super ez. you take a numba and you take another numba and than you do something with the numbaz to get a new numba. you can also come up with non existing numbaz to do theoretical operations with those to get theoretical numbaz. that's how I calculate how my piss moves thru our dimension into the next. it's quite ez, you just need some numbaz. now go out there and become the next Einstein. you can do it Mr. OmegeProxy!
Did you know 9 x any number (aside from a handful) all equal 9? 9 x 47 = 423. 4 + 2 + 3 = 9. Another? 9 x 285 = 2565 2 + 5 + 6 + 5 = 18. 1 + 8 = 9. This isn’t a coincidence or accident. There is purpose behind that.
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.
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.
@@marklarsen9894 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.
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.
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!!
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.
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 .
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.
I just tried it, and it got stuck in the lock. The digits aren't in the right order, so I guess it makes sense. Gonna have to go flip a coin to make a new universe and try again...
If you lose your key to the universe, call the LockPickingLawyer. He'll open it for you then he'll lock it back up and open it again just to show that it wasn't a fluke.
I noticed the matching digits as well (in a different order). I'm nowhere near smart enough to figure out if there's a connection, but it's a cool coincidence.
"A conspicuously simple and universal pattern is more likely a feature of the observer's perspective than the universe being observed." ... seems a more profound lesson than anything one could wring from an obsession over Tesla circles. Thanks!
What i found amazing about the doubling sequence is that the embryon (and all the cells ) is using this exact sequence of doubling as well as the processor architecture.
I really appreciate the fact that you spend time watching other TH-cam 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!
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.
Solution to the problem at 16:14 Start with this equation, which is true for every value of k: 5^k * 2^k = 10^k The digital root of any power of 10 is 1, so DR(5^k * 2^k) = 1 Using the multiplication rule you explained earlier, DR(DR(5^k) * DR(2^k)) = 1 In other words, DR(5^k) and DR(2^k) have to be multiplicative inverses of each other. Taking the “digital root” of an integer is equivalent to modding it by 9. (The only difference is that if DR(n) = 9, then n mod 9 = 0.) In mod-9 arithmetic, every number except for 0, 3, and 6 has a unique multiplicative inverse. Since the digital root of a power of 2 is never 3, 6, or 9, this means that DR(2^k) completely determines DR(5^k). As k increases, the value of DR(2^k) cycles as follows: 2 4 8 7 5 1 2 4 8 7 5 1 … Taking the multiplicative inverse of each number above gives the values of DR(5^k). 5 7 8 4 2 1 5 7 8 4 2 1 … So DR(2^k) and DR(5^k) cycle through the same values, but in reverse.
You don't need to evaluate all the numbers in the two cycles to check that one is the reverse of the other; 5 is the multiplicative inverse of 2, so 5^k is congruent to 2^(-k). So as k increases, it runs through the same cycle in the opposite order.
If you look at drawings from the father of geometry, Euclid was born around 300 B.C. and he has 369 theory shapes exactly like you describe all over his work. Thank you for the video we enjoyed it.
As an American born-and-raised who was in the public system as both student and teacher… our math education is disgustingly deficient in number theory. High school graduates (even some going into stem fields) do not even know the Euclidean algorithm. They have almost no experience working with modular arithmetic. Too many decades of parents complaining about this “useless” math subject has led to them and their children being mystified by the simplest of number theory diagrams. Thank you mathologer for making so much explanatory content paced for victims of the US public school number theory book banning. (Inb4 some other American tells a story about their one teacher that taught them number theory)
Yeah, every time there's an attempt to teach more theory in American math classes, a lot of parents get angry because they don't know how to help their kids with their homework. It happened with "New Math" in the '60s, and it happened with Common Core in the 2010s.
@@WarmongerGandhi Another problem with "New Math" was that it focused very strongly on the axiomatic method even in primary schools, where that isn't really appropriate. It tended to put theoretical foundations before practical examples, which is the opposite of how people normally learn math (and how it was historically developed). However, Common Core actually corrects these mistakes in a lot of way, focusing much more on comprehension and on solving problems in multiple ways. That still makes parents livid though, because now they complain "my student knows how to get the right answer, why does he have to do it a particular way? Isn't getting the right answer good enough?" As a tutor, I see these complaints all the time, and it is very frustrating. Because no, getting the right answer is definitely _not_ the point. Nobody cares if you can, say, long-divide two decimals. Your calculator will always do it faster and better. People only care if you _understand_ how the algorithm works, which most kids don't, and just following a list of instructions doesn't show you understand.
@@Dziaji you know roughly 10% of any US public school's funding comes from the federal government, right? We don't have a national education system, but the federal government still has a lot of control. Where did he even say the system was nationalized? The comment wasn't edited and I don't see what you're even talking about.
A friend and I had a driving game where we raced to see who gets the digital root from random cars' driving plates (back then the standard local driving plate contained 6 digits). Eventually I realized that 9's were inconsequential and could be ignored, immediately afterwards both of us sped up our game by "distributing" values, forming 9's and disregarding them. An example of what is our sped up mental process: 166384 = 1+8, 6+3, 6+4 = 1 I also just learned from this video that what we were doing is called Digital Root
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.
I was accused of cheating throughout grade school and really math classes in general bc I did everything in my head and writing my steps down made zero sense and would often mess me up. No work apparently means cheating instead of being logical and easy
I have looked at Math and Engineering in a longhand way until I realized that keeping things simple in the beginning will find a successful result in a physical form. Understanding is a never ending experience of relationships that is endless.
Agree. Wonderful channel. And that's how it should be done. I immediately lose respect for or won't continue listening to someone if they're acting like they're on the offensive, regardless if I think they are right or not or if they align with what I am inclined to believe. There's enough condescension and inflammatory behavior out there, plus you're not going to win any minds or hearts by acting like that, it's just pandering to people who already agree with you. Cheers.
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?
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.
@@dsdsspp7130 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.
@@captainunicode 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.
@@mathlegendno12 just search divisibily test for 11 and 7 in google you'll find it in no time. if you want to solve it yourself here is a hint: just calculate the remainders of powers of 10. here's how to do it for 11: remainder of 10^n to 11 is always 1 (if n is even) or -1 (if n is odd) example: 432 = 4*100 + 3*10 + 2*1 ===> 4 - 3 + 2 = 3 , so remainder of 432 divided by 11 is 3) so just like 9 you sum up all the digits except you have to negate every other digit with the rightmost digit being positive.
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!!
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!
@cdanielh128 The primate brain tricks itself into releasing a temporary burst of dopamine. The sensation fades and they feel worse than before. As with any drug, the rush fades as tolerance builds, as they ever increase the dosage. The anger that Mr. Webber was cultivating, starts to fester more and more until it becomes this very hate-filled and self-destructive loop seen here. That's when you realize that every hateful and ugly reply they made was that of a sad and very lonely person whom were subconsciously screaming to just be noticed. He doesn't feel any better or bigger. Never will acting like this either. I do hope @Edwin Webber gets his life all figured out and treats everyone, including strangers on the web, with respect. A little decorum can go a long way.
@@edwinwebber5776 Thats simply because you don´t understand it. That you don´t understand something doeasn´t make others anything:D Art has LITERALLY saved lives:)
As an ex Maths teacher in UK the reason this doesn't get taught is simply because it is not in the curriculum, and to actually get through the curriculum leaves no time to play with Maths, or indulge the class in whatever the teacher finds interesting or stimulating (supposing he/she has a higher understanding of Maths in the first place!).
Yes it is quite sad that the curriculum does not leave that room. I trust that Burkhard is not blaming the teachers for that! But it is quite sad that the social status of maths (and therefore the interest and learning speed of children!) is in such a deplorable state. It is something I try to battle against and especially Mathologer does a great job in this respect!
Yes , well said. The broad curriculum is the summation of alot of mankinds work of course. In the real world beyond + -* and / only a handful of the next generation actually find yearly let alone daily applications for Pythagoras, solving a quadratic or calculus. Alot of interesting math has niche applications. We can see the benefit of this , like considering the math the Rubiks cube can throw up , but we have to "weigh" this usefulness. However "casting out the 9s" IS very useful really. Take the summation of say 5 numbers all with varying decimal place information. Did you punch all the numbers into the calculator correctly ? Some calculators the information may have been lost off the screen...So using the maths here can at least apply a quick check ...
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 am a software application developer. I realized certain patterns regarding the success and stability of a software solution that actually applies to every system. It is so common that everyone is aware of them, but nobody realizes it. Every system that could possibly occur requires 3 pillars of support. It doesn't matter how simple or complex it is. In fact these 3 pillars not only support the system, but also support each other. Perhaps there is a way to expand these 3 pillars into multiple dimensions, which can easily generate highly complex systems that would likely appear chaotic. Interesting.
When I was in 8th grade back a 100 years ago😁, I remember a kid telling our math teacher about the mysterious 3-6-9 numbers! Our math teacher explained to us every single number could be magical if we deeply look for it. As a matter of fact he give us a group project assigning all different numbers to different groups to come up with the uniqueness of a particular number. By the end of the week we found out that every single number 0 to 9 can be unique and magical! So everytime I see these Tesla 369 videos, they remind me of my old math teacher!
This is linked to the following paradox. "n is the smallest positive integer which is not unique." But the very fact that it is the SMALLEST such number makes it unique!
Could be your teachers is from future to to teach you about secret code of universe, but she/he doesn't want to teach you directly to beyond our understanding because it will hurt.
Tesla didn't throw the 3-6-9 principle out there because there was anything super special about the numbers themselves, but because they correspond with certain realities about electromagnetism, waves, oscillation, vibration, spin, and curvature as found in nature. Or in other words, it's not about the bare math, but how well 3-6-9 applies in the context of physics. It's the basis of 240 VAC @ 60 cps as the most efficient formula for producing electrical power.
@Jearbearjenkins Your hindsight is just sharp as a tack. Wow. So impressive. I mean...if only you could have been there with your brilliant mind to illuminate him on electrons. Glad we didn't go forward with alternating current! Could you imagine the state of the world?! Wow-we-wowzers!
@@markomus1 Tesla also believed in the ether (already discredited back then) and said something brilliantly stupid about Einstein's curved space in 1932.
@@martingisser273 Your hindsight is just sharp as a tack. Wow. So impressive. I mean...if only you could have been there with your brilliant mind to illuminate him on the ether (which was NOT discredited universally back then OBVIOUSLY) or informed him about Einstein's curved space. Glad we didn't go forward with alternating current! Could you imagine the state of the world?! Wow-we-wowzers! I wonder what sort of scientific things YOU believe RIGHT NOW that someday will be part of someone's, "Martin Gisser also believed in blah blah blah so yeah there's that," narrative.
I was just about to write a similar comment then noticed yours. It's true that mathematicians usually either don't care about or are unable to grasp physical applications. Apart from that I did enjoy the video.
Dear Mathologer, I was not taught this pattern in school. In 3rd grade i observed the digital root pattern of multiples of 9 myself and used it for quick solving of any problems involving 9. Later in college I rediscovered this pattern and obsessed over it for a few years... What I found was very interesting and fulfilling as it relates to quotients, products, and a prime sieve. Eventually I moved to a base18 system of counting to account for the parity of digital roots, (like when a number like 31 adds up to 4, this does not account for the oddness of 31, but 13 does.) It happens then that this pattern takes a much more intuitive form when we allow for digital root as well as parity. The little "hiccups" are practically cured. At this point I've only watched half this video, but I felt like answering your question about schooling and sharing my own journey with digital root maths.
Something I was waiting for but wasn't mentioned: the horizontal symmetry, which can be explained by simply numbering the points with negative numbers going anticlockwise.
You must've been educated in u.s.! We gotta great math program right?! But no really teachers are great once you get into those higher level highschool classes. It's where the American education system actually works. Problem is you got phys. Ed majors teaching math classes at critical levels like algebra and their just not suited for the job.
That explains it. School doesn't do cool, so they nixed that lesson real quick. God forbid it be teachers and the education systems job to make learning interesting.
The connection between mathematics and physics or reality is something physicists are particularly fond of. I think one can overdo that, but underdoing it is also not good because many phenomena can be much more accurately described mathematically than with ordinary words. A balance seems to me to be the best path.
Thank God someone's finally talking about these things! I stumbled upon one of these Tesla 3 6 9 videos ages ago, and I knew that everything they said definitely wasn't magic or anything and probably had a simple explanation in number theory, but I could never put it into words myself. I'm so glad someone finally put together an understandable and informative response to those things.
Thank you! I was excatly the same, I figured it was just some base 10 shennanigans, even found the pattern was almost identical in base 8, but I don't have the education/smarts to prove anything. So they just laughed at me in the comments when I tried to explain to them.
Yeah, I did not know the "trick" in the video. But as soon as I saw it I was like "It's just a spirograph" or some other display of a function. So there is an underlying mathematical function, and it's a pretty way of displaying it. Interesting if used to show how leaves/petals form a certain shape, but just interesting and useful, not magic.
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.
Math is just an instrument, made by humans and has fallacy because the human mind cannot create anything that is perfect, we have no perfect knowledge and never we will, it's natural limit, therefore, mathematics is not better than history or philosophy when is about understanding life and the universe. Nowadays there is too much bias for math and STEM in general, a bit of brainwashing I would say. I'm happy I studied math and engineering many years ago when the academy wasn't a brainwashing institution yet.
He said it was A key to the universe not The key. Their is a very stark difference. With the work he did do, his findings with those numbers is astonishing. Limited but nothing short of astonishing.
@TrashLid Hi Trashlid, its because I read. Try some Manly P Hall, John Black and mystery school research. It was also my opinion. Certainly not a conspiracy theory. Why do 'smart' people like you whine so much instead of humility?
School and I parted ways when I was 13. I later fell for the beauty of mathematics, even more so once I learnt to read axioms and functions as dynamic realities. 15:07 the sequence just described doesn't repeat, it forms a resonance and a strange attractor for synchronicity. Translating math to experience repetition = resonance. Numbers are describing frequency.
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.
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
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 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 had an experience several years ago that led me to begin naturally perceiving some of these things. It's very intriguing to come across others who are aware of these natural/ fundamental mathematical phenomena. There's definitely something of great import to be learned or derived from this.
For a long time I've wondered about the multiplication tests using digital sums when working with systems outside of base 10. You're the first to show a proof that my hypothesis was correct. Thank you so much for this.
I believe it works with any base system above base 10 by using [system_base - 1] First time I was introduced to this type of math was a different process to verify binary divisions manually. This is also the first time I see it being used with base 10...
I have had difficulty with arithmetic since I learned to count. As a result I looked for patterns in numbers to make life easier. I learned the adding digits to find out if a number was a multiple of 3 and that a multiple of 9 always has the digits add up to 9. In fact I used a similar trick to add up a series of numbers from 1 to n by noticing that 1+n is the same sum as 2+(n-1) and so on...... I learned later in life that Gauss figured out this trick at age 9. I figured it out at age 11.
You figured out that adding 1 is the same as subtracting 1 and then adding 2? And you thought this “discovery” was a pattern that has value? At what age did you realize that all you did was prove that 1 + 1 = 2? I hope it wasn’t 10 seconds from [now].
@@Dziaji Awfully rude reply from you. This channel is focused on the study of mathematics and OP shared a happy memory of their childhood. Born in 1777, Gauss made several contributions to mathematics and OP shared a story where they made a similar mathematical discovery at a similarly young age as Gauss... From the anecdotes section on Gauss's wiki: "Another story has it that in primary school after the young Gauss misbehaved, his teacher, J.G. Büttner, gave him a task: add a list of integers in astigmatic progression; as the story is most often told, these were the numbers from 1 to 100. The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher and his assistant Martin Bartels. Gauss's presumed method was to realize that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050. However, the details of the story are at best uncertain..." Keep it real brother.
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. 😆
What perfect timing! I just remembered these claims about Vortex Math and mentioned the explanations of their patterns in the comments of a math meme about how 9 is only special due to the decimal system. :)
We are the victims of our own curiosity when we try to think objectively about mysterious phenomena. The same thing applies to alien abductions stories, sasquatch, etc. Our fascination with the unknown sometimes tricks our brains into ignoring obvious explanations. It's Sasquatch for me. I really want it to be true.
I was never taught this in elementary, middle or high school. It was until the early days of my major in maths, that proving a number is divisible by 9 if and only if the sum of its digits is was one of the easiest and prettiest exercises on divisibility we were assigned to do; that it also works for 3 is a corollary, since 9 is divisible by 3. We also were assigned to prove that a number is divisible by 11 if and only if the alternated addition/substraction of its digits is (e.g. 572 is divisible by 11, since 2-7+5=0 is); a sweet corollary was that any palindrome with an even number o digits (and some odds, e.g. 18381) is divisible by 11. It was really neat that both results sprung from the decimal expansion of any number and the whimsical fact that 10=9+1=11-1. It seemed more of a party trick than anything, until we were taught congruence in number theory; then it all made more sense.
Math is a language created to help people describe reality. Just like there is nothing special or miraculous about word association, there is nothing special or miraculous about number association. We all know how to make the calculator say BOOBS.
@@ZennExile ...And now we also know how to make a number circle draw butts. =:o} Which just demonstrates that the *real* key to the universe is... infantile body-part humour! =:o]
I don't know much about math, but that was very fascinating and quite intriguing. Thank you for the time and effort you invest in your productions they are very much appreciated and enjoyed -Thank you!💌🇨🇦
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
good to know. Nearing 60 Y.O. I still want for the learning of such things. I will look into getting a copy of that book. Thank you for sharing that knowledge.
In the US of America. As an industrial electrition. We use 3 colors for 3 phase power. You add the circute number's digits. When divied by 3. the remainder. Will tell you what color to use. If we had 9 colors. This would work as well. Bravo!
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!
@@brianwilson9828 couldn't be 1/prime. 1/2 = 0.5 has digital root 9. couldnt be base prime with the digits of 1/(b-1) either. Its always gonna be 0.11111111111. i think it's probably 1/(b+1) in whatever base. in base 10 it would make 0.090909, in base 8 it would be 0.070707, in base 16 it would be 0.0F0F0F, OP probably threw in prime numbers just to make it look more divine than it needs to be
In school we learnt the divisibility trick for 9's but it wasn't until I did a university course on number theory that I realised that when dividing by 9, the sum of digits has the same remainder as the original number. This also holds for division by 3, as 9 is divisible by 3.
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!
The number 1 is, without question, an important number in mathematics. That's why we call it the multiplicative identity. I contend that what we are seeing is a feature of the number -1. This "vortex" occurs when we choose numbers based on -1 mod n.
My favorite shape is the triangle=9top, 3bottomright, 6leftbottomright. Math is the universe along with sound, which can also be found with math👍 knowledge is power y'all 👍👍👍
When I was a kid, I learned the "casting out 9s" trick in some puzzle book (possibly by Jerome S. Meyer) my older brother had. I didn't learn why it worked until I read Martin Gardner's column about divisibility tests.
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
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.
the whole tone of this video fucking cracks me up. I love it! I learned so much and laughed along the obvious skepticism that comes with learning about these patterns from the actual math pov. Still, can't help but find it beautiful that, even though we understand it rationally, there's a degree of abstractness that is so incomprehensive for our minds that it simply feels like divine intervetion.
@@KipIngram It's most definitely mystical. There are other properties he is not discussing. And; did you notice? None of the other base models have the flip in polarity like that of 3 and 6. The others are continuous loops. The 369 does crazy things when applied to electromagnetism and such.
Edward Witten would have a soft spot for the diagram for 11 as his M theory of supergravity not only permits up to eleven dimensions but is in fact 11 is most elegant in this maximal number of dimensions. Maybe she who knows the secret of 4-7-11 knows how to continuously loop dimensions without having to unnecessarily compact them in the universe.
Similarly, if you numerize (consecutive integers beginning with 1) the alphabet, for example, A to Z corresponds from 1 to 26 And from 26 to 1 so that every letter of a word is represented by two numbers (A = 1 and 26, R = 18 and 9, T = 20 and 7); take the digital root of each of sum of the word {2: digital root 1, digital root 2}; add the digital roots; then the final digital root of the sum will always be 9. 9 is the final digital root of any word.
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.
It’s always interesting seeing how close genuine mathematics, particularly number theory, gets to numerology sometimes - the choice of base ten is essentially completely arbitrary. On a barely related topic, I would love to see a video which covers some of the bignum arithmetic algorithms, like karatsuba, toom-cook, and possibly even FFT based multiplication. We rely on these algorithms thousands of times per day for RSA in TLS, so I feel they deserve some love.
@@capturedflame Plenty of cultures have had numbering systems based on 6, 12, or 60. Even odd things like 17, 23 or 27 are not unheard of. There are other body parts than fingers one could enumerate. So, yes, base 10 is arbitrary in the sense that there are other equally valid choices that have been used. The fact that it's the dominant one today is little more than a historical accident.
@@capturedflame I mean that we have (on average) ten fingers to be pragmatic about, yes, but not because of God, destiny or some universal force, only happenstance.
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?
As someone born in Tx, I've never felt more texan than I do right this moment. I got confused by pretty art and tripped over a curb while telsa was winking and when I turned around had a knee jerk 'holy smokes! what is that-dear lord-that there ^spits tabaccy^ That there, is Maths.' I feel called out.
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
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.
In accounting, if your error in addition or subtraction is divisible by 9, it means you added one or more of the numbers with some of its digits switched. Example; if a column of numbers was added to the number 3456 but you added 3465 or 3546 or 4356 instead, the difference would be divisible by 9. So 9 'is' special, because it's everything and nothing at the same time.
Nine is one less than ten. We count in base ten. Adding nine to a number is essentially adding a 'one' to the tens column and subtracting a 'one' from the ones column.
I was experimenting with this sequence of numbers and found that if you apply the the 124875 pattern to the six lines of the I Ching, with the 3 and 6 representing yin and yang lines, you also get the same pattern with the king wen sequence as it moves through the 64 hexagrams.
Yeah because liking something tends to lead with playing with it. I never liked math. I could do some of it and I realised its importance. Mostly it bored me. I like more applied things. Of course there is applications for math but we all tend to find a way to work it out when we need to somehow.
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?"
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.
@@KnakuanaRka 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.
Thank you.👊🏼 I like answers. Long as I can remember, 3 has been my "spirit number" (?) When first hearing the rules and eccentricities of 9, my brain farted, "hmmm... does base 10 have anything to with this?" Now i know! 👍🏼🤸🏾♀ (Anybody else get Spirograph flashbacks at the beginning???)
16:20 In short, multiplying by 5 reverses the repeating sequence of digital roots and there's nothing in the argument that says you can't keep halving after 1. Dividing/multiplying a number by 10 doesn't change it's digital root because it doesn't add any non-zero digits to it's decimal representation. Halving is the same as multiplying by 5 and then dividing by 10. The digital root of 5 times a number is the digital root of half that number as can be seen in the following: In symbols, DR(n) = DR(10*n). Also DR(1) = 1. It follows that DR(1/2) = DR((1/2)*10) = DR((1/2)*2*5) = DR(1*5) = DR(5) and more generally DR((1/2)*n) = DR((1/2)*10*n) = DR((1/2)*2*5*n) = DR(1*5*n) = DR(5*n) which entails DR((1/2)^i) = DR(5^i).
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
@@Shoshana-xh6hc 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.
When you apply vortex based math to polygrams you see similar patterns form. Polygrams are a function of ratios so regardless what base number system you use the vortex pattern still emerges. The vortex patterns in nature are the result of similar ratios creating vortex patterns. Just because our base 10 system has some neat aspects does not discount the patterns that are inherent in the ratios of natural vortices.
Great way looking outside in. Vortex . Universe and natural vortex i gracious bow away. I am a speck of star 🌟 dust in a hugh Universe. Just a wonderful way of explaining adding to the video, here..🏁
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?
@@LostArchivist it’s a joke. What I meant is that Mother Nature has laid out the pattern for life. They are sometimes laid down by mathematical formulas carved within their being. Otherwise humans sometime make their own make carvings, and are bound by illusion to worship it.
As any French student at that time, I was taught the "casting the nine" ("preuve par neuf") when I was 7 or 8 years old. We used it all the time to check the results. I remember I was very confused and upset when I got the wrong result but the "casting the nine" test did not... I was probably off by nine, or I had interverted two digits, that I don't remember.
I am officially dissolutioned. I remember the Tesla 3-6-9 story for years. Thank you for demystifying this…. But every time you said “nine” I would scream “NEIN!”, and that made it hard to follow because you say nine a lot in this one
In relation to 3-6-9. Ken Wheeler made an experiment with molten bismuth cooling down over a powerful magnet. He predicted that the cooled metal would exhibit "bubbled cavities" at the extremities of the puck in this triangular, 369, formation. For those interested, I recommend.
Yes, they really are quite beautiful. Beautiful complexity arising from super-simple origins. The logistic equation similarly leads you into incredible complexity, and yet it's an amazingly simple equation.
(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: theadamabrams.com/modularmultiplication
Ed Collen: vortex-rho.vercel.app/
Andrew “Ash Mystic” Herman: codepen.io/hippiefuturist/full/NrvqgZ (check out the preset animations on this one. Also check out his fractal tree generator codepen.io/hippiefuturist/full/KRromj )
Man Hin Li: mandelbrot.vercel.app
Liam Applebe: tiusic.com/vortex.html
Owen Bechtel: owenbechtel.com/games/times-tables/
William Ward: scratch.mit.edu/projects/647469837/
Артём Маевский: tinyurl.com/yc8danxx
Baxi: baxi-codes.github.io/mathologer-vortex/
Marc Donis: madc0w.github.io/cardioid/
Rafael Castro Couto: codepen.io/rafaelcastrocouto/pen/KKyoKWm
Laurent Bucher: anceps.net/modularTimesTables.html
Hannes Wendt: htts://math.wendt.sbs/vertex
Hugo Cardoza: Code in p5js editor.p5js.org/hugomosh/sketches/1Sg1NxqI7
john Schoeman: www.doodles.camp/#/doodles/modular-times-table
Banjamin Elo: bnelo12.github.io/vortex-math/
Joe Lucette: jluqu.github.io/modmult.html
Federico Marotta: federico-marotta.shinyapps.io/tesla_vortex
T3CHN01200: victorsohier.github.io/
Tom DeRensis: github.com/tderensis/ModularTimesTableJavascript
Ehsan Kia: ehsankia.com/cjs/vortex
Jayson Vivet: www.geogebra.org/m/cufneprj
Tyler Wolfe-Adam: mathologer-vortex-app.herokuapp.com/
Andrea Coletta: mathologer-modular-time-table.lm.r.appspot.com/app
Mathis Aaserud: sirkular.ispaceyourtube.com/
Justin Kirk: intern-jck.github.io/vortex-math/
Jarred Branch: no online version
Álvaro Silva: mathlogervortexalvaro.web.app/
Rafael Castro Couto: codepen.io/rafaelcastrocouto/pen/KKyoKWm
planck_cst: www.jerpint.io/blog/mathologer-challenge/
Anton Shcherbinin: ch.ant-on.net/modulo/moire?p=1009&m=303
Cristian Merighi: js.pacem.it/2d/vortex
Krischna-Gabriel Schulz: no online version
András Kirisics: kiri-mathologer-vortex.web.app/
relikd: relikd.github.io/Vortex-Math/
Eclectic Gamer: th-cam.com/video/n_YLB0ncbpI/w-d-xo.html (Video on using Blender and Geometry nodes to make these diagrams)
Some existing implementations of the modular times table diagrams:
Aymeric Ramiere: www.aymericramiere.com/others_modular.html
Steve Phelps: www.geogebra.org/m/z8wrdret#material/dqKkQEv7
I did this a while ago: www.qedcat.com/cardioid.cdf
Marcus Metzler: 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 :)
...
@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.
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.
@@alflud 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?
@@alflud
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.
@@alflud
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.
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.
I am just a little younger than you, but I hated math in school because every teacher was so dry and boring, I love numbers now, where were all the people like you back then that could have spurred my curiosity much earlier in life. I love when you show your true passions and giggle about it.
When I was in school my math teachers would get together in the halls to play golf. I don't know where your math teachers came from, but mine must have busted outta tha looney bin at some point. :)
@@Nefylymlol I’m surprised they knew how to hold a golf stick, mine were taking tea while we were all out in the pouring down rain , oh the memories
im going through this right now!!
This a common belief system since the very beginning. Many know, most find it boring 😴
9:23
I'm a high-school maths teacher. I have taught that dumbed-down divisibility-by-9 test without going into digital-roots and the remainder property. I shall never do it again. Props to your deliciously made videos.
My maths skills have always been lacking but I find this absolutely fascinating. Just learning about digital roots, the shortcuts for dividing by nine and finding the remainders is blowing my tiny mind. I’ll probably have to watch it a few times.
Yep, definitely have to watch it a few times.
math is super ez. you take a numba and you take another numba and than you do something with the numbaz to get a new numba. you can also come up with non existing numbaz to do theoretical operations with those to get theoretical numbaz. that's how I calculate how my piss moves thru our dimension into the next. it's quite ez, you just need some numbaz. now go out there and become the next Einstein. you can do it Mr. OmegeProxy!
I respect you for that! May you have a life full of learning my friend
Did you know 9 x any number (aside from a handful) all equal 9? 9 x 47 = 423. 4 + 2 + 3 = 9. Another? 9 x 285 = 2565 2 + 5 + 6 + 5 = 18. 1 + 8 = 9. This isn’t a coincidence or accident. There is purpose behind that.
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.
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.
@@marklarsen9894 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.
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
@@cecilyschneider3631 epic, show me them lol
@@surferxblood isn't every other video the ones saying they're the secret to the 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!!
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.
@@BezalElle tell me too!
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.
@@watwthmot I had forgotten about it until I read your post, but in accounting some similar process was used.
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 .
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.
Division by 7 always produces 142857. Spare key to the Universe, if you lost the master copy
I just tried it, and it got stuck in the lock. The digits aren't in the right order, so I guess it makes sense. Gonna have to go flip a coin to make a new universe and try again...
Yeah, they’re in the same order, just starting in a different location in the sequence.
If you lose your key to the universe, call the LockPickingLawyer. He'll open it for you then he'll lock it back up and open it again just to show that it wasn't a fluke.
I noticed the matching digits as well (in a different order). I'm nowhere near smart enough to figure out if there's a connection, but it's a cool coincidence.
Wait, are you assuming that base ten is a fundamental part of the universe…?
"A conspicuously simple and universal pattern is more likely a feature of the observer's perspective than the universe being observed." ... seems a more profound lesson than anything one could wring from an obsession over Tesla circles. Thanks!
Great quote! Who said it?
"an obsession over Tesla circles"
So we are going use quotes as math proofs from now on?
Observer and object are both parts of the same totality.
now prove it.
What i found amazing about the doubling sequence is that the embryon (and all the cells ) is using this exact sequence of doubling as well as the processor architecture.
I really appreciate the fact that you spend time watching other TH-cam 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!
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.
Solution to the problem at 16:14
Start with this equation, which is true for every value of k:
5^k * 2^k = 10^k
The digital root of any power of 10 is 1, so
DR(5^k * 2^k) = 1
Using the multiplication rule you explained earlier,
DR(DR(5^k) * DR(2^k)) = 1
In other words, DR(5^k) and DR(2^k) have to be multiplicative inverses of each other.
Taking the “digital root” of an integer is equivalent to modding it by 9. (The only difference is that if DR(n) = 9, then n mod 9 = 0.) In mod-9 arithmetic, every number except for 0, 3, and 6 has a unique multiplicative inverse. Since the digital root of a power of 2 is never 3, 6, or 9, this means that DR(2^k) completely determines DR(5^k).
As k increases, the value of DR(2^k) cycles as follows:
2 4 8 7 5 1 2 4 8 7 5 1 …
Taking the multiplicative inverse of each number above gives the values of DR(5^k).
5 7 8 4 2 1 5 7 8 4 2 1 …
So DR(2^k) and DR(5^k) cycle through the same values, but in reverse.
Looks good :)
You don't need to evaluate all the numbers in the two cycles to check that one is the reverse of the other;
5 is the multiplicative inverse of 2, so 5^k is congruent to 2^(-k). So as k increases, it runs through the same cycle in the opposite order.
If you look at drawings from the father of geometry, Euclid was born around 300 B.C. and he has 369 theory shapes exactly like you describe all over his work. Thank you for the video we enjoyed it.
As an American born-and-raised who was in the public system as both student and teacher… our math education is disgustingly deficient in number theory.
High school graduates (even some going into stem fields) do not even know the Euclidean algorithm. They have almost no experience working with modular arithmetic.
Too many decades of parents complaining about this “useless” math subject has led to them and their children being mystified by the simplest of number theory diagrams.
Thank you mathologer for making so much explanatory content paced for victims of the US public school number theory book banning.
(Inb4 some other American tells a story about their one teacher that taught them number theory)
Yeah, every time there's an attempt to teach more theory in American math classes, a lot of parents get angry because they don't know how to help their kids with their homework. It happened with "New Math" in the '60s, and it happened with Common Core in the 2010s.
@@WarmongerGandhi Another problem with "New Math" was that it focused very strongly on the axiomatic method even in primary schools, where that isn't really appropriate. It tended to put theoretical foundations before practical examples, which is the opposite of how people normally learn math (and how it was historically developed). However, Common Core actually corrects these mistakes in a lot of way, focusing much more on comprehension and on solving problems in multiple ways. That still makes parents livid though, because now they complain "my student knows how to get the right answer, why does he have to do it a particular way? Isn't getting the right answer good enough?"
As a tutor, I see these complaints all the time, and it is very frustrating. Because no, getting the right answer is definitely _not_ the point. Nobody cares if you can, say, long-divide two decimals. Your calculator will always do it faster and better. People only care if you _understand_ how the algorithm works, which most kids don't, and just following a list of instructions doesn't show you understand.
You were a math teacher in the US and think the US has a national education system? Did you think you were a federal employee or what?
@@Dziaji you know roughly 10% of any US public school's funding comes from the federal government, right? We don't have a national education system, but the federal government still has a lot of control.
Where did he even say the system was nationalized? The comment wasn't edited and I don't see what you're even talking about.
I'm a high school senior taking discrete mathematics at UC Berkeley. I just learned the Euclidean Algorithm.
A friend and I had a driving game where we raced to see who gets the digital root from random cars' driving plates (back then the standard local driving plate contained 6 digits). Eventually I realized that 9's were inconsequential and could be ignored, immediately afterwards both of us sped up our game by "distributing" values, forming 9's and disregarding them.
An example of what is our sped up mental process: 166384 = 1+8, 6+3, 6+4 = 1
I also just learned from this video that what we were doing is called Digital Root
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.
seriously, you can do this in your head? I'm soooo phuked in the head with math! I'm jealous of everyone here in this lobby!
I was accused of cheating throughout grade school and really math classes in general bc I did everything in my head and writing my steps down made zero sense and would often mess me up. No work apparently means cheating instead of being logical and easy
he he!
@@Just10_Dime Agreed! Hell , it took me longer to "show my work" than it did to just do the problem... smh
Glad you said that. In the 1950s I couldn't learn long-division too, as I could do it in my head.
I have looked at Math and Engineering in a longhand way until I realized that keeping things simple in the beginning will find a successful result in a physical form. Understanding is a never ending experience of relationships that is endless.
He use 3 6 9 using an equal number as 5 then using -3 -6 -9. Now use an -5 as the equal number
I think this is the kindest, most conscientious debunking of mathematical mysticism I've ever seen. I love this channel so much lol
Agree. Wonderful channel. And that's how it should be done. I immediately lose respect for or won't continue listening to someone if they're acting like they're on the offensive, regardless if I think they are right or not or if they align with what I am inclined to believe. There's enough condescension and inflammatory behavior out there, plus you're not going to win any minds or hearts by acting like that, it's just pandering to people who already agree with you. Cheers.
You should get out more. 🤓
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?
why do you people talk like that
@@peaceenjoyer sorry, talk like what? I'd love to discuss the content in the video, I think I'm just missing some context
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.
@@dsdsspp7130 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.
@@captainunicode Out of curiosity what's the answer?
@@captainunicode 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.
@@mathlegendno12 just search divisibily test for 11 and 7 in google you'll find it in no time.
if you want to solve it yourself here is a hint:
just calculate the remainders of powers of 10. here's how to do it for 11:
remainder of 10^n to 11 is always 1 (if n is even) or -1 (if n is odd)
example: 432 = 4*100 + 3*10 + 2*1 ===> 4 - 3 + 2 = 3 , so remainder of 432 divided by 11 is 3)
so just like 9 you sum up all the digits except you have to negate every other digit with the rightmost digit being positive.
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!!
Thank you for your clear, intuitive, and expansive explanations, illustrations, and wry sense of humor!
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!
Math should never be optional in school. It is always the most important discipline and the basis of all else (including art).
I chose math. I always felt art was just welfare for idiots.
@@edwinwebber5776 If that makes you feel like a bigger person go for it.
@cdanielh128
The primate brain tricks itself into releasing a temporary burst of dopamine. The sensation fades and they feel worse than before.
As with any drug, the rush fades as tolerance builds, as they ever increase the dosage.
The anger that Mr. Webber was cultivating, starts to fester more and more until it becomes this very hate-filled and self-destructive loop seen here.
That's when you realize that every hateful and ugly reply they made was that of a sad and very lonely person whom were subconsciously screaming to just be noticed.
He doesn't feel any better or bigger. Never will acting like this either.
I do hope @Edwin Webber gets his life all figured out and treats everyone, including strangers on the web, with respect. A little decorum can go a long way.
@@edwinwebber5776 Thats simply because you don´t understand it. That you don´t understand something doeasn´t make others anything:D Art has LITERALLY saved lives:)
As an ex Maths teacher in UK the reason this doesn't get taught is simply because it is not in the curriculum, and to actually get through the curriculum leaves no time to play with Maths, or indulge the class in whatever the teacher finds interesting or stimulating (supposing he/she has a higher understanding of Maths in the first place!).
All hail lord curriculum
@Chris Lauden I agree.
Yes it is quite sad that the curriculum does not leave that room. I trust that Burkhard is not blaming the teachers for that!
But it is quite sad that the social status of maths (and therefore the interest and learning speed of children!) is in such a deplorable state. It is something I try to battle against and especially Mathologer does a great job in this respect!
Yes , well said. The broad curriculum is the summation of alot of mankinds work of course. In the real world beyond + -* and / only a handful of the next generation actually find yearly let alone daily applications for Pythagoras, solving a quadratic or calculus. Alot of interesting math has niche applications. We can see the benefit of this , like considering the math the Rubiks cube can throw up , but we have to "weigh" this usefulness.
However "casting out the 9s" IS very useful really. Take the summation of say 5 numbers all with varying decimal place information. Did you punch all the numbers into the calculator correctly ? Some calculators the information may have been lost off the screen...So using the maths here can at least apply a quick check ...
Math teachers be two weeks behind one week after class starts
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 am a software application developer. I realized certain patterns regarding the success and stability of a software solution that actually applies to every system. It is so common that everyone is aware of them, but nobody realizes it. Every system that could possibly occur requires 3 pillars of support. It doesn't matter how simple or complex it is. In fact these 3 pillars not only support the system, but also support each other. Perhaps there is a way to expand these 3 pillars into multiple dimensions, which can easily generate highly complex systems that would likely appear chaotic. Interesting.
I’m doing that with acupuncture
When I was in 8th grade back a 100 years ago😁, I remember a kid telling our math teacher about the mysterious 3-6-9 numbers! Our math teacher explained to us every single number could be magical if we deeply look for it. As a matter of fact he give us a group project assigning all different numbers to different groups to come up with the uniqueness of a particular number. By the end of the week we found out that every single number 0 to 9 can be unique and magical! So everytime I see these Tesla 369 videos, they remind me of my old math teacher!
This is linked to the following paradox. "n is the smallest positive integer which is not unique." But the very fact that it is the SMALLEST such number makes it unique!
Could be your teachers is from future to to teach you about secret code of universe, but she/he doesn't want to teach you directly to beyond our understanding because it will hurt.
@@kingki1953 there is no secret code for the universe! We are here for no reasons, just a result of a freak accident called the big bang!
@@mooneymooney251 our unknowledgeable is the secret of universe
Tesla didn't throw the 3-6-9 principle out there because there was anything super special about the numbers themselves, but because they correspond with certain realities about electromagnetism, waves, oscillation, vibration, spin, and curvature as found in nature. Or in other words, it's not about the bare math, but how well 3-6-9 applies in the context of physics. It's the basis of 240 VAC @ 60 cps as the most efficient formula for producing electrical power.
Exactly, he says he wants to debunk it but then doesn't talk at all about the relationship between the 3 numbers what so ever
@Jearbearjenkins Your hindsight is just sharp as a tack. Wow. So impressive. I mean...if only you could have been there with your brilliant mind to illuminate him on electrons. Glad we didn't go forward with alternating current! Could you imagine the state of the world?! Wow-we-wowzers!
@@markomus1 Tesla also believed in the ether (already discredited back then) and said something brilliantly stupid about Einstein's curved space in 1932.
@@martingisser273 Your hindsight is just sharp as a tack. Wow. So impressive. I mean...if only you could have been there with your brilliant mind to illuminate him on the ether (which was NOT discredited universally back then OBVIOUSLY) or informed him about Einstein's curved space. Glad we didn't go forward with alternating current! Could you imagine the state of the world?! Wow-we-wowzers!
I wonder what sort of scientific things YOU believe RIGHT NOW that someday will be part of someone's, "Martin Gisser also believed in blah blah blah so yeah there's that," narrative.
I was just about to write a similar comment then noticed yours. It's true that mathematicians usually either don't care about or are unable to grasp physical applications. Apart from that I did enjoy the video.
Dear Mathologer, I was not taught this pattern in school. In 3rd grade i observed the digital root pattern of multiples of 9 myself and used it for quick solving of any problems involving 9. Later in college I rediscovered this pattern and obsessed over it for a few years... What I found was very interesting and fulfilling as it relates to quotients, products, and a prime sieve. Eventually I moved to a base18 system of counting to account for the parity of digital roots, (like when a number like 31 adds up to 4, this does not account for the oddness of 31, but 13 does.) It happens then that this pattern takes a much more intuitive form when we allow for digital root as well as parity. The little "hiccups" are practically cured.
At this point I've only watched half this video, but I felt like answering your question about schooling and sharing my own journey with digital root maths.
I was, but not by a teacher. My best friend in school showed me. He is a cpa now, and the only reason I passed trig.
God bless numbers / patterns are in many things
If you explained this on some casual Math blog I would read it.
Have you published any literature around base 18 mathematics? I'm intrigued by the concept and have been looking into it myself when time permits.
@@Frankenstein786 I'm only a hobby mathematician, so no I have not published.
Something I was waiting for but wasn't mentioned: the horizontal symmetry, which can be explained by simply numbering the points with negative numbers going anticlockwise.
I was actually waiting for it as well
I wasn't even taught the divisibility test, let alone the remainder function! This is really cool!
You must've been educated in u.s.! We gotta great math program right?! But no really teachers are great once you get into those higher level highschool classes. It's where the American education system actually works. Problem is you got phys. Ed majors teaching math classes at critical levels like algebra and their just not suited for the job.
This reminded me a very old way to prove something called *9 prove* were we subtract 9.... details were gone
That explains it. School doesn't do cool, so they nixed that lesson real quick. God forbid it be teachers and the education systems job to make learning interesting.
Same :(
My 7th grade teacher taught us about the divisibility test and I've used it ever since for division by 9 and 3.
Man, I was never taught the divisibility test. Christ almighty that would have saved so much time.
The connection between mathematics and physics or reality is something physicists are particularly fond of. I think one can overdo that, but underdoing it is also not good because many phenomena can be much more accurately described mathematically than with ordinary words. A balance seems to me to be the best path.
Does it make you wonder that we are in a simulation ?
Thank God someone's finally talking about these things! I stumbled upon one of these Tesla 3 6 9 videos ages ago, and I knew that everything they said definitely wasn't magic or anything and probably had a simple explanation in number theory, but I could never put it into words myself. I'm so glad someone finally put together an understandable and informative response to those things.
But I believe that the root cause is simply using 10 as base is quite intuitive. As 10 is an arbitary choice, the whole stuff is nothing general
Thank you! I was excatly the same, I figured it was just some base 10 shennanigans, even found the pattern was almost identical in base 8, but I don't have the education/smarts to prove anything. So they just laughed at me in the comments when I tried to explain to them.
Maybe the real conclusion is that number theory is magic.
Yeah, I did not know the "trick" in the video. But as soon as I saw it I was like "It's just a spirograph" or some other display of a function. So there is an underlying mathematical function, and it's a pretty way of displaying it. Interesting if used to show how leaves/petals form a certain shape, but just interesting and useful, not magic.
Sumerians used base 60
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
Math is just an instrument, made by humans and has fallacy because the human mind cannot create anything that is perfect, we have no perfect knowledge and never we will, it's natural limit, therefore, mathematics is not better than history or philosophy when is about understanding life and the universe. Nowadays there is too much bias for math and STEM in general, a bit of brainwashing I would say. I'm happy I studied math and engineering many years ago when the academy wasn't a brainwashing institution yet.
um maths is a numeric philosophy that can only tell you anything about the model, rather than reality itself.
@@thetimeisland850 thats what you think
@@arthurw1604 thats what i philosophise! it is also technically true. Math can only prove its own internal models, never reality.
He said it was A key to the universe not The key. Their is a very stark difference. With the work he did do, his findings with those numbers is astonishing. Limited but nothing short of astonishing.
Bruh
Pythagoras who was a messianic type figure had this all nailed down in the mystery schools and i think Tesla got his knowledge from the same source
@TrashLid Hi Trashlid, its because I read. Try some Manly P Hall, John Black and mystery school research. It was also my opinion. Certainly not a conspiracy theory. Why do 'smart' people like you whine so much instead of humility?
Mathematicians have a sence of humor...? Who knew...?
Ja ja 😏
School and I parted ways when I was 13. I later fell for the beauty of mathematics, even more so once I learnt to read axioms and functions as dynamic realities.
15:07 the sequence just described doesn't repeat, it forms a resonance and a strange attractor for synchronicity.
Translating math to experience repetition = resonance. Numbers are describing frequency.
BINGO!
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'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 love this .
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 believe humanities savoir is outside the realm of physics
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 was not taught any of this math in school (as far as I can remember). This is so exciting! Thank you so much for your efforts and sharing them!
I had an experience several years ago that led me to begin naturally perceiving some of these things. It's very intriguing to come across others who are aware of these natural/ fundamental mathematical phenomena. There's definitely something of great import to be learned or derived from this.
For a long time I've wondered about the multiplication tests using digital sums when working with systems outside of base 10. You're the first to show a proof that my hypothesis was correct. Thank you so much for this.
I believe it works with any base system above base 10 by using [system_base - 1]
First time I was introduced to this type of math was a different process to verify binary divisions manually. This is also the first time I see it being used with base 10...
I didn't learn the "remainder rule" in school, but I discovered it on my own and it blew my little mind
I have had difficulty with arithmetic since I learned to count. As a result I looked for patterns in numbers to make life easier. I learned the adding digits to find out if a number was a multiple of 3 and that a multiple of 9 always has the digits add up to 9. In fact I used a similar trick to add up a series of numbers from 1 to n by noticing that 1+n is the same sum as 2+(n-1) and so on...... I learned later in life that Gauss figured out this trick at age 9. I figured it out at age 11.
You figured out that adding 1 is the same as subtracting 1 and then adding 2? And you thought this “discovery” was a pattern that has value? At what age did you realize that all you did was prove that 1 + 1 = 2? I hope it wasn’t 10 seconds from [now].
@@Dziaji Awfully rude reply from you. This channel is focused on the study of mathematics and OP shared a happy memory of their childhood. Born in 1777, Gauss made several contributions to mathematics and OP shared a story where they made a similar mathematical discovery at a similarly young age as Gauss...
From the anecdotes section on Gauss's wiki: "Another story has it that in primary school after the young Gauss misbehaved, his teacher, J.G. Büttner, gave him a task: add a list of integers in astigmatic progression; as the story is most often told, these were the numbers from 1 to 100. The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher and his assistant Martin Bartels. Gauss's presumed method was to realize that pairwise addition of terms from opposite ends of the list yielded identical intermediate sums: 1 + 100 = 101, 2 + 99 = 101, 3 + 98 = 101, and so on, for a total sum of 50 × 101 = 5050. However, the details of the story are at best uncertain..."
Keep it real brother.
Nobody tell Dziaji how much of mathematics is secretly adding zero or multiplying by one in clever ways...
@@dustinbird2090 I was joking. No need to copy pasta the entire encyclopedia.
@QuantumMan12 I understood what he was saying. That's a big r/whooosh for you my man.
Literally the first video in a long time I actually had to listen to at normal speed my man should be an auctioneer lmao
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. 😆
What perfect timing! I just remembered these claims about Vortex Math and mentioned the explanations of their patterns in the comments of a math meme about how 9 is only special due to the decimal system. :)
We are the victims of our own curiosity when we try to think objectively about mysterious phenomena. The same thing applies to alien abductions stories, sasquatch, etc. Our fascination with the unknown sometimes tricks our brains into ignoring obvious explanations.
It's Sasquatch for me. I really want it to be true.
I was never taught this in elementary, middle or high school. It was until the early days of my major in maths, that proving a number is divisible by 9 if and only if the sum of its digits is was one of the easiest and prettiest exercises on divisibility we were assigned to do; that it also works for 3 is a corollary, since 9 is divisible by 3. We also were assigned to prove that a number is divisible by 11 if and only if the alternated addition/substraction of its digits is (e.g. 572 is divisible by 11, since 2-7+5=0 is); a sweet corollary was that any palindrome with an even number o digits (and some odds, e.g. 18381) is divisible by 11. It was really neat that both results sprung from the decimal expansion of any number and the whimsical fact that 10=9+1=11-1. It seemed more of a party trick than anything, until we were taught congruence in number theory; then it all made more sense.
Math is a language created to help people describe reality. Just like there is nothing special or miraculous about word association, there is nothing special or miraculous about number association. We all know how to make the calculator say BOOBS.
This hurt my brain
@@ZennExile ...And now we also know how to make a number circle draw butts. =:o}
Which just demonstrates that the *real* key to the universe is... infantile body-part humour! =:o]
@@therealpbristow now yer gettin it.
I don't know much about math, but that was very fascinating and quite intriguing. Thank you for the time and effort you invest in your productions they are very much appreciated and enjoyed -Thank you!💌🇨🇦
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
Share that book with me
good to know. Nearing 60 Y.O. I still want for the learning of such things. I will look into getting a copy of that book. Thank you for sharing that knowledge.
Please could you also share that book with me?
Where can we get the book?
@@TK-sx4fr I would assume that this book has been out of print for decades, and I have no idea how easy or hard it may be to find.
What a hero this guy was. It's to bad we don't have someone like him around these days?
We do but they are either silenced or don't have the resources to get the knowledge out
@@02SplinterCell02 Could you imagine if Tesla had a TH-cam channel today?!
@@malayaleeking he would have died of a sudden heart attack before his channel got to 10 subscribers
Thank you for maintaining such a commendable pedagogical level in your videos.
this guy is awesome..wonder the accent?
In the US of America. As an industrial electrition. We use 3 colors for 3 phase power. You add the circute number's digits. When divied by 3. the remainder. Will tell you what color to use. If we had 9 colors. This would work as well. Bravo!
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!
If you take the inverses of the prime numbers, the sum of the digits also always adds to 9 (b - 1)
What is "inverse"? what is "prime numbers" what is "sum" what is "(9(b-1)?
@@brianwilson9828 couldn't be 1/prime. 1/2 = 0.5 has digital root 9.
couldnt be base prime with the digits of 1/(b-1) either. Its always gonna be 0.11111111111.
i think it's probably 1/(b+1) in whatever base. in base 10 it would make 0.090909, in base 8 it would be 0.070707, in base 16 it would be 0.0F0F0F, OP probably threw in prime numbers just to make it look more divine than it needs to be
In school we learnt the divisibility trick for 9's but it wasn't until I did a university course on number theory that I realised that when dividing by 9, the sum of digits has the same remainder as the original number. This also holds for division by 3, as 9 is divisible by 3.
What does this even mean?
Those videos are excellent to see just before bedtime
they are but I also usually end up staying up late and trying stuff out 😆
It's those diagrams and cool connections that make me love number theory. Please do more number theory videos.
Had an incredibly rough week, this was precisely the pick me up I needed!
The vortex is just the formula for calculating counter frequencies. It's really interesting what vibrations can do...
That's mind blowing 🤯 I really didn't want the video to end. Thank you so much 👍
Ive never understood math i would literally pound my head but you have helped me more in minutes than my teachers did in years
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
The number 1 is, without question, an important number in mathematics. That's why we call it the multiplicative identity. I contend that what we are seeing is a feature of the number -1. This "vortex" occurs when we choose numbers based on -1 mod n.
My favorite shape is the triangle=9top, 3bottomright, 6leftbottomright. Math is the universe along with sound, which can also be found with math👍 knowledge is power y'all 👍👍👍
When I was a kid, I learned the "casting out 9s" trick in some puzzle book (possibly by Jerome S. Meyer) my older brother had. I didn't learn why it worked until I read Martin Gardner's column about divisibility tests.
Right after you explained vortex, first thing that came to my mind was "Would it work the same in another number system?" .
I am intrigued.
I'm surprised how many people commenting under this video had the same initial thought. The video conveniently addresses this question at 16:30.
@@lvince4910 I know it does!
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
If we write in Base 9k+1, then our number and its digital sum would have the same reminder when divided by 9.
Yeah, that was rather trivial for a mathematician (or serious student of mathematics), being a 1st semester question in a homework.
"not being integral" ? What do you mean by that ?
@@nicholasleclerc1583 Not a whole number integer?
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.
the whole tone of this video fucking cracks me up. I love it! I learned so much and laughed along the obvious skepticism that comes with learning about these patterns from the actual math pov. Still, can't help but find it beautiful that, even though we understand it rationally, there's a degree of abstractness that is so incomprehensive for our minds that it simply feels like divine intervetion.
You know this man is the real deal when TH-cam’s subtitles gets it right
This didn't ruin vortex maths for me, just made it much more interesting and expansive
It *is* interesting, without a doubt. Just not... "mystical."
@@KipIngram It's most definitely mystical. There are other properties he is not discussing. And; did you notice? None of the other base models have the flip in polarity like that of 3 and 6. The others are continuous loops. The 369 does crazy things when applied to electromagnetism and such.
Edward Witten would have a soft spot for the diagram for 11 as his M theory of supergravity not only permits up to eleven dimensions but is in fact 11 is most elegant in this maximal number of dimensions. Maybe she who knows the secret of 4-7-11 knows how to continuously loop dimensions without having to unnecessarily compact them in the universe.
Similarly, if you numerize (consecutive integers beginning with 1) the alphabet, for example, A to Z corresponds from 1 to 26 And from 26 to 1 so that every letter of a word is represented by two numbers (A = 1 and 26, R = 18 and 9, T = 20 and 7); take the digital root of each of sum of the word {2: digital root 1, digital root 2}; add the digital roots; then the final digital root of the sum will always be 9. 9 is the final digital root of any word.
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.
Same here, Germany, late 70s before pocket calculators were commonly available.
It’s always interesting seeing how close genuine mathematics, particularly number theory, gets to numerology sometimes - the choice of base ten is essentially completely arbitrary.
On a barely related topic, I would love to see a video which covers some of the bignum arithmetic algorithms, like karatsuba, toom-cook, and possibly even FFT based multiplication. We rely on these algorithms thousands of times per day for RSA in TLS, so I feel they deserve some love.
"Once you abandon scientific rigor, you're no longer a mathematician--you're a numerologist!"
From the movie Pi.
+1 to a vid on Karatsuba / Toom-Cook / FFT.
@@capturedflame Arbitrary in a universal, cosmic sense dear, we just happen to have ten fingers, on average, as a species, due to evolution.
@@capturedflame Plenty of cultures have had numbering systems based on 6, 12, or 60. Even odd things like 17, 23 or 27 are not unheard of. There are other body parts than fingers one could enumerate. So, yes, base 10 is arbitrary in the sense that there are other equally valid choices that have been used. The fact that it's the dominant one today is little more than a historical accident.
@@capturedflame I mean that we have (on average) ten fingers to be pragmatic about, yes, but not because of God, destiny or some universal force, only happenstance.
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?
As someone born in Tx, I've never felt more texan than I do right this moment. I got confused by pretty art and tripped over a curb while telsa was winking and when I turned around had a knee jerk 'holy smokes! what is that-dear lord-that there ^spits tabaccy^ That there, is Maths.' I feel called out.
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
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.
Try doing the 2x, 5/ in base 12 and see if the trick still holds.
In accounting, if your error in addition or subtraction is divisible by 9, it means you added one or more of the numbers with some of its digits switched. Example; if a column of numbers was added to the number 3456 but you added 3465 or 3546 or 4356 instead, the difference would be divisible by 9. So 9 'is' special, because it's everything and nothing at the same time.
Nine is one less than ten. We count in base ten. Adding nine to a number is essentially adding a 'one' to the tens column and subtracting a 'one' from the ones column.
Wonderfully narrated and illustrated. Your channel is quite addictive! Thank you for your efforts, more please !
On behalf on everyone like me who tried hard to grasp what you're exposing us to, thank you.
I recommend everyone to find the forbidden book titled Whispers of Manifestation on borlest it goes deep into all of this, and it changed my life
Another bot commenting this capitalist book? Tesla wanted to give free energy to the world and cast light in dark places.
Bro stop the scam
Yo fr stop it
Forbidden?😂
How did it change your life?
I was experimenting with this sequence of numbers and found that if you apply the the 124875 pattern to the six lines of the I Ching, with the 3 and 6 representing yin and yang lines, you also get the same pattern with the king wen sequence as it moves through the 64 hexagrams.
There is a correlation between liking maths and being able to do maths. If only my maths teachers had known this.
Yeah because liking something tends to lead with playing with it. I never liked math. I could do some of it and I realised its importance. Mostly it bored me. I like more applied things. Of course there is applications for math but we all tend to find a way to work it out when we need to somehow.
@@Garycarlyle I agree!
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.
@@OldManShoutsAtCloudsThe way mathematical equations like those in physics work are not dependent on the base used to display the numbers.
@@KnakuanaRka 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.
Thank you.👊🏼 I like answers. Long as I can remember, 3 has been my "spirit number" (?) When first hearing the rules and eccentricities of 9, my brain farted, "hmmm... does base 10 have anything to with this?" Now i know! 👍🏼🤸🏾♀
(Anybody else get Spirograph flashbacks at the beginning???)
16:20 In short, multiplying by 5 reverses the repeating sequence of digital roots and there's nothing in the argument that says you can't keep halving after 1. Dividing/multiplying a number by 10 doesn't change it's digital root because it doesn't add any non-zero digits to it's decimal representation. Halving is the same as multiplying by 5 and then dividing by 10. The digital root of 5 times a number is the digital root of half that number as can be seen in the following: In symbols, DR(n) = DR(10*n). Also DR(1) = 1. It follows that DR(1/2) = DR((1/2)*10) = DR((1/2)*2*5) = DR(1*5) = DR(5) and more generally DR((1/2)*n) = DR((1/2)*10*n) = DR((1/2)*2*5*n) = DR(1*5*n) = DR(5*n) which entails DR((1/2)^i) = DR(5^i).
Nice. it seems you were the only one in this comment section with sufficient mathematical maturity to get the answer. Good job.
I LOVE THIS. I have been terrified of maths but I now sit in wonder. ❤️🙏
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.
@@ghettocowboy993 your username represents you well lol.
@@Shoshana-xh6hc 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.
Doubling and halving makes me think of "As above, so below."
When you apply vortex based math to polygrams you see similar patterns form. Polygrams are a function of ratios so regardless what base number system you use the vortex pattern still emerges. The vortex patterns in nature are the result of similar ratios creating vortex patterns. Just because our base 10 system has some neat aspects does not discount the patterns that are inherent in the ratios of natural vortices.
Great way looking outside in. Vortex . Universe and natural vortex i gracious bow away. I am a speck of star 🌟 dust in a hugh Universe. Just a wonderful way of explaining adding to the video, here..🏁
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?
It is less about a particular base and more in the patterns that show up in relations overall.
Try the pentadecimal system. It was banned by organized religion.
@@kenshultz2664 Specify, there is no monolithic overall body for organized religion. What do you mean?
@@LostArchivist it’s a joke. What I meant is that Mother Nature has laid out the pattern for life. They are sometimes laid down by mathematical formulas carved within their being. Otherwise humans sometime make their own make carvings, and are bound by illusion to worship it.
That's the root of the lie. Use of a wrong base to hide the real truth.
As any French student at that time, I was taught the "casting the nine" ("preuve par neuf") when I was 7 or 8 years old. We used it all the time to check the results. I remember I was very confused and upset when I got the wrong result but the "casting the nine" test did not... I was probably off by nine, or I had interverted two digits, that I don't remember.
There is a limitation to the method. Perhaps you saw one of those. en.wikipedia.org/wiki/Casting_out_nines
I am officially dissolutioned. I remember the Tesla 3-6-9 story for years. Thank you for demystifying this…. But every time you said “nine” I would scream “NEIN!”, and that made it hard to follow because you say nine a lot in this one
In relation to 3-6-9.
Ken Wheeler made an experiment with molten bismuth cooling down over a powerful magnet. He predicted that the cooled metal would exhibit "bubbled cavities" at the extremities of the puck in this triangular, 369, formation.
For those interested, I recommend.
Well that's just an equilateral triangle, it's not systematically related to 3-6-9
If math is the language of the universe, then these diagrams are poetry - not necessarily useful, but still beautiful and inspiring.
Key Word---USEFUL!!!
Yes, they really are quite beautiful. Beautiful complexity arising from super-simple origins. The logistic equation similarly leads you into incredible complexity, and yet it's an amazingly simple equation.
Man this is mind-blowing. Is this the key to the universe? It certainly seems so.