Tesla’s 3-6-9 and Vortex Math: Is this really the key to the universe?

[Music] welcome to another mathologer video have you heard of vortex maths or the 369 tesla code i have to admit that in half a century of obsessing about mathematics i'd never come across these terms until quite recently there that's what comes up when you search for the combination 369 tesla on youtube a pile of seriously viral videos 7 million views or better a lot of these videos feature a curious diagram in their thumbnails this diagram is usually referred to as the vortex and is one of the main topics covered in these videos you've all heard of nikola tesla the genius inventor of the tesla coil and other early electrical devices right the tesla car that tesla but did you know that tesla also had a host of idiosyncrasies centered around the number three for example tesla would walk three times around a block before entering a building he would only stay in hotel rooms with a room number divisible by three and so on in general he was convinced that the numbers three six and nine hold the key to the universe according to the champions of vortex mats the vortex is that key that sounds a bit nuts but as i said i'd never heard of vortex mathematics and so i was curious to find out more and seven million people can't be wrong right also although vortex math was new to me i'd already stumbled across the vortex diagram before in a different context anyway our mission today is to have a closer look at the vortex there nine points on the circle labeled one to nine innocent enough then there is this infinity shaped loop connecting six of the points the remaining three points three six and nine form an equilateral triangle and depending on which video you watch some extra lines get added like this or like this or like this the last version of the diagram is the one that i have been familiar with for many years it's part of a famous sequence of diagrams one diagram for each positive integer this sequence of diagrams starts out like this there's a diagram for one for two for three for four for five and so on nine that's the vortex and then things continue like this [Music] okay does this all look a little familiar no well and let's keep on going okay what's going on here well i'm sure a lot of mythological regulators will recognize these diagrams and the pretty curve that is starting to materialize we already encountered these diagrams in the methodology video on the times table the mandelbrot set and the heart of mathematics the curve is called the cardioid the mathematical heart curve it pops up in mathematics and nature all over the place for example it's the curve you get when you roll a circle around another circle of the same diameter like this it's also the curve that you often see in cups on sunny days okay and it's the curve that takes center stage in the mandelbrot set the mandelbrot set and there it is actually there's more much more every positive integer does not only give rise to one of these cardiod infused diagrams but to a whole family of line diagrams and a lot of these extra diagrams are also incredibly complex and beautiful here are just a few examples pretty spectacular isn't it it gets even more impressive when you color the segments and the diagrams according to their length whoa not better but that's enough pretty pictures we're on a mission remember our goal is to make sense mathematical sense of the vortex which includes making sense of its mysterious relatives interested well why wouldn't it be right so let's get going [Music] okay all the tesla code videos i mentioned earlier introduced the vortex in essentially the same way here we go start with the powers of two so begin with the number one and then every number is double the number before it next for each number in this table we calculate its so-called digital root for this we keep adding the digits of a number until we end up with a single digit for example in the case of 128 the sum of the digits is 1 plus 2 plus 8 is 11. now 11 is not a one digit number yet and so we keep on going 1 plus 1 is 2. and so the digital root of 128 is 2. easy right now let's do this for all the numbers in our sequence there let's string up those digital roots on the circle first 1 2 4 8 seven five one two four eight seven in fact we'll keep on going like this forever one two four eight seven five one two four eight seven five and so on over and over pretty cute and also pretty surprising right now instead of doubling let's look at the sequence we get by halving again starting with one one one-half is equal to 0.5 when force equal to 0.25 and so on let's calculate the digital roots of these numbers looks familiar right let's check what happens on the circle 1 5 7 8 4 2 the same digital roots as for doubling just in reverse order again repeating forever and ever after also pretty cute right but notice that there are three numbers that never get visited 3 6 and 9 tesla's 3 6 and 9. whoa at this point of the discussion the absence of tesla's 3609 from the cycle is usually interpreted as a tell-tale sign that we're dealing with some sort of divine message some secret code the powerful key to the understanding of the universe that tesla was raving about well maybe i have to admit that i'm not quite able to follow the line of reasoning here however judging by the zillions of likes these videos attract and the enthusiastic comments pretty much everybody else watching appears to be in awe and fully on board with what's going on here must be just me i guess of course there is more evidence that the vortex is the key to the universe much more now we're told to look at what happens when we keep doubling and halving starting with three and evaluating the digital roots of the resulting numbers there whoa the plot thickens both for doubling and halving the digital roots alternate between 3 and 6 there 3 6 3 6 3 6 and so on and there 3 6 and 3 6 and 3 6 again the alternating 3 6 then corresponds to a line between those numbers in the diagram definitely key to universe right and what about the nine at this point in time the makers of all those videos get really excited we get all nines amazing to round things off it's then also pointed out that a lot of the other famous numbers in maths have digital root nine for example 360 180 90 45 degrees the number 666 this guy here all those numbers have digital root nine g to the universe how can it be otherwise okay okay i can see plenty of you screaming at your computers trying to get a button and yes of course you're correct everything we've seen so far has a fairly simple mathematical explanation part of which just about everybody has been exposed to in school an explanation that by the way never gets mentioned in vortex matt's videos funny that [Music] [Applause] [Music] right where in school mathematics do you add digits of a number remember divisibility tests if you want to find out whether or not a number is divisible by 9 you just add its digits and check whether this digit sum is divisible by 9. that's how it's usually taught in school as a refresher let's do an example 527 okay 5 plus 2 plus 7 is 14 and 14 is not divisible by 9 and so 527 is also not divisible by 9. well of course if that works then you can repeat adding the digits until only the digital root remains and then very simply a positive integer is divisible by 9 exactly if its digital root is 9. in our example the digital root is 1 plus 4 is 5. so the digital root is not 9 and we come to the same conclusion as before 527 is not divisible by 9. in school they usually don't teach this simple digital root extension of the standard divisibility test for 9. of course they should teach this in school but they don't in fact what they should also teach is that if the digital root of a number is not equal to 9 then this digital root is simply the remainder of that number on division by 9. nicer so the remainder of 527 on division by nine is our five up there great now just out of interest were any of you out in viewer land taught this remainder extension in school anyway very much worth knowing and teaching don't you think i'll show you the simple proof for all this in a little while but for the moment let's keep on going to explain what's really going on with all that vortex math i need to remind you of two more super important properties of remainders on division by any number as well as a digital roots counterpart of those properties in the special case of nine nothing scary really just primary school level maths promise what are those properties well the first property is that the remainder of the sum of two numbers equals the remainder of the sum of the remainders of the two numbers and the second property is the exact corresponding statement for products of numbers that's all a bit of a mouthful but a quick example will make it clear what i mean and at the same time show you why it works okay let's just stick with division by nine and let's pick two random integers 527 and 38. now 527 is 9 times 58 plus 5. you can check this and therefore when you divide 527 by 9 you get a remainder of 5. similarly 38 is 9 times 4 plus 2 and so the remainder is 2. okay what if you are also interested in the remainder of the sum of 527 and 38 well of course you can just add the two numbers divide by 9 and this way find the remainder yes you can do that but there is a much much quicker way have a look again 527 is 9 times 58 plus 5 and 38 is equal to this okay adding the stuff on the right we get this so what this shows is that the remainder of the sum on the left is simply the sum of the original remainders five and two five plus two is seven and so the remainder 7. super simple right well mostly but sometimes we have to deal with a little hiccup for example if you replace 38 by 44 going up by 6 the 2 on the right becomes an 8 and 5 plus 8 is 13 which is greater than 9 and so not one of the possible remainders on division by 9 but that's easily fixed what's the remainder of 13 when you divide by 9 well 4 of course this means that the remainder of 527 plus 44 on division by 9 is 4. clear again this is the sum shortcut if you know the remainders of two numbers the remainder of their sum is simply the sum of the remainders or the remainder of that remainder sum that's also good to know right what's even more important for us is that the same also works for products so 527 times 44 has the same remainder as 5 times 8. 5 times 8 is 40 and when we divide 40 by 9 we are left with a remainder of 4. so the remainder of 527 times 44 and division by 9 is 4. okay what about digital roots same thing right the digital root of the sum or product of two numbers is equal to the digital root of the sum or product of their digital roots very nifty again to summarize at the level of remainders the sum and product property holds for division by any number division by 2 3 4 5 666 division by any number whatsoever however in the special case of 9 and 9 only we have this extra niceness that remainders essentially correspond to the digital rules all clear ok now let's use these properties to explain what's going on inside the vortex remember we started by looking at the sequence of powers of two in other words we kept multiplying by two starting with one but now it's clear from our discussion just now that to generate that sequence of digital roots highlighted in green we can also just keep multiplying by 2 and digital routing on the right right let's double check this okay starting with 1 on the right 1 times 2 is 2 2 times 2 is 4 2 times 4 is 8. 2 times 8 is 16 and the digital root of 16 is 1 plus 6 is 7. 2 times 7 is 14 and 1 plus 4 is 5. 2 times 5 is 10 and 1 plus 0 is 1 and so on works and so looking at it this way it's actually not such a big surprise that the numbers on the right will eventually repeat why well we are always doing the same thing over and over right multiplied by 2 followed by finding the root multiplied by 2 followed by finding the digital root and since there are only 9 different possible outcomes of this operation things are bound to repeat and then loop one forever and of course the same is true if you start with any number and keep doubling in digital routing eventually things are bound to repeat and from there on will loop forever starting with three we get a very small loop three six three six three six and so on and starting with nine well doubling keeps producing numbers divisible by nine which all have digital root nine so just the meaniest of mini loops in the case of nine okay that's great now what about those halving sequences they're a bit unusual and in fact i'd never seen anybody calculate the digital roots of decimal fractions before watching these tesla videos having said that with what we know it's also not hard to explain why we end up with the same sequence of digital roots as before running in reverse right to get those decimal fractions we keep dividing by two to get one-half is equal to 0.5 1 4 is equal to 0.25 1 8 is equal to 0.125 and so on now i'm sure that you've all seen these numbers a million times yes but did you ever notice the powers of five in these numbers wait what yes powers of five just get rid of the decimal point and all the zeros and you get 5 25 125 and so on the powers of five where do those powers of five come from well actually that's also not hard to explain you see dividing by a 2 is the same as first multiplying by 5 and then dividing by 10 right 5 divided by 10 that's one half and of course dividing by 10 only moves the decimal point this means digit-wise we end up with the powers of 5 and a couple of zeros neater and now the rest i'll leave is a little challenge for you why are the digital roots of the powers of 5 looping the same way as the powers of 2 just in reverse leave your answers in the comments hint again the key is that 2 times 5 is equal to 10 and what's the digital root of 10. [Music] okay getting there so as far as mathematics is concerned the vortex is simply a visualization of what happens when we multiply the remainders and division by nine by the number two in technical lingo what we are doing here is multiplication by 2 modulo 9. actually i almost forgot if we want to think of the vertex in terms of remainders and not digital roots we should replace the 9 at the top by 0. remember that little difference right and what about the other diagrams that i showed you earlier well those are visualizations of multiplication by two modular other numbers here's a diagram for five again right just a quick check there four times two equals eight and when you divide eight by five you get a remainder of three taking that three times it by two gives six and when we divide six by five we get a remainder of one and so on works and then as i already showed you before as we erase the modulus the number by which we divide the first real magic occurs with the card materializing out of nowhere there very nice but all this is really just multiplication by two the other diagrams i showed you you get when you multiply by other numbers so for example have a look at this crazy diagram here this is multiplication by 240 modulo 7417 who would have thought now multiplication modular different numbers is super important mathematics with myriads of applications within and outside of mathematics finite fields cryptographic algorithms number theory in general and so on in an app for drawing these diagrams we then have two basic controls one for setting the number we multiply with and one for setting the modulus in fact let's have another coding competition whoever among you submits an online app that implements drawing these diagrams enters into a draw for marty's and my new book that one there anyway for the vortex we have multiplier 2 and modulus 9 then changing the modulus to 50 we get this and if we now change the multiplier to 3 we get this actually on closer inspection there's at least one more aspect of these diagrams which we could also change can you guess what i've got in mind here it's a tricky one and easily overlooked let me give you a hint it's got to do with the nine occupying a special role in our discussion so far right only for modulus of nine can we use the digital root algorithm to construct these diagrams this does not work for any other diagram so what exactly is it that makes nine special in this respect well vortex mathematician will probably tell you that nine is special it's just part of tesla's 369 being the key to the universe of course nine has to be special right actually and closer inspection it turns out that in the first instance 9 is special because we're writing numbers in base 10. wait what yes divisibility test for 9 and all the other digital root magic is a direct consequence of us writing numbers in base 10. interesting huh you want proof no problem let me show you why the remainder of this number on division by 9 is the same as the remainder of the sum of its digits that's what makes the digital root work right well 2567 is just two times one thousand plus five times one hundred plus six times ten plus seven and 1000 is 999 plus 1 100 is 99 plus 1 and 10 is 9 plus 1. okay now expand and collect all the repeated nine numbers together there now 9 99 999 are all divisible by 9 and so the whole yellow bit is divisible by 9. and the green bit is just the sum of the digits and obviously the same is true for any integer any integer is equal to nine times something plus its digit sum but then when you're interested in the remainder of the number on division by nine we can just forget about the whole yellow bit since it's divisible by 9. and so the remainder of our number on division by 9 is equal to the remainder of the sum of the digits ta-da proof complete and that's where the digital sum does the trick for 9 and y-9 is special okay but now what happens if you're an alien with b fingers and you write numbers in base b and not base 10 like with 10 fingered earthlings well then everything i said in my little proof remains true except that 9 changes to b minus 1 and b minus 1 becomes the special number in turn the times 2 diagram for b minus 1 becomes the special vortex diagram for an alien tesla it's now this new diagram that can be constructed using digital roots for example for the eight finger tesla we have this vortex there and you can check that the digital root in base eight gives exactly these connections for example starting with the 4 we calculate 2 times 4 is 8 8 in base 8 is 1 0 and 1 plus 0 is 1. another example starting with 5 2 times 5 is 10 in base 8 10 is 1 2 and 1 plus 2 is 3 and so on okay so at least from a mathematical point of view the vortex is really not that special it's really just one of infinitely many diagrams that pretty much do the same thing and definitely as we've already seen many of the diagrams with large modulus are a lot more spectacular from a purely aesthetic point of view also even mathematically there are lots of diagrams that are superior to the vortex in many ways for example have a look at the diagram for 11. in this diagrams the powers of two create a loop that is as large as possible containing all the numbers except for 11 yes that is one continuous loop unlike in the vortex which consists of two loops that such a maximal loop exists has to do with the fact that 11 is a prime number and that two the so-called primitive element modulo is prime if you're familiar with these terms you'll also recognize that these loops illustrate affected for a prime number p the finite field zp has a cyclic multiplicative group effect which is of huge importance in mathematics okay so what about the claim that the vortex is the key to the understanding of the universe well today's discussion was really about presenting a sound explanation of the mathematics that comes with the vortex an explanation that demystifies its supposedly super special properties i hope that by now it's clear that the vortex is really not as special and amazing as it is made out to be by all those tesla videos and they're proclaiming it to be the key to the universe mainly based on these properties is simply ridiculous but of course you knew that already didn't you in fact i wonder what you now think of all those tesla videos and their creators please share your thoughts in the comments having said that i'm convinced that mathematics as a whole is the master key to understanding the universe and of course the maths we talked about today is a part a tiny tiny part of that key and if you're fascinated by that tiny tiny part and are interested in a real understanding of the universe well then simply familiarize yourself with more and deeper maths okay here's a nice challenge for you suggested by tristan take one of these diagrams let's just stick with the vertex multiply the modulus by some integers say let's multiply the vertex modulus 9 by 3 that gives 27 draw the new diagram then the loops of the first diagram are contained in the new diagram let me show you in this example there the infinity shaped loop and the horizontal mini loop of the vortex hiding inside this diagram there it's an infinity shaped loop and there's the other one whoa super vortex super key to the universe anyway can you explain why our diagrams have this mysterious modulus multiplication property [Music] what about all these other spectacular model times tables what is known about the crazy structures inside them actually i've not been able to find much about these diagrams in the mathematical literature maybe some of the pros among you can do something about the sorry state of affairs and fill in the gaps in our knowledge in this respect i know of proves that the curve that materializing the times two diagrams is really the cardioid this appears to be due to the famous 19th century italian mathematician luigi cremona also when you experiment a little with small multipliers 2 3 4 5 6 and large modulus another striking pattern jumps out at us there can you see the pattern i'm sure you can why do these petals appear and why is it always one fewer petals than the multiplier well the details are messy but it's possible to gain some intuition for the one fewer than the multiplayer bit have a look at this animation this is just the base case where we multiply by two that produces the cardioid what i'm doing here is raising the modulus while at the same time tracing the powers of two that fit in the circle notice that the cusp occurs where the last connection goes straight across makes sense right here's what happens when we set the multiplier to three okay so the first cusp occurs at the point x such that 3 times x is ideally on the opposite side of the circle for the next multiplier 4 this picture would look like this now 4x minus x that's the distance between the two points is half the circle so half the modulus now we just follow our nose and solve for x there we go of course x is really just the distance from the top around the circle and so the width of a flower petal is 2 times x very nice and that means that there will be a total of 4 minus 1 equals 3 petals around the circle the same calculation shows that in general we'll have multiplier minus one petals of course there are still quite a few details missing from this argument to make it into a complete proof anyway good enough for this video what do you think now even in this monster diagram with multiply 240 there are 240-1 that's 239 tiny little petals around the outer circle let's zoom in on part of the circle there there are lots and lots of little petals but can you see even at the border there's a lot more stuff going on for example how about this ring of smaller petals challenge for the keen among you how many of those little petals are there and how many loops does this monster diagram have who can find the answers to these questions but of course zooming out that's where the real spectacular stuff is happening how exactly is all this complicated and beautiful structure linked to the multiplier and the modulus the only place i know that makes some progress towards answering this question is an unpublished writer by simone plouffe that i've linked to in the comments you may know simone proof for his involvement in the establishment of the encyclopedia of integer sequences as the creator of the inverse symbolic calculator and the discovery of the spectacular bailly bowen proof formula for calculating individual digits of pi anyway challenge for the super keen and capable mathematicians among you check out simon proves write up and then go where no one has gone before and explore the secrets of these diagrams and that's all for today i hope you enjoyed our vortex adventure until next time [Music] [Applause] [Music] so [Music] [Music] you

Channel: Mathologer

Views: 453,015

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Id: 6ZrO90AI0c8

Length: 29min 59sec (1799 seconds)

Published: Sat Feb 19 2022

Reddit Comments

[u/dalkon]

This is a good explanation of what the 3-6-9 business could be about, but it contains a glaring error. This guy never mentioned that no one has ever provided the source for this supposed quotation. Without a source, there is no reason to think the quote is real. It appears to be fabricated or at least misattributed. It sounds more like Walter Russell than Tesla.

Tesla said a lot of very interesting things about physics and metaphysics, like about the nature of energy, radiation, cosmology, gravity, quantum mechanics, etc. but it's remarkably difficult to find any real information about that on the internet. It is available to read and attempt to interpret, but if you're interested in learning more about his thoughts, you're inundated by thousands of links about this numerology stuff that doesn't actually seem to be connected to Tesla at all. It almost seems like the point of it is to suppress interest in Tesla and consideration of the things he really did say.

One useful thing about this is that it makes it easy to identify people who actually care about the information enough to know this is not correctly attributed to Tesla. If someone is talking about this vortex math and Tesla, you know they believe any random thing they read so they probably don't know what they're talking about and they probably don't have anything interesting to say.