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

welcome to another

math

ologer video, have you heard about

vortex

math

or

tesla

369 code? I must admit that in half a century of obsession with mathematics I had never come across these terms until recently, that is what comes up when you search for the 369

tesla

combination on YouTube a lot of

really

viral videos 7 million views or more many of these videos feature a curious diagram in its miniatures. This diagram is generally known as the

vortex

and is one of the main topics covered in these videos. We've all heard of Nikola Tesla, the genius inventor of the Tesla coil and other ancient electrical devices, from the Tesla automobile to Tesla, but did you know that Tesla also had a number of idiosyncrasies centered around the number three, for example, Tesla he walked around a block three times before entering a building he only stayed in hotel rooms with a room number divisible by three and so on he was generally convinced that the numbers three, six and nine contain the key to the

universe

according to the champions of vortex mats, the vortex is that key sounds a little crazy, but like I said, I had never heard of vortex math, so I was curious to know more and seven million people can't be wrong, Although vortex mathematics was new to me, I had already done it.

I stumbled upon the vortex diagram before in a different context anyway, our mission today is to take a closer look at the vortex, there are nine points on the circle labeled one to nine, innocent enough for

this

loop to be in. infinity shape that connects six of the points with the remaining three. Points three, six and nine form an equilateral triangle and depending on the video you watch, some additional lines are added like

this

or like this or like this. The latest version of the diagram is the one I have been familiar with for many years.

It's part of a famous sequence of diagrams a diagram for each positive integer this sequence of diagrams starts like this there's a diagram for one for two for three for four for five and so nine that's the vortex and then things continue like this, okay? a little familiar not good and let's move on well, what's going on here well, I'm sure that many mythological regulators will recognize these diagrams and the nice curve that is starting to materialize, we already found these diagrams in the methodology video in the times. table the mandelbrot set and the heart of mathematics the curve is called cardioid the curve of the mathematical heart appears in mathematics and in nature everywhere, for example, it is the curve that is obtained when you roll a circle around another circle of the same diameter as this is also the curve that you often see on cups on sunny days, okay, and it is the curve that takes center stage in the mandelbrot set the mandelbrot set and there it is, actually, there are more, much more, each positive integer gives rise not only to one of these cardioid infused diagrams but to an entire family of linear diagrams and many of these additional diagrams are also incredibly complex and beautiful.

There are just some pretty spectacular examples here, right? It becomes even more impressive when you color the segments and diagrams. according to its length, it's no better, but that's enough pretty pictures, we're on a mission, remember our goal is to make mathematical sense of the vortex, which includes making sense of its mysterious interested relatives, well, why not it would be correct? So let's do it. Well, all of the Tesla code videos I mentioned above introduced the vortex in essentially the same way. Here we start with powers of two, so start with the number one and then each number is double the number before the next for each number in this table. we calculate its so-called digital root for this we continue 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 yet a single-digit number, so we continue: 1 plus 1 is 2.

Therefore, the digital root of 128 is 2. Easy now, let's do this for all the numbers in our sequence. There we will unite those digital roots in the circle first 1 2 4 8 seven five one two four eight seven in fact, we will continue like this forever one two four eight seven five one two four eight seven five and like this over and over again very nice and also quite amazing right now instead of doubling, let's look at the sequence we get by halving again, starting with one, one half is equal to 0.5 when the force is equal to 0.25 and so on, let's calculate the digital roots of these numbers, it seems familiar to us, let's see what happens in the circle. 1 5 7 8 4 2 the same digital roots as to duplicate only in reverse order again repeating forever and ever also pretty cute, but notice that there are three numbers that are never visited 3 6 and 9 Tesla 3 6 and 9.

Go in At this point in the discussion, the absence of Tesla's 3609 in the loop is generally interpreted as a telltale sign that we are dealing with some kind of divine message, some secret code, the powerful key to understanding the

universe

about which Tesla I was excited. Well, perhaps I have to admit that I am not able to follow the line of reasoning here, however, judging by the millions of likes these videos attract and the enthusiastic comments, almost everyone who watches seems to be amazed and completely in favor. agree with what is happening. 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 are told to look at what happens when we keep doubling and halving, starting with three and evaluating the digital roots. of the resulting numbers, the plot is complicated by both 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 3 Alternate 6 corresponds to a line between those numbers in the diagram is definitely key to the correct universe and what about nine? At this point the creators of all those videos get very excited, we get all the amazing nines to round things out, then it is also pointed out that many of the other famous numbers in mathematics 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 for the universe, how can it be any other way? computers trying to get a button and yes of course you're right, everything we've seen so far has a pretty simple mathematical explanation, part of which almost everyone has been exposed to in school, an explanation that, by the way , is never mentioned in Vortex.

Matt's videos are funny, right where in school math you add the digits of a number. Remember the divisibility tests. If you want to know if a number is divisible by 9, you simply add its digits and check if the sum of these digits is divisible by 9. This is how it is usually taught in school as a review. Let's do an example: 527, okay, 5 plus 2 plus 7 is 14 and 14 is not divisible by 9, so 527 is also not divisible by 9. Well, of course, if that works, 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. then the digital root is not 9 and I come to the same conclusion as before. 527 is not divisible by 9. In school they generally don't teach this simple digital root extension of the standard divisibility test for 9. Of course, they should teach this in school, but in fact they don't. 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 when divided by 9. The remainder of 527 when divided by nine had better be our five. up there.

Great, now just out of interest, did any of you in bystander country teach this remaining extension in school? In any case, it is worth knowing and teaching. Don't you think I'll show you the simple proof of all this in a moment? For now, let's continue explaining what's

really

going on with all that vortex math. I need to remind you of two other super important properties of remainders from division by any number, as well as a digital root counterpart of those properties in the special case of nine. nothing scary really just elementary school level math promises what those properties are, well the first property is that the remainder of the sum of two numbers is equal to 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 a bit complicated, but a quick example will clarify what I mean and at the same time show you why it works well, let's continue with division by nine and choose 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, 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 simply add the two numbers, divide them by 9 and this way find the remainder. Yes, you can do that, but there is a much faster way. Take a look again. 527 is 9 times 58. plus 5 and 38 equals this, okay, adding what's 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 rest 7. super simple, well, mostly, but sometimes we have to deal with a little hiccup, for example, if you replace 38 with 44 and go up by 6, the 2 on the right becomes 8 and 5 plus 8 is 13, which is greater than 9. and so it is not one of the possible remainders of division by 9, but that is easily solved.

What is the remainder of 13 when divided by 9? Well, 4, of course, this means that the remainder of 527 plus 44 from division by 9 is 4. Of course again, this is the addition 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 remaining sum. It's also good to know. What's even more important to us is that the same thing works for products too. 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 have a remainder of 4. So the remainder of 527 times 44 and the division by 9 is 4.

OK? The same thing about digital roots, true, 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 clever again to summarize at the level of remainders, the property of sum and product holds for division. by any number division by 2 3 4 5 666 division by any number however in the special case of 9 and 9 we only have this additional kindness that the remainders essentially correspond to the digital rules, everything is clear, now let's use these properties to explain what's happening inside the vortex, remember we started by looking at the sequence of powers of two; in other words, we keep 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 right to right, let's review this carefully, 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, looking at it this way, it's actually not a big surprise that the numbers on the right will eventually repeat themselves because well, always we are doing the same thing over and over multiplying 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 be repeated and then repeated one to forever and of course the same is true if you start with any number and keep doubling in digital routing eventually things will repeat and from there they will repeat forever, starting with three we get a very small loop. three six three six three six and so on and starting with nine, well the doubling still produces numbers divisible by nine, all of which have digital root of nine, so just the baddest mini loop in the case of nine is fine , that's great, now what about those halving sequences?

They're a bit unusual, and I'd actually never seen anyone calculate the digital roots of decimal fractions before watching these Tesla videos. That said, with what we know it is also not difficult to explain why we end up with the same sequence of digital roots that before running in reverse to the right to obtain those decimal fractions we continue dividing by two to obtain half equals 0.5 1 4 is equals 0.25 1 8 equals 0.125 and so on now I'm sure you've all seen these numbers a million times, yes, but have you everDid you ever notice the powers of five in these numbers? Wait, yes, powers of five, just remove the decimal point and all the zeros and you will get 5 25 125 and so on, powers of five, where are they found? those powers of five come from well, actually that's not hard to explain either, you see, dividing by 2 is the same as first multiplying by 5 and then dividing by 10, right, 5 divided by 10, that's half and so Of course, dividing by 10 only moves the decimal point this means that, at the digit level, we end up with the powers of 5 and a couple of more ordered zeros and now I will leave the rest as a little challenge for you, why do the roots digital powers of 5 are repeated in the same way as? powers of 2 just the other way around leave your answers in the comments hint again the key is that 2 times 5 equals 10 and what is the digital root of 10.

Okay so as far as math goes the vortex It is simply a visualization. of what happens when we multiply the remainders and divide by nine times the number two in technical jargon, what we are doing here is multiplying by 2 modulo 9. In fact, I almost forgot if we want to think of the vertex in terms of remainders.y not digital roots, we should replace the 9 at the top with 0. Remember that little difference, right? And what about the other diagrams I showed you before? Well, those are visualizations of multiplication by two other modular numbers. Here's a diagram for five again. 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 two gives six and when we divide six by five we get a remainder of one and so on it works and then as I already showed you before, when we delete the module, the number by which we divide, the first real magic happens with the card materializing out of thin air, very nice, but all this is really just a multiplication by two.

The other diagrams I showed you are obtained when you multiply by other numbers, so for example check out this crazy diagram here, this is multiplication by 240 modulo 7417, who would have thought that now modular multiplication of different numbers It is a super important mathematics with countless applications inside and outside of mathematics, finite fields, numerical cryptographic algorithms? theory in general, etc., in an application to draw these diagrams, we have two basic controls, one to configure the number with which we multiply and another to configure the module. In fact, let's have another coding competition, whoever among you submits an online application that implements drawing.

These diagrams are entered into a giveaway for Marty's and my new book. That's there anyway for the vortex, we have multiplier 2 and modulo 9, then we change the modulus to 50 and we get this. If we now change the multiplier to 3, we actually get it closer. inspection, there is at least one more aspect of these diagrams that we could also change. Can you guess what I have in mind here? It's complicated and easy to overlook. Let me give you a hint. It has to do with the nine who occupy a special role. In our discussion so far on the right, only for the modulus of nine can we use the digital root algorithm to construct these diagrams.

This doesn't work for any other diagram, so what exactly makes nine special in this regard? Well, the 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, and upon closer inspection it turns out that, in the first instance, 9 is special because we are writing numbers in base 10. Wait, what? Yes, the divisibility proof for 9 and all the other digital root magic is a direct consequence of us writing numbers in base 10. Interesting, huh? Want a proof? No problem, let me show you why the remainder of this number in division by 9 is the same as the remainder of the sum of its digits that's what makes the digital root work well 2567 is just two times a 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 put all nine repeating numbers together. Now 9 99 999 are all divisible by 9, so the entire yellow bit is divisible by 9. And the green bit is just the sum of the digits and is obviously the same thing. true for any integer, any integer is equal to nine times something plus the sum of its digits, but then when you are interested in the remainder of the number from division by nine, we can forget about the whole yellow bit, since it is divisible by 9. and so the remainder of our number in division by 9 is equal to the remainder of the sum of the digits ta-da full proof and that's where digital addition works for 9 and and-9 is special, okay, but now what if you are an alien with b fingers and you write numbers in base b and not in base 10 like with 10 fingered earthlings, well then everything I said in my little test is still true except that 9 changes a b minus 1 and b minus 1 becomes the special number in turn the timing diagram 2 for b minus 1 becomes the special vortex diagram for an alien tesla.

Now it's 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 verify that the digital root in base eight gives exactly these connections, for example starting with 4 we calculate 2 by 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, at least from a point of Mathematically speaking, the vortex is really not that special, it is actually just one of the infinite diagrams that do more or less the same thing and definitively, as we have already seen.

Many of the diagrams with large modulus are much more spectacular from a purely aesthetic point of view and, even mathematically, there are many diagrams that are superior to the vortex in many respects, for example, take a look at the diagram of 11. in these diagrams the Powers of two create as large a loop as possible containing all numbers except 11. Yes, that is a continuous loop. Unlike the vortex, which consists of two loops, the fact that a maximum 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 are familiar with these terms you will also recognize that these loops illustrate the effect of a prime number p the finite field zp has a cyclic multiplicative group effect which is of great importance in Mathematics, what about the claim that the vortex is the key to understanding the universe?

Well, today's discussion was really about presenting a solid explanation of the mathematics that comes with the vortex, an explanation that demystifies its supposedly super special properties. I hope it's clear by now that the vortex really isn't as special and amazing as all those Tesla videos make it out to be and proclaim it to be the key to the universe based primarily on these properties. It's just ridiculous. But of course, you already knew that, right? In fact, I wonder what you think now of all those videos of Tesla and the creators of it. Share your thoughts in the comments.

Having said that I am convinced that mathematics as a whole is the master key. to understand the universe and of course the mathematics that we talk about today is a small part of that key and if you are fascinated by that small part and you are interested in a real understanding of the universe, then just familiarize yourself with more and deeper mathematics , okay, here's a good challenge suggested by tristan, take one of these diagrams, let's continue with the vertex, let's multiply the modulo by some integers, say, let's multiply the vertex, modulo 9 by 3, which gives 27, draw the new diagram and then the loops. from the first diagram are contained in the new diagram, let me show you in this example the infinity shaped loop and the mini horizontal vortex loop hidden inside this diagram, there is one infinity shaped loop and there is the other, super key super vortex . to the universe anyway, can you explain why our diagrams have this mysterious property of module multiplication?

What about all these other spectacular multiplication table models? What is known about the crazy structures inside them? I haven't actually been able to find much about these diagrams in the mathematical world. The literature perhaps some of the professionals among you can do something about the sorry state of affairs and fill in the gaps in our knowledge in this regard to my knowledge demonstrates that the curve that materializes the times of two diagrams is actually the cardioid to which which seems to be due. to the famous Italian mathematician of the 19th century Luigi Cremona also when you experiment a little with small multipliers 2 3 4 5 6 and large modulus another surprising pattern comes to mind there you can see the pattern I am sure you can Why do these petals appear?

And why is there always one petal less than the multiplier? Well, the details are fuzzy but it is possible to get some intuition for the less than multiplayer bit. Take a look at this animation. This is just the base case where we multiply by two what it produces. the cardioid what I'm doing here is raising the modulus and at the same time plotting the powers of two that fit into the circle. Note that the cusp occurs where the last connection passes directly. Makes sense. This is what happens when we set the multiplier. to three then the first cusp occurs at point x so 3 times x is ideally on the opposite side of the circle for the next multiplier 4 this image would look like this now 4x minus x that is the distance between the two points is half the circle so half the module 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 so the width of a flower petal is 2 times x very pretty and that means there will be a total of 4 minus 1 equals 3 petals around the circle.

The same calculation shows that in general we will have one multiplier minus one petal. Of course, there are still some details missing from this plot to make it complete. Anyway, the test is good enough for this video, what do you think now? Even in this monster diagram with multiplication 240 there are 240-1, that is, 239 small petals around the outer circle, let's zoom in on one part of the circle, there are many small ones. petals, but can you see even at the edge that there is a lot more going on? finding the answers to these questions but, of course, zooming out, that's where the really spectacular thing happens.

How exactly is all this complicated and beautiful structure linked to the multiplier and the module? The only place I know of that makes any progress in answering this question is an unpublished writer by simone plouffe which I have linked in the comments, you may know Simone Proof from her involvement in establishing the whole sequence encyclopedia as the creator of the inverse symbolic calculator and the discovery of Baily Bowen's spectacular proof formula for Calculating Single Digits of Pi Anyway is a challenge for the super enthusiastic and capable mathematicians among you. Check out Simon's tests. He writes and then goes where no one has gone before and explores the secrets of these diagrams.

That's all for today. I hope you enjoyed our vortex adventure. until next time so