That said, be glad again, as it was in fact the accidental discovery that 75 squared minus 72 sq. rendered 21 sq.! I know a <441> when I sees one.

So I <had> to know why, and how it works when you draw it, visualize it, but my A3 sheet was not large enough, what pain I went through, but the next morning I discovered that it was a times three inflation of the 24-25-7 pythagorean triangle! But I still had to find the how/why, which really set me off from that point.

But the numerical underpinning that I now see, both in me and in nature, in both the material and vibrational world, e-n-e-r-g-y, has me quite often in deep thought, the connections, dependencies, and how "closed" a <"closed" circuit> really is...

Not In school, and neither in University, was I ever introduced to a concept like <digit sum> and <root digit>... They keep so much away from us.

Eg, 2744 = 14 cubed, 1+4=5 so 5 cubed is 125,=8, the root digit add up the digits 2744, which gives you 17, which is 8, which means 2744 is correct, whereas if you slipped up and got 2734, you know there is a mistake. Assuming you calculate in your head or use pen and paper. The numbers and patterns to be dicovered are infinite, and they all obide to this cardinal rule of the digit sum, and the root digit. In music and lyrics this is also very present, like Bowie who worked often with anagrams, but you'd know more about that.

Lucent's Higher Mathematics explains quite a number of related "rules" and patterns, which I found out last night, but it is in Hindi, and I want to discover by myself, so to hel with the Lucent papers!

Your err, h-e-a-l-t-h is most important, we're a partly closed system, Dom, what we imbibe eat and secrete is of the utmost importance, all cells need ATP energy packets, and there are A LOT of cells.

Back to numbers, give the sq root of 190096 -no calculator ...

Why? Because the final two digits of squares recycle every 50 moves. In that 50, one solution is n, the other is 50 - n.

So 14^2 gives us 196, which ends in the required --96. And 50-14 = 36, also ending in --96.

The initial 4 is obvious so these are the only options. A moment's thought shows the answer is 436.

Take two numbers, a and b.

Then a^2 + b^2, a^2 - b^2, and 2ab form a Pythagorean triple. There's a simple proof.

Which suggests that different areas of the brain are at work in maths and language.

<Niels>! How have you been? So long since you posted. I see that you are exploring your maths again, one of your favorite activities. Luckily <Dom> is up to the task of understanding such fare and contributing.

<Dom> said the brain is divided into parts, if I read him correctly. None of my parts have any maths in them, and I suspect several of the parts only have pictures of burritos in them.

<Tim> suffers a similar condition, if I'm not mistaken.

He speaks with a forked tongue.

<<You're tougher than me, in a few ways. For example, I couldn't handle people calling me a 'criminal drug addict' or whatever they throw at you. >I don't need that sheet ... and I'm neither a crim nor an addict these days anyway. But neither are you - those cretins don't need to have truth on their side.>>

Oh mate. It's just water off a ducks back. I couldn't care less what some saddos on the nutterweb say or think about me I'm too blessed to be stressed, even the people I haven't put on ignore don't bother me anymore, I just skip their posts... It was actually Daniel that made me see those people differently, he broke character and said something I never expected and I never thought or looked the same about trolls afterwards - not that <Focus> actually <<talking to BP!>> after everything that was said didn't bother me, I just didn't expect it from someone I liked.

Anyways.. I don't know where you've been (you've been in Armley again haven't you, Dom?? 😂 Lol) or what you've been up to but I'm glad you're safe and sound, glad to see you around again..

I don't know 'Armley', but I can guess.
Heh.

I, however, have. Probably too often. It may add to my understanding of lines like Marlowe's, but is bad for chess and other things requiring precision.

As the song (by Neil Innes & Grimms) goes...

Or maybe they need help?

On the Match - Carlsen played for penalties, in a soccer analogy, knowing that he is actually better at real chess than any other human.

To be fair, that no longer makes him much good at the game.

As a boy in primary school, interested in the game, but without others to play against, I would move the bits around on both sides of the board. Sort of playing against oneself, so to speak. Fifty years later, an AI machine teaches itself to be the greatest player in the history of chess in around 2 days by the same method.

Am I alone in finding this really scary?

What will be the intentions of the AI machines? Are we foolish enough to believe that static games like chess or Go will satisfice whatever their own determined aims might be?

Why? Because the final two digits of squares recycle every 50 moves. In that 50, one solution is n, the other is 50 - n.>

Impressive, another pattern, which is new to me! Yes, 414 was a second option, but it is too close to 400 sqd. - ie 160000 - drop the zeros, so sense of ratio steers toward 43, which sqd. is 1849, still below 19____, which indeed reveals 436 as the winner. Root digit check can be insurance, but no need, since we know 44² is over 1900__.

Just off the cuff, last night I tested myself on a 3-digit multiplication, get it in some 15 seconds max, quite hard, and ran coincidentally into a remarkable sum, so many 'weird' zero's:

783 x 894

9 times 21 - reduced...

And after a few seconds I saw the 0's appearing, and, supplies supplies, the answer was 7, hang on...

700002

Cool stuff, and hot at the same time.

Get back to <Jess> in a bit, as I had to sell my acoustic, needed the doe... blushes*

But it allowed me to buy a new digital, allowing me to play during the night, which is when I prefer to play and study, lights out, no visual distractions.

<Pythagorean triples> Haven't grasped the creation fully, yet, but alas, one step after the other, counting on the occasional, inevitable "leap", unless your name is <Euler>...

How to really tell? People have deemed it opportune to divide a hemisphere in 4 parts, because they have discovered <fissures>, but they are all intimately connected... Less than 100 years ago the lymbic system was called the Rhino-encephalon, the smell-area of the brain, so burritos fit perfectly in this context.

And yes, at times I do miss the sound and feel of the real keys, the vibes, and the emotions, unfortunately a few of my neighbours thought differently.

On <Py Triplets>

I remember I uncovered a lovely pattern, this is now some 7 months ago, that the sum of the "long legs" of the triangle, eg 24+25, equals the square of the short leg... 24+25=49, which is 7²

12+13=25, which easily renders another triplet: 12/13/5

15+17=32, and since 15 and 17 are two apart, double 32, which gives 64, which is 8 squared, et voila, the 15/17/8 triple/triangle/triplet offers itself...

Back to my original from 7 months ago, 72+75=147; 72 and 75 are three apart, so triple 147, and 441 is your answer, square root is 21.

40+41=81, rendering 9/40/41

This is quite awesome, but since I was fully in Geometry mode at the time, I didn't bother to pursue more numbers, triplets, triplo's und drei-ecks, and went on my merry way, following my nose, as we say in dutch, sniffing my way to my next "discovery". It really is that simple, and fun, and revealing and enlightening at the same time.

I really could have done this when I was 12, I reckon, but only "now" it comes out. It <has> to ... The Time is Ripe.

---->

click for larger view

<Tilted Eiffel Tower>, if you will...

Chess.com's online Stockfish 9 goes 36 ply deep, and says it is mate in <19>

-which is patently untrue, I easily mated Black in <11>, vs Stockfish 9