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[vigilance]

Yes, yes, no, no.

In my opinion, magic and things like that mean nothing without gnosis.

Let me know what you think.

[Tannur]

Let me know what you think.

Nice video. Quite biased towards the "autistic" side of maths though. I don't deny that many mathematicians are autistic but there's a huge difference between mathematicians and maths itself.

[vigilance]

yeah.. that's the left side. The "master". strictness and all that. It needs the right side, too. I was so like that. I honestly only skimmed your math. THATS what it looked like to me.

I was mentioning Bruno and Lull.. its left and right. I'd like to see more of what you do. I'd really follow it this time.

[Tannur]

yeah.. that's the left side. The "master". strictness and all that. It needs the right side, too. I was so like that. I honestly only skimmed your math. THATS what it looked like to me.

I was mentioning Bruno and Lull.. its left and right. I'd like to see more of what you do. I'd really follow it this time.

Why do you feel that Bruno and Lull's works are even mathematics to begin with? No serious mathematician would consider numerology, number symbolism or sacred geometry to be mathematics. They probably wouldn't deny their consistency and truth as separate disciples in themselves, but definitely not mathematics. On the other hand, no scientist would be able to deny Alchemy if it was openly revealed to him, because it is entirely scientific, only deepening its profundity and significance.

This is what I was attempting to show through the example of my work in Number Theory. I was working entirely within high school mathematics, and yet the result I found had immense spiritual significance, at least for me. As I said in that thread, I believe that this was precisely because of how I approached mathematics: without knowing it, I was attempting to reach the "ultimate" root of a particular problem - the one source of that problem from which the problem was completely explained and revealed. Problem solving doesn't work like this. It works by playing around with a problem until you discover a "crack" somewhere. Then you explore this further, always with the aim of solving the problem in question, but not exploring it further to reach its "root". Such ideas are completely foreign to the world of olympiad mathematics I was working within. I like how Grothendiek explains this in the following passage:

"Since then I've had the chance, in the world of mathematics that bid me welcome, to meet quite a number of people, both among my "elders" and among young people in my general age group, who were much more brilliant, much more "gifted" than I was. I admired the facility with which they picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle -- while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things that I had to learn (so I was assured), things I felt incapable of understanding the essentials or following through to the end. Indeed, there was little about me that identified the kind of bright student who wins at prestigious competitions or assimilates, almost by sleight of hand, the most forbidding subjects. In fact, most of these comrades who I gauged to be more brilliant than I have gone on to become distinguished mathematicians. Still, from the perspective of 30 or 35 years, I can state that their imprint upon the mathematics of our time has not been very profound. They've all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they've remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have had to rediscover in themselves that capability which was their birth-right, as it was mine: the capacity to be alone."

I couldn't explain it better myself. I completely resonate with what he says about people being faster and picking up ideas easily. I definitely was not one of those people and really struggled to even get to the stage where I could solve olympiad problems. But I stopped being interested in learning more and more theorems very early on and just kept exploring guided by my own spiritual longing. This is what eventually led to my work with that problem I talk about in my other post.

Why I am mentioning all of this? As I said in that thread I posted about my Number Theory research, I was just trying to give a blueprint or "philosophy" through which Alchemy can be understood. Alchemy is like that problem I encountered, but a more "absolute" version of it. Whilst that problem does not reach the absolute root of mathematics, Alchemy *does* reach the absolute root of the physical world - of the four elements. And it is in its focus on this root that Alchemy acquires its spiritual flavour and significance. Without this focus, it collapses back into ordinary Aristotelian natural philosophy. Similarly, if I hadn't attempted to reach the root of that problem (thus forging my own "relative" alchemical path within Number Theory), my solution would have collapsed into mere competition level mathematics. That may have led to a quick, "elegant" solution to the problem like others on the forum in which I encountered it, but at the cost of the more profound work I was to accomplish through it.

The dream visions I had during my work on that problem, the sheer euphoria, the all-pervasive feeling of being at the doors of a huge castle burning with desire to pass onto the other side, the constant influx of illuminations and eureka moments in waking consciousness (they tend to always occur subconsciously when one is *away* from the problem), and so on. It was definitely right brain mathematics alright, but mathematics it was - not numerology or some other science. Similarly, alchemy is science alright, just like modern science. The only difference is that it seeks the root, the origin, the source. That is what happened to me back in high school without me even realizing what was happening at the time. That is what happened to Grothendiek. That is what happened to the alchemists.

Note: I did not intend to write an essay. Seems I am more enthusiastic about this topic than I thought!

[vigilance]

This is what I found. I stopped when I realized it was already know. I'm going to have to upgrade my computer, and start getting into C#. For some reason I think it's going to be easy.

Thursday, May 16, 2013 at 11:13am EDT
Fractions with prime denominators [edit]

A fraction in lowest terms with a prime denominator other than 2 or 5 (i.e. coprime to 10) always produces a repeating decimal. The period of the repeating decimal of 1/p is equal to the order of 10 modulo p. If 10 is a primitive root modulo p, the period is equal to p − 1; if not, the period is a factor of p − 1. This result can be deduced from Fermat's little theorem, which states that 10p−1 = 1 (mod p).

The base-10 repetend (the repeating decimal part) of the reciprocal of any prime number greater than 5 is divisible by 9.[3]


i dont have a lot of time for an involved reply right now, but I'd like to revisit these topics with you at a later date. Gmail, facebook, here. Whereever is most comfrotable for you.