math research/skepticism in Theosophy

[David Melik]

This is for a thread on math in Theosophy even if one has ideas that may be seen as heretical.

I will write about Pi. As you may know, HPB said the Book of Dzyan involves Pi and gives examples in the stanzas she recorded.

For reference, Pi is
3.14159265358979
i.e. (in binary, a number base computers use, in which instead of counting up to 10 for a new place you count up to 1)
11.00100100001111110110
i.e. (in hexadecimal, a number base people use to program computers, in which you count up to 15 and have a 16s place)
3.243F6A8885A308D31319
i.e. (in any many more number bases) etc..

So you see there are no numbers that depend on the base or notation: they are ideal forms. Yet the stanzas of Dzyan are written as if the decimal system has great significance in the mathematical sacred keys. Well, some Sumerians counted up to 60 before they would make a place for a new number (again, like the tens place, but for 60s in this case.) So what? What is so important about the three and the one and the four and the 'five' and the nine and the two and the six and the eight and the seven and--whereever further it occurs in Pi--the 12?

First of all, how can you say 'the one and the four and the five' or whatever when it is really 'the one and the four and the fifteen?' If you ignore a repeated digit but then pick an arbitrary double-digit, e.g. 12, then how can you analyze it with any order at all?

Maybe the stanzas of Dzyan are about a base less than ten that happens to occur as stated without skipping digits. But, why should something esoteric do numbers-based math proofs? Maybe it really says something about the earthly universe, but should it not be saying something about the heavenly universe of ideal forms? And, what if I want to 'read into' Pi in a different base like hexadecimal. Then it should probably go 'the three and the two and the 3F.'

With the latter manner of not skipping digits and just taking the next chunk until a new number until all numbers in the base have been used you get some sort of unique data. Since Pi is infinite it will also repeat itself within itself--in parts--and have other different parts that also repeat with the repeated parts--and alone--ad infinitum. That is just why I think you should take chunks of digits and eventually you get back to something you have seen before.

Maybe this has nothing to do with Dzyan. I guess its idea is that it either has Pi in base 8, 9, or 13 or that it has approximation related to other symbolism. I say base 13 because HPB said 'the 12' and perhaps it should be its own digit in the analysis--like it would be in hexadecimal 'C,' i.e. from 9, A, B, C, D, E, F in which the letters are merely numbers.

In the latter case just ignore my statements about taking chunks of such numbers.

If the stanzas of Dzyan are really in a different base than ten one still must ask why it is using numbers and whether it would say the same thing if it used any base. Ideally it should. Maybe other parts that are not about Pi use other bases for something, and we do not even have the whole book. The stanzas of Dzyan are in any case limited but they try to express the illimitable. If they use (an)other base(s) there is a lowest and highest and maybe pattern and beyond that set that it uses there may be other truths.

I started out questioning the value of the stanzas of Dzyan from an optimist math viewpoint and then a more skeptical one because of what Paul Johnson may say in his books. We do not really know if the books of Kiu-te exist. Nevertheless, I think the symbolic language in the given stanzas are anaylzable with the two methods I gave above.

[Rodnoy]

DM> Yet the stanzas of Dzyan are written as if the decimal system
DM> has great significance in the mathematical sacred keys...

looks like petitio principii
(?)

Thanks.

SARVA MANGALAM! :)

[David Melik]

>looks like petitio principii

Maybe sort of, but not completely. Remember in the SD HPB does mention Pi in the decimal system when explaining the stanzas of Dzyan. So it is not my idea... though it may be wrong... and IIRC HPB also mentions the sefiroth, which are ten, in relation to the stanzas of Dzyan.

[Rodnoy]

It seems to me that SD was saying about the meaning of numbers whereas you are talking about forms of representation of numbers. I.e. it doesn't matter (as I got the SD) how one depicts a number of objects he sees before him: 10, X, (bin) 1010, (octal) 12, (hex) A, in sanskrit, senzar, kanji, etc... The meaning is the same :) Same story with Pi in SD: as long as you understood that she meant numbers 3,1,4, etc., - it doesn't matter how those numbers are represented. Probably, she did it in the decimal system only because nobody would've undestood her otherwise (they barely did anyway but it's another story).

(I am sorry if I am stating the obvious and thus insulting your intelligence... maybe, I just missed your point - my apologies if it is so)
(and sorry for very long explainations too)

Thank you.

SARVA MANGALAM! :)

[David Melik]

I thought when she was talking about Pi she was specifically talking about it being 3.14, but as I mentioned it can even be written in binary. I was talking about forms of representation because one needs to know about them to see what numbers really represent. If something is really represented in stanzas of Dzyan with Pi then one needs to know how. If it was represented with zero and one then there would only be two symbols unless you find a pattern in the fraction part, though there may be no number to symbolize them. HPB mentions numbers up to ten or twelve or so in the stanzas of Dzyan. However, how do we know at what number in her recorded stanzas stop at? That was the essence of my question.

For example, Senzar, which IIRC the stanzas are said to be in, may have said to be sort of translatable to Chinese or Sanskrit or have the same meaning when represented somehow with those languages. Sanskrit has over fifty letters, so maybe symbolism up to fifty would be significant. However, Chinese does not have letters and has many symbols for words, so maybe symbolism up to several thousand would be significant. Of course it depends more on the nature of the stanzas of Dzyan.

If someone shows HPB did not mean decimal was important for Pi or if I look that up I will change my initial post, but I guess we may as well leave these replies since they are here already.

The main topic of my post is analyzing both what the numbers mean in Dzyan and whether real numbers, such as Pi (in the stanzas) have any inherent symbolism about the universe within themselves. Seven has symbolism about the seven planes for example, but it is an integer, and real numbers (i.e. non-repeating decimals) may have more complex symbolism--or even infinite symbolism if there is such a thing. This seems to be a topic in Plato's theory of forms that is said to be resolved by Plotinus, though he said 'infinity is evil.' Hopefully there are some other translations.

I guess she was also talking about Pi as symbolizing a circle which has some symbolism with emanation of the universe. But that may have less to do with the decimal system and more to do with patterns in any number system which can represent the circle and enumerate mysteries of the universe.

[Rodnoy]

DK> I thought when she was talking about Pi she was specifically
DK> talking about it being 3.14, but as I mentioned it can even be written in binary.

as I remember, she was talking about Pi (among other things) as of sequence of numbers: 3, 1, 4, etc. I.e. we don't have to find any pattern here since she did it for us already and representing those numbers in the binary format will change nothing in this case.

DK> But that may have less to do with the decimal system...

Yes, I completely agree with that. I don't think she even cared about writing Pi in the decimal system... (since she explained the meaning of Pi she didn't have to, imho)

DK> However, how do we know at what number in her recorded stanzas stop at?

Oh, Ok... well, I think, we don't know :)

DK> ...and real numbers (i.e. non-repeating decimals) may have more
DK> complex symbolism--or even infinite symbolism if there is such a thing...

yeah... it seems to me that symbolism, of any kind, has this inherent problem: it is limited only by one's imagination ;-)

Thank you.

SARVA MANGALAM! :)

[J. E. Mead]

One, two, three are mathematical concepts with exact and universal meaning. The language is not important. Pi is an element that is well defined, and never changes. so.... why the focus on how it is represented? Four just means the cardinality of a specific set.

Also - the real numbers are only defined by their own properties. Anything(s) which exhibit the same abstract properties are equivalent to the real numbers. They are unique constructs of mind. Pi is defined upon any objects isomorphic to the properties of the real numbers. The words "Real", "Number" and "System" help to convey an abstract structure that is familiar to people. You are thinking of Numbers in rather exclusive, limited manner?? It has to do with the concept of a field, well-orderd, has least upper bounds and so on. These are purely mental constructs. Abstract math has no reality in Physics, however it exists uniquely in the mental realm, and is universal across the Universe.

Want to play roulette, craps etc. on alpha centauri ?

Pi is a property of all circles. Do circles exist regardless of culture, construction of matter in alien brains... location in space etc.

=> curious 

 

[David Melik]

Thanks for pointing these things out. I think I rambled too much on this topic. One thing that we have not really gotten into yet is what HPB said that came from pi, and why it is or is not that way... maybe I should quote it, but I paraphrased part of  it.

[Capt. Anand Kumar]

The question is for those with advanced knowledge in Physics. In another galaxy, or in another universe where the other constants of nature may be different, will Pi have the same value? Can the shape of a circle exist which will then have a relationship with its diameter.? 

[David Melik]

I think as previous posters were mentioning, things like pi are mostly mental forms... in another galaxy, circles would still seem to be the same on the mental plane, though ellipses have different circumferences.