Look forward to hearing back from you, Kyle.
Some thoughts that occur to me re: the very interesting expansions of pi you have given:
"pi = square root of {6 (1/1 + 1/4 + 1/9 + 1/25 + 1/36 + 1/49 + ...)}"
I think: looks like "6 quarks for Mr. Mark"
"Mr. Mark" as "self-reference" as "a deal or handshake between two "bases" (two perspectives).
Your numbers can be re-written as:
(6 ( (1/ 1 to power 1) + (1/ 2 to power 2) + (1/ 3 to power 3) + (1/ 5 to power 5) + (1/6 to power 6) + (1/7 to power 7) + ...) )
Is the term "+ (1/4 to power 4)" supposed to be missing?
Is it the only term missing? What about "+ (1/16 to power 16)?
Maybe the "1/4 to power 4" is distributed over the relationship between the 6 and the string of terms? So it is not seen?
"6" may be a quark view of "4" as "2 to power 2" can be thought of as "(base + unit) to power (base + unit)" where together the items in the brackets ( ) and ( ) could be a third perspective on "base + unit".
So we have "three in one" or a space for mutual agreement on building nuumber.
Since 6 is not divided by this term; perhaps it is already distributed over this term.
So perhaps pi here say looks like 6 quarks in space-time (in 4) divided by a string of ways bases can happen in 1 mutual base (as 1/"n" to power "n" is 1/local base) but 6 quarks in space-time (as my longer post shows) defines a mutual agreement scenario ....
So that gives pi as mutual agreement/mutual agreement which gives 3-in-1 mutual agreements = freedom consciousness love So is "pi" God's signature in mathematics? Or could it be seen that way.......
"pi = 2 {(2/1)(2/3)(4/3)(4/5)(6/5 )(6/7)(8/7)(8/9)...}"
might translate as:
the first "2" as "meeting"
the other terms as "a discussion where every way agreement can happen is included: every voice gets a hearing":
meeting(does anyone want to say something)(what do you think about what I said?)( you give your view and may invite my response)(I may reconsider my view on replying)(you give your view; taking account of any re-thinking I did, and may invite my response)(I may respond with further comment)(we discuss my further comment and this allows me to re-think)(you invite a new idea from me)...)"
According to my analysis of "pi" the very definition of "number" is mixed up with the definition of base. The decimal expansion of pi seems could be seen in many different ways? Maybe it is already a generalised series of "1s", or "2s" or "3s" or whatever?
No coercive numbering: but counting by mutual agreement..........by an agreed base...........optional counting.........as you count, so you are counted.........count God first, and you are freed from number-jails........................ (idea say)
What I am wondering is if our decimal expansion of pi is a kind of illusion about number; I am suggesting that "number" assumes equal-spaced divisions of a "base"; in reality "as you measure, so you are measured" it is said.
Re: the stuff I wrote; the accompanying post may help to understand it (physics readers might see that the way of defining words by broadening and narrowing categories where they intersect translates easily to the div. and curl of Maxwell's equations; and to Dr. Stafford's summation over Dirac delta functions. Also the "juggling" map I gave for sub-atomic particles is clear I think and maps physics very well)
Regards,
Alan |