Quote:
Originally Posted by abraxasinas
Hi berathebrain!
There are many, like Pascal's Triangle leading into polynomials and the binomial coefficients.
Much of this you can find on the internet.
Something you will not yet find on the internet is the 33-tiered Maria-Matrix. It is here on this forum in thread:
http://projectavalon.net/forum/showthread.php?t=18834
A very basic one and related to the above thread are the Perfect Numbers
of the Greeks.
Schismatic and Sacred Science & Perfect Numbers
The Greek alchemy of course became 'modern chemistry' and Plato's five elements mapped as his 'perfect solids' and later as say 'quantum gauge interactions' in the post-Newtonian science redefining itself.
The Aristotelean physics of precise measurement of the physical parameters was retained and the Platonist-Pythagorean physics of 'divine perfection' became largely abandoned in this scientific reformation.
Something of a remnant could not be erased in this new scientific paradigm however - the 'science of divinity' or the science of 'creative providence'.
This residue today pervades all sections and strata of society and is a powerful component of all political, religious and cultural institutions.
So even if this 'science of divinity' or 'omniscience' is a purely psychological construct and without any physical measurement significance whatsoever; it still plays an important, sometimes even dominant role in the affairs of states and national agendas of whatever political persuasion and affiliation.
So can one find a common factor UNITING all those psychological constructs in a form acceptable to the 'Mensuration Science' and perhaps in a form more akin the 'science of divinity' of Newton and the Greek alchemists?
One can do so, if one can discover a 'common denominator' for the divinity sciences, invariably coloured in the codes of language and interpretations.
And here one can introduce certain 'emotion charged' labellings or words, such as ALLAH and GOD and AL QAEDA as factors of the omniscience.
Then in other words, using the psychology of the historical residue of divinity science, this also holds the key to unite the religions, say linked to political constructs and affairs of state. This could be followed perhaps, by a more global and political unity, born from a new understanding of its own linguistic codes.
And then it does not really matter if the 'gods and allahs' exist in a physical reality or only as psychological constructs, created or invented by sentient 'citizens'.
Because 'they' most assuredly exist as psychological creations; 'they' carry a significant 'emotional energy', which perhaps can be modelled in a form of 'consciousness' in physical parameters following an unification of the language codes underpinning 'their' reality as 'emotion-charged' and say mental energy constructions.
This will introduce a scenario, where no numbers exist at all; so the decoding following is necessarily post-facto and assuming the Set of Natural Numbers N, say given in a statement, such as: N={1,2,3,4....n; nÞn+1 PMI}; and where PMI is a label for a procedure termed Principle of Mathematical Induction.
'Perfect Numbers' or PN's are those numbers of the set N, which add all their factors to sum their eigenstate or self-identity.
Then the first PN is PN1=6=1+2+3=1.2.3=√(6²)=(1.2.3)^1.
The second PN is PN2=28=1+2+4+7+14=√(28²)=√(1.2.4.7.14)^½=√784.
PN3=496=1+2+4+8+16+31+62+124+248=(1.2.4.8.16.31.62.12 4.248)^¼ and
PN4=8128=1+2+4+8+16+32+64+127+254+508+1016+2032+4064=
(1.2.4.8.16.32.64.127.254.508.1016.2032.4064)^1/6.
In more detail:
6=1+2+3=½[3][4]
28=1+2+3+4+5+6+7=½[7][8]=1³+3³=1+2+4+7+14
496=1+2+3+...+30+31=½[31][32]=1³+3³+5³+7³
=1+2+4+8+16+31+62+124+248
8128=1+2+3+...+127+128=½[127][128]=1³+3³+5³+7³+9³+11³+13³+15³
=1+2+4+8+16+32+64+127+254+508+1016+2032+4064
We shall reencounter the mathematical form of.. Σ=½[n][n+1] later, but note here, that there exists this 'special number' x=2 as the solution for the quadratic x+x=2x=x²=4 or x²-2x=0.
This is the only number of the set N, whose 'doubling' is identical to its 'squaring'.
It also defines the 'Derivative' of the 'Perfect Square' x² as d(x²)=2x.dx.
We may also define a set PN={PN1; PN2; PN3; PN4;...PNn}={6; 28; 496; 8128;...PNn} and as a subset of N.
AA |
In this thread
http://projectavalon.net/forum/showthread.php?t=18834 you mention that all perfect numbers are the sums of the ODD NUMBERS CUBED. That is true only if a number is perfect, but the other way around is not necessarily true. For example, take first 16 odd numbers and cube them, you will get 130816, which is the next number after 8128. This number is equal to 511*512/2, where 511 is not a Mersenne prime, so this can not be a perfect number. It is true that this number can be expressed as the sum of first 511 numbers, but that doesnt make it a perfect number. Here is the definition of a Perfect number:
http://mathworld.wolfram.com/PerfectNumber.html.
Interesting formula thou.
I have been always fascinated by numbers, and so I did notice the fabulous connection of number 2. Namely, number 2 satisfies the equation x+x=x*x=x^x. I have also noticed that 2^4=4^2. So I have wondered If any other numbers satisfies the equation x^y=y^x. So I found a formula to find infinite many numbers that satisfies the above condition.
Here it is:
x=n*n^(1/(n-1))
y=n^(1/(n-1))
where n is some real number.
If you take n=2 you will get 2^4=4^2.
If you take n=3, you will get (3*(3^(1/2)))^(3^(1/2))=(3^(1/2))^(3*(3^(1/2)))
and so on.
Could you elaborate on this equation. And Notice that when n goes towards number 1, x and y is equal to e=2.7182818284590452353602874713527.
I always thought this equation could be used to factorize numbers through some fractal type algorithm
Dejan