Fibonacci sequence

It's one of the simplest things.  Start with nothing, add one, then add them together, then keep adding the last two numbers.  0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233,…

Zero is the zeroth fibo, which makes 144 the 12th (twelfth?  twelveth?) and (I think) the only square in the sequence.  For sure, 144 is the highest fibo that does not have a novel prime number as a factor (the only other being the sixth fibo:  8).  Novel, here, means not being a factor of any fibo earlier in the sequence.   13 is itself prime; 21 has 7; 34 has 17; 55 has 11; 89 and 233 are both prime.  It goes on and on and on as infinitely long as the natural numbers themselves.

Some bizarrities rise up once you check deeper into it.  If the fibo's number in the sequence is prime, it's factors are all novel primes For examples, the 17th fibo is 1597, which is novel, the 53rd is 953 X 55945741, both of which are novel (the 106th is 953 X 55945741 X 119218851371, or the novel factors of the 53rd times its own novel prime).  263rd is 4733 X 93629 X some 46 digit monstrosity I'll spare you…these numbers get huge fast.   

There is something fundamentally comforting in this sequence for me.  It is a source of novelty, which is something I have wondered about for the Anyverse.  If there is no novelty, there is no free will and really where's the fun in that?  This simple algorithm returns constant and assured novelty for a countably infinite number of iterations. Anything is, therefore, possible.

Re: Fibonacci sequence

I've figured out cut and post (a nice typo) in FireFox, so here goes something clever I said elsewhere:

Mathematically (and I don't know where your skills are strong so I hope I don't come off pretentious or demeaning here), one of the most elegant of formulae is e to the power of pi's product with i is equal to -1.  To break this down some:

• e is the natural log, a transcendental number almost equal to 2.718
• pi is also transcendental, just a bit more than 3.1415.
• i is the imaginary number, the square root of negative one and a mighty useful idea for engineers
• equality indicates balance
• negativity is different than positive, implying 0 and once squared, lost (unlike positivity, which endures squaring)
  
• one is one and that's about it (and that's its power)
  

Somehow, all that transcendentalness (merely a mathematical state that sounds spiritual) works itself out into a simple integer.  That's neat.

I think I grok what you're trying to say using the '+1 is enlightenment' metaphor.  Personally, I think +1 was the consciousness needed for successful single-celled organisms some long time ago.  Where we are, I don't know, but I know we're a mighty young species in a mighty young Universe and whether we like it or not, we're trying to blaze a trail to whatever number is next for us.  

This advancement thing, it's not easy, so I extend the math metaphor to make surpassing an integer a long, long, ever getting harder slog.  Actually, I found this mathematic stuff out and applied it to my philosophy as the best metaphor so far.

Look at the sum of inverted primes.  (Gosh, I hope you don't fear or detest higher math, otherwise just consider this post aimed at, well, other parts of society).  Prime numbers are (stealing some mathemetician's daughter's phrase here) the “unfair” numbers, because you can't share with them. They go 2,3,5,7,11,13,17,19,23 and so on in a sophisticatedly irregular fashion.  Divide each into 1 and add up the results.  Infinite sums go one of two ways:  converging on a finite (usually singular) value or being as infinite as the set of integers.  Which way does the sum of inverted primes end up?

 Infinite, but really, really slowly.  1 only needs a few inverted primes, 2 a few more, 3 a bunch, 4 a lot and 5 needs millions of inverted prime numbers.  6 gets a little ridiculous and you couldn't make an abacus out of protons for higher numbers.

Co-creating, to me, is like combining sets of prime numbers and seeing what other values we can come up with.  Once I tell you a prime, and you tell me a prime, both end up with more primes to calculate with on an individual basis. We are each the sum of our individual prime numbers, and the more experience you accumulate, the higher your sum.  And for the value of 8 (and all its multiples), we would need three people to bring their 2 prime.

Enlightenment is, for me, is recognizing that you have accumulated enough prime numbers to go through the bother of inverting them and adding them up.  Each level presents a far more challenging and sometimes gruelling procedure.  

Some people don't bother, ever, and live very unsatisfied and unaware of why they're so friggin' disgruntled all the friggin' time.

Re: Fibonacci sequence

And I,
I negated i() by integrating e^(i*PI) di.
And that made a world of difference.