Einstein & Faith
I believe there's Something Out There so huge that we can't comprehend it at all. Whatever it is cannot be expressed in scientific terms. I don't know if it's particularly besotted with humans. I know that meditation is healthy. Prayer works, in my experience. That could be quantum physics playing with the observer, I dunno. All in all, it serves me better to allow the existence of ... G-d? I like the dash in the name because it reminds me that we don't know its name at all.
You ain't the only one. I'm becoming convinced that not only is there no pattern, but the very lack of pattern is vital to the proof. Hence, I think that I might have a bit of a grasp on how to show the Goldbach Conjecture to be of the same nature as Godel's unprovable statement.
Therefore there is a pattern.
The formulae for finding primes rely on all of the previous primes, and are too expensive to be of any value. If it were otherwise, modern encryption techniques would be trivially breakable. Moreover, IF there was such a formula, the twin primes conjecture would also be solved. Thus, there is no known pattern.
As to the savants, I'd like to see how large a prime they could recognize. i.e. how many fully filled sheets of digits they could still determine. My guess is that even one sheet of paper would be too much, and that they simply have somehow memorized the first few - no real pattern is implied.
I played around with them over last summer, trying to impose a group involving addition on primes, and quite simply, I believe that it can't be done. Now, certainly there are patterns, but they don't seem to exist in ANY mathematics involving addition.
Therefore there is a pattern.
The formulae for finding primes rely on all of the previous primes, and are too expensive to be of any value. If it were otherwise, modern encryption techniques would be trivially breakable. Moreover, IF there was such a formula, the twin primes conjecture would also be solved. Thus, there is no known pattern.
As to the savants, I'd like to see how large a prime they could recognize. i.e. how many fully filled sheets of digits they could still determine. My guess is that even one sheet of paper would be too much, and that they simply have somehow memorized the first few - no real pattern is implied.
I played around with them over last summer, trying to impose a group involving addition on primes, and quite simply, I believe that it can't be done. Now, certainly there are patterns, but they don't seem to exist in ANY mathematics involving addition.
Daniel Tanamet has handled numbers in the Sextillions.
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How good music and bad reasons sound when one marches against an enemy!
That sounds like it would fit on a single line of text, no? Certainly programs have handled much larger, and there is NO discernible pattern. Not that this is as telling as the apparent fact that addition simply does not seem to be imposable on a group only containing the primes.
http://fpx.de/fp/Software/Sieve.html
as to the savant's, the human brain is very complex. My guess (though I'm no psychologist) is that they have simply made these calculations and memorized them, probably without noticing.
as to the savant's, the human brain is very complex. My guess (though I'm no psychologist) is that they have simply made these calculations and memorized them, probably without noticing.
wow for someone who knows c thats a pretty sh***y way to calc prime numbers. this is a program i wrote in VB long time ago (i know vb is less effecent than c, but the overall method i think mine is more effecent)
Dim intN As Integer, intI As Integer, intII As Integer
Dim intPrime() As Integer, intPrimeCount As Integer
intN = 2 ^ 15 - 2
ReDim Preserve intPrime(intN) As Integer
intPrime(0) = 2
For intI = 3 To intN Step 2
For intII = 0 To intPrimeCount
If intI Mod intPrime(intII) = 0 Then GoTo NotPrime
Next intII
intPrimeCount = intPrimeCount + 1
intPrime(intPrimeCount) = intI
lstPrime.AddItem CStr(intI), 0
DoEvents
NotPrime:
Next intI
End Sub
i think i was 13-14 when i wrote this (i keep ALLLLL my old source codes) this was before i really knew much VB, if i where to code it now it would be a lot cleaner. anyways this gets all the prime numbers that will fit in an integer. it checks each number is not divisible by all the prime numbers up to it, witch is how i find prime numbers in my head. say a number like 49, it is divisible by 7, no prime. then i see a num like 89, i see no small prime number factors for it. i know the 7 "times tables", and thats the only weird one. so 89 must be prime.
i can count is prime numbers. i go by 2s starting at 3. 3,5,7,9,etc. than each num i see factors for i skip. 3 5 7 11 13 17 19 etc. i start having to really think when i get into 3 digit nums
sinsboldly
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here is how Einstin viewed the world, his own words from his own book
http://www.einsteinandreligion.com/worldsee.html
He also said:
I believe in Spinoza's God who reveals Himself in the orderly harmony of what exists, not in a God who concerns himself with fates and actions of human beings.
—Albert Einstein
to which I say, AMEN!
Merle