- #1
synergy
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I've posted this theory elsewhere, so unless someone wants a real thorough exposition on it I won't go into all the details. If you've already read this elsewhere, I don't plan on addressing this here very long.
I've found a way to express prime numbers that seems (to me) to have the property of synergy (synergy: the whole is more than the sum of the parts, etc.). I will give the theory, briefly, but my question (I didn't ask this question where I posted my theory before) is can anyone think of a way to apply the theory to other synergistic systems? For example, we put bread, sauce, and cheese together and call it pizza. Our tastebuds combine the experience of these flavors in a synergistic fashion to give us an experience that is new i.e. we might not have been able to predict our reaction to the combination based only on having eaten spoonfuls of sauce and bites of bread and cheese separately. Somehow, the combination has a property (enjoyment) that a spoonful of sauce just can't explain. This is synergy, the whole is more than the sum of the parts. My question is, can we somehow quantify the experiences of each part numerically, and then combine the numbers in a specific way that CAN predict the outcome of their combination? Btw, synergy plays a role not just in food, but psychology, economics, biology, physics, weather, artificial intelligence, any complex system with feedback loops.
Here's the math I've developed. Suppose we know ALL of the primes up to some value, say 2, 3, 5, 7, 11, 13 and that's all (I know we know a bunch more, but the theory's the same). Now square 13 to get 169 and set it aside for now. Take the rest of them and put them into two separate piles, say pile X is 2 and 7, and pile Y is 3, 5, and 11 (remember we set 13 to the side for now). Then we do this funky looking equation:
Q = abs( 2^a * 7^b +/- 3^c * 5^d * 11^e )
All this really means is take any exponents of all of the numbers in the two piles, then multiply the exponentiated numbers from the first pile together to get a number, say it is "A" and multiply the exponentiated numbers from the second pile to get "B", then do A plus or minus B, and if the result of the subtraction is negative take its absolute value. This will give two answers (one for plus and one for minus) for each choice of exponents a,b,c,d,e, so Q is actually a set of solutions. Oh, by the way, the exponents must all be integers greater than zero.
Now, my discovery is that if q is one of the solutions in set Q, and if q is less than 169 (remember the square of 13 that we set aside), then q will be prime. My conjecture (so far not disproven by anyone) is that ALL primes will be in the set Q. Of course, if you are looking for a prime bigger than 169 but less than, say, 529 which is the square of 23, then you will have to make two piles from all of the primes 2, 3, 5, 7, 11, 13, 17, 19 (and set 529 to the side for the "less than" test at the end), to make up your new set Q.
Now, I say the primes are synergistic because we are adding A and B, and the prime factors of A are some primes (2 and 7 in the example) and the prime factors of B are other primes (3, 5, 11 in the example) and all outputs less than 169 in Q are NEW primes BETWEEN 11 and 169. We have certain primes going in, and a set of NEW primes coming out - the whole is more than the sum of the parts - synergy. If you all think this is nonsense, I'll go down without a fight. But think for a moment: what if somehow we could express (or even arbitrarily assign) a certain quality (sauce-ness as perceived by a given person's tastebuds) as a prime, say "2", and then express another quality (bread-ness) as "3" and then the exponents would be the quantity of each that we're combining together in our pizza. Maybe certain outputs are favored - with 2 and 3 only, the primes output will be less than 25, so maybe people prefer smaller prime pizzas such as a "5 pizza" or a "7 pizza", or maybe people avoid pizzas that fit the prime scheme, only going for composite pizzas. Laugh at my example, perhaps, but we could also talk about artificial intelligence or the complex neural connections in the human brain this way. Isn't it true that neurons can each play different roles, depending on what "circuit" is activating them? Maybe each role has a different synergy. In physics and chemistry, some complex systems display entrainment or other emergent phenomenae. Who knows, really, how these things happen? This may not be the end-all theory, but could it be a start?
Aaron
I've found a way to express prime numbers that seems (to me) to have the property of synergy (synergy: the whole is more than the sum of the parts, etc.). I will give the theory, briefly, but my question (I didn't ask this question where I posted my theory before) is can anyone think of a way to apply the theory to other synergistic systems? For example, we put bread, sauce, and cheese together and call it pizza. Our tastebuds combine the experience of these flavors in a synergistic fashion to give us an experience that is new i.e. we might not have been able to predict our reaction to the combination based only on having eaten spoonfuls of sauce and bites of bread and cheese separately. Somehow, the combination has a property (enjoyment) that a spoonful of sauce just can't explain. This is synergy, the whole is more than the sum of the parts. My question is, can we somehow quantify the experiences of each part numerically, and then combine the numbers in a specific way that CAN predict the outcome of their combination? Btw, synergy plays a role not just in food, but psychology, economics, biology, physics, weather, artificial intelligence, any complex system with feedback loops.
Here's the math I've developed. Suppose we know ALL of the primes up to some value, say 2, 3, 5, 7, 11, 13 and that's all (I know we know a bunch more, but the theory's the same). Now square 13 to get 169 and set it aside for now. Take the rest of them and put them into two separate piles, say pile X is 2 and 7, and pile Y is 3, 5, and 11 (remember we set 13 to the side for now). Then we do this funky looking equation:
Q = abs( 2^a * 7^b +/- 3^c * 5^d * 11^e )
All this really means is take any exponents of all of the numbers in the two piles, then multiply the exponentiated numbers from the first pile together to get a number, say it is "A" and multiply the exponentiated numbers from the second pile to get "B", then do A plus or minus B, and if the result of the subtraction is negative take its absolute value. This will give two answers (one for plus and one for minus) for each choice of exponents a,b,c,d,e, so Q is actually a set of solutions. Oh, by the way, the exponents must all be integers greater than zero.
Now, my discovery is that if q is one of the solutions in set Q, and if q is less than 169 (remember the square of 13 that we set aside), then q will be prime. My conjecture (so far not disproven by anyone) is that ALL primes will be in the set Q. Of course, if you are looking for a prime bigger than 169 but less than, say, 529 which is the square of 23, then you will have to make two piles from all of the primes 2, 3, 5, 7, 11, 13, 17, 19 (and set 529 to the side for the "less than" test at the end), to make up your new set Q.
Now, I say the primes are synergistic because we are adding A and B, and the prime factors of A are some primes (2 and 7 in the example) and the prime factors of B are other primes (3, 5, 11 in the example) and all outputs less than 169 in Q are NEW primes BETWEEN 11 and 169. We have certain primes going in, and a set of NEW primes coming out - the whole is more than the sum of the parts - synergy. If you all think this is nonsense, I'll go down without a fight. But think for a moment: what if somehow we could express (or even arbitrarily assign) a certain quality (sauce-ness as perceived by a given person's tastebuds) as a prime, say "2", and then express another quality (bread-ness) as "3" and then the exponents would be the quantity of each that we're combining together in our pizza. Maybe certain outputs are favored - with 2 and 3 only, the primes output will be less than 25, so maybe people prefer smaller prime pizzas such as a "5 pizza" or a "7 pizza", or maybe people avoid pizzas that fit the prime scheme, only going for composite pizzas. Laugh at my example, perhaps, but we could also talk about artificial intelligence or the complex neural connections in the human brain this way. Isn't it true that neurons can each play different roles, depending on what "circuit" is activating them? Maybe each role has a different synergy. In physics and chemistry, some complex systems display entrainment or other emergent phenomenae. Who knows, really, how these things happen? This may not be the end-all theory, but could it be a start?
Aaron