akaMechsmith wrote: ... Simplest possible life (4 colors-elements) like a deck of cards.
4000X3999 --All possible ways to arrange 1,000 molecules with 4 elements
-15,996,000-
I need you to explain this to me.
I presume the atoms (cards) are oxygen, carbon, hydrogen, and nitrogen (O, C, H, N).
A deck consists of 1000 of these cards. How many ways can one arrange
a single, 1000 card deck of these 4 kinds of cards? A single deck could be all Os, or all Cs, or all Hs, or all Ns. Or a single deck could be OCHN repeated 250 times. Or a single deck could be say 250 Os, followed by 250 Cs, followed by 250 Hs, followed by 250 Ns or many other strange and wonderous sequences.
So let's look at position 1 of the sequence. There are 4 choices: which shall it be O, C, H, or N? The same is true for the nth position, the (n+1)th position, and of course for the thousandth position.
So what are the possibilities?
4 choices for position 1, 4 choices for position 2, 4 choices for position n, 4 choices for position n+1, and 4 choices for position 1000.
Suppose there were only 3 positions. then we would have 4 x 4 x 4 = 4^3 = 64 different possible sequences. If there were 10 positions then we would have 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 = 4^10 = 1,048,576 possible sequences.
In the case of 100 positions, we would have 4^100 = approximately 1.606938044 x 10^60 possible sequences.
In the case of 166 positions, we would have 4^166 = approximately 8.749002899 x 10 ^99 possible sequences (multiply that by 4 one more time and you would have over a googol sequences).
In the case of 1000 positions and 4 different kinds of "cards", we wouild have 4^1000 different possible sequences. Well, 4^1000 = approximately 10^602.059991 = 10^602, for short.
But I infer from you, you want to consider seqences as few as 4, 5, 6, up to as many as 998, 999, 1000. So the actual total would be the sum of all the possible sequences for each and every sequence length of 4 to 1000. Clearly a number much bigger than I calculated.
Yes, there IS something invalid about my calculation.
It presumes all the life intrinsic molecules consist of one dimensional sequences of the 4 elements. They probably do not. They can be two or three-dimensional configurations. I'll bet that it's some of the three dimensional configurations of atoms that form living molecules. I know!
You want me to calculate those odds.
Sorry, I don't know how (or at least at this time, I don't know how).
By the way, I assume that what you mean by a living molecule is: a molecule that can reproduce itself from its environment (e.g., sea water). Please correct me if I'm wrong about what you mean.
Another possibility is that any mix greater than a to be determined/discovered finite critical mix of the 4 atoms in sea water can form a living molecule. If that's the case, then you are probably correct, that life and its relentless evolution to higher intelligence is all but certain (i.e., so close to 1 that the difference isn't worth calculating).