Combinatorics and other things!

Hi there!

Apologies for the double post: seems I didn't toggle the previous post to visible...

So!

Exponentials, Variable-Rate Compound Interest and Combinatorics (oh alright, and Integrals) are SUPER USEFUL and IMPORTANT tools, amiright?

Approaching those tools from a Compatibilist, Communitarian, Constructivist, Agnostic at this point in time; these tools help unlock understanding of the whys and hows of things.

Following on from last post, about combinatorial genome considerations over on the biology stack exchange... We're essentially trying to reverse engineer the 'Encyclopedia Galactica" that Sagan spoke of: what Jorges Borges wrote about in 'Library of Babel'... via a process not unlike the Drake Equation. 

Before you laugh, if you read Kaku's work or Kurzweils "How to Create a Mind", its closer than you might think... 

Just remember too though, the 'museum of failure' concept of Burkeman... there'd have to be a set of solutions out there... some ideal, some optimal, some doomed from the start... who knows which iteration we happen to be in!

Tangent aside, and back to the original tangent;

I'm wondering, is there a "one-stop shop" for the combinatorial indices of all compounds in the universe? That'd probably be the first page I'd look up in the "Encyclopedia Galactica": after reading "Optimal Energy Solutions: The Hows and Whys" and the list of all known civilisations in the galaxy. I've seen combinatorial chemistry pop up in some databases, but no 'here's all of them that can be' as yet.

If we take the periodic table as a start point,

we'd be tempted to do 

118! = ~4.684526...e+194

Thats a big number, as with the example of the human genome on the biology stack exchange... there'd be a number of combinations/permutations which are the same, which could never occur (given constraints, such as the duration of the universe, M-Theory, etc).

I may also require the binomial coefficient/multiset coefficient to more accurately begin to contemplate the task...

How would we go about approximating that; but for all compounds?

We know that atoms can only combine in certain ways, in particular ratios and due to electron shells/subatomic composition (which by the way, we could do combinatorial indices for all these 'new' subatomic particles etc also, which might then alter the ways in which atoms can combine to form compounds/ERoEI ratios), ERoEI, etc... 

The upper limits of the number of atoms in the universe are known to within a 'reasonable' estimate, and as astrochemistry/astrophysics begins to understand the composition, the accuracy will improve.

 Is that --- producing a list of all possible compounds in the universe, and synthesising the optimal ones --- the ultimate ancillary aim of chemical process engineering/ combinatorial chemistry, from those of you out there in the know?

Anywho, so that huge number before of 118! would be whittled down to something 'tiny'.

There'd then be a list of all possible compounds, which may as with the genome example from the Biology stack exchange, contain more than is actually achievable in our universe.

It would then follow, recalling that we're trying to reverse engineer the "Encyclopedia Galactica", that there would be a subset of optimal compounds...and not so useful compounds.

We could even extend that reverse engineering mentality to the Kardashev scale: 

energy production solutions must be made of something real: that is, a set of compounds configured in a particular way, with particular constraints. 

In order to arrive at a configuration, an intellect probably had to make that solution (which, that intellect, if it is real, has to be made from a genome*) *(from life that we've so far encountered).

So, from sheer maths we can deduce the parts list given M-Theory and the constraints we've observed  through combinatorics  --- and if Project Blue Brain is a success, why not take the discussion from the biology stack exchange, and digitally re-create all of the possible genomes with it (in a controlled environment of course)? Seeing as how it doesn't seem that Alcubierre and co will be creating the Enterprise any time soon... its the next best thing.

Whoa, what a load of stuff, that was some waffle - loads of tangents.

thanks for reading: I'd like to hear your thoughts on all that stuff!

Can combinatorics + our understanding of the patterns/laws of nature enable the 'singularity' that technocrats often speak of?

EDIT: I've been informed that combinatorial methods are used in pharmaceuticals and materials science and have been since the 1980s; why hasn't an index/library of all possible combinations been made? Can we nut out a method to do this, based on a multivariable coefficient and 3D/4D framework?
I mean, there'd have to be limiting factors to that huge number of possible combinations: the atomic latice, the number of different elements in a compound... and perhaps even the subatomic composition acts in some way as an additional limit?