One of the least understood ideas of chemlambda is related to this question: which is the space where these artificial molecules live?
There are two different possible applications of chemlambda, each having a different answer for this question. By confusing these two applications we arrive at the confusion about the conception of space in chemlambda.
Application 1 concerns real chemistry and biology. It is this: suppose there exist real chemical molecules which in reaction with real other substances (which play the role of the enzymes for the moves, invisible in chemlambda). Then, from the moment these real molecules and real enzymes are identified, we get *for free* a chemical computer, if we think small. If we think big, then we may hope that the real molecules are ubiquitous in biochemistry and once identified the chemical reactions which represent the chemlambda moves, then we get for free a computational interpretation of big parts of biochemistry. Thinking big, this would mean that we arrive to grasp a fundamental manifestation of computation in biochemistry, which has nothing at all to do with numbers, or bits, or boolean gates, or channels and processes, all this garbage we carry from the experience (very limited historically) we have with computation until now.
In this application 1 space is no mystery, is the well known 3d space, the vessel where real molecules roam. The interest is here not in “what is space”, but “is life in some definite clear way a computational thing?”.
Application 2 resembles more to physics than biochemistry. It aims to answer to the question what is space? Ironically from neuroscience we know that clearly living brains don’t relate with space in any way which involves coordinates and crunching numbers. However, the most fundamental physics never escaped the realm of coordinates and implicit assumptions about backgrounds.
Until now. The idea proposed by application 2 of chemlambda is that space is nothing but a sort of a program.
I try to make this clear by using emergent algebras, and will continue this path, but here is the quick and dirty argument, which appears not to use emergent algebras, that chemlambda can explain space as a program.
(it does use them but this is a detail, pay attention to the main line.)
OK, so the artificial molecules in chemlambda are graphs. As graphs, they don’t need any space to exist, because everybody knows that a graph can be described in various ways (is a data structure) and only embeddings of a graph in a space need ahem … space.
Just graphs, encoded in .mol files, as used by the chemlambda visualiser I work on these days.
But, you see, chemlambda can do any computation, because it can do combinatory logic. The precise statement is that chemlambda with the reduction strategy which I call *the most stupid” is an universal computer.
What do you think about this bootstrapping?