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We compute additions and subtractions to model phenomena in Nature. That's perfect. In our first learnings, we play with stones, by arranging them on one side to add and by eliminating pairs, common to two piles, to subtract. And then later, we adopt for life the manual algorithms on decimal basis and computers on binary basis. However, one can have some clues that Nature operates by various natural algorithms, more symmetric for instance, where we only see trivial additions and subtractions. Is there some consideration in mathematics to distinguish alternative algorithms for computation, "Nature Based" ?

Bill Dubuque
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Frederic Dijoux
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  • Can you give an example of "natural algorithms"? I do not follow how in nature, only addition and subtraction are relevant, so I don't know what do you mean by "nature based"? - My first thoughts were genetic algorithms (inspired by natural selection) and ant colony optimization (inspired by ant colonies and other swarm behavior), among nature-inspired heuristic algorithms. But the context of your question seems to hint at something else? – Vepir Dec 11 '21 at 11:26
  • Sorry, I'm focused only on the natural algorithms that generate additions and subtractions. In particular, I work on the mathemarical models of chromatography and was surprised by a physical mechanism, more general, that is able to add and subtract two quantities; quite easy to simulate and check. "Nature" is herein for me, at least, restricted to the physical and chemical phenomena, but that's wider of course. This precised mechanism looks like what a child can do with pebbles to add or to subtract, but is a bit more clever. Is there a field that exhibit other algorithms ? – Frederic Dijoux Dec 11 '21 at 18:43
  • When you give the example of chromatography, it seems that by "subtraction" you mean "separation", i.e. separating/subtracting wanted from unwanted components. Would this be your definition of natural algorithms ("algorithms that generate additions and subtractions") ? In that case, algorithms found in things like neural networks come to mind, as they are trained in "separating" meaningful information from the rest. (on stack exchange: artificial intelligence and cross validated) – Vepir Dec 11 '21 at 19:46
  • Thanks. We are also interested by this aspects in our future practise. However, this adding/subtracting mechanism has just an indirect link with separation and can be found in very different phenomena. I'm looking for developments in fundamental arithmetic that can enrich the seminal concepts of addition/subtraction, commutativity/non-commutativity ; where hypercomplex concepts are probably not far. Do you have ideas ? – Frederic Dijoux Dec 11 '21 at 20:05

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