Kali: anharmonic lambda calculus

You can play with some examples of lambda terms (SKK, Y combinator, Omega combinator, Ackermann(2,2), some duplications of terms, lists, Church numbers multiplications). It is important to try several times, because the reduction algorithm uses randomness in an essential way! This justifies the “reload” button, the “start” which does the reduction for you (randomly), the “step” which choses a random reduction step and shows it to you. Or you may even use the mouse to reduce the graphs.

It may look kind of alike the other chemlambda reductions, but a bit different too, because the nodes are only apparently the usual ones (lambdas, applications, fanins and fanouts), in reality they are dilations, or homotheties, if you like, in a linear space.

I mean literary, that’s what they are.

That is why the name: anharmonic lambda calculus. I show you lambda terms because you are interested into those, but as well I could show you emergent (actually em-convex) reductions which have apparently nothing to do with lambda calculus.

But they are the same.

Here is my usual example Ackermann(2,2), you’ll notice that there are more colors than precedently:

The reason is that what you look at is called “kali24”, which for the moment uses 7 trivalent nodes, out of 24 possible from projective space considerations.

I will fiddle with it, probably I’ll make a full 24 nodes versions (of which lambda calculus alone would use only a part), there is still work to do, but I write all the time about the connections with geometry and what you look at does something very weird, with geometry.

Details will come. Relevant links:

• kali24, the last version
• kali, the initial version with 6 nodes, which almost works
• em-convex, the dilations enhanced lambda calculus which can be also done with kali
• and perhaps you would enjoy the pages to play and learn.

One more thing: when all fiddling will end, the next goal would be to go to the first interesting noncommutative example, the Heisenberg group. Its geometry, as a noncommutative linear space (in the sense of emergent algebras, because in the usual sense it is not a linear space), is different but worthy of investigation. The same treatment can be applied to it and it would be interesting to see what kind of lambda calculus is implied, in particular. As this approach is a machine of producing calculi, I have no preference towards the outcome, what can it be? Probably not quite a known variant of lambda, quantum or noncommutative, because the generalization does not come from a traditional treatment [update: which generalizes from a too particular example].

Lambda terms playground

Is here. More examples will be added. Is done by a variant of chemlambda v2 with 6 trivalent nodes, as alluded here.

If you want to help, you may really kick up the level by writing a lexer-parser from lambda calculus 2 mol.

Also you may enjoy the other pages to play and learn.

The life of a 10-nodes quine, short video

I’m working on an article on the 10-nodes quine (see here and here previous posts) and I have to prepare some figures, well rather js simulations of relevant phenomena.

I thought I’ll made a screencast for this work in progress and put it in the internet archive:

https://archive.org/details/the-life-of-a-10-nodes-quine

UPDATE: I found, by playing, an even more, apparently, assymetrical variant of chemlambda, but also I found a bug in the js version, which is, fortunately, not manifesting in any of the cases from the menu of this page.  For the moment is not completely clear for me if the more, apparently, assymetrical variant behaves so much better, when I reduce lambda terms, because of the bug. I think not. Will tell after I fix the thing. Is something unexpected, not in my current program, but exciting, at least because either way is beneficial: I found a bug or I found a bounty.

Cryptocurrency for life (2)

Continues from (part 1). Back home and almost healed I read Anand Giridharadas crusade where he has a very reasonable point:

“But then I had the following thought.

Why are the people not connected to Epstein leaving this orbit, while people connected to Epstein remain?

Shouldn’t it be the other way around?”

To have a direct confirmation of these self-protected circles of power is interesting. Rich donors and academia are some of the players. I’m directly interested about this from the point of view of somebody who tries to do Open Science since a long time: to paraphrase Anand

Why are the people not obeying old practices of academic publication leaving this orbit, while people connected with the useless legacy publishers remain?

Shouldn’t it be the other way round?

The same academic managers are in so friendly relations with publishers which do not offer anything to the scientific community. The honest effort of Open Access has become a caricature where it is entirely normal to baptize the_author_pays_for_publication as the way to do Open Access.

OK, so what is this having to do with the subject of this post? Simple: if the cryptocurrencies communities do want to explore new social models then research (of biological life as decentralized computing, as I suggest) should be a part of it. You can’t turn to the old fatigued elites, because they already gave what they can do to MS or others alike. They don’t have new ideas since a very long time. Hot air with old boys support.

But now comes my point: would these cryptocurrencies efforts support a new research structure? Why not? There are very clever people there who understand the importance.

But maybe they are in bed with the circle of power. Just maybe.

The following are beliefs only (what proof can you ask?). For reasons along the lines explained previously, since years I’m very skeptical about anything ethereum based, but I am really amazed by btc. Well, but who really know?

Does not the cryptocurrency community (or the parts of it which are not in bed with the enemy) want to make a point in research?

Cryptocurrency for life

Biological life is a billions years old experiment. The latest social experiments, capitalism and communism, are much more recent. Cryptocurrencies experiments are a really new response to the failures of those social experiments.

We don’t really understand biological life starting from it’s computational principles. As well, we don’t understand in depth decentralized computation which is at the basis of many cryptocurrencies experiments.

My point is that we try to solve the same problem, so that we shall be able to evolve socially at a human time scale. Not in hundred thousands years, in decades instead.

Therefore it would be only natural if the active people in the cryptocurrency realm would dedicate significant financial support to the problem of life.