How time flows: Gutenberg time vs Internet time

Based on  a HN comment, I made a page which proposes the hypothesis:

(Δ t-historic) = (Δ t-today)^(log 5/ log 2)

 

where the Δ t-historic is the time in decades from the invention of the printing press and Δ t-today is the time in decades from the opening of the ARPANET.

A collection of interesting correspondences is given, as well as some predictions, if this hypothesis is to be taken seriously.

The page has a small JS script for a calculator t-historic to t-today, so you can easily find new correspondences if you like the game. Please let me know in case.

UPDATE: There is now a very amusing python3 script by 4lhc, at this gist. It lets you write a year, recent or old, then it proposes two events, one from the old time and one from recent time. I played with it on my computer and it’s just cute!

[I had to install the wikipedia module and then the correct command is

“python3 The_Gutenberg_Internet_analogy.py”

wait a short moment and get the pair of events!]

 

 

Stick-and-ring graphs (I)

Until now the thread on small graph rewrite systems (last post here) was about rewrites on a family of graphs which I call “unoriented stick-and-ring graphs”. The page on small graph rewrite systems contains several formalisms, among them IC2, SH2 and system X are on unoriented stick-and-ring graphs and chemlambda strings is with oriented edges. Emergent algebras and Interaction Combinators are with oriented nodes. Pseudoknots are stick-and-ring graphs with oriented nodes and edges.

In this post I want to make clear what unoriented stick-and-ring graphs are, with the help of some drawings.

Practically an unoriented stick-and-ring graph is a graph with colored nodes, of valence 1, 2 or 3, which admit edges with the ends on the same node. We imagine that the nodes have 1, 2, or 3 ports and any edge between two nodes joins a port of one with a port of another one. Supplementary, we accept loops with no nodes and moreover any 3-valent node has a marked port.

marked-graphs

If we split each 3-valent node into two half-nodes, one of them with the one marked port, the other with the remaing two ports, then we are left with a collection of disjoint connected graphs made of 1-valent or 2-valent nodes.

marked-graphs-1

These graphs can be either sticks, i.e. they have 2 ends which are 1-valent nodes, or they can be rings, i.e. they are made entirely of 2-valent nodes.

marked-graphs-2

It follows that we can recover our initial graph by gluing along  the sticks ends on other sticks or rings. We use dotted lines for gluing in the next figure.

marked-graphs-4

A drawing of an unoriented stick-and-ring graph is an embedding of the graph in the plane. Only the combinatorial information matters. Here is another depiction of the same graph.marked-graphs-3

__________________________________________

 

Fold rewrite, dynamic DNA material and visual DSD

As it happened with chemlambda programs, I decided it is shorter to take a look myself at possible physical realizations of chemlambda than to wait for others, uninterested or very interested really, people.

Let me recall a banner I used two years ago

KeepCalmStudio.com-Shortest-Explanation-Of-Chemlambda-[Knitting-Crown]-Keep-Calm-And-Use-Rna-For-Interaction-Nets

It turns out that I know exactly how to do this. I contacted Andrew Phillips, in charge with Microsoft’ Visual DSD  with the message:

Dear Andrew,

I am interested in using Visual DSD to implement several graph-rewriting formalisms with strand graphs: Lafont Interaction Combinators, knots, spin braids and links rewrite systems, my chemlambda and emergent algebra formalisms.

AFAIK this has not been tried. Is this true? I suggest this in my project chemlambda but I don’t have the chemical expertise.

About me: geometer working with graph rewrite systems, homepage: http://imar.ro/~mbuliga/index.html or
https://mbuliga.github.io/

Some links (thank you for a short reception of the message reply):

Chemlambda:
– github project: https://github.com/chorasimilarity/chemlambda-gui/blob/gh-pages/dynamic/README.md
– page with more links: http://imar.ro/~mbuliga/chemlambda-v2.html
– arXiv version of my Molecular computers article https://arxiv.org/abs/1811.04960

Emergent algebras:
– em-convex https://arxiv.org/abs/1807.02058

 

I still wait for an answer, even if Microsoft’ Washington Microsoft Azure and Google Europe immediately loaded the pages I suggested in the mail.

Previously, I was noticed by somebody [if you want to be acknowledged then send me a message and I’ll update this] about Hamada and Luo Dynamic DNA material with emergent locomotion behavior powered by artificial metabolism  and I sent them the following message

Dear Professors Hamada and Luo,

I was notified about your excellent article Dynamic DNA material with emergent locomotion behavior powered by artificial metabolism, by colleagues familiar with my artificial chemistry chemlambda.

This message is to make you aware of it. I am a mathematician working with artificial chemistries and I look for ways to implement them in real chemistry. The shortest description of chemlambda is: an artificial chemistry where the chemical reactions are alike a Turing complete family of graph rewrites.

If such a way is possible then molecular computers would be not far away.

Here is a list of references about chemlambda:

– GitHub repository with the scripts https://github.com/chorasimilarity/chemlambda-gui/blob/gh-pages/dynamic/README.md
– page which collects most of the resources http://imar.ro/~mbuliga/chemlambda-v2.html

Thank you for letting me know if this has any relation to your interests. For my part I would be very thrilled if so.

Best regards,
Marius Buliga

Again, seems that these biology/chemistry people have problems with replies to mathematicians, but all ths makes me more happy because soon I’ll probably release instructions about how everybody could make molecular computers along the lines of Molecular computers.

I’ll let you know if there are future “inspiration” work. Unrelated to chemlambda, there are several academic works which shamelessly borrow from my open work without acknowledgements, I’ll let you know about these and I’ll react in more formal ways. I hope though this will not be the case with chemlambda, however, this happened before twice at least.  (I say nothing about enzymes/catalysts, category theory and cryptocurrencies… for the moment.)

Finally, here is a realization of the lambda calculus beta rewrite via a FOLD rewrite

arrowlink-2

which shares a relation with the ZIP rewrite from Zipper Logic. It seems I was close to reality,  now though I got it exactly 🙂 .

Let’s talk soon!

 

 

 

Small graph rewrite systems (5)

Here are some more tentative descriptions of system X and a play with the trefoil knot. This post comes after the intermezzo and continues the series on small graph rewrite systems.

Recall that system X is a proposal to decompose a crossing into two trivalent nodes, which transforms a knot diagram into an unoriented stick-and-ring graph.

2cols-spin-x

The rewrites are the following, written both with the conventions from the stick-and-ring graphs and also with the more usual conventions which resemble the slide equivalence or spin braids mentioned at the intermezzo.

The first rewrite is GL (glue), which is a Reidemeister 1 rewrite in only one direction.

2cols-spin-gl-x

The second rewrite is RD2, which is a Reidemeister 2 rewrite in one direction.

2cols-spin-rd2-x

There is a DIST rewrite, the kind you encounter in interaction combinators or in chemlambda.

2cols-spin-dist-x

And finally there are two SH rewrites, the patterns as in chemlambda or appearing in the semantics of interaction combinators.

2cols-spin-sh1-x

2cols-spin-sh2-x

One Reidemeister 3 rewrite appears from these ones, as explaned in the following figure (taken from the system X page).

2cols-spin-rd3

Let’s play with the trefoil knot now. The conversion to stick-and rings

2cols-spin-3foil

is practically the Gauss code. But when we apply some sequences of rewrites

2cols-spin-3f-2

we obtain more complex graphs, where

  • either we can reverse some pairs of half-crossings into crossings, thus we obtain knotted Gauss codes (?!)
  • or we remark that we get fast out of the Gauss codes graphs…

thus we get sort of a recursive Gauss codes.

Finally, remark that any knot diagram has a ring into it. Recall that lambda terms translated to chemlambda don’t have rings.

An example of “Official EU Agencies Falsely Report More Than 550 Archive.org URLs as Terrorist Content”

Today I read Official EU Agencies Falsely Report More Than 550 Archive.org URLs as Terrorist Content.  Two comments on this.

1. It happened to me in Feb 2019. I archived one of my stories from the chemical sneakernet universe. The original story is posted on telegra.ph. Here is the message which appeared when I checked the archived link:

GVFoyIh

What? I contacted archive.org and got an answer from the webmaster, pretty fast. The problem was with telegra.ph, not with my link in particular. Now the archived link is available.

After I sent the message to archive but before I received the answer, I searched for a way to contact EU IRU, to ask what the problem might be.  I was unable to identify any such way. However there was a way to send a message to EU officials, who might redirect my message to whom it may concern. It worked, but it took longer than the time needed by archive webmaster to respond and unblock the link. I was not contacted since.

2. As you see in the post from archive, it was not EU IRU the institution which sent the blocking orders. But nevermind, how can one try to block arXiv articles? This reminded me of a very recent story: Google Scholar lost my Molecular computers arXiv article. As the article is on the same subject as the story from point 1, I wonder if by any (mis)chance Google Scholar received a blocking order.

System X, semantic pain and disturbing news to some

This is a temporary post. Soon some news will come, some disturbing for some. This is just to entertain you with the System X, a small graph rewrite system proposed as a replacement for slide equivalence. Here is some prose I wrote while trying to understand 3 tiny graphic beta rewrites. This qualifies as semantic pain, but it was a very good exercice because it gives ideas (to those prone to have them, as opposed to those who lack personal ideas and take them without acknowledgement).

Small graph rewrite systems (4)

This post follows Problems with slide equivalence. A solution is to replace slide equivalence with System X.

This supposes to change the decomposition of a crossing like this:

2cols-spin-conv

I let you discover system X (or will update later) but here I want to show you that the Reidemeister 3 rewrite looks like that:

2cols-spin-rd3

There is now a page dedicated to small graph rewrite systems and stick-and-rings graphs.