An extension of hamiltonian mechanics

This is an introduction to the ideas of the article arXiv:1902.04598

UPDATE: If you think about a billiard-ball computer, the computer is in the expression of the information gap. The model applies¬† also to chemlambda, molecules have a hamiltonian as well and the graph rewrites, aka chemical reactions, have a description in the information gap. That’s part of the kaleidos project ūüôā

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Hamiltonian mechanics is the mechanism of the world. Indeed, the very simple equations (here the dot means a time derivative)

hamiltonian-1

govern everything. Just choose an expression for the function H, called hamiltonian, and then solve these equations to find the evolution in time of the system.

Quantum mechanics is in a very precise sense the same thing. The equations are the same, only the formalism is different. There is a hamiltonian which gives the evolution of the quantum system…

Well, until measurement, which is an addition to the beautiful formalism. So we can say that hamiltonian mechanics, in the quantum version, and the measurement algorithm are, together, the basis of the quantum world.

Going back to classical mechanics, the same happens. Hamiltonian mechanics can be used as is in astronomy, or when we model the behavior of a robotic arm, or other purely mechanical system. However, in real life there are behaviors which go beyond this. Among them: viscosity, plasticity, friction, damage, unilateral contact…

There is always, in almost all applications of mechanics, this extra ingredient: the system does not only have a hamiltonian, there are other quantities which govern it and which make, most of the time, the system to behave irreversibly.

Practically every  object, machine or construction made by humans needs knowledge beyond hamiltonian mechanics. Or beyond quantum mechanics. This is the realm of applied mathematics, of differential equations, of numerical simulations.

In this classical mechanics for the real world we need the hamiltonian and we also need to explain in which way the object or material we study is different from all the other objects or materials. This one is viscous, plastic, elsot-plastic, elasto-visco-plastic, there is damage, you name it, these differences are studied and they add to hamiltonian mechanics.

They should add, but practically they don’t. Instead, what happens is that the researchers interested into such studies choose to renounce at the beaustiful hamiltonian mechanics formalism and to go back to Newton and add their knowledge about irreversible behaviours there.

(There is another aspect to be considered if you think about mechanical computers. They are mostly nice thought experiments, very powerfull ideas generators. Take for example a billiard-ball computer. It can’t be described by hamiltonian mechanics alone because of the unilateral contact of the balls with the biliard and of the balls one with another. So we can study it, but we have to add to the hamiltonian mechanics formalism.)

From all this  we see that it may be interesting to study if there is any information content of the deviation from hamiltonian mechanics.

We can measure this deviation by a gap vector, defined by

hamiltonian-2

and we need new equations for the gap vector \eta.  Very simple then, suppose we have the other ingredient we need, a likelihood function \pi \in [0,1] and we add that

hamiltonian-3

where z = z(t) = (q(t), p(t)). That is we ask that    if the system is in the state z then the velocity \dot{z} and the gap vector \eta   maximize the likelihood \pi .

Still too general, how can we choose the likelihood? We may take the following condition

hamiltonian-4

that is we can suppose that the algorithm max  gives a  categorical answer when applied to any of the 2nd or 3rd argument of the likelihood.

(It’s Nature’s business to embody the algorithm max…)

We define then the information content associated to the likelihood as

hamiltonian-5

So now we have a principle of minimal information content of the difference from hamiltonian evolution: minimize

hamiltonian-6

 

In arXiv:1902.04598 I explain how this extension of hamiltonian mechanics works wonderfully with viscosity, plasticity, damage and unilateral contact.

[see also this]

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Stats of perennial posts

How perennial is this blog? I took the top 20 directly accessed posts in each year, for 2017, 2018 and 2019 up to Feb 10.

Conclusion:from the 665 posts from this blog (666 with this one)

  • in each year only 20% of the top 20 posts are from the same year. So this blog is not read as a news source, it ages well.
  • ¬†73% of all posts available ever were accessed directly in 2017, 62% in 2018 and already 20% in the first month and 1/2 of 2019. Because 2019 just started, it follows that at least 60% of all posts since 2011 are read every year.

Also, 2015 and 2016 are not well represented in top 20, probably because of the chemlambda collection. Sad, because there are many other things here than chemlambda, for example posts about OA and OS.

Here is the data. Mind that the data probably represents only post read by people who don’t use blockers, as seen via the stats page of the blog. Helas, I would like to know what is the real situation, while in the same time I advice everybody to use blockers, as I do. As an author, I do need a bit a love though, indulge me.

 

2019 (up to Feb 10):

  • 134 posts accessed,¬†¬† i.e. 20%¬† of all posts¬† up to 2019
  • 20% from same year, 30% of posts from same year in the top 20
  • 2011 (1), 2012 (4), 2013 (5), 2014 (2), 2015 (0), 2016 (1), 2017 (0), 2018 (3), 2019 (4)
  1. (2013) Graphic lambda calculus
  2. (2012) Conversion of lambda calculus terms into graphs
  3. (2011) The Cartesian Theater: philosophy of mind versus aerography
  4. (2012) Introduction to graphic lambda calculus
  5. (2019) Graphic lambda calculus and chemlambda (I)
  6. (2012) Right angles everywhere (I)
  7. (2014) Chemlambda
  8. (2019) Universality of interaction combinators and chemical reactions
  9. (2018) Diagrammatic execution models (Lambda World Cadiz 2018) compared with chemlambda
  10. (2012) Right angles everywhere (II), about the gnomon
  11. (2019) Graphic lambda calculus and chemlambda (II)
  12. (2014) The price of publishing with arXiv
  13. (2016) SciHub and patent wars
  14. (2013) Teaser: B-type neural networks in graphic lambda calculus (I)
  15. (2013) The Y combinator in graphic lambda calculus and in the chemical concrete machine
  16. (2019) Kaleidoscope
  17. (2013) A machine for computing the Ackermann function in graphic lambda calculus
  18. (2013) Dictionary from emergent algebra to graphic lambda calculus (II)
  19. (2018) I deleted Facebook, Twitter and entered the Invisible College
  20. (2018) Projects for 2019 and a challenge

2018:

  • 407 posts accessed, i.e. 62% of all posts up to 2018
  • 20% from same year, 15% of posts from same year in the top 20
  • 2011 (3), 2012 (3), 2013 (5), 2014 (3), 2015 (0), 2016 (1), 2017 (1), 2018 (4)
  1. (2013) Graphic lambda calculus
  2. (2012) Conversion of lambda calculus terms into graphs
  3. (2011) The Cartesian Theater: philosophy of mind versus aerography
  4. (2014) Chemlambda
  5. (2018) Diagrammatic execution models (Lambda World Cadiz 2018) compared with chemlambda
  6. (2011) Gromov’s Ergobrain
  7. (2013) Cartesian method, scientific method and counting problems
  8. (2013) A machine for computing the Ackermann function in graphic lambda calculus
  9. (2012) Right angles everywhere (II), about the gnomon
  10. (2012) Introduction to graphic lambda calculus
  11. (2014) The price of publishing with arXiv
  12. (2013) Teaser: B-type neural networks in graphic lambda calculus (I)
  13. (2014) Distributed GLC
  14. (2018) John Baez’ Applied Category Theory 2019 post uses my animation without attribution [updated]
  15. (2018) What about arXiv/figshare/zenodo and the EU copyright reform?
  16. (2011) How not to get bored, by reading Gromov and Tao
  17. (2017) Chemical Sneakernet
  18. (2018) I deleted Facebook, Twitter and entered the Invisible College
  19. (2016) Open peer review is something others should do, Open science is something you could do
  20. (2013) Example: decorations of S,K,I combinators in simply typed graphic lambda calculus

2017:

  • 454 posts accessed, i.e.¬† 73% of all posts up to 2017
  • 20% from same year, 23% of posts from same year in the top 20
  • 2011 (3), 2012 (3), 2013 (5), 2014 (5), 2015 (0), 2016 (0), 2017 (4)
  1. (2013) Graphic lambda calculus
  2. (2017) The price of publishing with GitHub, Figshare, G+, etc
  3. (2011) The Cartesian Theater: philosophy of mind versus aerography
  4. (2012) Conversion of lambda calculus terms into graphs
  5. (2014) Chemlambda
  6. (2014) Distributed GLC
  7. (2013) Cartesian method, scientific method and counting problems
  8. (2017) Chemlambda for the people (with context)
  9. (2014) The price of publishing with arXiv
  10. (2012) Introduction to graphic lambda calculus
  11. (2012) Right angles everywhere (II), about the gnomon
  12. (2011) Gromov’s Ergobrain
  13. (2014) How to use chemlambda for understanding DNA manipulations
  14. (2013) A machine for computing the Ackermann function in graphic lambda calculus
  15. (2013) Unlimited detail is a sorting algorithm
  16. (2011) How not to get bored, by reading Gromov and Tao
  17. (2013) Hewitt Actor Model, lambda calculus and graphic lambda calculus
  18. (2014) Zipper logic
  19. (2017) More experiments with Open Science
  20. (2017) Back to the drawing board: all strings

Scientific publishers take their money from the academic managers, blame them too

Wonderful thread  at HN: https://news.ycombinator.com/item?id=19114786

Starting with “All this is an excellent ad for sci-hub, which avoids most of the serious drawbacks of publishers like Elsevier. It was interesting how that was relegated to a veiled comment at the end, “or finding access in other channels”. But basically if the mainstream publishers can’t meet the need, we do need other channels, and right now sci-hub is the only one that actually works at scale.

Then the discussion goes to “Blame the academic administrators who demand publications in top tier journals – the same ones who charge a ton for access.

Or “ in market terms the clients (researchers) manifest a strong preference for other products than those offered by the publishers. Why do they still exist? Does not make any sense, except if we recognize also that the market is perturbed

Enjoy the thread!¬† It shows that people think better than, you choose:¬† pirates who fight¬† only for the media corporation rights,¬† gold OA diggers who ask for more money than legacy publishers, etc…

UPDATE: for those who don’t know me, I’m for OA and Open Science. I do what I support. I am not for legacy publishers. I don’t believe in the artificial distinction between green OA, which is said to be for archiving, and gold OA which is said to be for publishing. I’m for arXiv and other really needed services for research communication.

My first programs, long ago: Mumford-Shah and fracture

A long time ago, in 1995-1997, I dreamed about really fast and visual results in image segmentation by the new then Mumford-Shah functional and in fracture. It was my first programming experience. I used Fortran, bash and all kinds of tools available in linux.

There is still this trace of my page back then, here at the Wayback Machine. (I was away until 2006.) The present day web page is this.

Here is the image segmentation by the M-S functional of a bw picture of a Van Gogh painting.

vangogh2

 

And here is a typical result of¬† fracture propagation (although I remember having hundreds of frames available…)

fisuri

 

The article is here.

What’s new around Open Access and Open Science? [updated]

In the last year I was not very much interested into Open Access and Open Science. There are several reasons, I shall explain them. But before: what’s new?

My reasons were that:

  • I’m a supporter of OA, but not under the banner of gold OA. You know that I have a very bad impression about the whole BOAI thing, which introduced the false distinction between gold which is publication and green which is archival. They succeeded to delay the adoption of what researchers need (i.e. basically older than BOAI inventions, like arXiv) and the recognition that the whole academic publication system is working actively against the researchers interests. Academic managers are the first to be blamed about this, because they don’t have the excuse that they work for a private entity which has to make money no matter the price. Publishers are greedy, OK, but who gives them the money?
  • Practically, for the working researcher, we can now publish in any place, no matter how close or anachronically managed, because we can find anything on Sci-Hub, if we want. So there is no reason to fight for more OA than this. Except for those who make money from gold OA…
  • I was very wrong with my efforts and attempts to use corporate social media for scientific communication.
  • Bu still, I believe strongly in the superiority of validation over peer-review. Open Science is the future.

I was also interested in the implications for OA and OS of the new EU Copyright Directive. I expressed my concern that again it seems that nobody cares about the needs of researchers (as opposed to publishers and corporations in general) and I asked some questions which interest me and nobody else seems to ask: will the new EU Copyright Directive affect arXiv or Figshare?  The problem I see is related to automatic filters, or to real ways the researchers may use these repositories.  See for example here for a discussion.  In   Sept 2018 I filed requests for answers to arXiv and to Figshare. For me at least the answers will be very interesting and I hope them to be as bland as possible, in the sense that there is nothing to worry about.

So from my side, that’s about all, not much. I feel like except the gold OA money sucking there’s nothing new happening. Please tell me I’m very wrong and also what can I do with my research output, in 2019.

UPDATE: I submitted two days ago a comment at Julia Reda post Article 13 is back on – and it got worse, not better. About the implications for the research articles repositories, the big ones, I mean, the ones which are used millions of times by many researchers. I waited patiently, either for the appearance of the comment or for a reaction. Any reaction. For me this is a clear answer: pirates fight for the freedom of the corporation to share in its walled garden the product of a publisher. The rest is immaterial for them. They pirates not explorers.