Sequential versus parallel

We (Sabadini, Schiavio and I) have just finished a paper on the algebra and geometry of networks (which I must remember to put on Arxiv). In any case, we wanted to give one example involving Petri nets.

The difficulty of writing something precise about Petri nets is that there is huge literature, with an enormous number of variations in definitions of nets and their behaviours. We chose to talk about the simplest version we could find.

Most concurrent systems consist of sequential components which have occasional communication at critical points.  In writing about Petri nets one thing struck me (us) which I had not realized so clearly before: a sequential process  with say n states is represented as a Petri net with n parallel places. This means that the Petri net of an n state sequential process has an exponential (in n) number of possible states (markings).
Of course only n are intended to be reachable.

It seems to me to be crucial to separate the sequential from the parallel aspects of programs. A correct algebra of programs should have two types of operations (one sequential,  of colimit type , the other parallel, of type limit). The relation between them should be the exactness which we see in categories of spaces.

Even in classical sequential programming there is the beginning of this phenomenon, namely that if then else is based on the distributive law of products over sums.

Unfortunate equations

The following unfortunate claimed equations seem to be having a deleterious effect on development of Science and Academia:

1. The excellence of a scientist's work =  the number of papers published.

Correction: Volume is not excellence.

2.  The excellence of a paper  =  the number of citations it receives.

Correction : Popularity is not excellence.

3. Publication of articles about teaching = evidence of excellence in teaching.

Correction : Teaching is practice guided by theory.

4.  The excellence of a scientists work =  amount of research funding accepted.

Correction : Accepting money, in particular from non-scientific bodies with private agendas, is not excellence.

5. The appropriate bodies to collect information about scientific excellence = self-selected private companies aimed at profit for investors.

Correction: False.

6. Theoretical Mathematics = Physics; Theoretical Physics = Mathematics.

Correction: Mathematics and Physics each have their own separate logic and mode of development. The equations result in mathematical theorems without proofs, and physical theories without experimental evidence.

7. Mathematics = Type theory pseudocode.

8. Categorification = the inverse of abstraction.

Correction: Abstraction by its nature is not bijective. The are many things which have the same abstraction.

9. (from a comment by Bill) Being told that you are being given an explanation = receiving an actual explanation.

Correction: Continuing to believe this means becoming a cult member equipped with buzzwords but with little useable scientific content. This unfortunate equation is the basic lie of various popular science journals, of the Expository sections of some professional journals, and of self-styled gurus, both male and female.

Remark: to be continued.

Tim Gowers: the good guys and the bad guys

Tim Gowers has written two posts in his blog, one on joining the bad guys and one on joining the good guys.
Both are about free access publishing in mathematics. The first is about author/institute payment for publishing papers. The second is about journals based on free archives with neither cost to reader or writer.

Unfortunately I don't think Gowers has much idea about the state of decadence in science today.

I quote one paragraph:
"There is another argument in favour of what publishers currently do, which is that they help your paper appear on citation indexes, they give you journals with impact factors, and so on. I hate all that stuff: the measures are incredibly crude and far less useful than a well-written reference. I think most mathematicians share my distaste. But a lot of other scientists don’t seem to, and there is a danger that if mathematicians are perceived as “not really publishing” any more, then they will not be understood or taken seriously in situations where they are competing with people from other subjects."

He feels distaste but does not realize that this use of numerical indicators is the end of academia. As I have mentioned elsewhere (http://rfcwalters.blogspot.it/2012/09/the-future-of-journals-iii.html) the committees which choose new staff in Italy are restricted to people with high numerical indexes, before any consideration of quality. The more rubbish you write the more likely you can choose your successors.

Applying for research grants in Italy

Italians seem to like labyrinthine procedures for applying for research grants. It gives them more opportunity to exercise their ingenuity and political skills. In particular the more levels in the hierarchy the better. Each level can contradict the next.

Here is a quotation from a character in Agatha Christie's Crooked House, speaking about research funding:
"I doubt if endowments ever do much good. They're usually spent in the wrong way. The things that are worth while are usually accomplished by someone with enthusiasm and drive -and with natural vision. Expensive equipment and training and experiment never does what you'd imagine it might do. The spending of it usually gets into the wrong hands".