Mathematical treasures by Gregory Chaitin

My wanderings over various disciplines that usually lead mt to and fro, this time have led me back to gregory Chaitin. I have already read some of his articles while writing Country of Blindfolded bit this time the search has been started by a provocative paper How real are real numbers?.

This has directed me to Irreducible Complexity in Pure Mathematics and finally to a delightful, easy to read but very deep Meta Math! The Quest for Omega. The last one is especially worth recommending. Mathematics that is told with gusto and personal interest.

There are whole passages that are so close to my soul, that I can only quote them in extenso:

In my opinion, the view that math provides absolute certainty and is static and perfect while physics is tentative and constantly evolving is a false dichotomy. Math is actually not that different from physics. Both are attempts of the human mind to organize, to make sense, of human experience; in the case of physics, experience in the laboratory, in the physical world, and
in the case of math, experience in the computer, in the mental mindscape of pure mathematics.

And mathematics is far from static and perfect; it is constantly evolving, constantly changing, constantly morphing itself into new forms. New concepts are constantly transforming math and creating new fields, new viewpoints, new emphasis, and new questions to answer. And mathematicians do in fact utilize unproved new principles suggested by computational experience, just as a physicist would.

And in discovering and creating new mathematics, mathematicians do base themselves on intuition and inspiration, on unconscious motivations and impulses, and on their aesthetic sense, just like any creative artist would. And mathematicians do not lead logical mechanical “rational” lives. Like any creative artist, they are passionate emotional people who deeply care about their art, they are unconventional eccentrics motivated by mysterious forces, not by money nor by a concern for the “practical applications” of their work.

I know, because I’m one of these crazy people myself! I’ve been obsessed by these questions for my whole life, starting at an early age. And I’ll give you an insider’s view of all of this, a first-hand report from the front, where there is still a lot of fighting, a lot of pushing and shoving, between different viewpoints. In fact basic questions like this are never settled, never definitively put aside, they have a way of resurfacing, of popping up again in transformed form, every few generations. . .

So that’s what this book is about: It’s about reasoning questioning itself, and its limits and the role of creativity and intuition, and the sources of new ideas and of new knowledge. That’s a big subject, and I only understand a little bit of it, the areas that I’ve worked in or experienced myself. Some of this nobody understands very well, it’s a task for the future. How about you?! Maybe you can do some work in this area. Maybe you can push the darkness back a millimeter or two! Maybe you can come up with an important new idea, maybe you can imagine a new kind of question to ask, maybe you can transform the landscape by seeing it from a different point of view! That’s all it takes, just one little new idea, and lots and lots of hard work to develop it and to convince other people! Maybe you can put a scratch on the rock of eternity!

A good read ahead

Just a short note on a book I have found on the arXiv:
Complex and Adaptive Dynamical Systems: A Primer by Claudius Gros.

On first impression it looks interesting and accessible, an joind an already quite rich shelf of electronically available books on networked systems.

Antibiotics

A couple of news stories have drawn my worried attention to the status of medical research. The appearance of more and more bacteria strains that are highly resistive to the current generations of antibiotics is showing the difference between a natural process - such as evolution of bacteria - and the socially driven planned activity of medical research.

While it would be unjust to call the process under which bacteria reach resistance to new generations of drugs "easy" and "costless" (as the billions of dying bacteria for each one that survives and multiplies prove), the human effort, with its needed billions of dollars is much less flexible.

I recall a quote from Lem's Magellan Cloud, hwere infections are deemed to be long gone - one of very few blunders of Lem. Nope. It's a lost war.

And in the current political and social climate, the situation is even worse due to lack of concentrations, and anti-scientific sentiments. I have read some news stories in the Polish dailies - accompanied by lots of supporting WEB comments - condemning doctors and medical industry for its inability to fight "trivial diseases". Probably, many of these comments were by people who discarded their antibiotic treatment just after a couple of days, when they "felt better".

I am quite pessimistic for the next 20 years. If, as recent article in Science claims,

more people die from the methicillin-resistant Staphylococcus aureus (MRSA) bacterium than from HIV in the United States

then we need to start worrying. The number of new drugs is decreasing. The activity of bacteria is not and will not. You do the math yourself.

Revival - perhaps

Due to vacation season and lots of work I have almost abandoned the blog in the past months. Perhaps it is time to revive it? I'll try...

Reading `Trouble With Physics' the second time

As indicated on the front cover - `Read this book. Twice' - I went through L:ee Smolin's Trouble with physics again. And I found a nugget I have missed previously. It concerns the positioning of Science as social enterprise, as a very special social enterprise. Ethics of the scientific community that Smolin describes are very close to my heart. But there's one point I tend to disagree.

Membership in the community of science is open to any human being. Considerations of status, age, gender, or any other personal characteristic may not play a role in the consideration of a scientist's evidence and arguments, and may not limit a member's access to the means of dissemination of evidence, argument and information. Entry to the community is, however, based on two criteria. The first is the mastery of at least one of the crafts of a scientific subfield to the point where you can independently produce work judged by other members to be of high quality. The second criterion is allegiance and continued adherence to the shared ethic.

Well, formally I fulfill the first criterion - PhD in theoretical physics (however ancient) may be considered a sufficient proof of mastery of the craft. But in my little crusade for revival of amateur science I think of those who have only touched the scientific method and life during their studies. If we are able to promote their adherence to the scientific ethic, even when they do not produce the work judged to be `high quality', but just to spread the understanding and the ethic, would be a great and much needed success for science.

Anyway, the second reading was as much pleasure as the first one.

Almost final draft of Country of Blindfolded

The link for the In the Country of Blindfolded has been updated to an almost final draft of May 2008.

Fruitful reading!

Is there a place for Amateur Scientists?

I pride myself on being a contemporary Amateur Scientist. Whether this pride is justified or not is not for me to decide, but I staunchly believe in the need for such backing of institutional Science. Recently my dedication was strengthened. The story below shows how and why...

The story begins with an essay competition I read about in New Scientist

Wellcome Trust and New Scientist essay competition

In partnership with 'New Scientist', the Wellcome Trust runs an annual competition inviting postgraduates and postdoctoral researchers in science, engineering and technology to tell the world about their work.

The competition is about encouraging researchers to communicate their science and to explore the possible implications of their work for society. The judges look for interesting, creative and fresh approaches, in a style that would appeal to readers of New Scientist. The competition is open to entries from PhD students who are registered at an internationally recognised university.

I decided that while the amount of actual research I do is rather minimal (a few arXiv preprints) I do have something to say - mostly tongue-in-cheek - with particular motivation coming from the effort to defy the last limitation of the participation. There was no age limit - but you have to be registered at a recognized university? So, in direct violation of the rules I submitted the following essay, arguing that Science can be done outside such institutions, more, that such activities should be encouraged...

Sociophysics from Home


Today’s science is a domain of universities, international research projects and formalised grant processes. Groups of specialists communicate in a language that is incomprehensible to anyone outside their circle. Even the rules of this competition reflect such view – the participants are limited to those affiliated with appropriate research institutions. Is it because science is `done' only there?

On the other hand the social reception of science is getting less and less favourable, the appeal of scientific curiosity is diminishing. Other `narratives’ are growing in popularity, some of them openly irrational and anti-scientific. The conventional response is to try to get more and more young people to universities. This is, of course, important, but not enough. Many of these students leave science for other occupations and never return to the scientific frame of mind. My own story describes such a return to science. What I call for is restoration of the status of AMATEUR SCIENTIST.

Of course, there are disciplines where the huge machinery and funding are simply necessary condition for success. But there are discoveries that may be made by amateurs, and other useful roles they may play.

My involvement with applications of physical methods in sociology (sociophysics) is an interesting example. Long after I left semiconductor research I have heard someone mention Bose-Einstein condensation in computer networks. This sounded so ridiculous that I decided to look it up, and step by step got enthralled by the topic. The existence of freely accessible databases and search engines allowed me to track some of the new developments. Even to my untrained eye some publications were just begging for corrections or extensions. So I dusted off my FORTRAN skills (and in some cases simply used spreadsheets) and wrote my own simulations. I went through some of the discipline topics: assortative matching, theory of cooperation, influence of leadership strategies on opinion formation. Thanks to arXiv site anyone can `publish’, so I did. The result was not overwhelming – a few people downloaded the papers, some commented on them, as far as I know they were not cited. I’d be the first to admit their limited value. But – and this is, I guess, the most important part of amateur research – I was able, as a participant, to change my outlook on the topic profoundly. For by doing something myself, I was able to see the difficulties and the simplifications, to recognize the processes, which is much more than just seeing the results.

One of the first questions was: does modelling of social phenomena using simplistic tools have any sense? Do we really gain understanding or is it just a fad, a convenient way to get grants and publications? Some papers were obviously trivial. But there were others that seemed to detect mechanisms underlying our real social behaviour, sometimes quite surprising. Somewhat later, I began to get referee requests from established journals. I try to do this task conscientiously, feeling that my lack of bonds imposed usually by one’s own career and the web of mutual obligations and cooperation allows quite a lot of candour in the analyses. And it just spurs my own interests. I feel that in this relationship between institutionalised and amateur science both sides win.

And this is the reason why I call for re-establishment of the honourable status of the amateur scientist. Obviously, it is not limited to sociophysics. Ecology and observational biology are classical examples from Victorian era. But there are many more, I am sure. The cost of promoting such activities for traditional scientific institutions is minimal, compared to the grand projects. Guidance in topic choice for prospective participants, coordination, help in access to publications. Occasional funding for conferences. Yet the outcome may be tremendous. Many of the people who now leave the universities, with reasonable education but no wish for a full time research career, could be brought back to the scientific way of seeing and understanding the world. Moreover, they would become science’s ambassadors, sometimes much better than `proper’ scientists, because amateurs are used to talk in comprehensible language. To get the `part time research’ back on the list of interesting and fashionable hobbies seems well worth the trouble.

Well, a few days after my submission has been posted I received a curt reply from the Wellcome Trust:

Hi Pawel,
Very sorry, but you are ineligible to enter the competition.

Now, I was not particularly surprised. And I fully agree with the right of the organisers to set out and enforce all the rules for the competition. Their money, their show, their right. But I was saddened. Because I do believe that every means to get greater public involvement in Science is beneficial - to both Science and Society. And the particular choice of rules reflects the division between the `certified', academic world of universities and the public, which, at best, is a target of communication, never a participant.

My initial thoughts were that the competition rules seem to embody the basic principle that
1. `Proper' Science is done only in established institutions. This is where ALL the scientists are.
And it seems that indeed they are confirmed.

While this is true for most of the scientific effort, there are clear examples of achievements coming from outside of the academic circles.
Moreover, by stressing the origin, instead of content of the work, we arrive at several consequences that are not necessarily positive:

2. We create an image that any `science' done without the official support of an established institution is, by definition, uninteresting or crank.
3. The general public gets estranged from the ivory tower, and drawn to `alternative explanations', sometimes with disastrous results in policy determination
4. Science itself loses a lot of possible active supporters through a lack of `retention policy', which could encourage the low-level involvement in scientific development.

My motivation for submitting the essay was directly connected with the main goal of the competition "As well as communicating their science, researchers are encouraged to explore the possible implications of their work for society." In a sense, I see my submission - with full recognition of breaking of the formal rules - as a practical experiment in sociology of science. As for the results...

I am more than ever convinced that increasing the public involvement with DOING science, on every level, is sensible and much needed. But I seem to be rather alone in my feelings...