Articles – Konrad Voelkel's Blog

Ich bin hier gerade in Rot an der Rot in einem Seminar über die Rolle der Informationstheorie in den Naturwissenschaften. Mein Vortrag hat heute statt gefunden, es war der vierte von zwanzig und behandelte bedingte Entropie, zusammen mit den notwendigen Voraussetzungen aus der diskreten Wahrscheinlichkeitstheorie, der Begrifflichkeit der Entropie (Information) an sich und zahlreiche Anwendungen.

Vorgetragen habe ich mit Folien (am Beamer), es dauerte etwa 90 Minuten und ging am Ende ein bisschen zu schnell. Ich habe auch noch ca. 90 Backup-Folien mit deutlich mehr Informationen vorbereitet, bevor ich den konkreten Vortrag daraus destilliert habe. Die Folien sind mit der Latex-Beamer-class erstellt.

Die Folien zum Vortrag (ca. 35, zum Vortragen optimiert) gibt es hier, und
die deutlich umfangreichere Version (ca. 90, mit Text vollgestopft) gibt es hier.

Beides gibt es natürlich ohne Gewähr, allerdings habe ich (meines Wissens nach) alle (2) Fehler korrigiert, die das Publikum gefunden hat.

Quellen waren die Paper von Shannon und Weaver, das Buch von Brillouin (Science and Information Theory) und meine alten Notizen zur Stochastik aus dem Vordiplom (zusammen mit dem einführenden Buch von Hans-Otto Georgii, das ich immer noch gern zum Nachschlagen verwende). Einzelne Grafiken stammen von Wikipedia, andere habe ich gezeichnet (und auch als public domain in Wikipedia eingebracht). Meine Zeichnungen habe ich mit Inkscape erstellt.

Viel Spaß damit!

I just finished Decoding the Universe – How the new science of information is explaining everything in the cosmos, from our brains to black holes, written 2006 by the former mathematics student and now associate professor of journalism Charles Seife, apparently well known for his other books Zero and Alpha&Omega (which I didn’t read).
The book in Google Books and a much shorter review I wrote in German on Amazon.de

Overview

Overall, this is an edutainment book I would recommend to anyone who is remotely interested in either relativity theory, black holes, quantum mechanics, theories of everything or the nature of life.
Depending on your previous knowledge about physics, it will be a book you’ll read very fast or at your usual literature speed. It doesn’t contain any mathematics beyond talking about binary digits (0 and 1). In contrast to many other books, the passages about concepts I knew very well weren’t boring but written in a good expository way that will enable me to explain the concepts better to others in future. Each chapter contains some historical remarks and anecdotes (and not only the most commonly known stories). The passages which explained concepts that were new to me explained them very good and I didn’t have the feeling of missing anything (a problem I had with some parts of Penrose’s Road to Reality before I learnt the math elsewhere).
Perhaps I should stress that the ideas promoted in the book are fairly standard by now and there is not so much debate in the scientific community about it. It does not discuss string theory vs. loop quantum gravity or any other crackpot magnet debate. You can expect to get solid education from the text (at least most of it, see my discussion of chapter 9 below).

Now let’s see what the individual chapters are about:

1. Redundancy

Introduces codes and code-breaking (cryptography) in the context of the second world war, then uses this to illustrate redundancy in human languages. Contains some anecdotes about Turing.

2. Demons

First discusses Lavoisier’s caloric theory in chemistry, then its problems, the industrial revolution and Carnot’s theory of perfect (reversible) heat engines. The second law of thermodynamics (entropy increases) is presented, although entropy isn’t mentioned explicitly. Some stories about Boltzmann and Maxwell are told. The Bell curve (of a Gaussian distribution) is explained (with pictures and a throwing-marbles-in-a-box analogy). Then entropy is defined and its connection to time (reversibility) is stressed. Maxwell’s daemon is introduced.

Carnot engines are explained particularly well, you can’t get it wrong from this exposition.

3. Information

The history of information theory around Shannon. Definition of a bit (binary digit). Illustration of the importance of information with a story about Paul Revere and the American civil war. Then the relation between entropy and information is explained in-depth. Brillouin’s connection of thermodynamic entropy to Shannon’s information-theoretic entropy and Landauer’s work on limits of computation (cost of erasure) are presented, which ultimately leads to an explanation why Maxwell’s daemon is impossible.

The historical remarks about the importance of communication during the civil war and the discussion of the impossibility of Maxwell’s daemon were enlightening.

4. Life

This chapter starts with a discussion of Schrödinger’s lecture “What is life?” and continues with a discussion of the genetic code, DNA computers and the relation between evolution and information. The story of the Lemba Jews in Zimbabwe is told.

This chapter really takes its time to convince you that DNA is a storage device for information and can be used in a Turing machine device, so every cell is a computer of some kind.

5. Faster than light

Einstein and some history, special relativity and the double-slit experiment (wave-particle duality). The Michelson-Morley experiment. The spear-in-a-barn paradox. Quantum tunnelling.

This chapter might be a little bit boring if you know some special theory of relativity.

6. Paradox

More on wave-particle duality, self-interference and superposition. Schrödinger vs. Heisenberg and Schrödinger’s cat. Entanglement and the Einstein-Podolsky-Rosen (EPR) experiment. Gisin’s experiments in Geneva.

While the historical remarks and the explanation of Schrödinger’s cat is pretty similar to other books on the topic, I very much enjoyed the discussion of Gisin’s experiments and “spooky distance action”.

7. Quantum information

Qubits, more on Schrödinger’s cat, quantum computing, Shor’s and Grover’s algorithm. The quantum Zeno effect. Measurements undertaken by Nature and the Casimir effect (vacuum fluctuations). Decoherence. A new axiom: “Information can be neither created nor destroyed”.

The notion of qubits is explained with the example of Schrödinger’s cat and then the cat is debunked via decoherence occurring due to vacuum fluctuations. Nevertheless, decoherence doesn’t get enough room for a solid understanding.

8. Conflict

More on spooky distance action and Gisin’s experiments. Quantum teleportation and causality. Black holes, the no-hair theorem and Hawking radiation. Black holes as computers.

The author clearly favours the axiom that information can not be destroyed and lays out what you need to understand to get the next chapter’s ideas on information preservation in black holes. The passages on black holes as computers are interesting but slightly misleading, because it’s more a metaphor than a concept.

9. Cosmos

More on black holes and their entropy. The holographic principle. Discussion about the infinite universe and some version of the infinite monkey theorem, leading to a many–worlds theory. The Copenhagen interpretation and a many-worlds interpretation of quantum physics. The end of all life due to the second law of thermodynamics.

The holographic principle deserves more room than it is given in this chapter. The argumentation for many worlds because of an infinite universe is not very clear to me (I think it’s just wrong). The many-worlds interpretation of quantum physics is explained very nicely, although it contains no single word on science theory (which, in my opinion, dictates to abandon theories about the unfalsifiable…).

Appendices and bibliography

The first appendix explains logarithms and why the base is not that important. The second explains entropy in Shannon’s sense in more detail. The bibliography contains a lot of helpful references (including some ArXiv papers) but sadly, they aren’t references explicitly throughout the text.

Conclusion and recommendation

It was a nice to read survey of applications and instances of information theory and I guess for most people who are slightly interested in any of the topics mentioned, it would at least help to choose the next book to read. It’s not even expensive!

Writing from my very last day at the ICTP in Miramare (Trieste), Italy, I thought it’s time to summarise some impressions, as promised. First, some remarks on the ICTP and sightseeing around Miramare (which might be useful to future visitors), then I will comment on the Summer School and finally the Conference on Hodge Theory and Related Topics.

The ICTP

• The concept of the ICTP, founded 1964 by Nobel laureate Abdus Salam, seems to be, very broadly said, to give researchers in physics and mathematics from third-world-countries opportunities (including money) for research and learning with scientists from developed countries. To accomplish this goal, they have short-time visiting scientists (for about 6 months) and host a lot of summer schools, conferences and workshops in many different areas. Participants from not-that-much-developed countries get funding for housing and food, in the ICTP Guest Houses and restaurants. In my opinion, this works well, since I met several mathematicians from developing countries (like India or the USA ).
• The buildings I’ve heard of are: Leonardo Da Vinci Building, Enrico Fermi Building, Adriatico Guest House, Galileo Galilei Guest House. Just some small hints for anyone who intends to go to the ICTP:
  • In the Leonardo Building main lecture hall, there is only one point in the whole room where you can find outlets. So, if you intend to use a laptop the whole day, find this spot (above, in the centre) and stick to it
  • The coffee machine in the Leonardo Building (near the toilets, ground floor) isn’t that bad, if you choose the sugar level to be less than the default value of 6/8 points (more than 1/8 is already too sweet for me, and I like sweet coffee).
  • The library in the Leonardo Building is a very nice place to hang out and wander off.
  • In the Adriatico Guest House, there is a vending machine for beer. It costs only 60 cent and isn’t that bad. The problem is: if you come late, it’s empty.
• The food in the Leonardo restaurant at the ICTP was not as good as you might expect from Italy. Especially in the evening, you get exactly the same as for lunch – but now it’s probably cold and you have less choice. Therefore, a lot of people went to the next city to have dinner (which is, of course, more expensive).

Sightseeing around Miramare, Trieste and Venice

• Miramare: there is the famous Miramare castle, surrounded by an artificial (yet beautiful) park, which is a must-see (i.e. exotic birds, fishes, turtles, palm trees, small pathways etc.).
• Trieste: I have no idea what I saw, I just walked across the city randomly. It is a nice, small city with a lot of restaurants. The sea side is not that beautiful but the buildings often look like imported from Vienna. I totally recommend eating ice cream all the time.
• Walking from Miramare to Trieste: Probably a bad idea. I did it three times, but I have to admit that the last third of the way, which is about 30 minutes long, is not beautiful at all. If you don’t know where to go, you’ll end up walking down a big street with high walls to the left and the right side for the whole 30 minutes. It is impossible to walk this last part along the sea. The first part, speaking of the hour it takes to walk from Miramare to Barcola, is nice, although the way along the sea is also the way along a big street. Anyway, there is a bus.
• Grotta Gigante, a huge cave, probably (at least officially) the largest cave that you can visit as ordinary tourist, in the world. And it is really gigantic! I’ve never been to any cave before and it was impressive.
• Venezia – only 2 hours and 10 EUR away, very nice (I guess there is no need to say more).

Miramare park main gate, near the ICTP

View Larger Map

Summer School

The summer school took two and a half week, where the first week was devoted to (recall?) very basic material: the first lectures defined manifolds and varieties and rushed over to de Rham cohomology, Kähler forms, sheaves, schemes and by the end of the first week the lectures about variations of Hodge structures and mixed Hodge structures reached the limit of what I knew already before (since I used my train ride to skim through Voisin’s book).
Now seems to be a good time to thank Andreas Höring for having teached classical geometry of Kähler manifolds in Paris so well.
Since the lectures of Migliorini and de Cataldo on the Hodge theory of maps assumed knowledge of Abelian categories and spectral sequences, I still don’t understand why the summer school started with these basic courses. I can not imagine that anyone who understood any of the lectures in the second week, could have possibly needed to learn what a manifold or a variety is. Maybe there are some hidden motives behind this, I haven’t asked the organisers.
The organisation was very good, all course material was printed out in sufficient quantity, the lectures didn’t take more time than expected, there was coffee & cookies in sufficient quantity twice a day and the overall working and learning atmosphere was fine. I missed problem sessions a little bit, but the intended problem sessions might have just turned out to be example sessions instead because of people requesting this. I was impressed that the organisers found a quick replacement for Claire Voisin, who couldn’t come to Trieste. The replacement talks given by C. Schnell, F. Charles and M. Kerr were very good and understandable.
For the participants I recommend having a look at Charles Siegel’s blog and website for lecture notes he has taken.

(photo licensed from Mike Scoltock under a Creative Commons Attribution-NonCommercial 2.0 Generic License)

Conference

• D. Arapura: Beilinson-Hodge cycles on semiabelian varieties; his joint paper with Kumar on the Beilinson-Hodge-Conjecture is related. This was my favourite talk! (By the way, see also his (unrelated) exposition of D-Modules and related Hodge Theory which I didn’t know about before (thanks to Charles Siegel for pointing me to it)).
• L. Illusie: Semistable reduction and vanishing theorems, after Lan and Suh.
• P. Griffiths: Hodge domains and automorphic cohomology; there are some talk notes available. For the necessary background on Mumford-Tate groups, see Griffiths’ lecture notes from the summer school.
• M. Green: Vanishing of Chern Polynomials for Hodge Domains. He introduced his talk with a joke along the lines of “It’s my seventh talk since I came to the ICTP, and in many cultures, the number seven is special. After six days you should rest”. The talk was about his SIGMA joint paper with Carlson and Griffiths.
• C. Schnell: Néron models and Poincaré bundles. It wasn’t so much about Poincaré bundles than about mixed Hodge modules, Néron models and admissible normal functions.
• G. Pearlstein: The locus of the Hodge classes in admissible variations of mixed Hodge structure (joint work with Brosnan and Schnell).
• H. Movasati: Automorphic functions for moduli of polarized Hodge structures. He gave some intuition on modular forms as generating functions, then looked at the Hodge theory of elliptic curves, explained the notion of quasi/differential modular forms (the terminology seems to be unstable) and discussed some examples from physics.

• Doran: Normal forms for lattice polarized K3 surfaces and Siegel modular forms (I had to skip this talk in favour of sleep – but I was told that it was good).
• S. Usui: Neron Models in log mixed Hodge theory by weak fans; slightly related preprint.
• J. Carlson: Further speculation and progress on Hodge theory for cubic surfaces (joint work with D. Toledo); related preprints. He introduced the talk with a story which concluded by “if you’re confused, just keep going”.
• F. Charles: Remarks on the Lefschetz standard conjecture and hyperkähler varieties, see his preprint on the topic.
• L. Maxim: Characteristic classes of complex hypersurfaces, see related paper. He introduced the virtual tangent bundle of a (possibly singular) hypersurface in a smooth manifold (the difference between tangent and normal bundle in K-Theory) and functorial homology characteristic classes (like Todd, L, Chern, but on homology); the general case are Hirzebruch-type invariants. He proceeded to express the (complicated) Brasselet-Schürmann-Yokura “Milnor-Hirzebruch”-classes in terms of virtual Milnor-Hirzebruch classes and invariants of the singularities.
• M. Kerr: Mumford-Tate groups and the classification of Hodge structures (more accurately, classification of Mumford-Tate subdomains, joint work with Griffiths and Green).
• C. Siegel: The Schottky Problem. He explained the well-known genus 3 and 4 cases and his approach to genus 5.
• P. Dalakov: Deformations of the Hitchin section and DGLA’s.

• sadly, I missed the conference talks of E. Cattani, S. Cautis and L. Migliorini because I travelled back to Germany on Friday morning.

Again, Charles Siegel took notes for some of the conference talks, see here and here.

Conclusion

I would be happy to go to the ICTP again in this life. Also, Hodge theory seems to be nice (at least parts of it).

small remark: I heard some rumour about a conference last year where they decided about the pronounciation of “Hartshorne”. Clearly, the person is called Harts-horne, as several Australian mathematicians told me, but now the books name was decided to be Hart-shorne. Hilarious!

If you manage your (scientific) references, such as journal articles, arXiv papers and textbooks within some reference management system that uses BibTex as storage/export format, and you have local copies of your files, then the following might be of interest:

I wrote a JabRef export filter that takes a BibTex file with file links (so, BibTex fields of the form file={somefile.pdf}) and writes a linux shell script to rename the files systematically according to the scheme [bibtexkey] – [authors] – [title].[extension]. Then JabRef can find the file again via its automatic file association mechanism. I use lower-case bibtexkeys but the export filter is easily adaptable, read about it on the JabRef custom export filter documentation page.

Just create (or download) a file named “renamer.layout” and fill in this line:
\begin{file}mv "\format[FileLink]{\file}" "\format[ToLowerCase,FormatChars]{\bibtexkey} - \format[AuthorNatBib,ToLowerCase,FormatChars,RemoveBrackets]{\author} - \format[FormatChars,RemoveBrackets,ToLowerCase]{\title}.\format[Replace(.*:,),ToLowerCase]{\file}"\end{file}
then open JabRef and go to the menu entry Options->Manage custom exports->Add new where you enter (for example) “renamer” as Export name, the full path to your renamer.layout file in the Main layout file field and “sh” as File extension.

Then open your BibTex file (.bib) with JabRef and then select the menu entry File->Export and select in the drop-down-menu Files of Type your newly created export filter renamer (*.sh). This gives you a shell script which, if executed, renames all files linked from the BibTex document into a standardised format (and moves all into the directory from where you execute the script).

This is only useful if you have files linked from your BibTex file, so you might need to do this first. If you already have filenames that contain some metadata, like author names or document titles, you might be very happy with JabRef’s RegEx-capable automatic file finder, which can be configured in the menu entry Options->Preferences->External Programs->External file links.

Even if you don’t use JabRef, you can use this process as described by exploiting the export-as-BibTex-capabilities of your favourite reference management system.

 

You might ask “why”, and I respond: my files are all organised in a way from which I can easily extract metadata using only the tools some operating system provides, so in case I don’t have access to my BibTex file, I can still find the desired files using the GNU/Linux command locate. Of course, I also have included the BibTex information in XMP into the PDF files (which is another feature of JabRef that I like a lot), so nothing is lost if I ever switch the reference management system.

Another lesson learned from this blogpost: writing specific JabRef export filters is very easy. Another one I wrote is able to download automagically entries from the arXiv when the URL is supplied in the url BibTex field. I won’t post it here because you need to disguise wget as “Mozilla 5.0″, otherwise the arXiv won’t let you download stuff (robot protection). I hope those who are able to figure out the details are also responsible enough to not download huge amounts of papers from the arXiv.

Putting it together, this provided a convenient approach to get arXiv papers with full metadata included in filename, PDF and BibTex on my computer. The still-not-perfect part is the first, getting the metadata from arXiv in BibTex format – I use CiteULike as proxy (and would be happy to hear about better solutions with JabRef).

You might also ask why I keep copies of my references on my computer (or why they have to be linked from my reference management system). I just find it very convenient to use my laptop as eReader, even when no internet is available, and given that I have 100+ references in the system, it is good to have metadata such as keywords, abstract, reviews, annotations and so on.

I learned about JabRef export filters somehow by accident because of another project related to reference management, which you might hear about soon (not yet).