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Chronomaitre Design

Chronomaître Design

Montres à simplification

by Ilan Vardi


My name is Ilan Vardi and I am currently working in horology, the study of clocks and watches.

My article L'astronomie de la montre was published in the December 2011 issue of the Bulletin de la Société Suisse de Chronométrie.

Contemporary astronomy is focused on astrophysics and cosmology: black holes, the evolution of the universe, etc., and "old style" mathematical astronomy describing the motion of the Sun and Moon is often left behind. It can therefore be forgotten that these "elementary" phenomena are the basis of our time measurement and that our watches' function is to display astronomical events. The subject of this article is to explain the sometimes subtle phenomena indicated by our watches and the horological applications examined are the day, the month, the year, sidereal time and the orientation of the sky.

I also discovered a new astrolabe application to illustrate the precession of the equinoxes with my astrolabe commemorating mathematician and poet Omar Khayyam (1048-1131).



My paper Should Harrison have won the Longitude Prize? appeared in the Spring 2011 issue of the magazine Watch Around. I present arguments which show that the conditions of the Longitude Prize were inherently flawed so they were essentially impossible to fulfill.


My paper La Marche du Soleil, un affichage naturel de l'équation du temps appeared in the December 1999 issue of the Bulletin de la Société Suisse de Chronométrie.

The equation of time is the difference between true solar time and mean solar time, but in Switzerland and France it is the other way round, the difference between mean solar time and true solar time. And so the confusion begins....

In my paper, I present a new method of displaying the equation of time which removes all ambiguity arising from these confusing conventions since it relies on a rendering of the actual astronomical phenomenon.


My design philosophy is that aesthetics and functionality should serve each other with simplicity.

If you want to reach me, send mail to ilan@chronomaitre.org.

I appreciate all types of watches


Good times @ Baselworld 2010


Just for fun, here is a little experiment which demonstrates the effect of the mainspring torque curve.








I am a mathematician, and I have written a number of mathematical papers, see my old website.

One my research themes is continued fractions and my results are described in my survey article Continued Fractions from Euclid to the Present Day.



Continued fractions directly apply to the selection of gear ratios in a drive train and I am presently studying methods to compute optimal gearing for astronomical watches.

My scientific interests are fairly broad, for example, I applied ideas from probability theory and physics to number theory in my papers Prime Percolation and Deterministic Percolation which appeared in the journals Experimental Mathematics and Communications in Mathematical Physics, respectively.



I have also written books, the first one being Computational Recreations in Mathematica

In the book I use Mathematica , the computer algebra system, to program numerous experiments in mathematics and computer science. In fact, I wrote a number of the functionalities of this programme during my years working at Wolfram Research.

The book has a Japanese translation which was quite successful.


The second one is: You Failed Your Math Test, Comrade Einstein. Actually, it is a collections of articles by a number of people (I only wrote the biggest part) which were edited by Mikhail Shifman.

The book is about antisemitic practices at Moscow State University in the 1970's. The so-called ``killer problems'' and my solutions were originally the IHES preprint Mekh-Mat Entrance Examinations Problems, which you can download thus saving you the trouble of buying the book and reading the purely political sections. The subject matter inspired me to discover the  

Fractal of David


Most of my papers are "scholarly", but even if you're not too much into academics, you might be interested in such stuff as the legacy of Archimedes.

I wrote a number of papers about Archimedes including Archimède face à l'innombrable which appeared in Pour la Science, the French version of Scientific American.

and the paper was also translated into Italian in Le Scienze.

I wrote a more extended English version called Archimedes, the Sand Reckoner which is a detailed analysis of his paper most accessible paper, The Sand Reckoner. To gain a better understanding, it proved helpful to typeset Archimedes' original (up to minor changes through the centuries) Ancient Greek paper Ψαµµίτης which is even referenced in Βικιπαίδεια, the Greek Wikipedia.

So, I am very interested in ancient mathematics and astronomy. I tried to communicate this in my paper What is Ancient Mathematics? which appeared in the Mathematical Intelligencer. I also gave the lecture Pi... et tout le reste at the Centre Pompidou in Paris about knowing what you know, see if you pass the test (in French).

If you know some mathematics then you might want to check out if you understand what you know by proving that pi exists. If you understand why this is even an issue, then you are already doing OK. You can then look at my proof that pi exists.

If you don't know anything about mathematics and would like to know what I think about it, I have written written a play called What is Mathematics? Actually it's in French: C'est quoi les maths ?.

I was also interviewed on this subject, along with some of my colleagues, by the French TV channel Arte, on the (very coincidentally named) programme Archimède.