**Wednesday, December 31, 2008**

**Irad Yavneh**(Technion)

*Title: Multiscale Computation*Abstract

16:30 // Taub 2 (computer science)

**Wednesday, April 22, 2009**

**Uri Bader**(Technion)

*Title: The Miracle of the Loaves and Fish*Abstract

16:30 // Location: Amado 233

**Wednesday, May 20, 2009**

**Leo Corry**Tel Aviv University

*Title: Einstein Meets Hilbert on the Way to General Relativity: Who Arrives First?*Abstract

16:30 // Location: TBA

**Wednesday, June 24, 2009**

**Robert Adler**(Technion)

*Title: Making Decisions on the Basis of Shape*Abstract

16:30 // Location: Amado 233

(1) Getting a bunch of soldiers to stand in a straight line.

(2) Ranking internet pages by relevance.

A: Both can be solved efficiently by multiscale methods.

Multiscale methods are well-established as an important approach for solving

various types of large problems in science and engineering. Based on these

two problems - the first borrowed from Alfred M. "Freddy" Bruckstein and the

second from Sergey M. Brin and Lawrence E. "Larry" Page - this talk will

strive to expose the immense promise and grave challenges associated with

multiscale computational techniques.

to be collapsed eventually because of the finiteness of population/resources/money.

Mathematical objects are often infinite, though, and the Ponzi dream might very well come true.

In 1924 Banach and Tarski, following Hausdorff, showed that one can decompose a sphere

into finitely many pieces and reconstruct from these pieces two copies of the same sphere.

This is now called the Hausdorff-Banach-Tarski paradox, though it is not a paradox - it is a

mathematical fact! It shows, among other things, that the collection of subsets of the sphere

is too rich to support a reasonable preservation low. This insight is one of the corner stones

of measure theory. Some mathematical objects do admit preservation laws, they are called "amenable".

Others do not. The definition of amenability of groups was given by Von-Neuman, following

the HBT paradox. It influenced many branches of mathematics ever since.

complete and correct, generally-covariant field equations of gravitation, lying at the heart of his

General Theory of Relativity. This was the fourth consecutive week in which he presented, at the

weekly meetings of the Academy, what he believed to be the culmination of many years of intense efforts to

generalize his principle of relativity so as to cover cases of relatively moving reference systems more general

than the inertial ones, and so as to apply to gravitation. In the previous three opportunities he soon realized

that the version he had just presented was still in need of further improvement. After his talk of November 20,

Einstein was euphoric about his achievement, which he was ever to consider the most important one of his

entire scientific career.

Five days earlier, on November 20, David Hilbert presented in Gottingen his own version of the equations

that, in the published version that appeared in print several months later, contained the correct and explicit

equations of the theory. According to a view that was commonly accepted for many years, Hilbert had

anticipated Einstein in five days in correctly formulating this important part of the latter's work. Recent

archival research, however, has shown that this was not really the case, and the actual historical situation

was much more complex.

Einstein had visited Gottingen in the summer of 1915 and there he presented the current state of his theory,

including the problems that were yet to be solved before it could be considered to be complete. Einstein

was absolutely delighted by the audience, one of the few in the world that included a considerable number

of people who could follow his ideas, ask difficult questions and perhaps even help him overcome some

of the difficulties. Above all, the presence of Hilbert in the audience was of great impact for him. A strong

personal and scientific friendship developed. Over the following months, and especially over the crucial

months of November, they corresponded intensely. This correspondence has been thoroughly analyzed as

part of the story of their encounter and their respective talks in November. As this interesting episode involves

two of the foremost scientists and one of the most momentous developments of the beginning of the twentieth

century, the discovery and publication of the relevant documents aroused much interest and debate within

historians of science as well as in broader circles. Still, despite the intrinsic curiosity that it arises, priority

disputes ("Who arrived first?") are not the kind of foremost questions that attract the interest and research

efforts of historians of science. This is also the case in the story of Hilbert and Einstein.

The main point of historical interest in the story concerns the first half of the title of this talk:

"Einstein meets Hilbert on the Way to General Relativity". Here we have these two prominent scientists

working out their long-term research programs, each one with his specific aims in mind, working within

different disciplines, using different methodologies, and based on different bodies of knowledge as their

respective backgrounds. Their scientific and personal encounter raises important and difficult historical

questions: What was the essence of their research programs? Where was each of them heading with their

work? How did their programs meet and what kind of interaction ensued? How this influenced each of

them and their programs? Where did the meeting ultimate lead to?

My talk will address all of these questions and will attempt to provide some of the answers that recent

research by several historians has brought to light.