Sunday, January 30, 2011

The extravagant burial of super-star Leibniz.

"Although today we recognize his contributions to be of outstanding importance, he died essentially neglected, and only his secretary attended his burial." (

Another interesting tidbit, the crucial importance of a mentor:
"In 1672 Leibniz was sent to Paris on a diplomatic mission, beginning a crucially formative four-year period there. Christian Huygens (1629–1695), from Holland, then the leading mathematician and natural philosopher in Europe, guided Leibniz in educating himself in higher mathematics, and Leibniz’s progress was extraordinary"

Feels like the equivalent of a one on one MsC in higher mathematics.

Yet another interesting piece of information, which underlines how everything is so simplified and post rationalized in a way that a lot of useful information is lost, is the fact that the now 'obvious' 'Fundemental Theoreom of Calculus' originally came from a publication by Leibniz (ignoring the Leibniz/Newton debate) called "Supplementum geometriae dimensoriae, seu generalissima omnium tetragonismorum effectio per motum: similiterque multiplex constructio lineae ex data tangentium conditione " or in English "More on geometric measurement, or
most generally of all practicing of quadrilateralization through motion: likewise many ways to construct a curve from a given condition on its tangents" publish in the scientific journal "Acta Eruditorum"

Yes, he called it 'a supplement' ... please teach the history of math!

Which brings me to the find of the month: is a project that has a mission statement this is SO much in line with our attitude towards mathematics, and they even have books, stumbled upon it while reading about Leibniz.

Mission statement: "Our journey towards utilizing original texts as the primary object of study in undergraduate and graduate courses began at the senior undergraduate level. In 1987 we read William Dunham's ..."

Thursday, January 27, 2011

66 Points to score your shooter AI.

I present a table that tries to capture the amount of AI sophistication in current shooters.
It is based on my experience, conversations with AI programmers, reviews, user comments and gameplay videos.

The points are roughly sorted by difficulty of implementation with current standard techniques.

It has been laying on my disk for quite some time waiting for a proper article for which I am never finding the time, so I finally gave up and decided to release it in hope for it to be useful even in this summarized table format.

Thursday, January 20, 2011

The plagiarize series - Jan C. Willems - In Control, Almost from the Beginning Until the Day After Tomorrow

"The work involved in preparing publications comes for a large part at the expense of time to think. In science, more writing goes together with less reading. The sheer number of publications makes it also very difficult to get acquainted with, and evaluate a new idea.
I miss the emphasis on breadth and depth, on quality rather than quantity, on synthesis of ideas, on debate and scrutiny rather than passive attendance of presentations, and on reflection rather than activity.
Sure, euphoria bears creativity, and skepticism paralyzes. However, questioning and criticism is an essential part of science. I have seen too many high profile areas collapse under their own weight: cybernetics, world dynamics, general systems theory, catastrophe theory, and I wonder what the future has in store for cellular automata, fractals, neural networks, complexity theory, and sync."

"Life is what intrudes on you while you are learning mathematics" (Jad Nohra & Tom Lahore)

Monday, January 17, 2011

Sunday, January 16, 2011

The plagiarize series - EWD1036

what is an EWD: "Dijkstra was known for his habit of carefully composing manuscripts with his fountain pen. The manuscripts are called EWDs, since Dijkstra numbered them with EWD, his initials, as a prefix. According to Dijkstra himself, the EWDs started when he moved from the Mathematical Centre in Amsterdam to the Technological University (then TH) Eindhoven. After going to the TUE, Dijkstra experienced a writer's block for more than a year. Looking closely at himself he realized that if he wrote about things they would appreciate at the MC in Amsterdam his colleagues in Eindhoven would not understand; if he wrote about things they would like in Eindhoven, his former colleagues in Amsterdam would look down on him. He then decided to write only for himself, and in this way the EWD's were born. Dijkstra would distribute photocopies of a new EWD among his colleagues; as many recipients photocopied and forwarded their copy, the EWDs spread throughout the international computer science community. The topics were computer science and mathematics, and included trip reports, letters, and speeches. More than 1300 EWDs have since been scanned, with a growing number transcribed to facilitate search, and are available online at the Dijkstra archive of the University of Texas.[6]"

EWD1036 partially explains (pages 4,5) why we started at calculus :) Thank you Mr. Dijkstra!

Also of note:
"Computer science as taught today does not follow all of Dijkstra's advice. Following Dijkstra's earlier writings, the curricula generally emphasize techniques for managing complexity and preparing for future changes. These include abstraction, programming by contract, and design patterns. ....."
I wonder how that plays with the whole OOP vs. DOD topic.

Thursday, January 6, 2011

While doing some basic calculus exercises, I bumped into proving the expression below, that shows that the (Riemann) definite integral of x2 is independent of the choice of sampling number.

This is expected, but it is nevertheless very impressive how elegantly the algebra works out when get down to it, wow.

Tuesday, January 4, 2011

The plagiarize series - Felix Klein - Elementarmathematik vom höheren Standpunkte - 1908

"I can characterize its standing most clearly perhaps, by the somewhat paradoxical remark that anyone who tolerates only pure logic in investigations in pure mathematics must, to be consistent, look upon the second part of the problem of the foundations of arithmetic, and hence upon arithmetic itself, as belonging to applied mathematics."


"With the construction of the calculating machine Leibniz certainly did not wish to minimize the value of mathematical thinking, and yet it is just such conclusions which are now sometimes drawn from the existence of the calculating machine. If the activity of a science can be supplied by a machine, that science cannot amount to much, so it is said; and hence it deserves a subordinate place. The answer to such arguments, however, is that the mathematician, even when he is himself operating with numbers and formulas, is by no means an inferior counter-part of the error-less machine, "thoughtless thinker" of Thomae; but rather, he sets for himself his problems with definite, interesting, and valuable ends in view, and carries them to solution in appropriate and original manner, He turns over to the machine only certain operations which recur frequently in the same way, and it is precisely the mathematician - one must not forget this - who invented the machine for his own relief, and who, for his own intelligent ends, designates the tasks which it shall perform.
Let me close this chapter with the wish that the calculating machine, in view of its great importance, may become known in wider circles than is now the case. Above all, every teacher of mathematics should become familiar with it, and it ought to be possible to have it demonstrated in secondary instruction."