15 augustus bevrijding Nederlands-Indië: Interneringskaarten Nederlandse krijgsgevangenen online

imageVandaag wordt herdacht dat Japan 66 jaar geleden capituleerde.

Hiermee kwam voor Nederland op 15 augustus 1945 een einde aan de Tweede Wereldoorlog. Vanaf vandaag zijn 26.000 persoonskaarten – zogeheten interneringskaarten – van toenmalige Nederlandse krijgsgevangenen in Japanse interneringskampen online beschikbaar. De kaarten, met een enorme historische waarde, zijn in te zien op deze website en op de studiezaal van het Nationaal Archief.

To die for an idea: Hipassus and the Irrational numbers

When reading history it seems that every time someone has a ground breaking scientific idea he is either killed or expelled, normally we take “the earth is flat/round” as the prime example but the discovery of irrational numbers could be a good one to break with that cliché:

Greek philosophy on mathematics was strongly influenced by their study of geometry.

For example, at one time, the Greeks held the opinion that 1 (one) was not a number, but rather a unit of arbitrary length. A number was defined as a multitude. Therefore 3, for example, represented a certain multitude of units, and was thus not "truly" a number. At another point, a similar argument was made that 2 was not a number but a fundamental notion of a pair.

These views come from the heavily geometric straight-edge-and-compass viewpoint of the Greeks: just as lines drawn in a geometric problem are measured in proportion to the first arbitrarily drawn line, so too are the numbers on a number line measured in proportional to the arbitrary first "number" or "one."

These earlier Greek ideas of numbers were later upended by the discovery of the irrationality of the square root of two.

image Hippasus, a disciple of Pythagoras, showed that the diagonal of a unit square was incommensurable with its (unit-length) edge: in other words he proved there was no existing (rational) number that accurately depicts the proportion of the diagonal of the unit square to its edge.

This caused a significant re-evaluation of Greek philosophy of mathematics. According to legend, fellow Pythagoreans were so traumatised by this discovery that they murdered or expelled Hippasus to stop him from spreading his heretical idea. Despite the validity of his discovery, the Pythagoreans initially treated it as a kind of religious heresy and they either exiled or murdered Hippasus for having produced an element in the universe which denied the doctrine that all phenomena in the universe can be reduced to whole numbers and their ratios. Legend has it that the discovery was made at sea and that Hippasus’ fellow Pythagoreans threw him overboard.

The funny thing is that “in the world” that knowledge was already out there. The concept of irrationality was implicitly accepted by Indian mathematicians since the 7th century BC, when Manava (c. 750–690 BC) was aware that the square roots of certain numbers such as 2 and 61 could not be exactly determined.

Greek ideas remained dominant until the 17th century.

Source: http://en.wikipedia.org/wiki/Philosophy_of_mathematics
Source: http://en.wikipedia.org/wiki/Hippasus
Source: http://en.wikipedia.org/wiki/Irrational_numbers
Source: http://en.wikipedia.org/wiki/Commensurability_(mathematics)

Here: http://www.cut-the-knot.org/proofs/sq_root.shtml I found 19 proofs that √2 is irrational.

image There is always at the start just 1 single person who finds a new thing, after that he has to convince the whole world that his or hers idea is right. I wonder how many ideas actually “make it” through the “wisdom of the crowd”. How many ground-breaking ideas got lost?

There are however occasions when groups do help e.g. when estimating it has been found that the average guesses over a large group of humans do produce a more actual result. Which is, of course, something totally different.

In the uber connected world we have today however one thing that worries me is that we all are slowly becoming locked in. Maybe some of the most basic ideas are wrong and the ideas that once were there needed to form a correct tree got lost in time. Maybe we should start completely disconnected societies which have no interaction with each other to be able to verify some principles, ergo creating wisdom of crowds over multiple (virtual) planets who are totally disconnected. Maybe in one of these planets someone will find a completely other theory that would e.g. easily explain π − e or if they are real or not or even develop some set of philosophy or sciences that do not even exist in our interconnected crowd.

Europe 2.0: europeana


I wonder if the they did any real sizing before opening this website although 2777 requests per second is a lot obviously. Well… is it? Anyway on the project site we read that the cultural heritage of Europe (3.5 million assets to start with) will be available again in some weeks.

Personally I think they should wait until January. There will undoubtly be more technical problems with the site and around Christmas most people are not available, making it not wise to reopen just before that time.

“The interface will be multilingual. Initially, this may mean that it is available in French, English and German, but the intention is to develop the number of languages available following the launch.”  …. no Dutch while the project is run by a core team based in the national library of the Netherlands, the Koninklijke Bibliotheek. Well you can also satisfy your European arty needs here.

Where I found 100 highlights from the KB Netherlands which kept me interested for a pretty long time.