randform

Last time when I was in Göttingen I found a poster at the math department documenting an art science collaboration between mathematics professors William Thurston, Kazushi Ahara and Sadayoshi Kojima on one side and a team around clothing designer Issey Miyake, notably including chief designer Dai Fujiwara of Issey Miyake (here a link to a partial version of the poster, see also absnews article by Jenny Barchfield). A result of this collaboration is that the Issey Miyake Fall-Winter 2010-2011 ready-to-wear collection is inspired by the geometrization conjecture.

From the poster:

In the mid-October of 2009, Prof. Thurston showed us the detail drawings of the “8 Geometry Link models as Metaphor of the Universe” They inspired us to make the collection based on them, accompanying design study with rope and toile. Considering the body itself as the Universe, we have added our own interpretation of beauty to them. The new perception of the body shared by all the members of the team resulted in the discoveries of new lines and forms, which were then applied to textile, color and detail studies. Thus the new collection has taken shape steadily, revealing its whole picture eventually. To sum up the exchange with Prof. Thurston led us to find a completely new kind of beauty and embody it in clothing. This mission was, as it were, an odyssee to explore the Universe with infinite imaginations.

The geometrization conjecture roughly says (I am not an expert on this) that a three dimensional volume form without boundary (a two dimensional analog of such a form would be for example the surface form (i.e. the “skin”) of a ball or the surface form of a doughnut) can be decomposed into “pieces” which have one of 8 characteristic “geometric structures”, which means roughly that in a small neighbourhood of any such “piece” there is – out of only 8 characteristic ways – one specific way to measure length. A theorem states that any three dimensional (oriented) volume form without boundary can be obtained by cutting a “thick” (that is instead of a rope take a ribbon) link out of a three dimensional sphere. Thus you can characterize special types of three dimensional volume forms (here: “the pieces”) by assigning a link to them. This is – by what I understood sofar- why there are 8 links (or link models) on the poster – they characterize the 8 types of possible “pieces”, which built up three dimensional volume forms without boundary.

Why do they call these 8 links “Metaphor of the Universe”? I can only make wild guesses, which sound rather like science fiction than science: Maybe if you imagine the space of the universe to be eventually such a three dimensional volume then by cutting it into pieces (may be along black hole horizons huh?!) and “measuring distances” (determine a metric) one could make deductions about the actual form of the universe? Or – reversely by making assumptions about the form of the universe (like e.g. that its space is a three sphere) one may get informations about what could be inside black holes…given that one finds all black holes…(this is just a funny joke).

But joking aside – I think they call it Metaphor of the Universe because these simple 8 links may be used to describe quite complicated things.

->wikipedia link math and fiber arts

short video clip about jboard (1.4 MB) (link to 12.1 MB)

randform reader Lano Ferryman asked in a comment to a randform post:

If you are so interested in new input devices – so why don’t you report on the new iPad?

answer: First of all I think there had already been quite some media coverage about the Apple iPad thus I dont really think that testing the iPad on randform is really needed. And in order to be fair one would need also to report on other similar tablet computers or tablet PCs. Moreover I haven’t seen the iPad yet, apart from displays in in-depth video demonstrations. Tim is a bit skeptical about it, since you can’t run a programming language on the iPad, so he couldn’t e.g. install his string-rewriter jsymbol on the iPad. So he is rather waiting, like there is e.g. a Berlin company called neofonie, which produces a similar pad, called wePad (wikipedia site (sofar only in german)) which is announced to run like with an Android-like-OS that is it is some Linux, but able to run with Android applications (and rumor has it, that google is also about to release an android powered pad), furthermore Adobe Air is available on the wePad, thus Flash would run on it (i am not such a fan of flash though). However the webpage of the wePad isn’t really overly informative. On the wePad’s facebook site (in german) one can at least read (in german) that more information in particular regarding price etc. is to be released tomorrow.

It is also that I am getting more and more reluctant to promote new technologies which make people want to consume more.

On the other hand its not that randform is totally uninterested. Tim has meanwhile some new programs, which would run nicely on an iPad-like pad. The above short clip displays his program jboard (under development) for using an electronic board. I was asking him to implement something like stickers (on the right side of the board) where you can store little pieces of text and graphics, which you can freely move and copy to other pages. The stickers are automatically “tagged” with parts of what the sticker holds, but one can also tag them also with any other self-designed icon/text. So for example if you have a table you are constantly referring to throughout a lecture then you can get that table from the sidebar by clicking on your icon. We forgot to display the highlight feature in the clip.

update 13.04.10 – I forgot to mention: Tim is not sure wether jBoard will be GPL, LGPL or something similar, in any case jBoard will be open. There will also no ridiculous patents be filed (like for the stickers). Further development of jBoard will be rather slow, in particular next week the semester starts again and Tim will mutate again into a teaching machine.

Vlad Alexeev had created a website called Impossible World which collects “impossible figures”, from Vlad Alexeev’s website:

Since some time I became interested in such artworks and figures that look usual at a first sight, but there is something wrong with them if you look at them more attentively. For me, the most interesting such figures are “impossible figures” which make an impression that they cannot exist in a real world.

I wanted to know more and tried to find some information about these figures in the Internet. I found numerous sites containing three or four different impossible figures, but there was no site devoted exclusively to the study of impossible figures. During this pursuit I made the acquaintance of impossible figures of Swedish artist Oscar Reutersvärd and images of Dutch artist M.C. Escher.

It has been icy and cold the last days in Berlin with a lot of snow (see above image from today). In an earlier randform post I indicated that there is quite a lot to tell about badly built US houses. Like, when living in New England, it happened one cold day that the dishwasher didnt work. It took us quite a while to find the reason. The reason was that a pipe, which was INSIDE the house, however too close to the outer wall, froze. Yes you understood correctly – the insulation of the house was so sparsely that this pipe froze inside the house!

But back to the image – if you ever wondered what these strange signs on lamp posts and trees in Germany may mean (like the blue sign in the image above which you see if you follow the arrow). These signs are giving a detailled description of hydrants and facilities for water, natural gas, district heat and electricity use. So the above sign in the image should indicate a water gate (SCHIEBER in german). This sign methodology makes it considerably easy to detect frozen and/or broken pipes in the soil. Hopefully there will be a change in the US regarding the saving of energy, otherwise one should may be think about developping a sign methodology for frozen pipes inside US houses…

graphics looking as from cellular automata (game of life?) and fluids in a psychadelic 1970 animation by Schwartz and Knowlton.
via dataisnoture

Our friend Sophie Molholm coorganized recently a conference in multisensory research. Looking at the conference announcement I felt inspired to ask myself again to what extend rational cognitive instances do influence perception. An example: A traffic light in the western world is usually considered to have the colors red-yellow-green (or at least red and green (although the new LED lights look kind of bluish)). However I think it is important to note that in japaneese the green color for a traffic light – is not “MIDORI” (green), but “AOUI”, which is BLU! Did this make japanese people more prone to call something green-bluish “blue” instead of green? Doing experiments for this example might be difficult due to the ethnic pecularities, but I am sure there exist other examples and probably even studies on that subject.

here a little collection of randform posts related to the subject:

naming-gaming: evolution of languages
wirepullers: artwork challenging salience
manicone: artwork challenging 4 dimensional space perception
focus and context, part I: evolution and knowledge formation
focus and context, part IV: A Physicist Experiments With Cultural Studies: knowledge formation in humanities vs natural sciences
Le manoir du diable: conscientious coloring of astronomical data
common sense: designing computer minds at media lab
canny skinny skin scans perception and quantum computing (see also focus and context, part IIa: A quantum computation game)
error incognito:perception and space
Dreammachine: psychadelic effects in neuroscience
uncanny paintings: link to an experiment using facial expressions as a feedback interface for a painterly rendering algorithm
visualizing meaning: link to a survey concerning the usefulness of diagrams and charts in knowledge building (and a funny comment to that)

Last weakend we were doing a visit to the Deutsche Museum.

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The frequent randform visitor knows that randforms main issue is not “popularizing science“.

Although we eventually may post an article which could be finally considered as “popular science” (last not least because we like to talk about science in a rather easy understandable way) we are mainly interested in discussing the communicational and perceptional manifestations of science. The visual ways of communication are here of special importance and thus we are especially proud that we were included in a carefully and thoughtfully edited book about blogs that are related to graphic design.

From the book cover:

Blog, weblog, logbook – these are words of our time. Although blogs have existed since the end of the 1990’s, they flourished only in recent years. Weblogs gained its popularity as a medium to tell stories and develop thoughts through dialogue.

With advancement of the Internet technology, creating and publishing a blog is as simple as it is to check your emails. What makes the difference is therefore, outstanding content. Blogs, Mad about design is a collection of the most interesting and exiting blogs that are related to graphic design.

Blogs, Mad about design
Mao Mao publications (2009) (blog)
ISBN 978-981-245-715-8

The text about randform in the book:

A blog that is dedicated to investigating the intersection between mathematics, physics, art and design. This includes visualizations and mathematical representations in terms of images, symbols processes, etc. as well as the general fundamentals of perceptive/cognitive thought, including topics that range from computers capable of seeing, to the architecture of information and interactive design.

The area of the above squares shall visualize a certain amount of money.

A little puzzle for randform visitors:

The upper outer square visualizes an amount which is … times bigger as the amount of the upper inner square.

The lower outer square visualizes an amount which is … times bigger as the amount of the lower inner square.

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In a recent post on his blog Terence Tao had the idea to scale the US budget and other data with the scale factor of 3/100 million. In particular the US population of 306.44 million shrinks -if one uses this factor- to about 9 people (306.44million/(100 million/3) =3.0644*3 =(approx) 9 people) which is about one to two average families. He did that in order to facilitate the comparision of the US-budget with a normal one-to-two family household budget.

I found that a useful visualization experiment and thus tried to do the same with the german budget – that is I used a scale factor which scales the population of Germany (originally 82.099 million down to 9, i.e. I used the factor 0.000 000 11 = 11/100 million (82099000*0.00000011 = 9.03..) and multiplied it with the corresponding amount in euro and in US-dollar (since I did this with an online currency calculator on different days there may be some variations). All calculations are without guarantee and I hope mistakes will be pointed out to me in the comment section. I abbreviate the number 1 billion = 10^9=1 000 000 000 with the letter B. So 1 B$ means 1 billion US dollar. Interesting figures are highlighted with an ->.

The revenues and spending in Germany are divided into the federal government (”Bund“) on one hand and the federal states (”Länder“) and districts (”Gemeinden“) on the other hand (here details in german). Both shares are very roughly the same. For example in 2005 the spending was
Bund 294.0 BEuro
Länder 259.3 BEuro and Gemeinden 153.3 BEUro
alltogether: 625.9 Beuro

I found no survey on the federal states and districts, besides this overall Länder and Gemeinden revenues and spending. The federal states are for example in charge for schools, I think they do not pay for military (?). However besides this the federal government budget (”Bund“) gives already quite a good overview over priorities.

I recovered the other data (like GDP etc.) to a great part from the federal office of statistics which hosts confusingly also the statistikportal. The website of this federal office is -mildly put- uncomfortable. That refers not only to the overall webdesign like for example it took me more than quite a while to find detailed readings on the GDP (since I started out at the statistikportal), but also to the overall accessability of data. For example I was also interested wether things like the Abwrackpraemie raise or lower the GDP or wether paying for volunteering could raise the GDP in some way…(just as a trick for the upcoming elections…), however in this GDP document it is even not possible to deduce within a reasonable amount of time which positions are summed over and which are subtracted.

Here some

But back to the budget discussion. The federal government (”Bund”) budget (Bundeshaushaltsplan) which is as explained above about half of the overall german budget is available as a pdf document here. From it one can read off a lot of the following figures (I tried approximately to reflect the ones Terence Tao chose). If there is no other link provided then the corresponding number in the below list is from this document.

Example: If the federal government (”bund”) has a budget of 283.200 BEuro for 2008 then this is a scaled budget of 283 200 000 000 Euro * 0.00000011 = 31152 Euro. Since this is as explained above about one half of the overall german budget the state family of 9 has thus an approximate budget of 2*31152 Euro =
->(approx) 60 000 Euro (per year).

That is 2* 383.343 B$=2*383 343 000 000$ which gives a scaled budget of 2*42167 $ =(approx) 84 000 $ (per year) which is in the same range as the US budget of 75 000 $ (per year), which appears in Terence Taos list. Compare these 60 000 Euros to the salary of 500 000 Euros which are not enough for the best.

The green number is a real budget number which is rescaled to the budget of a “family of 9 people” in Euro, the blue number gives the same amount in dollar so that it is comparable with the US budget in Terence Taos list.

• Health insurance: 3.692 BEuro 4.993 B$ 406 Euro 549 $
• Children payments (Kindergeld): 0.3 BEuro 0.41 B$ 33 Euro 45 $
• Social Security/unemployment payments: 94.313 BEuro 127.614 B$ 10374 Euro 14038 $
• consequence of war payments: 3.200 BEuro 4.332 B$352 Euro 477 $

• Autobahn:3.323 BEuro 4.496 BEuro365 Euro 494 $

• economic collaboration and development:4.985 BEuro 6.748 B$548 Euro 742 $

• Department of Education: 2008 budget 9.350 BEuro 12.655 B$1028 Euro 1392 $
• Department of Education: 2009 budget (planned): 10.2 BEuro 14.262 B$ 1122 Euro 1569 $
• DFG (Deutsche Forschungsgemeinschaft) 0.840 BEuro
  1.136 B$ 92 Euro 125 $
• Maths & Physical Sciences: ?
  couldn’t find a total number but humanities, natural sciences (i.e. chemistry, physics, math, geosciences), life sciences and engineering hold each about an equal share) so
• natural sciences approx: 0.210 BEuro 0.284 B$ 23 Euro 31 $

• nuclear energy:0.222 BEuro 0.310 B$ 24 Euro

  34 $

• ->renewable energies: 0.039 BEuro 0.054 B$ 4 Euro 30 cents

  6 $
  (some additional support for renewables comes in through the Feed-in tarif)

• mining (mostly subsidies):2.164 BEuro 3.023 B$ 238 Euro

  303 $

• coal mining: 1.900 BEuro 2.650 B$ 209 Euro 291 $

• Abwrackpraemie (car scrapping bonus) (source) 5 BEuro 7.068 B$ 550 Euro 779 $
• Opel retrieval (which is without any environmental requirements if I understood correctly):
• bail: 4.5 BEuro 6.361 B$ 495 Euro 700 $
• temporary loan: 1.5 BEuro 2.120 B$ 165 Euro 233 $
• cars and electricity: economic stimulus for electromobility: 0.5 BEuro 0.706 B$ 55 Euro 77 $
  comment: de facto this amounts to a percentual decline in investments in renewable energies, which seems to be an overall trend – the International Energy Agency estimates that

  “for 2009 as a whole investment in renewables could drop by as much as 38%, although stimulus provided by government fiscal packages can probably offset a small proportion of this decline”

• up-to-the-second update on the budget deficit on the website of Bund der Steuerzahler (community of taxpayers)
• Additional appropriations (not included in regular budget)
  • Afghanistan: ?:
    • -military operations?
    • development aid ?
• Air force NY flyover helicopter flights politicians:?
• National GDP 2008: 2 489.400 BEuro 3336.527 B$ 273 834 Euro 367 018 $
• GDP per capita 2008: 30 322 Euros 42 366 $
  (note: the above gives for 2008: 3336.527 *10^9$/82.099 * 10^6 = 40640.287 $ = 30321.899 Euros which compares to 40415.409 $ in 2007)(quaterly report 2008. -> the report how the GDP recently decreased rather dramatically)
• ->estimated risks in german banks: 816 BEuro 1140 B$ 89 760 Euro 125 700 $
• World GDP 2008: 39 079 BEuro 54 589 B$Terence Tao: 1,680,000 *3.7=(approx) 6.2 million $ =(compares to) 6 004 700 $ = (approx) 6 million $ (2007)
• ->Credit Default swaps notional value (2008) 57 325 B$ 40 996 BEuro 4 509 600 Euro =(approx) 4.5 million Euros 6 305 700 $ =(approx) 6.3 million $ (note: Terence Tao used a different source)
• ->OTC derivatives notional value (2008): 489 354 BEuro 683 725 B$ 53 828 900 Euro =(approx) 54 million Euro 75 209 800 $ = (approx) 75 million $ (note: Terence Tao used a different source)