Tuesday, August 30, 2011

sea, sky

sea, sky ~ frank waaldijk
sea, sky (own work, 2010, 120 x 122 cm, click on the image for an enlargement)

i would like to post some fairly recent landscapes, now that i've been freed from the mathematical project `natural topology' (see one-but-previous post). however, i just realized that images will be better findable on the web if i dedicate a post to each image separately.

this is more work, but it also gives opportunity to describe the paintings separately, which should be added benefit. i just have to overcome my usual reluctance to add words to a painting.

the above painting is characteristic of my continuing resolve to paint `as is'. i don't know why a painting works or not, i just know when it does. and i know that by allowing my subconscious intuition free rein, eventually a painting will start to work. even though this may be a laborious and time-consuming process.

i think that i'm in the process of reducing some aspects of landscapes to their essence. this is probably an inevitable development, and i'm looking forward to start a new painting. each time it surprises me how strongly paint can speak, even when reduced to simple forms and strokes.

stolen drawing (art theft 1)

man (stolen drawing), frank waaldijk
man (own work, 1985-2005, 40 x 60 cm (approx.), click on the image for an enlargement)

the above drawing (of which i have only a poor photograph, and which has been slightly altered since) was stolen from the corridor in my studio building, last june. by someone with a key, even, which makes it all the more painful. i have since removed my paitings and drawings from the corridor.

obviously someone thought the drawing beautiful enough to steal. but for me it is a unique work, which i created primarily in art school (art academy utrecht) and which i later retouched and slightly modified for more effect. it was not for sale, because it is a dear example of how i started out as an artist.

i cannot put into words how cowardly and callous i find this theft. perhaps i will write some more posts on art theft in general.

Sunday, July 31, 2011

Natural Topology (mathematics book announcement)

ocho infinito xxiii, frank waaldijk
ocho infinito xxiii (cover drawing for the book `Natural Topology', own work, 2004-2011, click on the image for an enlargement)

Dear readers, some of you may know that Wim Couwenberg and I started a project called `Natural topology' some years ago. The aim of the project is a) to explain intuitionism to classical mathematicians b) to simplify aspects of formal topology c) to show that intuitionistic topology is elegant and constructive, and its results can be easily translated to Bishop-style mathematics if one inductivizes the definitions d) to clarify in-our-eyes-important aspects of the relation between foundations of constructive mathematics and the foundations of physics.

Last January, we gave an informal talk about this project at the University of Nijmegen for a general audience. Positive and sceptical reactions together prompted me to work out the basic idea rigorously, all the time linking it to other developments. I am happy to announce that the long-promised book Natural Topology is now available online, from my website at http://www.fwaaldijk.nl/natural-topology.pdf

An abstract of the book is given below. I hope it will provide food for thought and discussion, also for the philosophy of mathematics and physics. The book is essentially self-contained and on the advanced undergraduate level (I believe), meaning that anyone with a knowledge of basic topology and some perseverance should be able to read it. For a good appreciation of the whole book, a certain knowledge of constructive mathematics probably is necessary, I suspect. But enough interesting elements should be accessible to anyone, I hope. (An interesting general-audience example concerns the line-calling decision-support system Hawk-Eye used in professional tennis.)

Of course all comments and reactions are welcome.

Kind regards,
Frank Waaldijk


We develop a simple framework called `natural topology', which can serve as a theoretical and applicable basis for dealing with real-world phenomena. Natural topology is tailored to make pointwise and pointfree notions go together naturally. As a constructive theory in BISH, it gives a classical mathematician a faithful idea of important concepts and results in intuitionism.

Natural topology is well-suited for practical and computational purposes. We give several examples relevant for applied mathematics, such as the decision-support system Hawk-Eye, and various real-number representations.

We compare classical mathematics (CLASS), intuitionism (INT), recursive mathematics (RUSS), Bishop-style mathematics (BISH), formal topology and applied mathematics, aiming to reduce the mutual differences to their essence. To do so, our mathematical foundation must be precise and simple. There are links with physics, regarding the topological character of our physical universe.

Any natural space is isomorphic to a quotient space of Baire space, which therefore is universal. We develop an elegant and concise `genetic induction' scheme, and prove its equivalence on natural spaces to a formal-topological induction style. The inductive Heine-Borel property holds for `compact' or `fanlike' natural subspaces, including the real interval [α,β]. Inductive morphisms preserve this Heine-Borel property. This partly solves the continuous-function problem for BISH, yet pointwise problems persist in the absence of Brouwer's Thesis.

By inductivizing the definitions, a direct correspondence with INT is obtained which allows for a translation of many intuitionistic results into BISH. We thus prove a constructive star-finitary metrization theorem which parallels the classical metrization theorem for strongly paracompact spaces. We also obtain non-metrizable Silva spaces, in infinite-dimensional topology. Natural topology gives a solid basis, we think, for further constructive study of topological lattice theory, algebraic topology and infinite-dimensional topology.

The final section reconsiders the question of which mathematics to choose for physics. Compactness issues also play a role here, since the question `can Nature produce a non-recursive sequence?' finds a negative answer in CTphys. CTphys, if true, would seem at first glance to point to RUSS as the mathematics of choice for physics. To discuss this issue, we wax more philosophical. We also present a simple model of INT in RUSS, in the two-player game LIfE (Limited Information for Earthlings).

Thursday, June 23, 2011

ai weiwei released on bail (see previous post, art & society 2)

since i'm working extremely hard to finish a fair chunk of mathematical research, i haven't been able to write on this blog.

but this good news of course must be added: ai weiwei has been released on bail, although he may still face civil charges.

news sources say that the attention given to this case by western media and protesters have pressured the chinese authorities to release ai weiwei. many others who like him are critical of the authorities are however still detained under equally vague charges and with doubtful legality.

(read more in the l.a. times, and the l.a. times).

ai weiwei, china map
ai weiwei, china map

Friday, April 8, 2011

ai weiwei arrested in china (art & society 1)

one of my favourite modern artists, ai weiwei, was arrested this week in his home country china. he has been charged with economic crime, according to the LA Times. however, it is very very likely that this is just a form of censoring by the chinese government. ai weiwei has been arrested before, on trumped up charges, even leading to hospitalization.

sometimes i am just so fed up with the world.

ai weiwei is a very talented artist, and a very talented technical craftsman as well. he combines these talents to comment on our society, and sometimes this is especially about his home country china. his art is always respectful in every way, but it does have a message. that is one of the very important functions of art, imnsho.

i hereby wish to give my support to ai weiwei, and to all other artists and like who are hounded by governments, authorities or other organizations for speaking out for those values that are the very essence of a better humanity.

and shame on all those bureaucrats and power-hungry people who wish to muzzle the freedom of speech and other (artistic or not) expression in order to force their world vision on others, and in order to maintain their power positions.

(to be continued)

fukushima: our problems hoisted on future generations

the cleaning up of the millions of gallons of radioactive water at fukushima (which are a waste result of the attempts to cool the daiichi nuclear plant with water to prevent meltdown) could take decades, according to expert opinions reported in the LA Times, if it can be resolved at all.

these news items have a tendency to be understated, because the nature of news is like an extreme version of the nature of fashion, and seldom does public attention linger on any one issue if there are no `dramatic' turns of events.

but since we were discussing these topics on this blog, i felt i should mention this hoisting of our problems on future generations. the cleaning of this nuclear wastewater is actually but a minor issue compared to the nuclear waste that we are creating all over the world, for which we have no long-term solution either.

so, as an artist, perhaps you can see how serious i am on this issue when i say: forget about art, but do not forget about the next generations. who gave us the right to pollute the world in an irreversible manner for eons to come?

Thursday, March 31, 2011

what can art be and do? (shale gas development in the cévennes 2)

as a follow-up to the previous post, just let me post this link to a very informative news article on shale gas development in the cévennes on french news online.

in the recent posts, environmental issues feature prominently. one could ask if an art blog is the best place for these concerns, but i'm inclined to allow it (...;-)). first of all, one can't cut up the world in subjects and expect to never have to redefine or rethink categories. second, a real and important issue for me is the role of art in society. and a major role imnsho is to raise awareness about fundamental issues that society faces.

so, although this is not primarily meant as a protest blog, from time to time i will post on issues which i hold to be fundamental in arriving at a better society and world.

and this just begs the question: how many famous works of art are about environmental protection??