open access, elsevier boycott

On his blog Tim Gowers recently petitioned for a general boycott by scientists of Elsevier´s scientific journals.

His reasons I find excellent, as do many others, which has resulted in over 3,000 scientists now signing the petition on www.thecostofknowledge.com.

Let´s hope this initiative really takes off. I wrote on this subject on my visual arts blog earlier, and I find it truly heartening to see people taking a stand. Open access and open source can be (in my not so humble opinion) a way to reduce the poverty and the technology gap between rich and poor in this world.

Since society most often has already paid well for the research, it is extremely unfair that important knowledge should not be available to the public unless they can pay exorbitant prices.

We might think that mathematics is an important example (ok, I think so too, a little biasedly...) but consider important medical research, which can directly save lives...!

So open access is the first step, really. And money should not be a dominating force in the dissemination of human knowledge.


the open access logo

france bans fracking in shale gas development, netherlands gives permits

in an earlier post i wrote about shale gas protesting in france (protest song by my brother here).

this week the french government has banned the use of fracking in shale gas exploration/development.

this is extremely good news, and shows that protest can be effective.

sadly, at the same time my own government has given exploration permits to a number of companies to look for shale gas even in the area where i live. so i just signed a protest petition on www.gnmf.nl (in dutch). i hope that many people will sign, and protest in other ways as well.

mountain blaze

mountain blaze (own work, 2010, 80 x 200 cm, click on the image for an enlargement)

this large painting is hard to photograph, i find, because it is difficult to avoid reflections of light and also because it is difficult to get the colours approximately right. still, the photo should help to explain the sense of adventure that i had while painting it. i did not know where i was going, i just painted very boldly, as if i knew what i was doing...

going from very bold strokes to finer brushes, but maintaining the `firesome' spirit of the mountain, was quite a challenge. like i said in previous posts: it feels like it isn't really me who is painting. i'm just holding the brush.

i really wonder where this landscape journey will take me in future years.

clouds over fallow field

clouds over fallow field (own work, 2000-2010, 39 x 128 cm, click on the image for an enlargement)

this painting really took quite some time to finish. i worked on it (off and on) for 10 years. this is partly because i have to get used to a painting, especially when it contains something really new to me which i cannot place but which i feel is worthy of development.

lately, i have found new improvement in this process. it has become easier for me to discern in which direction i want to proceed, and which elements in a painting strengthen this direction and which elements weaken it. also, i find it easier to merge `old' work with new insights, for which i am grateful because i have a lot of `old' work which awaits finishing.

[postscript: i discovered that i already posted this painting, to illustrate an exhibition announcement. but it fits in the series of recent landscapes.]

sea, sky

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 (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.

Natural Topology (mathematics book announcement)

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
http://www.fwaaldijk.nl/mathematics.html


Abstract:

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).