The Royal Dutch Academy of Sciences (and formerly Arts) KNAW in Amsterdam had a session on both cancer and math. The issue of cancer is of general importance while math may require a bit more patience.
Roland Kanaar and 42° Celsius
From Douglas Adams and his Hitchhikers’ guide to the Galaxy we know that the number 42 is important. Roland Kanaar cs have discovered that 42º Celsius hinders cancer cells to maintain their wrong DNA. Heating cancerous cells makes them vulnerable to additional treatment that can cause their cell-death. It is a medical and complex story and I should not try to repeat it. Here is a page in wikipedia that I perhaps should not refer you to because it is not clear what their medical standards are.
My reason to mention the issue is rather something for general awareness. A review in (meta) epidemiology – I lost the reference, shame on me – showed that three factors are most important for cancer – apart from many others like genetics of course:
- time: thus, when you grow older then cells have more chance to go wrong
- number: thus, when you have more cells (you are bigger), then there is more chance that some cells go wrong
- non-specialisation: thus, cells that are specialised don’t change much, while non-specialised cells that still have to find a specialisation may make a wrong turn.
A key example is breast cancer. Women in the West are larger than women in the East, and thus run greater risk. Diet of fish rather than meat, and oil rather than butter, would not be so relevant, and mainly size is important. Looking for an example I came across this somewhat commercial “Double Dutch” crowdfunding video that argues that women in Holland would tend to have larger cup sizes. It is on record that the French philosopher Descartes and the painter Monet already had an issue with this, which eventually contributed to them leaving the country. Subsequently, there is also the specialisation of the breast cells. For mothers who have breast-fed, the cells have specialised to a function. For other women the cells are waiting what to do, and thus run greater risk that DNA transcription causes some error. One remedy to prevent breast cancer thus would be that women also without child still participate in breast feeding, or have equivalent hormone treatment. One would have to set up a (randomised controlled) trial to work out the parameters and verify this idea.
This session at KNAW also reminded me of my 2004 discussion of an STI passport, which may be an exercise in logic but which at least clarifies some of the points to consider.
Jan Bergstra and division by zero
Subsequently Jan Bergstra presented his ideas on calculation on the computer. Data types determine how numbers are handled. A crucial issue is how to deal with “division by zero”. This division is an error but it may not clear how to handle that error. Computer programs may make different choices. Apparently Intel might turn 1 / 0 into 0 but Wolfram Mathematica has 1 / 0 become Indeterminate. Professor Bergstra wonders what would be the best mathematical answer to this issue – which answer may also be seen as a transcription of 1 / 0. I wonder whether it wouldn’t be better to approach the issue from the angle of computer algebra – like Mathematica – so that the issue actually is already solved, and see this paper of almost 15 years ago about some technology choices. But perhaps the mathematical problem remains to select the criteria for deciding “that it is solved”.
Professor Bergstra was helpful with advice on this paper of mine: Education, division & derivative: Putting a Sky above a Field or a Meadow (September 2014). In some respects he might be regarded as a co-author since the paper develops along his objections and explains how those can be dealt with. We still disagree on various points, but I regard my paper as finished so it is up to him to indicate what his view is. I suppose that an academic can always find a new question – that is what academics are for, except when they abuse their leisure to ask silly questions. The main issue is what works for education, and here KNAW and the Ministry of Education are in an awkward dance. It is better that Parliament starts to enquire the issue. For Dutch readers: see the petition. For the rest of the world: see the idea of academic schools like academic hospitals. It is much better to talk to Roland Kanaar who has researched his issue than to Jan Bergstra who has little idea about education but thinks that he does.
Overall, readers must be aware of the paradox that I am a teacher of mathematics but not a (research) mathematician. I am willing to go along in a lot of theory but my bottom line is that students should benefit in understanding and competence. An issue like 1 / 0 must be solved in highschool this very instant and we don’t have the luxury that some seem to suggest.
After the lectures, it was fortunate that there was an opportunity for a longer discussion, that I can report upon, between me, Jan Bergstra and Bas Edixhoven (Leiden, KNAW). There were various topics, but let me now concentrate on this issue:
- See is this memo of mine to Jan and Bas on Cantor’s “diagonal proof” for the power set
- Bas follows Cantor & Hilbert and produces a theorem and proof, that I deconstruct, so that my book ALOE applies,
- Jan is caught in the middle, since I had been discussing the derivative and “division by zero” with him, and now there is a whole range of new issues to deal with.
Overall, though, the key issue remains the education of mathematics. I have reported that the integrity of science is at stake here. Jan Bergstra happens to be the secretary of the mathematics section of KNAW Royal Academy of Sciences of Holland. Let us hope that he can handle this issue without getting distracted by my other analyses on the derivative and Cantor and the Liar paradox and such.