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The Pernicious Influence of Mathematics on Science by Jack Schwartz

from a volume of unconventional essays convened by Reuben Hersh

  • single-mindedness, literal-mindedness, simple-mindedness
  • The mathematician converts the scientist’s ideas into axioms. The danger, then, is that the mathematician may convince the scientist that the axioms are true.
  • Science must deal with the unknown or imprecisely known, but mathematics must begin from a precise starting point.
  • absurdities in uniform
  • the sorry history of the Dirac Delta function
  • bad theory with a mathematical passport
  • science leaps ahead whilst mathematics plods behind
  • mathematics can deal only with simple things

reminds me of something @zentree tweeted: mathematics making biologists understand their own science less










The life forms on our planet have necessarily evolved to match the magnitude of [thermal] energy flows. But while “natural man” is in balance with these heat flows, “technological man” has used his mind, his back, and his will to harness and control energy flows that are far more intense than those we experience naturally….

A society based on power technology teems with heat transfer problems.

John H. Lienhard IV & John H. Lienhard V, A Heat Transfer Textbook

via the idea factory: learning to think at mit




It’s true that the financial sector enjoyed disproportionate rents but it’s not true that the smartest and brightest work there. …[T]he place is littered with failed scientists. Worse, it’s littered with idiot savants. There are once in a while people working there who have trained for the job — Very good PhDs in finance and economics, for example, or good M&A lawyers, and they usually strike me as the ones who offer the best contributions to their organizations.

@gappy3000

cf, Eric Falkenstein

(Source: condoroptions.com)




notstatschat:

There’s a paper in PNAS suggesting that lots of published scientific associations are likely to be false, and that Bayesian considerations imply a p-value threshold of 0.005 instead of 0.05 would be good. It’s had an impact outside the statistical world, eg, with a post on … Ars Technica…

3. If … you think p-value thresholds should be a publishing criterion, you’ve got worse problems than reproducibility.

4. False negatives are errors, too.  People already report “there was no association between X and Y ” (or worse “there was no effect of X on Y”) in subgroups where the p-value is greater than 0.05.  If you have the same data and decrease the false positives you have to increase the false negatives. 

5. The problem isn’t the threshold so much as the really weak data in a lot of research, …. Larger sample sizes or better experimental designs would actually reduce the error rate; moving the threshold only swaps which kind of error you make.

7. And finally, why is it a disaster that a single study doesn’t always reach the correct answer? Why would any reasonable person expect it to? It’s not as if we have to ignore everything except the results of that one experiment in making any decisions.  

HT @zentree




Fun coursera on virology.

  • Viruses are so numerous (10³⁰) and filling up everywhere. It gives this Boltzmann flavour of ‘enough stuff” to really do statistics on.

  • Viruses are just a bundle of {proteins, lipids, nucleic acids} with a shell. It’s totally value-free, no social Darwinism or “survival of the fittest” being imbued with a moral colour. Just a thing that happened that can replicate.
  • Maybe this is just because I was reading about nuclear spaces (⊂ topological vector spaceand white-noise processes that I think of this. Viruses have a qualitatively different error structure than Gaussian. Instead of white-noise it’s about if they can get past certain barriers, like:
    • survive out in the air/water/cyanide
    • bind to a DNA
    • spread across a population
    • adapt to the host’s defences
  • … it seems like a mathematician or probabilist could use the viral world of errors to set out different assumptions for a mathematical object that would capture the broad features of this world that’s full of really tiny things but very different to gas particles.
  • Did I mention that I love how viral evolution is totally value-neutral and logic-based?
  • Did I mention how I love that these things are everywhere all the time, filling up the great microspace my knowledge had left empty between man > animals > plants > > bacteria > > minerals?




Johannes Kepler on whether his wife Susanna Reuttinger was destined as "The One":

Though all Christians … declar[e] solemnly that they enter into married life owing to a special divine management, ….

Was it divine Providence or moral guilt on my part which has torn my mind … in so many different directions and which led me listen to so many people … so divergent from each other?

Was it divine management that brought in all these persons and their actions?

As I believe, nothing extraordinary has happened to me. I believe that everyone of us has an experience similar to mine, not only once but very often. The difference is only that the others do not worry about it, as I do, they forget more easily and get over it more quickly than I do, or that they have more self-control and settle their unhappiness by themselves.

There is something wrong with my feelings; I stirred them up anew every day ….

As far as [Susanna] is concerned there is still the question of why, though she was destined for me, G-d permitted that she had six rivals in the course of one year?

Johannes Kepler: Life and Letters by Carola Baumgardt





M31 is a globular cluster located 25,100 light years away from Earth. It consists of 300,000 stars and is about 145 light years in diameter.

via intothecontinuum

hi-res







3D map of the large-scale distribution of dark matter, reconstructed from measurements of weak gravitational lensing with the Hubble Space Telescope.
via davidaedwards

3D map of the large-scale distribution of dark matter, reconstructed from measurements of weak gravitational lensing with the Hubble Space Telescope.

via davidaedwards


hi-res