1859 marks not only the 150th birthday of the publication of Darwin’s On the Origin of Species, but also a somewhat less well-known occasion; It was the year Ernst Mach published the first of his 500 publications (his last was published five years after his death, in 1921).
Most will know of this man through his association with the speed of planes; Mach Number is the speed at which an object is moving divided by the speed of sound.
But Mach has offered much more to the world of Science; he lived in a time when Philosophy and Science went hand and hand, and he made many contributions not just in these areas, but also in Psychology and Educational Theory. He wrote a number of text-books for school science, but was very critical of the tendency of cramming as much as possible into the syllabus.
This quote sums up so much of what is wrong with our schooling:
I know nothing more terrible than the poor creatures who have learned too much . . . What they have acquired is a spider’s web of thoughts too weak to furnish sure supports, but complicated enough to produce confusion.
Mach was also an advocate of what are known as ‘thought experiments’, these later became famous through Albert Einstein and his idea of sitting on top of a light beam. Indeed Einstein went on to give credit to Mach for his ‘philosophical writings’. It’s probably no coincidence that Einstein’s views on education were not that dissimilar to Mach’s:
One had to cram all this stuff into one’s mind for the examinations, whether one liked it or not. This coercion had such a deterring effect on me that, after I had passed the final examination, I found the consideration of any scientific problems distasteful to me for an entire year.
Of course this was all over one hundred years ago. Obviously it’s all changed since then.
It would appear that we have some explaining to do.
We are all deeply conscious today that the enthusiasm of our forbearers for the marvellous achievements of Newtonian mechanics led them to make generalisations in this area of predictability which, indeed, we have generally tended to believe before 1960, but which we now recognise were false. We collectively wish to apologise for having misled the general educated public by spreading ideas about the determinism of systems satisfying Newton’s laws of motion that, after 1960, were to be proved incorrect.
An extract from a paper entitled The recently recognised failure of predictability in Newtonian Dynamics
Proceedings of the Royal Society of London, Series A, Vol 407, No. 1832
This is taken from a paper written by the late Sir James Lighthill, who at the time was President of the International Union of Theoritical and Applied Mechanics, and who incidentally also held the position of Lucansian Professor of Mathematics in Cambridge, a position which was first filled by Isaac Newton himself (Stephen Hawking is currently holding the post). The reference to Newtonian mechanics is significant here because it was in this area more than any other that the notion of absolute truth was (is?) most often associated.
The idea that Physics (built on mathematical rules) is the most fundamental knowledge that exists, and all other knowledge is built on this, can be traced back to the writings of the the positivist Auguste Compte.
Compte coined the term sociology; he saw it as giving meaning to all the other sciences – holding them all together as it were.
This is nicely caricatured in the cartoon below.
Compte didn’t actually consider Mathematics to be a science; it was merely a tool used by scientists!
Here’s a rather more profound clip from Jacob Bronowski’s Ascent of Man. At 2:00
We have to cure ourselves of the itch for absolute knowledge and power.
Thanks to my friend Prof Kirk Junker for pointing out the paper to me.