MOTION MOUNTAIN

thought and language 273
Ref. 252
Vol. VI, page 105
with the help of space and time. Being based on a circular definition, physics is thus
not modelledaftermathematics,even if many physicists and mathematicians, including
Hilbert, would like it to be so. Physicists must live with logical problems and must walk
on unsure ground in order to achieve progress. In fact, they have done so for 2500 years.
If physics were an axiomatic system, it would not contain circular definitions; on the
other hand, it would also cease to be a language and would cease to describe nature. We
will return to this issue in detail in the last part of our adventure.
Ref. 253
Ref. 254
Why use mathematics?
“DieForderungderMöglichkeit dereinfachen
ZeichenistdieForderungderBestimmtheit des
Sinnes.*
Ludwig Wittgenstein, Tractatus, 3.23”
Numbers, as well as most other mathematical concepts, were developed precisely with
the aim of describing nature.
⊳ Numbers and mathematical concepts were developed right from the start to
provide as succinct a description as possible.
This property is one consequence of mathematics being the science of symbolic necessities.
Mathematical concepts are tools that help our thinking. This is the reason that
mathematicsisusedinphysics.
Several well-known physicists have repeatedly asked why mathematics is so important.
For example, Niels Bohr is quoted as having said: ‘We do not know why the language
of mathematics has been so effective in formulating those laws in their most succinct
form.’ Eugene Wigner wrote an often cited paper entitledThe unreasonableeffectiveness
of mathematics. At the start of science, many centuries earlier, Pythagoras and his contemporaries
were so overwhelmed by the usefulness of numbers in describing nature
that Pythagoras was able to organize a sect based on this connection. The members of
the inner circle of this sect were called ‘learned people,’ in Greek ‘mathematicians’, from
the Greek µάθηµα ‘teaching’. This sect title then became the name of the modern profession.
But asking about the effectiveness of mathematics is akin to asking about the
effectiveness of carpenter tools.
Perhaps we are being too dismissive. Perhaps the mentioned thinkers mainly wanted
to express their feeling of wonder when experiencing that language works, that thinking
and our brain works, and that life and nature are so beautiful. This would put the title
question nearer to the well-known statement by Albert Einstein: ‘The most incomprehensiblefactabouttheuniverse
is that it is comprehensible.’ Comprehension is another
word for description, i.e., for classification. Obviously, any separable system is comprehensible,andthereisnothingstrangeabout
it.But istheuniverse separable? As long as
is it described as being made of particles and vacuum, this is the case.
The basic assumption we made at our start was the separability of nature. This is the
central idea that Pythagoras’ sect expressed in their core belief
* ‘Therequirement that simplesignsbepossibleistherequirement thatsensebedeterminate.’
Motion Mountain – The Adventure of Physics copyright © Christoph Schiller June 1990–November 2015 free pdf file available at www.motionmountain.net