3 Truth and Beauty
51
lie beneath. Schoenberg is an “acquired taste”, an attribute that he shares
with many other “beautiful” things. Spicy food, the bitterness of beer and the
dryness of wine are not tastes that the newly weaned infant is likely to enjoy.
Rather, that appreciation is brought about by familiarity, born of experience.
What then characterises a beautiful piece of physics, and why should we
care? After all, also for scientists “beauty is in the eyes of the beholder ”, while
science should be by definition objective. Sabine Hossenfelder in her provocative book, “Lost in Math: How Beauty Leads Physics Astray” has polled many
modern physicists over what they consider a beautiful theory. She writes:
“When asked to judge the promise of a newly invented but untested theory,
physicists draw upon the concepts of naturalness, simplicity or elegance, and
beauty. These hidden rules are ubiquitous in the foundations of physics. They are
invaluable. And in utter conflict with the scientific mandate of objectivity [8]”.
“Naturalness” implies that the free parameters in a theory are not finetuned to achieve agreement with experiments or observations. It also includes
an aversion to theories which contain very large or very small values for the
dimensionless constants (see Sect. 3.7). “Simplicity” will be discussed in the
next Section. “Beauty” usually involves underlying symmetries in the mathematical equations. Symmetries allow the prediction of more results from
fewer basic assumptions.
The pursuit of beauty is not just a recent interest in physics. The circle,
being the most symmetric plane figure, requires only the specification of a
central point and a radius to completely identify all of its properties. The early
Greek astronomers took it as given that the motion of the planets, Sun and
Moon were described by circles, which had for them almost divine properties.
Ptolemy wrote: “Our problem is to demonstrate in the case of the five planets, as
in the case of the Sun and Moon, all their apparent irregularities as produced by
means of regular and circular motions (for these are proper to the nature of divine
things which are strangers to disparities and disorders). [9]”. We shall describe
the Ptolemaic model of the solar system in more detail in Chap. 10.
This prejudice in favour of the circle persisted even after Kepler had shown
that the planetary orbits were, in reality, ellipses. Kepler himself struggled to
reconcile the observations made by Tycho Brahe with circular heliocentric
orbits, before giving up and accepting that the orbits had to be elliptical.
Galileo took no interest in Kepler’s elliptical orbits: he maintained that “only
circular motion can naturally suit bodies which are integral parts of the Universe
as constituted in the best arrangement ” [10].
Even in the twentieth century, beauty was an accepted criterion for the
assessment of a physical theory. Endorsements of this criterion by famous
scientists are easy to find:
51
lie beneath. Schoenberg is an “acquired taste”, an attribute that he shares
with many other “beautiful” things. Spicy food, the bitterness of beer and the
dryness of wine are not tastes that the newly weaned infant is likely to enjoy.
Rather, that appreciation is brought about by familiarity, born of experience.
What then characterises a beautiful piece of physics, and why should we
care? After all, also for scientists “beauty is in the eyes of the beholder ”, while
science should be by definition objective. Sabine Hossenfelder in her provocative book, “Lost in Math: How Beauty Leads Physics Astray” has polled many
modern physicists over what they consider a beautiful theory. She writes:
“When asked to judge the promise of a newly invented but untested theory,
physicists draw upon the concepts of naturalness, simplicity or elegance, and
beauty. These hidden rules are ubiquitous in the foundations of physics. They are
invaluable. And in utter conflict with the scientific mandate of objectivity [8]”.
“Naturalness” implies that the free parameters in a theory are not finetuned to achieve agreement with experiments or observations. It also includes
an aversion to theories which contain very large or very small values for the
dimensionless constants (see Sect. 3.7). “Simplicity” will be discussed in the
next Section. “Beauty” usually involves underlying symmetries in the mathematical equations. Symmetries allow the prediction of more results from
fewer basic assumptions.
The pursuit of beauty is not just a recent interest in physics. The circle,
being the most symmetric plane figure, requires only the specification of a
central point and a radius to completely identify all of its properties. The early
Greek astronomers took it as given that the motion of the planets, Sun and
Moon were described by circles, which had for them almost divine properties.
Ptolemy wrote: “Our problem is to demonstrate in the case of the five planets, as
in the case of the Sun and Moon, all their apparent irregularities as produced by
means of regular and circular motions (for these are proper to the nature of divine
things which are strangers to disparities and disorders). [9]”. We shall describe
the Ptolemaic model of the solar system in more detail in Chap. 10.
This prejudice in favour of the circle persisted even after Kepler had shown
that the planetary orbits were, in reality, ellipses. Kepler himself struggled to
reconcile the observations made by Tycho Brahe with circular heliocentric
orbits, before giving up and accepting that the orbits had to be elliptical.
Galileo took no interest in Kepler’s elliptical orbits: he maintained that “only
circular motion can naturally suit bodies which are integral parts of the Universe
as constituted in the best arrangement ” [10].
Even in the twentieth century, beauty was an accepted criterion for the
assessment of a physical theory. Endorsements of this criterion by famous
scientists are easy to find: