In hoped existed but had never been found.


In the fifth grade, I
learnt the standard model of physics. Back then the Higgs Boson was a particle
that the scientists hoped existed but had never been found. A couple of years
later, in 20121,
CERN announced the discovery of the very same “God Particle”, fulfilling the
hopes of scientists and proving that the knowledge of the model was rigorous.
By considering my experience with the quality of knowledge and my chosen title,
I decided to explore the extent to which
quality of knowledge produced in a discipline depends on the depth of
historical development of that discipline.

The quality of knowledge
is subjective over different disciplines. For example, in mathematics, in which
knowledge seems to be certain, knowledge of sufficient quality can be defined
as that which is discovered and then proven. An improvement in quality, may for
example be, a conjecture initially believed to be false which is then believed
to be true and then it is proven. However, in physics, in which knowledge is
formed through observation, reason and imagination, the quality of knowledge is
more subjective and difficult to define. Here I choose when referring to quality
in physics to define it as how reliable and how valid it is. In other words, it
is the extent to which the knowledge is a true representation of our
observations. A discipline can be described as a branch of knowledge which, to
some extent, focuses on a well-defined set of knowledge. Mathematics could be
considered a discipline within which there are multiple disciplines (Calculus,
Number Theory, Group Theory). Similarly, physics is a discipline and differs
from the other natural sciences, such as chemistry, in that it is concerned
primarily with nature at all sizes from the universe to the fundamental,
subatomic particles. In mathematics, historical development typically allows
the quality of knowledge to improve while in the natural sciences, although
knowledge does tend to become more reliable over time, it is to a lesser
extent. This may be due to time allowing rigorous proofs to be formed in
mathematics while in physics the numerous paradigm shifts implies an element of
uncertainty in any knowledge formed within the discipline.

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In mathematics, improving the quality of knowledge
requires first, exploration and forming conjectures, and next proving those
conjectures often through intuition and imagination. These ways of knowing must
reach a certain caliber before they are able to be effectively employed within
the subject, which requires time. Therefore, the duration of historical
development must improve the quality of knowledge within the discipline of
mathematics and tends to do so proportionally. For example, the Goldbach’s weak
Conjecture. This conjecture states that all odd numbers greater than 5 can be
expressed as a sum of three primes. The reason it is “weak” is because it
followed from the initial Goldbach’s conjecture, first proposed in 17422. About two hundred years
later, in 1937, a soviet mathematician, Ivan Matveevich Vinogradov proved that
it is true for “sufficiently large” odd numbers3. Constant developments
were made in this conjecture until 2013, when Harald Helfgott proved it for all
known odd numbers4.
However even today, Goldbach’s strong conjecture has not been proven, with
developments being slowly made in the area. From a conjecture to a partial
proof to a complete proof, the weak conjecture took almost three hundred years
to prove with new developments occurring regularly, indicating that here the
quality of knowledge improved proportional to time. During the Greek era,
mathematicians, such as example, tried to prove that the square root of two was
irrational. Today we learn the proof in high school, and know that many other
numbers such as Euler’s constant, pi and the golden ratio are all irrational.
This acts as an indication that over time, the quality of knowledge has
improved proportionally.

Although the quality of knowledge does improve over
time, it may fail to do so in a manner which is directly proportional to the
duration of historical development. Knowledge often stagnates in mathematics,
with some problems being unsolved for centuries, while sometimes numerous
developments occur within a short burst of time, leading to an exponential rise
in the quality of knowledge. The twin prime conjecture, which suggests that
there are infinitely many pairs of primes separated by only two, is an example
of this. Although the first official statement of the conjecture was made in
1849 by de Polignac5,
most mathematicians believe it had been in circulation long prior to that. It
was only in 2013 when any progress was made in this conjecture at all. Yitang
Zhan when he proved that if for a number, n, there are infinitely many primes
that are n apart, n must be less than 70 million. This led to numerous further
breakthroughs as the upper bound fell from 70 million. According to Terry Tao,
a mathematician who formed a project to reduce the bound, “at times, the bound
was going down every thirty minutes”. By 2014, the bound was reduced to 246 and
with an assumption of another conjecture to be true, the bound has been reduced
to 6. The problem had had no developments for centuries, the quality of
knowledge stagnating, until one development led to the mathematicians getting
much closer to the proof within just a year6. Previously the conjecture
seemed to be true and now evidence suggests that it may in fact be true,
therefore indicating that the quality of knowledge has improved and done so
exponentially. This suggests that while historical development does improve the
quality of knowledge, it fails to do so proportionally, instead the correlation
ranges from being almost none to an exponential one.

I believe that in physics, time allows scientific
theories to be developed with more rigor and therefore leads to a better
quality of knowledge. A well-known example of this is the history of the
numerous theories of light. To explain refraction, Rene Descartes proposed that
light was a wave that travelled faster in denser mediums than in a less dense
medium7, which although untrue
explained the observed property of light. Soon after Pierre Gassendi and Isaac
Newton suggested that light was made of particles, arguing that the wave theory
couldn’t be true since light didn’t bend around walls the way another wave,
sound did. While this theory could explain reflection and diffraction, it
failed to explain refraction. Young’s double-slit experiment led to a renewal
of a more advanced form of the wave theory around the 1800s. However, this
theory couldn’t explain how light could travel through the vacuum of space.
This was soon explained by the electromagnetic theory in 1847. This theory was
replaced by the more developed quantum theory in the early 1900s, when Albert
Einstein was able to explain a previous unexplained observation, the
photoelectric effect. Eventually, the current model of light was formed: it is
both a wave and a particle. This means that it can be described in certain
situations as a wave and others as a particle, but it is actually something
outside our realm of imagination. These developments8 in the theory of light
over time allowed our knowledge to better explain the natural phenomena we
observe. There is an improvement in the quality of knowledge of physics over
time.

Due to the numerous paradigm shifts that have occurred
during the historical development of physics, there is always an element of uncertainty
present in the knowledge of today, no matter how accurately it represents the
physical world. Thomas Kuhn, in the “The Structure of Scientific Revolutions”,
argued that science occasionally undergoes revisions that destroy previous
paradigms. To explain this, he used the idea of the Copernican Revolution and
the shift from Aristotelian mechanics to Newtonian mechanics, but there are
countless other examples of paradigm shifts in physics. One is the move from
classical (Newtonian) mechanics to Quantum mechanics9. Classical mechanics were
based on Newton’s laws of motion. In the late 1800’s, observations began to
suggest that Newtonian mechanics may not always be true. This led to the
formulation of the more general quantum mechanics, within which given certain
restrictive conditions, Newtonian mechanics occurred. This led to extensive revisions
of ideas that had been always held to be true. From the perspective of the scientists
of the 1900’s, the knowledge they presumed to be true had been proven unreliable
and false. As a result, even today there is an element of uncertainty present
in today’s knowledge.

Although the quality of knowledge produced increases
over time, the quality is not directly proportional to the length of historical
development. In mathematics, the quality tends to stagnate for extended periods
of time, and then suddenly increase over short intervals. In physics, although
the quality may increase, it is uncertain whether the knowledge is reliable at
all due to the presence of paradigm shifts. Experts in the discipline must
therefore keep an open mind that the knowledge they have believed to be true may
in fact be untrue.

Most of the exploration above is predicated on the
definitions of quality for each discipline. Differing definitions may have led
to separate conclusions. For example, in physics, if the quality of knowledge
were to be determined by the percentage of the experts who agree with the
knowledge, then certain theories, like the presence of the graviton, would be
of relatively high quality even though they have never been observed. In the
end, knowledge’s quality increases over time, though it does not increase
proportionally to the length of the time it has been in development.

1 “The Higgs Boson.” CERN,
home.cern/topics/higgs-boson.

2 Platt, David J. “Proving
Goldbach’s Weak Conjecture.” University of Bristol.

3 The Editors of Encyclopædia
Britannica. “Ivan Matveyevich Vinogradov.” Encyclopædia Britannica,
Encyclopædia Britannica, Inc.

4 Platt, David J. “Proving
Goldbach’s Weak Conjecture.” University of Bristol.

5 Nazardonyavi, Sadegh. “Some
History about Twin Prime Conjecture.” ArXiv, 3 May 2012.

6 Platt, David J. “Proving
Goldbach’s Weak Conjecture.” University of Bristol.

7 Descartes, Rene. The Treatise on
Light. Cambridge University Press, 1998.

8 “History of Research on Light.”
Photon Terrace.

9 “Classical and Quantum Mechanics –
in a Nutshell.” Center for Information Technology, U.S. Department of Health
and Human Services.

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