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.

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.