The holy grail of amateur linguistics is the construction of a language which is both “maximally precise” and “maximally concise”—in other words, packing more information into fewer symbols; in other, other words, increasing the “information density” of a language.

But if the oft-quoted Galilean adage about mathematics as a language is true, these armchair optimizers should latch onto their day jobs and never let go, because they won’t even come close to achieving the exactness and briefness of mathematical statements. To use a common example, the whole of “classical” electromagnetism is contained inside of just four equations—equations so accurate that the scientist need not correct them for quantum phenomenon until ‘exploring distances less than .0000000001 centimeters, 100 times smaller than the atom’ (Purcell, 2).

This disparity between natural human languages and math is, I will argue, the reason why popular science (as it pertains to ‘hard’ sciences) has devolved into pseudo-scientific bunk. Disclaimer: I will only be talking about physics and English in this article, but the argument extends to other quantitative fields and non-English human languages.

Math Builds on Itself

Expressing mathematical statements in English becomes increasingly difficult as one scales the tree of theorems, and if you can bear to look at a few equations with me, I can demonstrate that to you:

Pythagorean Theorem (proven in ~570BC by Pythagoras of Samos) stated mathematically:

Pythagoras of Samos (570-495 BCE). Mathematician and mystic. Cult formed around him and his metaphysical/religious beliefs.

Pythagorean Theorem written in English: “Let triZ be a right triangle. Then the area of a square on the hypotenuse of triZ is equal to the sum of the areas of the squares on the legs on triZ.”

Green’s Theorem (proven in 1851 by Bernhard Riemann) stated mathematically:

Green’s Theorem written in English: “Let C be a positively oriented, piecewise smooth, simple closed curve in a plane, and let D be the region bounded by C. If L and M are functions of (x, y) defined on an open region containing D and have continuous partial derivatives there, then….” 

George Green (14 July 1793 – 31 May 1841), self-taught mathematician. Veritable genius. No (known) associated cults. Image from http://www.dert2007.org.uk/

…I’ll spare you the rest. Verbosity notwithstanding, something is wrong here. In both translations we referred to mathematical ideas such as area, shape, addition, subtraction, planes, sets, derivatives, etc. That’s cheating, because we haven’t really translated the statement from math to English, we just said it in English. I won’t try again, since—as you may have already realized—it would only be an exercise in futility. 

There is just no way to understand either theorem without having some pre-embedded knowledge of mathematics and its objects. And remember that the first result is just geometry, something we teach our children; the physical world is understood in terms of stuff like Green’s Theorem: functions, limits, rates of change, infinite sums with infinite bounds, infinite sums with finite bounds, etc—ideas markedly more subtle, but not more remarkable, than the Pythagorean theorem.

Challenges

The daunting problems with which modern popularizes of science are faced now become clear:

• Since the turn of the 19^th century, many important results in physics have come directly from mathematical safe-cracking, and because of this it is nearly impossible (or at least, very, very difficult) to translate their meaning usefully into layman’s English.

• There is a widening gap between theoretical ‘results’ and experimental verification (i.e theoreticians are pumping out conclusions faster than experimentalists can verify them). This is due to the increasing number of theoretical physicists as well as the soaring cost of scientific instruments: the Large Hadron Collider (LHC) cost roughly $9 billion dollars and ten years to make; the verification of the Higgs Boson using the LHC occurred nearly 60 years after it was proposed to exist.

Moreover, the sheer amount of training it takes to be able to understand anything in physics is enough to make a grown man—or in this case, a nineteen year old RU undergrad—cry. As an educated layman, which would you rather do to ‘learn’ about the latest advances in quantum mechanics: pick up and casually browse through a copy of Popular Science, or ‘learn arithmetic, Euclidean geometry, high school algebra, differential and integral calculus, ordinary and partial differential equations, vector calculus, matrix algebra, and group theory’? (Sagan, 249).

The Spirit of Science and Debate

Even worse, popular science is giving the public a false idea of what science really is, and how it is done. The hard truth is that science can be, and often is, boring, political, monotonous, covered in red tape, bureaucratic, and filled with dead ends. Publishers know this, which is why the physics section in magazines are invariably about something cool-sounding and esoteric, like the Multiverse, String Theory, Quantum Foam, etc, etc.

‘The detailed, all-sky picture of the infant universe created from nine years of WMAP data. The image reveals 13.77 billion year old temperature fluctuations (shown as color differences) that correspond to the seeds that grew to become the galaxies. The signal from our galaxy was subtracted using the multi-frequency data. This image shows a temperature range of ± 200 microKelvin.’
Credit: NASA / WMAP Science Team

To be sure, the fact that people are at all interested in science is a good thing. So what if their idea of it is a little skewed, a little warped? Better than the alternative, no doubt.

What is completely unforgivable, however, is using science as a propaganda and money-grabbing tool—governments do this with environmental science, anti-religious scientists do this with physics and evolutionary biology, and the public (with its weird notion of what science is) has no defense against these dark arts. A particularly malicious example is the cosmologist Lawrence Krauss using his definitions of ‘quantum vacuum’ and ‘multiverse’ as some sort of muddled defense against religious thought, claiming debate after debate that he has ‘done away with the theologian’s notion of nothingness’ (pp), and that ‘the idea of a multiverse can solve the problem of infinite regress'(pp) (if god created the universe, who created god?). This contemptible cop-out stifles much needed communication between intellectual spheres and leaves laypeople with an empty feeling that they don’t know enough to be part of the conversation. It is the grown-up version of that lazy tactic parents use when they don’t want to keep answering their child’s question. So instead of “you’ll understand when you’re older, Timmy!”, it’s now “you’ll understand when you learn quantum mechanics, general relativity, and physical cosmology, Timmy!”.

A Good Popular Science Resource

Youtube has some damn good resources for popular science.

By far the best, in my opinion, is Sixty Symbols. The idea is simple: this dude (Brody) with a camera goes around the University of Nottingham and asks professional scientists what they think about different scientific questions (ranging from standardized physics tests to Fourier analysis, Transistors, and (my personal favorite) the physics of mosh pits). The discussion is not dumbed down to the point of insulting the viewer, and is not so technical that one feels overwhelmed. I encourage anyone interested in science (but not interested enough to learn the math) to watch it.

As this article discussed, the goal of popular science should be to minimize the amount of information lost in translation from math to English, and I think Sixty Symbols does this well. 

Leo Kozachkov (Staff Writer, Rutgers University)
Leo Kozachkov is an undergraduate at Rutgers University, studying physics and mathematics. He is currently working as an Aresty Research Assistant under Professor Thomas V. Papathomas. He enjoys writing, drawing, creating/playing music, going on long walks with his beloved dog, and reading/hoarding books.His grandest hopes are to discover a new physical law, have a mathematical theorem feature his last name, and to write many books.