{"id":6273,"date":"2014-12-01T01:10:38","date_gmt":"2014-12-01T09:10:38","guid":{"rendered":"http:\/\/cosmologyscience.com\/cosblog\/?p=6273"},"modified":"2025-12-26T16:35:09","modified_gmt":"2025-12-27T00:35:09","slug":"do-you-need-any-math-expertise-to-understand-physical-cosmology-principles","status":"publish","type":"post","link":"https:\/\/cosmologyscience.com\/cosblog\/do-you-need-any-math-expertise-to-understand-physical-cosmology-principles\/","title":{"rendered":"Do you need any Math Expertise to understand Cosmology Physics Principles ?"},"content":{"rendered":"

“Mathematics<\/a>, a veritable sorcerer in our computerized society, while assisting the trie<\/strong>r of fact in the search for truth, must not cast a spell over him.<\/strong>”<\/p>\n

– California Supreme Court ruling<\/strong> in\u00a0overturning a criminal conviction based entirely on fraudulent use of statistics<\/strong>.<\/a><\/p><\/blockquote>\n

\"Is

Is Mathematics Converting Cosmology into a Priesthood ? (Credit – Sydney Harris)<\/p><\/div>\n

Let’s start with an analogy.<\/p>\n

Question 1. Can you safely drive a car without understanding any mathematics<\/a> of vehicle dynamics ?<\/strong><\/p>\n

A: Of course. Every day Hundreds of millions<\/a> of people drive cars in full control and safety — without understanding any math<\/span><\/em>.<\/strong><\/p>\n

Obviously they learned vehicle dynamics physics using a “language” other than math.<\/strong><\/p>\n

Imagine if your government refused to let you drive — until you could pass tests about the specific mathematics of vehicle dynamics<\/a><\/strong> : mass, motion, moments of inertia, centrifugal and centripetal forces, Hooke’s law, geometry, friction, nonlinear differential equations<\/a>, understeer and oversteer<\/a>.<\/p>\n

While a lot of mathematicians might be pleased . . . the general public would be outraged.<\/p>\n

Question 2.<\/strong> Can you repeatably mix an alcoholic drink without understanding the mathematics of fluid flow, boundary layers, Navier\u2013Stokes equations<\/a>, turbulent flow and mixing<\/strong> ?<\/p>\n

A: Of course. Millions of people easily mix drinks without understanding any math.<\/p>\n

Question 3.<\/strong> Can you repeatably bake a loaf of bread without any understanding of the mathematics of thermodynamics, Joule\u2013Thomson effect and gas expansion<\/strong> ?<\/p>\n

A: Of course. Anyone can mix and bake a loaf of bread without understanding any of the higher maths that could be used to describe some of the dynamics involved.<\/p>\n

You get the idea. It’s simply silly to assert that anyone needs to understand any math<\/a> to understand principles of motion, dynamics, fluid flow, thermodynamics or cause and effect.<\/strong><\/p>\n

Come To The Nerd Side. We Have Pi. (To order T-shirt, click image)<\/p>\n

The same holds true for Cosmology. As a Cosmology expert who’s written one of the largest glossaries on the subject<\/a> and taught the principles to many non-scientists, it is my opinion that most people can understand most, if not all, of Physical Cosmology’s principles of motion, dynamics, fluid flow, thermodynamics<\/a> and so on — without understanding any math<\/a>.<\/strong><\/em><\/p>\n

Math Disease must be Self-Reinforcing Because it is barely Contagious
\n<\/strong><\/p>\n

But too many math advocates in charge of setting University physics curriculum currently refuse to let you study physical cosmology principles unless you have an enormous higher math background !<\/strong><\/p>\n

It is such a problem, Nature journal itself, editorialized against<\/a> an “overweight of mathematical formul\u00e6<\/em><\/strong>” in one prominent cosmologists’ (laudable) work.<\/p>\n

As an example — please take a moment to examine this seemingly reasonable list of pre-requisites<\/a> to start studying Physics (that’s before adding math fields specific to astrophysics and cosmology) prepared by Nobel Laureate Gerard ‘t Hooft<\/a>.<\/p>\n

His excellent starting point list includes nineteen major categories (19 categories) of subjects and dozens of subtopics.<\/strong>\u00a0 Every one of them is a fascinating facet in understanding our fabulous fields of physics.<\/p>\n

(Though it laudably includes a course in the English language<\/strong>, alarmingly it lacks any hint of study of scientific method<\/a>, logic and reasoning<\/a>, or fallacies<\/a>.<\/strong> That omission is sadly typical in physics degrees.)<\/p>\n

Innumeracy<\/a> — pages of equations overwhelm most students.<\/strong><\/p>\n

The problem is every one of Gerard ‘t Hooft’s<\/a> subjects and links are drenched in mathematics<\/strong> with very few photographs, diagrams, or graphs or even just charts; just page after page after page of equations.<\/strong><\/p>\n

Some people thrive on equations and even learn fastest using them. However, most people do not.<\/p>\n

This avalanche of math overwhelms, intimidates and discourages huge numbers of people who were otherwise fascinated by astrophysics or cosmology.<\/p>\n

In the words of Harvard’s esteemed E.O Wilson<\/a> —<\/p>\n

“During my decades of teaching biology at Harvard, I watched sadly as bright undergraduates turned away from the possibility of a scientific career, fearing that, without strong math skills, they would fail. This mistaken assumption has deprived science of an immeasurable amount of sorely needed talent. It has created a hemorrhage of brain power we need to stanch.”<\/strong><\/p><\/blockquote>\n

Thankfully, there are occasional minor counterexamples like this undergraduate Cosmology course<\/a> at Northwestern in Illinois. But as mentioned, that is an undergraduate course that only skims the surface of cosmology.<\/p>\n

Sadly, this gratuitous math barrier prevents millions of students from enjoying physics, astrophysics and cosmology.<\/strong> This makes the math requirement a de facto<\/a> example of a Priesthood<\/a><\/strong> (even if unintentional or unconsciously).<\/p>\n

When this is done deliberately it is called Obscurantism<\/strong><\/a>. That is where subject knowledge is a fiercely guarded secret<\/strong> revealed only to those who jump past barriers<\/strong> that are wholly unnecessary<\/strong> and often highly complex or expensive in time or personal sacrifice. This is not unlike the outrageously harmful and sometimes deadly college Hazing<\/a> required to obtain fraternity admission; or how the legal industry uses Latin terms to obscure legal ideas from us ordinary mortals.<\/p>\n

Oddly, its often the non-math fluent administrators who enforce such math barriers. The best Physics professors typically take great pains to increase the approachability of physics to maintain the student’s enthusiasm.<\/p>\n

\"Michael

Michael Faraday invented Electric Motors – with no formal math training<\/strong><\/p><\/div>\n

Its notable to recall how Michael Faraday<\/a><\/strong> had no formal math training<\/a><\/strong>, yet he was “one of the most influential scientists in history<\/strong>.”<\/p>\n

Faraday established the basis for the concept of the electromagnetic field in physics, inspired Maxwell’s equations<\/a> and essentially invented electric motors<\/strong>. He also discovered the principles of electromagnetic induction<\/a>, diamagnetism (the levitating frog trick)<\/a>, and the laws of electrolysis<\/a><\/strong>.<\/p>\n

A quick web search amazingly turns up a bunch of logical fallacies<\/a> arguing that you are<\/strong> forbidden from discussing or understanding cosmology<\/strong><\/em> until you have expertise in half a dozen higher maths. But in perusing the arguments, I have yet to find even one valid (fallacy-free) argument supporting that view. Here’s a concise analysis of a few of them.<\/p>\n

Myth 1:<\/strong> \u201cPhysics, by definition, is the subset of Mathematics which pertains to our universe<\/em>.\u201d<\/p>\n

Truth<\/strong>: Physics is not a subset of mathematics<\/strong>, nor vice versa.<\/p>\n

Physics is about understanding physical reality using <\/strong>experiments and observations.<\/p>\n

Math is merely a language, <\/strong><\/a>one of many languages<\/strong><\/em> to help understand natural phenomena. Math helps some people understand the physical laws of nature. However, in no sense is math an experimental science. Many would argue<\/a> that Math is not a science at all<\/a>.<\/strong><\/p>\n

Myth 2<\/strong>: “Mathematics is the language of physics and you can’t learn a subject without learning its langauage<\/em> (sic).\u201d<\/p>\n

Nobel Prizewinner Richard Feynman subscribed to this myth by writing :<\/p>\n

“To those who do not know mathematics it is difficult to get across a real feeling as to the beauty, the deepest beauty, of nature … If you want to learn about nature, to appreciate nature, it is necessary to understand the<\/span> language<\/strong> that she speaks in<\/em>“.<\/p>\n

Centuries before him, the great Galileo wrote:<\/p>\n

“<\/strong>Philosophy is written in this grand book \u2014 I mean the universe \u2014 which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language<\/span> in which it is written. It is written in the language of mathematics<\/span>, and its characters are triangles, circles, and other geometric figures, without which it is humanly impossible to understand a single word of it<\/span>; <\/strong>without these, one is wandering about in a dark labyrinth.”<\/p><\/blockquote>\n

Truth<\/strong>: Please forgive me most esteemed Messers Galileo and Feynman, but I must respectfully disagree. Mathematics is just\u00a0one<\/strong><\/span><\/em> language of physics; one of several ways to understand physics principles<\/strong>. Just like one can learn to drive a car without any vehicle dynamics math, or follow a recipe there are other ways to understand physics and cosmology; other “languages.”<\/strong><\/p>\n

Myth 3<\/strong>: “As long as you don’t have math (and hence can’t make quantitative descriptions and predictions), you are not doing physics – you are merely making up stories.”<\/em><\/p>\n

Truth<\/strong>: This is a two part strongly misleading claim. There is a gigantic gulf between using advanced math (e.g. Calculus or Algebra) and using quantitative descriptions.They are two separate things with nearly zero overlap.<\/strong><\/p>\n

\"You<\/a>

You Have A Problem (to order T-shirt, click on image)<\/p><\/div>\n

Of course, using quantitative descriptions is highly helpful in assisting understanding physics and cosmology. But measuring things does not inherently require using math <\/strong>beyond arithmetic. <\/strong>Just like driving a car — one should understand that (not how) vehicle speed is quantified by speedometer and understand how to compare that measurement to speed limit signs.<\/p>\n

You could get me to agree that this example uses Arithmetic<\/strong>, but comparing one quantity to another quantity is not really using math. In any case using quantitative descriptions is certainly not higher math.<\/strong><\/p>\n

Myth 4<\/strong>: “If you don’t have a mathematical description of something, you don’t really understand it<\/strong><\/em>.”<\/p>\n

Truth<\/strong>: One can understand physics phenomena, even extremely complex multi-variate, non-linear phenomena<\/strong> at a world class level without using any mathematical description.<\/p>\n

Here’s an example: Returning to the car driving and vehicle dynamics analogy — at most, only a handful of world class racing car drivers understand any math of vehicle dynamics<\/em> that their lives and careers depend upon.Yet they are paid tens of millions of dollars due to their exquisite and precise command of vehicle dynamics that most people<\/s> mathematicians can only dream about and admire. (aka the Fifth stage of competence<\/a>.) <\/strong><\/p>\n

While traveling at 140 to 180 mph (225-290 kph) and more, while turning so sharply their body is subjected to 2 to 3\u00a0<\/strong> sideways <\/strong> Gs (2 to 3 times their normal weight pressed against their “seat’s” side)<\/strong> <\/a>they can place a car to within an inch or so of the same spot on a sharply curved road<\/a> lap after lap after lap.\u00a0<\/strong><\/p>\n

These drivers unarguably “really understand” vehicle dynamics – while few have any more than the faintest whiff of mathematical understanding of it.\u00a0<\/strong> They absolutely fulfill Prof Feynman’s poetic appeal they they have “a real feeling as to the beauty, the deepest beauty<\/span>, of nature<\/strong><\/em>” for automobile dynamics.<\/p>\n

If you push me, I could easily show persuasively these drivers understand the physics far<\/em> better<\/em><\/span>\u00a0than mathematicians. <\/strong>This is in no small part because\u00a0math comes to a grinding halt <\/strong>with non-linear<\/a>\u00a0<\/strong>six degrees of freedom dynamics<\/strong><\/a> – which you and I employ to drive a car every day.<\/p>\n

And if you persist I’ll insist we discuss\u00a0G\u00f6del’s incompleteness theorems<\/a><\/strong>\u00a0– which prove that for all but the most trivial circumstances maths cannot be relied upon to be self-consistent<\/strong>. That would clearly include the General Relativity Field equations which Big Bang is based upon<\/a> . . .<\/p>\n

To resume, my experience has shown me that for Cosmology enthusiasts it is wholly unnecessary to have any advanced math expertise to understand Cosmology principles.<\/strong><\/p>\n

I’ll close with a thought from Professor Einstein —<\/p>\n

“As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality.<\/strong>“<\/p><\/blockquote>\n

What do you think ?<\/strong><\/p>\n

# # #<\/p>\n

More information<\/strong>:<\/p>\n

1. Here’s an illuminating Youtube video with Physics Noble Laureate Richard Feynman explaining the difference between math and physics<\/strong><\/a>.<\/p>\n

2. To some mathematicians merely asking this article’s title question is blasphemy<\/a> (Religious irreverence). The mere allusion that science could have blasphemy makes me queasy. Heresy is OK (differing opinions), but blasphemy – Youch! \u00a0Carl Sagan provides a useful guide for this —<\/p>\n

\u201cThere are no forbidden questions in science, no matters too sensitive or delicate to be probed, no sacred truths.\u201d<\/strong><\/p><\/blockquote>\n

 <\/p>\n

3. Book: Innumeracy: Mathematical Illiteracy and Its Consequences<\/a>\"\"<\/p>\n

4. Book:\u00a0Math for the Frightened: Facing Scary Symbols and Everything Else That Freaks You Out About Mathematics<\/span><\/p>\n