Numbers –Tricky Tricky Numbers: Part 1

Guest Opinion by Kip Hansen –  26 July 2022

I beg your forbearance if I step on your ideological or scientific-viewpoint’s toes with my essay today.     But I hope to attract your attention long enough to make a point so important that it affects almost all empirical knowledge in our modern world.  The point is so simple, yet so scientifically profound, that it might even sound silly to casual readers:

Numbers are just Numbers

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The most famous and illustrative example (albeit, fictional) is Douglas Adams’, the “Answer to the Ultimate Question of Life, the Universe, and Everything“, as calculated by an enormous supercomputer named Deep Thought, is “42”.

This is precisely my whole point here today; with a rather long afterword on why this is important enough to mention here at a science blog.  Readers who already understand why “Numbers are Just Numbers” is so profoundly true and those who already understand the significance of this for modern science can move on and read about (boring) climate change topics. 

[ Warning: This is not easy essay – it is a short dissertation on the scientific philosophy of numbers and their use in modern science with some cautions and will extend to  two parts, at least. ]

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From the book “The Science of Measurement:  Historical Survey” by Herbert Klein we get the following quotes:

“…the tools and techniques of measurement provide the most useful bridge between the everyday worlds of the layman and of the specialists in science.”

“Non-scientists may be similarly impressed to discover that units of measurement – for length, area, volume, time duration, weight, and all the rest – are essentials of science.”

“[This work] …should prove serviceable to professionals in science, but its main purpose is to make outsiders realize that in their daily lives and concerns they too are involved in the activities and ideas classified as metrology, the science of measurement – a subdivision of science that underlies and assists all others.”

And what is metrology?  “Metrology is the scientific study of measurement.”

And what is measurement?  “Measurement is the quantification of attributes of an object or event, which can be used to compare with other objects or events.”

And what is quantification? “…quantification is the act of counting and measuring that maps human sense observations and experiences into quantities. Quantification in this sense is fundamental to the scientific method.”

And what is counting?  “Counting is the process of determining the number of elements of a finite set of objects” such as its physical attributes.

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All measurement is, at its most basic, simply counting – the number of beans, coins, stars, inches, lightyears…(and all other units of measurement).  The result of counting is a number – the number of “elements” – of the things counted.

And what is a number? “A number is a mathematical object used to count, measure, and label. The original examples are the natural numbers 1, 2, 3, 4, and so forth.”

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So, the basic activity of Science is counting or measuring  — a specific type of counting against pre-established , internationally-agreed-upon units of some quality/property such as temperature or weight or length or foot/lbs and many many more.  There are a lot of different methods of measuring different things with vastly different tools at a wide variety of scales.  Nonetheless, they are all really just types of counting.

Alas, when we (or you or they) count,  the result is a number – which is nothing more than a mathematical object – “A mathematical object is an abstract concept arising in mathematics”.    The number counted alone, of course, is not a thing at all – only an abstract concept — until the counted number is clearly stated as “number of whatevers?” – number of peaches, number of inches of 2×4 board, number of monarch butterflies at any given moment, number of any of the SI units under the International System of Units of various physical properties of something.

Numbers can be tricky….just because they are numbers – like 1, 2, 85,  400  million, 3.432 — some think we can just willy-nilly apply all types of mathematical processes to them: add them up, subtract them, multiply them, add them up and divide them into averages and/or average them spatially with various methods of distance weighting and kriging – all this is meant to produce physically meaningful results

To make matters worse, statisticians often think that they can then take those numbers churned out by all the above processes and wring out even more meaningful results not otherwise visible to the human mind. 

But does all that Mathematica-ing  produce physically meaningful results?

While some interesting things can be done with numbers and statistics, many fields of modern science have often gone far down the slippery slope of reification of numbers – often creating whole fields worth of non-physical data – like Global Average Surface Temperature, an entirely imaginary nonphysical number.  Similarly, modern oceanic scientists have created the imaginary concept of Eustatic Sea Level – a “would have been” not-really-a-physical-level level

SIDE BAR:  “Reification is when you think of or treat something abstract as a physical thing. “   Remember, these numbers are mathematical abstracts.

In a two-decade old BMJ article, it is acknowledged that:

“Many people only respect evidence about clinical practice [think also: biology, climate science, geology, psychology, ad infinitum ]  that is couched in the highly abstract language of graphs and statistical tables, which are themselves visualisations of abstract relations pertaining among types of numbers, themselves again abstractions about ordinary phenomena.” [ source ]

Thus, we find ourselves reading articles and essays and journal papers filled with abstractions about abstractions about ordinary phenomena

In practice, we call these abstractions numbers or data sets or even “the data” and then we/somebody makes them into various visual presentations – charts and graphs and pretty pictures —  intended to sell their favorite hypothesis or to refute your favorite hypothesis.

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Preview of Part 2:

In Part 2, I will consider why it is that

“One cannot average temperatures.”

Really.

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Author’s Comment:

I have been accused in the past of not liking numbers, of hating numbers, of not understanding mathematics, of not understanding statistics and being a general math-o-phobe.  This is not true –not only do I love the beauty and certainty of mathematics, but I am also a true pragmatist.

“one who judges by consequences rather than by antecedents.”

Not a real fan of blind trust in so-called experts – experts, in my opinion, have to be able to show their work in the real world

I am well aware of the many problems of scientific modern research,  including that all fields of science are returning a lot of questionable results – even in fields closely monitored like medicine.  It is my belief that much of this is functionalized by  “too much math, not enough thinking” or the reification of mathematical and statistical results. 

“I could be wrong now, but I don’t think so.”

(h/t Randy Newman)

Free-for-all on this topic in comments.

Thanks for reading.

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via Watts Up With That?

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July 26, 2022 at 04:51PM

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