‘Isaac Newton decided he could never hope to [understand how the world works] and he was satisfied by (1) being in the world, (2) by being alive and (3) by putting words on paper to describe what happens (but never to explain it).’*
Particularly his third objective, ‘to describe what happens’, articulates succinctly my assertion a theory is not some sort of fundamental truth about the universe† but rather an arbitrary explanation of the way something works (for now please ignore distinctions between statements we describe as ‘hypotheses’, ‘theories’ or ‘laws’ and treat ‘models’ as generic. The differences, as I hope you will see, are not relevant to this essay).
This initial observation arose twenty-five years ago during my extensive reading while drafting Tactical Management, a book I published in 1999. One of my enquiries was into theories of leadership. Without exaggeration, the books on the shelf behind the chair in my study offered me twelve distinct theories of leadership, many contradicting at least one but usually most of the others. How could this be? Critical consideration of these led me to a conclusion: if there were such a thing as a theory of leadership, or a theory of anything else for that matter, and this expresses a fundamental truth then there must be one and only one—twelve contradictory theories to describe a single phenomenon make no sense.
My thesis is a model stands in relation to the phenomenon it seeks to explain in precisely the same way a map stands in relation to the portion of the earth it seeks to describe.
And just as every map includes limitations about the area it describes—streams in the real world are not blue, forests are not uniformly green and mountains don’t have brown lines snaking around them—it works for us as long as we are mindful of these limitations.
When flying cross country, glider pilots ordinarily use a ½ mil air chart (1:500,000 scale). This is a convenient size for the cramped confines of the cockpit. On this chart aerodromes are specified by small purple circles. This is absurd: in my experience aerodromes are neither round nor purple; certainly I’ve never known one. But as long as we recognize this, our chart works well for us. One of my gliding friends admitted he was not very good at chart reading: at looking at his chart then to the ground and confidently determining his location. He chose to use a ¼ mil chart (1:250,000 scale). On this chart aerodromes were still purple but specific runways were shown. When he looked out of his cockpit at a field he was approaching, he was confident of his location because he could compare what he read on his chart—his model, with what he saw on the ground—the world. He paid a price for this: he needed more space for his ¼ mil chart (and sometimes two charts if he were flying far). Here the ½ mil chart included a limitation he was not prepared to accept so he chose another model.
We could discuss this in more detail but two examples should suffice. On my air chart lines of longitude are parallel—lines of longitude in the real world are not parallel. The Earth is assumed to be flat—most of us accept the earth is not flat. Again, if we acknowledge these limitations we can navigate our glider cross country very nicely.
Isaac Newton proposed to explain certain phenomena in the world with the formula f = ma; Albert Einstein proposed to explain these with the formula e = mc2. Was Newton wrong or did Einstein ‘correct Newton’s errors’ as some writers suggest? I think not. What we see are two models with limitations and each works well when we acknowledge these limitations. Newton’s model works when we are playing snooker; Einstein’s model introduces complications we don’t need to get the job done. Newton’s model introduces some anomalies when we’re examining the path of a ray of light as it passes near a planet or star; Einstein’s model gives us a better result.
When we’re learning about the real number system, somewhere during week two we’re given the assignment to prove +1 x +1 = +1, -1 x +1 = -1 and -1 x -1 = +1, thus proving there can be no such thing as √-1. But then, likely during our second term when we’re learning about co-ordinate geometry, we find ourselves in the situation where to find the roots of a quadratic equation whose graph does not intersect or touch the x axis, we need to hypothesize the existence of √(b2 -4ac) where, using real values for a, b and c, we end up with a negative result, √(-1 x d) for some real, positive value d (if a, b and c are real then d must necessarily be real), clearly contradicting our proof in the second week of the previous term.
By the end of our second term we have learned three things: (1) from our first week in the first year that 0 x a = 0 for any real number a, (2) from our plane geometry that the area of any rectangle is l x w where l is the real value length and w is the width and (3) any real number added to ∞ is still ∞ and infinity is not a real number. Next when we study integral calculus, we face the absurd action of summing an infinite number of rectangles of various lengths and zero width and ending up with a real number result. I believe Newton, as one of the inventors of calculus—the other one’s being Leibnitz, understood this and I believe this an example of a situation reflected in his quotation at the beginning of this essay.
Confusion? Contradiction? Error? No, simply some adjustments to some of the models we use to predict the future: to design tall buildings which will not fall down in high winds, to build space stations where astronauts can live and work for a year, and to create magical machines which enable us to look inside our living brains. Soon we expect to see driverless cars on our roads and we assume these won’t crash into structures, people or other cars. These wonders of modern technology have all been created using models which include these contradictions.
These models work, and they work well—meaning they enable us to build things that work the way we predict or expect them to work.
Does the Higgs Boson exist? Maybe it does and maybe it doesn’t. I argue it doesn’t matter, what matters—the singular test—is whether it enables Professor Higgs et al. to describe what happens in the world.
It follows our definitions of ‘science’, ‘scientific method’ and ‘what scientists do’ might be modified to reflect this different approach to what the terms ‘hypotheses’, ‘theories’ and ‘laws’ mean. I expect, however, this is a step too far, especially with my complete lack of academic credentials.
Your comments are invited but please keep them as un-hysterical as possible and in reasonably good taste, particularly with respect to the marital state of my parents when I was born.
* As quoted by my good friend Christine Ogden.
† Here I do not propose we need to think about the meanings of ‘truth’ or ‘fundamental truth’ but simply accept these terms as undefined.