In this post I discuss part 2 of 3, Mathematical Construction versus Mathematical Conjecture, of how to read or write a journal paper that is not taught in colleges.

I did my Master of Arts in Operations Research (OR) at the best OR school in the United Kingdom, University of Lancaster, in the 1980s. We were always reminded that models have limits to their use. There is an operating range within which a model will provide good and reliable results. But outside that operating range, a model will provide unreliable, incorrect and even strange results.

Doesn’t that sound a lot like what the late Prof. Morris Kline was saying? We can extrapolate this further, and ask our community of theoretical physicists the question, what is the operating range of your theoretical model? We can turn the question around and require our community of theoretical physicists to inform us or suggest boundaries of where their models fail “ … to provide reasonability in guidance and correctness in answers to our questions in the sciences …”

A theoretical physics model is a mathematical construction that is not necessarily connected to the real world until it is empirically verified or falsified, until then these mathematical constructions are in limbo. Search the term ‘retrocausality’ for example. The Wikipedia article Retrocausality says a lot about how and why of the origins of theoretical physics models that are not within the range of our informed common sense. Let me quote,

“The Wheeler–Feynman absorber theory, proposed by John Archibald Wheeler and Richard Feynman, uses retrocausality and a temporal form of destructive interference to explain the absence of a type of converging concentric wave suggested by certain solutions to Maxwell’s equations. These advanced waves don’t have anything to do with cause and effect, they are just a different mathematical way to describe normal waves. The reason they were proposed is so that a charged particle would not have to act on itself, which, in normal classical electromagnetism leads to an infinite self-force.”

John Archibald Wheeler and Richard Feynman are giants in the physics community, and these esteemed physicists used retrocausality to solve a mathematical construction problem. Could they not have asked the different questions? What is the operating range of this model? How do we rethink this model so as not to require retrocausality?

This unfortunate leadership in retrocausality has led to a whole body of ‘knowledge’ by the name of ‘retrocausality’ that is in a state of empirical limbo and thus, the term mathematical conjecture applies.

Now, do you get an idea of how mathematical construction leads to mathematical conjecture? Someone wants to solve a problem, which is a legitimate quest because that is how science progresses, but the solution causes more problems (not questions) than previously, which leads to more physicists trying to answer those new problems, and so forth .… and so forth .… and so forth .…

In Hong Kong, the Cantonese have an expression “chasing the dragon”.

Disclaimer: I am originally from that part of the world, and enjoyed tremendously watching how the Indian and Chinese cultures collided, merged, and separated, repeatedly. Sometimes like water and oil, and sometimes like water and alcohol. These two nations share a common heritage, the Buddhist monks, and if they could put aside their nationalistic and cultural pride, who knows what could happen?

Chasing the dragon in the Chinese cultural context “refers to inhaling the vapor from heated morphine, heroin, oxycodone or opium that has been placed on a piece of foil. The ‘chasing’ occurs as the user gingerly keeps the liquid moving in order to keep it from coalescing into a single, unmanageable mass. Another more metaphorical use of the term ‘chasing the dragon’ refers to the elusive pursuit of the ultimate high in the usage of some particular drug.”

Solving a mathematical equation always gives a high, and discovering a new equation gives a greater high. So when we write a paper, we have to ask ourselves, are we chasing the dragon of mathematical conjecture or chasing the dragon of mathematical construction? I hope it is the latter.

Previous post in the Kline Directive series.

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Benjamin T Solomon is the author & principal investigator of the 12-year study into the theoretical & technological feasibility of gravitation modification, titled An Introduction to Gravity Modification, to achieve interstellar travel in our lifetimes. For more information visit iSETI LLC, Interstellar Space Exploration Technology Initiative.

Solomon is inviting all serious participants to his LinkedIn Group Interstellar Travel & Gravity Modification.