I have spent quite a bit of time, using much of the information provided in these posts, to argue that mathematics is in a unique position to show us that our thoughts (the silent language in our heads) that appear to be produced in the privacy of our imagination, have some independent reality. By this I mean that our thoughts are not just ‘in our heads,’ and perhaps the use, and the history of mathematics (which reflects our science-oriented imagination) could help us understand something new, or see something new, about the fundamental nature of thought itself. I have written a yet unpublished, book-length manuscript to make a thorough argument for this view.
Recently, however, maybe in the last four years, I have become a bit distracted by an alarming abuse of words in our sociopolitical world – what I would otherwise call a frightening disregard for the harm caused by lies. Deceitful narratives are produced by the same thoughtful imagination (our words and concepts) that build the arts and the sciences. But, without any fidelity to the facts to which these thoughts should be tied, their expression acts more like a flood, or a fire, that repeatedly weakens the stability of our cultural achievements and challenges the trustworthiness of all words. It looks to me like the protective walls of our civil systems have been badly damaged and may yet crumble. The helplessness that I have felt in response to this damage has given my interest in the true nature of an idea, or a thought, or a word, new impetus. It’s made my fascination with mathematics all the more striking to me, and led me to believe that there may be a cure for my sense of helplessness.
I think I found my way to mathematics along a zigzagy road that, as a young idealist, I hoped would lead to the truth. And I know that the very mention of ‘truth,’ brings with it a long and profound philosophical history. But as a young person, in my Italian-American family, I was often saddened by the effects of simple deceptions. They were mostly harmless, interpersonal distortions of the truth between my mother and my grandmother, or my mother and my aunts,…. but they fed unhappiness, dissatisfaction, and frustration. College was the first time I created some real distance between myself and my family – not geographically, but intellectually. And, while I may have said any number of things about my academic interests to friends and advisors, the classes I chose, the future I imagined, was probably motivated, by my trying to find a way to see what was ‘true,’ in life, and in people. I devoted a lot of time and energy first to philosophy, then psychology, and when I finally considered physics, I found liberation in mathematics.
There is no value to deception in mathematics. And I might argue that mathematics is probably the most consequential, when speaking pragmatically, of our imaginative efforts. Free of deception and profoundly meaningful, the satisfaction I felt from finding this purely symbolic, yet physically connected intellectual enterprise has never subsided. Mathematics bears witness to the worldly relevance of thought, and the power of deception-free analysis. Conjured up by idealizing experience and reasoning, and then letting it grow with a kind of self-organizing life of its own, mathematics may be the most visible evidence of the fact that the mind’s eye, and the eye’s in our heads, each have their own way of perceiving. This leads me to believe that physical structure and thoughtful structure must hold equal weight in nature.
It may be hard to see how all of this would apply to our current sociopolitical situation, but I have thought about it every time I hear some pundit insist that “words matter.” However, taking a broader look at the situation, my husband (who is an experimental physicist) and I developed an analog. We imagined that the law was like mathematics, and politicians were like physicists. By this we mean that the law is the careful and precise development of ideals, and politicians (or government officials) are charged with finding the ways that these ideals may exist in the world. Figuring this out is what the people and their elected leaders try to do together. Deception contaminates the effort.
For whatever reason, I find this analogy reassuring. Perhaps the body politic can recover, like with the pandemic.
There is no starker illustration of the fact that, in the body politic as in the bodies the virus infects, the host’s response can matter far more to the course of the disease than the direct action of the pathogen itself.”
The Economist, “The year of learning dangerously Covid-19 has shown what modern biomedicine can do.” 23 March 2021
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