Chapter 3: On Mathematics and Humanity
Philip: Part of the role of philosophy is to examine the contributions made to mankind by various systems or phenomena. I would like to ask you for your perspective on the contributions of mathematics.
Matthew: Where should I begin? Since the founding of mathematics, it has contributed a knowledge of reality and a representation of its beauty.[1] Mathematics has allowed us to study the multiplicities and the shapes found in our world, and it has given us a means of communicating these discoveries through an abstract symbolic system. In this way, mathematics has allowed humanity to investigate nature and successfully live within it.
Mathematics has also provided a fulfillment of natural human curiosity. The human mind is designed to look for patterns and search for explanations, and mathematics is one of the great products of this pursuit. Also, and this is something that people often don’t think about, mathematics contributes beauty to the world in the form of elegant argumentation and awe-inspiring results. When an unexpected connection is discovered by a mathematician or a particularly aesthetic theorem is proven, it can elicit the same emotional responses as a mural or a symphony.[2]
Philip: Okay, but now I’m going to push a little bit further by bringing value judgments into the picture. I think the three contributions of mathematics that you just alluded to could be categorized as “good,” as impacting humanity positively. My criterion for “goodness” is that it leads toward a more authentic humanity.
Matthew:What do you mean by authentic humanity?
Philip:Authenticity is a fairly fundamental term in existential philosophy, but to be brief I would say that it involves the following characteristics – human interaction, compassion, freedom, intellectual growth, and an acceptance of one’s facticity.[3] From your comments, I would say that mathematics obviously contributes positively in the realms of human interaction and intellectual growth, and perhaps even in the acceptance of facticity.[4] But we must not stop here, we must also consider whether or not mathematics contributes negatively to this pursuit of an authentic humanity. I’ve read an argument on this point.
Matthew: Let’s hear it.
Philip: Actually, I’ve heard similar arguments coming from several different sources. The main idea is that mathematics lies behind all technological advances, and that these severe increases in technology are working to dehumanize the population. Thus, mathematics deserves some, perhaps much, of the blame for what Heidegger calls the “darkening of the world.”
Matthew:Right away, I would like to challenge one of your premises. It is important to keep in mind the difference between mathematics, or pure science, and technology. Mathematics is just a natural human endeavor, the controlled use of the intellect. Mathematicians simply investigate and prove results, they do not determine how those results will be used. It becomes even more clear that pure science is separate from technology when you consider the fact that the same science can be put to use for good or for ill. As Erdős said, “everything that can be used for good things can also be used for bad things.” As an example, he discussed the differential equations that model the spread of gas, which can be used to prevent the dispersion of pollutants or used to deliberately distribute poison gas in warfare. Mathematicians only care about the differential equations, they do not choose either use for them.[5]
Philip: The fact still remains that without the mathematical engines behind them, today’s technologies would not be what they are. I agree that mathematics does not deserve the full blame, but the science must be at least somewhat responsible for the scions of its labors.
Matthew: I will grant you the point for now. So what is it about technology that is so detrimental to humanity? I have often thought about how new commercial technologies are nice for the people who can afford them, but for the people who cannot afford them it just adds one more thing to the list that the “haves” have and the “have-nots” do not. Thus, even if a new product makes someone at the top slightly more happy, it reduces the happiness of many who are aware of what they do not have.[6]
Philip: That’s a good point, but I don’t want to get too far into Utilitarianism.[7]
Matthew:Well, I would also say that technological warfare has had negative effects on humanity since weapons have become increasingly effective at killing people faster and from farther away. The massive stockpiles of nuclear weapons also come to mind.[8]
Philip: I agree that high-tech weaponry is bad for humanity because, thinking about our authentic model, it moves us away from certain freedoms – the freedom from fear and annihilation, it moves us away from intellectual growth – because effective learning does not take place under fearful conditions, and it is certainly not compassionate. But you are still not hitting on the points I was actually referring to concerning technology. Heidegger criticized technology because it changes us funda-mentally by controlling our language. We exist through our language, and when technology alters our language it also alters our essence.
Søren Kierkegaard also issued warnings concerning technology because he saw it being used as an escape from genuine, face-to-face communication. And if we lose our genuine interactions, we lose part of our humanity. Kierkegaard went on to observe that certain technologies allow us to create selective realities, where we can present ourselves as we want to be, not as we truly are. This moves individuals away from the acceptance of their facticity, and therefore, away from an authentic existence.[9]
Matthew: I have read something along those same lines. It was by C.S. Lewis and he argued that technology, contrary to popular opinion, does not give man power over nature, but instead gives some men power over other men. In particular, those who produce and distribute the technologies could remove their availability to the rest who depend on them. Additionally, people often forget the temporal dimension, wherein technology gives current generations power over future generations through things like the weaponry that we mentioned before and also through contraception and medical advances. The existence of humanity in the future is being altered through our use of technology at the present time.[10]
Philip:I’m going to step in as the devil’s advocate and say that technology is good for humanity because its expansive capabilities offer freedom.
Matthew:Indeed, since we’ve identified mathematics as a primary source of technology and there is an infinite supply of mathematical results, then the possibilities for technological innovation may also be endless.[11] But why is it that when faced with this multitude of choice, this vast amount of freedom, humanity seems to gravitate toward destructiveness. We employ technology more for pleasure and comfort than for compassion or cures, for status and power rather than for equity or balance.
Philip: I believe it is because an infinitude of freedom is actually just chaos, and we have a natural aversion to chaos so we look for some kind of order and direction. Unfortunately, those currently in power are able to impose their values and desires onto our technological choices and take advantage of humanity’s search for structure. In this way, we are witnessing what C.S. Lewis talked about with men controlling other men via technology.
Matthew: So if the technological possibilities are essentially infinite, this infinity of freedom is essentially chaos, and humanity rejects chaos, where does that leave us?
Philip:I think we need to place a bound on our freedom, while still realizing that we are free within that bounded space. We can venture forth knowing that we have a stable system in place upon return; so we are still free, but it is a grounded freedom. Furthermore, we are free to choose the bounds, but that choice should be made as a conscious, wakeful community – not simply by those in power who make the choice to suit their advantage. We must choose to limit our technology so as to best set ourselves on course toward an authentic existence.
Matthew: So we should participate in a reasoned dialogue concerning technology, with the purpose of maintaining our authenticity. By this, I think we mean the avoidance of its perversion of language, the reclamation of our genuine face-to-face interactions, the rejection of its empowerment of the already powerful, and the promotion of its potential for good. If we set limits on technology with these goals in mind, it should allow mathematical inquiry to continue as a naturally human endeavor with the assurance that novel results and new mathematical tools will not be used in a dehumanizing manner.
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[1] Skeptics may argue that we never truly “know reality” because all information is received through the senses, which are fallible. Also, Morris Kline and others would posit that mathematics in modern times has drifted significantly away from its natural foundations to an ungrounded, abstract place with no connection to the real world. While it is true that certain branches of mathematics are lacking in any real-world applicability, there remains overwhelming evidence of mathematics’ success in nature. Mathematics is heavily utilized by and often found at the root of the empirical sciences, and, through its powers of generalization, Richard Panek points out that “the ability of mathematics to make predictions is one that any science might envy.” Add to this the wide applications of algebra, geometry, trigonometry, dynamical systems, discrete mathematics, and the calculus, and it becomes hard to write mathematics off as a meaningless game of abstraction. Moreover, it has been said that mathematics is not certain knowledge since it is based on undefined terms and unproven axioms, but again, one must consider its incredible success throughout history.
[2] For instance, it would be a difficult task to find a mathematician who was not profoundly affected by the beauty of Euler’s formula, as it relates the five most important constants in mathematics.
[3] The term “facticity” in existential philosophy refers to all the concrete details of existence (i.e., time, place, inevitability of death) which serve as the context within which human freedom is to be exercised.
[4] If it is not apparent how mathematics contributes positively to human interaction, refer to Hoffman’s The Man Who Loved Only Numbers which contains the story of Paul Erdős who was a brilliant man that pioneered mathematics as a social undertaking.
[5] Another example can be found in Cat’s Cradle, by Kurt Vonnegut, where the scientist Felix Hoenikker develops an isotope of water with no ulterior motives in mind. Unfortunately, this development is not treated with the proper care and what was a purely scientific effort leads to catastrophic results.
[6] Some may argue that technology only makes life easier for those who can afford it, not necessarily happier. This is certainly worthy of discussion but is not contained here.
[7] Utilitarianism attempts to define morality as that which maximizes some quantization of happiness. As a crude example, consider an act A that makes everyone an average of 5.4 on the happiness scale and an act B that makes everyone an average of 5.2 on the same scale.Then under this philosophy, act A is the “right” thing to do. Obvious problems arise at the attempt to design a scale for happiness and at the attempt to collect universal happiness data.
[8] Some may claim that nuclear weapons are beneficial to mankind because they serve as a deterrent to war. Though it is true that several nations possessing nuclear capabilities is better than a single nation, the optimal situation would be for no nations to have such devastating weapons of destruction.
[9] In more recent times, Stephen Rowe has analyzed what he termed “Machine-ism.” Many people live their lives as if they were machines, consumed and overwhelmed with task-lists and duties to the point where human interaction is a bothersome interruption, and open space for conversation or real life is a thing to be feared. Machines have become powerful role models and much of technology has moved from serving human life to usurping it.
[10]C. S. Lewis, in The Abolition of Man, goes on to forecast a conquering generation that will master all aspects of nature through unchecked technology. He calls those in the powerful positions of this culminating generation the “Conditioners” because they will control everything around them, including other human beings, and define what is right and wrong forever afterward. If this vision of Lewis were to come to pass, it is quite possible that it would spur on the emergence of Dostoevsky’s “underground man.” When everything around an individual is controlled and prescribed, Dostoevsky believes that individuals will reject it, even at their own risk, because the exercising of their free will is paramount. They will sacrifice their own well-being to maintain their sense of free will.
[11] Gödel’s Incompleteness theorem stands as testimony that work in mathematics will be forever possible, at least as far as number and analysis are concerned, because within any formal system that contains arithmetic axioms a true statement can always be constructed that is not yet included in the system.