“Are we grown up enough to live with uncertainties, or will we repeat the 20th century mistakes, and plead blind allegiance to yet another uncertainty…”
The documentary of the BBC entitled “Dangerous Knowledge” made me realize that mathematics is more complex than I imagined it to be. It deals with different theories, axioms and postulates that even up to this very moment, are still unproved. It introduces me to another realm of mathematics, different from what I perceive it today.
As I was watching the video, I learned a lot of things especially from those four brilliant mathematicians who were featured in the documentary, namely Georg Cantor, Ludwig Boltzmann, Kurt Godel and Alan Turing. They are well known in the field of mathematics for their different achievements in the field yet they were all driven insane because of their too much attachment in the field. Attachment in a way that mathematics had become part of their lives. They devoted their entire lives proving those things that they believed is true.
The four mathematicians were able to formulate different theories that paved the way of uncertainty to elope in their lives. And the irony in this part is, uncertainties were revealed through certainties and so does logic reveals the limits of logic. They had sought certainty but found uncertainty. The presence of uncertainties made them “deviate” from what the other mathematicians were trying to do, that was to formulate certainties and decipher the “uncertainty” part of mathematics.
The so-called “deviations” in their part made it harder for them to understand more infinities and even the incompleteness of mathematics. For Cantor, who considered himself “a man of God”, it has been a very rough journey for him. He wants to conceptualize the certainty of mathematics to associate it with God’s handiwork. He may had died in a lonely asylum but still he had marked infinity to be more controversial driving himself to its extent and extremes. Godel spent his life proving that logic has its limits and that problems arise even outside the human logic. In his quest of proving his intuition or theory, he had a breakdown that affected his brain and later he starved himself to death because he did not want to eat for he believed that he would be poisoned. And also Boltzmann, a man inclined to music, who tried to pursue his theory of atoms and probability and the response he got was purely rejections . The rejection of his theories depressed him and while in a vacation, he committed suicide. And also for Alan Turing a homosexual, who made Godel’s theories more simpler in the context of computer .And because of his homosexuality, the government punished him by injecting estrogen in his body. This had affected his body and became one of the factor why he had committed suicide later on, by eating an apple which he injected with cyanide.
I believe that what made them more confused is the fact that at their time, nobody believed them and everyone kept on rejecting their ideas and theories. Those rejections somewhat depressed them that drove them from their sanity and later on made them commit suicide. But their deaths did not end the quest on the true nature of uncertainties, for they had changed the course of mathematics, making it more complex and more controversial than it has ever been before. Many are still trying to answer and pursue the true nature of reality in mathematics. And even up to now, they are still grasping for a certain answer that would end all the questions and even the loopholes of the fundamental theories of mathematics.
After watching the documentary, I have a lot of realizations. Mathematics is a broad subject. Some things that existed within mathematics are not even true or proven yet, but we keep on clinging and believing on them. For as David Malone said on his last lines, we cling to believe to certainty to make us safe.
I also realized that somewhat uncertainties often cause doubts on a lot of things, in religion, mathematics and in almost everything. I also shared the same dilemma with them in regards with uncertainties but only for a short span of time. Maybe because I am one of those “people” ,discussed by one of the professors featured in the documentary, that were fully aware of the “dirt” (uncertainties) yet they do not “sweep it away” (find solutions or even try to prove it) for I am having more fun living with the dirt/problem. In some way, I can relate myself with it but it could be that mathematics for me had been taught as finite and every infinities and uncertainties had been covered up by different axioms and postulates that we had been using for years.
The theory of infinity will always be a mystery for us, no matter how hard we try to grasp on its real nature, we will never understand it. And if yet another uncertainty will lead us to doubt the existence of different theories we already know, I guess the mathematicians behind it will never commit suicides again, for we are in a totally different situation.
But that does not mean that I will always settle for the present certainties and the “cover-up” axioms and postulates, for I too have my own set of doubts and questions in the behavior of how we deal with mathematics that takes a toll on my knowledge and even in my beliefs. I may not be like Cantor, Boltzmann, Godel and Turing, who perceived and pursued what their intuition told them. Maybe, I just settled myself with what my mind can only perceive. Human mind and mathematics are inseparable. But I do believe that whether we like it or not, there are things that our human mind cannot fully comprehend, and those things simply exist to make life more challenging, beautiful and dynamic, and more so does mathematics and the theory of infinity.