Mathematics and Being Less Wrong
February 16, 2007
How does Mathematics fit into the description of Science as a process of “Less Wrong”?
If we look at the three disciplines of academia, mathematics undoubtedly falls into the category of science. It has been praised as the language of science, lending itself to biology, chemistry and physics. Mathematics has a solid foundation, tested by different civilizations since the beginning of time. Every reason that I have been given to explain why science is only a process of getting it less wrong, do not stand up when it comes to math. Because of this, it is impossible to say that there is no right answer in science because mathematics has been tested and retested, and the story has never changed. Math is a science and if math has a correct answer, than evolution must also have a correct answer. However, there exists a great difference between the stories of mathematics and evolution. Because humans are a part of evolution, a “character” in the plot, it is impossible to achieve objectivity. While math provides evidence that a true answer exists, our role in evolution prevents us from understanding it fully.
Mathematics finds its roots growing independently from one another in multiple ancient cultures. In ancient Asian civilizations the rise of mathematics was brought about “as a practical science to assist in agriculture, engineering, and business pursuits,” (“Mathematics Development”). But the concept of the number, on which all of mathematics is based, reaches so far back into human existence that there is no record; “the birth of the idea of number is so hidden behind the veils of countless age… our remote ancestors must have felt the need to enumerate their livestock, tally objects for barter, or mark the passage of days” (Burton 1). Civilization after civilization independently found new ways to express the same concept, the number system. The earliest evidence suggests that notches or tallies were used in a one to one ratio, and the way these numbers were expressed ranged from hieroglyphics to cuneiform to a system in China with only nine symbols (Burton 1-29).
So far in lecture we have been told that human subjectivity prevents us from ever getting the story completely correct. We look at evolution, and everyone interprets the story differently, but this is not true in mathematics. So many civilizations developed math independently of each other, and all of them reached the same conclusion. There exists evidence of the use of the Pythagorean Theorem in ancient Egypt, long before Pythagoras came around. All of my observations point to the idea that mathematics is fact, and should be taken as such. The “less wrong” theory just doesn’t hold up here.
Hermann Hankel is quoted as saying, “In most sciences one generation tears down what another has built and what one has established another undoes. In Mathematics alone each generation builds a new story to an old structure”. Mathematics is unique in many ways, especially in the way that it relates to other sciences; “mathematics… is also penetrating into areas of knowledge one-sidedly, for their benefit” (Bochner 5). Mathematics as a subject of study holds up entirely on its own, we don’t need chemistry to define it, biology to reinforce it, it exists without help. What does this say about the other sciences? In science, there has to be a right answer; mathematics is proof of this.
There is one variable that differs between biology and mathematics, that is, that we are a part of biology, the science of life. Our observations are limited by the fact that we are a part of the process. We evolved from earlier species, and we can predict that we will evolve into more species. In mathematics, we are not a part of the science, we can apply the science to our lives, use it to build buildings, explain the laws of physics, but what is happening to us now, does not affect changes in mathematics, and the deeper understanding of the science.
Our desire to understand biology is clouded with the natural human desire to understand what is going to happen. Often in class we discussed whether or not we believed the story of evolution to be comforting. Some argued that the thought of having no control over what happens to future generations to be a frightening concept. Others believed that the fact that the concept of uncontrollable fate soothed them. Regardless of our position on this question one fact remained, as humans, an animal species constantly evolving; we are personally invested in the story.
This is where the concept of the crack comes in to play; this is not a feature of science, but rather a feature of our being both the studier and the studied. It is impossible for humans to be objective when studying themselves. The way in which we perceive what is happening is dependent upon all the concepts described in class. Our personal beliefs and what we hope to get out of our observations may skew what we choose to observe, and the conclusions we reach from them.
All of the reasons that humans cannot successfully study biology are not flaws of the science itself. We know that in science there is a truth; in mathematics we have successfully achieved truth through our study. Mathematics is a science of which we are not a part; when we study science, we are studying something separate from our own existence. However, when we attempt to study biology, we fail miserably. From the beginning our theories were varied, and our conclusions sporadic. This is because we are attempting to observe something that we are an integral part of, being both the studier and the studied. However, this does not mean that a truth does not exist, simply that we our involvement in the story prevents us from discovering it. Our personal temperament and beliefs cloud the science before us and the truth evades us.
Bochner, Salomon. The Role of Mathematics in the Rise of Science. Princeton University Press. 1966.
Burton, David M. The History of Mathematics: An Introduction. McGraw Hill. 2007.
Thinkquest.org. Mathematics: History. 14 February 2007. <http://library.thinkquest.org/22584/>.