Mathematics and Being Less Wrong

Katherine Redford's picture

Katherine Redford
English 223
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. 

Works Cited
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/>.

Comments

Anne Dalke's picture

mathematically

2/17/07
Katherine—
I’m delighted that you took me up on my challenge to use mathematics as a test case or exemplar for the notion that “science is story,” and I was interested to learn from you some of the history of mathematics, about which I know nothing—thanks for the instruction! You also provoked lots of questions for me (which I hope might spur your own further thinking). Here are some of them:

--why assume that math has to fit w/in one of the 3 divisions (you say disciplines, but there are far more than three of those..)? Is that where mathematicians or historians of math or sociologists of math always place it? Why is it placed there? (Why couldn’t it be—or isn’t it, for instance--counted as one of the languages? You call it a language….) I need to hear that point argued more fully before I can follow you in taking the next step, that--since math is one of the sciences, and math is not process of “getting it less wrong”--the account of science as storytelling is wrong. There’s a hole in your “proof.”

--what does it mean to say that “the story of math has never changed”? What is “the same conclusion” that every civilization reached? Surely there have been new theorems developed, new proofs…? Remember that you are writing for someone who is not a math major (confession? I never went beyond Algebra II, which is all my h.s. offered, and in college I met my quantitative requirement—or maybe it was a logic requirement??--with a Philosophy course!)

--I’m not following the logic of “math is a science and if math has a correct answer, than evolution must also have a correct answer.” Surely it’s possible that different branches of science operate differently? Perhaps Paul’s story works for bio, but the “more wrongness” has to do with generalizing from that to all science? The problem is not with the claim itself then, but with over-generalizing from that claim?

--Your strongest and sharpest argument is that, in biology, we are a part of what we study, a “character” in the plot, “both the studier and the studied,” and so can’t be objective. What I don’t understand is why that isn’t also the case with math. Isn’t it a human-made language? I’m also not sure I see why personal investment necessarily “clouds” understanding. Mightn’t it motivate and fuel it?

--I also didn’t understand what role the paragraph about having no control played in the development of your argument.

If you are interested in going on in thinking about this topic, pushing @ the edges of some of the claims that you make here, one source you might find helpful in the process is a faculty brown bag series sponsored here a couple of years ago by the Center for Science in Society. It was called “What Counts? Measuring Ourselves in the World” and all the conversations are archived. You’ll find there some challenges to the claims you make in your paper—I pass them on as impetus for further thinking. You might want to look in particular at one of the texts I drew on for my own talk; it’s by Temple mathematician John Paulos, and called Once Upon a Number: The Hidden Mathematical Logic of Stories….

Looking forward to hearing what you think of all this—
Anne

Post new comment

The content of this field is kept private and will not be shown publicly.