Posted in Culture, Mathematics, Philosophy | No Comments »
R.J. Lipton just posted on his blog a very nice dedication to Alan Turing's famous paper "On Computable Numbers, with an Application to the Entscheidungsproblem". While I recommend both the blog post and the paper, I want to write about an episode from the comments section of the post.
In a comment, John Sidles takes an essay from the preface to General Victor Krulak's book First to Flight and replaces every occurrence of the word "US Marine" with "mathematician". The result is breathtaking and somewhat awe-inspiring:
Why does the world need mathematicians?
Mathematics exists today—flourishes today—not because of what we know we are, or what we know we can do, but because of what the world believes we are and believes we can do.
Essentially, because of the unblemished achievements of mathematics over centuries, the world believes three things about mathematicians.
First, they believe that when trouble comes to the world, there will be mathematicians—somewhere—who through hard work have made themselves ready to do something about it, and do it at once. They picture mathematicians as mature individuals—dedicated members of a serious professional community.
Second, they believe that when mathematicians bend their minds to a task, they invariably turn in a performance that is dramatically and decisively successful—not most of the time, but always. The world’s faith and convictions in this regard are almost mystical. The mere association of the word “mathematics” to a challenge is an automatic source of encouragement and confidence everywhere.
The third thing that they believe is that training in mathematics is downright good for young people; that mathematicians are the masters of an unfailing alchemy that helps convert unoriented youths into proud, self-reliant stable citizens—citizens into whose hands the planet’s affairs may safely be entrusted.
The people believe these three things. They believe them deeply and honestly, so much that they are willing to pay for mathematicians to solve problems, and to teach young people.
Therefore, for reasons that completely transcend cold logic, the world wants mathematicians. These reasons are strong, they are honest, they are deep-rooted, and they are above question or criticism. So long as they exist—so long as people are convinced that mathematicians can really do the three things I have mentioned—we are going to have a mathematical profession.
And likewise, should people ever lose that conviction—as the result of the mathematics community’s failure to meet their high—almost spiritual—standards, the profession of mathematics will swiftly disappear.
Is there a chance that such a thing might happen? I think there is. I think that we ourselves can shake these convictions and the accompanying faith which really sustain us. By a lack of attention we can lose the inspirational personal relation that is shared between our senior members and our rank-and-file. Also, by carelessness or inordinate attention to less important things, we can lose the attributes of professional dedication and unfailing preparedness which, in centuries past, has deservedly made mathematics one of humanity’s treasures.
How serious it is, I don’t profess to estimate to you, but it certainly worries me. It does, because if the world wanted to try, she could get along without a profession of mathematics.
In this post, I primarily wanted to reproduce and share the above piece. That being said, I will conclude with a few brief comments. It seems to me that while all three things are generally believed about mathematicians, the second seems to be the most true. Ever since the mathematization of the sciences in the time from Galileo to Newton, there seems to be a push to mathematize anything and everything. This push, I believe, rests on a belief that by mathematically modeling a phenomenon we imbue said phenomenon with the certainty of mathematical truth.
I do also wonder what other professions could be substituted into the passage for "US Marine". Of course, given the career path that I will soon be embarking on (I am starting a Ph.D. in Philosophy at Stanford this Fall), I am most curious about whether "philosopher" fits. Judging by my interactions with a variety of people, their reactions lead me to believe that none of the three beliefs listed above are held in any kind of generality by "the people". Philosophers are not always associated with hard work, "dramatic and decisive" success is hard to define let alone achieve in philosophy, and not many people feel an urgent need for a philosophical education. While I would disagree with these assessments (sans maybe the second one), I would like to point out one thing about hard work in philosophy: the same attributes that make one a successful philosopher in modern academia are the same attributes that make one successful in any industry. Hard work---honest toil for those keen on the phrase---cannot be replaced. Whether or not that's a good thing I leave for another time.
. Two things directly affect the size of this number: 
and 
.