Experiments in Life

Lately, I have given a good bit of thought as to how I research new topics. There are two related concepts in philosophy, Holism and Reductionism, that play together in how I approach research. Holism was put forth by Aristotle as “The whole is more than the sum of its parts.” The concept of reductionism is defined as the opposite: “The whole is nothing more than the sum of its parts.” Which is the natural way for me to approach researching new topics?

When learning something new, I have a tendency to split my efforts into multiple strata. First, I get a broad overview of the topic and try to just get a feel for the basics. At this point, I am not concerned with doing calculations or working any types of problems. I just was to get a rough feel for the topic. As I study, I make a note of topics that interest me further. Once I feel like I have a good overview, I pick the most interesting topic and dig a deeper into it. This is the point where I start to try to apply what I am learning, either by working problems or writing programs. However, I never really go too deep on any one topic—I tend to bounce around all of the topics that interest me, chipping away at the terminology bit by bit, working a little more, until I feel like I have a good enough understanding of the topic to satisfy my interest.

So, where do I fall along the holism—reductionism line? Well, I would say that, in general, I take a more holistic view of research. To me, the whole is more important than the individual parts. I only want to know enough of the parts so that I feel like I have a good enough understanding of the whole. I think that plays into my Jack of All Trades syndrome. If I can grasp the Big Picture of a topic, it is infinitely more valuable to me than if I become an expert in all of the little pieces.

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On Monday, I explored two questions of Hardy’s:

1. Is what you are doing important?
2. Why do you do it?

I came to the conclusion that my endless pursuit of knowledge was not very important in the grand scheme of things, since I was not sharing it with other people. Afterwards, Ashley and I were talking about the different levels of importance. She made the point that, although I did not feel like what I was doing was important, my pursuit of learning set a very good example for Emily and, on that level, it was important.

There is no absolute scale in importance. How important an activity is lies in the context in which it is viewed. If you feel that your job is not very important, maybe you are demonstrating a good work ethic to your coworkers or your children. Each activity must be viewed through the prism of your life to find its significance. If you find an activity important enough to spend your time on it, do the be you can. If it is important to you, there is a good chance it is important to someone else as well.

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I am still reading through G. H. Hardy’s “A Mathematician’s Apology”; it is a very interesting essay, but it is fairly long after riding seven miles a night on the bike, I have not felt much like reading. However, Hardy has some ideas about the motives behind research that I found interesting:

There are many highly respected motives which may lead men to prosecute research, but three which are much more important than the rest. The first (without which the rest must come to nothing) is intellectual curiosity, desire to know the truth. Then, professional pride, anxiety to be satisfied with one’s performance, the shame that overcomes any self-respecting craftsman when his work is unworthy of his talent. Finally, ambition, desire for reputation, and the position, even the power or the money, which it brings. It may be fine to feel, when you have done your work, that you have added to the happiness or alleviated the sufferings of others, but that will not be why you did it. So if a mathematician, or a chemist, or even a physiologist, were to tell me that the driving force in his work had been the desired to benefit humanity, then I should not believe him (nor should I think the better of him if I did). His dominant motives have been those which I have stated, and in which, surely, there is nothing of which any decent man need be ashamed.

It is important to note that Hardy attributes these motives to be the driving reasons why people perform research; obviously, there are other professions, such as teaching or social work as a few examples, that may have alternate, altruistic motives.

Reflecting these motives back on myself, I find that they fit fairly well in that order. First and foremost, I want to know the answer to the question that I am pursuing. As an aside, I find myself asking questions during the most random times and wanting to know the answer. The other night while giving Em a bath, I couldn’t remember what eigenvalues and eigenvectors were, so I had to fetch my Linear Algebra text and look it up while Em was entertained with bath crayons. There was no particular reason why this flitted through my head, but it did and I had to know the answer. What can I say, I am a little weird. Secondly, when I am writing software, I want my programs to work correctly when other people get their hands on them. Finally, I want to be thought of well in whatever I am doing. Luckily, the first two motives usually help to drive this third one along.

I especially like Hardy’s statement that “there is nothing of which any decent man need be ashamed”. Yes, doing things for the greater good is noble, but if you do not get joy and satisfaction from what you do, you will become burned out and no longer want to do it. Maybe you get joy and satisfaction merely knowing that you are helping others; for me, there also has to be the hint that I am going to learn something new.

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This weekend, I began reading G. H. Hardy’s “A Mathematician’s Apology”. The essay is best known for the insight that it gives you into the mind of a mathematician. In it, Hardy is writing a defense of his life as a mathematician. Early on in the rather lengthy essay, he writes the following:

A man who sets out to justify his existence and his activities has to distinguish two different questions. The first is whether the work which he does is worth doing; and the second is why he does it, whatever its value may be.

Hardy says that, if you want to justify yourself, you have to answer the following questions:

1. Is what you are doing important?
2. Why do you do it?

If you cannot tell, I spend a lot of time trying to answer these two questions about myself. In the essay, Hardy states that the second question is a fairly easy one to answer but that the first is “is often very difficult, and the answer very discouraging”.

In this case, I want to justify my never-ending quest for more knowledge. So, let’s take the easy way out and answer the second question first. Why do I do it? Well, I study things simply because I enjoy it. My mind is like a sponge, soaking up new information, so it comes easy to me — it always has, much to my sister’s dismay (sorry Sis!). I like to be able to distill what I know down to the essentials and explain new concepts to people, not because I want to feel superior to them, but because I generally want to be able to share what I know with them and help them out if possible. Reading this, it sounds like I should go into teaching someday — that is a possibility I have considered once Em gets into college. Right now, I am having too much fun learning new things and applying them as an engineer. So, attacking the first question, is what I am doing important? Unfortunately, at this stage, I would say it is not. While I am spending a lot of time learning new things, I do not spend nearly enough time sharing them with other people. As Em gets older I am sharing more and more of my love of discovery with her. One of the things I most look forward to is working on Science Fair projects with her and helping to foster the same love of science that her mother and I share. As it is now, I try to answer her questions in ways that a 3 year old can understand.

Beyond fostering a love of learning in my daughter, what can I do to make what I do important? At this point, I would say learning how to share my knowledge more effectively with other people. Perhaps I finally need to get to the Toastmasters meetings that I have been meaning to attend. Writing here has helped give me a bit of an outlet. Are there any topics that people wish me to expound on?

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I am sure at this point that everyone is getting a little tired of me talking about Richard Hamming’s “You and Your Research” but there are just so many good points to the talk that I feel like I must share. At one point, Hamming recounts complaining to Hendrik Bode about one of Hamming’s coworkers being so much smarter than he:

[Bode replied] “You would be surprised Hamming, how much you would know if you worked as hard as he did that many years.” What Bode was saying was this: “Knowledge and productivity are like compound interest.” Given two people of approximately the same ability and one person who works ten percent more than the other, the latter will more than twice out-produce the former. The more you know, the more you learn; the more you learn, the more you can do; the more you can do, the more the opportunity! [I]t is very much like compound interest … given two people with exactly the same ability, the one person who manages day in and day out to get in one more hour of thinking will be tremendously more productive over a lifetime.

Fundamentally, this is why I spend so much time reading and studying so many different subjects. As I gather information, I form more connections between the topics in my brain. This is a variation on Metcalfe’s Law, which derives the value of a network as approaching the square of the number of nodes in a network as the number of nodes gets large — specifically:

Consider the classical example of a fax machine. A single fax machine is not very useful on its own. Add a second fax machine to the network and suddenly the machines can talk to each other with a single connection. Add a third and you have three connections. A fourth gives you a total of six connections, and so on and so on.

Now you can see the value in thinking that one more hour a day. By thinking one more hour, you can learn one more thing. However, that one thing can possibly be combined with every thing else you have learned in new and interesting ways. This also goes back to the classical education movement and the trivium that I discussed a few weeks ago. As you gain more and more information in the grammar stage of learning — about any topic — you can build more connections between the information and make more reasoned arguments during the logic and rhetoric stages of learning.

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