Thinking About Bioinformatics

As I discussed in a previous post, I want to emulate the admirable clarity and accessibility of Feynman’s Lectures on Physics in my own attempt to write an introductory textbook on information metrics for statistical inference.  Below are my thoughts on how I can apply the lessons that I drew from Feynman in my previous post.

More to the point, I’ve rewritten Chapter 1  What is Inference? based on these lessons.  So now I ask you: is this a genuine improvement?  Note that this is an intro chapter with only the simplest math (some addition and multiplication), so anyone should be able to understand it and critique it!  Please add comments to this post to give your opinion of whether you think the specific changes I outline below improve the chapter, compared with the original version.  I am particularly interested in both whether you think the ideas in my plan are the right direction to pursue, versus whether their actual “reduction to practice” in the new draft chapter works or not.  Above all, tell me how I need to improve my chapter and my writing!

How can I apply Feynman’s lessons to my own writing?

• Short, self-contained chapters following Feynman’s question and answer model. I’ve struggled a bit over where to put some topics in my current “whole subject” chapters. I think these topics (e.g. Law of Large Numbers; basic info theory relations, etc.) will work better as self-contained chapters, which also make the precise order of topics less important. This seems like a useful goal. It will force me to relate each topic to my fundamental questions. It makes the material more accessible, like John Baez’s introductions in each This Week’s Finds. Reducing the stress on exact linear order will make it much easier to use this material in multiple formats, and to get feedback from other people. (I’ve never been able to get feedback on more than one chapter, from anyone). Finally, it’s probably an egomaniacal delusion to stuff a whole subject entitled “Inference” into one chapter. This layout pretends that each subject can be treated separately. A larger number of short chapters may actually work better: while each chapter is self-contained, it will discuss fundamental questions that connect it to many other chapters.

• I can rework much of my material into dialog form. For example, when I introduce the Monty Hall problem, I say there are two points of view on Monty’s “twist”: it doesn’t make any difference: some people find the whole question odd… vs. it makes a difference: some people make the argument that…. This cries out to become an actual dialog (with named characters, quotes, exclamation points!).

• I definitely have a mild case of math-envy, and go out of my way to show that I can drop some equations where relevant. The problem is, this turns into a conventional authority / soporific effect. I’m not sure how to strike the right balance. I guess you just ask yourself what’s truly needed for learning the material best. For example, my little section on rearrangement rules seems more “optional” than “needed”.
• I need to define for my reader a “science of information” that is not just math. The subject matter (abstract information; statistical inference) implies that it is pure math, but I’m not sure that’s right (especially for me!). The whole point of my approach is to redefine information as empirical. This is not just a methodological detail. First and foremost, it’s my personality. I’m a scientist in outlook, not a mathematician. I can develop these ideas scientifically (i.e. “thought experiments” or computational experiments, or using math as a model just as people do in physics or any other science). It would be better for me to focus this text on my strengths, taking full advantage of the scientific approach that I can contribute, rather than allowing this to become a watered-down math textbook. What are the elements of my “science of information”?

  • the key principle of operational definitions

  • the fundamental distinction between observable vs. hidden states as the foundation for all inference.

  • correspondingly, defining all information as empirical, i.e. measuring our ability to predict observables.

  • consequently, the focus on being able to compute: first, numerical models of actual data; second, measurements of information yield.

• An essential corollary is that I must articulate the fundamental questions of this new science. Each chapter introduction will raise these questions in dialog form, showing that our thinking about basic things is confused and incomplete. This will be a huge improvement over my existing introductions, which tend to be pompous, empty statements of grand intentions. Actually, it would do me a lot of good to have clear statements of these fundamental questions. It will probably turn out that I am just as confused as everyone else, even about how to articulate what the key questions are. Let’s try a few obvious questions:

  • is there a quantitative, scientific theory of information? Can “information” be measured in a way that solves problems generally?
  • how can we establish a clear framework of operational definitions for the phenomena that matter in this field? E.g. “observable” vs. “hidden”; “prediction” in the absence of an “objective observer” etc.
  • what “counts” as information? This has a number of confusing aspects (randomness vs. uniformity; “hidden” information; mutual information; definition of “prediction”), and is the question that empirical information answers.
  • how can we do experiment planning (before we know the result!)?

  • what are the requirements for sustainable (unbounded) information production? What is the difference between biological evolution and, say, clouds forming in the sky (or geological formations underground)? What are the requirements for scalable information production, i.e. a powertool?

  • Can this be made a simple, general procedure for discovering any information structure, or solving any problem?

This entry was posted on Wednesday, August 13th, 2008 at 8:46 pm and is filed under inference, information, writing. You can follow any responses to this entry through the RSS 2.0 feed. You can leave a response, or trackback from your own site.