I have always liked logic puzzles. They exercise a curious fascination for me, extending even to my choice of reading. From the time I was very young, I was drawn to mystery novels of the Agatha Christie variety, which are essentially logic puzzles where the identity of the culprit is unknown until the end and the author lays out clues which the careful reader can use to solve the puzzle.

Needless to say, this extended to my choice of board games too, Clue and Master Mind being some of my favorites at one time. I also enjoy chess and card games like bridge, both of which contain a considerable element of puzzle solving.

So it should be no surprise that I have recently become addicted to doing the daily sudoku puzzle in the Plain Dealer. For those of you unfamiliar with this new craze, it is basically a logic puzzle consisting of 81 squares arranged in a 9×9 square grid in which about one-third of the squares contain numbers 1 through 9 from already filled in. The reader is required to fill in the rest containing subject to rules that are simple and can be found here.

The daily newspaper puzzle is labeled gentle, moderate, or diabolical, to indicate the expected level of difficulty, although the labeling does not always match my experience with the occasional diabolical being quite easy and the moderate quite hard.

The sudoku puzzles do not require any mathematics or even arithmetic to arrive at a solution. One could just as well do the puzzle with nine different fruits or symbols or whatever. But there is a lot of interesting underlying mathematics, and Brian Hayes has an interesting article in the January-February, 2006 issue of the American Scientist with a fascinating discussion of the mathematics of sudoku. involving such questions as how many different puzzles there are (Answer: 3,546,146,300,288) and what is the minimum amount of filled squares that must be initially provided so that there is a unique solution. It turns out that the latter question remains unsolved. “[T]he minimum number of givens is unknown. Gordon Royle of the University of Western Australia has collected more than 24,000 examples of uniquely solvable grids with 17 givens, and he has found none with fewer than 17, but a proof is lacking.” So there’s a nice challenge for the mathematically ambitious. Published problems usually have between 25 and 30 givens, with no simple correlation between the number of givens and the advertised level of difficulty.

One interesting question that the article does not answer is how the constructors of the puzzles know when they have given enough information so that there exists a unique solution. Do they have to work through the puzzles themselves and keep adding initial data until they have a unique solution? That seems tedious. In yesterday’s (January 31, 2005) Plain Dealer puzzle, it seemed to me that there were at least two solutions.

(The sudoku problems belong to a more general class of math problems associated with the term NP but there are some disagreements about whether it is NP or NP-hard or NP-complete, which I will leave to the more mathematically informed to figure out.)

After doing a few, it struck me that these puzzles are a good analogy for the way science research is done. Thomas Kuhn in his classic book The Structure of Scientific Revolutions points out that normal scientific research within a paradigm is largely a puzzle solving exercise in which there is an assurance that a solution exists to the problem and that it is only the ingenuity of the scientist that stands between her and a solution. The sudoku problem is like that. We know that a solution of a particular form exists and it is this belief that makes people persevere until they arrive at a solution.

Most of the sudoku solution strategy is deductive. One starts by filling in those empty squares with numbers that can be arrived at deductively, by rigorously ruling out all but the correct number. But in the more difficult puzzles, one reaches a stage where there may be two (or rarely) three possibilities for a crucial square and deductive logic alone cannot determine it. At that point, one has to resort to ‘hypothetico-deductive’ or ‘if-then’ reasoning. This kind of reasoning is an essential element of the scientific process. In scientific research one never knows exactly all the information needed to solve some problem. Hence one has to make reasonable assumptions about some things in order to proceed further and arrive at conclusions. And those assumptions can change in the light of new information.

Sudoku provides an example of this in that when one reaches such an impasse, one simply chooses one of the possible options and proceed to fill in all the rest of the squares using the standard deductive reasoning until either the puzzle is completed satisfactorily, confirming the correctness of the initial choice, or one runs into an obvious contradiction, indicating that one’s choice was mistaken and that one should have chosen the other option at the branch point.

In yet harder puzzles, one might encounter nested hypothetico-deductive situations, where after making one choice, one might encounter yet another impasse requiring another choice. Those are the hardest puzzles because they involve selecting between many possible options, each resulting in a different final solution. (As an aside, the mechanism of evolution by natural selection works similarly to this, with the choice options being provided by random genetic mutations and the choice being ‘made’ by natural selection.)

Scientific research is a lot like these harder sudoku puzzles, involving long chains of inferential reasoning, with assumptions being made along the way. One rarely arrives at solutions purely deductively, hence the popular notion of scientific truths being “proven” to be true is largely a mirage. There are always choices that have to be made at intervening stages. One has to make decisions as to what one assumes to be true and can be used as a basis for further investigations. Being able to do hypothetico-deductive reasoning is essential for science, and yet it is not skill we focus much on in our science teaching.

In doing this kind of hypothetico-deductive reasoning one also has to use one’s judgment and select which of the various possibilities is likely to be the most fruitful. Science also requires one to make such judgments and good scientists are those who, over time, develop a good ‘nose’ for which situations are best suited.

The extra wrinkle in scientific research that is not present in sudoku puzzles is that the correctness of the choice is also time-dependent. What may be a satisfactory choice at one time may turn out, in the light of subsequent research in a related field, to have been the wrong choice later. It is this kind of thing that causes the scientific community to sometimes reverse itself and declare that what was considered wrong once is now right and vice versa.

The hardest problems in science are those that challenge the very paradigm itself because then one is not guaranteed that a solution even exists. It is like working on a sudoku puzzle in which the data given may not be sufficient to guarantee the existence of a unique solution, or one in which the rules have changed but you are not aware of it. It takes a strong will and a great deal of perseverance to take on such problems. But it is just that kind of problem that leads to scientific revolutions.

POST SCRIPT: Warrantless wiretapping

Tom Tomorrow’s take on the NSA wiretapping story.

Due to the holiday season and to the fact that I need to write some articles for publication, this blog will be updated only sporadically over the next two weeks. The regular schedule of weekday postings will resume after the New Year, on Tuesday, January 3rd.

Today, here are some short items.

New member of the family

On the right is Baxter, the latest addition to our family. We brought him home on Monday, December 19. He was born on September 14, which makes him just 3 months old.

My op-ed published

The Plain Dealer has today published an op-ed by me titled Has the intelligent design movement passed its peak? dealing with the Dover IDC case. Thanks to the fact that I have been writing about these things on this blog, it only took me an hour or two to collect all the information together and write the piece. This was one of the benefits I foresaw in maintaining this blog, that it could serve as a repository for ideas that could serve as a first draft for publications.

What was strange is that when I write for online posting, I put in links to the original sources of quotes, facts, etc. I had to strip all those out for the op-ed piece, so newspaper readers have to take my word for it that I was not making stuff up. So although online material is still viewed with skepticism in some quarters, the printed stuff actually has less information.

Cheap laptops for the world

Read about the new $100 laptops that can be powered by a hand crank and can be used in poor areas where there is little electricity. The machines will run open-source software.

You can see an image of the laptop here.

This strikes me as a wonderful gift to the poor areas of the world, because the machines will be given free to poor schoolchildren. The inventors (MIT’s Media Lab) should be credited for making their devices freely available. I think it is terrific when scientists, engineers, inventors, and universities use their tremendous skills for the benefit of those who do not have access to this kind of advanced knowledge.

Mona Lisa smile

From the BBC we learn that:

A computer has been used to decipher the enigmatic smile of Leonardo da Vinci’s Mona Lisa, concluding that she was mainly happy.

The painting was analysed by a University of Amsterdam computer using “emotion recognition” software.

It concluded that the subject was 83% happy, 9% disgusted, 6% fearful and 2% angry, journal New Scientist was told.”

When I read that I was 64% intrigued, 25% amused, and 11% surprised.

Podcasting

The always helpful and tech-savvy people at Case are slowly nudging me into the 21st century. First Jeremy Smith got me started on blogging and now Aaron Shaffer (Manager of the Freedman Center) interviewed me for my first podcast.

A podcast, which has just been declared 2005’s Word of the Year by the New Oxford American Dictionary, is defined as “a digital recording of a radio broadcast or similar program, made available on the internet for downloading to a personal audio player”. The word is derived from a combination of “broadcast” and “iPod”. The chief benefit of a podcast is that once downloaded, it can be listened to at your convenience.

Aaron and I spoke about blogging and a lot of other things, lasting for about an hour, just so that I could get a sense of how podcasting works. I will try my hand at it some time in the future, if I can think of something that would benefit more from the spoken rather than the written word.

If you are curious about what Aaron and I spoke about, or are curious to hear what I sound like on radio (hint: terrible), the podcast has been posted on the Freedman Center blog here.

I am not sure what I would use a podcast for, at the moment. It would have to be for something where actual sounds were preferable or easier to create than the written word. A dramatic reading of a speech of the kind done by Harold Pinter or an interview would be appropriate, as would be anything involving music. But do not fear. There will be no podcasts of me singing.

Looking back on 2005

One of the things I dislike about the end of the year are the dreary “year in review” features in the media. But I will make an exception for Tom Tomorrow.

Playwright Harold Pinter gave his Nobel Prize for Literature acceptance speech to the Swedish Academy on December 7, 2005. Because he has been operated for throat cancer and is not well, he delivered the televised speech from England. His voice was hoarse and he was in a wheelchair but the speech was riveting. It was a lesson in how to give a great talk with the minimum of motion, and people who are interested in developing good rhetorical skills could learn a lot from him. You see a master of words and pauses and inflection, the trademarks of his success on the stage, use them here to brilliant effect as he stares at the camera, occasionally gestures with one hand, and moves easily between art and politics. Once I started listening to his forty-five minute speech, I was riveted. (You can read the text of his speech or watch it here but I strongly recommend watching it.)
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I read in the paper recently of an incident where the wealthy son of industrialist and his friends were about to enter a Los Angeles restaurant. Outside the restaurant was a homeless person and this person offered the homeless person $100 to pour a can of soda over himself. The homeless man did so and the crowd of rich people laughed uproariously at this, paid him, and went on their way.

This story infuriated me, as I am sure it will to most people who hear of it. It seemed that these people were humiliating the man, taking advantage of his poverty for their warped sense of what is amusing.
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I reached a kind of landmark this week with this blog. I have been making entries since January 26th, posting one item each weekday, except for a three-week break in June. As a result I have now posted over 100 entries and consisting of over 100,000 words, longer than either of my two published books.

Why do I blog? Why does anyone blog? The Doonesbury comic strip of Sunday, July 3, 2005 fed into the stereotype of bloggers as self-important losers who cannot get real jobs as writers, and feed their ego by pretending that what they say has influence. The idea behind this kind of disparaging attitude is that if no one is willing to pay you to write, then what you have to say has no value.

Of course, there are a vast number of bloggers out there, with an equally vast number of reasons as to why they blog so any generalization is probably wrong. So I will reflect on why I blog. Some bloggers may share this view, others may have different reasons. So be it.

The first reason is the very fact that because of the blog, I have written the equivalent of a complete book in six months. Writing is not easy, especially starting to write on any given day. Having a blog enforces on me a kind of discipline that would not exist otherwise. Before I started this blog, I would let ideas swirl around in my head, without actually putting them down in concrete form. After awhile, I would forget about them, but be left with this nagging feeling of dissatisfaction that I should have explored the ideas further and written them down.

The second benefit of writing is that it forces you to clarify and sharpen your ideas. It is easy to delude yourself that you understand something when you have the idea only in your mind. Putting those ideas to paper (or screen) has the startling effect of revealing gaps in knowledge and weaknesses of logic and reasoning, thus forcing a re-evaluation of one’s ideas. So writing is not a one-way process from brain to screen/paper. It is a dialectic process. Writing reveals your ideas but also changes the way you think. As the writer E. M. Forster said “How can I know what I am thinking until I see what I say?” This is why writing is such an important part of the educational process and why I am so pleased that the new SAGES program places such emphasis on it.

Another benefit for me is that writing this blog has (I hope) helped me become a better writer, able to spot poor construction and word choice more quickly. Practice is an important part of writing and the blog provides me with that. Given that the blog is public and can (in principle) be read by anyone prevents me from posting careless or shoddy pieces. It forces me to take the time to repeatedly revise and polish, essential skills for writers.

When I started this blog, I had no idea what form it would take. Pretty soon, almost without thinking, it slipped into the form that I am most comfortable with, which is that of a short essay around a single topic each day. I initially feared that I would run out of ideas to write about within a few weeks but this has not happened. In fact what happens is what all writers intuitively know but keep forgetting, which is that the very act of writing acts as a spur for new ideas, new directions to explore.

As I write, new topics keep coming into my mind, which I store away for future use. The ideas swirl around in my head as I am doing other things (like driving and chores), and much of the writing takes place in my mind during those times as well. The well of ideas to write about does not show any signs of going dry, although it does take time to get the items ready for posting, and that is my biggest constraint. Researching those topics so that I go beyond superficial “off the top of my head” comments and have something useful to say about them has been very educational for me.

Since I have imposed on myself the goal of writing an essay for each weekday, this has enabled me to essentially write the first draft (which is the hardest part of writing, for me at least) of many topics that may subsequently become articles (or even books) submitted for publication. If I do decide to expand on some of the blog item for publication, that process should be easier since I have done much of the preliminary research, organization, and writing already.

All these benefits have accrued to me, the writer, and this is no accident. I think most writing benefits the author most, for all the reasons given above. But any writer also hopes that the reader benefits in some way as well, though that is hard for the author to judge.

I remember when I was younger, I wanted to “be a writer” but never actually wrote anything, at least anything worthwhile. Everything I wrote seemed contrived and imitative. I then read a comment by someone who said that there is a big difference between those who want to be writers and those who want to write. The former are just enamored with idea of getting published, of being successful authors and seeing their name in print. The latter feel that they have something to say that they have to get out of their system. I realized then that I belonged to the former class, which I why I had never actually written anything of value. With that realization, I stopped thinking of myself as a writer and did not do any writing other than the minimum required for my work. It is only within the last ten years or so that I feel that I have moved into the latter category, feeling a compulsion to write for its own sake. This blog has given me a regular outlet for that impulse.

I would never have written so much without having this blog. I would recommend that others who feel like they have to write also start their own. Do not worry about whether anyone will read it or whether they will like it. Write because you feel you have something to say. Even if you are the only reader of your own writing, you will have learned a lot from the process.

POST SCRIPT

Paul Krugman is an economist at Princeton University and is a member of the reality-based community. His July 15, 2005 op-ed in the New York Times shows how far politics has moved away from this kind of world and into one in which facts are seen as almost irrelevant.

Thanks to Richard Hake for the following quote by F.M. Cornford, Microcosmographia Academica – Being A Guide for the Young Academic Politician (Bowes & Bowes, Cambridge, 4th ed., 1949 first published in 1908), which might well have been addressed to Krugman and other members of the reality-based community, although it was written over a century ago:

You think (do you not?) that you have only to state a reasonable case, and people must listen to reason and act upon it at once. It is just this conviction that makes you so unpleasant….are you not aware that conviction has never been produced by an appeal to reason which only makes people uncomfortable? If you want to move them, you must address your arguments to prejudice and the political motive….

I came across an interesting website recently. You type in the URL of any site and it comes back immediately with various measures of the site’s readability, including the years of education necessary to understand it, its clarity, and so forth. It also provides comparisons on these indices with various standard media such as newspapers and magazines.

So naturally the first thing that I did was put in this blog’s URL to see how I shaped up. Here is what I got:

Readability Results for http://blog.case.edu/mxs24
Average words per sentence 16.15
Words with 1 Syllable 3,230
Words with 2 Syllables 1,010
Words with 3 Syllables 561
Words with 4 or more Syllables 415
Percentage of word with three or more syllables 18.71%
Average Syllables per Word 1.65

That much was pretty straightforward. The other three numbers were more mysterious:
Gunning Fog Index 13.94
Flesch Reading Ease 51.07
Flesch-Kincaid Grade 10.15

The site helpfully explains that the Fog Index “is a rough measure of how many years of schooling it would take someone to understand the content. The lower the number, the more understandable the content will be to your visitors. Results over seventeen are reported as seventeen, where seventeen is considered post-graduate level.” Looking at the algorithm, it seems to depend entirely on the number of words per sentence and the percentage of words that have three or more syllables.

So it takes about 14 years of education (or up to college sophomore level) for someone to understand the content of my website. So clearly I am not going to get huge market share with my blog.

For comparison, some Fog Index Scores are given for other publications:

6 TV guides, The Bible, Mark Twain
8 Reader’s Digest
8 – 10 Most popular novels
10 Time, Newsweek
11 Wall Street Journal
14 The Times, The Guardian
15 – 20 Academic papers
Over 20 Only government sites can get away with this, because you can’t ignore them.
Over 30 The government is covering something up

Since my Fog Index score is close to 15, it seems like it is hard for me to shake the habits of writing in the style of academic papers even in the more casual setting of a blog.

The Flesch Reading Ease number “rates the text on a 100-point scale. The higher the score, the easier it is to understand the document. Authors are encouraged to aim for a score of approximately 60 to 70.” So I flunk this score pretty badly, it looks like. This algorithm, seems to depend entirely on the number of words per sentence and the average number of syllables per word.

The Flesch-Kincaid grade level, like the Gunning-Fog index, “is a rough measure of how many years of schooling it would take someone to understand the content. Negative results are reported as zero, and numbers over twelve are reported as twelve.” This seems like the same measure as the Fog Index, but uses average number of syllables per word instead on percentage of words with three syllables or more.

What is one to make of things like this? I find them fun even if I don’t take them too seriously. For one thing, you have to be skeptical of these instant computer-generated analyses of such complex things as writing. While these programs are great at doing numbers, one has to be wary of claims that they can accurately measure things like clarity and reading grade level. They all assume that the number of polysyllabic words and the length of sentences are the only factors, and that the nature of the content is immaterial.

This explains the results for the Bible, which had initially puzzled me. It is ranked together with TV Guide, although surely it is a more difficult book to understand. But it does use short words and sentences. This kind of algorithm also also might explain why the Wall Street Journal, which one might think is less readable than the New York Times, scores at three grades below it.

Suppose I want to become more easily readable. Should I use more words of one syllable? Or shorter sentences? Or both? Or is it the topics that cause the problem? When you write about academic topics, polysyllabic words (two already in this sentence!) creep in without any effort. Can I write about the Copernican Revolution (two more!) and avoid words like heliocentric (another one!)

To become more readable must I switch my focus from history and philosophy of science to Britney Spears? There are some prices that are too high to pay even for increased ease of readability…

In a previous post, I mentioned that my Race IAT results indicated that I had no automatic preference for black or white people. This surprised me, frankly. Although I am intellectually committed to thinking of people as equal, I am still subjected to the same kinds of images and stereotypes as everyone else in society so I expected to have at least a small automatic preference for white people. But the section on Malcolm Gladwell’s book Blink on ‘priming’ experiments might give an explanation for the null result.

The priming experiments were done by psychologist John Bargh. What he did was give two randomly selected groups of undergraduate students a small test involving words. The results of the word test itself were not relevant. What was relevant was that the first set of students encountered words like “aggressively”, “bold, “rude”, “bother”, etc. in their test while the second set encountered words like “respect”, “considerate”, “patiently”, “polite”, etc.

After they had done the word test, the students were asked to go down the hall to the person running the experiment to get their next assignment. This was the real experiment because it had been arranged to have a confederate blocking the doorway, carrying on an inane and seemingly endless conversation with the experimenter. The experiment was designed to see if the set of students who had been unknowingly ‘primed’ with aggressive words would take longer to interrupt this conversation than those who had been primed with polite words. Bargh expected to see a difference, but expected that difference to be measured in milliseconds. He said “I mean, these are New Yorkers. They aren’t going to just stand there. We thought maybe a few seconds, or a minute at most.”

What he found was that the people primed to be rude eventually interrupted after an average of five minutes, but 82% of the people primed to be polite did not interrupt at all, even after ten minutes which was the cut-off time that had been pre-set for the experiment, thinking that no one would ever wait that long.

What these and other priming experiments suggest is that the kinds of experiences we have carry their effects subconsciously over to the next events, at least for some time.

This may explain my negative result because for some time now I have been studying the achievement gap between black and white students in the US. The more I looked at it, the more I became convinced that the concept of race is biologically indefensible, that it cannot be the cause of the gap, and that the reasons for the gap have to be looked for elsewhere.

Since my book on the subject (***Warning! Shameless plug coming up!***) called The Achievement Gap in US Education: Canaries in the Mine is coming out in May, I have been thinking a lot recently about these ideas and so I was probably ‘primed’ to think that there is no fundamental difference between the races, and hence my null result on the Race IAT test.

This ties in with other research that I quote in my book that deals with the role that teacher expectations of students play in student achievement. Teacher expectations are an important factor but a lot of the efforts to improve teacher expectations of low-achieving students have been along the lines “All children can learn!” sloganeering. But having teachers just saying this or plastering it on school walls may not help much, if they are not convinced of its truth. If people are conscious that they are being primed, then the priming effect disappears.

What is needed is for teachers to improve their overall expectations of students is for them to have opportunities to actually see for themselves traditionally underachieving students excelling. If they can have such experiences, then the inevitable snap judgments they make about students, and which can have an effect on student performance, may be more equitable than they are now.

I have long been in favor of diversity in our educational environments but my reasons were more social, because I felt that we all benefit from learning with, and from, those whose backgrounds and experiences differ from our own. But it seems that there is an added bonus as well. When we have a broader base of experience on which to base our judgments, our snap judgments tend to be better.

POST SCRIPT

The interesting radio program This American Life (which airs locally on WKSU 89.7 on Saturdays at 5:00pm and WCPN 90.3 on Sundays at 11:00am) also recently had an episode that featured the work of John Gottman, who has carefully analyzed the behavior of married couples and is able to ‘thin slice’ very accurately and predict, based on things that the rest of us completely miss, which couples will stay together and which ones will separate. Gottman’s studies were reported on in detail in Gladwell’s book.

To listen to this particular audio clip from the program, go to This American Life, click on “Complete Archive” and then click on the audio symbol for “The Sanctity of Marriage” that appears in the list of 2005 shows, and is dated 4/1.

I just finished reading Malcolm Gladwell’s book Blink. It deals with how we all make snap judgments about people and things, sometimes within a couple of seconds or less. Gladwell reports on a whole slew of studies that suggest that we have the ability to ‘thin-slice’ events, to make major conclusions from just a narrow window of observations.

I first read about this as applied to teaching in an essay by Gladwell that appeared in the New Yorker (May 29, 2000) where he described research by psychologists Nalini Ambady and Robert Rosenthal who found that by showing observers silent videoclips of teachers in action, the observers (who had never met the teachers before) were able to make judgments of teacher effectiveness that correlated strongly with the evaluations of students who had taken an entire course with that teacher. (Source: Half a Minute: Predicting Teacher Evaluations From Thin Slices of Nonverbal Behavior and Physical Attractiveness, Journal of Personality and Social Psychology, 1993, vol. 64, No. 3, 431-441.)
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