Thoughts and experiences on various topics: puzzles, games, AI, collaboration, music, politics, and whatever else is on my mind

When it came time to apply to college, MIT was really the only choice that interested me.  I had read an article about the Artificial Intelligence Lab at MIT, and how they were working to program a robot to play with blocks.  I thought that was so cool.  I was already interested in A.I. as a result of reading Isaac Asimov and lots of other science fiction, which imagined the possibility of intelligent robots.   I also felt that machine intelligence might give humanity a little humility — I was getting tired of hearing how great humans were.  Examples: that humans were the “pinnacle of evolution” , the only animals with language, were the only creatures with “free will”, were devoid of instinctual behavior.  These claims seemed ridiculous to me.  Any thoughtful person would realized that evolution is a continuing process, and that we are just one stage in that process.  It also seemed clear to me that animals have varying degrees of intelligence and language, but humans seem to have a need to see themselves as “uniquely special”.   My plan was to study “cognitive science” (though that had not yet been defined as a discipline) by combining studies in computer science, mathematics, cognitive psychology, and neurophysiology.

MIT seemed like a great place to pursue these goals, so I applied.  I also applied to RPI and Michigan State (because I wasn’t certain I’d get into MIT, and there were remote chances of a full scholarship at these schools).   I was fortunate to qualify as a National Merit Semi-Finalist, and was eligible for an IBM Thomas Watson National Merit Scholarship, because my father worked for IBM.  I got into all three schools, and when I didn’t get a full scholarship to MSU or RPI, I happily chose to attend MIT.

MIT Experimental Study Group

Perhaps the single most transformative experience of my life occurred during my Freshman Year.   I joined and participated in the Experimental Study Group (ESG).  ESG is a special alternative educational program founded at MIT in 1969, so it was in its second year when I arrived as a Freshman.  I nearly missed out on this fantastic experience — I didn’t hear about until late in the summer, because I was away at the OSU Math program.  I came home to a deluge of accumulated mailings from MIT.  One of the mailings described a program (ESG) that sounded too good to be true – a program where students could design their studies, work at their own pace, choose their own textbooks, interact with faculty on a personal and informal basis.  Unfortunately, there were only a limited number (50) of openings available for incoming freshman, and preference was given to those who responded early expressing interest.  I was “certain” that a fantastic program like this would be oversubscribed – so I foolishly neglected to pursue it.   Later, after I arrived at MIT, and joined a fraternity (to try to do something about my pathetic social life), I completed one week of classes, and was mostly bored and frustrated.  Happily, one of my fellow fraternity pledges had joined ESG, and told me about it with great enthusiasm.  It turned out there were still openings!  I wasn’t going to miss out on this “second chance” so I immediately checked it out, talked with my advisor, and transferred into ESG!  Best decision of my life!

ESG was designed to give students the freedom to pursue their interests, and to work independently at their own pace.  There were no specific requirements, and freshman participants received 45 units of “free elective credit” per semester.  MIT’s graduation requirements included:

1. Amassing 360 units of credit (typically over 4 years)

2. “General Institute Requirements” in Math, physics, chemistry, and humanities

3. Completely the specific degree requirements of one’s major (corresponding to the department enrolled in)

4. A PE (Physical Ed.) requirement, along with passing a swim test

So the 45 “Free Elective Credits” of ESG put freshmen on track toward the 360 credit total.  We of course still had to satisfy all the other requirements at some time before graduation, but ESG allowed us to “defer” working on any requirements if we chose to.  I, like many of my ESG peers, choose to work on most of the typical freshman requirements, but to do so on my own terms and at my own pace.  I chose to work on calculus using the classic Apostol text, for example.  I worked on the 1st semester physics doing independent study from the notes for the “Advanced Mechanics” physics option (used more calculus).  There were also some interesting seminars offered by ESG faculty, and I joined the “Writing Seminar” offered by Peter Elbow, which was a terrific experience, and also satisfied 1 humanities requirement (the total humanity requirement was 8 semesters of humanities courses, with a distribution requirement (3 from different areas), and a concentration (of 3 courses within one area — I chose psychology).

ESG was a “learning community”

The ESG community consisted of 50 Freshmen, a number of sophomores (who had started out as ESG Freshman in 1969), faculty in the core areas of study (Math, Physics, Chemistry, Biology, Humanities), and administrative staff (director and secretary).  Everyone interacted informally and got to know each other on a first-name basis.   Our community space consisted of nearly the entire 6th floor of Building 24. There was a common room (with couches, chairs, and tables), a kitchen off the common area, a library, several seminar rooms, a lab and computer room, a music room (with turntable, stereo, and LP collection), and several seminar rooms.  The community was self-governing, with regular meetings, where everyone had a voice.  We had community lunches every Friday.  Basically people would “hang-out” around ESG (pretty much 24/7, though the faculty and staff were around primarily during daytime hours).  Interactions were serendipitous, and led to a stimulating free-flow of ideas, interests, and expertise.  Everyone was consider a “learner” – faculty were just senior (more experienced) learners!

One of the memorable dynamics I recall was the “ad hoc seminars”.   There was a bulletin board outside the administrative offices, strategically placed at the entrance to the ESG 6th-floor area.   There was an area on this bulletin board where any community member could post a “seminar proposal” — e.g. “I’m interested in learning about X – who would like to learn with me?”  Then anyone could sign up, and those interested would form a “study group” to share their learning and experience on the topic.  Some seminars never got off the ground, but others took on a life of their own, leading to fascinating explorations and learnings!

ESG blurred artificial boundaries

With traditional education, I chafed at what I consider “artificial boundaries”:

1. Temporal boundaries (compartmentalizing learning into courses with fixed beginning and end times)

2. Content boundaries (compartmentalizing learning into fixed course content chunks)

3. Class/role distinctions between teacher and student.

4. Academic vs. Non-academic learning and interaction

At ESG, these boundaries were loosened — learning could go on for as long (or as short) as interest continued.  Content of learning wasn’t necessarily chopped up into distinct disciplines, rather interdisciplinary exploration and learning was natural and easy.  As I mentioned, faculty and students were simply all learners, and the informal interactions facilitated sharing and learning.  Learning could be in any area, not restricted to traditional academic areas, for example, I learned to play the game of Go (spending an intensive week doing little else), and skills at lock-picking were shared and learned via informal interactions.

ESG surprised me by providing advantages beyond my expectations

I joined ESG primarily to gain greater individual freedom in pursuing my education.  What I found was that there was tremendous power in the learning community model!   ESG was a close-knit social community, that became almost like family, and was far more important in its influence on me than mere freedom.  I found that ESG become my “social group”, so much so that I dropped out my fraternity and moved to the dorms.  We sometimes joke about ESG being “Epsilon Sigma Gamma” – because it was like a fraternity in many ways.

Learning about Collaboration   

A very important lesson I learned through ESG was the power of collaboration.  Pre-college, I took a very individual approach to life (I didn’t have collaborators that shared my interests), and I prided myself on doing things on my own — I enjoyed the satisfaction of working hard and solving a difficult puzzle, and if someone gave me a hint or suggestion, I’d often feel cheated that I couldn’t do it “all on my own”. At ESG, I had many opportunities to work on problems and puzzles with others, and I found that there could be tremendous pleasure from a collaboration where each party was making contributions!  Moreover, via collaboration it was possible to do so much more (and to learn faster) than I could working strictly on my own.  One striking example was taking Winston’s “Introduction to Artificial Intelligence”, which a group of us (numbering 10 or more) from ESG took “together”.   I learned the material so much better by working on it as part of this group.  We even collaborated on problem sets and Exams (with the instructor’s blessings).   Note that this was a course offered through the “regular curriculum” as we referred to non-ESG courses, since ESG did not have a computer-science faculty member.  Because I did well in the course (Freshmen were on Pass-Fail, but my “hidden grade” was an “A”), I got to meet with Prof. Winston, who encouraged me to pursue my AI interests – he later became my Thesis Advisor in grad school.  I will explore this power of collaboration much further in future posts, but perhaps the single most significant advantage is having help readily available to get un-stuck whenever one hits a sticking point.

Extracurricular activities

I pursued a number of enjoyable “extracurricular” activities while an undergrad.  I took both Sailing (on the Charles River) and Folk-dancing as PE classes, and continued to enjoy both for many years to come.   I was actually surprised at how much I enjoyed folk-dance!  I was very much a rebel by nature, naturally challenging authority, and resisting external structure.  Folk-dance, on the other hand, involved a fair amount of structure — there were prescribed sequences of steps to perform, and not a lot of room for individual interpretation.  Nevertheless, the structure of dances is generally very hierarchical (there are basic patterns, and these get assembled into different groups for both verses and chorus of dances, and these verses and chores repeat in yet a higher-level structure.  This struck me as similar to the structure of computer programs, with subroutines written from basic language elements, and being assembled into larger subroutines and full programs – which I’m sure was a large part of the appeal.  I also loved the music (especially of traditional Israeli dance), and the collaboration involved in dancing as part of a group, or with a partner.  I also enjoyed the social aspect of the activity, it was a low-key, informal, and pleasant way to meet women!  In fact, it was through folk-dancing that  I met the woman who later became my wife and mother of my 3 children (but that story comes later).

Majoring in Math

I chose to major in mathematics.  Partly because I loved math and wanted to learn a lot of it, but also because it had fewer requirements than the alternative of Computer Science.   I wanted to continue pursuing my interdisciplinary studies toward the goal of working in AI and machine learning, and the math requirements gave me greater freedom to engage in a broader program of studies.  I have fond memories of learning a lot of abstract math (Abstract Algebra, Linear Algebra, Analysis, Point-set Topology, Algebraic Topology, Combinatorics, and more).

I particularly came to love Combinatorics, especially enumeration and graph theory.  One of the most influential courses I took was Intro to Combinatorics taught by Prof. Dan Kleitman.  The first day of class blew my mind.  He presented Cayley’s theorem for enumerating trees: the number of distinct trees on N labelled vertices is exactly N^(N-2) [that’s N taken to the power N-2].  This formula seemed amazing – it was beautiful and simple!  He gave an interesting proof (I’m not sure which one) and over the next days I worked to come up with my own proof, by creating a 1-1 correspondence between labeled trees and (n-2)-tuples of numbers taken from the range [1 to n].  It is easy to see that there are n^(n-2) such tuples, so establishing a correspondence of trees with tuples proves there are exactly n^(n-2) trees. My interest in Cayley’s Theorem led to a summer research project (UROP – Undergraduate Research Opportunities Program) exploring generalizations of this theorem to “higher dimensions”.  This led to my first mathematical publication, in Discrete Mathematics Journal, jointly authored by me and my advisor.  I often wonder what I would have learned if I had continued to regularly attend Kleitman’s course, but sadly I neglected going to “lectures” which were scheduled early in the morning, and I was already a “night-owl” who liked to sleep in. I only managed to attend 2 or 3 additional classes, solely for the purpose of handing in the 3 required project assignments [my first project was a programming project that computed the correspondence between trees and their tuple-encoding. I learned later that the German mathematician Prufer had first discovered such an encoding — mine was different and original yet similar].  If I had a “do-over” I’d make sure I attended every single one of Kleitman’s lectures in that course!   Kleitman later became one of the members of my “graduate school committee” (representing math in my interdisciplinary grad program).

I think it was my sophomore year that I first took the William Lowell Putnam Exam (college level competition in mathematics).  I was not on the MIT team, but anyone could sign up to take the exam and compete as an individual.  I remember being totally peeved at my dorm roommate who “kicked me out” of my room on the night before the exam because he was having a girl stay over.   I ended up finding a place to sleep in a Radcliffe dorm, courtesy of a female friend, but the result was that I overslept!  When I woke up, I had to scurry to get to MIT, and start the exam.  I arrived almost 2 hours late for the 3-hour morning session.  There was also, if I remember, a 2nd 3-hour afternoon session.  I was really tired, and rushed through the morning exam (6 questions, of which I answered maybe 2 or 3 reasonably, and did some hand-waving on a few of the other, which might have garnered some partial credit, who knows).  I had the full 3 hours in the afternoon, but still could only answer a few of the questions — they are designed to be extremely difficult and challenging.  Imagine my surprise when I learned that, despite my lack of sleep and tardy arrival, I received an Honorable Mention  which meant I was ranked in the top 50 scorers, nationally. Based on this performance, I was invited to join the MIT team the following year, and I made sure to get more sleep, and show up on time – nevertheless, I did terribly, and felt bad that I hurt the team’s overall ranking.  I think I ranked somewhere just above 300, but my memory is cloudy at this point.  Maybe there are advantages to taking an exam with less time and less sleep!

Approaching graduation

As graduation approached, I became very nervous about my future.  Graduate school was the natural next step in pursuing a career in AI/machine learning, but what if I didn’t get accepted?  There were only a few major centers where AI work and studies were possible around 1974, so I applied to the “big 3” in the U.S.:  MIT,  Stanford, and CMU.   I was relieved, and extremely pleased to be accepted at all 3!  I was honored to receive a personal phone call from Don Knuth (Stanford) informing me of my admission, and encouraging me to come to Stanford.  I remember vividly that the call was on a Saturday morning, and that it woke me up  — so I was no doubt somewhat groggy.  Still, I was really excited!   Knuth, for those of you who don’t know, is famous for his multi-volume  series of books “The Art of Computer Programming”.   It wasn’t until 2009 that I met him in person (at the International Puzzle Party in San Francisco), and was able to thank him for honoring me with that call!   I also got accepted to both CMU and MIT, and was offered a full-fellowship at MIT through the interdisciplinary DSRE (Division for Study and Research in Education), where I’d have the opportunity to work with Seymour Papert, co-director of the MIT AI Lab.  Papert had a broad range of interests, including math (he did seminal work with Minsky on Perceptrons), education (he helped create and promote the LOGO computer language for children’s education),  developmental psychology (he had worked with Piaget in Geneva), and puzzles (he was an avid puzzle collector and solver, and loved “thinking about thinking” often using puzzles for that purpose).  Working with Papert seemed like the best fit to my interdisciplinary interests, and having a full-fellowship rather than Teaching or Research Assistantships seemed like a big plus.  The interdisciplinary program in DSRE provided an almost ESG-like freedom to design my own course of studies — I’d get to work with my committee to define all my own requirements! Finally, I was already familiar with MIT, and the Cambridge/Boston environment, so I figured I could “hit the ground running”.  I accepted the MIT / DSRE Fellowship offer and the next stage of my career was mapped out.

MIT Graduation

I received my SB Mathematics degree from MIT in 1974.  Amazing even myself, I had achieved a 4.9/5.0 gpa, and graduated Phi Beta Kappa.  Embarrassing was the fact that my only “B” was in a math course — the fact that I hadn’t completed all the homework was held against me 😦   Nevertheless, I was proud of my accomplishment, and my parents and siblings came to attend my graduation!

To be continued … next up: Grad School at MIT

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