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


My intention is to provide a “life overview”, so that any readers can have a better sense of who I am, and thus place my writings in some context. It’s a little overwhelming to try summarizing 60+ years of life experiences – but I’ll start with an overview sketch, and elaborate as inspiration guides me in subsequent posts.

I decided to go with the “milestones” approach to hitting highlights:

(and it was my intention to be brief, but it turns out I wasn’t very successful at that — you may want to read in “installments”)


I was born on the 4th of July, 1952.  I love having that holiday as my birthday – I like to think that everyone is celebrating with me!  I was born in Lebanon (that’s a town in PA, not the country).  I was the first-born to my parents, and so was the oldest of 4 siblings growing up.  We lived with my grandfather (on my Dad’s side, we called him “PawPaw”).  I remember when he died – I was about 3 years old.  Only time I ever saw my Dad cry!  I never met my father’s mother – she died a few days before I was born.

Move to Hershey, PA

Our family moved to Hershey when I was about 3 or 4 years old.  I remember being confused about what was going on.  I think we moved to be closer to Harrisburg for several likely reasons:  my father worked for IBM (as a Field Engineer) and the “area” he covered was in the vicinity of Harrisburg (Hershey is half-way between Lebanon and Harrisburg), also my mother’s Christian Science Church was located in Harrisburg, and finally Hershey was well-known as having an excellent school system.  I started Kindergarten in 1957.

Falling in Love with Music

My father was a talented amateur keyboard player – he played piano, organ, and accordion.  I remember his playing his favorite Beethoven sonatas: the Pathetique and the Moonlight, which quickly became my favorites.  I also remember an amazing (but less well-known) piece called Suite Gothique by Boellmann (written for pipe organ, but my father played it on the piano in our dining room).  I was so struck that I implored my father to show me how to play it myself!  I tried to memorize the Toccata riff (my favorite), and soon my Dad agreed to start me on piano lessons.  He was the only piano teacher I ever had, and I studied through middle school, by which time I was playing and enjoying the Beethoven sonatas for myself!  I’ve been passionate about music ever since, but now my favorite music is the blues (did I mention that I listen to Sunday Morning Blues every week?), and I now try my hand at songwriting and performing at open mic nights.  I also studied trumpet from 4th-12th grade, but I didn’t love it like piano.  I still enjoy playing keyboards whenever I get the chance!

Falling in Love with Math

In 5th grade, our teacher told us the story of Gauss (in grade-school) figuring out the “short-cut” method for adding consecutive numbers (e.g. 1 through 100).  I’m sure she explained his technique, but either I didn’t understand it, or I forgot it.  While at Overnight Summer Camp (Nawakwa) the summer after 5th grade, I started thinking about this while lying awake in bed.  I started by looking for patterns with small sequences like 1 – 9 (sums to 45) and 1 – 10 (sums to 55).  Somehow I guessed the formula:  n * (n+1) / 2,  and verified that it worked for all the examples I could check.  I continued pondering this to try to understand what it meant – finally realizing that every number pairs up with a “twin” so the pair adds to n+1 (e.g. when adding 1-10 the 1 pairs with 10 to add to 11, 2 with 9 is also 11, etc.  This makes 10 pairs of 11 (if you order the pairs), but that counts each pair twice, so 10 * 11 is the sum of the ordered pairs, but must be divided by 2 since we only want to count each pair once!   I was extremely excited by this insight!  I recall being afraid that I might forget it while asleep, and not remember it in the morning — thankfully I did remember it, and my deep love for mathematics was born.

Falling in Love with Puzzles

I don’t know as precisely when this happened, but sometime around 5th, 6th, or 7th grade, my father started bring home puzzles that were shared with him through his work.  These were brain-teasers, that programmers (even in the early days of mainframes) and computer engineers loved to challenge each other with.  My father shared these puzzles with me, and I have fond memories of working on puzzles together with him.  One puzzle I remember in particular was the “Who is the Engineer?” logic puzzle that we found in Reader’s Digest.  Also known as the Smith, Jones, Robinson puzzle – they were the fireman, engineer, and brakeman on a train (in some order) and there were 3 passengers named Mr. Smith, Mr. Jones, and Mr. Robinson.  As is standard with such “logic puzzles” there were a list of clues having to with who did or did not have certain jobs, live in certain cities, have particular salaries, and so on.  The object is to reason out which one was the engineer.  I remember not being quite able to solve this – because I didn’t realize that a salary of $20,000 was not exactly divisible by 3.  I think the clues were something like:  Person X’s salary is exactly 3 times as much as Person Y’s salary, and the person living in City Z earns exactly $20,000. Knowing that $20,000 is not exactly divisible by 3, one could conclude that Person X does not live in City Z.   I felt cheated when I learned the answer, but grappling with such puzzles was a lot of fun, and started me on a lifetime passion for brain puzzles in their many forms!  In fact, now my professional life revolves around puzzles – primarily designing logic puzzles for smartphones (check out Monorail for iPhone and Android, if you haven’t already).

Discovering that I had some serious mathematical talent

I knew that I loved math, and that I was pretty good at it – I was one of 5 or so “top math students” in my school class (we all got straight A’s in math).  I was blessed with terrific math teachers throughout my middle school and high school grades.  In 7th grade I remember driving my teacher crazy by always raising my hand to point out technicalities (e.g. “that won’t work if x is 0”).  After the math final exam in 7th grade (which I must have finished early since my teacher graded it immediately), I’ll never forget how he came to my desk and asked me to come “out in the hall with him” — I was terrified that I was about to be punished for something — these were still the days when corporal punishment was permitted, and I had received spankings in school.  When we got outside the classroom, I was relieved to learn that my teacher wanted to shake my hand and congratulate me for being his first student to get a perfect score on the final!

I didn’t realize I was a “math nerd”, but I did spend the Summer after 7th grade reading all the math books I could find at our local public library.  I remember being especially intrigued and perplexed at the notion of imaginary numbers.  The first day of math class in 8th grade, I asked my Algebra teacher what was up with these imaginary numbers.  He went back to my 7th grade teacher to ask “who is this guy who spends his summer reading math books?”.  I suppose I was aware that not everyone shared my passion for math – so my explorations were largely a solitary endeavor (I wish I had friends and co-learners to explore with, but that didn’t come until later).

I absolutely loved Euclidean Geometry in 9th grade.  The spatial/geometric aspect combined with formal and rigorous proofs had remarkable appeal for me!  It was this year that I learned I had a special and unique talent (at least compared with my immediate peers).  Other students started struggling a bit with geometry, but I simply “ate it up”.

In 7th or 8th grade we took the JET “Engineering Aptitude Test”, and I scored 99 percentiles in all the technical subjects (math and science).  My guidance counselor met with me to suggest that I should be thinking about colleges like MIT and Carnegie Tech (now CMU).  First I had ever heard of either of those, but it made an impression, and years later I did end up at MIT.

A budding electrician / computer designer?

Sometime around 4th or 5th grade, my father gave me a wonderful present:  an “electrical kit” consisting of 2 dry cell batteries, several toggle switches, and some small (3 volt) light bulbs, along with wires for connecting them!  I loved playing with these, and learning about “parallel” and “series” circuits.  My father was an Electrical Engineer (Bucknell College on the G.I. bill).  I’m forever grateful that he shared this interest with me!  It was my first exposure to Boolean Logic (though I didn’t know it by that name) – series circuits are ANDs, and parallel are ORs.  Dad also showed me how to wire 2-way switches (so that toggling either switch will toggle the light (this is how lights in a house can be controlled from 2 different switches).  I later learned that this represents the XOR (Exclusive Or) logic function.

In 7th grade my father taught me about electro-magnetic relays.  These were used in IBM equipment at the time.  I hand-wrapped a nail to make an electromagnet and used a flexible piece of sheet metal as the “switch element”, and did my 7th-grade science fair project on How a Relay Works.

I remember wanting to design my own computer, so I decided to start by designing an “Adder Circuit”.  I knew about binary numbers and binary addition. I also had a collection of relays (2-position, 4-throw), discarded parts that my father brought home from IBM.  First I had to come up with a design.  Naturally I started out as simple as I could by designing a 1-bit adder.  Adding 2 single bits can yield a 2 bit answer so I needed 2 lights to display the result.  I realized that the unit digit of the result was the XOR of the 2 input bits – on only if exactly 1 of the inputs was on (1 = “on”, 0 = “off”), and off otherwise. The “carry bit” (the 2’s bit of the result) should be on only when BOTH the inputs are on, so it represented an AND of the input bits.  Cool – I was off to a great start.  Next I set about designing the circuitry for adding the 2’s bits.  This suddenly got a lot more complicated — now there were 3 input bits (two 2’s bits from the input numbers, and a possible carry-over bit from adding the 1’s digits.  This stage also required 2-outputs (1 to the light for the 2’s bit of the sum result, and another carry output to go to the “next stage” (4’s place).  I immediately realized that once I designed this module (3-input, 2-output) I could simply iterate it to obtain and adder for as many bits as I wanted (and had relays to work with).  I struggled with the logic and circuitry for this stage, and went through a number of design iterations.  I remember feeling stuck at one point, and gave to take a break to watch one of my favorite shows “The Man from UNCLE”.  After the show, when I took up the problem afresh – things immediately clicked into place.  This was my first memorable experience of the well-known psychological phenomenon of subconscious  problem-solving (the can mind continue to work on a problem even when not consciously aware of it).  I’ll spare you the remaining details of my design [after all, I did want to keep this post brief!  As one of my brothers is fond of pointing out: “Way too late, Glenn!” — brevity is not one of my long suits, as you must be learning by now], other that to say that my key insight was to “feed back” the carry result from stage n+1 to turn off the light if there was a carry, which is almost correct, working great for the first stage, failing to work for the general modules with 3 inputs.  In that case I needed to “override the turnoff” and have light stay on if all 3 inputs were 1’s.  I implemented my design using the spare relays (my Dad gave me serious help creating the 40-volt power supply with a spare transformer) and did all the wiring myself.  When I was ready to turn it on for the first time, my father cautioned me to be prepared for it not working (he knew how easy it was to have bugs in both wiring and logic circuitry).  I was puzzled – why wouldn’t it work?  My design seemed correct, and I was super careful doing the wiring.  Well, I didn’t learn my lesson that day, because it did work correctly the first time!    My working device was a 5-bit binary adder.  The binary inputs were set by the position of 2 rows of 5 toggle switches, and the output displayed on 6 lights.  This became my 8th grade science fair project which won 1st place in my high-school, and an honorable-mention at the Regional level.  The judges at the regional fair asked me if I knew about Boolean Algebra, and I had to confess that I didn’t (it should have been obvious from the fact that my designs – presented in a logbook as part of my project – where decidedly non-optimal).  Later, when I did finally learn Boolean Algebra, I was able to simplify my design a good bit.  Still, I’m pretty proud of the accomplishment.

A budding philosopher?

In middle school I recall thinking a lot about “deep questions”, such as the nature of reality, is there a God?, what happens when we die? is there absolute truth? and can we know it?  I was educated during the “Sputnik era”, so I had an intense exposure to Science because there was a big educational push in that direction at that time.  So I absorbed the “scientific method” and became a strong “believer” in science and empiricism.  My curiosity led me to explore philosophy and I read through Will Durant’s “History of Philosophy”.  I found the questions and various philosophical arguments fascinating.   I’ll write more about this later, because it overlaps with my spiritual / religious journey, and deserves it’s own post at some point.  Suffice it to say that I spent many nights pondering “big questions” before falling asleep.  Thinking about math and philosophy  were my favorite ways to fall asleep, along with reading by my “dry-cell powered night light”.

First Entrepreneurship

In Middle School (we actually called it “Junior High”)  I took over a paper route.  I’d deliver papers riding my bicycle every day, in order to obtain some income to supplement my meager allowance.  I recall being a pretty good saver – and after a few years (on May 27, 1968) I bought my first (and only) share of IBM stock. That single share cost $334.25 + $6.00 trade commission.  I still have that share, which has split multiple times so it is now 16 shares. The story I want to tell about my paper route concerns my mother, and illustrates what an amazing mother she is!  When I wanted to get involved with Basketball (I was tall, so I felt obligated to give it a try, but I was never very good) after school, I was confronted with the possibility of losing my paper route – if I let someone else take over, I might never get it back.  So my mother (bless her heart!) agreed to take over the route for me, during the winter when I was involved with basketball.  Being young and naive, I didn’t truly appreciate what a sacrifice she made for me — after all, she was the mother of 4 children who were all active, and I’m sure quite a handful.  Mom – thank you so much! 

NSF Summer Math Program at Ohio State

I was extremely fortunate and grateful to be selected to attend the Arnold Ross SSTP (Summer Science Training Program) at Ohio State for 2 summers (1969, and 1970).  The program was amazing on many levels!  I got to study “advanced” mathematics — a Number Theory course which forms the core of Prof. Ross’s program for high-ability high-school students.  I later learned that this was actually a graduate course at OSU, and there were math grad students taking the course along with us high-schoolers!   It was also my first exposure to other math geniuses (many much brighter than me) who shared my passion for mathematics.  Socially, it was my first interactions with any Jews (when I was growing up, Hershey had no minorities, other than the Italian Catholic community – Hershey was predominantly WASP, and extremely conservative).  I must say that my initial impression of Jews and Jewish culture was extremely positive.  More on all that later when I discuss my spiritual journey.   Perhaps the most influential aspect of my experience studying with Prof. Ross is the way he taught Number Theory — by discovery!   Every day we had a new problem set, and the typical problem was to “Prove, or Disprove and Salvage”.  This was not typical h.s. math where you are given problems to prove.  Rather we were given questions to explore — our task was to determine whether a proposition was true or not.  If it was true, we needed to prove it.  If it was false we were to come up with a counterexample, and try to find a related proposition that was true (a “salvage”) and prove that. Number Theory was a wonderful vehicle for learning this skill of doing mathematics – because the topics are accessible (they don’t require a lot of advanced math knowledge), yet rich and deep.  Perhaps Prof. Arnold’s most enduring quote (and most influential advice) was to “Think deeply about simple things!”   This idea is itself extremely profound, and we should all think deeply about just how powerful it is!  Another smaller (but still influential) aspect of my summer experience, was that of “falling behind” — the daily problem sets were so difficult that I couldn’t finish them all everyday, so I was constantly playing catch up.  Later, when I got to MIT, I was fearful that we’d have problem sets like at OSU every day, and I’d be taking 4 or more courses instead of just 1 or 2 (I actual tried to learn Linear Algebra that summer, but it only met 3 times a week).  Much to my relief, most problem-sets at MIT were easier than the OSU ones, and they were only given out once per week, not every day.  My summers at OSU were  perhaps the most intense and most rewarding intellectual experiences of my life.

High School Graduation

I graduated Hershey High in 1970.  I was a co-valedictorian (there were 4 or 5 people who had straight A’s through high-school).  I also received medals in English and Physics, but I was devastated at not receiving the Math Medal (which was the only one that meant anything to me)!   It was my first exposure to “back-room” politics — when I asked my math teacher why the medal went to someone else, he agreed that I deserved it, but said I shouldn’t be “greedy” since I had received 2 other medals.  It became obvious that the teachers had “negotiated” who would  get which medals, and they probably thought that it would make me appear more “well-rounded” for college applications, and that the math medal would help another student with his college applications.  I felt really burned to learn that the medals were not truly “merit-based” as I felt they should have been!

to be continued …

I’ll pick up next week with my College years at MIT.

Notes on Procrastination

Wow – 2 months (to the day) since my first post.  So far, all promise and no substance, despite my “good intentions”.  So I thought I’d try to remedy things, and decided to get  started by examining  procrastination.

So what causes procrastination?

It is natural to postpone doing things that are unpleasant, frustration-prone, unrewarding, difficult, intimidating, and so on.  In addition,  having other tasks with deadlines or higher priorities can cause things to be put off.

So what can be done to overcome  procrastination?

Here are some things I’ve tried, with some success (they seem to work for me):

1.  Simplify (break tasks into smaller units)

When a task seems overwhelming, simplify it (radically!) until the first step is almost trivial (eg. get a pencil, open blog page, or something that only takes a minute or less).  Getting started on even the smallest piece of the task can generate momentum and help me get “unblocked”.

2.  Combine an unpleasant task with a more rewarding task

This provides motivation, and  reduces the overall unpleasantness.

3.  Schedule and commit to a regular time

This helps make ongoing tasks into a routine (habit).  A related idea is to schedule a block of time, not a fixed part of the task – i.e. see how much you can accomplish on a task in 1 hour (or whatever block of time seems reasonable), and then schedule a continuation block of time for later if there is more to do.

4. Commit and share intention with a friend

Knowing that your friend will be expecting you to do something can provide extra motivation (leverages the inherent desire to keep one’s word).

5. Avoid perfectionism (do a rough-draft or first-pass)

Aim to do a rough draft, or “quick and dirty” version of the task, when appropriate.  Then iterate to improve!  Too often, striving to “get it completely right” on the first attempt is a serious obstacle to getting started.


I don’t like exercising, but I need to do it.  So I’ve recently tried combining my morning stretching and exercise routine with watching TV (DVR recordings).  Catching up on recorded shows is more pleasant and something I like to do, so I combine this with the exercise routine, and so far it’s working.  I also try to swim a mile 3 times each week.  My default schedule is to swim for an hour sometime between noon and 2pm Monday, Wednesday, and Friday.  Of course, it is sometimes necessary to modify or deviate from the schedule (e.g. Monday Holidays when pool is closed, or when other activities or appointments get scheduled in conflict).  Still I find it helpful to have the target schedule – when possible I schedule other things around it.

I also don’t like writing, but my son encouraged me to write this blog to share my experiences, thoughts, and ideas.  I also know and believe (at an abstract level) that writing is a powerful tool for clarifying one’s own thinking.  I made a commitment to my son to write a blog.  Still,  it took me many months before I even created the blog page, with the 2 short posts (introductory and promissory notes).  Then I got bogged down over how to write my set of “bio” posts.  So I decided to “simplify” by writing this 1  (intended to be short)  post on procrastination. I’m also making a commitment to write at least 1 blog post every Sunday morning.  I love listening to music, and every Sunday morning I listen to Carter Alan’s “Sunday Morning Blues” on WZLX (100.7 FM Boston).  So I’m combining my blog writing with this very pleasant (and already routine) activity.  Seems to be working for today – we’ll see how it continues to work for me in subsequent weeks.

Promissory Notes

This is a quick preview of some of the topics I intend to explore in future posts (a promise to myself and my readers):

My (brief) Life History  – to fill out a picture of who I am, my life trajectory, and formative experiences.

The power of Collaboration – in learning, education, problem-solving, knowledge-sharing, science, and engineering.

My favorite Logic Puzzles

What makes a good puzzle?

Approaches to fundamental AI research

… and much more, I’m sure


Introductory Notes

Greetings. This is a note of introduction. My name is Glenn A. Iba (I use my middle initial because A.I. is one of my intellectual interests, and also because it turns out there is a Glenn E. Iba who is not me).

This is my first time blogging, so forgive me if things seem a bit rough at first.

Who Am I?
Briefly, I am a 60-yr old male  (born July 4, 1952) who grew up in Hershey, PA, went to college at MIT (SB ’74, SM ’79), worked as both a teacher and researcher in AI/machine learning, and fathered 3 wonderful and talented children. My passionate interests are: puzzles and games, AI/machine learning, and music. Other strong interests include: math, programming, philosophy, education and politics. I’ll tell you more about me in future posts, but in the meantime you can visit Glenn Iba’s home page to learn a bit more.

I currently live in Lexington, MA, and do free-lance design of puzzles and games, especially focusing on smartphones. [Check out my Monorail logic puzzle app by IBA Puzzles, available for both iPhone and Android]

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