Category Archives: Rants & Speculations

Good Will Hunting Problem Solved

I love the movie Good Will Hunting for lots of reasons: It’s about being different and finding yourself, dealing with demons, the struggles with the ladies, but (much more superficially) it was at my school and deals with math. The movie glosses over some of the actual math problems, and I assumed that they were all way out of my league. Let’s be honest, although I went to MIT, there were many students beyond my capabilities. Do you remember the part of the film where the professor puts up a problem with these figures made up of dots and lines & claimed it was a problem it took the professors years to solve? The problem just looked cool and one day I got curious enough to look it up.

Here it is: Draw all the irreducible, homeomorphic trees of degree n=10

It’s actually not that hard, you just have to understand what that means to solve it. Here are the rules:

  • Make as many figures as you can
  • with 10 dots and lines that connect them
  • that are unique (homeomorphic)
  • that don’t create any internal shapes (i.e. closed loops)
  • that don’t have any dot with just 2 lines connected (1 or 3+ is ok)

Here’s my solution (don’t look if you want to try yourself)


Oops had to cross out a mistake, but still pretty happy how quick & fun it was to solve.

Oops had to cross out a mistake, but still pretty happy how quick & fun it was to solve.

Every city has a Question

(Fully aware this post is laden with bias, prejudice, stereotypes, classism, narcissism, racism, neo-natzism… obviously, I hope you see the intended humor in this post, not the any of the above)

I’ve always felt that each city I’ve spent a decent amount of time in had an underlying, often times unspoken, question that established your respective standing in their minds.  Even if the issue was not addressed directly, initial conversations often skirt around the core issue, hoping it might be offered or derived from other information.

  • Boston:  “Where did you go to school?”  (i.e. how educated are you?)
  • NYC:  “How much money do you make?” (or “Where do you work?” – just a proxy for the first)
  • DC: “How much power do you have?” (or “Who do you know?” in terms of political/government power)
  • LA: (a quick glance from head to toe), ostensibly seeing how good your plastic surgeon is OR “Who do you know?” (different than DC à in terms of fame)
  • San Fran: “How are you changing the world?” (two acceptable forms here: innovation/start-up or environmentally)

Then there are cities that have some blend of the above, highly distinctive cities:

  • Philly (so far): “Where did you go to school?” + “How much money do you make?”
  • Seattle: “How are you saving the world?” (usually environmentally) + “what eco-friendly, outdoor activity are you passionate about”

Yes, this might be for a specific slice of the population in many cases, but I sensed some degree of these questions from a good majority of the people I interacted with.

If agree/disagree with any of these let me know.  And, more importantly, if your city is not on here, let me know what you think that underlying question is in your experience.

Personal Philosophy

I’ve tried to challenge myself to develop a moral framework by which I could be judged against, here’s where I am at:


“The Philosophy of Realism”

(wow, that might sound a bit too pretentious -> name suggestions? Objectivism, etc. already taken)


Objective Truth – Objective truths exist.  We may never fully comprehend them, but striving to attain these truths will gradually improve our collective understanding of our surroundings and ourselves.  (as in my longer paper, think of full knowledge on any topic as an asymptote that we collectively strive to climb towards as we learn new supporting evidence)

Objective Morality (may be derived from the first) – Although broad-sweeping moral absolutes do not exist (e.g. murder is wrong), given the full context of a situation, there is a “best” way to act.  Full knowledge of the context and consequences of an action is nearly impossible, nonetheless, through better understanding of the prevailing factors and results of past, similar decisions, we can make a fact-based judgment on which course of actions would achieve our collective goals most effectively.


Personal Code

  1. Apply the scientific method broadly – require objective, verifiable, replicable evidence to support your stances.
  1. Constantly pursue better understanding of yourself and the universe around.  Educate yourself and enlighten others about topics you have knowledge. Be active in pursuing knowledge and creating new ideas.
  1. Constantly question held beliefs and assumptions.  Where possible, strive to only hold beliefs for which you have adequate reasons that can be objectively supported.  Value rational & reasoned debate with opposing views.  Be alert and open to contrary evidence.
  1. Aim to seek out, expose, and minimize dogma through respectful conversation, publications, and legal efforts (where appropriate).  Conversationally, make it intellectually shameful to use logical fallacies or faith arguments (“because I believe it to be so”) to support a view/conclusion.


Societal Goals

  • Maximize eudemonia (yourself, those around you, and future generations).  Start by being happy and treating those around you well.
  • Minimize innocent suffering.
  • Strive to equal the initial playing field.  There is a wide range of situational inequality at birth (through no fault of the child); as much as possible, help bring equal opportunity for success from early childhood.
  • Continuous progress towards understanding and implementing objective truths (& associated morality).
  • Do your best to leave the world a better place without causing undue burden on yourself (not to an unhealthy cost to yourself or those depending on you).
  • Enable the lasting survival of as many ecosystems as possible – we not only depend on the survival of these species and ecosystems, they also may hold insights into our own species, medical cures, and solutions to large scale problems (e.g. pollution).


As with anything, I am open for feedback and invite thoughtful disagreement – fire away!