Saturday, March 17, 2018

Logical Fallacies

I'm developing new respect for the field of Statistics, nowadays rebranding as Data Science, given its 21st Century willingness to amalgamate (converge) what had been considered two mutually exclusive approaches:  frequentist versus Bayesian.

As Terry Bristol and I discussed at Tom's over breakfast not long ago, sometimes the most mature science is the one that overcomes a core either/or mentality.  Reality is made of particles.  Reality is made of waves.  Rather than a single Grand Unified Theory, why not have two?  Part of our GUT is we need two ways of looking at minimum.

Operation DuckRabbit.

The prejudice against Bayesian thinking, expressed as antipathy towards its champion, Laplace, might trace in part to a school days lesson most of us learn.

If A then B does not imply B therefore A.  Example:  if it's raining, I will not go to the zoo.  I'm not at the zoo, ergo it's raining.  That does not follow.  It's a bright sunny day, but I didn't feel like going to the zoo, OK?

However, a Bayesian would say, the fact "I'm not at the zoo" constitutes new information vis-a-vis the hypothesis "it's raining".  P(it's raining, given I'm not at the zoo) > P(it's raining).  Given I'm not at the zoo, I'm more willing to bet that it's raining.

Shifting to a more eugenic set of memes, what is the probability a randomly selected member of the population has blue eyes?  Lets say 36%, regardless of hair color.  Now I tell you said person has blond hair.  The chance said person's eyes are blue just went up to 45%.  Why?  Because having blond hair increases the likelihood of having blue eyes.

Draw some probability distribution.  That's my reality right now.  I just draw an invisible landscape of what I consider likely.

How let the data stream in for awhile.  Roll the dice a few times.  What's my probability distribution now?  How about now? 

My prior beliefs, "compromised" by subsequent data, yield my posterior beliefs.

The credibility curve, in light of new data, stems from the ratio between the likelihood of said data given old beliefs, and the probability of said data for any reason.

My old belief is there's one chance in thousand that I have medical condition X.  Then I take a test that's almost always positive when a person has X.  The test registers positive.  My old belief modifies somewhat, but not a lot, because it was already close to certain that I don't have X.

For years, per the sources I'm studying, Bayesian thinking was delegitimized.  But in the 21st Century, Bayesian thinking was finally accepted, keeping the door open to forms of Machine Learning that had been developed to a high level at Bletchley Park.

Saturday, March 10, 2018

Systems Science

Harder House

Thanks to a grapevine stretching to John "the Architect" Driscoll, the Systems Science PhD program, headquartered in the Harder House (PSU campus) invited me to give a brown bag lunch presentation, an almost weekly event when school is in session, this past Friday (March 9).  Dr. Wayne Wakeland introduced me.  Some people lurked from remote locations.

My topic:  the concept of "dimension" in Synergetics.

"Dimension" is a slippery concept in some ways, as mass, temperature, time, pressure are dimensions, relative to standard units of each, while space is commonly given three dimensions to establish location, named X, Y and Z dimensions.

Conceptually, we may need only an XY grid to establish which piece goes where on a chessboard (King to (r3, c2)), so we say chessboards are 2D, whereas rulers might be 1D.  However a chessboard is more obviously spatial and we simply choose to neglect the board's thickness.  Does "neglect" of a dimension make it go away entirely?  Out of sight, out of mind.

The dimension concept is even more complicated than that though, and we got into that in the midst of making some elbow room for Fuller's meaning, which starts pretty much where Kant starts:  space is a priori, a given of experience.  Adding time the way Einstein does, is different from adding more dimensions of space the way Coxeter does.  Different language games arise, each making use of "4D".

Fuller's paradigm volume, in terms of shape, is neither a cube nor a sphere, but a tetrahedron, of four corners, four faces.  The language games he builds around his core space concept somewhat diverge from those we learn in school, so much of this was new information to those present.  I'm aiming to share some of the same info with summer school students, as part of their literary heritage.

I also learned quite a bit, as one of the students mentioned being led to the writings of Donella H. "Dana" Meadows through Fuller's. I wasn't sure who that was, and as it turned out, my friend Patrick, with whom I went walking that same Friday afternoon, had been in her courses at Dartmouth.  He filled me in.  Dana Meadows, and her husband Dennis, have a lot to do with Systems Science as we know it today.

My overlap with Systems Science is General Systems Theory (GST).  I see these as quasi-synonymous, in terms of opening a large umbrella, under which we'll find many approaches to modeling and data representation.  There's a cybernetic flavor, meaning we're equipped with all the tools of Cyberia, our Global U.  The so-called Noosphere is a temporal-energetic phenomenon these days.

I talked about the Fuller Projection for data sharing as another invention, relating to his "geoscope" or "macroscope" (the "concentric hierarchy" having been my main focus), and how after the World Game chapter, it mostly stays back burner and on the shelf because of its apolitical nature (no political boundaries mar its surface).

"Talk about quixotic!" quipped the same student who mentioned Meadows.  I raise the question of Fuller's "quixoticness" with reference to his daring naively to critique XYZ thinking at the "three dimensionality" of space, conventions we mostly never revisit in later life.

As children we may have our doubts, about the sustainability of "nation-states" included, but in the press of events we usually come to abandon our both our skepticism and idealism, along with our teddy bears.  We stop pooh poohing zero dimensional points creating infinitely long lines, and settle in to take them seriously, for the duration.

Sunday, March 04, 2018

Youtube Teachers

When I first started my gradient descent into that hell hole (just kidding) called Machine Learning, I discovered a cast of teachers hitherto not on my radar, Siraj among them.  My first response was one of annoyance, but that didn't last.  Nowadays I have a healthy respect for the Siraj Youtube corpus and recommend them without hesitation to anyone I think might be entertained by his somewhat manic style.

Speaking of manic, another quirky teacher I highly respect is Daniel Shiffman, who covers a lot of the same topics in Machine Learning.  I was learning from both teachers today.  Even though I'm mostly looking at ML / AI through the lens of Python, I'm happy to watch Shiffman coding in Java and Javascript.

With teachers as entertaining and as intelligent as these, I'm thinking the threat of AI is not that serious, or at least not as serious as the threat of serious learning opportunities on-line, to traditional schooling.  You'd rather ride a bus half across town to enjoy far more restricted access to information?  I guess that's your right.  Just realize a lot of kids are rocketing ahead, as peer groups, not just as solo scholars.  Homeschoolers may rule, in generation Z (or have we rolled around back to A, B... already?).

These two teachers are not the only superstars out there, even limiting the sample to the few I know about.  However they're among the best in the knowledge domain I'm currently exploring.  That just tells you I like it quirky.  Demented even.