Author Archive

Blessed Are the Pure of Heart

April 25, 2016 Leave a comment

I have looked at Mathematica Meta site and dared (somewhat apprehensively)to answer and comment.
The questions (from my viewpoint) were more philosophical in nature.

This post is motivated by a comment that prompted introspection. The comment expressed concern that users were quick to code at the expense of quality and rigor, and that this was self-reinforcing (a mutual admiration society) resulting in an overall degradation in quality. Users were offering answers beyond their depth of understanding.

I think this is a legitimate and that I certainly may be one of the users contributing to this trend. I would apologize unreservedly for that. I think, therefore, encouraging users (“pure of heart”) to sermonize (to borrow the metaphor in question title and not pejoratively)  is valuable. Such users could  post answers where they thought deeper explanations were valuable or that an important misconception was being promulgated. The deep reasoning (I think) helps everyone.

I am not sure if it is a trend. I do think (and have directly experienced through my own mistakes and over-reach) that expert users are very quick to identify problems and edit, comment or answer to deal with conceptual issues.

I also believe that MSE is a diverse community. The diversity includes:

  • age
  • education
  • special areas of interest
  • culture
  • personality
  • and many more

I think that is a strength.  The site is primarily aimed at using Mathematica/Wolfram Language and so it is natural that “code” has primacy. However, the intersection with Mathematics, Statistics, Physics, Engineering etc. is large.  Therefore, insights, constructive criticism and correction would only enhance the value of the site.  I think this already occurs but perhaps not enough.  I think it is a matter of balance.

I believe, with absolutely no disrespect, the site is a playground.  There are novice users  who want guidance. There are expert or experienced users who enjoy  challenges (be it efficiency, terseness, a completely different approach). There is the dense middle that I occupy that likes to play the game. Sometimes spectacularly fail but almost all the time learning  new approaches.

MSE may have a lot of academic and commercial users. It is a site  where people with a shared interest can get help with specific problems and contribute all sorts of ideas.  I have enjoyed the creativity. The site is not producing answers for peer-review manuscripts or commercial intent. Of course, some of the ideas and approaches may developed for such purposes.  However, a clarion call to keep well above a minimum standard is important.  I think that finding the balance between academic purity/integrity and just playing with the black boxes without understanding the assumptions or limitatons (with the dangerous potential of misuse) is difficult.  I thought the balance was ok. However, this may be because I am blinded by the shiny black boxes and the colorful outputs. I know that I have worried about this for a long time.

I have spent 20 years teaching people “a particular set of skills”. At the start they have a lot of enthusiasm, a lot of (frequently wrong pre-conceptions) and the teaching involves long periods of “play” before they enter the “real world”.

I am not an expert and I may have contributed to some quality degradation. If so, I am sorry. I like the community. I hope I can be a better citizen.


No man is an island,
Entire of itself,
Every man is a piece of the continent,
A part of the main.
If a clod be washed away by the sea,
Europe is the less.
As well as if a promontory were.
As well as if a manor of thy friend’s
Or of thine own were:
Any man’s death diminishes me,
Because I am involved in mankind,
And therefore never send to know for whom the bell tolls;
It tolls for thee.




Categories: philosophical rants

Euler and Bessel

April 22, 2016 Leave a comment

This post was some fun with Euler’s method and an ODE:


Categories: Uncategorized

The Garden of Forking Paths

April 20, 2016 Leave a comment

The post title relates to a phrase (from Andrew Gelman) quoted  in “The Seven Pillars of Statistical Wisdom” by  Stephen Stigler. It refers to the frequently hidden, frequently unrecognized (or recognized) decisions in the path from hypothesis to conclusion.

I enjoyed and learned a lot from this book.  It provides a historical framework under-pinning the authors construction of a framework to understand statistical science. This naturally includes misconceptions, personalities and unintended sources of progress or innovation.

The seven pillars are:

  • aggregation
  • information
  • likelihood
  • intercomparison
  • regression
  • design
  • residual

Professor Stigler also hints at an emerging eighth pillar.

I particularly enjoyed this excerpt (quote from Alfred Marshall 1885):


the most reckless and treacherous of all theorists is he who professes to let facts and figures speak for themselves, who keeps in the background the part he has played, perhaps unconsciously, in selecting and grouping them and in suggesting the argument post hoc ergo propter hoc.

I was kindly made aware of Professor Stigler’s invited address which covers the seven pillars.

Categories: books, Mathematics Tags:

Basket Weaving with Pi

April 13, 2016 Leave a comment

It has been a very difficult time, Some basket weaving to pass the time…


Categories: Mathematica

Playing By The Rules

April 13, 2016 Leave a comment


Categories: Uncategorized

Triangles and Circles

April 11, 2016 Leave a comment

This post is inspired from a tweet by Clifford Pickover. It visualizes Miquels theorem. The blue point is Miquels point.


Categories: Mathematica, Mathematics

Not Seeing the Triangles for the Squares

March 29, 2016 Leave a comment

I could take solace in very active illness. However, it never ceases to amaze me how my stupidity and laziness can contrive an answer and miss the beauty and simplicity that a little thought could provide.

This post is a penance for an MSE question which sought (analytical) probability that 2 points within unit square will greater than 1 apart.

In the following there is a derivation of difference of independent uniformly distributed random variables. The points in top plot are sampled from triangular distribution {-1,1}.

Using (the answer evaluates quickly with w=1):

pd = ProductDistribution[{TriangularDistribution[{-1, 1}], 2}]
Probability[a^2 + b^2 > w, {a, b} \[Distributed] pd]


Categories: Mathematica, Mathematics

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