The spookiest and funniest time of the year is hard upon us this weekend.  Despite the “new normal” of the pandemic, we expect that trick-or-treaters will be out in something that resembles force.  After all, prior to the pandemic, Halloween was the one time of the year where wearing a mask was exactly what everybody wanted to do.  Throw in a dash of dazzlingly array of free expression (that makes for true diversity) with candy and ‘after-dark’ merriment and it is hard to see this holiday taking a backseat for long virus or no-virus.

That said, the month of October is often a tough month in terms of obligations and activity and the Blog Wyrm staff has had more than its share of distractions.  As a result, we are a bit tardy in getting this month’s blogs out and rather than rush them we’ve decided to simply wish everybody a Halloween with the promise that next month’s posts will be a treat.

Enjoy!

As the Labor Day Holiday recedes into the past, schools all around the US are beginning again – and this time in person.  Despite the issues associated with the new normal of the pandemic, it is gratifying that many students will be experiencing in-person learning again.  Nothing replaces the classroom setting where a good teacher (sadly a vanishing breed) can read and react to the non-verbals students are continuously sending in response to the material they are being taught.  An eye roll here or a puzzled look there do a lot more to reveal the inner state of mind during a lesson.  One-to-one interactions can never be fully mimicked no matter how good distance learning techniques become.  Hopefully when the pandemic also recedes into the past we will all have a better appreciation for the harm visted on students by distance learning.

Now onto the columns.

Aristotle2Digital begins a new series of blogs devoted to the Monte Carlo method.  While it might be surprising to some, there is an amazing amount of structure that can be coaxed stochastic processes provided that the randomness is introduced in an intelligent way into deterministic systems.  It is this mix of chaos and structure that makes the Monte Carlo methods so useful and so interesting.

Even the most casual of observers of economic news can see that the powers that be are worried about inflation.  A simple search on the financial websites unearths many articles fretting over the degree to which prices have risen in the past couple quarters.  CommonCents explores the macroeconomic roots of these fears by looking back at the stagflation of the 1970s and explains why everyone should be keeping a watchful eye on just what the Federal Reserve does.

Curvilinear coordinates are some of the most difficult concepts a student in engineering and science must wrestle with.  Understanding how to adapt the laws of physics to cylindrical or spherical geometry is essential since nature tends to favor these shapes.  And yet, most practitioners simply look up the formulae for the divergence, the curl, the material derivative, and the Laplacian without a solid understanding as to why the terms have their particular form.  UnderTheHood presents, in two acts, a ‘mantra’, useful to new and experienced folk alike, that explains the origins of the differences.

Enjoy!

It seems like only yesterday that we were ushering in the summer and now the start of the 2021 football season is upon us.  Regardless of how we feel about the relentless march of time it is nice to see that some things remain constant.   Training camps have been held.  The anemic pre-season, foisted upon us by the incessant need for more revenues, serves to single out the casual fans who, clueless of the inner workings of the NFL, celebrate when their team is undefeated.  A sense of normalcy will begin to creep back in when fans fill the stadiums to watch the games.  Whoever thought drunken shenanigans and nachos could look so good.

Speaking of looking good, we have a fine set of columns this month.

Aristotle2Digital digs into a very interesting concept that comes from the world of computing but which has profound philosophical implications.  The idea is that a programming paradigm works by taking away degrees of freedom.  In other words, the usefulness of a particular approach to programming (e.g. object-oriented) comes from the fact that it constrains our way of doing things.  This observation, which generalizes to any mode of intellectual inquiry is surprisingly deep.

Recent polling has uncovered the fact that an alarming percentage of young people (~20%) have a favorable view of socialism/communism.  One out of every five college students, provided their discontent with capitalism, using the very infrastructure provided by the system they doubt or despise.  CommonCents explores the depth of ignorance that these unexamined communists exhibits.

In recent columns, UnderTheHood has argued the point made by Robert Swendsen that entropy is misunderstood and mistaught by many practitioners and textbooks.  This month’s column, building on Swendsen’s colloid analysis, presents a simple Monte Carlo model of that demonstrates that the resolution of the Gibbs paradox does not depend on the introduction of quantum indistinguishability.

Enjoy!

We at Blog Wyrm are taking our summer break in July and will return in August.  In the mean time we hope that all have had a splendid summer and we wish you all a Happy 4^th of July and remind all of you to take a few moments to reflect on the blessings we have in the United States of America.

Enjoy the Summer!

Well, the summer of 2021 is officially here.  In 1967, we had the Summer of Love.  1984 had Don Henley’s Boys of Summer.  What does the summer of 2021 have?  Well, certainly not the good music that came from either the 1960s or the 1980s.  Not the sense of carefree abandon of the 1960s nor the sense of defiant hope of the 1980s.  On the surface, the summer of 2021 is much the same as 2020, pandemic woes hang over everything.  Despite that, there are definite signs of hope as more and more people stand up to the desperate obsession of some of our leaders to control all of our actions and the fear-mongering they use to ensure cooperation.  People again are going to movies, and concerts, and sporting events – exercising their right to free assembly and learning to put the risk of COVID and the inevitability of death into perspective.  We at Blog Wyrm have faith and hope that the summer of 2021 is the starting point for a freer world going forward.

Now onto our columns.

Most everyone appreciates a good example to illustrate the core concepts of an idea.  The more abstract the idea the greater the appreciation for that example.  In the case of category theory, the ideas are often quite abstracted and practical examples are hard to find due to the fact that the combinatorics quickly grow too large to make hand examples worth it.  Thankfully, a little bit of code goes a long way. This month’s Aristotle2Digital presents a python-based approach for producing the family of mappings needed to analyze actual problems in the category of sets.

One of the key concepts in economics is the idea of externalities in which a third party to a transaction either benefits (positive externality) or suffers (negative externality) as a result.  Examples abound ranging from water pollution due to upstream industrial activities to piggybacking on a neighbors unsecured wireless signal.  When the externalities are the result of government laws they are often grouped under the heading of unintended consequences.  CommonCents looks that the unintended consequences stemming from a law in San Francisco that argues that petty shoplifting is a victimless crime.  Tell that to the third-party victims having to live in city areas devoid of pharmacies.

This month’s UnderTheHood presents a fascinating analysis of how one of the most common kitchen staples opens vistas into quantum and statistical mechanics, the structure of phase space, and the ways in which academic traditions are handed down with little self-examination.  The humble substance in question is whole milk and, based on Robert Swendsen’s analysis, it seems that the physics community has been misunderstanding the definition of entropy for decades.

Enjoy!

For those of us in the eastern portion of the United States this May has once again brought the invasion of the 17-year cycle of the Brood X cicadas.  For those who haven’t had the experience, once every 17 years, millions of bizarre-looking insects burrow their way up out of the ground.  Climbing onto the trunks of trees, these underground dwelling nymphs wait on their perches until their exoskeletons harden enough for them to molt and turn into the even more bizarre-looking adult shown in the inset of the figure below.

But what follows puts the rest of the ‘science fiction’ story to shame.  Once mature, the adult cicadas get to feeling a ‘little anxious’ and, in droves, begin a song of sex and attraction that has to be experienced to be truly believed.  The sound these guys make is surreal and grows louder and louder each day as their mating reaches a crescendo.  The constant hum is everywhere during most daylight hours and, depending on one’s mood and temperament can present a pleasant distraction to a maddening torment.

Despite their size (over an inch long) the adults can get everywhere: covering sidewalks, swamping mailboxes, and generally bumping into things.  Dogs and cats love these things although it also seems to be literally a matter of taste as to whether any given pet will eat them versus playing with them.

Once the mating is done, the entire population up and dies leaving carcasses everywhere.  Eventually, the experience winds down and, mercifully, one soon forgets that it ever happened.  But while it is happening what a strange experience each day is.

Well, enough cicada strangeness, now onto the columns.

This month’s Aristotle2Digital continues the multi-part look at category theory, which while often strange-looking, can’t hold a candle to cicada strangeness.  Nonetheless, the primary focus is on the so-called division problems within the category of sets.  The specialized machinery that results, the retraction and section defined to automorphisms, provides a new way of expressing some old ideas about when a mapping has an inverse.

As if the common eastern seaboard motorist didn’t already have enough to deal with during the month of May with COVID and cicadas, he was then hit with the additional whammy of gasoline shortages and long lines due to the ransomware attack on the Colonial Pipeline.  Although it turned a difficult month into something even more nerve-wracking, the economic fallout from this event was rich and varied.  This month’s CommonCents touches on some of the big issues that will, no doubt, be the conversation of economists for years to come.

Despite the fact that the basic concept of entropy has been around for over a hundred years, a deep understanding of it remains elusive.  Nothing drives this home as much as the Gibbs Paradox that arise from what is most tractable of all multi-body physical systems, the ideal gas.  UndertheHood examines the basic structure of the Gibbs Paradox, the orthodox solution to the problem, and some ideas by a researcher who believes that there is something new in something old.

Enjoy!

Well, an entire year has gone by under the pall of COVID-19 with no clear end in sight.  It is curious to note that back in April 2020, the powers that be were projecting a return to normalcy by June of that year.  Here we are, charging into May of 2021 and the only light perceivable on the horizon is the current, wide-spread availability of a vaccines of limited efficacy.  Much like the housing crash of 2008 and the wild fire debacles in California, the only thing that is clear is that reality has a way of humbling us and our attempts at control. Unfortunately, it is unlikely that the powers that be will actually take time to reflect on that.  At least life goes on and summer is only 7 weeks away.

Speaking of life, let’s say a few words about our columns.

Much like a fruit ripening upon the vine until it is sweet, occasionally ideas take time to mature.  This month’s Aristotle2Digital provides some much-needed clarity on the determination problems in the category theory of sets.  Finding a rich harvest there, the post then extends the discussion to the companion viewpoint – the choice problem.

It’s important for the functioning of a free society that individuals are rewarded for both their good ideas their hard work and industry bringing these ideas to life.  The patent system looks to provide that protection but every system has its flaws.  This month’s Common Cents looks at one such flaw and the man who exploited it to great fortune but only a small fame (or infamy).

From its modest roots in the industrial revolution to its prominent position in fields as diverse as statistics and image processing, no modern concept seems to be more universal and yet as poorly understood as entropy.  This month’s Under The Hood begins multi-part investigation on this most slippery of physical concepts.

March is the month of spring and, while spring may mean different things to different people, without fail these various notions of spring have one thing in common – a sense of lightness and whimsey.  Don’t believe me?  Why else would the annual men’s college basketball tournament be called March Madness?  Why else would Alfred Lord Tennyson have written that famous line “In the Spring a young man’s fancy lightly turns to thoughts of love”?  Why else would we entertain that most barbaric modes of time keeping the losing of an hour of sleep in the name of ‘daylight savings’?

It is with a most profound sense of whimsey (can whimsey be profound?) that we present the hundred‑eleventh issue of Blog Wyrm.  111 is a fine number.  It has a nice symmetry to it being comprised of only one single digit which itself is 1.  And it reads the same forwards and backwards; a numerical palindrome.

Palindromes are some of the most whimsical components of speech.  Perhaps the most famous example is the ever trite statement about Napoleon that reads “Able was I ere I saw Elba!”  The writer/illustrator Jon Agee has produced the most delightful books presenting interesting palindromes accompanied by engaging illustrations – just the thing for young and corruptible minds.  His book So Many Dynamos brings a smile to every face we’ve ever seen reading it.

Our own favorite palindrome is ‘animal lamina’, which the attentive reader has already noticed is a kind of meta palindrome.  Not only does this two-word description of road kill read the same forwards and backwards but it also can me juxtaposed to form ‘lamina animal’, yet another palindrome describing organisms such as the flatworm or the Surinam toad.

That sense of whimsey, engendered by Spring, has crept into our columns as well this month.

In our first example, consider this month’s Aristotle to Digital.  Some may say that category theory is a little dry, especially when trying to navigate through the essential details of mappings between finite set.  But not true if the sets in question deal with the gritty world of street gang crime in New York City.  Mappings between gang members, their weapons of choice, and the targets of their wrath, all inspired by the cult movie classic The Warriors, serve to bring a big dose of whimsey to an otherwise sedate philosophical/mathematical pursuit.

For our next example, consider the whacky world of Theodore Geisel Seuss – aka Dr. Seuss.  It is hard to get much more whimsical than a truffula tree, Whoville, or the Grinch; that is until the dust up about Dr. Seuss book’s being banned (‘Oh the books you can burn’).  Of course, both sides of American politics overreacted to what was, as Common Cents clear shows, a really clever marketing ploy by the Seuss estate.

Finally there is this month’s installment of Under the Hood on heat and partial derivative.  There is not much in the way of whimsey in this practical description of how to use Maxwell’s relations in thermodynamics (how could there be?).  But the attentive reader will notice the use of spring colors highlighting the various sides of the thermodynamic square.  These beautiful shades of blue, yellow, and green are perfect hues for decorating Easter eggs.

Enjoy! (And get outside and enjoy the nice weather as well)

There are a variety of factors in our lives that tend to ‘shrink the world’.  Even before COVID-19 hit there was a tendency for many of us to stay glued to small windows on the world.  Computer screens, hi-def TVs, and cell phones command ever larger amounts of our time and we willingly obey them even if our health and safety is at risk.  Consider how often we find some motorist a good 100 yards from the cars stopped in front of him at a red light.  Why such a large distance?  The charitable soul might say that such cushion was provided in an over-abundance of caution but most of us recognize that the real reason: the red light provides a chance to spend more time with the smart phone.  After all, who knows what interesting development has arisen in the last 30 microseconds.  After the arrival and rise of the pandemic, things have only gotten a lot worse.  Many of us work from home, a situation that more and more closely resembles house arrest rather than telework.

And the sad part is that the world is a lot bigger than many of us appreciate.  It seems that desperation is on the rise and some people think that the only way out is suicide.  That point-of-view is extremely tragic.  Regardless of its many flaws, life is always about fresh starts and new beginnings but, sadly, one only sees that if one steps back from the small windows to see the big world full on.

Now onto the columns.

This month’s Aristotle to Digital continues the in-depth look at category theory.  The current topic is that very special of all mappings from sets to sets – the isomorphism.  An isomorphism allows us to trace the mapping back from the target set to the initial set with no guess work or ambiguity.  Perhaps surprisingly, this notion is rich with real world applications that sit outside and/or above the usual mathematical contexts in which it is defined.

Common Cents looks at what happens when crowd sourcing on the internet and Wall Street trading and hedging collide head on.  For what is likely the first time in history, a group of loosely affiliated group of retail traders put the squeeze on some of the big institutional traders and left them holding useless short sells of Game Stop.  Truly a February to remember.

Finally, Under the Hood shows a physical context for the partial derivative machinery developed in the January column.  The subject is thermodynamics and the context are the various thermodynamic potentials, such as the internal energy and the entropy, which are oh so useful and oh so abstract.  Just where does one buy an entropy meter?  Applications of the partial derivative identities derived earlier and the Maxwell relations equating various second-order partials derivatives demonstrates that one does need to.

Enjoy.

Happy New Year?

Each new year brings the promise of renewal, of repurposed goals, and recharged zeal.  And, as best typified by resolutions to exercise, very little in the way of staying power.  It is simply a sad fact that the transition from the late months of one year to the early months of the year following is little more than show.  Most people may feel that this time it will be different but in reality emotional resolution last only as long as the blood is warm.

Nonetheless, the staff at Blog Wyrm wishes the world a truly happy new year.  We pray that people will become a little more forgiving, a little more trusting, and a little more concerned with others.  It is in that spirit of true hope and optimism that we bring our first set of articles of 2021.

Aristotle to Digital launches into the new year with an open-ended exploration of category theory.  Hailed as a revolutionary approach that knits together much of mathematics, category theory seems to deal not with the usual underlying objects of mathematical reasoning (e.g. numbers, sets, vectors, etc.) but with the relationships that one may conceive between various collections of these objects.

It seems to be in vouge to be down in the middleman.  This so-called superfluous member of society is often disparaged and maligned.  The fashionable opinion is that the internet has finally allowed us to be rid of this parasite.  But, as this month’s Common Cents demonstrates, the functioning of a middleman is one we not only need but we find in almost every nook and cranny of the world wide web.

The physical world is filled with systems in which lots of independent variables are in play.  Whether it is the fact that we live in three dimensions, or that the most common materials around us are governed by many different variables, such as temperature and density, our models of nature require us to think about more than one thing at a time.  Unfortunately, the idea of partial derivatives, which are the most common way of taming these systems is one of the more difficult things for students in the physical sciences to internalize.  This month’s Under the Hood tries to rectify that by presenting a ‘complete’ look at partial derivatives.