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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.

We at Blog Wyrm will be brief in this month’s installment.   As is customary, we usually take the month of December off to prepare for Christmas and to spend time with our families.  This year it is especially important  to spend to take time and tell those around us that we love and need them.  Next month we will be back with fresh content but for now we will simply say Merry Christmas and may God bless each and every one of you.

Well Thanksgiving is upon us and, despite these ‘unprecedented times’, we at Blog Wyrm would argue that there is plenty to make us pause and be thankful.  Yes times are tough for a lot of us but we still live in a dynamic country where people often rise to the challenge.  Business have adapted to new protocols, schools to new approaches to teaching, and more and more you see people helping people.  All of these are real, tangible blessings for which each and every one of us can be thankful, if only we approach the world with some humility and wonder.  We at Blog Wyrm have had a particularly trying year with grave illness lurking through our staff but we still assert that it’s a miracle being alive and, especially, living in the United States.  It is with that spirit that we brings these thankful holiday columns.

Speech is one of those human capabilities that all of us use but few of us ever stop to consider.  This month’s Aristotle To Digital examines the mysterious faculty that we all possess that allows us to learn our mother tongue, to extract the essential natures of the objects around us, and to abstract to those important things, like truth and beauty, that we cannot sense.  Truly it is a miraculous capability that each of us should be quite thankful for.

Sports talk radio often displays strong opinions and heated debate.  Which player is best, which team will win, which coach is overrated and so on.  Such exchanges are natural This is to be expected and This month’s Common Cents examines a curious exchange on sports radio and how many common economic fallacies

Finally, we are thankful to have accomplished something that we were not sure would happen when we embarked on the program of studying fluid mechanics over a year ago.  This month’s Under The Hood is the last installment of both compressible fluid flow and of fluid flow in general.  It’s been a long and fruitful run but we are delighted that it’s finally over.

Election cycles have always been trying, taxing, and generally painful but in the age of tribal politics and hyperpartisan behavior it downright stinks.  The propaganda is so think that one wonders if any semblance of journalism will take hold again.  The endless onslaught of campaign advertisements, many of which bend the truth in so many varied and imaginative ways, threaten the very sanity of the country.  And, worst of all, is the sanctimonious prattle of frankly stupid people trying claim the moral high ground based on an amazing combination of ignorance and entitlement.

Thankfully it will all be over soon, at least the part where advocates and partisans campaign for the candidates.  The part where people campaign against the newly elected will surely continue onwards for the foreseeable future.

Anyway, enough about the election.  Now onto the columns.

Aristotle To Digital examines the very interesting and very disturbing notion that elections involving more than two candidates can be engineered so that any of them can win, regardless of public opinion, simply by the skillful choice of innocent-seeming rules for summarizing the votes cast.  This theorem, called Arrow’s Impossibility Theorem, not only serves to sober one’s thinking about how statistical summaries can tell many stories but it also reminds us of the ambiguities surrounding the idea that we can ever hope to know just what is the will of the people.

This month’s Common Cents presents some of the behavioral economics that lead to the very statistical tangles that are explored in the companion Aristole To Digital column.  In particular, some of the most cherished myths many of us have about how government should work whither under the blistering analysis of how voters and politicians actually behave given their goals and the incentives under which they operate.

This month’s Under The Hood journeys through the interplay between thermodynamics and fluid flow to arrive at one of the most important relations describing how one-dimensional compressible fluid flows can be made to produce supersonic flow in a converging-diverging nozzle.  While not directly applicable to the current election cycle, we all may want to take advantage to rocket somewhere else the day after.

Enjoy!

Modern times being what they are, one cannot move through life without being bombarded with continuous efforts to brand, market, and distinguish.  These advertising activities are so prevalent that, without even noticing it, we all begin to construct tag-lines and memes.  Next thing one knows, a phrase is everywhere, is then overused to the point that it doesn’t mean anything, and then is discarded when the new fad comes along.

The expression ‘unprecedented times’ is just such a thing.  First of all, these are not unprecedented times.  When the black plague was ravaging Europe, somewhere between 2/3 and 3/4 of the entire European population was destroyed.  The Spanish Flu of 1918 killed far more people than COVID-19 has, with per-capita deaths increasing the fatality gap even more.  Second, even advertisers are aware that ‘unprecedented times’ is overused.  There are adverts playing now in which the announcer says something along the lines of “… in these, dare I say it, unprecedented times…” clearly indicating that they understand that we are all sick and tired of hearing that phrase.

Against that backdrop is the even more frustrating “do as I say, not as I do” crowd from our entertainment intelligentsia.  Not only do these empty heads tell us that we are living in unprecedented times, they have the temerity to tell us all to both practice social distancing and to wear a mask.  The picture below, taken at the local grocery store magazine rack on August 30^th of this year, shows that these pinheads, while being quite willing to lecture, are also quite unwilling to lead by example.

Not a single picture shows the ‘models’ (models of what? Certainly not good behavior) wearing a mask or separated by the CDC-recommended 6 feet (does 5 feet 11 inches spell disaster?).   A particularly interesting example of this hypocrisy is the large blurb in white from the cover of Cosmopolitan reading “Wear a Damn Mask” positioned to the left of a maskless model’s hip as she poses with a come-hither look, which if, acted upon, would entice the male readers to violate the proper distance.  It would be emotionally satisfying to say that this in unprecedented hypocrisy, but the fact that it is all too common means that we can’t even have that fillip.

Anyway, enough ranting.  Now onto the columns.

Aristotle To Digital departs from the recent topic of classification to sport its own rant about leaky abstraction.  Finally, a name can be given to one of the biggest ailments to ever be visited upon any user community.  It strikes down users in their prime, leads to premature frustration, and explains why certain tools get a bad reputation.

This month’s Common Cents fills in some of the details left hanging about financial arbitrage from last month’s introduction.  Specifically: what assets should be used in evaluating the relative worth of a security, how are the risk premiums determined, and how stable is the algorithm to  uncertainty..

One-dimensional steady fluid flow offers a really interesting laboratory for exploring how fluid mechanics and thermodynamics intersect.  Central to all the ideas is the concept of the Mach number.  Under The Hood works through the relevant equations, presents the concept of choked flow, and sets the stage for one of the most interesting practical devices – the converging-diverging nozzle that makes jet aircraft and rocket flight possible.

Enjoy!

As the country nears Labor Day, kids all around the country are gearing up to go back to school, … maybe.  As summer draws near to it end, parents everywhere are buying school supplies and readying their children for school, … maybe.  Educators are writing syllabi and lesson plans, fretting over lectures and homework, and are preparing to teach, … maybe.  For the first time in most anyone’s living memory, the back-to-school ritual has encounter an insurmountable snag and so, a new normal has descended.  Will we cope with this new wrinkle in the education system?   Maybe.  We at Blog Wyrm can only hope for a few things.  First, that parents, kids, and educators stay as healthy as possible, both physically and mentally.  Second, perhaps this new normal will cause us to finally overhaul the education system and give it its long-overdue reform.  Maybe that will happen.

Now onto the columns.

Aristotle To Digital begins exploring an interesting machine learning system – naïve Bayesian classification.  A rather simple algorithm to implement, this supervised learning technique is popular because of its high value – it requires only a relatively small amount of training data and it performs reasonably well.

One of the most important places where market inefficiencies motivate profit-seekers to really go the extra mile is the financial markets.  The lure of big money without actually having to transport any concrete good makes this an excellent laboratory for studying arbitrage opportunities and how macroeconomic forces come into play.  Common Cents explores the basic mechanism by which the securities bought and sold in these contexts are valued.

Incompressibility is a central pillar of common fluid models.  However, every good thing comes to an end.  This month, Under The Hood begins a multi-part look at compressible fluid flow.  This new regime adds a bit new spice as the energy equation comes front and center bringing thermodynamics along with it.

Enjoy!

In the first time in recent memory, summer in the U.S. lacks spectator sports, summer blockbusters, and grounded pools.  Of course, all of these sunny staples of American culture have fallen victim to COVID-19 but, interestingly, new summer blockbusters have come to the front.  Families are spending more time together, new hobbies and interests are developing, and people everywhere are finding new outlets for the real summer blockbuster – American ingenuity.

Now onto the columns.

Expert judgement is hard to come by.  It takes a long time to accumulate the experience and practice needed to accurately pick the true from the false, the authentic from the fake, and find the right category for each object that comes our way.  This month, Aristotle To Digital begins a multi-part analysis of one the key machine learning applications: classification.

Markets work best when there is transparency.  Of course, not everybody in a market place wants transparency and, even if they do, it can rarely be achieved.  Regardless of the reason, the lack of information leads to market inefficiencies.  Interestingly, one of the more powerful methods for dealing with certain macroeconomic market inefficiencies is also one of the more ignored in introductory texts.  Common Cents introduces the concept of arbitrage and sets the ground work for later columns that look in depth at how arbitrage opportunities provide a mechanism to smooth out imbalances and how frustrating these opportunities can lead to some very undesirable outcomes.

This month’s Under The Hood finishes the two-part study of the exact solutions of Navier-Stokes equations.  The focus in this column is on two very important examples of Couette flow: steady flow in cylindrical geometry and time-varying linear flow.

Enjoy!

As we come into the beginning of summer and are on the heels of the 244^th anniversary of the nation’s independence from England, it must be said that things look less than rosy.  The riots that range across many cities and the continued presence of the 21^st-century plague that is COVID-19 have certainly bruised and battered the American psyche.  And for good reason.  There are many areas where the USA could stand revamping and improving.  That said, the staff of Blog Wyrm continue to believe in the American Experiment.  We agree that there linger injustices but we are hopeful for a more just future.  We agree that there is a new normal but we are hopeful that American ingenuity will prevail.  We agree that there are structural imbalances but we are hopeful that reason and sanity will again prevail so that, together, we may address them.  In short, while the nation is certainly far from perfect, we still believe that we can form a more perfect union.

Now onto the columns.

There are many ways in which random process and outcomes play a role in the world around us.  Some of them are presented themselves in fun diversions, such as games of chance.  Other faces of randomness are more profound and are seemingly essential for the world around us to function.  But the power of randomness is often over-imagined by the average person.  This month’s Aristotle To Digital takes a look at just how much monkeying around can chance and randomness really pull off.

Very few art forms are as uniquely American as the comic book.  For over a century, sequential art in the form of comic strips and then books have entertained and intrigued us and sometimes driven collectors and speculators to some of the most outrageous behaviors.  The very names of Superman and Batman are part of our cultural DNA to the point that we sometimes forget that, above all else, the business of comics is a business. Spurred on by the recent announcement that DC Comics is breaking from a comic book distribution monopoly that’s existed nearly 25 years, Common Cents looks at the business of how comic books go from publisher to customer, and all the implications that the modern direct market entails.

The Navier-Stokes equations are considered to be some of the most difficult models to grasp and deal with in all of theoretical physics.  Numerous real-world effects, including viscosity, thermodynamics, and compressibility, complicate the situation to the point that general solutions to these equations have, so far, remained elusive.  Nonetheless, simple situations can provide exact solutions that, while not capturing all the fine details, can serve to at least hone the intuition and provide baselines against which one can measure more subtle phenomena.  This month, Under The Hood begins a two-part look at some simple but important exact solutions of the Navier-Stokes equations.  The flows examined, which result from the influence of gravity or are driven by pressure differences, underpin some of the more important results about lubrication and fluid flow through pipes.  And we all love these effects because they keep our modern machinery running and provide drinking and bathing water directly in the home.

Enjoy!

Each year we celebrate Memorial Day, but it isn’t clear that many of us really appreciate the holiday.  Some of us regard it as the beginning of summer, despite the solstice being about a month away.  Others regard it as a time to go to the beach to start working on that all over tan.  Some think it is the event that gives tacit permission to wear white pants.  The Blog Wyrm staff likes to remind ourselves of the men who fought for us.

Some of the men came back with minor injuries.  Some came back lame or dismembered.  Some came back with demons that haunt them forever after, and some came back in a daze of forgetfulness brought on by an addiction acquired ‘over there’.  And some simply never came back.

Each of those lives, marred and warped in some way or another by the horrors endured, is just as noble and successful and inspiring as the ‘most beautiful’ amongst us.  In this age were we cling to life and comfort for their own sakes (after all, what else is the panic over COVID-19 really about), there is a strong tendency to push those who’ve sacrificed themselves on our behalf out of our sight.  Like the elderly, their presence is a downer at a party we pray never ends.  Well, we want to remind everyone of who picks up the bar tab for incessant self-centered hedonism – it is those brave soldiers who fought so we didn’t have to.

Now onto the columns.

Reasoning and language tend to get tied in knots when arguing about probabilities.  These knots take on almost legendary status when we fail to distinguish probabilities of outcome versus probabilities of guessing correctly.  This month’s Aristotle To Digital considers the kinds of knots that can arise from such simple situations as flipping a coin and making a guess as to how many daughters a couple with two kid s has.

Given the new normal of social distancing and virtual meetings, it is tempting to ask ‘what if’-type questions.  How would things be different if most of us didn’t have high speed internet?  What do we do without social media to keep us in touch?  How would we be able to function without Zoom?  Common Cents gives into the temptation and wonders how things would be different if one of the world’s greatest inventors, George Eastman, were alive today.  Prepare an alternative history dripping with drama and economic meaning.

In 1904, at a fairly unknown and unassuming conference, a ten-minute presentation was given that would change the world of fluid dynamics forever after.  In that short span of time, Ludwig Prandtl introduced the boundary layer, a thin section of fluid flow past a solid object such as a wing, in which friction effects dominate.  This concept put to rest a 150-year old ‘paradox’, ushered in practical estimations of drag forces on solids, and gave new insights into turbulence.  Under The Hood examines Prandtl’s astonishingly far-reaching concept.

The narrative below was written and ready for public viewing on schedule.  However, things being what they are, it never saw the light of day when the columns did.  Oops!

Well April is upon us and the world is still topsy-turvy.  At least the weather is beginning to change and the hope for warmer days is ahead.  As we all adapt to social distancing, online learning, and massive stagnation in the economy, it is worth remembering that we still have many blessings.  Despite the strains on our medical system, on our infrastructure, and on our common spiritual and mental well-being, most of us are healthy and sound and will see this troubling time through.  Far more concerning is whether many of our most basic rights will make through unscathed.  That, of course, is up to each of us and only time will tell.

Now onto the columns.

Random chance.  A common phrase that gets bandied about in routine conversation.  But precisely defining what is and is not random is surprising hard to do.  Aristotle To Digital presents a few aspects of the amazingly rich structure found when considering random events with no patterns.

As the Corona virus alters life in the United States, there are things to gladden the soul, to madden the heart, and to disgust common sense and good taste.  As social beings, we can’t help but live in a collective economy where we all depend on each other.  Common Cents presents the good, the bad, and the ugly of living in the socially-distant world of COVID-19.

Somewhere in an introductory physics class, the student briefly encounters simple fluid flow and, typically, Bernoulli’s equation with its accompanying notion of streamlines.  These presentations rarely impart the richness and complexity of real fluid flow, fail utterly to emphasize how important fluid dynamics is in wide swaths of physical research, and sell short the variety of descriptions and tools that practitioners use to understand.  This month’s Under The Hood tries to address this last point by looking at path-, streak-, and streamlines and showing how even simple-looking situations can lead to some counter-intuitive conclusions.