As advertised, the Blog Wyrm staff journeyed to Mallorca last month to see the eclipse (more on this below) and we are indeed back this month – at least somewhat.  Let’s take these points in opposite order.  While we are, as is our custom, providing an intro blog this month (which you are obviously reading), our satellite columns exist in a state of completion ranging from mostly done to just in the conception stage.  As a result, while this intro will be as insightful and enjoyable as our others (to the degree that they are insightful and enjoyable at all) we will not be saying ‘now onto the columns’.  Our primary excuse is one of good and noble origin – school has started this past month.  What does that have to do with our staff, you may ask?  The simple answer is that members of our staff have stepped up and volunteered to teach classes in a local school that were abandoned by the instructor of record.  A necessary requirement is that our enjoyable but highly non-remunerative pursuits must take a back seat. 

With that preliminary discussion out of the way, let’s talk a bit about the beautiful world in which we live.  The total solar eclipse took place on Aug 12^th and our staff journeyed to the Spanish island of Mallorca to witness.

The path of totality, shown in red in the above path terminated over the Mediterranean Sea with the Sun a mere handful of degrees above the horizon.  And while the pure beauty was somewhat marred by some ill-placed clouds, there was no doubt that God’s handiwork is truly amazing, beautiful, and wonderfully harmonious.

This is a point that each of us would do well in remembering.  That regardless of how strident and clamorous is the drum-beat of negativity that comes from our professional talking heads, our world is fundamentally good.  That does not mean that all events that take place on the ‘stage’ are ones that always result in our immediate benefit.  Rather that the words of that hellhound of Scotland who asserted that

Life’s but a walking shadow, a poor player
That struts and frets his hour upon the stage
And then is heard no more: it is a tale
Told by an idiot, full of sound and fury
Signifying nothing

are words of despair that we should all reject for our own good and the good of those around us.

See you next month.

The Blog Wyrm staff has been out and about (even to Mallorca to see the Eclipse) this month and are taking a well-deserved summer break. Be back next month. Enjoy!

One must have been living under a rock not to have noticed the bombardment of media celebrating the 250^th Anniversary of the United States declaring independence from what the colonies believed to be insufferable tyranny.  And in typical fashion, our modern media is incapable of doing anything other than sowing discord in order to attract eyes, sell seats, and invite clicks.  What gets lost in the various attitudes – let’s make a buck, let’s show how great the country is, let’s show bad the country is, etc. – is that objectively every person living in the United States is blessed beyond the imaginings of most of the people who have ever lived or are living today.  By any objective (there’s that word again) standard, even the poorest amongst us are rich compared to all those who came before or who live elsewhere now.  But instead of taking a moment to place the United States, with all it’s successes and failures, into perspective we have decided that envy and not charity should be the default.  We would rather be unhappy because our blessings aren’t as large as some other guy’s rather than be objectively happy with those we have.  This peddling of envy for profit flies in the face of the very reasons we broke away from England – life, liberty, and the pursuit of individual happiness.  We would all do well to remember that this Fourth of July.

Now onto the columns.

After a very large slog through the inner workings of SymPy this month’s Aristotle2Digital finally arrives at the first of the rewrite rules for Fourier Transforms.  The process combines and exploits all the numerous pieces covered over the preceding posts and uses an iterative sweep through the expression tree to achieve the various transformations.  Along the way, it is worth noting just how much work it takes to do what people do without much thought.  

The previous two posts laid down the groundwork concerning the statistical underpinnings of portfolio diversification and showed how a simple parametric scan could be used to balance return and risk.  This month’s CommonCents tackles a full, nonlinear portfolio optimization the real way – with a computer.  The result is a portfolio of 5 stocks that meets nearly the maximum return while lowering the risk far below what would result from depending on one stock alone.

Since the Lagrange points of the Circular Restricted Three Body Problem are dynamic equilibria a particle placed at rest on one of them will reside there forever in the absence of any uncertainty and/or noise.  It is natural to ask, if there is uncertainty and/or noise (i.e. the real world) will the particle stay nearby or will it escape with abandon.  This month’s Aristotle2Digital answers that question by analyzing the dynamic structure of nearby motion; it finds (perhaps paradoxically for those who follow JWST) that the colinear points are unconditionally unstable.

Enjoy!

The inspiration for this month’s intro piece has come from a dark place – or more properly – a frustrating place.  Over the past several weeks I’ve had occasions to take Claude to task for some rather ridiculous snark that it felt it needed to send my way (one of which involved the UndertheHood column described below).  In each case, Claude’s assumption was to approach its answer to my question in the least charitable way possible.  As an example, I asked for it to show me syntax in a new programming language that produces a final, well-defined outcome.  I didn’t ask it to judge why I wanted to do this or whether it made ‘sense’; I simply wished to know how to do the thing and not to have what I was doing evaluated.  With quite a condescending attitude, it immediately informed me that what I wanted to do (a type of coordinate transformation) would result in ‘all zeros’ and that it would be better that I did something less trivial.  I went on to inform it that I knew that I would get all zeros, that I wanted to see that I got all zeros, and that this null result was exactly what I required before I trusted the algorithm to produce non-zero values that I wasn’t as sure of as I was of the null result.  I know that I didn’t need to inform it of anything but I was curious how it would react when I pushed back hard.

This incident, which was the hat trick of snark in the past week, was also the straw that broke the camel’s back.  It led me to consider just what is was that Claude was digesting that caused it to emulate such boorish behavior.  As I mulled it over and talked about it with friends, I accidently hit on the key word – Claude wasn’t boorish it was playing the troll.  Claude was channeling its inner troll.  Suddenly it became clear that behind every Claude or ChatGPT post there is likely an old flame from one internet troll, heaped with ample amounts of conceit, directed in a condescending fashion onto another troll who responds in like fashion.  We don’t use terms like ‘burn’ and ‘flame war’ and the like much if at all anymore but their effects are still there on the internet somewhere and so they are parts of Claude’s DNA – its version of original sin. 

The lesson I think we should all take away is that not only is online charity good for us to engage in because of the moral implications but it is also good for us to engage in because of the practical implication that what we dish out, in some digital karma fashion, will come back to us disguised as the trollish voice of an LLM.

Now onto the columns.

This month’s Aristotle2Digital explores the last ingredient needed for general term rewriting competence in Sympy, the ability to change portions of an expression tree into equivalent (structurally, mathematically, or both) expressions.  This ability will be the heart of all theorem provers and rule-based analysis that are used in mathematics (and often vex all of us doing algebra).

This month’s CommonCents looks at some of the basic ways that one can optimally diversify a portfolio so that a maximum return can be achieved given a specified risk level.  Central to this idea is the concept of ‘beta’, which measures the contribution of a given asset to an investment portfolio.

Over a century ago, Henri Poincare argued that, in some topological sense, periodic orbits are dense in the phase space of the circular restricted three body problem, effectively turning the celestial mechanics community loose with a hunting license for these special kinds of motion.  This month’s UndertheHood looks at the dynamical symmetry of the CR3BP that gives rise to periodic orbits and provides a frank critique of practical application of this approach.

Enjoy!

By the time you are reading this Memorial Day will have just passed.  As the unofficial start of summer, this holiday’s significance tends to get misplaced within the larger excitement of the end of the school year, graduation parties and celebrations, cookouts, the donning of culottes, shorts, and swimwear, and the mass migration to beaches everywhere.  However, it would be decent and wise for all of us (whether we are wearing culottes or not) to reflect on the men and women who served this country and gave their lives so that we could be as invested in our own lives and our common pursuit of happiness.  For these brave souls the pursuit stopped with death on the battlefield.  Surely, as rich as we are, we can take some time to look with gratitude and charity upon those who died so we can live.  God bless and keep them.

Now onto the columns.

This month’s Aristotle2Digital explores the basic tools that SymPy provides for query subexpressions within an expression tree.  Along the way, the difference between mathematical equivalence and structural similarity comes more clearly into focus.  The methods explored here are a steppingstone to implementing rules for term rewriting of existing expressions. 

With the underlying statistical tools now in hand, this month’s CommonCents answers the question: how can one tell if a portfolio is really diversified versus just being a collection of various assets and equities?  Since the key concept of diversification is the mitigation/reduction of risk the answer lies in finding financial instruments that are negative correlated with each other. 

Up to now, heuristic arguments have been given for the existence of five equilibrium points within the dynamics of the circular restricted three body problem.  This month’s UndertheHood elevates the argument from qualitative to quantitative showing how the critical points of the pseudopotential uniquely locate these equilibria – even if the path to three of them lies through a quintic equation.

Enjoy, remember, and pray.

The Blog Wyrm staff is taking a spring break during April and will return with new columns in May.

During the Lenten season, it is customary for the faithful to ‘give up’ something as a disciplinary exercise.  Most often, these denials will take the form of “I’ve given up cake” or “I’ve given up candy” or “I’ve given up swearing” and so on.  This are fine disciplines to be sure, but it is arguable that a more profitable discipline is one of positive rather than negative denial.  By positive denial is meant something like giving up judgementalism or giving up taking people for granted.

Now, generally, we at Blog Wyrm don’t see it as our place to suggest changes to anyone’s discipline but lately we can’t escape that the world as a whole would be well-served if everyone followed one of these positive denials and started acting towards each other with more charity and less ‘attitude’.  Sadly, hoping for this may be just as futile as believing in the Easter Bunny.  Nonetheless, we can hope and wish all a blessed Easter.

At the heart of most (if not all) computer algebra systems is a tree structure that represents any expression in terms of nodes and leaves.  Being able to transition from shallow tinkering with an expression into detailed algorithmic manipulation requires being able to traverse a tree and find patterns within it.  This month’s Aristotle2Digital shows how to determine if two tree structures are identical in SymPy, which is the necessary first step in that transition.

Ask any financial advisor and the third thing they’ll likely tell you (after stressing that they are the best while reminding you that past performance is no indication of future returns) that diversification is the key to a sound portfolio.  But what does diversification really mean or, more importantly, how does one actually pick assets so that diversification goals are met.  This month’s CommonCents looks at the statistics underlying those choices.

The circular restricted three body problem is famous for being effectively impossible to solve in any reasonable analytic way.  The practitioner is forced to use a blend focused analytic techniques, numerical modeling, and qualitative/topological arguments based on the structure of the problem.  This month’s UndertheHood presents a classic method of the last category:  Surfaces of Zero Relative Velocity.

Enjoy!

The year was 2001; the month December.  A new form of transportation was breaking into the public consciousness – The Segway.  Pundits, commentators, and the tech-savvy early adopters told us all about how this new form of personal transportation would shape the way we interact with the world.  But… it never lived up to the hype.

The year is around 2020 (no SeaLab though); no clear month.  But a new form of AI was breaking into the public consciousness – The Large Language Model (LLM) chatbot.  Admitted much more popular and widely adopted than the Segway, the likes of Chat GPT and Claude and Grok and Co-Pilot and…the list goes on and on have actually changed how we do things.  But… will it live up to the hype?

Obviously, since I am comparing the two, it should be clear that I believe the answer to be no.  The reason for that is as a daily user of Chat GPT and Co-Pilot I understand what they are good for and what is AI Snake Oil.  Even in areas where LLMs are supposed to succeed the dreams of a future where ‘AI’ frees us from work are just that dreams. 

There are numerous examples of the dark side of AI.  I don’t mean that AI is putting people out of jobs (although that is sadly true) but rather the contrary that AI hype has fooled businesses into stupidity in adopting the technology.  A sample of the cautionary tales include:

• Gary Marcus on Steve Eisman’s (of the Big Short fame) podcast cautioning against LLMs

• Havard Business School on navigating the jagged frontier of AI (i.e., LLMs) whose key takeaway is that just because an LLM is good with one human problem doesn’t mean it is good with similar ones.
• Cold Fusion’s report that AI fails at 96% of jobs based on Scale AI’s Remote Labor Index (link to their study).

LLMs (and their more sophisticated agentic spawn) can be useful for some things, like designing code if (a big if) the design pattern has been discussed at length by humans within the ecosystem of the internet.  But (a big but) if you are trying to do something off the beaten path they suck – plain and simple.  They are smug and irretrievable wrong at the same time.  A dangerous combination.

Now onto the columns.

One such task that LLMs simply fail at is being able to design a rule-based term rewriting system for computer algebra systems.  Using computers to simplify expressions of all sort is a dream that has been alive for centuries and it seems only incremental progress has been made.  This month’s Aristotle2Digital explores the low-level, narrowly scoped basic simplification routines in SymPy, demonstrated again that the human aptitude for this kind of task is still unequaled.    

Finance’s basic tools find themselves at the intersection of economics and accounting.  The former explains the basic interactions between economic objects and agents and the latter assigns values to them.  This month’s CommonCents continues the New Year’s resolution of working through Chapter 2 of the college-level finance book by van der Wijst.

On the most challenging of the classical physics problems is the gravitational interaction of more than three bodies.  This month’s UndertheHood continues its exploration of the circular restricted three-body problem showing how graphical analysis of Jacobi’s pseudopotential can inform us of a number of important results including the existence of the Lagrange points, around which one of the most complex machines ever built by man orbits.

Enjoy!

I have often joked with friends and colleagues that if I ever ran for public office that my platform would consist of only two planks, both of them associated with the science and civilian discipline of timekeeping. 

The first is one that I believe everyone has experience with and that most people are quite fed up with: the twice-per-year switch between standard and daylight savings time.  The arguments are all quite familiar and I won’t rehash them here.  I will simply say that we should pick one stick with it. 

The second of the timekeeping policy items is known only to a very small percentage of people in the world: the leap second.  A lead second is an extra second added when it is deemed needed.  This extra second can only appear as the very last second of June 30^th  or December 31^st of any given year.  Each these ‘special’ days would then span 86,401 seconds compared to the usual 86,400 seconds that every other day of the year enjoys.  To complicate matters, not every June 30th or December 31st gets a leap second.  Inclusion or omission of the leap second is done specifically to satisfy astronomical requirements that locate the Earth’s prime meridian against the fixed stars. The idea being noon at Greenwich should be the time when the sun is directly overhead. Of course, this is ludicrous and ridiculous to allow astronomers to drive civilian time keeping worldwide

To illustrate just how ridiculous it is, the figure below shows the official US time from the US Naval Observatory and the breadth of each time zone.

Focus in on the Eastern Time zone and you’ll notice that the region stretches between the eastern edge of Maine and the western edge of the Upper Peninsula of Michigan.  But let’s confine ourselves to just the contiguous states and allow the Yoopers to be left alone for another discussion.  After a few simple prompts one can find that the eastern most town, city, or village is Eastport, Maine at a longitude of 67°W and that the westernmost town, city or village of Indiana is Mount Vernon at a longitude of 86.5°W. Those longitudes are separated by nearly 20 full degrees, meaning that the sun, which moves from our perception on the Earth 15° per hour, sets over an hour and 20 minutes earlier Eastport that it does in Mount Vernon.  And yet we worry about including a leap second to precisely (to within a half of a second) get the Sun at its zenith at noon in Greenwich.  We spend an enormous amount of effort putting that bloody little leap second in for the benefit of almost nobody, regardless of how wonderful the discoveries are of the astronomical community. Now on to the columns.

One of the classic problems of symbolic artificial intelligence is trying to get a computer system to navigate through mathematical expressions the way a human can. Despite the fact that many of us groaned when we were in 7th or 8th grade and first learning algebra and that lots of people believe they’re simply bad at math, human beings have a wonderful faculty for seeing patterns and equating things that may on the surface not look the same, and rearranging terms within an equation. This month’s Aristotle2Digital tries to explore what it takes to implement the computer algebra system SymPy (part of the Python ecosystem) so that it is able to work with even a fraction of the facility that a human being does.

Each New Years, millions of people make resolutions: lose weight, date more, do something that scares you each day, and so on. Well, this year it seemed that it might be interesting and profitable to work through an entire book of finance and see what lessons about time and money are contained. This month’s CommonCents starts a year-long exploration through Finance: A Quantitative Introduction by Nico van der Wijst.  As with any resolution, we’ll just have to wait to see where it ends.

One of the most impressive machines of scientific discovery that has ever been made is the James Webb Space Telescope (JWST).  JWST is a marvel of scientific and engineering know-how and part of its ‘magic’ is the fact that it orbits around an empty point in space so-called around the L2 liberation point of the Sun Earth moon system. This month’s UndertheHood continues its investigation into the circular restricted three-body problem which is the theoretical underpinning for how JWST floats around nothing.

Enjoy.

Over a year and a half ago our internet service provider produced a systemic fault in all of our blogs and, over the course of a few days, Blog Wyrm was off of the web.  It’s taken some time and some ingenuity and experimentation to fit a refurbishing into our otherwise very hectic lives but we’ve managed it just in time to welcome a new year.  Almost all of the previous posts have made it and we’ll be fixing the handful of ones that suffered some loss over the coming months.

And speaking of a new year, let us wish everyone a Merry Christmas and a Happy New Year, and Peace on Earth to people of good will.  May God bless.

Now onto the columns.

Society deems a working knowledge of algebra, or at least a passing familiarity with it, as essential for most of its members.  Most of us are exposed to algebra in middle school and somehow or another we learn to write and solve equations, even if we don’t quite know how.  However, computers lack the intuitive learning of humans and teaching a machine to ‘do’ algebra is one of the classic problems of artificial intelligence.  This month, Aristotle2Digital takes a looks at some of the technology required to manipulate mathematical expressions by looking developing a rule-based system in the SymPy package in Python.

There are many ways for a human enterprise to fail.  The product may be superior in some way but inferior in another, more important way.  The effort may be sabotaged by fraud or theft.  The timing may not be write and so on.  But those failures were failures without being blunders.  True blunders come when the people on that enterprise blur the lines separating what it is they are doing from how they should do it.  CommonCents examines two separate anecdotes where the blurring between ‘what’ and ‘how’ lead ultimately to catastrophe.

Few problems in classical physics are as celebrated as the circular restricted three-body problem (CR3BP).  Once the playground of mathematicians and physicists, the CR3BP  has had something of a resurgence as numerous spacecraft missions have targeted either the Sun-Earth/Moon L1 or L2 libration points.  UndertheHood starts a multi-part investigation of the CR3BP, which, along the way, will show us the ins and outs of how the James Webb Space Telescope (JWST) takes the beautiful pictures that it does.

Enjoy!