I get excited about edge cases. This is why it’s called Crisis on Varia, and not ‘Stasis’ on Varia. In a normal distribution, which purports to characterize the relative occurrence of unusual situations relative to the common, there are both left (bad) and right (good) tail events — crisis tends to imply more of a left tail bias, but I’d argue that many right tail events can indirectly catalyze crises as well.
I’ve often thought that my sensitivity to edge cases was related to my training in financial derivatives, many of which essentially involve thinking about the likelihood of unlikely events, and then using leverage to take positions on those views. Temperamentally, I prefer to make long shot bets which tend to lose more often but have outsized payoffs, than bets on favorites which win more frequently, but with only small rewards. The sad story of the person who bet the Chargers would defeat the Jaguars last year in the NFL playoffs after running out to a 27-0 halftime lead is an example of a bet I would be more likely to take the long shot position, given the payoffs.
Definitions
Just to be clear about what we’re discussing, edge cases are situations which are the result of some extreme parameter — i.e. they are outside of normal expectations. Corner cases are the result of multiple extreme parameters — in common parlance they are “perfect storms” — a term which is used so frequently that either they aren’t that rare, or people exaggerate circumstances to diminish their own responsibility.
The edge case term is primarily used in computer programming, AI, and machine learning, but I think the concept is useful as applied to real life as well. They are slightly different from boundary conditions, which describe the range of possible (including extreme) parameters — so boundary conditions explain what is impossible, edge cases describe what is highly unlikely but still possible.
As far as I’m aware, the idea of ‘penalty functions’ (the relative difficulty of the solutions to edge cases) isn’t part of the traditional thought process, although I think it should be, because all edge cases were not created equal.
Real world examples
The EV vs traditional car question
The edge case concept is useful in thinking about whether to buy an electric vehicle (EV), for instance. The extreme values of these edge cases are either running low on fuel, or being in unfamiliar territory, but they have to be combined with the penalty function of recharging differentials of EVs and traditional cars.
Usage: because personal cars are primarily used for defined (commuting to work or school) or short trips with primarily one passenger, EVs work well in these well defined ‘normal’ situations, because the trips are short enough that we don’t need to recharge, or because the recharging solution is well known in advance (and reliable). However, the edge cases of our usage (road trips to unfamiliar areas, in addition to carrying multiple passengers or large items, etc) are the less frequent situations where commuter-focused EVs have trouble, because of the penalty dimension below.
Recharging penalty: the recharging infrastructure in most countries other than Norway or small city/states like Hong Kong and Singapore is far less built out than the traditional network of gas stations. While the quotidian task of recharging is largely similar to filling up a gas tank (except far more frequently), once someone strays from the usual routine on a road trip, the issue of range anxiety starts to create static discharge. Unlike traditional fossil fuel vehicles, where someone can pull up with a few gallons of gas to get you to the nearest station, EVs which completely run out of power need to be towed away, which is a far greater hassle. The “close to the edge” cases aren’t great either — if the EV battery is low but hasn’t fully run down, a significant percentage of the ‘last chance’ charging stations will require long charging times (especially as one ventures far from urban centers, which one is likely to do on a road trip), and there will be few alternatives; whereas even the dinkiest gas station in the middle of nowhere can fill up your environmentally unfriendly gas powered car on the road in about 10 minutes.
Because Tesla has built out a (currently) superior charging infrastructure, with a large number of fast superchargers, the “safe” zone of Teslas is broader than non-Tesla EVs (and may be Tesla’s strongest moat) — but it the supercharger zone is defined by Tesla and this may not help you if you are looking to head up to Crater Lake in Oregon (there is one slow Tesla Destination Charger, and another (slow) Level 2 charger in Klamath County, about 7 miles from the lodge at Crater Lake). I mention Crater Lake because I was running out of gas when I visited in June 2020 and was relieved to get a full tank of gas in 10 minutes next to the gift shop. Plus when you factor in the effect that low temperatures and mountain driving have on realized EV range, this only adds to EV range anxiety.
As another solution to the climate crisis / high gas prices / range anxiety optimization problem, hybrid sales are up dramatically, rising 48% (Jan-Sep, YoY), with Toyota’s hybrid models in particular all at record setting levels.
However, there is another (admittedly more expensive) solution to this edge case dilemma: buy a (used) gas powered SUV to deal with those edge cases. It makes sense to make it a used car because it won’t be your primary car; an SUV makes sense because it can handle both road trips and uncertain charging destinations, as well as the ability to carry cargo and more passengers. This ‘solution’ assumes you have enough room in your garage, and don’t mind paying for insurance for the additional car… if that doesn’t work, then renting an SUV for road trips probably makes more sense, even if it’s not available at a moment’s notice.
In the US, the attraction and importance of the personal vehicle is the sheer freedom it affords, but in tying you to a not-ready-for-prime-time charging infrastructure (less so for Tesla owners), this ‘freedom’ is materially curtailed. If you have to meticulously map out a road trip based on charging facilities and alternatives, the spontaneous vibe of road trip movies like Easy Rider (1969) is sadly lost.
Travel: geographical edge cases
Like any new experience, the dimension of travel can be full of edge cases from an individual perspective because the world is large, complex, and ever-changing. For people who travel very little, every little step is new, stressful, and unfamiliar. For those who travel a lot, there are far fewer edge cases in the cities and countries that are well known to them, and there is a meta-level confidence that they have the skills to figure out travel related situations, because travelers necessarily build up those problem solving muscles. In places they have lived before, the only edge cases will be areas where there have been changes.
In post-COVID Hong Kong, I activated my normal pre-COVID exit routine by going to the In-town Check-in at Hong Kong Station, only to discover that that function had been completely closed and the check-in process could only be done at the airport. Fortunately I had budgeted more time than usual (part of the meta-level flexibility) and it wasn’t an issue. For the record, In-town Check-in opened again in July 2023, but only for passengers on Cathay Pacific. I once tried to fly to Brazil without a visa, not knowing that the visa rules had changed in the year since I last went to Brazil, because of a US-Brazil diplomatic spat of which I was unaware.
Venturing to a totally new place, even for experienced nomads, means trying to find out as much about those unknown areas as possible, or piggybacking off someone who does — but finding trustworthy guides can often be a dicey proposition (see my recent issue on trust).
The penalty function for travel-related edge cases can be considerable, since the rules and regulations can vary widely from one’s home country. I once tried to bring a small bottle of whiskey into Kuwait, where alcohol consumption is illegal — it was discovered in the luggage x-ray — I had merely assumed that the penalty wouldn’t be large but I didn’t know… thankfully they just confiscated the errant bottle rather than chopping my hand off. But whether it’s bringing legal marijuana from the US to a country where it is illegal, to the extreme of bringing drugs to non-tolerant countries like Singapore, the penalties for making erroneous assumptions in unfamiliar territories can be very high indeed. And since not only the systems (medical, police, judicial, customs, immigration) have different protocols but probably a different language, this can further complicate the ability to navigate the penalty functions.
Edginess in entertainment
At a higher level, the primary focus of entertainment is finding edge cases, because they are what the masses in the middle find ‘interesting.’ Hence the disproportionate representation of murders, shootings, and car crashes in action movies (and the dearth of traffic which enable the high speed chases!), as well as the sheer number of convenient coincidental meetings, meet-cutes, and love-at-first-sight moments (to say nothing of improbable happy endings) in romances and romantic comedies. Every hero seems to have the perfect funny thing to say at just the right moment (unlike real life), and the carefully chosen music usually amplifies the emotional experience.
[Related aside: I remember a moment in a taxi to CDG airport along the Quai du Louvre, where the radio music (Bach’s Air on the G-string?) was perfect for the melancholy but romantic feeling I had about leaving Paris on Sunday spring morning, and it did feel a little like being happily followed by the sound designer from Before Sunrise.]
Since we are not very entertained by the purely ordinary, it is normal to feature a combination of ordinary and extraordinary (so we can both relate to it, while finding it entertaining): the everyman superhero (Nobody and the Equalizer, for instance), or just the story of someone truly ordinary where there is a hidden edge case (Searching for Sugarman). Even “reality TV” is a total misnomer — if we are being truthful, it highlights the most extreme (interesting) things that happen within a reality context which has been artificially manufactured to heighten the potential dynamic tension… which isn’t very realistic, but it can be amusing.
Edge cases in finance
Investing is easy, because over the long term equities, bonds, and bills go up in the long run (so sayeth Credit Suisse, over the last 123 years). But knowing what to do during the edge cases — the recessions, rallies, and revolutions — is far less clear, because thought processes about the long run turn emotional and chaotic when portfolios are plunging.
Quite a lot of macro financial research is focused on the edge cases, for precisely this reason. When equity markets rise, it’s usually gradual and sector thematic (tech or energy, for instance) rather than a broad market phenomenon; when markets crash, everything tends to implode at the same time. And it’s more subtle than that — mini-crashes happen all the time, and in the moment, it’s hard to tell which of them will become T. Rex level circular meltdowns and which are just friendly iguana-sized blips.
The near zero interest rate periods between the GFC and COVID were, in hindsight, edge cases that investors became comfortable with because they lasted so long — which is extremely unusual. But the appearance of undeniable inflationary pressure, despite Fed assurances to the contrary, have probably ended the central banks’ ability to lower rates to zero with impunity, and now the investment world finally realizes that for a period of 15 years, we were benefiting from a highly benevolent edge case where free money lubricated all sorts of rusty machinery. Those days are over, and now we return to a world where money in most places can return 5% for doing nothing, which has the effect of raising asset strategies which were previously “low-hanging fruit” to levels out of arm’s reach.
In venture capital, the general assumption is that a majority of even carefully selected investments will return nothing, but the huge returns of the positive edge cases will more than make up for the accumulated losses. A VC will spend most of their time in edge case space: they’d almost rather a company fold up than plod along, because there is an opportunity cost to spend time with any startup which isn’t going to result in an enormous return.
I would be remiss if I didn’t mention insurance, which is an entire industry focused on management of edge cases. The insurance world benefits from cognitive misunderstanding and risk aversion about edge cases with high penalty functions; diversifying their risk into collective pools enables them to provide products which seem reasonably priced, for taking away the fear of left-tailed outcomes.
Sociological edge cases
Since the GFC, the monetary tools used to stimulate growth, for the most part, drove higher returns to capital and therefore lower relative returns to labor; this in turn led to increasing levels of wealth inequality (within countries) in most advanced countries where there is a disproportionate amount of capital wealth (and tax policies which favor capital over labor).
While the Gini coefficient and income inequality progressions (both based on annual income) show more modest increases than measures of wealth concentration, the issue of income inequality is increasingly divisive because it deviates from what people feel is ‘fair’ — in addition to confusing annual income with accumulated wealth, my hypothesis is that the media’s fascination with Bernard (Arnault) / Elon / Jeff / Sam (Altman) et al has done an excellent job of lionizing and overemphasizing the wealthiest people, and making the masses deliriously envious of this relatively small category.
Walter Schiedel, in his comprehensive survey The Great Leveler, makes a reasonably strong case that continuous economic growth leads to increasing inequality; the major corrections of inequality happen for four reasons: mass mobilization wars (WWI, WWII), revolution (Russia 1917), complete state failure (the Roman Empire), or pandemics (Black Plague). He notes that magnitude is important — only true edge cases will create change — most marginal wars, attempted revolutions, or minor pandemics do not produce much of a leveling effect; even after the Civil War in the US, which was pretty comprehensive, he finds little evidence for a decline in inequality (maybe it would have been different had the poorer South won instead). COVID, for all its global reach, has indirectly made inequality worse because of economic policies which have helped the wealthy more than it has helped the un-wealthy, and because it has not led to major regime collapse (yet). So these are examples of edge case preconditions (high inequality) which can catalyze edge case responses (violent redistribution of wealth).
There have been some studies looking at youth unemployment growth, youth as a % of the population, and inflation as a foundation for popular uprisings — under this methodology, Saudi Arabia appears to be at risk, but China is following Japan in aging too quickly to have the necessary youthful tinder or revolutionary spark (according to this model, anyway).
In the legal world, contracts aim to lay out obligations and responsibilities under a wide variety of scenarios, but force majeure clauses, which would free one or both parties from obligations, are an explicit acknowledgement that there is a class of edge cases under which the contract would not be enforceable.
Finding edge cases: AI and machine learning
I was in a Bay Area brainstorming group a few years back; one evening we were discussing training AI / GPTs, and the moderator tried to induce a modicum of controversy by saying that training AIs on synthetic data would be essential for efficient future AIs, a hypothesis which we all sadly (for him) agreed. Synthetic data, as opposed to real-world data, is artificially generated, and attempts to cover the full range of potential situations the AI might encounter. In addition to compensating for issues like data-borne biases, scarcity, or privacy issues, synthetic data can be critical to train AIs to correctly identify edge cases — since those are the errors that inevitably make headlines about why AI is deeply flawed because of their capacity to “go rogue” for inexplicable reasons.
For the self-driving car problem (I prefer “autonomous vehicle” (more neutral), or even “integrated transportation system node,” which captures the idea that the future of transportation is a mesh of connected vehicles, not standalone systems for protecting dumb human drivers), training for edge cases is important because of the high penalty for errors in vehicular transport. Almost by definition, all of the errors and accidents will occur because of some edge case which the algorithm was not prepared to deal with appropriately, and in a world where autonomous vehicles, traditional low-tech vehicles, and humans interact, there will naturally be a lot of edge cases.
To this point, some of the autonomous vehicle startups have had issues with edge cases (including entry into temporarily taped-off areas and collisions with emergency vehicles, resulting in revocation of their operating license, and stimulating the exit of one of their higher profile CEOs). Even though autonomous vehicles have had no issues with texting-and-driving, drunk or sleep-deprived driving, and the usual spectrum of common human errors, these edge cases where the algorithms did not capture ‘common sense’ call into question their viability. It is important to note, however, that these vehicles will learn from these unfortunate edge cases, which should reduce the error rate over time, whereas human drivers continue to make systematic mistakes, especially as the driver pool is adding new inexperienced teenaged drivers all the time. By contrast, new autonomous vehicles are essentially just as ‘smart’ as the most experienced ones, because the algorithms learn and transfer knowledge and learning.
Nowadays, many new luxury cars have some version of super cruise control for highway driving: the system senses objects and vehicles around you as well as the road lanes, and regulates both your speed subject to a set maximum, and keeps the car in the appropriate lane (as well as driver initiated autonomous lane switching). Compared to the zero-sensor one-speed dumb cruise control of the past, this is a huge uptick for most of the (relatively boring) highway driving one does, but it leaves the human driver to control the wide variety of edge cases, which makes good sense.
Tesla and others are trying to get to full automated driving, but their handling of the edge cases will determine how accepted they become, and how quickly. Generally speaking there are too many edge cases in high flexibility high chaos environments (urban streets), compared to defined systems like train networks, which are highly rigid and controlled — full automation makes more sense in less complex systems which have fewer edge cases by definition.
Edge reflectivity
I’ve never been an adrenaline junkie, like Bodhi and his buds from Point Break, surfing, skydiving, and robbing banks — surfing out on the edges to gain perspective on the human condition, but I can appreciate the impulse for looking to the edges for revelatory experiences. Similarly, I suppose the power of near death experiences or the passing of loved ones can induce strong changes in life perspective.
At some level I suppose what’s what much of entertainment is — taking us to the edges, so we can peep through that keyhole and experience some of those emotions, while remaining safely cuddled in our comfy sofas and poofy pillows, surrounded by tortilla chips, salsa picante, and adaptive climate control.
Coincidentally, I watched an avant garde Japanese movie the other day about an ordinary salesman whose desire to make sense of his boring life leads him to a spontaneous dominatrix service (a black latex clad Amazon appears out of nowhere to kick him in the head, for instance) — enlightenment of his ultra-ordinary condition by periodic collisions with the extraordinary and uncomfortably unexpected. I did feel bad for the highly lamentable treatment of the sushi, for what it’s worth, but it definitely generated shock and awe.
Final words
My natural inclination to be a Cassandra means I spend more time than most thinking about potential edge cases, and I get excited about their probabilities and dynamics. Most people linearly extrapolate current trends, and while that’s a good approximation for short term outcomes, it can be a poor guide to the medium and long term.
Fundamentally, I think most edge cases are underestimated, underappreciated, and undervalued — Nassim Taleb has made his reputation on explaining the perception disconnect around ‘black swans’ — but his framework is probably applicable to far more than just financial markets. I feel that edge case analysis should be given more effort than it gets, both because of the empirical frequency of edge cases, and the penalty functions which accompany them.
I keep thinking of more edge case examples, so in the interest of reader sanity, I’ll leave off here.