Bruce Lee had a way of making everybody feel kind of okay about their mistakes, and I can appreciate that. I think we could all use a little bit more Lee way. I've been traveling more than I usually do recently, but I've noticed that when it comes to flying, there are two general categories of people. There are those who get to the airport super early. Me and their smuggly through the security checkpoint and proceed to twiddle their thumbs while they wait for their flight to board, sometimes sitting around for hours in the mind-numbing tedium of an airplane terminal. In contrast, some people prefer to breathlessly sprint to their gate, carrying their belt and passport awkwardly in one hand as they run, in the desperate hope that they'll make their flight. I fall pretty squarely into the first group, mostly because I'm an exceptionally boring person and think of airport time as an opportunity to catch up on my reading, but also because of a principle which has some curious philosophical and practical implications. We've talked in previous episodes about two central concepts for engineering, tolerance and safety factors, both of which seem to share a deep connection to the same idea, something like wiggle room or slack. Tolerance is the carefully calculated maximum amount of slop that engineers build into their designs, allowing the widest possible margin of error in the production of parts. It's much more expensive to make every single feature, every hole in plate, conform precisely to a set of exacting specifications. Engineers prefer to just calculate how bad a part can be made before it absolutely won't work. Just reject any parts that are worse than that, and you've got a much cheaper functional device. Safety factors are arbitrary multipliers that engineers throw onto their rigorous calculations to provide some margin for error. You might calculate that your bungee cord needs to withstand exactly 867.3 newtons, but end up quadrupling that number, a safety factor of 4 just to be on the safe side. You can never be sure if a sudden gust of wind or slight manufacturing defect might screw up the ideal conditions necessary for your original number to hold, so an engineer will invest in some technically extraneous beefiness to make sure that nothing unacceptably bad happens. Both tolerance and safety factors are intimately related to the idea that there should be some sort of allowance made for the variations between what's expected or hoped for in a perfect predictable world and what will probably end up happening. That is to say, something a bit worse than that. That's a good idea for all sorts of reasons, but I want to focus on one in particular. What you get in return for a little bit of extra margin. If you were of a reductionist bent, you might view these allowances as nothing more than a linear increase in the capacity of these systems. More tolerance in a bolt hole lets you match up with holes that are that much further out of spec. A larger safety factor on your bungee cord lets you deal with that much more load, but we're actually getting a great deal more than that. A part designed with much wider tolerances can sometimes be manufactured using categorically different techniques than one that needs to be tightly controlled. Other than carefully machining something using expensive CNC equipment, it might be possible to cast it in a rough mold, or even replace it with some easily purchased mass produced item. A high safety factor doesn't just allow a structure to withstand higher loads without failing. It makes it better able to resist sudden impacts. It increases its longevity and can even allow it to be used in conditions that it wasn't explicitly designed for. The offices of these observations are also true. Reducing the margins on these quantities can cause adverse consequences beyond simply reducing rated capacity. One way to think about the effects of a little extra wiggle room is the concept of degrees of freedom, the number of possible arrangements of a given set of items in a finite space. If you've ever seen one of these little sliding square puzzles, you can probably appreciate how only having one space to push squares into severely limits how many options the player has to manipulate the order of the squares. A puzzle with two spaces is much easier to solve, and with enough spaces it becomes totally trivial. The difference between just barely enough and a comfortable margin can be huge. Degrees of freedom increase combinatorially with the number of available spaces, and as we've discussed before, that function gets insanely big, insanely fast. In that vein, an engineering design with slim margins isn't just more exacting this requirements, it vastly constrains options for manufacturing, material, usage, all sorts of things. Sometimes that sacrifices necessary to achieve some other goal, but for an engineer it can be tempting to design down to the wire just to feel accomplished. There are clear corollaries of this idea for areas outside engineering. For example, in their 2012 paper titled Some Consequences of Having Two Little, Shaw and colleagues offer some observations about the psychology of poverty, how people who are struggling to make ends meet actually have different mental responses to certain stimuli than people who have more than enough resources. In one of their experiments, participants played a variant of wheel of fortune. Some test subjects were given an abundance of guesses to get the right word, while others only had a few. One might expect the total cognitive burden on a player to increase with their budget of guesses. After all, people with more turns end up thinking about and playing the game for longer than those who have fewer. But the opposite turns out to be true, having only a few tries to get the right answer created greater mental fatigue, faster, leaving poor players much more cognitively exhausted than their rich counterparts. In a different experiment, they found that players in a poverty condition were also more likely to overbarrow, taking punishingly high interest loans for short term gain and ultimately shooting their score in the foot. These results might seem counterintuitive as they undermine a player's ability to succeed if dealt a bad hand from the start, but they could be partially explained by this idea of the advantages of wiggle worm. As the authors of the paper point out, the poverty condition limits options. In the wheel of fortune game, a player with an abundance of turns can afford to throw away a few on stupid guesses, saving the mental resources that more limited players have to burn on ensuring that every turn counts. Poor players were also powerless to avoid taking brutal loans that eventually tanked their score, as the only other option was an immediate loss. Another example of the importance of wide margins can be found in Black Swan Theory, a concept popularized, vehemently, by Nossum Nicholas Taylor, numerous books and other works. Taylor notes that we generally expect the magnitude of new instances of any phenomenon to lie somewhere between its highest and lowest values that have been recorded to date, but that this approach discounts the existence of extreme values that simply haven't occurred yet, so-called Black Swan events. Black Swan events are unprecedented, sent new boundaries for what we can expect, and can't be predicted with any real certainty. If a levy is built to withstand the highest ocean levels ever recorded in an area for the past 100 years, one might very well expect it to hold against the vast majority of floods, but one might also expect it to fail in a flood the likes of which have never been seen. Such an event would be surprising, but Taylor argues it really shouldn't be. Why should we expect that the largest flood ever seen would necessarily be in the past? Shouldn't we assume that our position in history isn't privileged and place equal odds on it being in the future? With the potential for Black Swan events setting new limits for what's possible, the idea of a just barely enough approach seems obviously and woefully inadequate. It's always a gamble whether your business will have record profits or record losses any given year, but whether your building will see the worst storm that has ever happened in that part of the world, or whether you'll have the best or worst day that you've had yet. You can't really say for certain just how good or bad these scenarios will be. You can only try to build enough of a buffer into the systems designed to deal with them that Black Swan events won't immediately result in disaster. It's hard to appreciate the value of a little bit extra. Without a perfect description of all the myriad situations we might subject a particular system to, it might seem that the only result of such allowances is waste. Engineers are especially prone to scoffing and overbuilt designs that exceed their specified requirements many times over, but a little bit of wiggle room can allow space for a huge number of options, while warding off dangerous pitfalls of both psychology and the impacts of the unprecedented. At least that's what I tell myself while I wait for hours in the airport coffee shop for my plane to arrive. What instances can you think of where a little bit of wiggle room can result in huge advantages? Please leave a comment below and let me know what you think. Thank you very much for watching. Don't forget to subscribe, don't forget to subscribe, and don't stop thinking.