Engineering stuff people often miss

Area under the curve versus peak height of curve

• Distance traveled is the integral of speed over time; that is, if you graph speed over time, the area under that curve is distance.  The tortoise wins the race because it applies a low speed, but continuously, whereas the hare attains high speeds for only a few short amounts of time.
• Yield force versus work to destroy; a carbon fiber bicycle fork will withstand a tremendous force, but if that force is exceeded, it takes little work to completely destroy it, where a steel fork will yield at a lower force but continue to resist, tortoise-like, requiring much more energy to actually destroy it.
• Time with mask off versus risk per minute.  If the guard at airport security asks you to take your mask down for 5 seconds and your mask is 99% effective, that is the same risk as waiting for your plane (mask on) for 500 seconds, or less than 9 minutes.  How long do you wait for your plane, how long do you spend in the plane?  Yes your risk is briefly very high, but, BRIEFLY, the total risk does not change by much.

You get what you optimize what you measure

• Focus on mass transit cost, not mass transit service.  The MBTA that we have in 2023 is the result of years of measuring and optimizing cost instead of service.  What we got, is worse service.  If someone makes a lot of noise about controlling costs and does not make as much noise about maintaining or improving service, expect worse service.
• Is it more important to ride your bicycle as fast as possible when you ride it, or more important to ride your bicycle for as many miles as possible?  The inconvenience of attaining ultimate speed may cause you to ride less often (see also, tortoise, hare, area under the curve)
• Road design focused on throughput for cars instead of people movement or people safety.  Why would you expect this to produce safety, if that is neither measured nor optimized? The result is some of the least-safe roads in the OECD. (No, this is not just because we drive a lot, though good for you that you notice the risk multiplier of excess driving. We DO drive a lot, but we’re also pretty bad at safety per kilometer.)

The Intermediate Value Theorem

• If your function of x has a low value for Xsmall and a high value for Xlarge, then somewhere in between those two points, it has intermediate values.  An example where this is relevant is considering the effect of bicycle speed on bicycle safety, versus motorcycle speed and safety.  You may not know this, but per-trip, riding a motorcycle is 25 times more likely to result in a crash death than riding a bicycle.  Lots of people like e-bikes and other forms of bicycle assist because they “feel safer”, but the given measured unsafely of riding a motorcycle at motorcycle speeds, there has to be some bicycle speed at which the risk quits declining and starts increasing.

Exponential functions

• Any non-constant dollar graph of anything financial will always look like a hockey stick because inflation is exponential.  Don’t be swayed by such graphs.
• On a log scale, you can see that the “September” upward trend in Covid levels began in late June.
• From @vb_jens / https://github.com/mountainMath/xkcd_exponential