The odds of that happening

A woman pushing a baby carriage stepped into the intersection…

Turn signals
Turn signals – plural – on the front of the car. (The little dent on the bumper was there when I bought the car.)

“Mistakes are as big as the results they cause,” said Doctor House. But few accidents or near-accidents exist in isolation: there were contributory factors, with antecedents going back more than a month.

The absence of any of those components would probably have resulted in no incident at all – just another routine day. I’m going to focus on the most mundane one: a light bulb. It was not the “cause” of the incident any more than a single pin lining up with the cylinder “causes” the lock to open. But it certainly played a part.

Analyzing a near-accident

Recently I had a near-accident with a pedestrian who was pushing a baby carriage. It would be a comically awful moment, had there been anything funny about it. It was a complex turn, the woman stepped into the intersection, I didn’t see her right away, then there was a distraction. Very nearly all the pins lined up, except she stopped in the crosswalk before reaching my path. Afterward; car is stopped, heart pounding, people arguing. Bottom line? Lucky. Just damn lucky.

Bulb lore

When a turn signal starts clicking faster than usual, it usually means a burned-out bulb. The click interval depends on the combined resistance of all the bulb filaments in the circuit. This happened in my car about 6 weeks ago, so I bought a two-pack of bulbs, replaced the bad bulb, and tossed the extra bulb into the car tool kit for later.

Just one week later, the turn signal started clicking fast again. I asked a family member to stand outside the car and observe the turn signals, and they were working. So… that’s weird. A mystery to solve later, I thought.

New and burned bulbs, compared
New and burned bulbs, compared

It didn’t take long for “later” to arrive. A woman pushing a baby carriage stepped into the complex intersection I was driving through, just as I began a turn. She wasn’t there, then I looked the other way, then there was a moment’s distraction, and then she was there. It happens to every pedestrian, every driver.

I had signaled a left turn, as the signal went “click-fast, click-fast, click-fast”. The pedestrian was standing off the front right of the car. My family member, who checked the signals, had been standing off the left side of the car. My turn signal “worked” from one point of view, but not from the other.

I pulled out the offending bulb. It had turned from clear to a milky white color.

Can you see the break in the filament? It's less than five thousandths of an inch across.
Can you see the break in the filament?

A bulb filament weighs about 0.0176 grams. Household bulbs have a coiled coil of extremely thin tungsten wire (about 0.05 mm). This automobile bulb filament is a single coil of much thicker 0.1 mm tungsten wire; clearly built for vibration resistance and lower operating voltage. When electricity passes through it, the filament heats up to about 3,000K. Most of the energy is dissipated as infrared heat, but some of it is visible light.

The glass envelope is filled with (usually) argon gas, which prevents tungsten atoms from wandering away. But eventually enough do just that, and the filament becomes thinner and thinner… and breaks. The break can be quite small; in this case about 0.2mm in length.

There it is: a break about 0.2mm in length, forming a cylinder 0.0016 mm^3 in volume
There it is: a break about 0.2mm in length, forming a cylinder 0.0016 mm^3 in volume, and weigh about 30 micrograms.

If the missing wire were sitting on your thumbnail, you would need a very good magnifier to see it at all. At about 30 micrograms, it would take a hundred pieces like that to weigh as much as a typical snowflake.

OK, so an impossibly small bit of tungsten can be a factor in a horrible accident. Changed lives from something very tiny.

But keep going: you could fit several thousand viruses into the space vacated by that bit of tungsten.

When I hear people talking about “the odds of that happening”, as if there were, even in principle, some combinatorial  algorithm that could predict an outcome, I think of Spock on Star Trek. He would often say something like “Captain, our odds of survival are 1,212.7 to 1”. And the captain would say; “One thousand, two hundred twelve to one?” Spock would reply; “Point seven. I do endeavor to be precise.”

Which is, of course, utter nonsense. Was there anything special about that particular 30 micrograms of tungsten? Of course not; it could have been a section from anywhere on the coil. Or corrosion on the bulb contacts could keep it from working. Or there could have been a burnt-out fuse. Or the pedestrian’s phone could have rung at that exact moment. Or not, which is sort of the point.

So while individual events are pretty much impossible to predict, conditions do contribute to events. A bad turn signal bulb is likely to contribute to an accident, sooner or later. But we don’t know when, or where, and I can’t tell you the odds. The frequency of accidents, in aggregate as a function of a large statistical universe is predictable. That is the work of actuaries, and is reflected in our common sense on some days. The best we can say is that it is worth continuously building better conditions… to improve our odds.

(Yes, this is a metaphor.)


  • I don’t say “near miss”.  What does that even mean? It was a near-accident, or a near-collision if you prefer.
  • To be clear, the pedestrian did nothing wrong at all.
  • See also Things We Used To Say; A Stitch In Time