I hate the units which you cannot easily add: 10 micromorts + 10 micromorts = 19,999999 micromorts
500 milimorts + 500 milimorts = 750 milimorts
Playing russian roulette using a sixshooter loaded with 3 rounds is 50% chance of death. It's 75% if you do another try. "Adding" another try does not translate to "adding" the metric. It just adds confusion.
To expand on barbegal's comment, in my opinion the genius of the "micromort" unit is the observation is that you can add them.
In fact, 10 micromorts + 10 micromorts is 19.9999 micromorts (you have too many nines). But within the relevant standard of accuracy, 19.9999 = 20.
The same is true for more complicated estimates. For example, 10 micromorts every day for a year is 3643.3 micromorts, which is practically 10 times 365.
It's not completely accurate, but it's certainly good enough for the intended flavor of computation.
Also, as you observed, the system breaks down with large probabilities. I think a good analogy here is Newtonian mechanics. If you drop a ball of a building, and want to know how long it will take to fall, then for all practical purposes you can ignore the effects of relativity. But if you were to throw the ball at half the speed of light, then you would need to be more careful. (In more ways than one...)
I guess it depends on how you're adding those 50% together: add three bullets to a 6 chamber revolver for a game of Russian roulette and 3 bullets = 50% chance of death. If you take two tries, sure, that's not 100% chance of death. But 3 bullets = 50% chance, so if you add another another 3 bullets then those percentages combine quite well for 100% chance of death :)
(assuming your aim is good & lethality on hit is 100%)
Of course, even your example units don't always behave like you want. For velocities, 150 megameters/second + 150 megameters/second ≈ 240 megameters/second.
Sorry, can you explain why the velocities should add that way? I've always just seen velocities add like regular old vectors, so this looks very strange.
Well, then you're gonna love electrical engineering: Adding a 10 Ohm resistor in parallel to another 10 Ohm resistor gives you a total resistance of 5 Ohm. Which is why you don't write 10 Ohm + 10 Ohm in this case, but 10 Ohm || 10 Ohm = 5 Ohm.
This would solve your problem as well – just overload a different operator: 500 millimorts || 500 millimorts = 750 millimorts.
lol i don't know why this is being downvoted it just plainly wasn't a good example to use... there are two ways to combine resistors and they just arbitrarily took the one that doesn't add linearly, while the other one... does. and if you asked me (ie a layman) to "add two resistors together", i sure as hell wouldn't wire them in parallel lol.
> [...] it just plainly wasn't a good example to use... there are two ways to combine resistors and they just arbitrarily took the one that doesn't add linearly [...]
Nothing arbitrary about it. But if you don't like putting resistors in parallel, go ahead and put them in a series, and then compute the electrical conductance of the pair:
10 S "+" 10 S = 5 S
("S" is Siemens)
> and if you asked me (ie a layman) to "add two resistors together", i sure as hell wouldn't wire them in parallel lol
Maybe that's the reason why people don't ask you to fix their wiring or to design their schematics for them? Parallel impedances are just as ubiquitous and important as serial ones.
So in your particular example you can't add micromorts - you can only die once, so if you die in the first round, you don't get to play the second round. And if you could, the number of known-to-be-empty-chambers and/or bullets has changed, which changes the probability.
But you can add micromorts in the case where n people are playing separate games of Russian Roulette.
As another example, the Wikipedia page says that this is equivalent to 1 micromort:
> Traveling 6000 miles (10,000 km) by jet (cancer due to increased background radiation)
If you're just trying to calculate your own risk as a passenger, you can't just multiply 1 micromort by the number of 10,000 km trips you take. But if you're operating a flight, then you can multiply it by the number of passengers on this 10,000 km flight.
It has more to do with the nature of the thing you're trying to model, than it does with the nature of the unit.
In almost all cases adding is a valid approximation. Until you get into the 10s or 100s of milimorts range you can add them and the error will be less than 1%.
I think a better way is to say that 500 millimort + 500 millimort = 1000 millimort like normallly. And then say that you can't add millimorts of successive events to get the millimorts of the sequence.
That doesn't make sense to me: 500 millimorts means "50% chance of death." 1000 millimorts means "100% chance of death." Flipping a coin twice doesn't guarantee that you got heads.
his point is that the problem is not that you can never add millimorts together, but rather people try to add them together when the two things being added are correlated. i can add the millimorts of playing russian roulette once w/ the millimorts of playing 5 more rounds with the same gun just fine.
I think you have it backwards. The addition fails hardest when things are independent - which is true of most millimort risks in these tables. Smoking a cigarette and riding a motorcycle are totally uncorrelated in terms of how they cause death, so adding their millimorts naively won’t work at all.
I'd argue adding is the right calculation in many situations, since in most cases you wouldn't receive the benefits of the next risk if you die the first time.
So for example, if working in a coal mine is 10 micromorts per work day, and you choose to do it each day, it seems pretty reasonable to call that 10 * 5 days * 50 work weeks = 2500 micromorts per year. You're "paying" that cost each time you decide to go to work, and if you decide to work next year it won't somehow "cost" less micromorts – the possible yous who died last year won't be around to make the decision.
First, yes, if you want to figure out your chance of dying from doing two things, you would have to do the math as you describe.
You’re Russian roulette example isn’t a problem with the units. The chance of the bullet firing is not constant in each round, which is why the odds work as you describe. Each round has a different micromort number.
The point of a micromort is to compare activities for risk, not to calculate the total chance of dying after some series of activities. That would be impossible anyway; there are infinite activities you go through, each with their own micromort level.
from NYT: Converting this to micromort language, an individual living in New York City has experienced roughly 50 additional micromorts of risk per day because of Covid-19. That means you were roughly twice as likely to die as you would have been if you were serving in the U.S. armed forces in Afghanistan throughout 2010
And Bill Gates and I have an average net worth in the billions of dollars.
Point is that we know Covid has very different risk profiles based on who you are. Saying "That means you were roughly twice as likely to die as you would have been if you were serving in the U.S. armed forces in Afghanistan throughout 2010" probably underestimates your risk if you live in a nursing home, but it vastly, vastly overestimates your risk if you're 20 and in good health.
If you're interested in your own, personal, risk, then you can keep applying factors relevant to your situation and get a more refined estimate.
I don't see that as an issue with the measure.
Moreover, average micromort increase in a population is a useful metric, in the same way GDP is a useful metric, even if your individual productivity is very different.
it's not a criticism of the measure, it's a (correct) criticism of people using averages in misleading/wrong ways.
though i'm actually a big fan of this unit (e.g. as an expression of the relative risks of various activities), it's clear from the comments section that when people are presented with a simple number they tend to treat the underlying reality that it reflects as simple too. this is FAR from the only domain where people reduce complicated things to scalars, and then do atrocious, hideous, unspeakable things to those scalars (take standard deviations, %changes over time, and the like), and then make claims about reality based on the results of those mathematical perversions (i take particular aim at the social sciences here. sorry. they certainly don't have a monopoly on statistical innumeracy, but their domain is just more rife for this sort of abuse).
Micromorts feature a fair amount on Tim Harford's excellent More or Less¹ show. It strikes me that people who like the micromort as a topic would probably find the podcast generally interesting too.
Edit: After following dang's links to previous micromort discussions I see that other people will bring up More or Less in these threads too ;)
The value here I mostly see is comparative - would you rather smoke N cigarettes or have Y steaks? That kind of tradeoff comparison tends to be what people are better at, and is what tends to modify my own behavior the most.
I was surprised to see that 1 cigarette equals to about 140 charcoal-broiled steaks. From this point of view, you should never ever in your life worry about eating charcoal-broiled steak.
I think about this sometimes from a slightly different angle - not the "expected value" number of deaths, but rather the (utilitarian?) math of actions which affect a huge number of people a little bit each. If you waste, say, 5 minutes each of a million people's time, in some sense that's almost 10 years of life lost. I think about this a lot when there are discussions about whether performance matters any more in software.
It would be more interesting to break these down. Example, "Travelling 6 miles (9.7 km) by motorbike (accident) = 1 micromort"
That can be broken down to motorcycle on the freeway (light traffic) vs congested city vs N traffic lights vs curvy mountain roads, riding around sunset, etc.
Knowing how dangerous something is in aggregate is not as useful as the specifics.
This is a problem for both the people who are and are not interested in participating in extreme behavior.
Those who are will more likely have a false sense of lower risk than their actions would subject them to. Those who aren't might be scared away by a larger value than they would actually be subject to.
This could even become a self fulfilling prophecy where activities with high average micromorts will only attract people more willing to engage in risky behavior, thus inflating the tail of extreme behavior that causes most of the mortality, increasing the activity's average micromorts over time.
Does anyone remember the scifi short story where the whole economy is based on micromort credits? E.g. a nice dinner might be 2 micromorts. To pay for it you stick your finger in a device that does absolutely nothing 999,998 times out of a million, and kills you the other 2 times.
Since everyone starts with the same number of credits, I suppose that's a sort of equity.
There was an episode of Sliders where you can withdraw however much money you want from an ATM, but each dollar is a ticket in a euthanasia raffle to keep overpopulation down. A little different from micromorts though.
Interesting. I've recently been thinking of something similar as a form of population control in a post-aging world. Rather than individual resource consumption, every time you reproduce, you jump forward in the euthanasia line. I suspect this would not work very well.
There's got to be some more formal line of research or thought about population management in a post-aging world.
Well the general Sci-Fi solution is some form of galactic expansion, sometimes preceded by a massive die off before people get the point that their planet has exceeded maximum capacity.
As per our current science, we're forever limited to our galactic local group. Exponential growth tends to consume even very big things surprisingly quickly.
I also question whether a mass die off event on this planet won't lock us out from ever rebuilding a spacefaring civilization. We've already used up all the readily accessible fossil fuel that was necessary for us to get this far.
But what are the alternatives if people stop dying of old age? If the birth rate is even marginally higher than the very small death rate, we eventually over populate. The only way to resolve that is some kind of culling mechanism. War, starvation, and disease are what usually happens to humanity when resources get too constrained.
I wonder how many micromorts a shotgun to the head would be. A million? Ten million? A hundred million? And what would the LD50 of micromorts be? 500k?
It's probably easier to think about how rare it'd be to survive a shotgun blast to the head. Maybe one a million chance? It's happened before. So perhaps 999,999 micromorts.
People survive self-inflicted shotgun blasts. I understand because they flinch as they fire and the shot is not "head on". A notibil eexample is from the 1990 Judas Priest lawsuit.
"[] placed a 12-gauge shotgun under his own chin and proceeded to fire the weapon, dying instantly. [] followed, but survived the self-inflicted gunshot wound with a severely disfigured face"
The first thing I did back in February with the Coronavirus was figure out how much coming down with it would increase my yearly exposure to micromorts (it doubled it). That was good for figuring out how afraid I should be compared to other sources of danger in my life.
"doubled" sounds ominous. twice tiny is still tiny.
for instance, flying 100 times/year (100 times tiny risk) is hardly riskier than flying once (tiny risk). most people don't even give that risk a second thought.
How did you go about calculating that? Did you just use the deaths / population measure that the Wikipedia article mentions, or was it trickier than that? Sounds like a "fun" way to calculate risk.
That's great and all but did you also consider your impact on others? Also, I sincerely doubt you were able to get an accurate picture of risk in February.
That is an interesting limitation of micromorts in this context—-they’re kind of statistically focused on the individual.
I wonder if there’s some similar measure where we could basically treat everyone as slightly radioactive. Entering an enclosed space would reduce the maximum separation of everyone and increase the minimum possible exposure (and by consequence, everyone’s chance of death).
Since we’d then have a useful quantity to measure and track, we could then do accounting with our risk of death by COVID-19 (i.e. “I’m not going to the store today because I’m over my exposure limit for the week”)
Oh, I wasn't really thinking about my impact on others until I was considering whether to go to MODEX early in March. But early estimates of SARS-2 lethality from February have stood up pretty well even if we didn't understand many of the mechanisms at the time. For instance at the time I was very worried about Covid-19's effect on the brain and had no idea that clotting could be an issue.
There are ways to figure that out based on average infection chains and risk, and I've done this for flu. But you couldn't do that now with available information. The value you'd get is highly dependent on the R_naught (which you can get a reasonable guess of right now) and the percentage of the population which ultimately gets infected. (Which is a much more uncertain value.)
500 milimorts + 500 milimorts = 750 milimorts
Playing russian roulette using a sixshooter loaded with 3 rounds is 50% chance of death. It's 75% if you do another try. "Adding" another try does not translate to "adding" the metric. It just adds confusion.