One of the amazing subtleties in this article... if you're a fast reader you'll stop paying attention to the stories as they go through... kind of amazing that this article is layered like that.
Second-to-last story should have been about a person that did not fall afoul of the rock. Then in the last segment ask the reader if they developed their own rock.
Generally agree with the article, though the reverse is obviously, "Heuristic which almost never works", and all the stories are about the 1 out 100000 times the weirdo was right and everyone lauded them as a genius but really they just got lucky the once.
The reverse is heuristic that works 50% of the time.
If you have heuristic that works 0.0001% of the time - it's almost as good as one that is correct 99.999% of the time. You will notice and learn to just invert it.
>The only problem is: he now provides literally no value. He’s excluded by fiat the possibility of ever being useful in any way. He could be losslessly replaced by a rock with the words “THERE ARE NO ROBBERS” on it
except for the value of having a security guard visible so that 99% of the robbers who might conceivably want to rob a Pillow Mart decide to go rob Quilting Heaven down the road instead.
Instead of a rock you just need an inflatable security guard.
What's frightening about all this is that this article has gotten 15 upvotes despite 100% of the comments so far being about what a pointless article this is.
yeah I don't know I think people might spot the difference. But maybe most of these robbers have a method that says if you see anything like a security guard don't figure out if it is one just go rob somewhere that definitely doesn't have it because there's always somewhere else to rob - but maybe one of the groups of robbers is better than everyone else and they have a real robber mastermind in charge who determines the security guard is inflatable. Then it's on.
on edit: added in missing two words that clarified meaning.
I suspect a lot of them are stopping when they see that when is bogus and aren't bothering to poke holes in the rest of them. Readers have their own heuristics, but that doesn't mean the rest of the examples aren't full of holes.
It's really not about several examples of the same thing, but interrogating our intuitions around each one. I at least found I felt differently about different heuristics being replaced by rocks.
Seems like the article writer has fallen for the very issue they're trying to portray, by writing so many examples that they've stopped thinking and just resorted to writing "PERSON CAN BE REPLACED WITH ROCK". If this isn't ironic then I don't know what is.
All of them are missing a big part of the analysis, that it is often not a choice of “a rock” but of a person with a heuristic that works way less than 99.9% of the time. A security guard that constantly harasses shoppers, a “futurist” that buys into every new fad, the conspiracy theorist that believes everything on Facebook.
Would anyone really think a weatherman that had say a 70% correct heuristic was good? Or go to a doctor like that?
I didn't unvote it and I think each of the example is missing subtle aspects.
But I think it's interesting enough to discuss. The main thing is that are a whole lot of human activities where one can imagine completely rote activity could replace thinking. But in all of these, a deeper look shows to subtle factors actually require a human being to be present.
It's a bit like self-driving cars. 90% of driving is really easy to get working. 99% is moderately hard. 100% looks like it won't arrive for quite a while.
The author is very popular among the tech/rationalist crowds (they are not the same crowd, to be clear), the topic is of interest for the same crowd, but the examples get a C-. It is challenging to write interesting and accurate pieces twice a week, and this is neither. That would be another heuristic.
It's not 99% of the robbers, you're exaggerating. Maybe at best you fool 5% of them, after all if they were that dumb to be fooled so easily they would have been caught by now. But now you have diminishing returns. Just like you, they know a security guard isn't effective, ... and down the game theory rabbit hole we go.
A coworker and I were once stuck in an office building for an hour or two. We were working as consultants at a client's building and ended up working rather late. Not particularly late by software programmer standards, but clearly exceptionally late by the culture of the client company.
At some point in the evening all the exit doors, including the front door, became armed, and this was conspicuously noted as when we packed up for the night and tried to exit to the parking lot, we realized we couldn't open the door without an alert being sent to the police (not just the security company). There should have been a guard at his station (desk, CCTVs, etc) in the entryway, but we found none.
We waited for awhile. Then we walked up, down, and through every corridor and restroom of that 4-5 story building, multiple times, looking for the guard. When that failed, we called the security company to ask them if it was okay to open the door. They swore there was a guard on duty and asked us to wait a little longer in case he was doing rounds. Despite knowing that couldn't possibly be the case, we obligingly passed more time waiting in the entryway. Then we walked up, down, and around the building again, but this time splitting up and shouting. Nothing. Nobody.
We go back down and inform the security company that we weren't going to wait any longer and that we'd be triggering the silent alarm as we left. And guess who exits the elevator just as we were about to open the door.... Apparently he had been sound asleep in a cozy nook somewhere in the upper floors--presumably in a conference room or more likely a private office, the former being something we inspected in passing (glass walls), the latter we didn't feel comfortable opening and entering, and both being the last place you'd expect to find a security guard. IIRC, he wouldn't admit it outright, but just played coy. We weren't mad. A little tired and frustrated because as consultants we still had to get in early the next morning, but that was mostly offset by the sheer absurdity of the situation, and by the fact that he seemed quite elderly.
Anyhow, you may assume too much if you assume the security guard actually maintains some kind of useful presence. I guess these days it's more common to have electronic way stations to log a guard doing rounds. I dunno if this building had such measures (this was circa 2001-2002), but as the sole guard he probably was expected to spend most of his time, if not all of his time, manning the security desk, providing ample opportunity to be doing something else, instead.
That security guard was performing the important function of allowing the management to legally tick the "we have a security guard" box on the insurance form.
That's true, but the (poorly expressed) analogy is specifically referring to the security guard's decision whether to leave his office and investigate a noise. Of course, the mere existence of the security guard in an office (if known to potential burglars) does likely provide some deterrent, but I think the analogy is referring specifically to cases where a burglar would make an attempt regardless of the burglar's knowledge of the existence of a security guard.
Specifically around the security guard example, the mere presence of a security guard should deter thieves (in theory), so I think the analysis is a little more nuanced than "security guards investigate weird noises".
Unless this all went over my head and that's all sort-of the point of what he's getting at . . ?
You'd do a lot better with one strong example rather than seven weak examples.
For instance, if you are interested in Bayes Theorem like a lot of rationalists say they are, you could talk about the medical test which is 99.99% accurate but for which 90% of the positives are false positives.
Imagine that a driver gets hit by accident. He's tested as part of company policy, and tests positive. He gets fired, even though the test only really tells us there's a 33.2% chance he was actually using the drug.
Real world drug tests are a lot worse than 1% false positive and false negative rate.
Every time someone gets fired for a positive test, or loses custody of their kid, or so on, it reinforces whatever statistics are being collected as if the test were a ground truth. They're hardly ever questioned, and there's usually no recourse without an expensive legal fight.
The false positive rate for drug dogs is higher than 40%, for contrast. When a dog "alerts" its worse than a flip of a coin. All that matters is if an officer feels like fucking up your day.
Testing used in situations that are legally significant in people's lives should be required to reach a statistically valid threshold of accuracy, like 99.999% of the times this process is performed, it matches reality. A high sensitivity and high specificity aren't enough, but they're framed as highly accurate and reliable by often well intentioned people who simply aren't thinking in a Bayesian way.
>All that matters is if an officer feels like fucking up your day.
This is what most people don't seem to get. Devices like the ADE 651 or the GT200 were bought by the thousands by law enforcement agencies worldwide, not because they were stupid, but instead, so they could have another "data point" against you that they can use at their discretion.
"Sorry, this dot blinked three times so I'm gonna have to detain you: It's standard procedure, I'm only doing my job."
What's relevant isn't whether a technology or forensic discipline is good, just whether courts will accept it.
Antonin Scalia (in)famously commented in one of the Supreme Court's dog-sniff 4th Amendment cases that obviously the police would want dogs that didn't produce false positive alerts, since they wouldn't want to waste their time searching where there were no drugs. The resulting caselaw sets up a situation where a dog can be wrong over half the time and still be used.
The concept that "probable cause on four legs" would be used simply in order to get to search where they otherwise couldn't was apparently unthinkable.
Animals are great at reading people emotionally. Given that the handler has some subjectivity odds are pretty good the handler perceives the dog alerts if the cops are themselves suspicious.
> You'd do a lot better with one strong example rather than seven weak examples
Tend to disagree. It's easy to dismiss one example as "well, medicine is special because XYZ." Multiple examples are the core aspect of showing a general pattern.
He could probably have stopped at 3, 4, or 5 though, not 7.
For the security guard, hearing a single noise is likely to be nothing. However, what if you heard two noises, and the sound of tires outside?
Same thing with the doctor. Most good doctor's I know have a sixth sense, about when something is off and needs further tests beyond just take an aspirin. So maybe the person had a stomach ache, and they had lost some weight, and they were looking a little yellow. All of a sudden the probabilities start looking a lot different.
You would think Bayesian inference is good at integrating multiple information sources but practically you have to model the dependencies between different information sources and even doing a good job of that doesn't save you away from logical fallacies such as "Explaining away". In real life people use Naive Bayes a lot because properly modelling a Bayesian network is hard and trying to learn the network gets you in all sorts of problems -- allow arbitrary dependencies between N inputs and you are talking eᴺ coefficients in your model and you'll never solve it.
This is one of the reasons why people got frustrated with Expert Systems as real-life reasoning requires reasoning with uncertainty and we don't have a satisfactory general way to do it.
The whole point of Bayesian networks is to have something that's asymptotically simpler than "arbitrary dependencies between N inputs" while still being able to model useful scenarios.
Sure, relying too much on heuristics can be a bad idea in tail risk situations.
But other times, they make perfect sense and save a lot of time and effort.
This post reads like a series of straw men created to show that heuristics are dangerous. I’m not sure who is going to argue that heuristics are appropriate in those situations.
This is what Nassim Nicholas Taleb has been writing books about. He calls them black swan events, because if you took a sample of 1000 swans, chances are you'd conclude that all swans are white, but it just isn't so. People tend to round down the probability of very rare events to zero, even when the upside of them is small and the downside is catastrophically bad. Examples: the 2008 housing crisis, Fukushima, and our current supply chain problems.
It's an annoying metaphor anyway. If you've defined a swan as a particular type of white bird, it's impossible for a black swan to ever come. "Black swan" is just a tautological term for new thing we've never seen before, but pretending to be a term for known thing that suddenly behaved differently.
Sometimes things happen that, in order to make money or cut costs, we convinced people were impossible.
> "Black swan" is just a tautological term for new thing we've never seen before, but pretending to be a term for known thing that suddenly behaved differently.
Right. "Black swan" means "a new thing we've never seen before," but of course few people go around thinking "I will never encounter a new thing that I've never seen before."
Maybe you’re right but I don’t see why this addresses the reply to (at least when I loaded it) the first comment on the post which claims the same thing and is disagreed with by the author.
These are NOT black swan events. These are probably all White Swan events (possibly grey swan events, but i'd have to review stuff that i don't want to right now). E.g. High certainty, just low predictability. From the book, when you know the statistics of a rare event, and then the even occurs, it's absolutely not a black swan event.
For an event to be a Black Swan event, you literally need to have no possibly for the event in your deductive framework (e.g. the problem of induction which is what the book is actually about). In every single one of these examples, the possibly of the event occurring is accepted by everyone.
This is why Taleb lost his mind when people started calling the Covid Pandemic a "black swan event," which it was absolutely not. We know pandemics happen, we know about what power law they happen at. The fact we were not prepared at all is a problem of not being prepared for something we know will happen with certainty.
We know pandemics happen but we have no idea which viruses will become pandemic viruses - until one emerges, we're generally confident that there is not an imminent pandemic.
Neither of those became pandemic viruses though. And the specific year over year risk was essentially unknown until a new virus emerged at such point we had a couple of months to determine what we thought would happen.
That's the specific event risk: pretty obviously if we had maintained effective pandemic response measures, and maybe focussed on general infectious agent spread control measures as a society (i.e. a year over year goal to reduce influenza cases, update building codes to require less touchable surfaces to navigate) then we'd be better off then we are.
Who is we? The CDC is actively watching for pandemic signals all the time.
We know pandemics happen, we know their rough power law occurrences. We know the most dangerous vectors of transmission. We can prepare for them. We typically don’t.
Just look at all the aging housing infrastructure on the California coast. We know there will be major earthquakes and we know how often they happen, yet the general populace cares more about how pretty the historic buildings look, even though we know they will kill people.
IIRC, a black swan event highlights the problem of induction when there is _no_ prior event that you can use to learn from. Eg: humans thought all swans were white until the first black swan was encountered. So not just exceedingly rare but outside what you know AND extremely rare. Eg: Neither the housing crisis, Fukushima, supply chain crisis, nor the pandemic are black swans (they were seen before and was predicted/theorised) but the internet is.
I think it's what he calls "fat tails" : events happening at low frequency at the tail of the probability distribution, but which have a significant impact.
Heuristics? For amateurs and lazy folk. We find metrics that reliably measure something, find or make a gauge that measures that metric, then make sure our gauge stays good over time by doing R&Rs or recalibrations.
Great article, really enjoyed it. I second the Talib connection.
But anyways... Does anyone else struggle with Substack's typeface, specifically it's width and spacing between characters? I'm a bit of a typeface nerd, and I genuinely like or enjoy most of our common fonts. Substack is the only site that I find the typeface to significantly affect the reading experience.
I tend to agree with you about the typeface they use, Spectral. I think it's a combination of factors: loose tracking designed to permit slightly over-emphasized differences in weight (which were a design goal for the font) and somewhat selective replacement of inktraps from the inspiration face (Elzévir) with angular serifs, which creates a bit of a visual discordance. I don't find it unreadable, personally, but it does call attention to itself.
Very well put. I agree with your analysis. There's a lot of things I like about Spectral, and in general I like the "genre" of faces that it belongs to. The loose tracking+over-emphasized font weights is the core of my challenge.
Barks at everything all the time, people learn to ignore it. Then, when there's real danger, no one cares, providing literally no value and becoming only an annoyance.
It's kind of like a dual for the security guard one.
Yes, but one important difference is that on OP's examples there is some sort of system that you put in place for a specific purpose, and it fails to do so in practice.
It would be akin to that lying boy being the officially appointed wolf-spotter for his village.
This is like the turkey on the day before Thanksgiving. "They fed me today. They fed me yesterday. They fed me the day before that. Of course they're going to feed me tomorrow!" Except they aren't.
So, yeah. Our heuristics fail on black swan events. There needs to be a balance between "trust your heuristics" and "watch out for black swans".
I think history has shown it is far more profitable to amplify fringe theories and capitalise on everyone’s fears that we are being deliberately mislead by corrupt authorities claiming false expertise.
This story reminded me of a story written by a Czech biologist who studied animals in Papua-New Guinea and went to a hunt with a group of local tribesmen.
The dusk was approaching, they were still in the forest and he proposed that they could sleep under a tree. The hunters were adamant in their refusal: no, this is dangerous, a tree might fall on you in your sleep and kill you. He relented, but silently considered them irrational, given that his assessment of a chance of a tree falling on you overnight was less then 1:5000.
Only later did he realize that for a lifelong hunter, 1:5000 are pretty bad odds that translate to a very significant probability of getting killed over a 30-40 year long hunting career.
It's a great example. This is the very reason I have scaled back the amount of time I rock climb as I've gotten older -- not because any individual outing is dangerous, but there's an element of Russian roulette wherein the mere act of doing it more often dramatically changes the risk.
Also known as the Kelly criterion. If one possible outcome of an action is associated with a great enough loss, it doesn't make sense to perform the action no matter how unlikely the loss.
* turn a predictive model for financial prices into a profitable trading system
In the case where the bet loses money you can interpret Kelly as either "the only way to win is not to play" or "bet it all on Red exactly once and walk away " depending on how you take the limit.
That is a much narrower view of the Kelly criterion than the general concept.
The general idea is about choosing an action that maximises the expected logarithm of the result.
In practise this means, among other things, not choosing an action that gets you close to "ruin", however you choose to measure the result. Another way to phrase it is that the Kelly criterion leads to actions that avoid large losses.
"The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate"
In real life people often choose to make bets smaller than the Kelley bet. Part of that is that even if you have a good model there are still "unknown unknowns" that will make your model wrong some of the time. Also most people aren't comfortable with the sharp ups and downs and probability of ruin you have with Kelley.
I've long found that Wikipedia article woefully lacking in generality.
1) The Kelly criterion is a general decision rule not limited to bet sizing. Bet sizing is just a special case where you're choosing between actions that correspond to different bet sizes. The Kelly criterion works very well also for other actions, like whether to pursue project A or B, whether to get insurance or not, and indeed whether to sleep under a tree or on a rock.
2) The Kelly criterion is not limited to what people would ordinarily think of as "wealth". It applies just as well to anything you can measure with some sort of utility where compounding makes sense.
The best overview I've found so far is The Kelly Capital Growth Investment Criterion[1], which unfortunately is a thick collection of peer-reviewed science, so it's very detailed and heavy on the maths, too.
Pascal's wager is an example of motivated thinking - there were very real and certain consequences to him if his wager didn't demonstrate you should obey the Catholic Church.
Which of course directly leads to Pascal's Mugging: I can simply say "I'm a god, give me $10000 or you will burn in hell for all eternity". Now if you follow Pascal's Wager or GP's logic you have to give me the money: I'm probably lying, but the potential downside is too great to risk upsetting me.
There's actually a rational explanation for that: humans don't care very much about burning in hell for all eternity, when it comes down to it.
There's actually a similar though experiment that might seem even more bizarre: I could tell you "give me $100 or I will kill you tomorrow" and you probably wouldn't give me the $100. That's because when it comes down to it, humans don't see the loss of their life as that big a deal as one might think. It's a big deal, of course, but in combination with the low likelihood, still not big enough to forgo the $100.
Psychologically, behaving in a certain way makes it more likely that you'll behave in the same way in the future. That's an integral idea underpinning justice systems.
True but it would be incorrect to assume that you can safely keep basejumping every day in a year, just because you haven’t died in the last 50 days. Eventually the stats say you will be 87% likely to have an accident when you consider your choice at the beginning of the year. It might be day 20 or day 300, but you won’t know what case you end up in. The chance of your next jump being your last is always the same, but that doesn’t decrease the risk of repeated trials.
Not exactly. If you've done it 50 days without an accident, your current chances of the accident happening in the remainder of the year are NOW less than 87%.
If you've made it Jan 1 to July 1 months without an accident, the chances of you making it to Dec 31 are now better than they were on Jan 1 -- because now they are just the chances of you making it six months, not a year.
The chances of flipping 6 heads in a row are 1/64. But if I've already flipped 3 in a row... the chances of flipping three _more_ heads in a row is 1/8, the same as always for flipping 3 heads in a row. The ones that already happened don't effect your future chances.
Yes, but when you make a plan to find an acceptable cumulative future risk, planning to do it once a week for the rest of your life is planning to expose yourself to significantly more risk than doing it twice a year for the rest of your life.
You might still die in one of the next 20 instances. But you've added a lot more not-dead time in between them!
Saying "I can do one more with minimal added risk" every single time after not dying is true and yet pointless, because it's not a given that "minimal added risk" = "not dying." It's survivorship bias to not think frequency doesn't affect the cumulative odds of your future planning solely because you've already done a lot of trials.
Slippery slope arguments aren't inherently fallacious. If you can justify one more climb on the grounds that probability of injury or death is very low then you will be able to justify every subsequent climb on the same basis.
Slippery slope arguments are inherently fallacies. They don't prove that something will happen.
Just because you can justify the next climb on the same basis, that doesn't mean you will. You could decide that you've already tested the odds one too many times.
"You could decide that you've already tested the odds one too many times" was the original point. Someone responded that the N previous times don't matter and N + 1 has barely any risk. Another poster countered that that argument as stated applies not just for N + 1 but for (N + 1) + 1 etc and therefore the slippery slope principle applies.
Of course if you add in "you could decide that you've already tested the odds one too many times" then it's a fallacy to invoke slippery slope because an off-ramp is explicitly specified. In this case slippery slope was mentioned only because N was dismissed as irrelevant.
Don't get on that greased sliding board that ends at the top of a cliff. Once you start sliding, it will be hard to stop because of the grease, and then once you slide off then end you will fall and die.
Do you really think this slippery slope argument is a fallacy? FWIW, wikipedia acknowledges slippery slope can be a legit argument when the slope, and it's chain of consequences, are actually real. https://en.m.wikipedia.org/wiki/Slippery_slope . Indeed, this is the very basis of mathematical induction.
> The fallacious sense of "slippery slope" is often used synonymously with continuum fallacy, in that it ignores the possibility of middle ground and assumes a discrete transition from category A to category B. In this sense, it constitutes an informal fallacy.
"If you take N steps, you will take N+1 steps" is a fallacy whenever it's possible that you won't take N+1 steps.
When accounting for human psychology it does have validity: doing an enjoyable activity "one more time" has a risk of a habit forming, which has a non-zero probability. It is indeed possible.
The argument can certainly be used in a fallacious manner (e.g. by greatly exaggerating the probability of the further steps, saying they are inevitable if the first step is taken, etc.). It's logically valid to say that the first step enables subsequent steps to be taken.
Edit: I'd say that the slippery slope is perfectly valid rule of thumb in a lot of 'adversarial' situations. Once one side makes an error or fails somehow, the balance between the two sides can be disrupted leading to one 'side' gaining momentum. Just as between people, a similar 'adversarial' process can occur within the minds of individuals: between two ideas or patterns of thought/behaviour, one idea can gain momentum after a decision has been reached. Precedence is a strong force.
Maybe fallacies could be renamed "logical hazards" or something like that. Arguments that are at high risk of being false and require extra care, but not automatically false.
That's not how this works as a rational investment choice.
It's true that you can never win a lottery you don't enter, but the expected value of that ticket is vastly lower than what you paid for it. That means, as an investment, your $10 will be expected to do better in literally anything with a positive return.
If you are buying > $10 worth of dreaming (for you), fine - but that's consumption.
If you've already done it for 12 months without it happening though, the next 3 months are no more dangerous for you than for someone starting from scratch.
That's true, but usually when we are deciding which actions to take, we're not comparing "I take actionA" versus "I take actionB," rather than comparing "I take actionA" versus "some random other person takes actionA."
OK, the next 3 months are no more dangerous for you than if you hadn't spent the last 12 months doing it. What you did in the past has no bearing on the chances going forward. I'm not sure if it's more clear to say it like that or not. Clearly, humans have a lot of trouble speaking and thinking clearly about statistics.
The next three months are no riskier than your first three months were. They don't become more risky because they will add up to 15 months total -- once you've already finished the first 12 without incident.
For the dice roll example that is true. But other examples it isn’t. For example the MTBF of a device that has run for x hours approaching the MTBF is probably more likely to fall in the next x hours. Or if there is some cyclic behavior. Like waiting outside for a hot day.
Dice (typically) do not have a memory, so whatever happened yesterday will not influence what happens today. If you roll it daily, your chance of surviving at least N days is (215/216)^N, for the specific case of "rolling three 6 on three 6-sided dice" that puts you at ~50% at 149 days and at ~10% at 496 days.
At sufficient scale, even incredibly unlikely things become quite probable.
runs <- 10000
x <- vector(mode = "numeric", length = runs)
for (i in 1:runs){
while (sum(sample(1:6, size = 3, replace = TRUE)) != 18){
x[i] <- x[i] + 1
}
}
summary(x)
quantile(x, c(0.5, 0.8, 0.9))
> summary(x)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0 62.0 149.0 216.2 300.0 1902.0
> quantile(x, c(0.5, 0.8, 0.9))
50% 80% 90%
149 350 495
A simple simulation. Run 10K times. Count the number of times it takes for three dice to add up 18.
The numbers very much agree with you. The median is 149. The 90th is 495 in the simulation, which is close enough to 496. There is very much a long tail in the data. So, the median and the average will not be the same. Is it a coincidence that mean is a 216?
Off the top of my head, I don't know. It MAY be related to the fact that 6*3 is 216, but I don't have deep enough statistics knowledge to say for sure. You coudl try it again with 3 8-sided dice and rolling 24, that should give you ~50% at 344 iterations, and ~90% at 1177 iterations. If my supposition that the mean is related to the possible rolls, then the mean should end up being 512.
Iteration counts gathered with Python and a (manual) binary search (actually faster than writing code).
RandomSwede's comment is accurate, but maybe the below can help add some 'flesh' to their response.
Basically, the problem is that you can't just multiply it all together.
(1/6) ^ 3 is correct, and the probability of rolling 3 sixes is indeed 1/216 today, but if you repeat independent events, you don't just add up the probability.
Imagine instead of dice it's coins, and it's only two. Your odds of getting HH today are 1/4, but the odds of getting HH by day four are not now 4/4. We know that it's possible, although unlikely, you could flip coins for the rest of your life and NEVER get two heads. So we know that you can't ever have odds of 4/4 (or 1), only odds that approach 1. So that means that we can't say 216 days from now will be 216/216.
Instead, you need to work out the probability of the event NOT happening, and then repeatedly NOT happening independently (so we can multiply together to get the probability.
For our four coins, the probability of NOT getting HH is 3/4. On Day 2, the probability of NOT getting HH on both occasions will be (3/4)×(3/4), (9/16, 56.25%). By day 3, it will be (3/4) × (3/4) × (3/4), or 27/64. On day 4, it'll be 81/256, or 31.6%. Now we can subtract from 1, to work out that by day 4, the odds of us having hit HH are almost 70%.
As RandomSwede explains, there's a 50% chance that you will have rolled three sixes by day 149. By day 496, you're down to 10%.
runs <- 10000
x <- vector(mode = "numeric", length = runs)
for (i in 1:runs){
while (sum(sample(1:6, size = 3, replace = TRUE)) != 18){
x[i] <- x[i] + 1
}
}
summary(x)
quantile(x, c(0.5, 0.8, 0.9))
> summary(x)
Min. 1st Qu. Median Mean 3rd Qu. Max.
0.0 62.0 149.0 216.2 300.0 1902.0
> quantile(x, c(0.5, 0.8, 0.9))
50% 80% 90%
149 350 495
A simple simulation. Run 10K times. Count the number of times it takes for three dice to add up 18.
The numbers very much agree with you. The median is 149. The 90th is 495 in the simulation, which is close enough to 496. There is very much a long tail in the data. So, the median and the average will not be the same. Is it a coincidence that mean is a 216?
No, I don't think this is a coincidence, but I'm not completely confident in saying that.
Thinking about it doesn't make me feel like I'm solving a maths problem. I start stacking ideas and concepts in a way which makes me feel like I'm overlaying them in a way which is incorrect.
It makes me feel like I'm solving a riddle, which hints to me that maybe it's actually a question of semantics and definitions rather than a maths problem.
You forget: once you roll three 6s in a row, you're dead, and you don't roll any more. Your expected calculation assumes that people keep rolling after they get 666.
Though I'm not sure where they got their figure from, because there isn't an “expected time to live”; there's a 90% probability to live time, a 5% probability to live time…
There’s a difference between expected value of number of days you’ll survive and the number of days a given fraction of the subjects will survive, but I don’t see either supporting the claim “If you do it every day, you have about 15 months to live”.
(215/216)^450 ≈ 0.124
, so about one in eight will survive for 15 months or more. The “5% probability to live” time is around day 645 (about 1¾ years):
(215/216)^645 ≈ 0.0501
the “half will survive at least for” point is around 5 months:
The parent comment talks about scaling back the amount of rock climbing they do in order to reduce risk.. And now you are saying that they should go one more time, because a single climb is low risk?
After a long life of rock climbing, there's no significant risk of doing it one last time or 10 last times (ignoring the effect of old age itself and whatever).
But when you're in earlier stages of your life, you're asking a different question: You're asking, is this something I want to do hundreds or thousands of times in my life, knowing that each of those times has a small chance of ending my life? This becomes a completely different question.
If I'm 35, maybe I will climb 30 times per year on average for 30 years until I'm 65. That's 900 climbs in total. If my goal is to not die or experience serious injury from rock climbing even once in my life, I have to consider the chance that any one of those 900 climbs will result in serious injury or death. I don't know the numbers for the risks involved, but it seems reasonable to be cautious.
Maybe I don't want to give up on rock climbing altogether, but maybe I can scale it back. If I limit myself to 1 climb per year, that's 30 climbs in total. Much lower risk than with 900 climbs.
The assumption is that it's desirable to have a descending climbing frequency instead of uniform.
This makes a lot of sense, as when you're younger frequent climbing would help you to develop proficiency quickly and your body allows you to joy it fully. Plus the social benefits are probably higher when younger.
Once you're older, it's potentially less enjoyable (as your body ages) and you don't need to worry as much about rapidly gaining proficiency.
You're making it sound like it's a decision they made when they got into rock climbing initially, that they would climb frequently while young and then scale back as they get older.
Now, making that decision at the outset does make sense, because it will drastically reduce the number of climbs you make in your life compared to climbing frequently throughout your life, and rock climbing while young is less risky than rock climbing while old.
But importantly, I don't think that's what GP did. It sounds to me like GP spent their youth climbing a lot without considering their mortality, but then decided to scale back because they realized climbing that often for the rest of their life would be dangerous. Maybe they spent the time from 20 to 35 climbing 30 times per year, in keeping with my earlier example. That means they've already climbed 450 times. Risky, but they made it through alive. At 35, they start to consider their own mortality, and they have the choice between climbing 900 more times by keeping to their current rate, and climbing 30 more times by reducing their rate (or something in between). Deciding to scale back makes sense.
I think what you're missing is that they are not avoiding "going rock climbing one more time"; they are avoiding "being a person who habitually rock climbs", because while each excursion is low-risk the aggregate effect will be high risk. It's like smoking -- one cigarette won't appreciably impact your health, but "being a smoker" will.
None of this intended to cast aspersions on rock climbing in particular, just pointing out that a reasonable person, understanding independence of events and not falling prey to any fallacy, could reasonably make this decision based on their personal risk tolerance
Yes, or more accurately there is a frequency of climbing outings at which the marginal increase in satisfaction from an extra climbing is no longer sufficient to justify the increased risk.
I don't know how you can make this claim objectively without knowing that individual's preferences.
If an individual decides their risk tolerance is that they will not accept a one in a million chance of injury from rock climbing, how is their analysis incorrect?
Under this assumption, by the principal of mathematical induction, you can easily do it K more times for any K without taking on barely any risk at each step of the way.
This is called the Turkey fallacy: the turkey was feed by humans for 1000 days, and after each feed event he updated his belief that humans care for him until it's now almost a statistical certainty.
Is this the reverse of the Gambler's Fallacy? Instead of "The numbers haven't hit in a while, therefore they're going to hit soon." it's "The numbers haven't hit yet, therefore they're never gonna hit."
Also known as complacency. Working in a woodshop, one of the things you are most vulnerable to is failing to respect the danger you're in. This is why many experienced woodworkers have been injured by e.g. a table saw - you stop being as careful after such long exposure.
A related thing is normalization of deviance. You start removing safety because you see nothing bad happened before, until you are at a point where almost no safety rules are respected anymore. You can see this a lot in construction videos.
Wow, that's terrifying and a good cautionary tale.
Also, when I read
> I’m hoping you can you forgive me as a minister of religion for likening this story to a spiritual cautionary tale. Yes, we do need to live each day as if it might be our last.
I thought, "Hmm, sounds adventist", and sure enough :-)
Oh man, that's terrible. I can certainly understand how someone without a checklist that is verified by two people can do that, especially if you have a backpack on to mask the fact that the parachute is missing.
Many times if I wear a tight jacket in the car, I forget to put my seat belt on, because I unconsciously mistake the pressure of the jacket for the seatbelt's, even though putting on a seat belt is usually the first thing I do.
Probably not. But they aren't affected by the previous N climbs, at least as described by GP post. They are considering a fixed odds event, and the probability of (bad thing happens) over a sample path through time. That's not the turkey fallacy.
In other words , the difference between the turkey and the climber is the climber knows the odds (at least nominally) , and it’s important .
This assumes a lot about the underlying process, particularly independence. Whilst assuming independence might hold reasonably well for low numbers of samples, the assumption might be increasingly (and dangerously) misleading. The intuition expressed by GP captures that.
The point is that they're changing their habits. Of course we ignore the n times they've gone before, now instead of their habits meaning they'd go m more times in the future, they're going to be going p times in the future for some p that is much less than m.
So it's not about how often they've done it over their lifetime so far, but about how many times they will be doing it over the rest of their life.
> It's a great example. This is the very reason I have scaled back the amount of time I rock climb as I've gotten older -- not because any individual outing is dangerous, but there's an element of Russian roulette wherein the mere act of doing it more often dramatically changes the risk.
Indoor climbing, and especially bouldering, can be a lot of fun at the right gym, and with dramatically reduced risk of death (though injury is still a very real possibility, I say, recalling all the time I spent nursing my sprained ankle).
This is called ergodic theory, the more you repeat an action that could result in catastrophe, the likelihood of that catastrophe occuring will be close to 100% if the number of events is high enough.
Right, but it's easy to conflate two very things here:
"What are my chances of dying in a climbing accident", and
"What are my chances of dying today if I go climbing".
If you are on a plane, you* have a lower risk of some kinds of cancer than the airline staff do. This has nothing to do with the flight you are both on, and everything to do with accumulated flights
"you*" = for most people, i.e. barring a counteracting risk factor.
The risks are highest when learners are at a beginner to intermediate stage. They know the basics, and have gained some confidence, but don't know enough to get themselves out of trouble.
This is called Stage 1 in the Gordon Model of learning: unconscious incompetence.
While this is true, in the context of alpine climbing where I first heard this statement, the bold alpinists who die young are very much not beginner-intermediates. I've interpreted this differently than just the "Bathtub Curve"[1] applied to dangerous pursuits.
Rather, there is a certain amount of objective risk in alpine environments, and the more time you put yourself in that environment, especially in locations you aren't familiar with, the greater the chance that something will eventually go wrong.
I'm always surprised by the number of famous alpinists who weren't killed on their progressive, headline-capturing attempts but rather on training attempts and lesser objectives.
My wife teaches people to ride horses for a living so we talk about the safety of that.
You hear a lot about people who get seriously injured riding who are often professionals or people who ride competitively at a high level. They are doing dangerous things and doing a lot of them.
We don't think it is that dangerous for people who ride at the level we do, out of maybe 15 years we've had one broken bone.
The other day I noticed that we had acquired a used horse blanket from another barn in the area which is a running joke at our barn because of their bad safety culture. They are a "better" barn than ours in that they are attached to the show circuit at a higher level than the bottom, but we are always hearing about crazy accidents that happen there. When I was learning to ride there they had a confusing situation almost like
with too many lessons going on at once where I wound up going over a jump by accident after a "near miss" in which I almost did. (I never thought I could go over a jump and survive, as it was I had about two seconds to figure out that I had to trust the horse and hang on and I did alright...)
Another good allegory is that, in the US Air Force, the flight crews considered most dangerous are those with the highest collective rank. Sure, the young crews are learning but the old ones still think they know it all and have often forgotten critical details.
(Example) When you go climbing somewhere, you have like a 40% of getting killed that you can mitigate completely by skill, and an additional 0.1% chance that something goes wrong by some fluke, that you can’t mitigate at all.
Pretty good if you go climbing 10 times a year. Pretty bad if you go 1000 times.
They wouldn't be famous if they didn't succeed on headline-capturing attempts and there are only so many you can realistically do in life. They are dead however as doing dangerous things often enough will kill a substantial number of practitioners.
No, the risks are greatest when you reach complacency. Beginners, even bold ones, take some care. You mostly see this in things like forklift drivers because it takes years of doing the same thing every day before you really get expert enough to be complacent
There is also something called "Normalization of Deviance", defined better by a quote: "Today, the term normalization of deviance — the gradual process by which the unacceptable becomes acceptable in the absence of adverse consequences — can be applied as legitimately to the human factors risks in airline operations as to the Challenger accident." *
Most of you have probably heard of it in the context of fighter pilots doing riskier and riskier maneuvers, but it seems to apply to drivers who speed a lot. 80 starts seeming really slow to them after doing it for years.
Thanks for posting these, I'd only seen Normalisation of Deviance mentioned in these two youtube videos by Mike Mullane and never thought to look any further:
including these two excerpts I found interesting in this context:
"Chapter nine she explains how conformity to the rules, and the work culture, led to the disaster, and not the violation of any rules, as thought by many of the investigators. She concludes her book with a chapter on lessons learned."
"She mainly emphasizes on the long-term impact of institutionalization of the political pressure and economic factors, that results in a “culture of production”."
Vaughn's book The Challenger Launch Decision doesn't tell this truth: the root cause of the accident can be traced back a decade to the acceptance of a design that was "unsafe at any speed".
Every other manned space vehicle had an escape system. The crew of the Challenger was not killed by the failure of the SRB or the explosion of the external tank, but rather when the part of the orbiter they were in hit the ocean. They could have build this into a reinforced pod with parachutes or some other ability to land but they chose not to because they wanted to have the payload section in the rear.
In the case of Columbia it was the fragile thermal protection system that did the astronauts in. There was a lot of fear in the first few flights that the thermal tiles would get damaged and failed and once they thought they'd dodged that bullet they didn't worry about it so much.
"Normalization of deviance" was a formal process in the case of the space shuttle of there being meetings where people went through a list of a few hundred unacceptable situations that they convinced themselves they could accept, often by taking some mitigations.
When the design was finalized it was estimated that a loss of vehicle and crew would happen about 2%-3% of the the time which was about what we experienced. (Originally they planned to launch 50 missions a year which would have meant the continuous trauma of losing astronauts and replacing vehicles.)
It's easy to come to the conclusion that it was a particular scandal that one particular concern got dismissed during a "normalization of deviance" meeting but given a poorly designed vehicle it was inevitable that after making good calls for thousands of concerns there would be a critical bad call.
"Normalization of deviance" is frequently used for a phenomenon entirely different than what Vaughn is talking about, something informal that happens at the level of individuals and small groups. That is, the forklift operators who come to the conclusion it is OK to smoke pot at work, the surgeon who thinks it is OK to not wash his hands, etc. A group can pressure people to do the right things here, but it's something different from the slow motion horror of bureaucracy that tries to do the right thing but cannot.
I'm reminded of Louis Slotin experimenting with the "Demon" core.
The core was surrounded by 2 half spheres of beryllium.
The core would go critical if the 2 spheres were not separated from each other.
The standard protocol was to use shims between the halves, as allowing them to close completely could result in the instantaneous formation of a critical mass and a lethal power excursion. Under Slotin's own unapproved protocol, the shims were not used and the only thing preventing the closure was the blade of a standard flat-tipped screwdriver manipulated in Slotin's other hand. Slotin, who was given to bravado, became the local expert, performing the test on almost a dozen occasions, often in his trademark blue jeans and cowboy boots, in front of a roomful of observers. Enrico Fermi reportedly told Slotin and others they would be "dead within a year" if they continued performing the test in that manner. Scientists referred to this flirting with the possibility of a nuclear chain reaction as "tickling the dragon's tail", based on a remark by physicist Richard Feynman, who compared the experiments to "tickling the tail of a sleeping dragon".
On the day of the accident, Slotin's screwdriver slipped outward a fraction of an inch while he was lowering the top reflector, allowing the reflector to fall into place around the core. Instantly, there was a flash of blue light and a wave of heat across Slotin's skin; the core had become supercritical, releasing an intense burst of neutron radiation estimated to have lasted about a half second. Slotin quickly twisted his wrist, flipping the top shell to the floor. The heating of the core and shells stopped the criticality within seconds of its initiation, while Slotin's reaction prevented a recurrence and ended the accident. The position of Slotin's body over the apparatus also shielded the others from much of the neutron radiation, but he received a lethal dose of 1,000 rad (10 Gy) neutron and 114 rad (1.14 Gy) gamma radiation in under a second and died nine days later from acute radiation poisoning.
That reminds me of when a family friend from church needed help clearing his land and thought the easiest approach would be to teach an overconfident 14 year old (me) to drive his tractor. He told me I would never be worse at operating it than the second time we went out. He was right.
A WTA top 70 tennis player from my country (aged 35+, thus possibly facing the end of her pro career) recently rephrased a well known proverb: "What doesn't kill you, makes you stronger -- or, crippled."
There's chance of death, but there's also duration of suffering while dying.
I'm guessing that falling from a cliff is "better" than dying from a poisonous mushroom. The latter scares the hell out of me. The former is a glorious ride until the ride is over (regrettably).
I would imagine that if you scale back enough tho, you won't be as sharp. Sure the odds increase the more you do it, but not just because you do it, but often because of other variables, such as the weather, not listening to your body, over confidence, etc.
That's the reason why I don't cycle in London. When I moved there, I thought I would be using my bike daily like I was used to. But over the span of a few years, I'm pretty sure the risk of serious injury becomes significant.
For rock climbing, you're probably right. I remember training in a climbing hall, when I saw someone falling off the highest wall. The tenant of the hall didn't look surprised at all. Apparently, it happens frequently.
That being said, if you serious about security, I'm sure the risk can be minimal.
You can contrast the odds of getting injured with the health benefits. The cardiovascular benefits would seem to outweigh the risks of getting injured from a mathematical point of view.
I took the same approach with motorcycling. I decided to do it for 3 years while at university because it had a transformative impact on my lifestyle. But I also decided the odds were way too bad to keep doing it my whole life. So I stopped and haven't done it since then.
I only owned a bicycle for several years at the same age, and have since mostly used a car to get around. I've been in various, relatively minor accidents with both, and have always wanted to try using a motorcycle, but it seems to take the risks of both biking and driving and puts them together!
"Climb if you will, but remember that courage and strength are nought without prudence, and that a momentary negligence may destroy the happiness of a lifetime. Do nothing in haste; look well to each step; and from the beginning think what may be the end" ~Edward Whymper
You could calculate it by taking the average lifetime of a tree and dividing by the length of time slept and the number of trees in squashing distance.
Only if tree death is uniformly distributed over a tree's lifetime for some bizarre reason. And it isn't.
The logic in the story is BS. First, you would never, ever get into a car with that logic. Second, trees just aren't that ephemeral. People who live in a forest would be very aware of when they do or don't fall (or more problematically, drop large branches.) It's not as straightforward as just avoiding storms or dead-looking trees. Sustained wet weather, especially after a period of dry weather, is a common cause. As is the opposite for some trees (eg oak trees drop limbs in sustained hot dry weather.) As for disease or other causes, an experienced hunter in a familiar area could tell at a glance.
The message I got from the story is that they probably did have a very good reason. They either thought it would be too hard to communicate, or they were themselves cargo-culting the falling tree excuse when the reality was more likely to be... I dunno, snakes or nasty bugs or annoying sticky sap or whatever.
I think your explanation is pretty plausible, I wonder why people are downvoting it.
Like these guys probably have homes, with bedding of some sort, maybe they'd rather sleep next to their wives than some caterpillars. If I was giving somebody from a far-off place a tour of my workplace and, on the bus ride home, they suggested it was getting dark and we should camp on the sidewalk I'd probably not go for it. If they were really insistent I'd probably amplify the danger of sleeping on the sidewalk to shut them up.
> First, you would never, ever get into a car with that logic.
The logic isn't applicable to any set of risks. As deadly as cars are, the risk of car crash death is much, much lower than 1/5000 per trip. It's probably closer to applicable to being a drunk driver, and "you would never operate a car drunk" is pretty accurate for many people.
1:5000 would suggest an average lifetime of 13.7 years for a grown tree (i.e. not counting the years where it's too young to sleep under), and that's before the ability to avoid trees that look more likely to fallover.
I don't know anything about trees around there, maybe they're really short-lived? For forests around here, it's a gross overestimate.
or perhaps the main difference between Papua New Guinea and the GP's location is that people feel entitled to make up weird questionable stories about PNG and not about their place.
Remember that the relevant set isn't the set of all trees, but the set of trees old enough to be large enough to sleep under. That means the average lifetime would be: (number of years it takes for a tree to become big enough to sleep under) + 13.7.
I would still guess that the number is wrong, I suspect that trees have a longer life on average from becoming what we would consider "big" until they fall over. But it's still an important detail.
I mean “big enough to sleep under” is around 50+ years for most hardwoods IIRC. Also, you have to consider groups of trees that can fall on you in the surrounding area. So it’s really the probability that a tree falls within any given 50m radius, towards the center. I think the stated probability is pretty accurate. Also as humans, we tend to pick trees that provide the best shelter, thus older. From experience, if one of those big older branches decide to fall, you don’t want to be underneath. As a kid, a huge oak tree lost a huge branch right in front of me. It scared the crap out of my 8yr old self, so much that I still remember it quite vividly, it would have killed my brother and I if we hadn’t just moved out of the area. The limb looked perfectly healthy btw, green and all. There was no indicating factors, according to the adults at the time.
Even if you multiple by ten this still means you'll end up with one dead hunter every few decades (depending on how often they hunt and how many hunters there are exactly). That seems like quite a high risk for a small self-sustained community.
Also, I bet it's not just the tree you're sleeping under that poses a risk, but also other trees in the vicinity that might fall on you. In a forest there are probably a bunch of trees "in range".
All of that said, I've often camped and slept in forests, as have many of my friends, and I've never heard of anyone being killed or injured by a falling tree, or ever heard or seen any "don't sleep under a tree, it might kill you"-advice, so I don't know...
PNG has a lot of eucalyptus trees, and some species drop their branches with zero warning, which originated as a mechanism for surviving droughts. I don't know enough to tell whether that's what's going on in the estimate.
The tricks in this article might work in the short term. However, over the length of a career, it's difficult to outrun a negative reputation forever. Especially in the age of the internet, people will eventually catch on to what you're doing.
Also: in the version of the story I remember reading somewhere, all night they kept hearing trees fall. And that had a significant effect in affecting their impression of the probability.
Great example of a non-ergodic event. The outcome (odds of dying) when considering of one individual longitudinally is entirely different from the outcome when considering a population of individuals at a single point in time.
I am just wondering what skydivers must think every time they do it ... given so many trials, the odds of nothing happening are going down exponentially right?
Reminds me of the fact that on overage, one out of every hundred places you know will be experiencing a once-in-a-hundred-years event.
When you hear once-in-a-hundred-year event, it makes it sound quite rare. One might look around and say (for example, in relation to climate) "why are so many of these happening?"
But it is unsurprising statistically. If you know just a thousand distinct geographic places, about 10 of them would experience such an event each year.
There's something intuitively misleading here, though I'm not sure what it is. I am looking at 100 square inches of floor right now and nothing unusual is happening in any of them.
Are there 100-year events associated with 100 square-inch plots of floor? No... But there are with coastlines, cities, dams, forests, deserts, islands, volcanoes, etc.
Of course there are other compounding factors. Not all events are one-in-one-hundred; some are one-in-ten, others are one-in-five-hundred, and with increasing scarcity by order of magnitude.
Another compounding factor is that the borders for "geographical areas" are fuzzy. Does a one-in-a-hundred year event that happens in Vermont also qualify as having happened in New Hampshire? Probably depends on the type and the specific measurements and the expectation according to history.
And what about aggregate events? E.g. "It's been five hundred years since we've seen this many tornadoes, which tend to happen once every ten years."
And in the opposite direction of the 100 square-inch plot of ground, there is blurring in the other direction: What do they mean in aggregate if they are fewer than expected at a global scale?
So my original comment was just a simple way of taking the average of all of these competing factors and stating a general truth that's somewhere in the middle. If you have X things that are expected to have 1/Y probabilities, then the probability of you experiencing any of them is not 1/Y, it's more like X/Y. (As in very likely.. that's more than 1 so obviously not mathematically correct.) But we often don't think about rare events this way - as no specific event being probable, but some collection of improbable events being almost certain. We perceive them all as 1/Y. It's just a very local way of thinking.
It has to do with how correlated conditions are in your 100 places. Conditions on one square inch of your floor are very highly correlated with conditions on another square inch of your floor, so they wouldn't be able to experience a 1-in-100 event independently -- if one part of your floor did something unusual, the other parts probably would too. Conditions on the floor the next room over are also pretty highly correlated, but not quite as high (maybe a fissure could open up and swallow the kitchen, but not your office). So in order for the parent comment to be true, their thousand distinct geographic places would need to be statistically independent from each other.
Of course in practice, it's quite hard to know whether conditions in one location are independent from another, or whether there's some degree of correlation or an underlying causal factor. This is why we have climate scientists.
>>All these things are almost always true. But Heuristics That Almost Always Work tempt us to be more certain than we should of each
The most important thing to realize about risk is this:
The difference between [using knowledge, skill, technology, and planning to manage risk] vs. [getting away with something]
If you aren't managing risk, it is managing you. And you can get away with something for a long time, but it is always a matter of until you don't, and then it is too 'effin late for you.
When you are managing the risk, you can make an entire career or lifetime of doing things that will otherwise kill you in seconds, scuba diving, flying, mountaineering, building tall structures, working with molten metal or dangerous chemicals, etc., etc., etc.
You can also get away with very dangerous things for at least enough time to fool you into thinking you are smart. The article discusses this at length.
This is why when you need to understand and manage the risks, and also be very alert to close calls - they mean that even though you thought you're managing, you've actually gone into the land of [getting away with it], just saved by Pure Dumb Luck. Don't say "it's okay it worked", look at why, because you might not have as much PDL next time.
I'd like to see the average life expectancy graph rephrased as "probably of dying today given current age".
Back of the envelope calculation: Life expectancy of 72 years times 365 gives about 26k days, so your average chance of death on a given day is on the order of 1 in 26,000.
Even if you're going to do it only once it is still very dangerous compared to the risks we normally take. 1:5000 is 200 micromorts, about 25x as dangerous as hang gliding! [1]
But the odds aren’t additive. If you sleep under a tree 4999 times and nothing happens, that doesn’t mean the 5000 time you sleep under one you’ll get crushed.
I don't believe the odd that you get crushed once if you play it multiple times are not as good as the odd of not getting crushed when playing only one time.
So you have 0.02% chance of getting crushed each time.
(1 - 0.0002)^10950 = 0.1119
1 - 0.1119 = 0.8881
So the probability of getting crushed at least one night over 30 years is ~89%
I think, my stats are from school over 10 years ago.
This is because, for example, if you flip a coin, each time you still only have 50% chance of getting tails. But the chances that you flip it 10 times in a row and never get heads are a lot less than 50%.
That's said. Another tricky bit is, what was measured when we said 1/5000 chance? This is where data can get confusing. Was that the odd of a tree falling at any given night? Or was that the odd of someone being crushed by a tree in their sleep at night? Or was it the odd of someone being crushed by a tree ever? Or the odd of a particular tree falling at night?
That's often where any prediction already begins to break down. For example, sorry to use the vaccines as an example, but when we say 90% efficacy, it means, out of x number of people who got a vaccine during the trial, 90% of those didn't get covid during some period, while in the placebo group it would be some other % who got it.
Reasoning about this already is tricky. You don't know the priors. What was the odd your participants were exposed to COVID? What if you'd measured over a longer period of time? What if that was just a lucky bunch?
I often wonder these days how it was to live in so much risk and unknowns in prehistory. Nothing was sure, understanding of the world was so limited ..
Compound interest? Exponential decay? Both apply here.
Probability of surviving a night under a tree is (1-1/5000).
15 years of hunting is roughly 5000 nights. The chances of never getting hit by a tree over that period are (1-1/5000) for each night, which compounds to
(1-1/5000)^5000 ≈ 1/e ≈ 1/2.7 < 0.4
That's to say, the odds are 3:2 (at least!) that you'd get killed by a tree in 15 years.
Make it at least 5:1 for 30 years.
That's to say, at least 5 out of 6 hunters who sleep under a tree every day wouldn't survive doing it for 30 years.
And that, children, is why credit cards are a scary thing.
Ergodicity?
E.g. A single player playing Russian roulette for a 100 times v/s 100 players playing it once are very different risks for the single player :)
It seems like 1:5000 is not an accurate probability, but just a number which he chose in order to convince himself that sleeping under a tree was not a risky activity. But he chose a bad number and later realized that an argument based on that number was not convincing.
If the chance was actually 1:5000, the longevity of trees would be similar to that of hunters sleeping under them - or lower, since hunters can sometimes avoid the hazard, but trees are exposed to it every night (and all day as well). Actual data on tree mortality seems to indicate that the chances are much lower than this. Almost certainly they do not make sleeping under trees a significant risky activity.
The hunters said 'a tree might fall on you and kill you'? This is supposed to be a nugget of ancient wisdom. Now it turns out it's actually a coconut falling out of the tree? Are you providing this extra information? Or was it somehow implicit in the original telling?
Is it possible that both the original teller, the reteller and you too, are starting from the (unfounded) assumption that the hunters know what they're talking about, and are adapting the facts to fit this assumption?
I read somewhere that the Mongolians believed flowing water was sacred and they had a taboo about defecating near it. For the wrong reasons they accidentally prevented cholera. If avoiding sleeping under trees prevents tree falls, lightning strikes, coconut comas, snakes from dropping on you, and whatever else then it doesn't really matter why the hunters don't sleep under them does it? Not having coconuts to worry about is just a happy bonus to the survival statistics.
Even if it is, no one suggested that local hunters sleep every night in the forest. If they happen to sleep under the tree once in a year, it won't increase their risk of death significantly.
There could be another reason why sleeping in the forest was dangerous – e.g., poisonous snakes or dangerous animals etc. Also if the temperature drops at night and they didn't have enough clothing, they could get hypothermia and so on.
There’s a real dearth of info around coconut fatalities. This 1984 paper examined a 4 year timespan of all trauma-related admissions to one hospital in Papua New Guinea. 9 of them (2.5% overall) stemmed from coconuts. In 3 of the cases, all children, the patients slipped into coma.
From what I’ve read elsewhere (no good links, sorry), coconut injuries worldwide seem to have fallen significantly due to better harvesting practice - the age of a coconut and their chance of falling appear to be linked. While I can’t find a good paper saying this, I do buy it.
So, perhaps not 1:5000, but (at least at one point in time) definitely a risk.
One way to solve this is that instead of asking for a yes - no answer, you ask for a ranking, and you disallow equally likely. Is bigfoot more or less likely than telepathy? Is telepathy more ore less likely than the vaccines being dangerous? Are the vaccines being dangeroues more or less likely than some guy achieving cold fusion in his garage?
A ranking forcibly brings the metric away from accuracy (which the heuristic can score well on) to something based around precision-recall (which it cannot).
What is the impetus for this writing style that repeats different versions of the same analogy 10 times when one would have sufficed? Surely Substack doesn't have a word count minimum.
I actually found the ramp-up from security guard to sceptic pretty clever. Demonstrate the principle on an easy, constructed case; verify on a real-world example; then present the applications you care about and have somewhat more controversial content. Although I agree that the number of repetitions is higher than optimal here.
A long article is a sign of effort expended, which rationalists value as a sign that a lot of thought has gone into the ideas the article puts forward. (They have a rock in their heads saying "DON'T BOTHER YOURSELF WITH BRIEF EXPOSITIONS.")
“Scientists have calculated that the chances of something so patently absurd actually existing are millions to one.
But magicians have calculated that million-to-one chances crop up nine times out of ten.”
It seems to make its point pretty clearly to me: "just naysay" is a strategy that is extremely effective/accurate in many domains, but provides no actual value compared to people attempting more honest evaluations or predictions.
I just realized it's possible I'm being whooshed by your comment.
Well he also claims that the rock has higher Brier scores than all the futurists, which would imply that in this example the futurists aren't actually adding any value with their attempts at honest evaluations and predictions.
I mean, this is a weird example, but i feel like it's like Scott Auckerman says in Comedy Bang Bang, when he introduces the show. He'll do the welcome, and explain the show, and inevitably some guess will retort that this is silly, since everyone knows what the show is about, but he constantly responds with: "every episode is somebody's first episode."
These ideas that should be obvious to anyone who's studied advanced statistics, or formal logic, or read some books about extreme events, all likely already know, but the fact is, not everyone... better yet most people have not every studied these things.
These ideas are inherently interesting, and every year, there are new people coming of age that are introduced to these interesting ideas via an article like this, and then it'll get upvotes. The world is like a fire hose of young people. Add in a popular author who will likely get attention anyway, and here we are at the top of the feed.
But it's not interesting, it's not introducing anyone to advanced statistics or formal logic, it's not showing any real world uses that can be applied by anyone coming of age.
It's just generalized parables by someone not in any of the fields or positions mentioned, some weak conclusions, and a "Heuristics That Almost Always Works" book title.
I mean most people I know that are "very smart people" including myself regularly exercise the cool customer vibe of "yea right, that'll never happen." I think it's a good parable. I mean, it's not really important, and I didn't learn anything, but it's a good reminder that "probably not" is a lot different than "definitely not."
It's only a good parable if you don't follow the author to the conclusion. The heuristics almost always work. Full stop. You should listen to them, because they almost always work. You should not in any case work off the assumption that you're in the 0.01% of the time that the heuristic is wrong.
You will get surprised 0.01% of the time, and that's fine. If you don't follow the heuristic you'll be surprised far more often by way of being wrong.
This gets further weighted by costs. If the cost of a false negative is high and the cost of a false positive is nothing, always assume the positive and do whatever is required: check the window, palpitate the whatever, etc. You are certain it is nothing, but the cost of being wrong is so high that you do it anyway.
The author's whimsical point about needing people who buy into fairy-tales isn't useful or valid. You make these decisions based mostly on the costs of being right and wrong, and within that you assume things based on the stats of occurring.
For some context, Scott Siskind (of SlateStarCodex fame) has been a favorite blogger of this site for years, though admittedly this isn't one of his stronger pieces. Some of Scott's observations are super profound and enlightening, some of them are a bit more obvious. I enjoy his prose, so I tend to at least skim nearly everything he posts.
I'm with you. SSC posts are high on rhetoric and low on actual conceptual knowledge/insights. The examples are ridiculously long and somewhat contrived. s.
> This reads like some generic LinkedIn CEO post that sounds deep on the surface but actually means nothing.
I felt exactly the opposite. In my career as an engineer I regularly encounter experts who claim to be so, but offer no qualifications or expertise. Having the ability to respond to this type of stuff is valuable.
In my personal life, I've felt that many therapists exhibit this exact response. They choose to give heuristics and platitudes because, often times, they work. But it means they are giving up the expertise which they claim possession of.
I'm reminded of quite the childish thing by this article: "With great power comes great responsibility." If you claim to be an expert, you need to actually be an expert. I consider this the social contract of expertise and prestige.
In real life some people are more or less diligent about their jobs, and more or less contrarian, and have different expertise, strengths and weaknesses.
Each of the vignettes portrays the counter position as stupid (literally using a rock as a metaphor).
The reality is much different. In each of the cases there’s an argument to be made that the proposition was flawed- the security guard never finds anything but instead of just not looking anymore, maybe they propose installation of cameras. The volcanologists aren’t very helpful if they don’t have predictive value - if they are always waffling then they are no more useful than the rock cult. And if they are over-activated, then they run the risk of “boy who cried wolf” or of being dismissed because too frequent false positives cost the rest of the society too much.
Overall I think the essay is shallow and not a useful treatment of the subject.
I think you're correct in thinking the situation is complicated, and wrong in thinking the author disagrees! Each situation is subtly different, and some seem more wrong than others. Regardless, a security guard recommending cameras is different from a rock precisely because they suggested that!
What I really don't get is how this article is getting so many upvotes but the comments are unanimous about how vacuous it is... Unless Aella asked her "fans" to vote it up or something. (I for one manufacture my flying monkeys with a statistical model but it's been a really long time..)
If you think you have something that no one else in the world has noticed, you're probably wrong. You're going to need a LOT of evidence to prove yourself right. Lots of people & companies spend years, decades even, proving themselves right. You're not going to do it overnight and you're not going to do it with a wikipedia article.
> He comments on the latest breathless press releases from tech companies. This will change everything! say the press releases. “No it won’t”, he comments. This is the greatest invention ever to exist! say the press releases. “It’s a scam,” he says.
He's got the name backwards on this one. What he's describing is more of an anti-futurist. IMHO, futurists and the ones that make implausibly grand predictions about the future that almost always end up not being true.
Legitimate futurists are objecting to some pop-culture nonsense with NFT's, cryptocurrency, etc., often describing such things as scams. I suspect that the author may've had that in mind there.
It may be sorta like the problem with science: there's real science and pop-culture science-flavored junk, and pop-culture audiences may perceive real scientists as dismissive because they're always so critical of the latest pop-culture fads.
So while futurists may love new-tech and scientists may love science, pop-culture may see things differently because they see futurists/scientists dismissing (what they perceive to be) new-tech/science.
This seems like the weakest example. I immediately thought of that Paul Krugman quote from the 1990s where he pooh-poohed the internet, something that's stuck with him forever and made him a laughingstock where futurism is concerned.
540 comments
[ 2.5 ms ] story [ 317 ms ] threadIf you have heuristic that works 0.0001% of the time - it's almost as good as one that is correct 99.999% of the time. You will notice and learn to just invert it.
except for the value of having a security guard visible so that 99% of the robbers who might conceivably want to rob a Pillow Mart decide to go rob Quilting Heaven down the road instead.
What's frightening about all this is that this article has gotten 15 upvotes despite 100% of the comments so far being about what a pointless article this is.
on edit: added in missing two words that clarified meaning.
Would anyone really think a weatherman that had say a 70% correct heuristic was good? Or go to a doctor like that?
But I think it's interesting enough to discuss. The main thing is that are a whole lot of human activities where one can imagine completely rote activity could replace thinking. But in all of these, a deeper look shows to subtle factors actually require a human being to be present.
It's a bit like self-driving cars. 90% of driving is really easy to get working. 99% is moderately hard. 100% looks like it won't arrive for quite a while.
At some point in the evening all the exit doors, including the front door, became armed, and this was conspicuously noted as when we packed up for the night and tried to exit to the parking lot, we realized we couldn't open the door without an alert being sent to the police (not just the security company). There should have been a guard at his station (desk, CCTVs, etc) in the entryway, but we found none.
We waited for awhile. Then we walked up, down, and through every corridor and restroom of that 4-5 story building, multiple times, looking for the guard. When that failed, we called the security company to ask them if it was okay to open the door. They swore there was a guard on duty and asked us to wait a little longer in case he was doing rounds. Despite knowing that couldn't possibly be the case, we obligingly passed more time waiting in the entryway. Then we walked up, down, and around the building again, but this time splitting up and shouting. Nothing. Nobody.
We go back down and inform the security company that we weren't going to wait any longer and that we'd be triggering the silent alarm as we left. And guess who exits the elevator just as we were about to open the door.... Apparently he had been sound asleep in a cozy nook somewhere in the upper floors--presumably in a conference room or more likely a private office, the former being something we inspected in passing (glass walls), the latter we didn't feel comfortable opening and entering, and both being the last place you'd expect to find a security guard. IIRC, he wouldn't admit it outright, but just played coy. We weren't mad. A little tired and frustrated because as consultants we still had to get in early the next morning, but that was mostly offset by the sheer absurdity of the situation, and by the fact that he seemed quite elderly.
Anyhow, you may assume too much if you assume the security guard actually maintains some kind of useful presence. I guess these days it's more common to have electronic way stations to log a guard doing rounds. I dunno if this building had such measures (this was circa 2001-2002), but as the sole guard he probably was expected to spend most of his time, if not all of his time, manning the security desk, providing ample opportunity to be doing something else, instead.
Unless this all went over my head and that's all sort-of the point of what he's getting at . . ?
For instance, if you are interested in Bayes Theorem like a lot of rationalists say they are, you could talk about the medical test which is 99.99% accurate but for which 90% of the positives are false positives.
https://www.mun.ca/biology/scarr/4250_Bayes_Theorem.html
Imagine that a driver gets hit by accident. He's tested as part of company policy, and tests positive. He gets fired, even though the test only really tells us there's a 33.2% chance he was actually using the drug.
Real world drug tests are a lot worse than 1% false positive and false negative rate.
Every time someone gets fired for a positive test, or loses custody of their kid, or so on, it reinforces whatever statistics are being collected as if the test were a ground truth. They're hardly ever questioned, and there's usually no recourse without an expensive legal fight.
The false positive rate for drug dogs is higher than 40%, for contrast. When a dog "alerts" its worse than a flip of a coin. All that matters is if an officer feels like fucking up your day.
Testing used in situations that are legally significant in people's lives should be required to reach a statistically valid threshold of accuracy, like 99.999% of the times this process is performed, it matches reality. A high sensitivity and high specificity aren't enough, but they're framed as highly accurate and reliable by often well intentioned people who simply aren't thinking in a Bayesian way.
This is what most people don't seem to get. Devices like the ADE 651 or the GT200 were bought by the thousands by law enforcement agencies worldwide, not because they were stupid, but instead, so they could have another "data point" against you that they can use at their discretion.
"Sorry, this dot blinked three times so I'm gonna have to detain you: It's standard procedure, I'm only doing my job."
Antonin Scalia (in)famously commented in one of the Supreme Court's dog-sniff 4th Amendment cases that obviously the police would want dogs that didn't produce false positive alerts, since they wouldn't want to waste their time searching where there were no drugs. The resulting caselaw sets up a situation where a dog can be wrong over half the time and still be used.
The concept that "probable cause on four legs" would be used simply in order to get to search where they otherwise couldn't was apparently unthinkable.
The flawless logic of our leaders is astonishing.
Tend to disagree. It's easy to dismiss one example as "well, medicine is special because XYZ." Multiple examples are the core aspect of showing a general pattern.
He could probably have stopped at 3, 4, or 5 though, not 7.
For the security guard, hearing a single noise is likely to be nothing. However, what if you heard two noises, and the sound of tires outside?
Same thing with the doctor. Most good doctor's I know have a sixth sense, about when something is off and needs further tests beyond just take an aspirin. So maybe the person had a stomach ache, and they had lost some weight, and they were looking a little yellow. All of a sudden the probabilities start looking a lot different.
This is one of the reasons why people got frustrated with Expert Systems as real-life reasoning requires reasoning with uncertainty and we don't have a satisfactory general way to do it.
If you make a confusion matrix its precision and recall is 0. If it almost always worked then its precision and recall would be close to 1.
No, you are getting misleading results because you have an imbalanced dataset.
But other times, they make perfect sense and save a lot of time and effort.
This post reads like a series of straw men created to show that heuristics are dangerous. I’m not sure who is going to argue that heuristics are appropriate in those situations.
Fun and clever article, but for it all to land on that was jarring and disappointing. Preaching to the choir I guess.
Sometimes things happen that, in order to make money or cut costs, we convinced people were impossible.
Right. "Black swan" means "a new thing we've never seen before," but of course few people go around thinking "I will never encounter a new thing that I've never seen before."
For an event to be a Black Swan event, you literally need to have no possibly for the event in your deductive framework (e.g. the problem of induction which is what the book is actually about). In every single one of these examples, the possibly of the event occurring is accepted by everyone.
This is why Taleb lost his mind when people started calling the Covid Pandemic a "black swan event," which it was absolutely not. We know pandemics happen, we know about what power law they happen at. The fact we were not prepared at all is a problem of not being prepared for something we know will happen with certainty.
https://medium.com/incerto/corporate-socialism-the-governmen...
Than Taleb wrote that book and I wished I'd written something about "exceptional events".
Then Taleb just coasted, drifted and became irrelevant.
That's the specific event risk: pretty obviously if we had maintained effective pandemic response measures, and maybe focussed on general infectious agent spread control measures as a society (i.e. a year over year goal to reduce influenza cases, update building codes to require less touchable surfaces to navigate) then we'd be better off then we are.
We know pandemics happen, we know their rough power law occurrences. We know the most dangerous vectors of transmission. We can prepare for them. We typically don’t.
Just look at all the aging housing infrastructure on the California coast. We know there will be major earthquakes and we know how often they happen, yet the general populace cares more about how pretty the historic buildings look, even though we know they will kill people.
These are not black swan events.
But anyways... Does anyone else struggle with Substack's typeface, specifically it's width and spacing between characters? I'm a bit of a typeface nerd, and I genuinely like or enjoy most of our common fonts. Substack is the only site that I find the typeface to significantly affect the reading experience.
I'll leave it up to the reader to determine when that is
The Barking Dog
Barks at everything all the time, people learn to ignore it. Then, when there's real danger, no one cares, providing literally no value and becoming only an annoyance.
It's kind of like a dual for the security guard one.
It would be akin to that lying boy being the officially appointed wolf-spotter for his village.
So, yeah. Our heuristics fail on black swan events. There needs to be a balance between "trust your heuristics" and "watch out for black swans".
The dusk was approaching, they were still in the forest and he proposed that they could sleep under a tree. The hunters were adamant in their refusal: no, this is dangerous, a tree might fall on you in your sleep and kill you. He relented, but silently considered them irrational, given that his assessment of a chance of a tree falling on you overnight was less then 1:5000.
Only later did he realize that for a lifelong hunter, 1:5000 are pretty bad odds that translate to a very significant probability of getting killed over a 30-40 year long hunting career.
It's essential if you want to:
* make money by counting cards at Blackjack (the odds are a function of how many 10 cards are left in the deck)
* make money at the racetrack with a system like this https://www.amazon.com/Dr-Beat-Racetrack-William-Ziemba/dp/0...
* turn a predictive model for financial prices into a profitable trading system
In the case where the bet loses money you can interpret Kelly as either "the only way to win is not to play" or "bet it all on Red exactly once and walk away " depending on how you take the limit.
The general idea is about choosing an action that maximises the expected logarithm of the result.
In practise this means, among other things, not choosing an action that gets you close to "ruin", however you choose to measure the result. Another way to phrase it is that the Kelly criterion leads to actions that avoid large losses.
https://en.wikipedia.org/wiki/Kelly_criterion
"The Kelly bet size is found by maximizing the expected value of the logarithm of wealth, which is equivalent to maximizing the expected geometric growth rate"
In real life people often choose to make bets smaller than the Kelley bet. Part of that is that even if you have a good model there are still "unknown unknowns" that will make your model wrong some of the time. Also most people aren't comfortable with the sharp ups and downs and probability of ruin you have with Kelley.
1) The Kelly criterion is a general decision rule not limited to bet sizing. Bet sizing is just a special case where you're choosing between actions that correspond to different bet sizes. The Kelly criterion works very well also for other actions, like whether to pursue project A or B, whether to get insurance or not, and indeed whether to sleep under a tree or on a rock.
2) The Kelly criterion is not limited to what people would ordinarily think of as "wealth". It applies just as well to anything you can measure with some sort of utility where compounding makes sense.
The best overview I've found so far is The Kelly Capital Growth Investment Criterion[1], which unfortunately is a thick collection of peer-reviewed science, so it's very detailed and heavy on the maths, too.
[1]: https://www.amazon.com/KELLY-CAPITAL-GROWTH-INVESTMENT-CRITE...
There's actually a similar though experiment that might seem even more bizarre: I could tell you "give me $100 or I will kill you tomorrow" and you probably wouldn't give me the $100. That's because when it comes down to it, humans don't see the loss of their life as that big a deal as one might think. It's a big deal, of course, but in combination with the low likelihood, still not big enough to forgo the $100.
One-time games and repeated games have different strategies.
Life is a repeated game of decisions that compound on each other, so that difference is irrelevant.
Kind of. However, you already know that the first N outings didn't have a disaster. So those should be discarded from your analysis.
Doing it N times more has a lot of risk, doing it the N+1th time has barely any.
If you've made it Jan 1 to July 1 months without an accident, the chances of you making it to Dec 31 are now better than they were on Jan 1 -- because now they are just the chances of you making it six months, not a year.
The chances of flipping 6 heads in a row are 1/64. But if I've already flipped 3 in a row... the chances of flipping three _more_ heads in a row is 1/8, the same as always for flipping 3 heads in a row. The ones that already happened don't effect your future chances.
You might still die in one of the next 20 instances. But you've added a lot more not-dead time in between them!
Saying "I can do one more with minimal added risk" every single time after not dying is true and yet pointless, because it's not a given that "minimal added risk" = "not dying." It's survivorship bias to not think frequency doesn't affect the cumulative odds of your future planning solely because you've already done a lot of trials.
It's a convincing fallacy because sometimes you do take N+1 steps. But just like in the article, heuristics aren't always right.
Just because you can justify the next climb on the same basis, that doesn't mean you will. You could decide that you've already tested the odds one too many times.
Of course if you add in "you could decide that you've already tested the odds one too many times" then it's a fallacy to invoke slippery slope because an off-ramp is explicitly specified. In this case slippery slope was mentioned only because N was dismissed as irrelevant.
Do you really think this slippery slope argument is a fallacy? FWIW, wikipedia acknowledges slippery slope can be a legit argument when the slope, and it's chain of consequences, are actually real. https://en.m.wikipedia.org/wiki/Slippery_slope . Indeed, this is the very basis of mathematical induction.
> The fallacious sense of "slippery slope" is often used synonymously with continuum fallacy, in that it ignores the possibility of middle ground and assumes a discrete transition from category A to category B. In this sense, it constitutes an informal fallacy.
"If you take N steps, you will take N+1 steps" is a fallacy whenever it's possible that you won't take N+1 steps.
"Not A -> Not B" is different logic than "A -> B". A is necessary but not sufficient for B.
Reminds me of Terry Pratchett quote "No excuses. No excuses at all. Once you had a good excuse, you opened the door to bad excuses.”
Full quote is fifth here: <https://www.goodreads.com/work/quotes/819104-thud>
The argument can certainly be used in a fallacious manner (e.g. by greatly exaggerating the probability of the further steps, saying they are inevitable if the first step is taken, etc.). It's logically valid to say that the first step enables subsequent steps to be taken.
Edit: I'd say that the slippery slope is perfectly valid rule of thumb in a lot of 'adversarial' situations. Once one side makes an error or fails somehow, the balance between the two sides can be disrupted leading to one 'side' gaining momentum. Just as between people, a similar 'adversarial' process can occur within the minds of individuals: between two ideas or patterns of thought/behaviour, one idea can gain momentum after a decision has been reached. Precedence is a strong force.
Otherwise, it's just a regular d argument.
A fallacy should be a incorrect shape of an argument, a incorrect reasoning, not just a false statement.
Or a few minutes ... or 20 years.
That's the thing w/ statistically independent trials.
You could win 100mm in the lottery (true statement!)
Lottery tickets are a good investment (almost always, false statement).
Planning on "well it could happen, technically" isn't a good approach.
Your chance of winning goes from No Chance to A Chance, which is an infinite improvement.
It's true that you can never win a lottery you don't enter, but the expected value of that ticket is vastly lower than what you paid for it. That means, as an investment, your $10 will be expected to do better in literally anything with a positive return.
If you are buying > $10 worth of dreaming (for you), fine - but that's consumption.
The next three months are no riskier than your first three months were. They don't become more risky because they will add up to 15 months total -- once you've already finished the first 12 without incident.
At sufficient scale, even incredibly unlikely things become quite probable.
The numbers very much agree with you. The median is 149. The 90th is 495 in the simulation, which is close enough to 496. There is very much a long tail in the data. So, the median and the average will not be the same. Is it a coincidence that mean is a 216?
Iteration counts gathered with Python and a (manual) binary search (actually faster than writing code).
Basically, the problem is that you can't just multiply it all together.
(1/6) ^ 3 is correct, and the probability of rolling 3 sixes is indeed 1/216 today, but if you repeat independent events, you don't just add up the probability.
Imagine instead of dice it's coins, and it's only two. Your odds of getting HH today are 1/4, but the odds of getting HH by day four are not now 4/4. We know that it's possible, although unlikely, you could flip coins for the rest of your life and NEVER get two heads. So we know that you can't ever have odds of 4/4 (or 1), only odds that approach 1. So that means that we can't say 216 days from now will be 216/216.
Instead, you need to work out the probability of the event NOT happening, and then repeatedly NOT happening independently (so we can multiply together to get the probability.
For our four coins, the probability of NOT getting HH is 3/4. On Day 2, the probability of NOT getting HH on both occasions will be (3/4)×(3/4), (9/16, 56.25%). By day 3, it will be (3/4) × (3/4) × (3/4), or 27/64. On day 4, it'll be 81/256, or 31.6%. Now we can subtract from 1, to work out that by day 4, the odds of us having hit HH are almost 70%.
As RandomSwede explains, there's a 50% chance that you will have rolled three sixes by day 149. By day 496, you're down to 10%.
The numbers very much agree with you. The median is 149. The 90th is 495 in the simulation, which is close enough to 496. There is very much a long tail in the data. So, the median and the average will not be the same. Is it a coincidence that mean is a 216?
Thinking about it doesn't make me feel like I'm solving a maths problem. I start stacking ideas and concepts in a way which makes me feel like I'm overlaying them in a way which is incorrect.
It makes me feel like I'm solving a riddle, which hints to me that maybe it's actually a question of semantics and definitions rather than a maths problem.
Also, “not really in a lot of danger”? Those odds are worse than that of a 100 year old in the USA (they have a life expectancy of over two years)
Certainly, as an additional risk, it’s high.
Though I'm not sure where they got their figure from, because there isn't an “expected time to live”; there's a 90% probability to live time, a 5% probability to live time…
The more frequently you take a risk, the greater the chance that risk materialises.
Parent wants to lower their overall risk, but doesn't want to stop climbing entirely. So they climb less often.
After a long life of rock climbing, there's no significant risk of doing it one last time or 10 last times (ignoring the effect of old age itself and whatever).
But when you're in earlier stages of your life, you're asking a different question: You're asking, is this something I want to do hundreds or thousands of times in my life, knowing that each of those times has a small chance of ending my life? This becomes a completely different question.
If I'm 35, maybe I will climb 30 times per year on average for 30 years until I'm 65. That's 900 climbs in total. If my goal is to not die or experience serious injury from rock climbing even once in my life, I have to consider the chance that any one of those 900 climbs will result in serious injury or death. I don't know the numbers for the risks involved, but it seems reasonable to be cautious.
Maybe I don't want to give up on rock climbing altogether, but maybe I can scale it back. If I limit myself to 1 climb per year, that's 30 climbs in total. Much lower risk than with 900 climbs.
This is not a logical fallacy.
This makes a lot of sense, as when you're younger frequent climbing would help you to develop proficiency quickly and your body allows you to joy it fully. Plus the social benefits are probably higher when younger.
Once you're older, it's potentially less enjoyable (as your body ages) and you don't need to worry as much about rapidly gaining proficiency.
Now, making that decision at the outset does make sense, because it will drastically reduce the number of climbs you make in your life compared to climbing frequently throughout your life, and rock climbing while young is less risky than rock climbing while old.
But importantly, I don't think that's what GP did. It sounds to me like GP spent their youth climbing a lot without considering their mortality, but then decided to scale back because they realized climbing that often for the rest of their life would be dangerous. Maybe they spent the time from 20 to 35 climbing 30 times per year, in keeping with my earlier example. That means they've already climbed 450 times. Risky, but they made it through alive. At 35, they start to consider their own mortality, and they have the choice between climbing 900 more times by keeping to their current rate, and climbing 30 more times by reducing their rate (or something in between). Deciding to scale back makes sense.
There is no logical fallacy.
None of this intended to cast aspersions on rock climbing in particular, just pointing out that a reasonable person, understanding independence of events and not falling prey to any fallacy, could reasonably make this decision based on their personal risk tolerance
If your tolerance is X% death/life, you can calculate the climbing frequency that falls below the threshold.
On the plus side, if you assume the events are independent, you can recalculate and increase the frequency after each climb.
If an individual decides their risk tolerance is that they will not accept a one in a million chance of injury from rock climbing, how is their analysis incorrect?
In this case [0], a skydiver forgot to put on his parachute...
https://reverentialramblings.com/2018/08/15/the-skydiver-who...
Also, when I read
> I’m hoping you can you forgive me as a minister of religion for likening this story to a spiritual cautionary tale. Yes, we do need to live each day as if it might be our last.
I thought, "Hmm, sounds adventist", and sure enough :-)
Many times if I wear a tight jacket in the car, I forget to put my seat belt on, because I unconsciously mistake the pressure of the jacket for the seatbelt's, even though putting on a seat belt is usually the first thing I do.
Poor guy.
In other words , the difference between the turkey and the climber is the climber knows the odds (at least nominally) , and it’s important .
So it's not about how often they've done it over their lifetime so far, but about how many times they will be doing it over the rest of their life.
Indoor climbing, and especially bouldering, can be a lot of fun at the right gym, and with dramatically reduced risk of death (though injury is still a very real possibility, I say, recalling all the time I spent nursing my sprained ankle).
The 1000th time you go climbing the chances of dying are still 1/1000.
If you get 100 heads in a row, the 101th time you launch a coin the chance of getting heads is still 50%.
"What are my chances of dying in a climbing accident", and
"What are my chances of dying today if I go climbing".
If you are on a plane, you* have a lower risk of some kinds of cancer than the airline staff do. This has nothing to do with the flight you are both on, and everything to do with accumulated flights
"you*" = for most people, i.e. barring a counteracting risk factor.
Replace X with any practitioners subject to sufficient risk as a result of their practice.
I first heard it in the context of mushroom foraging.
This is called Stage 1 in the Gordon Model of learning: unconscious incompetence.
Rather, there is a certain amount of objective risk in alpine environments, and the more time you put yourself in that environment, especially in locations you aren't familiar with, the greater the chance that something will eventually go wrong.
I'm always surprised by the number of famous alpinists who weren't killed on their progressive, headline-capturing attempts but rather on training attempts and lesser objectives.
[1]: https://en.wikipedia.org/wiki/Bathtub_curve
You hear a lot about people who get seriously injured riding who are often professionals or people who ride competitively at a high level. They are doing dangerous things and doing a lot of them.
We don't think it is that dangerous for people who ride at the level we do, out of maybe 15 years we've had one broken bone.
The other day I noticed that we had acquired a used horse blanket from another barn in the area which is a running joke at our barn because of their bad safety culture. They are a "better" barn than ours in that they are attached to the show circuit at a higher level than the bottom, but we are always hearing about crazy accidents that happen there. When I was learning to ride there they had a confusing situation almost like
https://aviation-safety.net/database/record.php?id=19810217-...
with too many lessons going on at once where I wound up going over a jump by accident after a "near miss" in which I almost did. (I never thought I could go over a jump and survive, as it was I had about two seconds to figure out that I had to trust the horse and hang on and I did alright...)
Pretty good if you go climbing 10 times a year. Pretty bad if you go 1000 times.
They wouldn't be famous if they didn't succeed on headline-capturing attempts and there are only so many you can realistically do in life. They are dead however as doing dangerous things often enough will kill a substantial number of practitioners.
Most of you have probably heard of it in the context of fighter pilots doing riskier and riskier maneuvers, but it seems to apply to drivers who speed a lot. 80 starts seeming really slow to them after doing it for years.
* https://flightsafety.org/asw-article/normalization-of-devian....
https://www.youtube.com/watch?v=Ljzj9Msli5o
https://www.youtube.com/watch?v=jWxk5t4hFAg
and the uploader references some further links:
https://www.fireengineering.com/leadership/firefighter-safet...
https://www.flightsafetyaustralia.com/2017/05/safety-in-mind...
and references this book (about the Challenger Disaster):
https://www.amazon.com/gp/product/B011DAS53Y/
which has an overview here:
http://web.mit.edu/esd.83/www/notebook/The%20Challenger%20La...
including these two excerpts I found interesting in this context: "Chapter nine she explains how conformity to the rules, and the work culture, led to the disaster, and not the violation of any rules, as thought by many of the investigators. She concludes her book with a chapter on lessons learned."
"She mainly emphasizes on the long-term impact of institutionalization of the political pressure and economic factors, that results in a “culture of production”."
Every other manned space vehicle had an escape system. The crew of the Challenger was not killed by the failure of the SRB or the explosion of the external tank, but rather when the part of the orbiter they were in hit the ocean. They could have build this into a reinforced pod with parachutes or some other ability to land but they chose not to because they wanted to have the payload section in the rear.
In the case of Columbia it was the fragile thermal protection system that did the astronauts in. There was a lot of fear in the first few flights that the thermal tiles would get damaged and failed and once they thought they'd dodged that bullet they didn't worry about it so much.
"Normalization of deviance" was a formal process in the case of the space shuttle of there being meetings where people went through a list of a few hundred unacceptable situations that they convinced themselves they could accept, often by taking some mitigations.
When the design was finalized it was estimated that a loss of vehicle and crew would happen about 2%-3% of the the time which was about what we experienced. (Originally they planned to launch 50 missions a year which would have meant the continuous trauma of losing astronauts and replacing vehicles.)
It's easy to come to the conclusion that it was a particular scandal that one particular concern got dismissed during a "normalization of deviance" meeting but given a poorly designed vehicle it was inevitable that after making good calls for thousands of concerns there would be a critical bad call.
"Normalization of deviance" is frequently used for a phenomenon entirely different than what Vaughn is talking about, something informal that happens at the level of individuals and small groups. That is, the forklift operators who come to the conclusion it is OK to smoke pot at work, the surgeon who thinks it is OK to not wash his hands, etc. A group can pressure people to do the right things here, but it's something different from the slow motion horror of bureaucracy that tries to do the right thing but cannot.
The standard protocol was to use shims between the halves, as allowing them to close completely could result in the instantaneous formation of a critical mass and a lethal power excursion. Under Slotin's own unapproved protocol, the shims were not used and the only thing preventing the closure was the blade of a standard flat-tipped screwdriver manipulated in Slotin's other hand. Slotin, who was given to bravado, became the local expert, performing the test on almost a dozen occasions, often in his trademark blue jeans and cowboy boots, in front of a roomful of observers. Enrico Fermi reportedly told Slotin and others they would be "dead within a year" if they continued performing the test in that manner. Scientists referred to this flirting with the possibility of a nuclear chain reaction as "tickling the dragon's tail", based on a remark by physicist Richard Feynman, who compared the experiments to "tickling the tail of a sleeping dragon".
On the day of the accident, Slotin's screwdriver slipped outward a fraction of an inch while he was lowering the top reflector, allowing the reflector to fall into place around the core. Instantly, there was a flash of blue light and a wave of heat across Slotin's skin; the core had become supercritical, releasing an intense burst of neutron radiation estimated to have lasted about a half second. Slotin quickly twisted his wrist, flipping the top shell to the floor. The heating of the core and shells stopped the criticality within seconds of its initiation, while Slotin's reaction prevented a recurrence and ended the accident. The position of Slotin's body over the apparatus also shielded the others from much of the neutron radiation, but he received a lethal dose of 1,000 rad (10 Gy) neutron and 114 rad (1.14 Gy) gamma radiation in under a second and died nine days later from acute radiation poisoning.
https://en.wikipedia.org/wiki/Demon_core#Second_incident
I'm guessing that falling from a cliff is "better" than dying from a poisonous mushroom. The latter scares the hell out of me. The former is a glorious ride until the ride is over (regrettably).
If you sense you're falling to death, it wont be too glorious (personally), but freakish. It can also always fail to bring death!
For rock climbing, you're probably right. I remember training in a climbing hall, when I saw someone falling off the highest wall. The tenant of the hall didn't look surprised at all. Apparently, it happens frequently.
That being said, if you serious about security, I'm sure the risk can be minimal.
See e.g. https://blogs.bmj.com/bjsm/2018/12/12/pedal-power-the-health...
The logic in the story is BS. First, you would never, ever get into a car with that logic. Second, trees just aren't that ephemeral. People who live in a forest would be very aware of when they do or don't fall (or more problematically, drop large branches.) It's not as straightforward as just avoiding storms or dead-looking trees. Sustained wet weather, especially after a period of dry weather, is a common cause. As is the opposite for some trees (eg oak trees drop limbs in sustained hot dry weather.) As for disease or other causes, an experienced hunter in a familiar area could tell at a glance.
The message I got from the story is that they probably did have a very good reason. They either thought it would be too hard to communicate, or they were themselves cargo-culting the falling tree excuse when the reality was more likely to be... I dunno, snakes or nasty bugs or annoying sticky sap or whatever.
Like these guys probably have homes, with bedding of some sort, maybe they'd rather sleep next to their wives than some caterpillars. If I was giving somebody from a far-off place a tour of my workplace and, on the bus ride home, they suggested it was getting dark and we should camp on the sidewalk I'd probably not go for it. If they were really insistent I'd probably amplify the danger of sleeping on the sidewalk to shut them up.
The logic isn't applicable to any set of risks. As deadly as cars are, the risk of car crash death is much, much lower than 1/5000 per trip. It's probably closer to applicable to being a drunk driver, and "you would never operate a car drunk" is pretty accurate for many people.
I don't know anything about trees around there, maybe they're really short-lived? For forests around here, it's a gross overestimate.
I would still guess that the number is wrong, I suspect that trees have a longer life on average from becoming what we would consider "big" until they fall over. But it's still an important detail.
Also, I bet it's not just the tree you're sleeping under that poses a risk, but also other trees in the vicinity that might fall on you. In a forest there are probably a bunch of trees "in range".
All of that said, I've often camped and slept in forests, as have many of my friends, and I've never heard of anyone being killed or injured by a falling tree, or ever heard or seen any "don't sleep under a tree, it might kill you"-advice, so I don't know...
The tricks in this article might work in the short term. However, over the length of a career, it's difficult to outrun a negative reputation forever. Especially in the age of the internet, people will eventually catch on to what you're doing.
https://taylorpearson.me/ergodicity/
When you hear once-in-a-hundred-year event, it makes it sound quite rare. One might look around and say (for example, in relation to climate) "why are so many of these happening?"
But it is unsurprising statistically. If you know just a thousand distinct geographic places, about 10 of them would experience such an event each year.
"highest temperature ever recorded in town X" does not mean much.
"highest temperature recorded in country Y" on the other hand is more significant, especially if the country is large.
Of course there are other compounding factors. Not all events are one-in-one-hundred; some are one-in-ten, others are one-in-five-hundred, and with increasing scarcity by order of magnitude.
Another compounding factor is that the borders for "geographical areas" are fuzzy. Does a one-in-a-hundred year event that happens in Vermont also qualify as having happened in New Hampshire? Probably depends on the type and the specific measurements and the expectation according to history.
And what about aggregate events? E.g. "It's been five hundred years since we've seen this many tornadoes, which tend to happen once every ten years."
And in the opposite direction of the 100 square-inch plot of ground, there is blurring in the other direction: What do they mean in aggregate if they are fewer than expected at a global scale?
So my original comment was just a simple way of taking the average of all of these competing factors and stating a general truth that's somewhere in the middle. If you have X things that are expected to have 1/Y probabilities, then the probability of you experiencing any of them is not 1/Y, it's more like X/Y. (As in very likely.. that's more than 1 so obviously not mathematically correct.) But we often don't think about rare events this way - as no specific event being probable, but some collection of improbable events being almost certain. We perceive them all as 1/Y. It's just a very local way of thinking.
Of course in practice, it's quite hard to know whether conditions in one location are independent from another, or whether there's some degree of correlation or an underlying causal factor. This is why we have climate scientists.
>>All these things are almost always true. But Heuristics That Almost Always Work tempt us to be more certain than we should of each
The most important thing to realize about risk is this:
The difference between [using knowledge, skill, technology, and planning to manage risk] vs. [getting away with something]
If you aren't managing risk, it is managing you. And you can get away with something for a long time, but it is always a matter of until you don't, and then it is too 'effin late for you.
When you are managing the risk, you can make an entire career or lifetime of doing things that will otherwise kill you in seconds, scuba diving, flying, mountaineering, building tall structures, working with molten metal or dangerous chemicals, etc., etc., etc.
You can also get away with very dangerous things for at least enough time to fool you into thinking you are smart. The article discusses this at length.
This is why when you need to understand and manage the risks, and also be very alert to close calls - they mean that even though you thought you're managing, you've actually gone into the land of [getting away with it], just saved by Pure Dumb Luck. Don't say "it's okay it worked", look at why, because you might not have as much PDL next time.
Back of the envelope calculation: Life expectancy of 72 years times 365 gives about 26k days, so your average chance of death on a given day is on the order of 1 in 26,000.
They can and do drop large limbs at any time without warning.
There are gum trees in PNG.
[1] https://en.wikipedia.org/wiki/Micromort
Each and every time you have a 1 in 5000 chance.
So you have 0.02% chance of getting crushed each time.
(1 - 0.0002)^10950 = 0.1119 1 - 0.1119 = 0.8881
So the probability of getting crushed at least one night over 30 years is ~89%
I think, my stats are from school over 10 years ago.
This is because, for example, if you flip a coin, each time you still only have 50% chance of getting tails. But the chances that you flip it 10 times in a row and never get heads are a lot less than 50%.
That's said. Another tricky bit is, what was measured when we said 1/5000 chance? This is where data can get confusing. Was that the odd of a tree falling at any given night? Or was that the odd of someone being crushed by a tree in their sleep at night? Or was it the odd of someone being crushed by a tree ever? Or the odd of a particular tree falling at night?
That's often where any prediction already begins to break down. For example, sorry to use the vaccines as an example, but when we say 90% efficacy, it means, out of x number of people who got a vaccine during the trial, 90% of those didn't get covid during some period, while in the placebo group it would be some other % who got it.
Reasoning about this already is tricky. You don't know the priors. What was the odd your participants were exposed to COVID? What if you'd measured over a longer period of time? What if that was just a lucky bunch?
>If you sleep under a tree 4999 times and nothing happens, that doesn’t mean the 5000 time you sleep under one you’ll get crushed.
No, but it means you have far more overall chances of getting crushed if you do it 5000 times, than if you do it once or twice.
https://www.nytimes.com/2013/01/29/science/jared-diamonds-gu...
There’s a term for this which I’m unable to recall and it’s not easy to Google. Would greatly appreciate if someone could help me out here!!
https://news.ycombinator.com/item?id=30267553
Probability of surviving a night under a tree is (1-1/5000).
15 years of hunting is roughly 5000 nights. The chances of never getting hit by a tree over that period are (1-1/5000) for each night, which compounds to
That's to say, the odds are 3:2 (at least!) that you'd get killed by a tree in 15 years.Make it at least 5:1 for 30 years.
That's to say, at least 5 out of 6 hunters who sleep under a tree every day wouldn't survive doing it for 30 years.
And that, children, is why credit cards are a scary thing.
If the chance was actually 1:5000, the longevity of trees would be similar to that of hunters sleeping under them - or lower, since hunters can sometimes avoid the hazard, but trees are exposed to it every night (and all day as well). Actual data on tree mortality seems to indicate that the chances are much lower than this. Almost certainly they do not make sleeping under trees a significant risky activity.
Is it possible that both the original teller, the reteller and you too, are starting from the (unfounded) assumption that the hunters know what they're talking about, and are adapting the facts to fit this assumption?
There could be another reason why sleeping in the forest was dangerous – e.g., poisonous snakes or dangerous animals etc. Also if the temperature drops at night and they didn't have enough clothing, they could get hypothermia and so on.
There’s a real dearth of info around coconut fatalities. This 1984 paper examined a 4 year timespan of all trauma-related admissions to one hospital in Papua New Guinea. 9 of them (2.5% overall) stemmed from coconuts. In 3 of the cases, all children, the patients slipped into coma.
From what I’ve read elsewhere (no good links, sorry), coconut injuries worldwide seem to have fallen significantly due to better harvesting practice - the age of a coconut and their chance of falling appear to be linked. While I can’t find a good paper saying this, I do buy it.
So, perhaps not 1:5000, but (at least at one point in time) definitely a risk.
Any payoff from a trade which has even a very tiny probablity of making you go bust is zero.
Because once you go bust you are not going to be doing trading anymore.
He calls these Uncle Points.
A ranking forcibly brings the metric away from accuracy (which the heuristic can score well on) to something based around precision-recall (which it cannot).
Substitute “this” for SAN array, core switch, or entire data centre.
I’ve had someone argue with me at length that simultaneous multi disk failures in a RAID5 never happen.
Two weeks later it did and the main SAN disk array went up in smoke.
Terry Pratchett
This reads like some generic LinkedIn CEO post that sounds deep on the surface but actually means nothing.
I just realized it's possible I'm being whooshed by your comment.
These ideas that should be obvious to anyone who's studied advanced statistics, or formal logic, or read some books about extreme events, all likely already know, but the fact is, not everyone... better yet most people have not every studied these things.
These ideas are inherently interesting, and every year, there are new people coming of age that are introduced to these interesting ideas via an article like this, and then it'll get upvotes. The world is like a fire hose of young people. Add in a popular author who will likely get attention anyway, and here we are at the top of the feed.
It's just generalized parables by someone not in any of the fields or positions mentioned, some weak conclusions, and a "Heuristics That Almost Always Works" book title.
You will get surprised 0.01% of the time, and that's fine. If you don't follow the heuristic you'll be surprised far more often by way of being wrong.
This gets further weighted by costs. If the cost of a false negative is high and the cost of a false positive is nothing, always assume the positive and do whatever is required: check the window, palpitate the whatever, etc. You are certain it is nothing, but the cost of being wrong is so high that you do it anyway.
The author's whimsical point about needing people who buy into fairy-tales isn't useful or valid. You make these decisions based mostly on the costs of being right and wrong, and within that you assume things based on the stats of occurring.
Author is an MD (doctor)...
I felt exactly the opposite. In my career as an engineer I regularly encounter experts who claim to be so, but offer no qualifications or expertise. Having the ability to respond to this type of stuff is valuable.
In my personal life, I've felt that many therapists exhibit this exact response. They choose to give heuristics and platitudes because, often times, they work. But it means they are giving up the expertise which they claim possession of.
I'm reminded of quite the childish thing by this article: "With great power comes great responsibility." If you claim to be an expert, you need to actually be an expert. I consider this the social contract of expertise and prestige.
In real life some people are more or less diligent about their jobs, and more or less contrarian, and have different expertise, strengths and weaknesses.
Each of the vignettes portrays the counter position as stupid (literally using a rock as a metaphor).
The reality is much different. In each of the cases there’s an argument to be made that the proposition was flawed- the security guard never finds anything but instead of just not looking anymore, maybe they propose installation of cameras. The volcanologists aren’t very helpful if they don’t have predictive value - if they are always waffling then they are no more useful than the rock cult. And if they are over-activated, then they run the risk of “boy who cried wolf” or of being dismissed because too frequent false positives cost the rest of the society too much.
Overall I think the essay is shallow and not a useful treatment of the subject.
This is why we have 2727272 self help books that I can't read past chapter 3 as they regurgitate the same idea in every sentence
If you think you have something that no one else in the world has noticed, you're probably wrong. You're going to need a LOT of evidence to prove yourself right. Lots of people & companies spend years, decades even, proving themselves right. You're not going to do it overnight and you're not going to do it with a wikipedia article.
> He comments on the latest breathless press releases from tech companies. This will change everything! say the press releases. “No it won’t”, he comments. This is the greatest invention ever to exist! say the press releases. “It’s a scam,” he says.
He's got the name backwards on this one. What he's describing is more of an anti-futurist. IMHO, futurists and the ones that make implausibly grand predictions about the future that almost always end up not being true.
It may be sorta like the problem with science: there's real science and pop-culture science-flavored junk, and pop-culture audiences may perceive real scientists as dismissive because they're always so critical of the latest pop-culture fads.
So while futurists may love new-tech and scientists may love science, pop-culture may see things differently because they see futurists/scientists dismissing (what they perceive to be) new-tech/science.
It's kind of an aside, but I think a lot of people (most?) who strongly identify with "science" really identify with science fiction.