5 ms·

Unless one in every 33 asteroids that have 3% impact probability at some point in time actually impacts earth, there is clearly some unwarranted assumption in t

Unless one in every 33 asteroids that have 3% impact probability at some point in time actually impacts earth, there is clearly some unwarranted assumption in the error bar/distribution calculation. "The measurement data has noise" does not explain why the noise has a bias towards "the asteroid will hit earth" whereas reality so far has been biased towards "the asteroid will not hit earth". (This assumes that significantly more than 33 asteroids have had >= 3% impact probability predicted at some point. The opposite would not be less concerning.)

noduerme 3y ago
One explanation would be the Anthropic Principle. In 3% of universes you were killed today, you're just not living in one of those.
- jacquesm 3y ago
  In 97% of the universes dinosaur descendants rule planet earth. But on this one they got unlucky.
- MauranKilom 3y ago
  This only works if there is nothing between "no impact" and "you die the same day as the impact". But we know that's not the case.
  - noduerme 3y ago
    Why "same day" and not same week or month? If it's not the same instant, then you're hypothesizing some kind of back-propagation (where alternate futures in which you die influence the likelihood of current events)[0]. Under that hypothesis, it would only matter whether some event would cause you to die sooner than you otherwise would. [0] https://arxiv.org/abs/0707.1919 https://arxiv.org/abs/0707.1919 [edit] FWIW, I actually corresponded with one of the authors of this paper back in 2007, and from what I could tell, this wasn't an attempt at parody, although now it might be dismissed as one. Personally I'm not willing to declare my (non)commitment to the theory either way.
jacquesm 3y ago
That's because Earth has gravity, and an asteroid that comes close enough can get deflected onto the planet even if right now it seems to be on a trajectory to miss it entirely. The closer they get and the lower the relative speeds the larger the chance that they will collide and that's not a linear relationship. Beyond a certain boundary impact is certain, then the question is what the time of the impact is and how precise the observations up to that point are in order to figure out where and when exactly it will come down. That won't happen very long before the impact itself happens even if you could say some time in advance roughly in which hemisphere and roughly when. But not precise enough to be very useful.
- fouc 3y ago
  I wouldn't expect earth gravity to affect it sufficiently enough to cause it to crash unless it was moving very slowly, but I'm not sure asteroids ever move that slowly?
  - jacquesm 3y ago
    Like the moon is moving slowly? About 1 km/second for an object that weighs ~10^18 tons at a distance of 300,000 km? Now think of what that kind of force would do on a much lighter object that moves faster.
    - MauranKilom 3y ago
      I'm not sure I understand your point... The object mass does not impact its trajectory (unless it either touches our atmosphere or is so massive as to measurably change earth's orbit). The gravitational force earth exerts on the moon and some asteroid is also very different, because the force is proportional to both object masses.
      - jacquesm 3y ago
        Think 'gravitational slingshot' but without missing the planet. The object will change direction and accelerate into us. It could end up grazing the atmosphere or it could go from grazing the atmosphere or even non-impact to impact.
msandford 3y ago
Imagine you see a car 1 mile away as you're preparing to cross the street. 1 sec later, it's a bit closer. You wonder "will this car hit me?". It's hard to say since the car is so far away and your measurements of its speed are so poor. You wait 5 sec and it's still only imperceptibly closer. You realize there is no way it could possibly hit you. You cross the street unconcerned.
- muzani 3y ago
  3% seems much higher though. If I crossed the street at 3%, I probably would be dead by now. Cars may not be a great analogy, because they swerve, but it is quite high. Space is pretty damn big too so the odds are really low of being hit by space things. But unlike cars, space stuff tend to swerve towards the larger bodies.
  - jacquesm 3y ago
    > But unlike cars, space stuff tend to swerve towards the larger bodies. That's exactly it. And at the speeds these objects are going and the uncertainty of the observations you would have to be observing an object for a really long time to get the kind of accuracy required to pick a mitigation method that would work. And even then, assuming you could nail the point of impact of something going 2000 km / second of unknown mass in a strong gravity field: given the COVID response I have a hard time believing that the response to 'Houston, Texas is going to be obliterated on Jun 1st 2024' would be met with anything but skepticism and laughter. Right up to the moment of impact.
- s1artibartfast 3y ago
  That makes perfect sense. Where it breaks down is if you put percentages on it. If you say the car is a 3% chance of hitting you, it doesn't and you repeat the process a thousand times, and it never hits you something is wrong with your math
  - gyrovagueGeist 3y ago
    The uncertainty is epistemic not aleatoric. The percentage represents our knowledge about the system at the time of measurement propagated through the forward model and is not an inherit random process in the system/model itself.
gyrovagueGeist 3y ago
To simplfy, let's assume you have perfect knowledge of everything else & that the only variable that matters is asteroids current position. By triangulating observations you have a point estimate. Due to calibrating your instruments in the past you know that they tend to have uniform additive noise that is the same in each dimension. Let's say it shifts measurements by up to 1km randomly. So the best guess you have is that the true asteroid is 99% likely to be somewhere within a 2km box centered at the observation point. For each possible location in this box you use it as a hypothetical starting point and run a simulation forward creating a trajectory. In 3% of these trajectories the asteroid hits the earth. The 3% is only a probability over the measurement uncertainty. It represents our knowledge about the system in a bayesian sense. The true asteroid was always ever going to hit the earth or not. There is no uncertainty inherent in the system. That many asteroids have non negligible probability only means the physics is sensitive to initial conditions or that the measurements are loose. (Both are true)
- MauranKilom 3y ago
  Given everything you said is true, under those assumptions 3% of those asteroids that we identify as being in said 2km box will hit earth, unless the forward simulation is wrong (implausible) or the measurement error distribution is substantially wrong (also seems unlikely). What your analysis is not touching on is the prior probability that an asteroid will hit earth (you collapse this to "any asteroid will either hit or not", but that is not helpful for "model calibration" or whatever you want to call this) - or, equivalently, the prior probability of making (a series of) observations with a certain uncertainty/error distribution. If that prior were actually as uniform as each measurement error suggests, I don't see any Bayesian wiggle room left for why we don't have those 3% of impact actually happen. (I'm no expert, but presumably you need multiple measurements to predict a trajectory, and while their measurement error distributions may be independent, it seems plausible to me that the prior probability of making two specific noise-affected observations, i.e. of the asteroid being on a certain trajectory, is most likely not so uniform. That's the part that I'd like to learn more about though.)
  - gyrovagueGeist 3y ago
jryb 3y ago
> Unless one in every 33 asteroids that have 3% impact probability at some point in time actually impacts earth There would be a ~63.4% chance that at least one would hit us if there were 33 such asteroids. To compute this, take 1-(0.97^33). I agree with your broader point though.
credit_guy 3y ago
Most likely the estimation is conservative. In many situations, erring on one side results in worse outcomes than erring on the other side. In our case, a false positive has pretty much zero consequences, while a false negative could wipe out the dinosaurs.

noduerme 3y ago

One explanation would be the Anthropic Principle. In 3% of universes you were killed today, you're just not living in one of those.

jacquesm 3y ago
In 97% of the universes dinosaur descendants rule planet earth. But on this one they got unlucky.
MauranKilom 3y ago
This only works if there is nothing between "no impact" and "you die the same day as the impact". But we know that's not the case.
- noduerme 3y ago
  Why "same day" and not same week or month? If it's not the same instant, then you're hypothesizing some kind of back-propagation (where alternate futures in which you die influence the likelihood of current events)[0]. Under that hypothesis, it would only matter whether some event would cause you to die sooner than you otherwise would. [0] https://arxiv.org/abs/0707.1919 https://arxiv.org/abs/0707.1919 [edit] FWIW, I actually corresponded with one of the authors of this paper back in 2007, and from what I could tell, this wasn't an attempt at parody, although now it might be dismissed as one. Personally I'm not willing to declare my (non)commitment to the theory either way.

jacquesm 3y ago

That's because Earth has gravity, and an asteroid that comes close enough can get deflected onto the planet even if right now it seems to be on a trajectory to miss it entirely. The closer they get and the lower the relative speeds the larger the chance that they will collide and that's not a linear relationship. Beyond a certain boundary impact is certain, then the question is what the time of the impact is and how precise the observations up to that point are in order to figure out where and when exactly it will come down. That won't happen very long before the impact itself happens even if you could say some time in advance roughly in which hemisphere and roughly when. But not precise enough to be very useful.

fouc 3y ago
I wouldn't expect earth gravity to affect it sufficiently enough to cause it to crash unless it was moving very slowly, but I'm not sure asteroids ever move that slowly?
- jacquesm 3y ago
  Like the moon is moving slowly? About 1 km/second for an object that weighs ~10^18 tons at a distance of 300,000 km? Now think of what that kind of force would do on a much lighter object that moves faster.
  - MauranKilom 3y ago
    I'm not sure I understand your point... The object mass does not impact its trajectory (unless it either touches our atmosphere or is so massive as to measurably change earth's orbit). The gravitational force earth exerts on the moon and some asteroid is also very different, because the force is proportional to both object masses.
    - jacquesm 3y ago
      Think 'gravitational slingshot' but without missing the planet. The object will change direction and accelerate into us. It could end up grazing the atmosphere or it could go from grazing the atmosphere or even non-impact to impact.

msandford 3y ago

Imagine you see a car 1 mile away as you're preparing to cross the street. 1 sec later, it's a bit closer. You wonder "will this car hit me?". It's hard to say since the car is so far away and your measurements of its speed are so poor. You wait 5 sec and it's still only imperceptibly closer. You realize there is no way it could possibly hit you. You cross the street unconcerned.

muzani 3y ago
3% seems much higher though. If I crossed the street at 3%, I probably would be dead by now. Cars may not be a great analogy, because they swerve, but it is quite high. Space is pretty damn big too so the odds are really low of being hit by space things. But unlike cars, space stuff tend to swerve towards the larger bodies.
- jacquesm 3y ago
  > But unlike cars, space stuff tend to swerve towards the larger bodies. That's exactly it. And at the speeds these objects are going and the uncertainty of the observations you would have to be observing an object for a really long time to get the kind of accuracy required to pick a mitigation method that would work. And even then, assuming you could nail the point of impact of something going 2000 km / second of unknown mass in a strong gravity field: given the COVID response I have a hard time believing that the response to 'Houston, Texas is going to be obliterated on Jun 1st 2024' would be met with anything but skepticism and laughter. Right up to the moment of impact.
s1artibartfast 3y ago
That makes perfect sense. Where it breaks down is if you put percentages on it. If you say the car is a 3% chance of hitting you, it doesn't and you repeat the process a thousand times, and it never hits you something is wrong with your math
- gyrovagueGeist 3y ago
  The uncertainty is epistemic not aleatoric. The percentage represents our knowledge about the system at the time of measurement propagated through the forward model and is not an inherit random process in the system/model itself.

gyrovagueGeist 3y ago

To simplfy, let's assume you have perfect knowledge of everything else & that the only variable that matters is asteroids current position. By triangulating observations you have a point estimate. Due to calibrating your instruments in the past you know that they tend to have uniform additive noise that is the same in each dimension. Let's say it shifts measurements by up to 1km randomly. So the best guess you have is that the true asteroid is 99% likely to be somewhere within a 2km box centered at the observation point. For each possible location in this box you use it as a hypothetical starting point and run a simulation forward creating a trajectory. In 3% of these trajectories the asteroid hits the earth. The 3% is only a probability over the measurement uncertainty. It represents our knowledge about the system in a bayesian sense. The true asteroid was always ever going to hit the earth or not. There is no uncertainty inherent in the system. That many asteroids have non negligible probability only means the physics is sensitive to initial conditions or that the measurements are loose. (Both are true)

MauranKilom 3y ago
Given everything you said is true, under those assumptions 3% of those asteroids that we identify as being in said 2km box will hit earth, unless the forward simulation is wrong (implausible) or the measurement error distribution is substantially wrong (also seems unlikely). What your analysis is not touching on is the prior probability that an asteroid will hit earth (you collapse this to "any asteroid will either hit or not", but that is not helpful for "model calibration" or whatever you want to call this) - or, equivalently, the prior probability of making (a series of) observations with a certain uncertainty/error distribution. If that prior were actually as uniform as each measurement error suggests, I don't see any Bayesian wiggle room left for why we don't have those 3% of impact actually happen. (I'm no expert, but presumably you need multiple measurements to predict a trajectory, and while their measurement error distributions may be independent, it seems plausible to me that the prior probability of making two specific noise-affected observations, i.e. of the asteroid being on a certain trajectory, is most likely not so uniform. That's the part that I'd like to learn more about though.)
- gyrovagueGeist 3y ago

jryb 3y ago

> Unless one in every 33 asteroids that have 3% impact probability at some point in time actually impacts earth There would be a ~63.4% chance that at least one would hit us if there were 33 such asteroids. To compute this, take 1-(0.97^33). I agree with your broader point though.

credit_guy 3y ago

Most likely the estimation is conservative. In many situations, erring on one side results in worse outcomes than erring on the other side. In our case, a false positive has pretty much zero consequences, while a false negative could wipe out the dinosaurs.