4 ms·

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

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.
  - s1artibartfast 3y ago
    If your model is consistently wrong in a statistically predictable way, either your measurement or model is inaccurate. A 3% chance that never occurs is an inaccurate prediction.
    - msandford 3y ago
      Right! Yes absolutely! It's wrong because the measurements are suggestive of possibility, rather than certain of it. If we observe an asteroid that with two poor measurements is determined to be headed away from Earth, that's the end. Look no further. If we observe an asteroid with two poor measurements that has some significant chance of hitting, more and better measurements are made. Then very often those better measurements show it was never actually going to hit anyhow. But we never would have known without the better measurements, and we never would have devoted more time to making better measurements without a reason to do so. A 3% chance that never occurs is because that 3% is based on data that's at the limit of what the telescopes can provide, not based upon bad math.
      - MauranKilom 3y ago
        Then what does 3% mean? Surely it means "given the data we have, one in every 33 will hit". Since that empirically doesn't happen, it must be that "the data we have" has a very low prior probability of being real. In other words, the measurement noise seems distributed in a way that over-represents unlikely trajectories. Hence it seems that it would lead to more accurate predictions if the measurements and their uncertainties were fitted to a model that corrects for the prior probability of observing an asteroid on a given trajectory/making a certain observation. This discrepancy between distribution of measurement error vs distribution of actual trajectories is what people are wondering about, because it seems interesting to know more about (e.g. "why are certain trajectories less likely?").

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.
- s1artibartfast 3y ago
  If your model is consistently wrong in a statistically predictable way, either your measurement or model is inaccurate. A 3% chance that never occurs is an inaccurate prediction.
  - msandford 3y ago
    Right! Yes absolutely! It's wrong because the measurements are suggestive of possibility, rather than certain of it. If we observe an asteroid that with two poor measurements is determined to be headed away from Earth, that's the end. Look no further. If we observe an asteroid with two poor measurements that has some significant chance of hitting, more and better measurements are made. Then very often those better measurements show it was never actually going to hit anyhow. But we never would have known without the better measurements, and we never would have devoted more time to making better measurements without a reason to do so. A 3% chance that never occurs is because that 3% is based on data that's at the limit of what the telescopes can provide, not based upon bad math.
    - MauranKilom 3y ago
      Then what does 3% mean? Surely it means "given the data we have, one in every 33 will hit". Since that empirically doesn't happen, it must be that "the data we have" has a very low prior probability of being real. In other words, the measurement noise seems distributed in a way that over-represents unlikely trajectories. Hence it seems that it would lead to more accurate predictions if the measurements and their uncertainties were fitted to a model that corrects for the prior probability of observing an asteroid on a given trajectory/making a certain observation. This discrepancy between distribution of measurement error vs distribution of actual trajectories is what people are wondering about, because it seems interesting to know more about (e.g. "why are certain trajectories less likely?").