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Thanks for the comment, James!

Whatâ€™s the main evidence base guiding this approach and whatâ€™s the expected increase in accuracy attendees can expect the course to have?

I am tagging @jsteinhardt in case he wants to reply.

Am I confident that someone born in 2024 can't grow to be 242cm? Nope. I just don't trust the statistical modeling all that much.

(If you disagree and are willing to offer 1,000,000:1 odds on this question, I'll probably be willing to bet on it).

I do not want to take this bet, but I am open to other suggestions. For example, I think it is very unlikely that transformative AI, as defined in Metaculus, will happen in the next few years.

Thanks, Linch. Strongly upvoted.

Now for normal distributions, or normal-ish distributions, this may not matter all that much in practice. As you say "height roughly follows a normal distribution," so as long as a distribution is ~roughly normal, some small divergences doesn't get you too far away (maybe with a slightly differently shaped underlying distribution that fits the data it's possible to get a 242 cm human, maybe even 260 cm, but not 400cm, and certainly not 4000 cm).

Since height roughly follows a normal distribution, the probability of huge heights is negligible.

Right, by "the probability of huge heights is negligible", I meant way more than 2.42 m, such that the details of the distribution would not matter. I would not get an astronomically low probability of at least such an height based on the methodology I used to get an astronomically low chance of a conflict causing human extinction. To arrive at this, I looked into the empirical tail distribution. I did not fit a distribution to the 25th to 75th range, which is probably what would have suggested a normal distribution for height, and then extrapolated from there. I said I got an annual probability of conflict causing human extinction lower than 10^-9 using 33 or less of the rightmost points of the tail distribution. The 33rd tallest person whose height was recorded was actually 2.42 m, which illustrates I would not have gotten an astronomically low probability for at least 2.42 m.

This is why I think it's important to be able to think about a problem from multiple angles.

I agree. What do you think is the annualised probability of a nuclear war or volcanic eruption causing human extinction in the next 10 years? Do you see any concrete scenarios where the probability of a nuclear war or volcanic eruption causing human extinction is close to Toby's values?

I usually deploy this line ["any extremal distribution looks like a straight-line when drawn on a log-log plot with a fat marker"] when arguing against people who claim they discovered a power law when I suspect something like ~log-normal might be a better fit. But obviously it works in the other direction as well, the main issue is model uncertainty.

I think power laws overestimate extinction risk. They imply the probability of going from 80 M annual deaths to extinction would be the same as going from extinction to 800 billion annual deaths, which very much overestimates the risk of large death tolls. So it makes sense the tail distribution eventually starts to decay much faster than implied by a power law, especially if this is fitted to the left tail.

On the other hand, I agree it is unclear whether the above tail distribution suggests an annual probability of a conflict causing human extinction above/below 10^-9. Still, even my inside view annual extinction risk from nuclear war of 5.53*10^-10 (which makes no use of the above tail distribution) is only 0.0111 % (= 5.53*10^-10/(5*10^-6)) of Toby's value.

Thanks, Bradley, and welcome to the EA Forum! Strongly upvoted.

Given that it is unlikely that incorporating humidity would decrease heat-related mortality, my own view here is that this pushes current estimates towards a lower bound.

If adequately modelling humidity would increase heat deaths, I wonder whether it would also decrease cold deaths, such that the net effects is unclear.

In practice, these assumptions limit the ability to model things like extreme heat waves and heat domes, which can cause large fatality spikes (e.g. figure below from Washington State in 2021). Missing these features in some locations might be akin to missing almost all the possible heat related mortality in cooler climates.

As illustrated below, deaths from extreme cold and heat accounted for only a tiny fraction of the deaths from non-optimal temperature in 2015 in some countries, which attenuates the effect you are describing.

Thanks for the comment, Linch.

That's an odd prior. I can see a case for a prior that gets you to <10^-6,

maybeeven 10^-9, but how can you get to substantially below 10^-9 annual with just historical data???

Fitting a power law to the N rightmost points of the tail distribution of annual conflict deaths as a fraction of the global population leads to an annual probability of a conflict causing human extinction lower than 10^-9 for N no higher than 33 (for which the annual conflict extinction risk is 1.72*10^-10), where each point corresponds to one year from 1400 to 2000. The 33 rightmost points have annual conflict deaths as a fraction of the global population of at least 0.395 %. Below is how the annual conflict extinction risk evolves with the lowest annual conflict deaths as a fraction of the global population included in the power law fit (the data is here; the post is here).

The leftmost points of the tail suggest a high extinction risk because the tail distribution is quite flat for very low annual conflict deaths as a fraction of the global population.

The extinction risk starts to decay a lot as one uses increasingly rightmost points of the tail because the actual tail distribution also decreases for high annual conflict deaths as a fraction of the global population.

Sapienshasn't been around for that long for longer than a million years! (and conflict with homo sapiens or other human subtypes still seems like a plausible reason for extinction of other human subtypes to me). There have only been maybe 4 billion species total in all of geological history! Even if you have almost certainty that literally no species haseverdied of conflict, you still can't get a prior much lower than 1/4,000,000,000! (10^-9).

Interesting numbers! I think that kind of argument is too agnostic, in the sense it does not leverage the empirical evidence we have about human conflicts, and I worry it leads to predictions which are very off. For example, one could also argue the annual probability of a human born in 2024 growing to an height larger than the distance from the Earth to the Sun cannot be much lower than 10^-6 because Sapiens have only been around for 1 M years or so. However, the probability should be way way lower than that (excluding genetic engineering, very long light appendages, unreasonable interpretations of what I am referring to, like estimating the probability from the chance a spaceship with humans will collide with the Sun, etc.). One can see the probability of a (non-enhanced) human growing to such an height is much lower than 10^-6 based on the tail distribution of human heights. Since height roughly follows a normal distribution, the probability of huge heights is negligible. It might be the case that past human heights (conflicts) are not informative of future heights (conflicts), but past heights still seem to suggest an astronomically low chance of huge heights (conflicts causing human extinction).

It is also unclear from past data whether annual conflict deaths as a fraction of the global population will increase.

Below is some data on the linear regression of the logarithm of the annual conflict deaths as a fraction of the global population on the year.

Slope (1/year) | Intercept | Coefficient of determination |

-0.00279 | -3.40 | 8.45 % |

As I have said:

There has been a slight downwards trend in the logarithm of the annual conflict deaths as a fraction of the global population, with the R^2 of the linear regression of it on the year being 8.45 %. However, it is unclear to me whether the sign of the slope is resilient against changes in the function I used to model the ratio between the Conflict Catalogâ€™s and actual annual conflict deaths.

Makes sense. Just to clarify, the data on deaths and disease burden from non-optimal temperature until now are from GBD, but the projections for the future death rates from non-optimal temperature are from Human Climate Horizons.

I think I remain confused as to what you mean with "all deaths from non-optimal temperature".

I mean the difference between the deaths for the predicted and ideal temperature. From OWID:

The deaths from non-optimal temperature are supposed to cover all causes (temperature is a risk factor for death rather than a cause of death in GBD), not just extreme heat and cold (which only account for a tiny fraction of the deaths; see my last comment). I say "supposed" because it is possible the mortality curves above are not being modelled correctly, and this applies even more to the mortality curves in the future.

So to me it seems you are saying "

I don't trust arguments about compounding risks and the data is evidence for that" whereas the data is inherently not set up to include that concern and does not really speak to the arguments that people most concerned about climate risk would make.

My understanding is that (past/present/future) deaths from non-optimal temperature are supposed to include conflict deaths linked to non-optimal temperature. However, I am not confident these are being modelled correctly.

I was not clear, but in my last comment I mostly wanted to say that deaths from non-optimal temperature account for the impact of global warming not only on deaths from extreme heat and cold, but also on cardiovascular or kidney disease, respiratory infections, diabetes and all others (including conflicts). Most causes of death are less heavy-tailed than conflict deaths, so I assume we have a better understanding of how they change with temperature.

Thanks for the great post, Lynette!