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You are welcome to answer any of the following:

- Do you have any thoughts on the value (or lack thereof) of my posts?
- Do you have any ideas for posts you think I would like to write?
- Are there any opportunities you think would be a good fit for me which are either not listed on 80,000 Hours' job board, or are listed there, but you guess I might be underrating them?

Feel free to check my posts and interests below, and see if we can collaborate to contribute to a better world. I am open to part-time volunteering, and part-time or full-time paid work. In this case, I typically ask for 20 $/h, which is roughly equal to 2 times the global real GDP per capita.

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My answer to both questions would be yes. In other words, whether the entire universe is finite or infinite is not a meaningful question to ask because we will never be able to gather empirical evidence to study it.

Thanks for elaborating!

I agree it makes sense to have some probability mass on the universe having null or negative local curvature. However, I think there is no empirical evidence supporting a null or negative global curvature:

- One can gather empirical evidence that the observable universe has a topology which, if applicable to the entire universe, would imply an infinite universe.
- Yet, by definition, it is impossible to get empirical evidence that the topology of the entire universe matches that of the observable universe.
- Inferring an infinite universe based on properties of the observable universe seems somewhat analogous to deducing an infite flat Earth based on the obervable ocean around someone in the sea being pretty flat.

Wikipedia's page seems to be in agreement with my 2nd point (emphasis mine):

If the observable universe encompasses the entire universe, we might determine its structure through observation. However, if the observable universe is smaller [as it would have to be for the entire universe to be infinite], we can only grasp a portion of it, making it

impossible to deduce the global geometry through observation.

I guess cosmologists may want to assume the properties of the observable universe match those of the entire universe in agreement with the cosmological principle. However, this has only proved to be useful to make predictions in the observable universe, so extending it to the entire universe would not be empirically justifiable. As a result, I get the impression the hypothesis of an infinite universe is not falsifiable, such that it cannot meaningly be true or false.

Thanks for following up, Will!

if the universe’s large-scale curvature is exactly zero (and the universe is

simply connected), then by definition it’s infinite

I agree. However, my understanding is that it is impossible to get empirical evidence supporting exactly zero curvature, because all measurements have finite sensitivity. I guess the same applies to the question of whether the universe is simply connected. In general, I assume zeros and infinities do not exist in the real world, even though they are useful in maths and physics to think about limiting processes.

I’m not sure what kind of a background you already have in this domain, but if you’re interested in reading more, I’d recommend first going to the “

Shape of the universe” Wikipedia page, and then, depending on your mileage, lectures 10–13 of Alan Guth’sintroductory cosmology lecture series.

Thanks for the links. I had skimmed that Wikipedia page.

Thanks for the post, Chi and Will. Somewhat relatedly, I liked Veritasium video on What Game Theory Reveals About Life, The Universe, and Everything.

Spatio-temporal expanse.The universe is very plausibly spatially infinite.

I do not think there is any empirical evidence for this. We can only measure finite quantities, so any measurement we make would be perfectly compatible with a large finite universe. In other words, empirical evidence can update one towards a larger universe, but not from a finite to an infinite one. So my understanding is that claims about the universe being infinite rest entirely on having a prior with some probability mass on this possibility.

The universe is

measured to be almost exactly flat: to a first approximation, under a uniform prior and ignoring anthropic considerations, this gives us 50% probability that the universe is positively curved and therefore finite, and 50% probability that the universe is negatively curved and therefore infinite.

Note the universe is measured to be almost exactly flat locally. If I am looking into a straight railway track which extends a few kilometers in my field of view, it would maybe not be reasonable for me to conclude it is infite in expectation. A reasonable probability density function (PDF) for its length would decay sufficiently fast to 0 as the length increases, such that the expected length is still finite. Similarly, even though the universe looks flat locally (like the Earth does in some places, even though it is not), I feel like it would be reasonable to have a PDF describing its size which decays to 0 as the size increases. The tail of the PDF would have to decay faster than the squared size for the expected size to be finite^{[1]}.

^{^}The mean of a Pareto distribution would be infinite otherwise.

Hi Mitchell,

Not strictly related to your question, but you may be interested in checking Marginal Revolution University's courses and series.

Thanks for sharing!

Somewhat relatedly, readers may want to check the thoughts of participants in the Existential Risk Persuasion Tournament (XPT) on the global catastrophic risk from engineered pathogens^{[1]} (pp. 241 to 251), including:

- "Sources of agreement, disagreement and uncertainty".
- "Arguments given for forecasts ≤ 6.3%".
- "Arguments given for forecasts ≥ 7.69%".

It is just worth having in mind:

The sample drew heavily from the Effective Altruism (EA) community: about 42% of experts and 9% of superforecasters reported that they had attended an EA meetup. In this report, we separately present forecasts from domain experts and non-domain experts on each question.

^{^}"Probability that a genetically-engineered pathogen will be the cause of death, within

a 5-year period, for more than 1% of humans alive at the beginning of that period".

Thanks for sharing, Yanni, and it is really cool that you managed to get Australia's Assistant Minister for Defence interested in creating an AI Safety Institute!

More on that can be found here.

Did you mean to include a link?

In 2020, it was estimated that an AI would pass university entrance exams by 2050.

The Metaculus' question you link to involves meeting many conditions besides passing university exams:

For these purposes we will thus define "AI system" as a single unified software system that can satisfy the following criteria, all easily completable by a typical college-educated human.

- Able to reliably pass a Turing test of the type that would win the Loebner Silver Prize.
- Able to score 90% or more on a robust version of the Winograd Schema Challenge, e.g. the "Winogrande" challenge or comparable data set for which human performance is at 90+%
- Be able to score 75th percentile (as compared to the corresponding year's human students; this was a score of 600 in 2016) on all the full mathematics section of a circa-2015-2020 standard SAT exam, using just images of the exam pages and having less than ten SAT exams as part of the training data. (Training on other corpuses of math problems is fair game as long as they are arguably distinct from SAT exams.)
- Be able to learn the classic Atari game "Montezuma's revenge" (based on just visual inputs and standard controls) and explore all 24 rooms based on the equivalent of less than 100 hours of real-time play (see closely-related question.)

Hi Bob,

Could you clarify how you aggregated the welfare range distributions from the 8 models you considered? I understand you gave the same weight to all of these 8 models, but I did not find the aggregation method here.

I would obtain the final cumulative distribution function (CDF) of the welfare range aggregating the CDFs of the 8 models with the geometric mean of odds, as Epoch did to aggregate judgement-based AI timelines. I think Jaime Sevilla would suggest using the mean in this case:

If you are not aggregating all-considered views of experts, but rather

aggregating models with mutually exclusive assumptions, use themean of probabilities.

However, I would say the 8 welfare range models are closer to the "all-considered views of experts" than to "models with mutually exclusive assumptions". In addition:

- The mean ignores information from extremely low predictions, and overweights outliers.
- The weighted/unweighted geometric mean of odds (and also the geometric mean) performed better than the weighted/unweighted mean on Metaculus' questions.
- Samotsvety aggregated predictions differing a lot between them from 7 forecasters
^{[1]}using the geometric mean after removing the lowest and highest values (and the geometric mean is more similar to the geometric mean of odds than to the mean).

^{^}For the question "What is the unconditional probability of London being hit with a nuclear weapon in October?", the 7 forecasts were 0.01, 0.00056, 0.001251, 10^-8, 0.000144, 0.0012, and 0.001. The largest of these is 1 M (= 0.01/10^-8) times the smallest.

Thanks for jumping in, Michael!

I agree it is essentially the same problem. I would think about it as follows:

Sorry for the lack of claririty. I did not mean to argue for a finite universe. I like to assume it is finite for simplicity, in the same way that it is practical to have physical laws with zeros even though all measurements have finite precision. However, I do not think there will ever be evidence for/against the entire universe being finite/infinite.