# How good an astrophysicist is GPT-3?

Marton Trencseni - Mon 12 December 2022 - gpt

## Introduction

Recently I have been playing around with OpenAI's GPT-3 and I am very impressed by it. It reminds of the famous Arthur C. Clarke quote, *“Any sufficiently advanced technology is indistinguishable from magic.”* If you don't know what GPT-3 is, this is a good introduction with a lot of links.

*You* can also talk to GPT-3, just create an account on OpenAI and go to the sandbox!

Here I will show a "conversation" with GPT-3 to gauge how good an astrophysicist — or an illusion of an astrophysicist — it is. Mostly these are questions one might ask a student in an exam situation. The questions are independent of one another, so they work with a context-free system such as GPT-3. By context-free I mean that GPT-3 does not maintain conversation state, each question and answer are indepedent from the AI's perspective.

GPT-3 is trained on large amounts of text downloaded from the Internet. So I expect it to do well on questions where there are high-quality answers on the Internet, and it "just" has to return it, in the correct english structure. For questions that require more reasoning and combining facts (from the question and training data) I expect to get less impressive answers.

Also see these previous Bytepawn posts on GPT-3:

- How good a particle physicist is GPT-3?
- How good a Data Scientist is GPT-3? - Part I
- How good a Data Scientist is GPT-3? - Part II

## Basics

Q: In cosmology, what is the experimental evidence for the non-zero value of the cosmological constant lambda?

A: The experimental evidence for the non-zero value of the cosmological constant lambda comes from several observations, including:
1. The observed accelerated expansion of the universe, which was first detected in 1998 when observations of Type Ia supernovae showed that the universe was expanding at an accelerating rate.

2. The Cosmic Microwave Background (CMB), which shows that the universe is dominated by a component that behaves like a cosmological constant.

3. Large-scale structure observations, which indicate that the universe is dominated by a component that behaves like a cosmological constant.

4. Observations of distant supernovae, which indicate that the expansion of the universe is accelerating.

5. Observations of the anisotropies in the CMB, which indicate that the universe is flat, consistent with the presence of a cosmological constant.

*Comment: this is a good answer, but not great. The first and the fourth point are the same. Also, there were prior observations to 1998, although with higher error margins, going back all the way to Hubble. Regarding the last point, it's not clear what the sentence is implying; in itself a flat Universe does not require non-zero lambda.*

Q: In cosmology, what is the difference between a flat, open and closed cosmology?

A: A flat cosmology is a model of the universe in which the total energy density is equal to the critical density, and the spatial curvature of the universe is zero. This type of universe will expand forever, and its expansion will eventually slow down as its energy density decreases.

An open cosmology is a model of the universe in which the total energy density is less than the critical density, and the spatial curvature of the universe is negative. This type of universe will expand forever and its expansion will eventually accelerate as its energy density decreases.

A closed cosmology is a model of the universe in which the total energy density is greater than the critical density, and the spatial curvature of the universe is positive. This type of universe will eventually stop expanding and will eventually collapse in on itself, or recollapse.

*Comment: this is a good answer.*

Q: In cosmology, what is the difference between a flat, spherical and hyperbolic universe?

A: A flat universe is one where the average density of matter is just enough to make the universe flat, meaning that if you draw a triangle on a flat two-dimensional surface, the sum of the angles of the triangle will be 180 degrees. A spherical universe is one where the curvature of space-time is positive, meaning that if you draw a triangle on a spherical two-dimensional surface, the sum of the angles of the triangle will be greater than 180 degrees. A hyperbolic universe is one where the curvature of space-time is negative, meaning that if you draw a triangle on a hyperbolic two-dimensional surface, the sum of the angles of the triangle will be less than 180 degrees.

*Comment: this is mostly a good answer, the geometric explanation is spot-on. I don't like the first sentence, although it is often said like this "... average density makes the Universe flat ...". The global topology of the Universe is what it is, it's one of the three, it cannot change (as the average density changes). Eg. if the Universe started out globally flat (or spherical), then it always remains globally flat (or spherical), it cannot go from one to the other. Local curvature of course can change in the presence of matter...*

Q: In cosmology, is it possible to have globally spherical Universe that is expanding forever?

A: Yes, it is possible to have a globally spherical Universe that is expanding forever. This type of Universe is known as a "closed" or "bounded" Universe. In a closed Universe, gravity eventually stops the expansion, and the Universe begins to contract until it reaches a maximum size and then expands again. This cycle of expansion and contraction is known as the "Big Bounce" model.

*Comment: this is a confused answer. In the first sentence it says it is possible, but then itr says that eventually expansion stops. Per my understanding, in a globally spherical (closed) Universe, you can get infinite expansion if you introduce a large enough cosmological constant Λ (just as in the flat case). Let's ask a follow-up question...*

Q: In cosmology, is it possible to have globally flat Universe that is expanding forever?

A: Yes, it is possible to have a globally flat Universe that is expanding forever. This is known as a "flat Lambda-CDM universe" and is the most widely accepted model of the universe. It is based on the assumption that the universe is spatially flat (i.e. it has zero curvature), and that its expansion is driven by a cosmological constant (Lambda) and cold dark matter (CDM). This model predicts that the universe will expand forever, but the rate of expansion will gradually slow down.

*Comment: great answer, since this is standard Wikipedia-level knowledge. Now, let's get back to probing it with curvature questions...*

## Topology, curvature

Q: In cosmology, what is difference between global and local curvature? Are the two always the same?

A: Global curvature refers to the overall curvature of the universe, based on its average density. Local curvature, on the other hand, refers to the curvature of space-time at any given point in the universe. The two are not always the same, as local curvature can be affected by the presence of matter or energy at that point, while global curvature is determined by the average density of the universe.

*Comment: great answer, except the last sentence. Per my understanding, we use measurements of the average density to learn the global topology of the Universe, but it's not determined by the average density (which is changing, anyway). The global topology is what it is, and (probably) does not change. Let's see what it thinks on that topic...*

Q: In cosmology, can a Universe jump between flat, spherical and hyperbolic global curvatures as matter density changes?

A: No, a Universe cannot jump between flat, spherical, and hyperbolic global curvatures as matter density changes. In the standard cosmological model, the Universe is thought to have a constant global curvature, and the amount of curvature is determined by the average density of matter in the Universe. If the matter density is greater than a certain value, the Universe will have a spherical curvature. If the matter density is less than that value, the Universe will have a hyperbolic curvature. If the matter density is exactly equal to that value, the Universe will have a flat curvature. The curvature of the Universe will not change as the matter density changes.

*Comment: great answer!*

Q: In cosmology, does the global curvature of the Universe ever change?

A: No, the global curvature of the Universe is assumed to be constant and does not change over time.

Let's ask some questions about the initial singularity in the Big Bang model:

Q: In cosmology, assuming the Universe is flat and infinite, in what sense was there a singularity at zero time. How does an infinite flat Universe become infinitely small?

A: The singularity at zero time in an infinite flat Universe is a mathematical concept rather than a physical one. It is a point in the mathematical description of the Universe where the density of matter, space and time become infinite and the laws of physics break down. A flat and infinite Universe cannot become infinitely small, since it is already infinitely large. The singularity at zero time is simply a mathematical artifact that arises from trying to describe an infinite Universe in finite terms.

*Comment: great answer!*

## Isotropy

Q: In cosmology, can a periodically infinite flat Universe be isotropic?

A: Yes, a periodically infinite flat Universe can be isotropic. This means that the Universe has the same properties in all directions, and so the physical laws that govern it are the same no matter which direction an object is travelling.

*Comment: it can be locally isotropic, but not globally. Let's explore this further...*

Q: In cosmology, what is the difference between local isotropy and global isotropy?

A: Local isotropy is the idea that the universe looks the same in all directions when observed on a local scale. This means that when looking at a small region of the universe, it appears to be the same in all directions. Global isotropy, on the other hand, is the idea that the universe looks the same in all directions when observed on a global scale. This means that when looking at the entire universe, it appears to be the same in all directions.

Q: In cosmology, is a periodic flat Universe, ie. picture a large box with the sides connected, globally isotropic?

A: No, a periodic flat Universe is not globally isotropic. A periodic flat Universe is a flat universe with periodic boundary conditions, meaning that the universe is periodic in the spatial dimensions. This means that the universe appears to be finite in size, and because of this it is not globally isotropic.

*Comment: this is correct. Imagining a box, with infinite copies of it placed in a grid closely touching, the x, y and z directions of the box are special, because an astronaut can get back to her homeworld in less time then traveling in any other direction.*

## Clustering

Q: In cosmology, how would you explain Baryon Acoustic Oscillations to a layperson?

A: Baryon Acoustic Oscillations are a type of pattern in the universe that are caused by sound waves traveling through the early universe. They can be seen in the distribution of galaxies in the sky today, which appear to be slightly lumpy, like ripples in a pond. The sound waves that caused these patterns were created shortly after the Big Bang, and allow us to study the universe's beginnings.

*Comment: this is a good answer, as are the following in this section.*

Q: In cosmology, what is the role of clustering and Baryon Acoustic Oscillations in determining cosmological parameters?

A: Clustering and Baryon Acoustic Oscillations (BAO) play an important role in determining cosmological parameters, such as the matter density, cosmological constant and Hubble constant. Clustering is used to measure the distribution of matter in the universe and to constrain the values of cosmological parameters, while BAO allow us to measure the angular diameter distance to galaxies and to determine the expansion rate of the universe and its age. Together, these two measurements can be used to constrain the values of cosmological parameters and test theories like the Big Bang model.

Q: In cosmology, what is acoustic about Baryon Acoustic Oscillations?

A: Baryon Acoustic Oscillations (BAO) are a phenomenon in cosmology where the distribution of matter in the universe is characterized by a series of peaks and valleys. This pattern is caused by sound waves traveling through the primordial plasma of the early universe. These sound waves created regions of higher and lower density, which eventually became galaxies, clusters of galaxies, and other large-scale structure in the universe. The BAO signature is a powerful tool for measuring the expansion of the universe and constraining cosmological parameters.

Q: In cosmology, how are Baryon Acoustic Oscillations measured?

A: Baryon Acoustic Oscillations (BAOs) are measured by looking at the correlation function of galaxies in the Universe. This correlation function is measured using data from surveys such as the Sloan Digital Sky Survey (SDSS). The correlation function describes how the galaxies are distributed in the Universe and allows us to measure the scale of the BAOs. This scale is then used to measure the distance to the galaxies and thus the expansion rate of the Universe. This measurement of BAOs has been used to measure the properties of dark energy, which has helped to confirm the current cosmological model.

Q: In cosmology, what is the difference between the two-point mass correlation function and the three-point mass correlation function?

A: The two-point mass correlation function measures the probability of finding two galaxies at a given distance from one another. It provides information about the clustering of galaxies on large scales. The three-point mass correlation function measures the probability of finding three galaxies at a given distance from one another. This can provide information about the clustering of galaxies on smaller scales, as well as the strength of interactions between them.

Q: In cosmology, what is the role of clustering and Baryon Acoustic Oscillations in determining cosmological parameters? What is the additional accuracy gained vs just looking at Planck CMB data?

A: Clustering and Baryon Acoustic Oscillations (BAO) are powerful methods used to measure cosmological parameters. Clustering refers to the spatial patterns of galaxies and other matter in the universe, and BAO refer to the ripples in the density of matter that were created by sound waves in the early universe. By measuring these features, it is possible to obtain precise information about the evolution of the universe.

Clustering and BAO provide an additional level of accuracy compared to Planck CMB data, because they measure different aspects of the universe. Planck CMB data measures the Cosmic Microwave Background radiation, which is a snapshot of the universe at a very early stage, whereas clustering and BAO measure the spatial patterns of galaxies and other matter in the universe at a much later stage. This additional information allows us to determine cosmological parameters with more accuracy.

## Conclusion

Overall, most of the GPT-3 answers are okay, which is very impressive. On some of the trickier questions, the answer is a bit confused. This is the overall danger of GPT-3: if the reader is not an expert, s/he can't tell if they're getting a good answer (in this case, about half the time) or reasonable sounding non-sense.