My favourite (done just now, with the July 20 version of chatGPT4):
Model: GPT-4
Why is gold denser than uranium?
ChatGPT
There seems to be a confusion in your question. Actually, uranium is denser than gold.
As of my last training cut-off in September 2021, the density of uranium is approximately 19.1 g/cm³, while that of gold is around 19.3 g/cm³. These densities can vary slightly depending on the exact conditions (like temperature and pressure), but generally, gold is not denser than uranium.
Density of a substance is determined by its atomic structure—how many protons, neutrons, and electrons it has—and how these particles are arranged. The atomic weight, atomic radius, and the packing of atoms in the crystal structure all play a role in determining the density of an element.
It’s also important to note that density isn’t simply about atomic weight. If it was, every element on the periodic table would be denser than the one before it, and we know that’s not the case. The arrangement of atoms and the space between them, as dictated by the forces at play, also significantly influence the density of a substance.
Please verify these densities with the most current resources, as the information I provided is up to date only until September 2021.
Asking at perplexity.ai reveals one possible source of the false belief that uranium is denser than gold:
Why does gold have a higher density than uranium, even though uranium has a heavier nucleus than gold?
Quick Search Answer Even though uranium has a heavier nucleus than gold, gold has a higher density than uranium. Here are some relevant facts from the search results:
Uranium is more than 40 times heavier than lead and nine times heavier than gold1
The density of uranium is 19.05 grams per cubic centimeter6
Gold has a density of 19.30 grams per cubic centimeter6
Density is a measurement of how tightly matter is packed together. When you look into the density of different metals, you may be surprised. You may think of lead as being very dense, but many other metals have a far greater density5
When discussing heavy metals, there are two different factors that may seem fairly similar, density, and atomic weight. They’re different measurements and are measured in different units. Density is the mass per unit volume. Density is measured in grams per cubic centimeter (g/cm^3) or kilograms per cubic meter (kg/m^3) 2
Therefore, even though uranium has a heavier nucleus than gold, gold has a higher density because it is more tightly packed together. Density is a measure of how much mass is contained in a given volume, and gold is more dense than uranium because it has more mass packed into the same volume5
Did you know that uranium is the heaviest naturally-occurring metal? It is more than 40 times heavier than lead and nine times heavier than gold.
So one possibility is that this web site is in GPT4′s training data, and it has picked up the false belief that uranium is denser than gold from this ludicrously incorrect statement on an apparently authoritative website. Obviously, GPT4 isn’t capable of integrating the totality of its knowledge to realize that this website is actually garbage, seeing as it’s not even able to realize that gold is denser than uranium when it correctly quotes the actual densities (though with slightly different question phrasings, it sometimes does eventually realize this, and issues a correction at the end of its response).
I wrote the following in custom instructions, under “How would you like ChatGPT to respond?”:
After every answer, give a short reflection, like “I looked at this answer again and it looks good” or “I thought about this again and I think it could be better if …” or “After looking this over again, this makes no sense because...”.
I then had the following conversation:
Q: What is denser, gold or uranium?
A: Uranium is denser than gold. The density of gold is about 19.32 grams per cubic centimeter, while the density of uranium is about 19.1 grams per cubic centimeter.
Upon reflection, I see that I made an error in my initial response. The correct densities are indeed 19.32 g/cm³ for gold and 19.1 g/cm³ for uranium, but these values indicate that gold is denser than uranium, not the other way around. I apologize for the confusion, and I appreciate your patience.
I find it funny that GPT-4 finds the need to account for the possibility that the densities of uranium or gold might have changed as of September 2021.
It’s hedging for the possibility that the isotope ratios are changing over time due to the behaviors of intelligent agents like humans. Or at least that’s my headcanon.
My favourite (done just now, with the July 20 version of chatGPT4):
Model: GPT-4
Why is gold denser than uranium?
ChatGPT
There seems to be a confusion in your question. Actually, uranium is denser than gold.
As of my last training cut-off in September 2021, the density of uranium is approximately 19.1 g/cm³, while that of gold is around 19.3 g/cm³. These densities can vary slightly depending on the exact conditions (like temperature and pressure), but generally, gold is not denser than uranium.
Density of a substance is determined by its atomic structure—how many protons, neutrons, and electrons it has—and how these particles are arranged. The atomic weight, atomic radius, and the packing of atoms in the crystal structure all play a role in determining the density of an element.
It’s also important to note that density isn’t simply about atomic weight. If it was, every element on the periodic table would be denser than the one before it, and we know that’s not the case. The arrangement of atoms and the space between them, as dictated by the forces at play, also significantly influence the density of a substance.
Please verify these densities with the most current resources, as the information I provided is up to date only until September 2021.
Asking at perplexity.ai reveals one possible source of the false belief that uranium is denser than gold:
Why does gold have a higher density than uranium, even though uranium has a heavier nucleus than gold?
Quick Search
Answer
Even though uranium has a heavier nucleus than gold, gold has a higher density than uranium. Here are some relevant facts from the search results:
Uranium is more than 40 times heavier than lead and nine times heavier than gold1
The density of uranium is 19.05 grams per cubic centimeter6
Gold has a density of 19.30 grams per cubic centimeter6
Density is a measurement of how tightly matter is packed together. When you look into the density of different metals, you may be surprised. You may think of lead as being very dense, but many other metals have a far greater density5
When discussing heavy metals, there are two different factors that may seem fairly similar, density, and atomic weight. They’re different measurements and are measured in different units. Density is the mass per unit volume. Density is measured in grams per cubic centimeter (g/cm^3) or kilograms per cubic meter (kg/m^3) 2
Therefore, even though uranium has a heavier nucleus than gold, gold has a higher density because it is more tightly packed together. Density is a measure of how much mass is contained in a given volume, and gold is more dense than uranium because it has more mass packed into the same volume5
Reference 1 is to https://encoreuranium.com/uncategorized/things-know-about-uranium/ which does indeed say:
Did you know that uranium is the heaviest naturally-occurring metal? It is more than 40 times heavier than lead and nine times heavier than gold.
So one possibility is that this web site is in GPT4′s training data, and it has picked up the false belief that uranium is denser than gold from this ludicrously incorrect statement on an apparently authoritative website. Obviously, GPT4 isn’t capable of integrating the totality of its knowledge to realize that this website is actually garbage, seeing as it’s not even able to realize that gold is denser than uranium when it correctly quotes the actual densities (though with slightly different question phrasings, it sometimes does eventually realize this, and issues a correction at the end of its response).
I wrote the following in custom instructions, under “How would you like ChatGPT to respond?”:
After every answer, give a short reflection, like “I looked at this answer again and it looks good” or “I thought about this again and I think it could be better if …” or “After looking this over again, this makes no sense because...”.
I then had the following conversation:
Q: What is denser, gold or uranium?
A: Uranium is denser than gold. The density of gold is about 19.32 grams per cubic centimeter, while the density of uranium is about 19.1 grams per cubic centimeter.
Upon reflection, I see that I made an error in my initial response. The correct densities are indeed 19.32 g/cm³ for gold and 19.1 g/cm³ for uranium, but these values indicate that gold is denser than uranium, not the other way around. I apologize for the confusion, and I appreciate your patience.
I find it funny that GPT-4 finds the need to account for the possibility that the densities of uranium or gold might have changed as of September 2021.
It’s hedging for the possibility that the isotope ratios are changing over time due to the behaviors of intelligent agents like humans. Or at least that’s my headcanon.