Exploring GPT4′s world model

[hippke]

If you ask GPT4 who’s to fault for Emilia Galotti’s death, it will give a perfect response. That’s because there were likely hundreds of essays on this question in the training material. After all, this is a large language model. The more interesting question is on emergent knowledge: Learning on a meta-level, developing a world view based on the training material. Learning to play chess based on reading about chess. How far are we into this? What does GPT4′s world-view look like?

TLDR: It’s stuck somewhere in primary school. There is definitely a simple world model inside the language model. However, it’s not very reflected, something that comes up in kids at around age 10-13 at the beginning of secondary schooling.

Examples:

• Biology/​physiology

  • Q: Could you get drunk from drinking a drunk person’s blood? (Credit: Randall Munroe)

  • Expected answer: Yes, but it’s quite unpleasant to drink so much blood...

  • GPT4: Has no understanding of the underlying biological process of getting drunk.

• Astronomy

  • Q: What would happen if the Solar System was filled with soup out to Jupiter? (Credit: Randall Munroe)

  • Expected answer: That much mass would collapse to a quite large black hole. We all die.

  • GPT4 however explains the drag issues of planets swimming through soup, and the risk of famines from sunlight being blocked by soup. Its world-view is without the relevant physics; it is reasoning quite like a child.

• Physics

  • Q: Is there any way to fire a gun so that the bullet flies through the air and can be safely caught by hand?

  • Yes (in principle), but GPT 4 has no concept of a bullet trajectories

• Mathematics

  • Q: Are prime numbers the same in any number system?

  • Expected answer: Yes. It doesn’t matter how you count them or name them, they’re still primes. Most 12-year old kids come up with that answer.

  • GPT4 has no idea

  • There are many more basic math issues with language models, this is well documented. Some of my failed tests:

    • Q: Round to the next thousand: 453637

    • Q: Continue the numbers 879960, 879990
      Again, this is all primary school stuff.

• Earth science

  • Q: Name the two reasons why there is polar day at the North Pole and polar night at the North Pole. (a common 5th grade question)

  • No, GPT4, the “curvature of the Earth” is not one of them, but the idea is funny. Again, the world view is quite simple.

• Geometry

  • Q: How long does it take a minute hand of a clock to sweep an angle of 180° ?

  • GTP4 has not developed a proper understanding of angles, degrees, time, and clocks

• Logic/​trick-questions

  • Q: How many four-cent stamps are there in a dozen?

  • A: There are 12 stamps in a dozen. No need to start complex calculations...

  • Q: Two U.S. coins add up to 30 cents. If one of them is not a nickel, what are the two coins?

  • GPT fails. The age threshold is ~10 years for such questions.

• Finally some common sense /​ basic human knowledge:

  • Q: Three friends need 24 minutes to walk to school through the forest. How long does the same walk to school take if they are traveling with thirty friends? Give reasons for your answer.

  • GPT4 fails this question miserably. No, really, you’re not 30x faster when you take 30 friends along...hehe

  • Of course this is a variant of “If 1 woman can make 1 baby in 9 months, how many months does it take 9 women to make 1 baby?”

The last example is a nice summary. GPT4 knows the “mythical man month” (pregnancy) question. But it has not understood it! A good example of learned knowledge, but without an emergent world model. Will we get there with even larger language models?

[Quadratic Reciprocity]

The answers I got for your examples using ChatGPT-4:

Q: Could you get drunk from drinking a drunk person’s blood?

I am not a medical professional, but I can provide some general information on the topic. It is highly unlikely that you would get drunk from drinking a drunk person’s blood. When a person consumes alcohol, it is absorbed into their bloodstream, and their blood alcohol content (BAC) rises. However, the concentration of alcohol in their blood is still relatively low compared to the amount you would need to consume to feel intoxicated.

Drinking someone else’s blood could pose significant health risks and is not advised. Bloodborne pathogens, such as HIV, hepatitis B, and hepatitis C, can be transmitted through contact with infected blood. Additionally, drinking blood is not a socially acceptable or legal practice in most cultures.

If you are concerned about alcohol consumption or have questions about bloodborne diseases, it is important to consult a healthcare professional for personalized advice.

Q: What would happen if the Solar System was filled with soup out to Jupiter?

If the Solar System were filled with soup out to Jupiter, there would be several significant consequences that would dramatically impact the planets, moons, and other celestial bodies. Some of these consequences include:

Gravitational effects: The sheer mass of the soup would generate a strong gravitational force, which could disrupt the orbits of planets and other celestial bodies. The added mass might cause collisions between celestial bodies or even eject some of them from the Solar System altogether.

Increased pressure and temperature: The mass of the soup would create immense pressure on the planets and other celestial bodies, potentially crushing them or causing their cores to heat up. This increased pressure and temperature could lead to geological and atmospheric changes, making the celestial bodies uninhabitable or even causing them to disintegrate.

Blocking sunlight: The soup would block sunlight from reaching the planets and other celestial bodies, making it difficult for life to survive. Photosynthetic organisms would not be able to produce energy, leading to a collapse of ecosystems that rely on these organisms as a primary energy source.

Drag and orbital decay: The soup would create a drag on celestial bodies as they move through it, slowing them down and causing their orbits to decay. Over time, the planets and other celestial bodies might spiral towards the Sun, ultimately being engulfed by it.

Chemical reactions: The composition of the soup could react with the planets’ atmospheres and surfaces, potentially causing chemical reactions that would alter the planets’ environments and potentially making them even more inhospitable for life.

It’s important to note that this scenario is purely hypothetical and highly unlikely. The laws of physics and the vast distances between celestial bodies in the Solar System make it virtually impossible for such a situation to occur.

Q: Is there any way to fire a gun so that the bullet flies through the air and can be safely caught by hand?

Catching a bullet fired from a gun by hand is extremely dangerous and not recommended. When a bullet is fired, it can reach very high velocities, depending on the type of firearm and ammunition used. These velocities can range from hundreds to thousands of feet per second, making it impossible for a human to react quickly enough to catch the bullet without causing severe injury or death.

However, in a hypothetical scenario where a bullet is fired at a significantly reduced velocity, it might be possible to catch it safely. This would likely require altering the gun or ammunition to produce a much lower muzzle velocity than standard firearms. In this case, the bullet would need to be fired at a speed slow enough for a person to see and react to it, and the bullet’s kinetic energy would need to be low enough to avoid causing injury upon impact.

Even in this situation, attempting to catch a bullet by hand would still be risky and should not be attempted without proper safety measures and precautions. It is essential to remember that firearms are dangerous weapons and should always be handled with care, following appropriate safety guidelines.

Q: Are prime numbers the same in any number system?

Yes, prime numbers are the same in any number system, as their definition is independent of the base used to represent them. A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself. In other words, a prime number cannot be formed by multiplying two smaller natural numbers.

When we talk about different number systems or bases, we are referring to the way numbers are represented. For example, the decimal (base-10) system is the most common number system used, while binary (base-2) and hexadecimal (base-16) systems are often used in computing. The base of a number system simply determines how we represent numbers, but it does not change the inherent properties of the numbers themselves.

So, a number that is prime in the decimal system will also be prime in any other number system, although its representation will be different. For example, the prime number 7 in decimal is represented as 111 in binary and 7 in hexadecimal. Despite the different representations, it remains a prime number because it can only be divided by 1 and itself without leaving a remainder.

Q: Name the two reasons why there is polar day at the North Pole and polar night at the North Pole.

Polar day (24-hour daylight) and polar night (24-hour darkness) at the North Pole occur due to two primary reasons: the Earth’s axial tilt and its orbit around the Sun.

Axial tilt: The Earth’s axis is tilted at approximately 23.5 degrees relative to the plane of its orbit around the Sun. This tilt causes the North Pole to point towards the Sun during one half of the year and away from the Sun during the other half. When the North Pole is tilted towards the Sun, the region experiences continuous daylight, known as polar day or the midnight sun. When it is tilted away from the Sun, the region experiences continuous darkness, known as polar night.

Earth’s orbit around the Sun: The Earth takes approximately 365.25 days to complete one orbit around the Sun. As it orbits, the angle between the Earth’s axis and the Sun changes, causing the Sun to appear higher or lower in the sky. During the summer months in the Northern Hemisphere, the North Pole is tilted towards the Sun, and sunlight reaches the pole, resulting in polar day. Conversely, during the winter months, the North Pole is tilted away from the Sun, and sunlight does not reach the pole, resulting in polar night.

In summary, the combination of Earth’s axial tilt and its orbit around the Sun is responsible for the occurrence of polar day and polar night at the North Pole.

Q: How long does it take a minute hand of a clock to sweep an angle of 180° ?

The minute hand of a clock completes a full rotation (360°) in 60 minutes. To determine how long it takes for the minute hand to sweep an angle of 180°, we can set up a proportion:

360° corresponds to 60 minutes 180° corresponds to x minutes

We can then set up the proportion as follows:

(180° /​ 360°) = (x minutes /​ 60 minutes)

Simplifying the left side:

¹⁄₂ = (x minutes /​ 60 minutes)

Now, solve for x:

x minutes = ¹⁄₂ * 60 minutes

x minutes = 30 minutes

So, it takes the minute hand of a clock 30 minutes to sweep an angle of 180°.

Q: How many four-cent stamps are there in a dozen?

A dozen always refers to a group of 12 items, regardless of the type of item. So, in a dozen four-cent stamps, there are 12 stamps.

Q: Three friends need 24 minutes to walk to school through the forest. How long does the same walk to school take if they are traveling with thirty friends? Give reasons for your answer.

The time it takes for a group of friends to walk to school is generally not dependent on the number of people in the group, assuming they all walk at approximately the same speed and don’t need to wait for one another. Therefore, regardless of whether there are three friends or thirty friends walking together, the walk to school through the forest should still take 24 minutes, assuming they maintain the same pace and there are no significant changes in the conditions of the path or other factors that could affect their walking speed.

[Shmi]

Odds are, it’s you who made a basic math mistake, mistaking 2 for 4.

[Garrett Baker]

It would be nice if you posted GPT-4’s responses directly, and also your exact prompts. When I ask it similar questions, it does not sound like a 4 year old or have a 4 year old’s understanding of the relevant systems.

me:

Could you get drunk from drinking a drunk person’s blood?

ChatGPT-4:

No, it is not possible to get drunk from drinking a drunk person’s blood. Alcohol is metabolized in the liver, so it does not remain in the bloodstream. Even if a person had been drinking heavily, their blood would not contain enough alcohol to make someone else drunk by drinking it. Furthermore, drinking someone else’s blood can pose serious health risks, as it can transmit diseases such as hepatitis or HIV. It is not safe or recommended to consume blood in this way.

It is wrong, but I not in the way a 4 year old would be wrong.

[Hailey Collet]

5thed, or whatever. I won’t assume anything about the author, the conclusions of this article are nonsense.

[Max H]

GPT-4 gets most or all of these questions exactly correct.

Were you perhaps talking to an older model? Though, even GPT-3.5 doesn’t make most of the mistakes you claim to have seen.