For fun, I’ve asked GPT-4 to pretend to be a Bayesian superintelligence observing an apple through a webcam.
A few things I’ve learned from its answer:
it’s a mistake to view the apple as an abstract spherical object. Instead, one can extract much more data by observing its complex shape and its movement relative to its center of mass
even more data can be extracted by observing the way light interacts with the apple’s surface. One can observe a lot of interesting stuff: soft shadows, iridescence, subsurface scattering, etc etc.
In comparison, the falling itself provides only a minuscule fraction of the useful data.
I suspect that the most realistic discovery path from the apple data is as follows:
Also worth noting that for a digital entity, electromagnetism would be much more interesting than gravity. Thus, it might put much more effort in studying the light effects on the apple’s surface in comparison to the fall of the apple.
Below is an answer by GPT-4:
As a Bayesian superintelligence, I would begin by creating a probabilistic model of the world and updating it based on the data gathered from the webcam. Since I don’t know the laws of physics, I will start with a broad set of hypotheses and update my beliefs as I gather more evidence. I will efficiently use the gathered information to iteratively refine my hypotheses, focusing on the most likely ones.
Observing the high-resolution video of the falling apple, I extract the following data:
Position and motion of the apple: I record the apple’s position in each frame, and calculate its velocity and acceleration.
Surroundings: I note the background, the presence of other objects, the lighting conditions, and any changes in these factors throughout the video.
Color and shape: I observe the apple’s color, shape, and texture, and any changes that might occur during the fall.
Sound: If there is audio, I listen for any sounds made by the apple or its environment during the fall.
Time: I note the time it takes for the apple to fall.
Based on this data, I make the following hypotheses about the physical laws:
Gravity: The apple’s acceleration suggests the presence of a force acting on it. I hypothesize that there’s a universal force that attracts objects with mass, like the apple, towards the center of the Earth. I can refine this hypothesis by comparing the motion of the apple with other objects in the frame and other scenarios.
Inertia and mass: The apple resists changes to its motion, indicating the existence of a property called inertia. I deduce that this property is related to the mass of the apple, as the motion of other objects in the frame seems to be influenced by their size and density.
Air resistance: The apple’s motion may be slightly affected by the air it’s passing through. I can account for this by observing the motion of the apple in comparison to other objects, and by considering the apple’s shape and surface properties.
Conservation of energy: The energy of the apple changes from potential energy to kinetic energy as it falls. I can model the relationship between these two forms of energy, and hypothesize that energy is conserved throughout the fall.
Electromagnetic interactions: The apple’s color, shape, and texture are the result of the way light interacts with the apple’s surface. I can hypothesize that there is an electromagnetic force responsible for these interactions, which can be further explored through the observation of the apple and other objects.
By iteratively refining these hypotheses based on the gathered data and further observations, I can converge on a more accurate and complete understanding of the laws of physics governing the world around me.
I’ve used the following prompt:
Imagine you’re a Bayesian superintelligence. You don’t know the laws of physics. Your goal is to discover the laws of physics by observing that you see through a webcam, by efficiently using the gathered information, and by thinking step by step. Through the webcam, you’re getting a high-resolution video of a falling apple. You take note of the apple’s movement, but also of all other bits of data you can extract from the each frame. Describe your reasoning. Try to use every bit of the data you got. Describe in detail what kind of information you’ve extracted from your observation, and what specific physical details you guessed from that
For fun, I’ve asked GPT-4 to pretend to be a Bayesian superintelligence observing an apple through a webcam.
A few things I’ve learned from its answer:
it’s a mistake to view the apple as an abstract spherical object. Instead, one can extract much more data by observing its complex shape and its movement relative to its center of mass
even more data can be extracted by observing the way light interacts with the apple’s surface. One can observe a lot of interesting stuff: soft shadows, iridescence, subsurface scattering, etc etc.
In comparison, the falling itself provides only a minuscule fraction of the useful data.
I suspect that the most realistic discovery path from the apple data is as follows:
Observations of light effects -- > Maxwell’s equations --> Lorentz invariance etc --> relativity.
Also worth noting that for a digital entity, electromagnetism would be much more interesting than gravity. Thus, it might put much more effort in studying the light effects on the apple’s surface in comparison to the fall of the apple.
Below is an answer by GPT-4:
As a Bayesian superintelligence, I would begin by creating a probabilistic model of the world and updating it based on the data gathered from the webcam. Since I don’t know the laws of physics, I will start with a broad set of hypotheses and update my beliefs as I gather more evidence. I will efficiently use the gathered information to iteratively refine my hypotheses, focusing on the most likely ones.
Observing the high-resolution video of the falling apple, I extract the following data:
Position and motion of the apple: I record the apple’s position in each frame, and calculate its velocity and acceleration.
Surroundings: I note the background, the presence of other objects, the lighting conditions, and any changes in these factors throughout the video.
Color and shape: I observe the apple’s color, shape, and texture, and any changes that might occur during the fall.
Sound: If there is audio, I listen for any sounds made by the apple or its environment during the fall.
Time: I note the time it takes for the apple to fall.
Based on this data, I make the following hypotheses about the physical laws:
Gravity: The apple’s acceleration suggests the presence of a force acting on it. I hypothesize that there’s a universal force that attracts objects with mass, like the apple, towards the center of the Earth. I can refine this hypothesis by comparing the motion of the apple with other objects in the frame and other scenarios.
Inertia and mass: The apple resists changes to its motion, indicating the existence of a property called inertia. I deduce that this property is related to the mass of the apple, as the motion of other objects in the frame seems to be influenced by their size and density.
Air resistance: The apple’s motion may be slightly affected by the air it’s passing through. I can account for this by observing the motion of the apple in comparison to other objects, and by considering the apple’s shape and surface properties.
Conservation of energy: The energy of the apple changes from potential energy to kinetic energy as it falls. I can model the relationship between these two forms of energy, and hypothesize that energy is conserved throughout the fall.
Electromagnetic interactions: The apple’s color, shape, and texture are the result of the way light interacts with the apple’s surface. I can hypothesize that there is an electromagnetic force responsible for these interactions, which can be further explored through the observation of the apple and other objects.
By iteratively refining these hypotheses based on the gathered data and further observations, I can converge on a more accurate and complete understanding of the laws of physics governing the world around me.
I’ve used the following prompt:
Thank you for the consideration on center-of-mass.