I’ve got another article at 3 Quarks Daily:
World, Mind, Learnability, Large Language Models, and the Metaphysical Structure of the Cosmos
I take another crack at something I’ve looked at before, the idea that LLMs embody a metaphysics of the cosmos, whatever those are. We’re not dealing with the physical structure of the cosmos, we’re not dealing with the totality of things-as-such, but rather with the (conceptual) structures through which we apprehend them. Given the wide range of texts that have been digested and distilled into these models, their internal structure somehow is responsive to, reflects and refracts, those structures.
Let me emphasize: Foundational LLMs implicate the metaphysical structure of the cosmos.
I set up the argument by starting with the 1977 short film, Powers of Ten, which traverses the cosmos from very large to very small in the compass of nine minutes. Then I ride one of my favorite hobby horses, Disney’s Fantasia, which also encompasses the cosmos. After that I ask: What must the world be like so that we can learn its structure?
And so forth and so on.
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In the course of working on this piece I decided to ask GPT-4 about the film, Powers of Ten. Of course it knew about the film. I then asked to summarize what that film shows. It did so and with great confidence. And it got it wrong. First, I present the dialog I had with GPT-4, and then I present a summary of the film from Wikipedia. That summary, cursory though it is, makes it clear that GPT-4’s summary is incorrect. The Chatster was up to its old tricks, just making stuff up. I didn’t make any effort to nail down all the errors in GPT-4’s summary.
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[April 22, 2023 – 3:15PM – Mar 23 version]
Do you know about the short 1977 film “Powers of Ten”?
Yes, I am familiar with the short film "Powers of Ten." It was directed by Ray and Charles Eames and was released in 1977. The film explores the relative sizes of things in the universe, from the scale of the observable universe all the way down to the subatomic level.
The film starts with an aerial view of a man and woman having a picnic in a park in Chicago, and then zooms out to show the Earth from a distance of ten meters, then ten times farther, and so on, until it reaches the limit of the observable universe. It then zooms back in, but this time at a smaller and smaller scale, revealing the structure of atoms and subatomic particles.
The film is a classic of science education and has been widely praised for its innovative use of scale and its ability to convey complex ideas in a clear and accessible way. It has been used in classrooms and science museums around the world, and is often cited as an example of effective science communication.
Could you talk your way through the first part of the film, starting with the couple and zooming out? What do we see at each higher power of 10?
Sure, I'd be happy to describe the first part of the film "Powers of Ten" to you.
The film begins with a shot of a couple, a man and a woman, having a picnic on a sunny day in a park in Chicago. The camera then begins to zoom out from the couple, at a rate of 10 times the distance every 10 seconds. As the camera zooms out, we see the park getting smaller and smaller, until it disappears from view.
At the first power of ten (10^1), we see the view of the park from an altitude of 10 meters above the couple. We can see the couple clearly, as well as the surrounding park and nearby buildings.
At the second power of ten (10^2), the camera has zoomed out to an altitude of 100 meters. Now we can see not just the park, but also the surrounding neighborhoods and the city of Chicago in the distance.
At the third power of ten (10^3), the camera has zoomed out to an altitude of 1,000 meters, or one kilometer. Now we can see not just the city of Chicago, but also the entire Lake Michigan shoreline and beyond.
At the fourth power of ten (10^4), the camera has zoomed out to an altitude of 10,000 meters, or 10 kilometers. Now we can see not just the city of Chicago and Lake Michigan, but also the entire state of Illinois and neighboring states.
At the fifth power of ten (10^5), the camera has zoomed out to an altitude of 100,000 meters, or 100 kilometers. Now we can see not just the Midwest region of the United States, but also the entire continent of North America.
At the sixth power of ten (10^6), the camera has zoomed out to an altitude of 1,000,000 meters, or 1,000 kilometers. Now we can see not just North America, but also the entire planet Earth.
At the seventh power of ten (10^7), the camera has zoomed out to an altitude of 10,000,000 meters, or 10,000 kilometers. Now we can see not just the Earth, but also the entire solar system, with the planets orbiting the sun.
At the eighth power of ten (10^8), the camera has zoomed out to an altitude of 100,000,000 meters, or 100,000 kilometers. Now we can see not just the solar system, but also the entire Milky Way galaxy, with its hundreds of billions of stars and countless other celestial objects.
At the ninth power of ten (10^9), the camera has zoomed out to an altitude of 1,000,000,000 meters, or 1 billion kilometers. Now we can see not just the Milky Way galaxy, but also the entire Local Group of galaxies, a cluster of more than 50 galaxies that includes the Milky Way.
At the tenth power of ten (10^10), the camera has zoomed out to an altitude of 10,000,000,000 meters, or 10 billion kilometers. Now we can see not just the Local Group of galaxies, but also the entire observable universe, with its hundreds of billions of galaxies and vast expanses of empty space.
That's a brief overview of the first part of "Powers of Ten." The film is an excellent way to explore the vastness of the universe and the different scales at which we can observe it.
OK, very good. Now let’s go in the opposite direction, from the couple deep into the world of very small things.
Certainly! After the camera zooms out to the limits of the observable universe, it then begins to zoom back in towards the couple having a picnic. As the camera zooms in, we see the surface of the man's hand, which is covered in hairs.
At the first power of ten (10^-1), the camera zooms in to the skin's surface, where we can see individual skin cells and bacteria.
At the second power of ten (10^-2), the camera zooms in further to show the nuclei of the skin cells and the structure of the individual bacteria.
At the third power of ten (10^-3), the camera zooms in to reveal the DNA molecules within the cell nuclei.
At the fourth power of ten (10^-4), the camera zooms in to show the individual atoms that make up the DNA molecules.
At the fifth power of ten (10^-5), the camera zooms in further to show the subatomic particles within the atoms, including protons and neutrons.
At the sixth power of ten (10^-6), the camera zooms in even further to show the quarks that make up protons and neutrons.
At the seventh power of ten (10^-7), the camera zooms in to show the limits of our current understanding of particle physics and the structure of matter.
This journey from the observable universe to the subatomic world illustrates the incredible range of scales that exist in the universe, and the film's use of the powers of ten to zoom in and out on these scales provides a powerful visual representation of this vast range.
What have we learned about very large things and very small things since that film was first made? Can we add some powers of ten?
Since the film "Powers of Ten" was first made in 1977, we have made tremendous progress in our understanding of both the very large and the very small. Here are a few additional powers of ten that we can add to the journey:
On the large scale: - At the 11th power of ten (10^11), we can see the superclusters of galaxies, which are groups of galaxy clusters that can span hundreds of millions of light-years.
- At the 12th power of ten (10^12), we can see the filaments and walls of the cosmic web, a vast network of gas, dust, and dark matter that connects the galaxies and other cosmic structures.
- At the 13th power of ten (10^13), we can see the cosmic microwave background radiation, the afterglow of the Big Bang that fills the entire universe.
- At the 14th power of ten (10^14), we can see the inflaton field, a hypothetical field that is thought to have driven the rapid expansion of the universe during the first fraction of a second after the Big Bang.
On the small scale:
- At the -8th power of ten (10^-8), we can see the individual subatomic particles that make up the quarks, such as gluons, which are the carriers of the strong nuclear force.
- At the -9th power of ten (10^-9), we can see the Higgs boson, a subatomic particle that was discovered in 2012 and is responsible for giving other particles mass.
- At the -10th power of ten (10^-10), we can see the limits of our current understanding of the fundamental nature of reality, and the mysteries that remain to be solved by physicists and other scientists.
These additional powers of ten demonstrate the incredible range of scales that exist in the universe, from the largest structures in the cosmos to the smallest building blocks of matter. As we continue to explore and learn more about the universe, it is likely that we will discover even more powers of ten that expand our understanding of the universe and our place within it.
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Wikipedia summary of the film:
The film begins with an overhead view of a man and woman picnicking in a park at the Chicago lakefront — a 1-meter (3.3 ft) overhead image of the figures on a blanket surrounded by food and books they brought with them, one of them being The Voices of Time by J. T. Fraser. The man [...] then sleeps, while the woman [...] starts to read one of the books. The viewpoint, accompanied by expository voiceover by Philip Morrison, then slowly zooms out to a view 10 meters (33 ft) across (or 10^1 meters in scientific notation). The zoom-out continues (at a rate of one power of ten per 10 seconds), to a view of 100 meters (330 ft) (10^2 meters) (where they are shown to be in Burnham Park, near Soldier Field, then 1 kilometer (3,300 ft) (10^3 meters) (where we see the entirety of Chicago), and so on, increasing the perspective and continuing to zoom out to a field of view of 10^24 meters, or a field of view 100 million light years across. The camera then zooms back in at a rate of a power of ten per 2 seconds to the picnic, and then slows back down to its original rate into the man's hand, to views of negative powers of ten: 10^−1 meters (10 centimeters), and so forth, revealing a skin cell and zooming in on it—until the camera comes to quarks in a proton of a carbon atom at 10^−16 meters.
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