On Wednesday, Amanda Peet gave a Public Lecture at Perimeter on string theory and black holes, while I and other Perimeter-folk manned the online chat. If you missed it, it’s recorded online here.
We get a lot of questions in the online chat. Some are quite insightful, some are basic, and some…well, some are kind of strange. Like the person who asked us how holography could be compatible with irrational numbers.
In physics, holography is the idea that you can encode the physics of a wider space using only information on its boundary. If you remember the 90’s or read Buzzfeed a lot, you might remember holograms: weird rainbow-colored images that looked 3d when you turned your head.
Holograms in physics are a lot like that, but rather than a 2d image looking like a 3d object, they can be other combinations of dimensions as well. The most famous, AdS/CFT, relates a ten-dimensional space full of strings to a four-dimensional space on its boundary, where the four-dimensional space contains everybody’s favorite theory, N=4 super Yang-Mills.
So from this explanation, it’s probably not obvious what holography has to do with irrational numbers. That’s because there is no connection: holography has nothing to do with irrational numbers.
Naturally, we were all a bit confused, so one of us asked this person what they meant. They responded by asking if we knew what holograms and irrational numbers were. After all, the problem should be obvious then, right?
In this sort of situation, it’s tempting to assume you’re being trolled. In reality, though, the problem was one of the most common in science communication: people can’t tell you what they don’t understand, because they don’t understand it.
When a teacher asks “any questions?”, they’re assuming students will know what they’re missing. But a deep enough misunderstanding doesn’t show itself that way. Misunderstand things enough, and you won’t know you’re missing anything. That’s why it takes real insight to communicate science: you have to anticipate ways that people might misunderstand you.
In this situation, I thought about what associations people have with holograms. While some might remember the rainbow holograms of old, there are other famous holograms that might catch peoples’ attention.
In science fiction, holograms are 3d projections, ways that computers can create objects out of thin air. The connection to a 2d image isn’t immediately apparent, but the idea that holograms are digital images is central.
Digital images are the key, here. A computer has to express everything in a finite number of bits. It can’t express an irrational number, a number with a decimal expansion that goes on to infinity, at least not without tricks. So if you think that holography is about reality being digital, rather than lower-dimensional, then the question makes perfect sense: how could a digital reality contain irrational numbers?
This is the sort of thing we have to keep in mind when communicating science. It’s easy to misunderstand, to take some aspect of what someone said and read it through a different lens. We have to think about how others will read our words, we have to be willing to poke and prod until we root out the source of the confusion. Because nobody is just going to tell us what they don’t get.