No-One Can Tell You What They Don’t Understand

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.

On a computer screen, they instead just look awkward.

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.

Please state the nature of the medical emergency.

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.

7 thoughts on “No-One Can Tell You What They Don’t Understand

  1. Wyrd Smythe

    Okay, first of all, that is not Amanda Peet! I’ve seen The Whole Nine Yards, so I know what Amanda Peet looks like! You can’t fool me that easily! XD

    Kidding aside, there is a very interesting question there about math and reality. The world looks smooth (“analog”) on the macro level, but is quantum (“digital”) when looked at closely. But the math behind QFT uses real numbers (even, I believe, complex numbers), so we’re back to smooth again. But go further down and information theory suggests a digital reality of bits. But information theory is described by real numbers (right?).

    [I’ve shared my fantasy with you that the dichotomy continues. Matter and energy quantized, space and time Einstein smooth. If only! 🙂 ]

    It does seem pretty clear that “god” invented the integers, because “god” invented countable objects. It seems less clear how much of an invention the reals are. And there’s the whole “eerie effectiveness” thing. It’s a fun topic to chew on!

    Your main point about trying to communicate science effectively really hit home with me. I see myself as someone who understands (and loves!) a number of science topics well enough to want to try to share that with others, but I’ve realized I may not be very good at it. I tend to get too detailed and too complex.

    I once tried multiple times to show a co-worker how, yes, the Moon does rotate despite always keeping one face towards the Earth. We physically acted out the roles of Earth and Moon, but somehow I was unable to find the right lever to pull with him.

    My buddy, who has a gift for simplification, had a similar experience but was successful when he pointed out how the view of the walls behind moved across the vision of his co-worker. He sat the guy down in an office chair and rotated him while pointing out the view of the walls from the rotating chair. Then he had the guy revolve around him, acting out the role of the Moon, and pointed out how the walls moved across the visual field the same way.


    But I keep trying. For Einstein’s birthday I decided to write a series of posts about SR — a series that turned out to be nearly 30 posts long! (You pointed me to a website a few months ago that was extremely helpful in clearing some things up for me, and I used some of the ideas there in my own posts. If you’re curious and have some free time, here’s the index to the posts.)

    I’m not sure how successful my series was. A few readers seemed to enjoy it, and the whole thing led up to the punchline about why FTL is (almost certainly) impossible. I kind of see it as a “first draft” although it’s questionable whether there will be a more polished version. I’d like to do a really good re-write for my personal website — the official version, so to speak.

    Writing it sure clarified some things in my mind, though! I feel I have a pretty good grasp of SR. (Now I just have to figure out tensors so I can learn more about GR!) Proves once again that you never learn something so well as when you try to explain it to others!

    Liked by 1 person

    1. 4gravitonsandagradstudent Post author

      Incidentally, I’ve been thinking a bit more about how to explain the “quantum is discrete, but quantum field theory is continuous” thing. I think a better way of thinking about it is that quantum mechanics says that solutions are discrete, that rather than fields being able to take any arbitrary configuration they have discrete choices they can take. The fields themselves are still continuous, but the discreteness lies in how they can be configured.


      1. Wyrd Smythe

        I think I get that. A “particle” is the smallest allowed change from “nothing” to “something,” right? Matt Strassler has often written about the ‘smallest possible ripple’ in the field.


  2. Tienzen (Jeh-Tween) Gong

    “No-One Can Tell You What They Don’t Understand: (… we have to be willing to poke and prod until we root out the source of the confusion.)”

    But, we can tell them what they don’t understand and help them to get the right QUESTION and right answer.

    Does that questioner understand the relationship between Hologram/holograph and irrational number? Probably not. Is it a good question on that issue? Definitely Yes. Thanks for mentioning it, and I will definitely write about it soon, of course, not here.

    Your article shows me that there are two attitudes.
    One, dismiss, dismiss, …, dismiss,…
    Two, taking the hint, hint,…, and hint,…

    I am the “Two’ man. Why dismiss an ignorant question? Other’s ignorance is often a great hint for a new insight.

    For Peet’s lecture, Peter Woit (May 7, 2015) wrote about it: “For the latest in the string wars, you can watch last night’s Perimeter Institute public lecture by Amanda Peet. … I think it’s their [Perimeter Institute] responsibility to look into this and issue a public correction. Or do they really feel that it is all right for their public lecture series to be used to mislead the public about science?”

    Should we dismiss Peter? I don’t and am on his side. There are many hints on this issue.
    First, an analogy:
    Nature produces: thermodynamics, electromagnetism, etc.
    Human invents: steam-engine, air plane, computer, iphone, etc.

    Yet, steam engine was (can be) invented without knowing the thermodynamics. On the same token, the current string theory (especially the M-theory) is at the same level as steam engine or iphone; the emergences, not the fundamental. By all means, the mainstream string-theory is great work similar to the steam engine (without the understanding of its foundation, the thermodynamics).

    Second, we have DISMISSed ‘string-unification’ as a part of string theory. G-string is a LANGUAGE for string-unification but it is DISMISSed as a non-falsifiable THEORY. A language might not be a physics theory but could be a great HINT.

    Anyway, what do you think about Peter Woit’s comment and demand?


    1. 4gravitonsandagradstudent Post author

      It’s not immediately obvious that Dr. Peet was talking about what Woit thinks they were talking about. The “test the assumptions of string theory” phrasing makes me think they were referring to things like tests of Lorentz invariance. These aren’t “tests of string theory” per se, so what Peet said was definitely misleading. On the other hand, these sorts of “basic assumptions” tend to get thrown out in most other theories of quantum gravity. String theory is in this sense quite conservative, preserving successful principles of older physics in a way that other projects don’t.

      We can’t “tell them what they don’t understand” when it isn’t clear to us either, it takes some skill to suss out. For instance, I still haven’t managed to figure out what your fundamental misunderstanding is. 😉

      Liked by 1 person

      1. Tienzen (Jeh-Tween) Gong

        “For instance, I still haven’t managed to figure out what your fundamental misunderstanding is.”

        My fundamental misunderstanding could be a great HINT for a true fundamental UNDERSTANDING.



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