Thought representation

I’ve watched from 5-12 minutes on this video and had some initial thoughts.

• Prompted by his discussion of algebraic notation being invented as a nice UI for that kind of maths: it’s good because it’s concise and because it’s 100% precise, as opposed a paragraph describing same idea which could be logically incomplete. On one hand, the precision is the key improvement here, as this is crucial for doing maths. On the other hand, it is actually the concision that is most important, as it is just not possible to reason about these abstract concepts with the old representation format (text).
• So the key idea, which I think is his point but I have now convinced myself of, is that to do good work in some domain (maths, economics, whatever) you need the right representation format/notation for your ideas.
  • He mentions this: “A lot of the power of an idea lies in the form in which it is expressed”
  • Although it was useful to think this through myself
• He also mentions how ideas build on each other, facilitated by how they’re represented. If multiple people share a representation and independently build on it, does it not need to be precise? In other words, if a representation can be interpreted to mean different things at its most basic level by different people, it is not a good representation. Obviously people can get different takeaways from different graphs, but the “it goes down here and up here” is indisputable. The level of precision required in a representation depends on what you’re going to do with it.
• His point that “ideas live in representations” is made well. To make this most useful to us we should be more specific about what benefits a good representation has
  • I’ve convinced myself that compression is a key, because it lets you hold and manipulate more thoughts at once (classic 7 item limit of working memory)
  • I think loss of precision is interesting – it doesn’t matter for line graphs where what is interesting is the general trend rather than smaller movements, but it definitely does for algebra. Maybe text is more like the former, but I think that’s highly specific to domain and application.
• From that, my immediate question is “what domain is being held back because of poor representation of ideas”. One way of rephrasing this more specifically is “what domain holds lots of information as paragraphs, and is therefore one in which it’s difficult to combine ideas”
• I tend to avoid this type of thought as it’s dangerously close to techno-utopianism, but here goes. He talks a lot about medium being important. It’s easy to stick to variations of what we already have (text, graphs, pictures) we think bigger. I wonder what options are opened if you start storing ideas in formats that are more easily composed – in algebra you can easily substitute in variables for other equations (e.g. if I have x = 2y + z I can just chuck that in elsewhere). It’s impossible to do this for raw text in a logically consistent way (i.e. on that precision axis I mention earlier), but it could maybe still be useful. It’s tempting to think about this representation as being vectors. I’m not going to go down the rabbit hole of the many flaws in this idea, but maybe it’d be sufficient for some purposes.
  • Maybe it’s not logically combining two ideas but just surfacing them next to each other?
  • On being stuck to variations on a theme: if you squint, is the internet just a more efficient printing press? In some ways yes, everyone can now more easily publish their thoughts + access others’; in others, e.g. thinking about richer or linked media, or search, then no.
    • Maybe this is a thread to pull. What were some concrete benefits of the internet to knowledge workers, and could this list inspire any thought about analogous step changes that might be possible now?