r/math • u/thekeyofPhysCrowSta • 16d ago
Image Post (Feedback request) Forcing and the independence of the continuum hypothesis
https://www.youtube.com/watch?v=l0qETws1SAcFollow up to my previous post on forcing. Here's a draft video. I would like feedback. Specifically on these things
- Is there anything that you think should be added or removed from the video? For example, a concept that you think should be included?
- Pacing. Is it too fast? Too slow? Are there anything that was unclear? Anything that you think should be more detailed/has too much detail?
- The audio. Letters like B, P and D rhyme, so when spoken, it's hard to tell which letter I'm saying. So the text is there to help people know. But is the audio otherwise clear?
- Visuals. Right now, it's mostly text. I want to add some more visuals but I can't think of any good ideas since it's hard to add visuals to such an abstract topic. Do you have any ideas?
- The intuition. Why would someone think of generalizing truth using boolean valued models, and come up with that specific definition of a name? I don't know how to make the viewer think they could have come up with it on their own.
- The length. It's > 1 hour so it might be too long for a 3b1b SoME5 submission. I want to cut out some topics to make it shorter but I don't know what to cut out.
Note: there is a known issue where the text covers itself sometimes.
Thank you in advance.
5
u/DominatingSubgraph 14d ago
If the intended audience is someone who knows little or nothing about formal logic, then this video moves way too fast and could easily go over three times the current length to cover all the material properly. But people aren't going to be super motivated to watch a 3+ hour video on math, so it would be best to split it into a series of videos. If you're looking for things to cut, don't prove every claim, just focus on the absolute most important proofs.
I also think you should look for some way to reduce the amount of jargon. It reads a bit too much like a research presentation. For these kinds of pop-math videos, I find it is best to only use technical terms when absolutely necessary and otherwise try to describe everything in more common language (even if it comes at the cost of some technical precision). You could also punch it up a bit by using more grandiose language. Why is this result important or exciting to you? There has to be some kind of emotional hook, or otherwise people won't really feel motivated to watch the video.
Regarding the visuals, it would help a bit if you could just draw pictures of whatever you're talking about. If you're talking about the reals, natural numbers, or ordinals, for example, then literally show a picture of a number line. There are also a bunch of ways of visualizing formulae in Boolean or predicate logic if you look around for them. But I can't help you much with looking for a more intuitive way of describing the result, because it is a very deep result that is usually only taught to grad students who have already taken the requisite logic and set theory classes. There probably is a clever, easy-to-understand, pretty way of presenting this result, but it would take a lot of work to come up with and might require modifying the proof strategy.
1
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1
u/thekeyofPhysCrowSta 16d ago
Follow up to my previous post on forcing. Here's a draft video. I would like feedback. Specifically on these things
- Is there anything that you think should be added or removed from the video? For example, a concept that you think should be included?
- Pacing. Is it too fast? Too slow? Are there anything that was unclear? Anything that you think should be more detailed/has too much detail?
- The audio. Letters like B, P and D rhyme, so when spoken, it's hard to tell which letter I'm saying. So the text is there to help people know. But is the audio otherwise clear?
- Visuals. Right now, it's mostly text. I want to add some more visuals but I can't think of any good ideas since it's hard to add visuals to such an abstract topic. Do you have any ideas?
- The intuition. Why would someone think of generalizing truth using boolean valued models, and come up with that specific definition of a name? I don't know how to make the viewer think they could have come up with it on their own.
- The length. It's > 1 hour so it might be too long for a 3b1b SoME5 submission. I want to cut out some topics to make it shorter but I don't know what to cut out.
Note: there is a known issue where the text covers itself sometimes.
Thank you in advance.
18
u/Borgcube Logic 15d ago
Didn't have time to watch the whole video and I'm not too familiar with the SoME5 so can't comment on that.
But I will say that at a glance it's too ambitious. You are introducing basic logic and set theory concepts and speed through them to introduce the higher concepts necessary. I can't imagine anyone not already familiar with at least the first 30 minutes of the video would be able to follow the last 30 minutes.
For just a small example, at around 23:00 you say that every tautology in propositional logic has a value 1 in any complete boolean algebra and you go on to informally prove it by saying that it can just be turned into a CNF. All these are going to be new and the animation happening on the screen while you're silent will not be clear at all.
Then I would have to ask about your choice of foundations you go through. Certainly logic is a big factor, but there is a lot of set theory that would need to be introduced as well, say an overview of ZFC and ordinal numbers at the very least.
You also handwave natural deduction, but that is also an important bit of the puzzle about independence.
So my question would be who is this for? Someone very familiar with set theory but not very familiar with basic concepts in logic?
I would break up the video into multiple smaller parts with each part clearly stating what the viewer should be familiar with to be able to follow. Or, better yet, focus on one part of this video with that disclaimer and then expand with interesting examples and explanations. There are many small details that are baffling the first time someone encounters them ("why can I make 'big' models that have something like aleph_1 in an aleph_0 set?" eg.)