I think because it’d be largely unhelpful, for others? I’m not sure actually I didn’t think too much about it.
downsides of posting disorganised stuff brainstorm:
put less effort into my posts
not contributing much
embarrassing
can seem like i’m expecting people to help me
want to look like i’m doing a good job
upsides:
gives people a window into my organisation
might get some feedback
more evidence of what i might be thinking
Good question. I think basically I got stuck on it being too hard/big. I am interested in it, and thinking about it now, I think just got stuck on it being a kinda big project. I didn’t consider trying to break it down and ask for help to work through it. Maybe I was considering it to be extra-tutoring stuff. I’d actually be interested in that.
I had started working on a post mortem. As a test of posting some less organised/finalised stuff, here is what I had at the time:
MFDMM Post Mortem Start
Elliot said:
Make sense? @Eternity too. If so, the next thing to consider may be revisiting Multi-Factor Decision Making Math to evaluate what you didn’t understand previously, and if/why you thought you did understand that, and post mortem what’s going on there. Then continue with the Friedman article.
So what to do:
- evaluate what I didn’t understand previously
- if/why I thought I did understand it
- post mortem what’s going on there
When writing that last post, I had an inkling that this was related to what was in the MFDM article. But I didn’t then go and read it. I don’t know why. I think partly I had spent too long on it already and I wanted to post something.
The maximising problem:
From the article:
How can we mathematically combine multiple factors to get an overall evaluation that lets us rank the options to decide which is best?
I can see that the article presents approximately the same problem. When we’re looking for what maximises x and y, we’re looking for an overall evaluation of the three options based on the factors x and y.
From the article:
We can also determine the best option if an option is the best for every factor. That option is strictly better. But in many cases, including our example, no option is strictly best.
There was no option in the maximising problem that was strictly the best for every factor. I chose option 1 though, thinking that it ‘maximised’ x and y.
Bold added:
This shows how unit conversion matters (you couldn’t combine them without doing a conversion first) and how your goals matter. Instead of ranking [pounds of bacon and number of apples] by calories, you could rank by carbohydrates, fat, protein or a nutrient like vitamin C. Which ranking(s) matter to you, and are suitable for making your decision, depends on your goals. However, often you care about multiple things, e.g. both calories and carbohydrates. No single ranking will take into account your goals about both calories and carbohydrates unless you find a way to convert calories and carbohydrates into the same dimension.
After reading the MFDM article, I realised one of my confusions with this problem was that I didn’t know if y and x were or weren’t of the same dimension. They weren’t defined. But now I realise in math it’s just standard to assume x and y are of a different dimension; they are unlike terms after all. I’m not sure why this happened.
I think it might have something to do with my intuition here:
I think what didn’t ‘seem right’ to me was that I knew on one hand that you can’t add like terms, but on the other hand that depends on what x and y are in a real-world situation, and whether they are in the same dimension. Maybe I was somehow blurring the two problems together (the mathematical one and the real world one) and getting myself confused.
I think also that I hadn’t learned the ideas from the article well because my main goal when I read it last (which I think is the only time I had read it fully) was to find math I didn’t understand, so that Elliot could know where to focus my math tutoring. So I’m not totally surprised that I didn’t make the connection to this problem. I hadn’t fully engaged with the article’s ideas and so hadn’t practised with the ideas and how they relate to decision making.
I should’ve followed up on my suspicion that the MFDM article was relevant, and I should’ve realised that was an option when I got stuck.
Last I read this article was in April '24 near the very start of my tutoring. My goal when reading it was to look for math that I didn’t understand.
Freewriting
If you want to compare two things, you need some way that they can be converted into the same thing first.
Take apples and oranges. Which one is better? To answer that we need to compare them. But to compare them we need to know which aspect of them to compare. We could compare their weight, their sugar content, vitamin content, calories.
This is similar to combining them. They are different things, so in what respects can we combine them?
Which aspect of them should we compare?
Well it depends on your goal. If we want to compare them to each other, we need to know what to compare them in terms of. It could be weight, calories, sugar content, price. So we need
It seems more complete and less disorganised than I remember, actually. In addition to it being too big, I think I was disorganised about writing it and left too much time between attempts to work on it and I kinda lost my train of thought. I can see how those would be related. Also, I remember at the time working on stuff across a few threads like with the debate too. I think I was working on too many things at once?