I had this discussion in August 2021 while working on my article, Multi-Factor Decision Making Math. Justin was studying math. I saw an opportunity to explain the issue he was working on and also relate it to my article. Justin had not seen an article draft. I’m sharing this because it has some useful summary of my main point. And it was practice/research writing for my article.
writing a variable (x) in terms of another variable (y) means you know something that is equal to x but which is in terms of y. in other words, the something contains only y as a variable, but not x or z. when simplified it might be x = 3y. now you know how much x is worth in terms of y. it’s the same as knowing what a foot is in terms of inches: f = 12i. it allows conversion between units or reducing the number of separate variables in an equation since you can substitute instances of one variable (x) with another (y) so there are no x’s left, so you’ve reduced the total number of variables by 1 by removing all x’s. which is similar to converting all feet to inches and then there are no mentions of feet left. does that makes sense? i have been writing about this in the last few days b/c it’s related to YesNo.
Yep makes sense 👍
in philosophy, ppl want to evaluate options like how good different candidate pets are, or anything. so they look at many factors, like cuteness and price, which are in different dimensions (money and cuteness). and then ppl want to get an overall score or ranking for an option based on multiple factors. so the first dog might be -20d + 5c (d being dollars, c cuteness), ignoring for now the dozen other factors.
the thing is, you cannot add -20d + 5c. there’s literally no way to combine them. whether you view them as units in different dimensions or variables, that is maximally simplified. the only way to simplify further is if you have another equation, such as a conversion factor, like 5d=1c that tells you how many dollars are worth a cuteness.
in short ppl try to make decisions by making up conversion factors to convert all factors into goodness points, but the factors are made up and don’t work well.
CF’s solution is stop adding factors together. combine with multiplying. multiplying is problematic in general, e.g. if you multiply -20d with 5c you get -100dc which is not useful b/c the number is in terms of a multi-dimensional unit of cuteness-dollars. (this is familiar with multiplying and dividing other units, such as miles divided by hours. that is one of the special cases where a multi-dimensional unit is useful and equates to a real world concept that we use in our thinking. most don’t).
Right "converting" cuteness to dollars is nothing like converting yen to dollars.
yes, yen and dollars convert btwn each other (approximately) b/c they are in the same dimension (money). within dimension conversion is so easy that we often don’t even list things as separate factors when they’re in the same dimension. just list one factor per dimension.
e.g. if walking to the store involves walking 20 feet + 20 feet + 20 feet + 20 feet, i’m just gonna call it 80 feet
one factor not four
however, multiplying dimensions always works to get a useful result if the factors are binary. if you multiply pass/fail factors, it’s the same as using “and” on them. the result is 1 (pass) if every factor works and 0 (fail) otherwise. so in other words, do you have at least one decisive criticism or not?
does this make sense?
Ya if there's a 0 anywhere in one of the dimensions then the whole thing fails (goes to 0)
so instead of making up a conversion from cuteness to goodness, you convert from cuteness to a binary factor. you do this by asking yes or no questions like “is this pet cute enough to satisfy me?”
that's a neat way to think about it 🙂
one thing i noticed is that you can have one non-binary factor and it still works. you will then get a result of either 0 or the value of that one non-binary factor. this lets you rank things by one factor in addition to doing the pass/fail factors. and this connects to Goldratt’s idea of optimizing the one bottleneck and for everything else you just want it to be good enough with excess capacity.
it’s when you multiply 2+ non-binary factors that you get trouble.
trying to maximize more than one factor at once is problematic and basically requires a conversion factor, e.g. 3x = 1y. then you can maximize the sum x + 3y. you need to be able to convert btwn factors/dimensions to optimize more than one dimension.
however, you can also think in a fully binary way like i talked about in CF course. e.g. for the one factor you want more of, you can have a goal of maximizing it (given a pass on everything else) and then reject everything that is below the max.
if you're ranking universities by closeness to home (cuz u wanna stay nearer to home) and the other factors are pass fail, u could reword that ranking as a pass fail "is this the closest university to home of the universities that pass the other criteria?" or something like that
ok i’m glad this makes sense to you. now i just have to figure out how to explain it to ppl who don’t already know lots of CF….
they don’t necessarily have to learn the mathy way first but every starting point seems hard if u don’t know any of the other things yet…
btw, related, you can’t add 1/7th and 1/17th without converting first. the “units” or “dimensions” here are being sevenths or seventeenths. fortunately, we can convert b/c they are actually both in the same dimension: numbers.
similarly, you can’t add 2sqrt(5) with 3sqrt(8) without first converting. but again conversion is possible cuz it’s all numbers.
you do this by asking yes or no questions like “is this pet cute enough to satisfy me?”
and to do that well, you look for digital or binary issues, or breakpoints.