There are no numbers in the coin itself, but you reasonably can state the probability of the coin coming up heads and even state your certainty in this estimate. These are numbers you made.
No, those are numbers you found. The inherent tendency to produce numbers when tested in that way (“fairness/unfairness”) was already a property of the coin; you found what numbers it produced, and used that information to derive useful information.
Making numbers, on the other hand, is almost always making numbers up. Sometimes processes where you make numbers up have useful side-effects
Of course, the point of a subjective Bayesian calculation wasn’t that, after you made up a bunch of numbers, multiplying them out would give you an exactly right answer. The real point was that the process of making up numbers would force you to tally all the relevant facts and weigh all the relative probabilities.
but that doesn’t mean that making numbers is at all useful.
Basically, I think it’s important to distinguish between finding numbers which encode information about the world, and making numbers from information you already have. Making numbers may be a necessary prerequisite for other useful processes, but it is not in itself useful, since it requires you to already have the information.
That phrase is so general as to be pretty meaningless.
I do not subscribe to the notion that anything not expressible in math is worthless, but “in most circumstances” the inability to find any numbers is a strong indication that you don’t understand the issue well.
the inability to find any numbers is a strong indication that you don’t understand the issue well.
Yes, that’s the whole point. There aren’t always numbers you can find, even when there are, finding them is nontrivial, and you often have to deal with the ambiguous situation or problem regardless.
{ the ability to navigate ambiguity } I think this is one of the most important skills you get from the humanities.
Statistics is precisely that, but with numbers.
What you said here is a vast oversimplification; if you have gotten to the point where you can find relevant numbers, you have already successfully navigated most of the ambiguity.
Is there still an inferential gap here? I thought I made my point clear about three comments ago, but this is clearly not as obvious a distinction as I expected it to be.
if you have gotten to the point where you can find relevant numbers, you have already successfully navigated most of the ambiguity.
And that’s where you are being misled by your insistence on “finding” numbers instead of “making” them.
It’s pretty easy to construct estimates. The problem is that without good data these estimates will be too wide to the point of uselessness. But you can think, and find some data, and clean some existing data, and maybe narrow these estimates down a bit. Go back to 1. and repeat until you run out of data or the estimate is narrow enough to fit its purpose.
Ambiguity isn’t some magical concept limited to the humanities. The whole of statistics is dedicated to dealing with ambiguity. In fact, my standard definition of statistics is “a toolbox of methods to deal with uncertainty”.
I understand your point, I just think it’s mistaken.
I consider all the things you’ve said to be my best arguments why you’re wrong, so there’s clearly something wrong here. But I’ve run out of novel arguments and can’t figure out where the disconnect is.
You seem to think that it is generally easy to turn arbitrary ambiguities into numbers in a way amenable to using statistics to resolve them. I find that to be obviously, blatantly false.
Where you see things like this:
It’s pretty easy to construct estimates. The problem is that without good data these estimates will be too wide to the point of uselessness. But you can think, and find some data, and clean some existing data, and maybe narrow these estimates down a bit. Go back to 1. and repeat until you run out of data or the estimate is narrow enough to fit its purpose.
I see something more like
In order to get an estimate narrow enough to fit the purpose, gather data, make a bad estimate, gather more data, refine the estimate, gather still more data, refine further, repeat until you can’t find any more data and then hope you got something useful out of it.
Where the difficult part is gather data. If you can gather data that is relevant, then statistics are useful. But often, you can’t, and so they aren’t. I outlined the exact same process as you, I’m just significantly more pessimistic about how often and how well it works.
You seem to think that it is generally easy to turn arbitrary ambiguities into numbers
Yes, I do.
in a way amenable to using statistics to resolve them.
No, I do not. I said nothing about “resolving” things.
When I say “numbers” in the context of statistics, I really mean probability distributions, often uncertain probability distributions. For example, the probability of anything lies somewhere between zero and one—see, we don’t have any information, but we already have numbers.
You’re likely thinking that when I am turning ambiguities into numbers, I turn them into nice hard scalars, like “the probability of X is 0.7”. No, I don’t. I turn them into wide probability distributions, often without any claims about the shape of these distributions. That is still firmly within the purview of statistics.
Where the difficult part is gather data. If you can gather data that is relevant, then statistics are useful.
If you have no data, nothing is useful. Remember, the original context was how humanities teach us to deal with ambiguity. But if you have no data, humanities won’t help and if you do, you can use numbers.
I’m not saying that everything should be converted to numbers. My point is that there are disciplines—specifically statistics—that are designed to deal with uncertainty and, arguably, do it better than handwaving common in the humanities.
No, those are numbers you found. The inherent tendency to produce numbers when tested in that way (“fairness/unfairness”) was already a property of the coin; you found what numbers it produced, and used that information to derive useful information.
Making numbers, on the other hand, is almost always making numbers up. Sometimes processes where you make numbers up have useful side-effects
but that doesn’t mean that making numbers is at all useful.
Basically, I think it’s important to distinguish between finding numbers which encode information about the world, and making numbers from information you already have. Making numbers may be a necessary prerequisite for other useful processes, but it is not in itself useful, since it requires you to already have the information.
I don’t think this is a useful distinction, but if you insist...
You said: “That only works if you have numbers.” Then the answer is: “Luckily, you can find numbers.”
Finding relevant numbers is significantly difficult in most circumstances.
That phrase is so general as to be pretty meaningless.
I do not subscribe to the notion that anything not expressible in math is worthless, but “in most circumstances” the inability to find any numbers is a strong indication that you don’t understand the issue well.
Yes, that’s the whole point. There aren’t always numbers you can find, even when there are, finding them is nontrivial, and you often have to deal with the ambiguous situation or problem regardless.
What you said here is a vast oversimplification; if you have gotten to the point where you can find relevant numbers, you have already successfully navigated most of the ambiguity.
Is there still an inferential gap here? I thought I made my point clear about three comments ago, but this is clearly not as obvious a distinction as I expected it to be.
And that’s where you are being misled by your insistence on “finding” numbers instead of “making” them.
It’s pretty easy to construct estimates. The problem is that without good data these estimates will be too wide to the point of uselessness. But you can think, and find some data, and clean some existing data, and maybe narrow these estimates down a bit. Go back to 1. and repeat until you run out of data or the estimate is narrow enough to fit its purpose.
Ambiguity isn’t some magical concept limited to the humanities. The whole of statistics is dedicated to dealing with ambiguity. In fact, my standard definition of statistics is “a toolbox of methods to deal with uncertainty”.
I understand your point, I just think it’s mistaken.
I consider all the things you’ve said to be my best arguments why you’re wrong, so there’s clearly something wrong here. But I’ve run out of novel arguments and can’t figure out where the disconnect is.
What is that statement of mine to which you are assigning the not-true value?
You seem to think that it is generally easy to turn arbitrary ambiguities into numbers in a way amenable to using statistics to resolve them. I find that to be obviously, blatantly false.
Where you see things like this:
I see something more like
Where the difficult part is gather data. If you can gather data that is relevant, then statistics are useful. But often, you can’t, and so they aren’t. I outlined the exact same process as you, I’m just significantly more pessimistic about how often and how well it works.
Yes, I do.
No, I do not. I said nothing about “resolving” things.
When I say “numbers” in the context of statistics, I really mean probability distributions, often uncertain probability distributions. For example, the probability of anything lies somewhere between zero and one—see, we don’t have any information, but we already have numbers.
You’re likely thinking that when I am turning ambiguities into numbers, I turn them into nice hard scalars, like “the probability of X is 0.7”. No, I don’t. I turn them into wide probability distributions, often without any claims about the shape of these distributions. That is still firmly within the purview of statistics.
If you have no data, nothing is useful. Remember, the original context was how humanities teach us to deal with ambiguity. But if you have no data, humanities won’t help and if you do, you can use numbers.
I’m not saying that everything should be converted to numbers. My point is that there are disciplines—specifically statistics—that are designed to deal with uncertainty and, arguably, do it better than handwaving common in the humanities.
Your confidence in your ability to do statistics to everything is clearly unassailable, and I have no desire to be strawmanned further.