Flannel Jesus wrote: ↑Sun Jul 17, 2022 8:18 pm
Sounds like you're actually not into ideas that much, given your reply here. You're uncomfortable with talking about probabilities as ideas
You seem to be using the word "idea" in some way that's not conducive to clear communication.
idea noun 1. a thought or suggestion as to a possible course of action.
See. I keep telling you I am not the problem...
Last edited by Skepdick on Sun Jul 17, 2022 8:20 pm, edited 1 time in total.
Skepdick wrote: ↑Sun Jul 17, 2022 8:22 pm
You know. Since you are actually abusing the word "idea" and ruining any hope for common ground/communication.
We found our common ground already. As soon as you experimentally showed, with your code (that I'm very grateful for by the way, good job on that), that the probability that we've selected the 100+100 box increases from 50% to 66.666...% after we pull the first bill and see that it's a $100, that was our common ground.
You've spent the rest of your participation in this thread denying our common ground.
bobmax wrote: ↑Sun Jul 17, 2022 8:06 pm
The mistake is not to treat the bills as different.
But in not considering the perfect equivalence of the two 100 bills.
This does not happen with regard to the box of 100 and 1 because the question of equivalence does not arise.
Which instead is present in the box of 100 and 100.
Bob, you still haven't addressed the main inconsistency of your post -- you said people are overestimating that the box is 100+1, but if peoples mistake is because they're treating the two 100s as different (or treating them as not perfectly equivalent), then wouldn't that cause them to overestimating the 100+100 box, and not the 100+1 box?
This is what I'm not getting.
When I have the $ 100 bill in my hand, it is uniquely identified, this is it right here.
It can be of the box of 100 and 1 or of the box of 100 and 100.
In both cases I take it off and it stays in the first box $ 1 and in the other $ 100.
And so I conclude that the probability is 1/2.
Why am I wrong?
In my opinion, because I do not consider that in the second box the 100 bill I have in my hand is not unique, but it is perfectly equivalent to that other one.
bobmax wrote: ↑Sun Jul 17, 2022 8:32 pm
When I have the $ 100 bill in my hand, it is uniquely identified, this is it right here.
It can be of the box of 100 and 1 or of the box of 100 and 100.
In both cases I take it off and it stays in the first box $ 1 and in the other $ 100.
And so I conclude that the probability is 1/2.
Why am I wrong?
In my opinion, because I do not consider that in the second box the 100 bill I have in my hand is not unique, but it is perfectly equivalent to that other one.
The majority of people who treat the 2 100s in the double box as 'not unique' are the ones saying that the probability is 1/2. The people who treat them as unique are the ones saying the probability is 2/3. That's why I'm not jiving with this explanation - I think it's exactly the wrong way around.
When you treat the 2x 100s as unique, you INCREASE the surface area of the probability to be the second box. Treating them as unique is arguably one of the biggest reasons why we say it's 2/3 and not 1/2. When you treat them as identical, rather than unique, you don't count them twice, you count them together once, and that line of reasoning is exactly why a lot of people intuit that the probability is 1/2.
Skepdick wrote: ↑Sun Jul 17, 2022 8:22 pm
You know. Since you are actually abusing the word "idea" and ruining any hope for common ground/communication.
We found our common ground already. As soon as you experimentally showed, with your code (that I'm very grateful for by the way, good job on that), that the probability that we've selected the 100+100 box increases from 50% to 66.666...% after we pull the first bill and see that it's a $100, that was our common ground.
You've spent the rest of your participation in this thread denying our common ground.
Is THAT what you call "common ground" ?!? No wonder we disagree!
For an idea-driven person finding common ground amounts to finding a common goal. An objective we can work towards. And then we can discuss possible courses of action (actual ideas!) to achieve the common goal.
You know like trying to find the answer to the question "Which hypothesis has probability true-value of 1?"; and "Is the initial estimation and over; or under-estimation with respect to the true value?"
Skepdick wrote: ↑Sun Jul 17, 2022 8:40 pm
You know like trying to find the answer to the question "Which hypothesis has probability true-value of 1?"
Is that your goal? What hypotheses are in question?
I said that already...
No matter. I'll repeat myself (since you don't hear/understand so good).
The two options are:
A. Now that I have a $100 bill in my hand I must have chosen box 100/100
B. Now that I have a $100 bill in my hand I must have chosen box 1/100
Which hypothesis has true-value (e.g NOT an estimate!) probability of 1?
There's 1 way to turn the probability into 1 - by looking in the box at the second bill.
We look in the box, we see which one it is, we know which one it is, end of conversation. What more is there to say about it than that? I don't see why that line of inquiry interests you so much. The story is straight forward, completely unambiguous, completely without challenge and boring.
Am I missing something? What's interesting about it to you?
Flannel Jesus wrote: ↑Sun Jul 17, 2022 8:48 pm
Ah, no, that question doesn't interest me at all.
Oh, OK. Godspeed on your journey.
Flannel Jesus wrote: ↑Sun Jul 17, 2022 8:48 pm
There's 1 way to turn the probability into 1 - by looking in the box at the second bill.
We look in the box, we see which one it is, we know which one it is, end of conversation. What more is there to say about it than that? I don't see why that line of inquiry interests you so much. The story is straight forward, completely unambiguous, completely without challenge and boring.
Am I missing something? What's interesting about it to you?
Well if you know and understand this, then surely you understand that the only time you can speak of over and under-estimation is after you've looked at the 2nd note?
Yet you seemed confused about the way I was using those terms (which is what led down this path).
If 2nd note is a 1 then 0.666... was an over-estimation.
If 2nd note is a 100 then 0.666... was an under-estimation.
I said that. You didn't agree.
Last edited by Skepdick on Sun Jul 17, 2022 8:53 pm, edited 1 time in total.
No, that's not the only way to talk about it, that's the LEAST interesting, LEAST useful way to talk about it, that's the way to talk about it that only you would think of, and nobody else cares about.
Do you want me to explain the other way that everybody else would talk about over/underestimation?
Flannel Jesus wrote: ↑Sun Jul 17, 2022 8:53 pm
No, that's not the only way to talk about it, that's the LEAST interesting, LEAST useful way to talk about it, that's the way to talk about it that only you would think of, and nobody else cares about.
Do you want me to explain the other way that everybody else would talk about over/underestimation?
How are you making any judgments about the "usefulness" of anything when you haven't stated any particular goal?
I have a goal - to explain to you the actual way that over/underestimation was meant, that you haven't been able to see, because you're so caught up in your incredibly dry, boring interpretation of it that nobody else cares about. That's my goal.
Flannel Jesus wrote: ↑Sun Jul 17, 2022 8:55 pm
I have a goal - to explain to you the actual way that over/underestimation was meant, that you haven't been able to see, because you're so caught up in your incredibly dry, boring interpretation of it that nobody else cares about. That's my goal.
Use is meaning. You aren't using your words towards any goals.
So I have no idea what your words could possibly mean (if anything) - they don't serve a higher purpose.
Last edited by Skepdick on Sun Jul 17, 2022 8:57 pm, edited 1 time in total.