I just had a click moment, and click moment should be shared so here I go.
I was thinking—why shouldn’t I be able to make 10,000 statements similar to 2+2=4 and get them all right? 1,000,000 even? 1,000,000,000? Any arbitrary N∈N?
All I have to do is come up with simple additions of different numbers, and since it’s all math and they are all tautologies there is no reason why I can’t get be right on all of them. Or is it?
So the obvious reason is that it takes time, and my life are limited. Once I’m dead, I can’t make any more statements. But… is this really a valid reason? Why should my death, in the future, affect the the confidence I put in 2+2=4 now?
So, let’s assume for the sake of the argument that I’m going to live forever. Or at least until I can come up with all the statements I need to come up with.
Next problem—I’m going to get tired. 16 hours a day? For years? I don’t think I can talk straight for more than an hour!
Since I assumed myself immortality I can also assume myself infinite stamina, but there is an easier way to solve this—just use my immortality. Eliezer used 16 hours a day and 20 seconds per statement to give a feeling of how large these numbers are, but since time is not an issue I can just do one statement a day. Eventually I’ll hit whatever arbitrary quota I need to hit.
And here we reach the problem that made it click—while there is no limit to the number of operand I can put in my additions, the number of small operands sure is limited. And by “small” I mean representation - 2 and 6 is larger than 0.003464326436432662364326 and 0.04326432632626243665432, but the former are much easier to add up than the later.
So, eventually I’ll run out of additions that involve only simple numbers, and have to use at least one operand with ten digits. Later on, hundred digits. Thousand digits!O(log10N) digits, but N is unbounded…
I am not 100% confident I can do math with these numbers and never make a wrong calculation.
Sure, I can write it down, and reduce the chance of error—but not to zero. And I can double check and triple check, but since no single check has 100% probability of finding all potential mistakes, the combination of all checks can’t do that either.
Intuitively the more digits there are the more likely I am to err. I’m more confident in my ability to add numbers with 100 digits than in my ability to add numbers with 200 digits. And I’m even more confident in my ability to add numbers in 50 digits. So generally speaking, I’m more confident in my ability to add numbers with n digits than in my ability to add numbers with n+1 digits.
But there is no n that I’m 100% confident in my ability to add numbers in n digits but less than 100% confident in my ability to add numbers with n+1 digits.
So why should I assign a zero probability to me butchering the addition of single digit numbers?
Imagine you set up a program that will continually resolve 2 + 2 after your death. Perhaps it will survive much longer than entropy will allow us to survive. It has a very nice QPC timer.
It uses binary, of course. After all, you can accomplish binary with some simple LEDs, or just, dots. Little dots. So you accomplish your program, set it to run using the latest CMBR-ran entropic technology, and no one attends your funeral, because you are immortal, but immortality does not survive entropy. At least, within the same uncertainty as you failing to state 2 + 2 = 4. Your brain remains remarkably logical through this. After all, it is highly overgeared, now, having been immortal. You are the 2 + 2 master equivalent of Ronnie O’Sullivan. Flawed, yes, but goodness, you can play a mean game of snooker. Sometimes you even get sneaky, and throw in a 4 = 2 + 2.
Your entropic death approaches. You write the code, and having made sure₁ of it, you set your canary to alert it of your death- the moment you fail to accomplish the scheduled 2 + 2 = 4 which continues the cosmic clock the universe’s entropy.
It is a simple equation. It takes very few bits to accomplish. 10 + 10 = 100₂ ~
Oh. Wait. It’s now 10 + 10 = 100? That doesn’t fulfill our need for 2 + 2 = 4, since the semantics aren’t preset. Well, what if we try this?
• • + • • = • • • •
Ah, yes, back to something reasonable. There are two dots and two dots which indicate 4 dots. This makes sense, possibly.
But the question wasn’t to resolve • • + • • ; but 2 + 2. So, in the spirit of integrity, we need to convert it to a displayable format for some future god-king race of the Anunaki to come witness our last, single work of humanity. Thus, you convert
• • + • • = • • • •
into
10 + 10 = 100
into
2 + 2 = 4
Since it only necessitates one character as the result, it is also the most efficient on power.
Are you 100% confident in anything aside from yourself, even if you made it?
Because you made 2 + 2 = 4. It’s just your idea. At that later immortal point in time, you are the only thing that still thinks 2 + 2 is relevant. The free floating quarks can barely find a date, let alone double :wink: date.
And this has at least three points of failure.
₁The code has at least fifteen points of failure.
₂This has at least eight points of failure.
Much like how I cannot assign a probability of 1 to my brain for any task, no matter how simple, I cannot assign a probability of 1 to a fallible CPU, no matter the quality. It could very well be the computer in Hitchhiker’s. I’ve been wrong on too many easy simple things by accident more than once to realize this.
I just had a click moment, and click moment should be shared so here I go.
I was thinking—why shouldn’t I be able to make 10,000 statements similar to 2+2=4 and get them all right? 1,000,000 even? 1,000,000,000? Any arbitrary N∈N?
All I have to do is come up with simple additions of different numbers, and since it’s all math and they are all tautologies there is no reason why I can’t get be right on all of them. Or is it?
So the obvious reason is that it takes time, and my life are limited. Once I’m dead, I can’t make any more statements. But… is this really a valid reason? Why should my death, in the future, affect the the confidence I put in 2+2=4 now?
So, let’s assume for the sake of the argument that I’m going to live forever. Or at least until I can come up with all the statements I need to come up with.
Next problem—I’m going to get tired. 16 hours a day? For years? I don’t think I can talk straight for more than an hour!
Since I assumed myself immortality I can also assume myself infinite stamina, but there is an easier way to solve this—just use my immortality. Eliezer used 16 hours a day and 20 seconds per statement to give a feeling of how large these numbers are, but since time is not an issue I can just do one statement a day. Eventually I’ll hit whatever arbitrary quota I need to hit.
And here we reach the problem that made it click—while there is no limit to the number of operand I can put in my additions, the number of small operands sure is limited. And by “small” I mean representation - 2 and 6 is larger than 0.003464326436432662364326 and 0.04326432632626243665432, but the former are much easier to add up than the later.
So, eventually I’ll run out of additions that involve only simple numbers, and have to use at least one operand with ten digits. Later on, hundred digits. Thousand digits!O(log10N) digits, but N is unbounded…
I am not 100% confident I can do math with these numbers and never make a wrong calculation.
Sure, I can write it down, and reduce the chance of error—but not to zero. And I can double check and triple check, but since no single check has 100% probability of finding all potential mistakes, the combination of all checks can’t do that either.
Intuitively the more digits there are the more likely I am to err. I’m more confident in my ability to add numbers with 100 digits than in my ability to add numbers with 200 digits. And I’m even more confident in my ability to add numbers in 50 digits. So generally speaking, I’m more confident in my ability to add numbers with n digits than in my ability to add numbers with n+1 digits.
But there is no n that I’m 100% confident in my ability to add numbers in n digits but less than 100% confident in my ability to add numbers with n+1 digits.
So why should I assign a zero probability to me butchering the addition of single digit numbers?
Imagine you set up a program that will continually resolve 2 + 2 after your death. Perhaps it will survive much longer than entropy will allow us to survive. It has a very nice QPC timer.
It uses binary, of course. After all, you can accomplish binary with some simple LEDs, or just, dots. Little dots. So you accomplish your program, set it to run using the latest CMBR-ran entropic technology, and no one attends your funeral, because you are immortal, but immortality does not survive entropy. At least, within the same uncertainty as you failing to state 2 + 2 = 4. Your brain remains remarkably logical through this. After all, it is highly overgeared, now, having been immortal. You are the 2 + 2 master equivalent of Ronnie O’Sullivan. Flawed, yes, but goodness, you can play a mean game of snooker. Sometimes you even get sneaky, and throw in a 4 = 2 + 2.
Your entropic death approaches. You write the code, and having made sure₁ of it, you set your canary to alert it of your death- the moment you fail to accomplish the scheduled 2 + 2 = 4 which continues the cosmic clock the universe’s entropy.
It is a simple equation. It takes very few bits to accomplish. 10 + 10 = 100₂ ~
Oh. Wait. It’s now 10 + 10 = 100? That doesn’t fulfill our need for 2 + 2 = 4, since the semantics aren’t preset. Well, what if we try this?
• • + • • = • • • •
Ah, yes, back to something reasonable. There are two dots and two dots which indicate 4 dots. This makes sense, possibly.
But the question wasn’t to resolve • • + • • ; but 2 + 2. So, in the spirit of integrity, we need to convert it to a displayable format for some future god-king race of the Anunaki to come witness our last, single work of humanity. Thus, you convert
• • + • • = • • • •
into
10 + 10 = 100
into
2 + 2 = 4
Since it only necessitates one character as the result, it is also the most efficient on power.
Are you 100% confident in anything aside from yourself, even if you made it?
Because you made 2 + 2 = 4. It’s just your idea. At that later immortal point in time, you are the only thing that still thinks 2 + 2 is relevant. The free floating quarks can barely find a date, let alone double :wink: date.
And this has at least three points of failure.
₁The code has at least fifteen points of failure.
₂This has at least eight points of failure.
Much like how I cannot assign a probability of 1 to my brain for any task, no matter how simple, I cannot assign a probability of 1 to a fallible CPU, no matter the quality. It could very well be the computer in Hitchhiker’s. I’ve been wrong on too many easy simple things by accident more than once to realize this.