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Version: 1
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"Measuring how good people are at guessing final conclusions in reality - whether, when they say 'I assign 90% probability this triangle is large', the triangle is actually large 9 times out of 10 - sure is a metric of how much Law people contain and are using correctly!  But there's more than one kind of Law you need to build an agent, and the piece of Law we're trying to isolate is the one that's about using necessary truths correctly.  One way of looking at that part is that it's about which conclusions follow from which premises.  To demonstrate -"

Keltham has seen one or two fragments of algebra in his reading, enough that he has some idea of what Chelish algebra conventions look like.  Though it's a bit weird that they teach algebra without, like, teaching people what algebra means.  Hopefully it's not a piece of knowledge that's infohazardous here but not in dath ilan.

He sketches a series of equations:

[1]      x = 1 (premise)
[2] y = 1 (premise)
[3] 1 = 1 (id. 1)
[4] x = y (subst lh [1] ; subst rh [2])
[5] x*x = y*x (mult. x)
[6] x*x - y*y = y*x - y*y (sub. (y*y))
[7] (x + y)*(x - y) = y*(x - y)      (diff-squares lh. x, y ; factor rh. y)
[8] x + y = y (cancel. (x - y))
[9] 2 = 1 (conclusion)
Version: 2
Fields Changed Content
Updated
Content

"Measuring how good people are at guessing final conclusions in reality - whether, when they say 'I assign 90% probability this triangle is large', the triangle is actually large 9 times out of 10 - sure is a metric of how much Law people contain and are using correctly!  But there's more than one kind of Law you need to build an agent, and the piece of Law we're trying to isolate is the one that's about using necessary truths correctly.  One way of looking at that part is that it's about which conclusions follow from which premises.  To demonstrate -"

Keltham has seen one or two fragments of algebra in his reading, enough that he has some idea of what Chelish algebra conventions look like.  Though it's a bit weird that they teach algebra without, like, teaching people what algebra means.  Hopefully it's not a piece of knowledge that's infohazardous here but not in dath ilan.

He sketches a series of equations:

[1]      x = 1 (premise)
[2] y = 1 (premise)
[3] 1 = 1 (id. 1)
[4] x = y (subst lh [1] ; subst rh [2])
[5] x*x = y*x (mult. x)
[6] x*x - y*y = y*x - y*y (sub. (y*y))
[7] (x + y)*(x - y) = y*(x - y)      (diff-squares lh. x, y ; factor rh. y)
[8] x + y = y (cancel. (x - y))
[9] 2 = 1 (conclusion)
Version: 3
Fields Changed Content
Updated
Content

"Measuring how good people are at guessing final conclusions in reality - whether, when they say 'I assign 90% probability this triangle is large', the triangle is actually large 9 times out of 10 - sure is a metric of how much Law people contain and are using correctly!  But there's more than one kind of Law you need to build an agent, and the piece of Law we're trying to isolate is the one that's about using necessary truths correctly.  One way of looking at that part is that it's about which conclusions follow from which premises.  To demonstrate -"

Keltham has seen one or two fragments of algebra in his reading, enough that he has some idea of what Chelish algebra conventions look like.  Though it's a bit weird that they teach algebra without, like, teaching people what algebra means.  Hopefully it's not a piece of knowledge that's infohazardous here but not in dath ilan.

He sketches a series of equations:

[1]      x = 1 (premise)
[2] y = 1 (premise)
[3] 1 = 1 (id. 1)
[4] x = y (subst lh [1] ; subst rh [2])
[5] x*x = y*x (mult. x)
[6] x*x - y*y = y*x - y*y (sub. (y*y))
[7] (x + y)*(x - y) = y*(x - y)      (diff-squares lh. x, y ; factor rh. y)
[8] x + y = y (cancel. *(x - y))
[9] 2 = 1 (conclusion)
Version: 4
Fields Changed Content
Updated
Content

"Measuring how good people are at guessing final conclusions in reality - whether, when they say 'I assign 90% probability this triangle is large', the triangle is actually large 9 times out of 10 - sure is a metric of how much Law people contain and are using correctly!  But there's more than one kind of Law you need to build an agent, and the piece of Law we're trying to isolate is the one that's about using necessary truths correctly.  One way of looking at that part is that it's about which conclusions follow from which premises.  To demonstrate -"

Keltham has seen one or two fragments of algebra in his reading, enough that he has some idea of what Chelish algebra conventions look like.  Though it's a bit weird that they teach algebra without, like, teaching people what algebra means.  Hopefully it's not a piece of knowledge that's infohazardous here but not in dath ilan.

He sketches a series of equations:

[1]      x = 1 (premise)
[2] y = 1 (premise)
[3] 1 = 1 (id. 1)
[4] x = y (subst lh [1] ; subst rh [2])
[5] x*x = y*x (mult. x)
[6] x*x - y*y = y*x - y*y (sub. (y*y))
[7] (x + y)*(x - y) = y*(x - y)      (diff-squares lh. x, y ; factor rh. y)
[8] x + y = y (cancel. *(x - y))
[9] 2 = 1 (conclusion)
Version: 5
Fields Changed Content
Updated
Content

"Measuring how good people are at guessing final conclusions in reality - whether, when they say 'I assign 90% probability this triangle is large', the triangle is actually large 9 times out of 10 - sure is a metric of how much Law people contain and are using correctly!  But there's more than one kind of Law you need to build an agent, and the piece of Law we're trying to isolate is the one that's about using necessary truths correctly.  One way of looking at that part is that it's about which conclusions follow from which premises.  To demonstrate -"

Keltham has seen one or two fragments of algebra in his reading, enough that he has some idea of what Chelish algebra conventions look like.  Though it's a bit weird that they teach algebra without, like, teaching people what algebra means.  Hopefully it's not a piece of knowledge that's infohazardous here but not in dath ilan.

He sketches a series of equations:

[1]            x = 1 (premise)
[2] y = 1 (premise)
[3] 1 = 1 (id. 1)
[4] x = y (subst lh [1] ; subst rh [2])
[5] x*x = y*x (mult. x)
[6] x*x - y*y = y*x - y*y (sub. (y*y))
[7] (x + y)*(x - y) = y*(x - y)      (diff-squares lh. x, y ; factor rh. y)
[8] x + y = y (cancel. *(x - y))
[9] 2 = 1 (conclusion)