Hi everyone,

What follows is a brief and informal argument that "enforcing the 14th amendment" is computationally easy--in particular, it is in a certain sense feasible in L, which is also known as LOGSPACE, and is a subset of PTIME.

To begin with, consider a finite collection D of constants denoting sets, much like the domain D of ZFC. These elements are constant symbols in a structure in a descriptive complexity context. In addition, consider the following five relations in the vocabulary of the structure: 1) "Citizen Status"--when given a set constant in D that contains no other elements, it can be thought of as a "citizen," i.e., a set that corresponds to one US citizen in the USA. The relation is true when, given element of D as input, this element is a US citizen. 2) Set element--given two sets A, B, in order, this relation outputs "true" if A is an element of B, and "false" otherwise. 3) "Too Much Protection Under the Law"--if a given element of D, whether that's a set of people or an individual citizen, has obtained "unusually high amounts of protection from US law," then this relation on such an element returns true; it returns false otherwise. 4) "Too Little Protection Under the Law"--if a given element of D, whether that's a set of people or an individual citizen, has obtained "unusually low amounts of protection from US law," then this relation on such an element returns true; it returns false otherwise. 5) "About Average Level of Protection Under the Law"--if a given element of D, whether that's a set of people or an individual citizen, has obtained "about the average level of protection from US law, strictly within (in terms of being above or below) some fixed amount epsilon of tolerable inequality," then this relation on such an element returns true; it returns false otherwise.

The idea is, if one were to input a structure that represents all 300 million or so US citizens and all organizations that such citizens (and such organizations themselves) are members of, we want to find a descriptive complexity query that, after the application of some efficient modifications to the structure, "checks" the idea that all US citizens and organizations have close-enough-to-equal protection under the law that is LOGSPACE computable, i.e., it needs to be computed in FO (first order).

As it turns out, even when we test for "valid structures," rejecting absurd inputs that have non-empty sets that have true citizen status, or an improper partitioning of elements into the three relations for "too much," "too little," and "about average," or elements that have improper set element relations (e.g., a set that is a member of itself), we can write this query easily, as a (proper, with newly assigned variable names as needed) conjunction of the first three conditions ("!(exists d in D such that (R1(d) and (exists e in D such that R2(e,d))))" for the first one and "!(exists d, e in D such that (R2(e,d) and R2(d,e)))" for the second one and "(for all d in D, (R3(d) xor R4(d) xor R5(d)))"), and a fourth condition that simply checks to see if the third and fourth relations accept no elements of D ("!(exists d such that (R3(d) or R4(d))").

This query essentially "checks" to see if there are no violations of the 14th amendment in the US. It can be modified to form analogous FO queries that test for any set of intervals (intersected with the natural numbers) in terms of the number of people/organizations who have been subjected to unfair (too good or too bad) treatment under the 14th amendment, e.g., "over 500 organizations and between 2000 and 3000 citizens have received insufficient protection under the law" is something that we can test for with an FO query such as this.

The interesting thing is, given this "LOGSPACE checking query" and the fact that any well-understood-enough strategic action that is known to modify the sets and relations--changing the structure to produce a new structure with a different result given the query--is also LOGSPACE, we have that, given a finite set of "well-understood-enough strategic actions" and a goal-query that would confirm that we've achieved a strategic 14th amendment goal (e.g., "modify the US so that fewer than 10,000 people have insufficient protection under the law"), we can compute which strategic actions, if applied, would achieve the goal in LOGSPACE in the size of the structure, since we are merely composing some queries that all run in L when we test a strategy.

The conclusion of this is that, computationally speaking at least, modifications to the 14th amendment posture of the US are easily assessed given access to good enough data. Under the assumption that lawyers and other citizens who support the 14th amendment greatly outnumber and can overpower those who don't, it would appear that the 14th amendment is likely to be highly enforceable and in a sense maintainable, particularly given the existence of the internet and ease of developing and deploying modern computer technology to pursue positive key political/legal interests.

-Philip White (philipjwhite@yahoo.com)

On Friday, 3 December 2021 at 00:47:57 UTC+8, B.H. wrote:
> Hi everyone,
>
> What follows is a brief and informal argument that "enforcing the 14th amendment" is computationally easy--in particular, it is in a certain sense feasible in L, which is also known as LOGSPACE, and is a subset of PTIME.
>
> To begin with, consider a finite collection D of constants denoting sets, much like the domain D of ZFC. These elements are constant symbols in a structure in a descriptive complexity context. In addition, consider the following five relations in the vocabulary of the structure: 1) "Citizen Status"--when given a set constant in D that contains no other elements, it can be thought of as a "citizen," i.e., a set that corresponds to one US citizen in the USA. The relation is true when, given element of D as input, this element is a US citizen. 2) Set element--given two sets A, B, in order, this relation outputs "true" if A is an element of B, and "false" otherwise. 3) "Too Much Protection Under the Law"--if a given element of D, whether that's a set of people or an individual citizen, has obtained "unusually high amounts of protection from US law," then this relation on such an element returns true; it returns false otherwise. 4) "Too Little Protection Under the Law"--if a given element of D, whether that's a set of people or an individual citizen, has obtained "unusually low amounts of protection from US law," then this relation on such an element returns true; it returns false otherwise. 5) "About Average Level of Protection Under the Law"--if a given element of D, whether that's a set of people or an individual citizen, has obtained "about the average level of protection from US law, strictly within (in terms of being above or below) some fixed amount epsilon of tolerable inequality," then this relation on such an element returns true; it returns false otherwise.
>
> The idea is, if one were to input a structure that represents all 300 million or so US citizens and all organizations that such citizens (and such organizations themselves) are members of, we want to find a descriptive complexity query that, after the application of some efficient modifications to the structure, "checks" the idea that all US citizens and organizations have close-enough-to-equal protection under the law that is LOGSPACE computable, i.e., it needs to be computed in FO (first order).
>
> As it turns out, even when we test for "valid structures," rejecting absurd inputs that have non-empty sets that have true citizen status, or an improper partitioning of elements into the three relations for "too much," "too little," and "about average," or elements that have improper set element relations (e.g., a set that is a member of itself), we can write this query easily, as a (proper, with newly assigned variable names as needed) conjunction of the first three conditions ("!(exists d in D such that (R1(d) and (exists e in D such that R2(e,d))))" for the first one and "!(exists d, e in D such that (R2(e,d) and R2(d,e)))" for the second one and "(for all d in D, (R3(d) xor R4(d) xor R5(d)))"), and a fourth condition that simply checks to see if the third and fourth relations accept no elements of D ("!(exists d such that (R3(d) or R4(d))").
>
> This query essentially "checks" to see if there are no violations of the 14th amendment in the US. It can be modified to form analogous FO queries that test for any set of intervals (intersected with the natural numbers) in terms of the number of people/organizations who have been subjected to unfair (too good or too bad) treatment under the 14th amendment, e.g., "over 500 organizations and between 2000 and 3000 citizens have received insufficient protection under the law" is something that we can test for with an FO query such as this.
>
> The interesting thing is, given this "LOGSPACE checking query" and the fact that any well-understood-enough strategic action that is known to modify the sets and relations--changing the structure to produce a new structure with a different result given the query--is also LOGSPACE, we have that, given a finite set of "well-understood-enough strategic actions" and a goal-query that would confirm that we've achieved a strategic 14th amendment goal (e.g., "modify the US so that fewer than 10,000 people have insufficient protection under the law"), we can compute which strategic actions, if applied, would achieve the goal in LOGSPACE in the size of the structure, since we are merely composing some queries that all run in L when we test a strategy.
>
> The conclusion of this is that, computationally speaking at least, modifications to the 14th amendment posture of the US are easily assessed given access to good enough data. Under the assumption that lawyers and other citizens who support the 14th amendment greatly outnumber and can overpower those who don't, it would appear that the 14th amendment is likely to be highly enforceable and in a sense maintainable, particularly given the existence of the internet and ease of developing and deploying modern computer technology to pursue positive key political/legal interests.
>
> -Philip White (philip...@yahoo.com)

What is the difference of computational complexity and the real world problem?
You seemed to have the same problem with Daniel.

On Thursday, December 2, 2021 at 7:16:37 PM UTC-5, wij wrote:
> On Friday, 3 December 2021 at 00:47:57 UTC+8, B.H. wrote:
> > Hi everyone,
> >
> > What follows is a brief and informal argument that "enforcing the 14th amendment" is computationally easy--in particular, it is in a certain sense feasible in L, which is also known as LOGSPACE, and is a subset of PTIME.
> >
> > To begin with, consider a finite collection D of constants denoting sets, much like the domain D of ZFC. These elements are constant symbols in a structure in a descriptive complexity context. In addition, consider the following five relations in the vocabulary of the structure: 1) "Citizen Status"--when given a set constant in D that contains no other elements, it can be thought of as a "citizen," i.e., a set that corresponds to one US citizen in the USA. The relation is true when, given element of D as input, this element is a US citizen. 2) Set element--given two sets A, B, in order, this relation outputs "true" if A is an element of B, and "false" otherwise. 3) "Too Much Protection Under the Law"--if a given element of D, whether that's a set of people or an individual citizen, has obtained "unusually high amounts of protection from US law," then this relation on such an element returns true; it returns false otherwise. 4) "Too Little Protection Under the Law"--if a given element of D, whether that's a set of people or an individual citizen, has obtained "unusually low amounts of protection from US law," then this relation on such an element returns true; it returns false otherwise. 5) "About Average Level of Protection Under the Law"--if a given element of D, whether that's a set of people or an individual citizen, has obtained "about the average level of protection from US law, strictly within (in terms of being above or below) some fixed amount epsilon of tolerable inequality," then this relation on such an element returns true; it returns false otherwise.
> >
> > The idea is, if one were to input a structure that represents all 300 million or so US citizens and all organizations that such citizens (and such organizations themselves) are members of, we want to find a descriptive complexity query that, after the application of some efficient modifications to the structure, "checks" the idea that all US citizens and organizations have close-enough-to-equal protection under the law that is LOGSPACE computable, i.e., it needs to be computed in FO (first order).
> >
> > As it turns out, even when we test for "valid structures," rejecting absurd inputs that have non-empty sets that have true citizen status, or an improper partitioning of elements into the three relations for "too much," "too little," and "about average," or elements that have improper set element relations (e.g., a set that is a member of itself), we can write this query easily, as a (proper, with newly assigned variable names as needed) conjunction of the first three conditions ("!(exists d in D such that (R1(d) and (exists e in D such that R2(e,d))))" for the first one and "!(exists d, e in D such that (R2(e,d) and R2(d,e)))" for the second one and "(for all d in D, (R3(d) xor R4(d) xor R5(d)))"), and a fourth condition that simply checks to see if the third and fourth relations accept no elements of D ("!(exists d such that (R3(d) or R4(d))").
> >
> > This query essentially "checks" to see if there are no violations of the 14th amendment in the US. It can be modified to form analogous FO queries that test for any set of intervals (intersected with the natural numbers) in terms of the number of people/organizations who have been subjected to unfair (too good or too bad) treatment under the 14th amendment, e.g., "over 500 organizations and between 2000 and 3000 citizens have received insufficient protection under the law" is something that we can test for with an FO query such as this.
> >
> > The interesting thing is, given this "LOGSPACE checking query" and the fact that any well-understood-enough strategic action that is known to modify the sets and relations--changing the structure to produce a new structure with a different result given the query--is also LOGSPACE, we have that, given a finite set of "well-understood-enough strategic actions" and a goal-query that would confirm that we've achieved a strategic 14th amendment goal (e.g., "modify the US so that fewer than 10,000 people have insufficient protection under the law"), we can compute which strategic actions, if applied, would achieve the goal in LOGSPACE in the size of the structure, since we are merely composing some queries that all run in L when we test a strategy.
> >
> > The conclusion of this is that, computationally speaking at least, modifications to the 14th amendment posture of the US are easily assessed given access to good enough data. Under the assumption that lawyers and other citizens who support the 14th amendment greatly outnumber and can overpower those who don't, it would appear that the 14th amendment is likely to be highly enforceable and in a sense maintainable, particularly given the existence of the internet and ease of developing and deploying modern computer technology to pursue positive key political/legal interests.
> >
> > -Philip White (philip...@yahoo.com)
> What is the difference of computational complexity and the real world problem?
> You seemed to have the same problem with Daniel.

Hi internet poster,

For more information about theoretical computer science, check out this helpful textbook on Amazon.com:

https://www.amazon.com/Introduction-Theory-Computation-Michael-Sipser/dp/113318779X

-Philip White (philipjwhite@yahoo.com)