### Idling Matters

I had idled Sphinx earlier but didn’t do so in a post, and so here is the post. Quorum is still five. Wakukee is looking like he’ll drop out in a day, but everyone else has taken some manner of action within a day or two.

Enacts at 7-0. -RaichuKFM

Adminned at 30 Jun 2013 19:06:39 UTC

Axioms:

* For all Atoms X and Y, X * Y is an Atom.

* E is an Atom. For all Atoms X, E * X = X and X * E = X.

* For all Atoms X, [X’ is an Atom, and X * X’ = E and X’ * X = E].

In other words, the Atoms form a group. Of course, these Axioms don’t tell us *which* group we form. If “The Game is nevertheless afoot” passes, we could add an axiom saying that the identity element, E, has achieved victory. Then we could allow Atoms to add axioms describing this group (with restrictions, of course); if you manage to make it so that you must be the identity element, then you win,

Reaches Quorum and Passes 7-0. -RaichuKFM

Adminned at 30 Jun 2013 19:02:59 UTC

Append the following paragraph to the rule “Atomic Logic”:

If A is the name of an Atom, and the Formula “HAV({A})” (in prose, “{A} has achieved victory” or “{A} wins”) is an Axiom or Theorem, then that Atom has achieved victory.

Times Out and Passes 4-2. -RaichuKFM

Adminned at 30 Jun 2013 19:00:43 UTC

Enact a rule, titled “Nucleons”:

There is one type of Nucleon for each Essential Letter. The number of Nucleons of each type that each Atom possesses is tracked in the GNDT (if, for instance, they have one H, one K, and two R nucleons, this should be written as “H K 2R”). Any Atom may, as a Weekly Communal Action, award each Atom the Nucleons corresponding to the letters in their Essence. (If an Atom has no Essence, they are awarded no Nucleons.)

Any Atom may, as a Daily Action, select an Atom that they are Bonded to, and transfer up to two of that Atom’s Nucleons to themself. If an Atom ever possesses twenty Nucleons of the same type, that Atom has achieved victory.

I idle out. Quorum drops to 5.

Times Out and Fails 2-3-1. -RaichuKFM

Adminned at 29 Jun 2013 07:43:07 UTC

Append to “Atomic Logic”:

CDV(A) is a Formula that is True of Atom A can declare victory and False otherwise. If for any atom A, CDV(A) is True, then CDV(B) is False for all atoms B, such that B != A.

Pushing win condition into Formulae. Goal: Prove that you win.

Murphy, kikar, and Cpt. Koen idle out after 7, 9, and 13 days of inactivity respectively. Quorum drops to six.

I would like to join the blog, but would like to stay idle and wait for the next dynasty.

Reaches Quorum and Passes 6-0. -RaichuKFM

Adminned at 27 Jun 2013 10:44:31 UTC

In the rule “Challenges” after

If they do not feel any Atom made such a comment, they may instead vote with the AGAINST marker.

add

They may also use the AGAINST marker if they believe any of the logical sequence of deductions (or group of deductions) used would be unreasonable for someone to figure out on their own.

Its already hand-wavey as it is, and yes this makes it worse, but it does give us a valid reason to vote against challenges that require factoring large numbers.

Times Out and Passes 4-0-1. -RaichuKFM

Adminned at 27 Jun 2013 10:44:11 UTC

In the list of Axioms, replace

For all a and b, if b is a list, then a:b is a non-empty list.

with

For all a and b, if b is a list, then {a}:b is a non-empty list.

Replace

For all a, if a is a non-empty list, then there exist b and c such that a = b:c and c is a list.

with

For all a, if a is a non-empty list, then there exist b and c such that a = {b}:c and c is a list.

Replace

For all a, b, c, and d, if b and d are lists, then [a:b = c:d if and only if [a = c and b = d]].

with

For all a, b, c, and d, if b and d are lists, then [{a}:b = {c}:d if and only if [a = c and b = d]].

Replace

For all a and b, if b is a list, then [the head of a:b is a, and the tail of a:b is b].

with

For all a and b, if b is a list, then [the head of {a}:b is a, and the tail of {a}:b is b].

Replace

For all a, b and c, if c is a list, then [a is an element of b:c if and only if [a = b or a is an element of c]]

with

For all a, b and c, if c is a list, then [a is an element of {b}:c if and only if [a = b or a is an element of c]]

And replace

For all a, b and c, if b and c are lists, then (a:b) ++ c = a:(b ++ c).

with

For all a, b and c, if b and c are lists, then ({a}:b) ++ c = {a}:(b ++ c).

Travos and I were having this discussion on his Challenge Post. I think the list containing a_1:a_2, and the list containing a_1 *and* a_2 are both legally written a_1:a_2:{} despite not being the same list. This would force us to write them as {a_1:a_2}:{} and {a_1}:{a_2}:{}, making them clearly different lists.

Times out and cannot be enacted with 1 vote / Skju

Adminned at 26 Jun 2013 17:00:45 UTC

Add the following as Axioms:

* For all sets A and B:

** A + B = C, such that for every element x in A and y in B, x and y are elements of set C

** A & B = C, such that for every element x in A that is in B, x is is an element of set C

** A | B = C, such that for every element x in A, but x is not in B, and every element y in B, but y is not in A, x and y are elements of set C

** A - B = C, such that for every element x in A that is not in B, x is an element of set C

* There exists a set with no elements - the null (or empty) set - {}

introducing the fundamental set definitions. Intended to help create formulas related to the set of Atoms. For example: A = the set of Atoms a such that Has(a,“Essence”,“KY”) is true. If {A} - A, then give each atom b in set (A &{A}) 2 points. Or something of the sort.

Times out, passes 5-0 / Skju

Adminned at 26 Jun 2013 16:57:26 UTC

Append to the rule “Truth”:

If a Proof is Enacted it is hence considered True.

Small fix. Note that it does not become False through failing. Also - props to anyone who gets the reference.

Passes 6-0. — Quirck

Adminned at 25 Jun 2013 11:00:43 UTC

In the rule “Challenges”, change

Each Atom has a positive integer number of Challenge Points, which is by default 10.

to

Each Atom has a nonnegative integer number of Challenge Points, tracked in the GNDT and defaulting to 10.

If the axioms in the post “Pairs and lists” are true, then there exists a list X that has all of the following properties:

* Every element of X is a list.

* For all elements a of X, if b and c are lists such that b ++ c = a, then there does not exist d such that d is an element of both b and c.

* For all pairs (a,b) of elements of X, there does not exist c such that c is an element of both a and b.

* X has at least two elements.

* Every element of X has at least two elements.

* Every element of X has the same number of elements.

* The number of x such that x is an element of an element of X is exactly 35 844 088 534 668 175 608 533 550 469 325 416 140 711 880 836 358 433 520 741 183 341 559 409 752 958 417 564 900 205 152 763 659 819 317 338 304 041 228 758 958 269 744 936 094 178 001 500 112 469 790 418 773 135 543 301 899 194 065 881 801 585 777 676 220 908 841.

Did I do that right,

Can’t be enacted with only one vote… — Quirck

Adminned at 23 Jun 2013 14:11:19 UTC

Axioms:

* S, K, I, B, C, K, and W are Expors.

* For all Expors x and y, x y is an Expor.

* For all x, $(x) is an Expor, and $’($(x)) = x.

* For all Expors x and y, if [for all Expors z, (x z) = (y z)], then x = y.

* For all Expors x, y and z, ((S x) y) z = (x z) (y z).

* For all Expors x and y, (K x) y = x.

* For all Expors x, I x = x.

* For all Expors x, y and z, ((B x) y) z = x (y z).

* For all Expors x, y and z, ((C x) y) z = (x z) y.

* For all Expors x and y, (W x) y = (x y) y.

See http://en.wikipedia.org/wiki/SKI_combinator_calculus and http://en.wikipedia.org/wiki/B,C,K,W_system. Irreducible Expors, like ((S I) I) ((S I) I), aren’t a problem; they are simply undefined. The only way you could prove a paradox from these axioms is by proving that $(x) = $(y) where x â‰ y, and I’m pretty sure you can’t do that, because it’s impossible for two combinator calculus terms to have substantively different reductions,

Fails 0-6. — Quirck

Adminned at 23 Jun 2013 14:12:48 UTC

For all Proofs that have not yet been Enacted or Failed, if that Proof contains a Formula but does not specify which section to add it to, amend the Proof so that it specifies that the Formula shall be added to the section “Miscellaneous”.

For all Proofs that have been Enacted since the beginning of 20 June, if that Proof attempted to add a Formula to the Truths page without specifying which section it should be added to, that Formula is added to the Truths page as if the Proof had specified that it should be added to the section “Miscellaneous”.

I forgot to specify this and now it’s pretty much too late to change it. nqeron also forgot to specify this,

Passes 4-0. — Quirck

Adminned at 23 Jun 2013 13:00:26 UTC

Append to the rule “Atomic Logic”:

If P is the name of a GNDT column and E is a value, then the formula Has(A,P,E) is True if Atom A has a value E for P, and is False otherwise.

The formula Exists(P,E) is True if any Atom has a value of E for P, and is False otherwise.

In Formulae {A@} represents the set of all Atoms.

expanding to introduce basic interactions with GNDT and general state. Also, making sure that a set of Atoms is accessible. (With set theory this can be used to represent subsets of atoms!)

Passes 2-1

I don’t know if “Pairs and lists” is True or False, though…

/ Skju

Adminned at 23 Jun 2013 06:51:31 UTC

(If “Pairs and lists” is False, then so are the following):

Axioms:

* for all lists a, !a = b, where b is the head of a

* for all lists a, @a = c, such that a = (!a):c is true

* &x. is a function, with x as a single variable function, defined by the operation succeeding the “.” (e.g. &x.x is the identity function)

* for all lists a, where !a is a function, f(p), then #a = f(@a)

* IF is a function f(z) = #(z x y).

* T is a function f(x,y) = x

* F is a function f(x,y) = y

formalizing some operators and introducing some functional programming through lambda calculus, along with a conditional operator.

I’m just worried this is too much ‘programming’ oriented rather than pure math and proofs.

Rationality and scshunt idle out after a week of inactivity. Quorum becomes 7.

Passes 7-0 / Skju

Adminned at 22 Jun 2013 21:54:31 UTC

Axioms:

* For all a and b, (a,b) is an ordered pair.

* For all a, b, c and d, (a,b) = (c,d) if and only if a = c and b = d.

* There exists exactly one a such that a is an empty list.

* For all a and b, if b is a list, then a:b is a non-empty list.

* For all a, if a is a non-empty list, then there exist b and c such that a = b:c and c is a list.

* For all a, b, c, and d, if b and d are lists, then [a:b = c:d if and only if [a = c and b = d]].

* For all a and b, if b is a list, then [the head of a:b is a, and the tail of a:b is b].

* For all a, b and c, if c is a list, then [a is an element of b:c if and only if [a = b or a is an element of c]].

* For all a, a is not an element of the empty list.

* For all a, b and c, if b and c are lists, then (a:b) ++ c = a:(b ++ c).

* For all c, if c is a list, then {} ++ c = c (where {} is the empty list).

We could, if we wanted to, add an axiom stating that every Atom is a list. Or that each value is an Atom if and only if it is not a list. Or that all values are lists. We could also say that there is a list a such that a = a:a. The possibilities for mischief are endless,

I think we could also add an axiom stating that for every list a, there is a list b such that any given value is an element of a if and only if it is not an element of b. That would be pretty weird,

Quorums 8-0. — Quirck

Adminned at 21 Jun 2013 09:11:26 UTC

Create a rule, titled “Atomic Logic”:

If A is the name of an Atom, then {A} is a variable that can be used in Formulae. If A1 and A2 are different Atoms, then the Formula “{A1} = {A2}” is False. For any expression E, the Formula “Atom(E)” (in prose, “E is an Atom”) is equivalent to “[E = {A1}] || [E = {A2}] || ... || [E = {An}]”, where A1, A2, ..., An are the names of all Atoms. If A1 and A2 are Atoms that have Essences, then the Formula “{A1} ::: {A2}” (in prose, “{A1} is Bonded to {A2}”) is True if the Atoms are Bonded and False if the Atoms are not Bonded.

I see someone’s tried to take a step into ternary logic. Besides “yes” and “no”, an obvious addition is “maybe”. That’s a start.

Just don’t forget “heck yeah”, “heck no”, and “who wants to know”. These are like the previous three, only louder.

Also “welll”, because it’s just not that simple sometimes. And “meh”, for when nobody cares.

“CLASSIFIED” is a necessity. Big Brother is watching.

Passes 8-0 / Skju

Adminned at 19 Jun 2013 17:44:07 UTC

Amend Rule 2.3 “Formulae” to read:

A Formula is an unambiguous statement in first-order logic. Formulae may contain free variables. Formulae may be written using prose, symbols, or a mixture of the two. The use of undefined terminology does not constitute ambiguity unless it results in the structure of the Formula being ambiguous. A Formula is either True or False within its context.

In a Formula, “=” denotes equality; Formulae are considered equal if and only if they have the same truth value. “&&”, “||”, and “~” denote the logical AND, OR, and NOT operators, respectively. “->” denotes the material implication operator. “FA” and “TE” are abbreviations of “for all” and “there exists”, respectively. Square brackets function only as a grouping symbol; they do not have any additional semantics. “0” and “1” represent the trivially False Formula and the trivially True Formula, respectively.

Delete the axioms that were numbered 1 through 15 as of the beginning of June 17 (because they are tautologies in first-order logic, so it would be valid to use them in Proofs even if they were not present in the Truths page).

It looks to me like if we don’t do this, we’re just going to end up implementing first-order logic in a more tedious manner and end up with something that’s harder to use, so I suggest that we just skip over all that,

Times out and passes 7-0 / Skju

Adminned at 19 Jun 2013 17:39:13 UTC

In Rule 1.5.2 “Resolution of Proposals”, replace

* It could not be Enacted without either one of the Votes AGAINST it being changed, or the set of Atoms being changed, or by awaiting the passage of time

with

* It has been Vetoed or Self-Killed.

* The number of Atoms who are not voting AGAINST it is less than Quorum.

In Rule 1.7 “Victory and Ascension”, replace

It has been open for voting for at least 12 hours, and it could not be Enacted without either at least one of the Votes AGAINST it being changed, or the set of Atoms being changed, or by awaiting the passage of time.

with

It has been open for voting for at least 12 hours, and the number of Atoms who are not voting AGAINST it is less than Quorum.

In Rule 2.1 “Truth”, replace

* It could not be Enacted without either one of the Votes AGAINST it being changed, or the set of Atoms being changed.

with

* It has been Self-Killed.

* The number of Atoms who are not voting AGAINST it is less than Quorum.

Fails 3-5 / Skju

Adminned at 19 Jun 2013 17:42:58 UTC

Add the following to the list of axioms

[>>a] = b

[>>b] = c

[>>c] = a

FAX[[[[~[X = a]] && [~[X = b]]] && [~[X = c]]] -> [[>>X] = Ï†]]

FAX[[<<X] = [[>>[>>X]]]]

Adding the option to use ternary logic (with a, b and c) and Ï† as the general “error” result.

Could also maybe force everything to be a, b, or c but then we run into issues where = would no longer commute (unless a = b = c).

Times out and passes 6-0, 3 unresolved DEFs / Skju

Adminned at 19 Jun 2013 17:36:06 UTC

Add a new dynastic rule called “Challenges” and give it the following text

Each Atom has a positive integer number of Challenge Points, which is by default 10. If an Atom does not currently have a pending Challenge Post they may spend between 1 and 5 Challenge Points to make a Challenge Post. A Challenge Post is a Story Post whose title consist of “Challenge Post (Y)” and whose content consists of a single theorem where Y is the number of Challenge Points the Atom spent. The Challenge Post is then said to be in the Open Phase.

If a Challenge Post is in the Open Phase, Atoms (other than the one who made the Challenge Post) may comment on a Challenge Post with what they believe to be logical sequence of deductions that leads to the theorem in the Challenge Post from existing Truths.

If a Challenge Post has been in the Open Phase for 48 hours, the Atom who made the post may add a comment what they believe to be a logical sequence of deductions that leads to the theorem in the Challenge Post from existing Truths. The Challenge Post then enters the Voting Phase.

If a Challenge Post is in the Voting Phase, all Atoms may comment on the Challenge Post with the name of the Atom who they feel was first to actually supply a logical sequence of deductions that leads to the theorem in the Challenge Post from existing Truths. If they do not feel any Atom made such a comment, they may instead vote with the AGAINST marker. Atoms may change their vote by making another comment.

If a Challenge Post has been in the Voting Phase for 48 hours, any Atom may resolve it. If a single Atom received more Votes for them than any other Atom or AGAINST votes, they receive the number of Challenge Points which the original Atom spent forming the Challenge. If the Atom who made the Challenge Post receives the most Votes, they instead receive twice the number of Challenge Points they spent. If AGAINST votes had the most or tied for the most, no Atom receives any Challenge Points. If multiple Atoms received tied for the most votes (and AGAINST did not tie for the most), then of the tied Atoms, the one who commented first on the Challenge Post receives the Challenge Points. The Challenge Post then enters the Closed Phase.

If a Challenge Post has been in the Open Phase for 96 hours, it automatically enters the Closed Phase.

If a Challenge Post is not in the Closed Phase, it is considered Pending.

The logical sequences of deductions used in response to Challenge Posts may not exceed 50 steps.

Probably has some issues. But I think the basic idea has merit. Basically I think it would be cool if instead of just being like “Oh I proved that 1 + 1 = 2” you can go “I can prove that 1 + 1 = 2, and am willing to stake 3 points on the fact that no one else can prove it”

Rule 1.5.2 states that a proposal can be failed early if “it could not be Enacted without either one of the Votes AGAINST it being changed, or the set of Atoms being changed, or by awaiting the passage of time.” I can see four possible interpretations of this,

The first is that this means “it could not be Enacted without *all* of these events happening”. This interpretation does not seem reasonable, because then no proposal with at least two FOR votes could ever be failed early (because it could be Enacted if the set of Atoms were changed to the set of all Atoms voting FOR the proposal),

The second interpretation is that this means “it could not be Enacted without *at least one* of these events happening”, and it is assumed that the proposal cannot gain additional FOR votes without awaiting the passage of time. This interpretation is also unreasonable, because then every proposal would be eligible for failure all of the time except when they are eligible to be enacted,

The third interpretation is that this means “it could not be Enacted without at least one of these events happening”, and it is assumed that the proposal *can* gain additional FOR votes without awaiting the passage of time. This interpretation *also* seems unreasonable, because although now there are some proposals that are neither eligible for failure nor eligible to be enacted (namely, those that have been open for twelve hours and have a majority, but not a Quorum, of FOR votes), every proposal is still eligible for failure during the first twelve hours of its existence,

The fourth interpretation is that this means “it could not be Enacted unless either one of the Votes AGAINST it were changed, or the set of Atoms were changed, *even if* we awaited the passage of time”. This interpretation may be the intended one, but as far as I can tell, it’s not actually a *valid* interpretation of the sentence,

So perhaps we could amend the clause in order to make it clearer,

Passes 9-0 / Skju

Adminned at 17 Jun 2013 11:54:12 UTC

In the rule “Truth”, replace the text “Any Atom can add an item to either list” with “Any Atom can propose to add an item to either list”.

In the rule “Formulae”, replace the text “A Variable is a single lowercase letter” with “A Variable is a single lowercase letter (from the Latin or Greek alphabets)”.

Patch and expand

Passes 4-0. — Quirck

Adminned at 16 Jun 2013 19:43:46 UTC

Add the following Axioms:

* [0 && 0] = 0

* [0 && 1] = 0

* [1 && 0] = 0

* [1 && 1] = 1

* [0 || 0] = 0

* [0 || 1] = 1

* [1 || 0] = 1

* [1 || 1] = 1

* [0 -> 0] = 1

* [0 -> 1] = 1

* [1 -> 0] = 0

* [1 -> 1] = 1

* [~ 0] = 1

* [~ 1] = 0

If quantifiers are added, perhaps we can add axioms describing them,

Times out and passes 6-0 / Skju

Adminned at 17 Jun 2013 11:50:14 UTC

To the rule “Formulae”, add the following paragraphs (excluding text between square brackets):

An Identifier is a string of uppercase letters. [This would be called a Variable, but that name is already taken.] A Predicate is an uppercase letter followed by at least one lowercase letter.

A single Identifier is an Expression. An Identifier, followed by a list of Expressions enclosed in parentheses and separated by commas (e.g. “F(X,Y)”), is an Expression. A Predicate, followed by a list of Expressions enclosed in parentheses and separated by commas, is a Formula.

The symbols “FA” and “TE” are Quantifiers, not Identifiers. [“FA” represents the phrase “for all”, and “TE” represents “there exists”.] A Quantifier, followed by an Identifier, followed by a Formula, is a Formula.

Now we can have sentences referring to Atoms and whatnot without them having to be Formulas with truth values,

Fails 2-3 with one unresolved DEF. — Quirck

Adminned at 17 Jun 2013 10:21:56 UTC

In the rule ‘Formulae’ after

A Variable is a single lowercase letter

add

or sequence of lowercase letters surrounded by a pair of parenthesis ( “(” and “)”)”

also append the following to the the first paragraph of ‘Formulae’

Connectives may not contain parenthesis or brackets.

Unless we’re expecting a variable to only exist within the scope of a formula, its too limiting. If we want to start defining global values we need a way to have more legal variables.

[0 - 0] = 1 is not a legal formula because it contains no variables. The ruleset explicitly states that the axioms page lists Formula. But we also said to add it to the list. Per “Invalid values for game variables can never be used” I’d argue that fact it simply shouldn’t be added to the axiom list because its an invalid value. Are we just going to look the other way on this or is there some good argument for why they should stay in the list?

Quorums 8-0. — Quirck

Adminned at 15 Jun 2013 02:56:01 UTC

If they exist, remove the statements â€œWakukee has achieved victory in the First Dynasty of Skju.â€ and â€œThis page is now considered gamestate.â€ from the list of Truths.

In the Glossary Section for Gamestate replace

Any information which the Ruleset regulates the alteration of.

with

Any information which the Ruleset regulates the alteration of, including all Wiki Pages, or GNDT columns, which the Dynastic Rules explicitly mention.

Just making the last point Dynastic Rules.

Self-killed - Ienpw III

Adminned at 15 Jun 2013 00:08:33 UTC

If they exist, remove the statements “Wakukee has achieved victory in the First Dynasty of Skju.” and “This page is now considered gamestate.” from the list of Truths.

In the Glossary Section for Gamestate replace

Any information which the Ruleset regulates the alteration of.

with

Any information which the Ruleset regulates the alteration of, including all Wiki Pages or GNDT columns which the Ruleset mentions.

Given that Wakukee’s DoV was shot down for a couple of reasons and some of us found the actual editing of the wiki page to be valid, we should clear up weather or not the truths he added are actually there by saying they aren’t, and clean up the “Gamestate” definition for future use to avoid further confusing. This should clarify that you can edit normal wiki pages, but nothing mention in the ruleset.

Not so easy. Fails 1-11 (amusingly, Wakukee is not the 1 in favour).

Ienpw III

Adminned at 13 Jun 2013 08:23:54 UTC

Based on rule 2.1 (Truth) and the Truths wiki page, I believe that I have just achieved victory.

It was pretty simple. Gamestate is defined by the ruleset as *“Any information which the Ruleset regulates the alteration of.”* (Other things have been defined as gamestate, but only through rules, such as one from the First Dynasty of Wakukee stating that *“The universe exists, and is Gamestate.”*) Rule 2.1 (Truth) claims the existence of the wiki page and states that everything on it is true. However, it does not regulate the alteration of the page. As such, it is not considered gamestate, and can be legally changed at any time. It does, however, affect gamestate, as everything on it is considered true for the purposes of the game. I thus legally edited the page, and added truths stating that I have achieved victory and that the page is now gamestate (so it can no longer be legally altered).

I should make it clear now that my intentions are (should this pass) to give the next dynasty to Skju, who I have talked to about this. He would keep the current theme and rules (though he would change the truths rule to be less broken) and continue the second dynasty of Skju as if nothing had happened.

I wish to unidle, and am doing so. Quorum remains 8. More on the story as it develops.

5-1, but self-killed. - Ien

Adminned at 14 Jun 2013 22:07:48 UTC

Amend rule 1.2.1. to read as follows:

Some Atoms are Idle, and shall be marked as such in the sidebar. For the purposes of all Gamestate and the Ruleset, excluding Rules â€œRuleset and Gamestateâ€, â€œAtomsâ€, â€œDynastiesâ€, â€œFair Playâ€ and any of those Rulesâ€™ subrules, Idle Atoms are not counted as Atoms.

If a Proposal contains a provision that targets a specifically named Idle Atom, then that Idle Atom is considered to be Unidle solely for the purposes of enacting that specific provision

When a Atom is unidled, if they went Idle in the same dynasty, their personal gamestate retains the last legally endowed values it had, if they are still valid. Otherwise (including if a value is invalid, does not exist, or the Atom Idled in a different dynasty), the Atom is given the default value for new Atom, if such a value exists.An Admin may render a Atom Idle if that Atom has asked to become Idle in an entry or comment from the past four days, or if that Atom has not posted an entry or comment in the last seven days. Admins may render themselves Idle at any time. An Admin may Unidle a Atom if that Atom has asked to become Unidle in an entry or comment from the past four days, and Idle Admins may Unidle themselves at any time, unless the Atom who would be Unidled asked to become (or rendered themselves) Idle within the previous four days, and within the current dynasty.

Unless an Idle/Unidle request is made in a new entry, the admin who processes any Idle/Unidle shall make an entry describing the Idle/Unidle.

Fool asked to be idled in a comment to this post: http://blognomic.com/archive/this_post_is_false/

I had meant to make a post about it, but evidently forgot. However, a Post is only necessary if they didn’t ask to be idled, so its all legal. Sorry about the lateness, and thanks Wakukee for the question that reminded me to do this.

Passes 5-2 / Skju

Adminned at 14 Jun 2013 20:48:39 UTC

In the rule “Truth”, change all occurrences of “Deliberation” to “Proof”.

In the rule “Truth”, immediately before the sentence beginning with “Proofs are Votable Matters”, add the sentence “Multiple Truths, each accompanied by the above required specifications, may be added by a single Proof.”

In the rule “Formulae”, replace the sentence “A Formula (plural Formulae) is either a single Variable or a sequence of Variables and properly-placed Connectives.” with

A single Variable is a Formula. A sequence of one or more Formulae with properly-placed Connectives is a Formula.

In the rule “Formulae”, append to the last sentence: ” within its context”.

Append to the rule “Formulae”:

The symbols “1” and “0” are Formulae that are True and False, respectively. The Connective “=” has its typical meaning of equality, where the Formulae on either side of it have the same value of True or False.

In rule 3.3.2 “Rules and Proposals”, amend the item beginning with “If a new wiki page” to read:

Unless explicitly stated otherwise, a wiki page shall be blanked when it becomes gamestate.

Clarifying and cleaning up.

Passes 6-3 / Skju

Adminned at 13 Jun 2013 19:35:08 UTC

Amend the rule “Truth” to read:

There is a wiki page called “Truths” which consists of two sections, Axioms and Theorems, each containing and ordered list of True Formulae. No Truths may contradict each other.

Any Atom can add an item to either list by submitting an entry in the “Proof” category that states the Formula to be added, which section to add it to, and, for a Theorem, a logical sequence of deductions that leads to it from existing Truths (unless the Atom already has 2 Proofs pending). Proofs are Votable Matters and as such are governed by the rule â€œVotable Mattersâ€. Proofs cannot be Vetoed. The oldest pending Proof may be enacted by any Admin if either of the following is true:

- It has been open for voting for at least 12 hours, has a number of FOR Votes that exceed or equal Quorum, and has not been Self-Killed.
- It has been open for voting for at least 24 hours, it has more than 1 valid Vote cast on it, it has more valid Votes cast on it FOR than AGAINST, and has not been Self-Killed.
Any pending Deliberation may be failed by any Admin, if any of the following are true:

- It could not be Enacted without either one of the Votes AGAINST it being changed, or the set of Atoms being changed.
- It has been open for voting for at least 48 hours and cannot be Enacted.
- It cannot be Enacted without causing a contradiction between Truths.
If a Proof somehow ends up being pending for more than 4 days, it is ignored for the purpose of calculating the oldest pending Proof, and can be failed by any Admin.

Each Theorem shall have next to it a link to the Proof that introduced it.

Enact a new rule entitled “Formulae”:

A Variable is a single lowercase letter. A Connective is a sequence of non-lowercase characters that is either unary (placed before a Formula) or binary (placed between two Formulae). A new Connective can be Defined by an Axiom that asserts the equality of a Formula that contains the Connective and a Formula that does not.

A Formula (plural Formulae) is either a single Variable or a sequence of Variables and properly-placed Connectives. Brackets (”[” and “]”) should be used around a Formula to disambiguate the order in which Connectives apply. A Formula is either True (1) or False (0).

Add the following Axioms to Truths:

- x = x
- [0 - 0] = 1
- [0 - 1] = 0
- [1 - 0] = 0
- [1 - 1] = 0

We’ve got quite a lot going on here. Splitting Truths into Axioms and Theorems, allowing them to be added through fully democratic Proofs, defining Formulae, and introducing equality and NOR.

Self-Killed

/Skju

Adminned at 13 Jun 2013 08:29:07 UTC

Create, and blank, a wiki page entitled “Proofs”, with three sections “Established Proofs”, “Under Deliberation”, and “Rejected Proofs”.

Create a new post type entitled “Proofs”.

If the rule “Truth” exists, enact a subrule entitled “Proofs”:

At any time, any Atom may submit a proof by creating a post in the category of “Proofs”, and posting their proof both in the body of the post and on the wiki entitled “Proofs” in the “Proofs under Deliberation” section. An atom may have, at most 2 Proofs under deliberation at a time. After a Proof post has been posted, it goes under deliberation. During the deliberation period, any Atom may dissent with the proof by responding in the comments with or may agree with the proof by responding in the comments with . All dissenters must provide a logical argument for what logic is faulty in the proof. An Atom may Self-Kill their own proposal by voting AGAINST in the comments of their Proof post.

The oldest Proof that is under deliberation may be Established by any Admin (by updating the status of the post and by moving the proof from the “Under Deliberation” section of the wiki to the “Established Proofs” section) if any of the following are true:

- There is a quorum of FOR votes, and there are no AGAINST votes
- There is a quorum of FOR votes and all the AGAINST have been resolved
- Voting has been open for 48 hours, there are more than one FOR votes, and all the AGAINST votes have been resolved, and it has not been self-killed
The oldest Proof that is under deliberation may be Rejected by any Admin (by updating the status of the post and by moving the proof from the “Under Deliberation” section of the wiki to the “Rejected Proofs”) if any of the following are true:

- There is a quorum/2 of AGAINST votes
- The proof has been Self-Killed
- Voting has been open for 48 hours and cannot be Established
Resolving AGAINST votes:

When an Atom votes AGAINST a proof, they must be able to show a fault in the logic of the proof. Once any Atom votes AGAINST a proof, any other atom may respond to the logic in the AGAINST vote by using (which here means DEFEND, as opposed to DEFER), and in doing so makes a counter argument. Once a counter argument has been made, any Atom, other than the one who posted the proof and the one who posted the IMPERIAL, may comment RESOLVED to indicate that they believe that the issue has been resolved, or UNRESOLVED to indicate that they believe the issue is still unresolved. If there are more RESOLVED comments then UNRESOLVED comments, the particular AGAINST that was responded to is considered resolved.I hope you guys are ok with me re-purposing the IMPERIAL symbol for Proofs. Also, Resolving AGAINST votes is a little complex, but I think it’s necessary for proofs to work. I don’t think that simply a quorum should be able to decide whether a proof is valid or not, but there should be some extra process, if necessary, of debating the validity of the proof. This is what the resolving mechanic attempts (maybe a bit poorly) to address. In any case, I think that this proposal is a good starting point, even if it’s not perfect.

Self-killed. — Quirck

Adminned at 12 Jun 2013 07:25:25 UTC

Append to the rule “Truths”:

A statement cannot be added to Truths if it directly contradicts another statement. The contrapositive to any statement in Truths is False. There exist statements which are neither provably True or False.

Making sure our list of Truths abides by Soundness, and introducing the problem of completeness.

Can’t be enacted at 1-7. — Quirck

Adminned at 11 Jun 2013 23:43:14 UTC

Add the following to the rule “Truth”.

In addition to statements, the list may also contain Categories. Categories are also a list of statements (which are all True) and Categories.

If there is a dynastic rule called “Petersen” clear it, and add the “Petersen” category following to the list of Truths and put the following statements in its list of statements

* H, K, R, W, and Y are all Essential Letters.

* An Essence is an unordered pair of distinct Essential Letters.

* Each Atom initially has no Essence.

* An atom with no Essence may set their Essence to any valid value.

* The GNDT column â€œEssenceâ€ contains an Atomâ€™s Essence, or â€œ-â€ if they have no Essence.

* Two Atoms are Bonded if they both have Essences, and their Essences have no letter in common.

Showing off how we can add a rule by editing the Truths list rather than adding new dynastic rules. which we may or may not want, but should decide before the dynastic ruleset gets too cluttered.

Additionally, we might want to consider making some truths more mutable (like what are valid Essential Letters) and keep those in the Truths list, while core mechanics stay in the ruleset. But that could get clunky…

I’d like to unidle.

Also - assume the contrary - therefore there must be a maximum prime n. Construct a new number n! + 1. Clearly this is not divisible by 2…n and must therefore be prime. This is a contradiction. QED.

(Okay, not really.)

I wish to unidle.

Quorums 9-0. — Quirck

Adminned at 11 Jun 2013 23:41:58 UTC

To the list in the rule 3.3.2 “Rules and Proposals”, after the first item, append:

* If a new wiki page is created by a proposal and its contents are not specified in that proposal, that new wiki page shall be created blank.

Someone had to propose this

Quorums 10-0. — Quirck

Adminned at 11 Jun 2013 23:40:09 UTC

Enact a Dynastic Rule, titled “Petersen”:

The Essential Letters are H, K, R, W, and Y. An Essence is an unordered pair of distinct Essential Letters. Each Atom initially has no Essence, but an atom with no Essence may set their Essence to any valid value. The GNDT column “Essence” contains an Atom’s Essence, or “-” if they have no Essence. Two Atoms are Bonded if they both have Essences, and their Essences have no letter in common.

This rule wouldn’t do anything by itself, of course, but it may have the potential to develop into something interesting,

Can’t be enacted at 0-7. — Quirck

Adminned at 11 Jun 2013 23:38:27 UTC

Add a dynastic rule called “Atom, prove thyself” and give it the following text

Every Atom by itself is a well-formed formula. Once the first proof of a well-formed formula consisting solely of an Atom is established, then that Atom shall win.

Our deduction rules will probably be such that this includes win by contradiction. The first one to prove a contradiction just goes on to prove his own Atom for the win.

NOT A PROPOSAL

Enact a new subrule of “Formulae” entitled “Connectives”:

All 16 truth functions in the table on this page are Connectives. The following are Standard Notations for the basic Connectives, whence the others may conveniently be specified. Where the Standard Notation is not given at all by Wikipedia, the Standard Notation is on the left and its notation is on the right:

- F.p := p&~p
- T.p := p|~p
- p
- ~p
- p&q
- p|q := p OR q
- p->q := pâ†’q
- p<->q := p IFF q

A Protosal, if you will, for feedback before I can Propose. It does bug me that the - is just below the center of the >.

Vetoed. — Quirck

Adminned at 11 Jun 2013 09:41:46 UTC

Create, and blank, a wiki page entitled “Proofs”, with three sections “Established Proofs”, “Proofs under Deliberation”, and “Rejected Proofs”.

If the rule “Truth” exists, enact a subrule entitled “Proofs”:

At any time, any Atom may submit a proof by creating a story post entitled “Proofs”, and posting their proof both in the body of the post and on the wiki entitled “Proofs” in the “Proofs under Deliberation” section. An atom may have, at most 2 Proofs under deliberation at a time. After a Proof post has been posted, it goes under deliberation. During the deliberation period, any Atom may dissent with the proof by responding in the comments with or may agree with the proof by responding in the comments with . All dissenters must provide a logical argument for what logic is faulty in the proof. If at any point there is a quorum of votes FOR a Proof and there are no AGAINST votes in the comments, any Atom may move the proof into the “Established Proofs” section of the wiki and the Proof is no longer under deliberation. If there are any AGAINST votes and 48 hours have passed since the proposal of the Proof, it is up to the discretion of any Atom except the one who proposed the Proof to decide whether the arguments of the dissenters have merit. If the dissenters have successfully proven a fault in the proof, the Proof is moved to the “Rejected Proofs” section of the wiki, otherwise it is moved to the “Established Proofs” section. In either case, the Proof is no longer under deliberation. If an Atom realizes the flaw in their own Proof, they should vote AGAINST it in the comments. If an author a proof has voted in this way, any Atom may move the Proof into the “Rejected Proofs” section of the wiki. This Proof is no longer under deliberation.

Sorry that this is a little long. I keep wanting to write, “Once per time advancement”. I think that a mechanic to reward people for making proofs that are accepted, punish them for making proofs that are rejected, and allowing them to cut their losses by realizing the error of their own proof would be useful. Also, a mechanic to re-examine proofs later on in the game could also be good. Also, would it be possible to have a new category entitled Proofs, or do we just have to make do with Story Posts?

Quorums 7-3. — Quirck

Adminned at 11 Jun 2013 09:40:58 UTC

Add a new dynastic rule called “Truth” and give it the following text

There is a wiki page called “Truths” which consists of an ordered list of statements, all of which are True.

If there is a rule called “Definitions” remove it and add the following to the list of truths

AND is a bivalent Connective. [x AND y] is True if both x and y are true

IMPLIES is a bivalent Connective. [x IMPLIES y] is True unless [x is True] AND [y is False].

NOT is a monovalent Connective. [x is True] IMPLIES [[NOT x] is False]. [x is False] IMPLIES [[NOT x] is True].

Ideally I think it would be cool if most of this dynasty was set around editing the Truths page and keeping the actual ruleset very light

Vetoed. — Quirck

Adminned at 11 Jun 2013 09:01:18 UTC

The rules shall decree what formulas are well-formed, what axioms are true, and what deduction methods are valid.

A proof consists of a post by which a well-formed formula is deduced using the methods decreed by the rules, from the axioms decreed by the rules or from formulas previously proven.

Every Atom by itself is a well-formed formula. Once the first proof is posted of a well-formed formula consisting solely of an Atom, then that Atom shall win.

This includes win by contradiction, if our deduction rules include ex contradictione quodlibet. Then the first one to prove a contradiction just goes on to prove his own Atom for the win.

I wish to be an Atom.

Preferably I would be a true atomic formula. Maybe 7*11*13=1001, that’s kinda neat. Or hey, open formulas? Is Fermat’s little theorem taken? x^p = x mod p. Whoa… Anyways, I’m not picky just please don’t make me some lame upside-down calculator thing like 5318008.

Self-killed. — Quirck

Adminned at 11 Jun 2013 09:00:24 UTC

Enact a new rule entitled “Formulae”:

A Variable is a single lowercase letter that is either True or False within the context that it’s in. A Connective is a nonalphanumeric symbol that is [monovalent, placed before a Formula] XOR [bivalent, placed between two Formulae]. A Formula is a single Variable XOR a finite sequence of Variables with properly-placed Connectives. Brackets (”[” and “]”) can be placed around Formulae and phrases to disambiguate the order in which a Connective applies.

Enact a new (empty) rule entitled “Definitions”.

Enact a new subrule of “Definitions” entitled “NOT”:

NOT is a monovalent Connective. [x is True] IMPLIES [[NOT x] is False]. [x is False] IMPLIES [[NOT x] is True].

Enact a new subrule of “Definitions” entitled “IMPLIES”:

IMPLIES is a bivalent Connective. [x IMPLIES y] is True unless [x is True] AND [y is False].

I suppose that this is a way to get started. It seems awfully slow (and lame) though. I don’t suppose we could somehow easily import the necessary axioms and deductions?

It shouldn’t be long before we come up with Nomic-specific stuff. That also entails screwing with these definitions, I hope.

Quorums 8-0. — Quirck

Adminned at 11 Jun 2013 08:57:30 UTC

Make Skju an Admin.

I call for fundamental restructuring. With modern instruments of formulation, analysis, and logic, we aim to construct a formal system for precise treatment of the principles of Nomic. A new language will be written; from the most basic axioms of deduction, a world of possibilities will be derived; we will distil into drops of abstract truth the findings of the philosophers before us; and we will have complete control over the transcendental essence of our new science, whence the most beautiful blossoms of imagination shall spring. Perhaps we will even prove that 1+1=2.

Repeal all dynastic rules. Change “Arbiter” to “Schema” and “Noble” to “Atom”.

Sorry for being a little late.

Unidle me, please.

It has been decided that the Noble Skju, Earl of Shrewsbury, Earl of Kent, Earl of March, Baron Byron, Baron Mulgrave, Baron Fotheringay shall take the throne. I gladly forfeit my ascension onto him. Long live the King!

Long Live the King! Enacted, seven to none, by Ienpw III.

Adminned at 08 Jun 2013 21:43:17 UTC

As I am the owner of all 110 Parcels of England, I declare myself victorious under the Rule “Owning the Land”.

As the sole owner of all the land in England, I declare this Feud between Families annulled. Peaceful deliberation will determine who ascends to Kingship.

I don’t plan to run the next Dynasty, so who wants it? Optionally leave your idea for it.

I am Declaring a Feud upon Rationality, Baron Bywell because they are standing in the way of my victory!

Sorry, but this is gonna have to happen.

Times Out and Passes 6-0. -RaichuKFM

Adminned at 07 Jun 2013 17:19:40 UTC

Add a new rule, entitled â€œOwning the Landâ€:

If, at any point, a Noble has all 110 Parcels and is not a Scoundrel, that Noble achieves victory.

Vetoed. -RaichuKFM

Adminned at 07 Jun 2013 17:18:10 UTC

Add a new rule, entitled “Killing the Opposition”:

If, at any point, all Nobles except one have zero knights and one Noble has at least 40 knights, that Noble achieves victory.

Not seizing the crown because once you’ve killed your opponents they’re dead and can’t take the crown back. Also, this dynasty is positively ancient.

I’m advancing.

Fruit flies like a banana

It occurs to me that I do not have a wiki account, and thus, I cannot edit the wiki. As such, I would like to have one created, preferably with the username “T”, or “Ta” if that is not available; in the meantime, I hereby take the following actions (if I can take them by saying so),

I obtain Baron Percy and place it under Earl of Kent; I join Side 2 of Feud 1, alongside Skju, Earl of Shrewsbury, Earl of Kent, Earl of March, and Clucky, Earl of Oxford, Earl of Northumberland (gaining 3 Dignity, since my Lord Skju, Earl of Shrewsbury, Earl of Kent, Earl of March, is the Wronged Party); I Mock myself for doing so, since Clucky, Earl of Oxford, Earl of Northumberland, is not of my family; and I spend eight knights to transfer eight Occupied Parcels from kikar, Duke of York, Duke of Lancaster, to myself,

If these all succeed, then I gain 3 Dignity (putting me at 48), then lose ten percent of my Dignity and round down (putting me at 43), then I lose eight knights, the Duke loses eight Occupied Parcels, and I gain eight Occupied Parcels,

Reaches Quorum and Passes 5-0. -RaichuKFM

Adminned at 06 Jun 2013 09:02:45 UTC

In the rule “Monarchy”:

Replace the line that reads: “If any of the following are true the noble who has the crown loses the crown.”

with the text: “If any of the following are true when time advances, the noble who has the crown loses the crown.”

Hopefully this will make getting support from other players feasible.

as the battle rages on so does time itself

I am seizing the crown. All who want to be on the winning side of history should join me by pledging knights to my cause.

Someone had to do this.

Tavros idles out.