From owner-nomic-official@teleport.com Thu Feb 8 05:24:49 1996 Received: from desiree.teleport.com (desiree.teleport.com [192.108.254.21]) by Shamino.quincy.edu (8.6.12/8.6.9) with ESMTP id FAA29774 for ; Thu, 8 Feb 1996 05:24:47 -0600 Received: from localhost (daemon@localhost) by desiree.teleport.com (8.6.12/8.6.9) with SMTP id DAA12142; Thu, 8 Feb 1996 03:06:01 -0800 Received: by desiree.teleport.com (bulk_mailer v1.3); Thu, 8 Feb 1996 03:06:00 -0800 Received: (from daemon@localhost) by desiree.teleport.com (8.6.12/8.6.9) id DAA12128 for nomic-official-outgoing; Thu, 8 Feb 1996 03:06:00 -0800 Received: from wing4.wing.rug.nl (wing4.wing.rug.nl [129.125.21.4]) by desiree.teleport.com (8.6.12/8.6.9) with SMTP id DAA12120 for ; Thu, 8 Feb 1996 03:05:56 -0800 Message-Id: <199602081105.DAA12120@desiree.teleport.com> Received: by wing4.wing.rug.nl (1.37.109.8/16.2) id AA03463; Thu, 8 Feb 1996 12:03:33 +0100 From: Andre Engels Subject: OFF: CFJ 855 Judgement: FALSE To: nomic-official@teleport.com Date: Thu, 8 Feb 96 12:03:33 MET Mailer: Elm [revision: 70.85] Sender: owner-nomic-official@teleport.com Reply-To: nomic-discussion@teleport.com Precedence: bulk Status: RO ====================================================================== JUDGEMENT CFJ 855 "It is legal to transfer a complex number of Currency as long as the number is evenly divisible by the Currency's MUQ and consists of a positive Real component." ======================================================================= Judge: KoJen Judgement: FALSE Eligible: Chuck, dcuman, favor, Jtael, KoJen, Steve, Wes, Zefram, Morendil (if he is a Player) Not Eligible: Caller: Swann Barred: Kelly On Hold: Blob, Dave Bowen, elJefe 1005: Andre, Michael, Murphy, Pascal, Swann, Vanyel, Vlad Effects: KoJen gains 3 Points for timely Judgement ====================================================================== History: Called by Swann, 31 January 1996, 12:53 -0800 Assigned to KoJen, 2 February 1996, 15:01 MET Judged FALSE by KoJen, 7 February 1996, 14:51 -0500 ====================================================================== Arguments: The question is if it is legal to make transfers of the form a+bi, where i is the square root of negative one. Transfers of complex or imaginary numbers are not explicitly forbidden, or even referred to, in the Rules regarding Currency Transfers. We must look to what the transfer Rules do refer to and/or prohibit. Rule 1467 has this to say about transfers: "The minimum unit quantity (MUQ) of a Currency is the smallest amount of that Currency which may be transferred. All transfers, holdings, and calculations involving a given Currency shall be rounded off to the nearest multiple of its MUQ. The MUQ of a given Currency is 1, unless another Rule specifies a different MUQ for that Currency." Therefore, we have our first restriction. In any transfer of the form a+bi, a+bi must be an integral multiple of the currency's MUQ. Or, another way, a+bi must be equal to MUQ(x+yi) where x & y are integers. Since no current MUQ is greater than one, all cases where a & b are themselves integral are not forbidden by 1467. Rule 1468 has this to say about Treasuries: "A Treasury may contain a positive, negative, or zero quantity of a given Currency, unless otherwise prohibited by the Rules. This might seem to forbid the ability of a Treasury to hold quantities that are other than positive, negative, or zero-- but note that this is not a restrictive clause. It doesn't forbid anything itself, it relies on other rules to do the forbidding for it. There is nothing in this Rule that forbids a treasury's possessing an imaginary or complex amount of currency. Of course I believe this means that possession of imaginary and complex currencies is neither prohibited or regulated by 1468, leaving them permitted and unregulated via 116 unless another Rule should pick up the slack. The only real Rule we have left is the much-beleaguered 1472. Now since no Rule currently mandates complex transfers, let's see what it takes to make a Class II or III transfer legal: 1472 says: "It shall be legal to transfer Currencies between Treasuries, provided this is done in accordance with the Rules. Every transfer shall involve a positive amount of exactly one Currency. . . A Class II or Class III Transfer is not permitted if the Treasury from which the Currency is being transferred will possess a negative quantity of that Currency after the transfer has been completed." Assuming the transfer (initiator, detector, recordkeepor &c.) is otherwise legal, what does this tell us about the amounts involved? It says two things: I) You can't leave a negative number in a treasury. However, as long as we begin with a real amount of currency (even zero) and transfer out a complex number, we're left with a complex number. And taken as a _whole_ (this is important for the next condition; Within Treasuries we must consider whole amounts. Within transfers we are not so limited) complex numbers are neither positive or negative. We need not worry about this condition. II) The transfer "shall _involve_ a positive amount of exactly one Currency." Note the wording. It says "involve," not "be" or "is" or "consist solely of." The use of the word "involve" allows a broad interpretation, where the "positive amount of exactly one Currency" is not necessarily the whole of the transfer. If I were to transfer, say, 30+30i Win Tokens, there is no doubt that there are 30 positive Win Tokens involved in the Transfer. Since there's no prohibition on including an imaginary component (even of a different or non-existent currency) I contend that currency transfers as described in my Statement are legal by virtue of rule 116. ====================================================================== Decision & Reasoning Judge: My decision of CFJ 855 is FALSE. Reasoning: Implicit in the wording of the collective Currency Rules is the requirement that the units of all Currencies are restricted to real numbers. For example: Rules 1468 and 1472 mention "a positive amount of currency". However -- There is no such concept "positive" for complex numbers. Although we *could* simply say that 1468 and 1472 are inconsistent -- talking about complex quantities of currency yet also using the relation "positive" -- there is no worthwhile reason to do so. Such an interpretation would only lead to chaos, and there is absolutely no reason why I should choose this interpretation over the other. ====================================================================== Evidence: ---------------------------------------- Rule 1467/1 (Mutable, MI=1) Definition of a Currency A Currency is a type of Nomic Entity. Only those Nomic Entities which are specifically defined by the Rules as being Currencies are Currencies. A Currency must have a Name (which must not be the name of any other Currency), a minimum unit quantity, a Recordkeepor, and a Mintor. The Mintor of a Currency is the Mint if it is not otherwise defined. The minimum unit quantity (MUQ) of a Currency is the smallest amount of that Currency which may be transferred. All transfers, holdings, and calculations involving a given Currency shall be rounded off to the nearest multiple of its MUQ. The MUQ of a given Currency is 1, unless another Rule specifies a different MUQ for that Currency. The Recordkeepor of a Currency is the Player who is required to maintain a record of the amount of that Currency held in the various Treasuries which exist. If a Currency ceases to have a valid Recordkeepor, the Banker (or, in eir absence, the Speaker) shall fulfill that responsibility until a new Recordkeepor is selected according to the appropriate procedures. If no procedure exists to select a new recordkeepor, all units of the Currency are instead destroyed, and the Currency ceases to exist. The Mintor of a Currency is the Nomic Entity which is authorized to create and destroy units of that Currency. If the Mintor of a Currency ceases to exist, all units of the Currency are immediately destroyed, and the Currency also ceases to exist. The Banker shall maintain a record of all existing Currencies and their MUQs, Recordkeepors, and Mintors. History: Created by Proposal 1601, Jun. 19 1995 Amended(1) by Proposal 1685, Sep. 1 1995 ---------------------------------------- ---------------------------------------- Rule 1468/0 (Mutable, MI=1) Definition of a Treasury A Treasury is a repository for holding Currencies. Currencies may exist only within a Treasury. A Treasury may contain a positive, negative, or zero quantity of a given Currency, unless otherwise prohibited by the Rules. Currencies may be transferred between Treasuries only as specified in the Rules. Only those Nomic Entities which are authorized by the Rules to possess Treasuries may possess Treasuries. No Treasury may be possessed by more than one Nomic Entity. The possession of Treasuries may never be changed, once created. Each Player and each Group has a Treasury of its own. Whenever an Entity possesses only one Treasury, it shall be a permissible and unambiguous abbreviation to state that the Entity possesses the Currencies within its Treasury. [CFJ 802: If an Entity ceases to exist, its Treasury does too.] History: Created by Proposal 1601, Jun. 19 1995 ---------------------------------------- ---------------------------------------- Rule 116/0 (Semimutable, MI=3) Permissibility of the Unprohibited Whatever is not prohibited or regulated by a Rule is permitted and unregulated, with the sole exception of changing the Rules, which is permitted only when a Rule or set of Rules explicitly or implicitly permits it. History: Initial Immutable Rule 116, Jun. 30 1993 Mutated from MI=Unanimity to MI=3 by Proposal 1483, Mar. 15 1995 ---------------------------------------- ---------------------------------------- Rule 1472/2 (Mutable, MI=1) Transfer of Currencies It shall be legal to transfer Currencies between Treasuries, provided this is done in accordance with the Rules. Every transfer shall involve a positive amount of exactly one Currency, which shall be transferred from exactly one Treasury into exactly one other Treasury. Every transfer has an initiator, which is the Entity which causes the transfer to take place. A transfer which is explicitly and directly required to take place by a Rule is initiated by that Rule, and is called a Class I Transfer. A transfer which is required to take place by an Entity (other than the Rules) to which the Rules have granted the power to require Currency Transfers to take place is initiated by that Entity (_not_ the Rule which grants that power to that Entity), and is called a Class II Transfer. A transfer which is not required to take place, and which is instead the consequence of a Player's action, is initiated by that Player, and is a called a Class III Transfer. For the purpose of this Rule, a Rule, or an Entity other than the Rules to which the Rules have granted the power to require Players to perform actions, which requires a Player to initiate a transfer is _not_ requiring the transfer. Such a transfer is a Class III transfer initiated by that Player. This Rule takes precedence over any Rule which would require a Player to initiate a transfer which is prohibited by this Rule. A Class I transfer is not permitted if there is no Rule which specifies a Player who is to detect and report the transfer. A Class II transfer is not permitted if there is no Rule, or Entity other than the Rules to which the Rules have granted the power to require Players to perform actions, which specifies a Player who is to detect and report the transfer. A Class II or Class III Transfer is not permitted if the Treasury from which the Currency is being transferred will possess a negative quantity of that Currency after the transfer has been completed. A Class III Transfer is not permitted unless the transfer is initiated by the Executor of the Owner of the Treasury from which the Currency is being transferred. This Rule takes precedence over any Rule which would permit a transfer prohibited by this Rule. The Recordkeepor of a Currency must be notified of a transfer involving that Currency within seven days, unless another Rule specifies a different time limit for reporting a certain type of transfer. For a Class I or Class II transfer, the notification shall be made by the Player required to detect and report it. For a Class III transfer, the notification shall be made by the Player who initiated it. Class I and Class II transfers take place at the time they are required to take place. Class III transfers take place at the time they are reported. [CFJ 793: Notification may take place as part of an Official Report to the Public Forum.] History: Created by Proposal 1601, Jun. 19 1995 Amended(1) by Proposal 1649, Aug. 1 1995 Amended(2) by Proposal 1702, Sep. 1 1995 ----------------------------------------