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 <blahedo@quincy.edu>; 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 <nomic-official@teleport.com>; 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 <csg419@wing.rug.nl>
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

----------------------------------------