That said, I should perhaps also mention that I was ... using ...
Apple's fine "macbook" product, which in this case means most of my
time composing that message was spent trying to get the mouse pointer
into the positions that the underlying software needed it to be
positioned.

I don't know for sure whether I would have made the same mistakes if I
had been able to type and read unhindered, but I don't know for sure
that I would not have, either.

Thanks,

-- 
Raul
On Tue, Jun 12, 2018 at 11:14 AM Raul Miller <rauldmil...@gmail.com> wrote:
>
> I guess I was distinguishing between set up statements and concluding
> statements. And I tried to ignore set up statements which were not
> Bo's.
>
> In other words, I saw
> >    NB. That is, Lucy (either sane or insane) is a vampire and
> >    NB. Minna (either sane or insane) is a human
>
> And presumed that that was meant to represent your result set.
>
> Thanks,
>
> --
> Raul
>
> On Tue, Jun 12, 2018 at 11:04 AM Jose Mario Quintana
> <jose.mario.quint...@gmail.com> wrote:
> >
> > Raul wrote:
> >
> > > Hmm... here was my approach. I think I got different results:
> > .
> > .
> > .
> > > My way of summarizing this would be:
> > >
> > > "Lucy is a vampire",
> > > "Minna is human",
> > > "They are either both sane or both inane".
> >
> > responding to a post where Roger wrote:
> >
> > > Jose, I agree with you exactly.  Here is my calculation:
> >
> > (I also agree with him) responding to a post  where I wrote:
> >
> > > [...] they have to be either both sane or both
> > > insane.  [...]
> > .
> > .
> > .
> > >    find o #: o i. 2^4
> > > 0 0 1 0
> > > 0 1 1 1
> > >
> > >    NB. That is, Lucy (either sane or insane) is a vampire and
> > >    NB. Minna (either sane or insane) is a human
> >
> > So, what makes you think you got different results from Roger and me?  (I
> > cannot see any difference.)
> >
> >
> > On Tue, Jun 12, 2018 at 7:09 AM, Raul Miller <rauldmil...@gmail.com> wrote:
> >
> > > Hmm... here was my approach. I think I got different results:
> > >
> > > lucy=: {."1
> > > minna=: {:"1
> > > species=: 2&|
> > > diagnosis=: 1&<
> > > human=: 0=species
> > > vampire=: 1=species
> > > sane=: 0=diagnosis
> > > insane=: 1=diagnosis
> > > invalid=: ~:/"1@(2 2&#:)
> > > both=:*/"1
> > >
> > > showSpecies=: ;@{&(;:'human vampire')@species
> > > showDiagnosis=: ;@{&(;:'sane insane')@diagnosis
> > > show=: showSpecies, ' and ', showDiagnosis
> > > possible=: 3 :0"1
> > >  echo 'Lucy is ',(show lucy y),' and Minna is ',show minna y
> > > )
> > >
> > > NB. all possibilities
> > > S=: 4 4 #:i.16
> > >
> > > NB. He knew that one was a vampire and one was a human
> > > S=: S=:S#~~:/"1 species S
> > >
> > > NB. Lucy: "We are both insane"
> > > S=:S#~(invalid lucy S)~:both insane S
> > >
> > > NB. Minna: "We are not both insane"
> > > possible S=:S#~(invalid minna S)~:-.both insane S
> > >
> > > Running this script gives me two plausible seeming results:
> > >
> > > Lucy is vampire and sane and Minna is human and sane
> > > Lucy is vampire and insane and Minna is human and insane
> > >
> > > In the ordinal fraction representation, the second possibility was
> > > expressed as 2221 and rejected at the final step of the process:
> > >
> > > "Now we know that Minna is an insane human, and so they are not both
> > > insane,"
> > >
> > > But Mina's statement was that they are not both insane and insane
> > > humans always make false statements according to the rules here.
> > >
> > > I am not sure what to make of that part of the ordinal fraction approach.
> > >
> > > My way of summarizing this would be:
> > >
> > > "Lucy is a vampire",
> > > "Minna is human",
> > > "They are either both sane or both inane".
> > >
> > > Thanks,
> > >
> > > --
> > > Raul
> > >
> > > On Tue, Jun 12, 2018 at 4:30 AM roger stokes <rogerstokes...@gmail.com>
> > > wrote:
> > > >
> > > > Jose, I agree with you exactly.  Here is my calculation:
> > > >
> > > > NB. There are four independent propositions: Lucy human, Lucy sane, 
> > > > Minna
> > > > human, Minna sane.
> > > >
> > > > NB. Therefore there are 16 possibilities, each representable as a 4-bit
> > > > string.
> > > >
> > > > P =: #: i. 16 NB. set of all possibilities: 0000, 0001, 0010 etc
> > > >
> > > > NB. A proposition is modelled as a function to select a single bit.
> > > >
> > > > Lh =: 0&{ NB. Lucy is human
> > > >
> > > > Ls =: 1&{ NB. Lucy is sane
> > > >
> > > > Mh =: 2&{ NB. Minna is human
> > > >
> > > > Ms =: 3&{ NB. Minna is sane
> > > >
> > > > truthteller =: = NB. x= human, y = sane : both or neither
> > > >
> > > > Ax =: Lh ~: Mh NB. Axiom: if Lucy human, then Minna not, and vice versa
> > > >
> > > > Lucy =: (Lh truthteller Ls) = (Ls +: Ms) NB. "we are both insane"
> > > >
> > > > Minna =: (Mh truthteller Ms) = (Ls +. Ms) NB. "not both insane"
> > > >
> > > > (Minna " 1 # ]) (Lucy "1 # ]) (Ax "1 # ]) P
> > > >
> > > > 0 0 1 0
> > > >
> > > > 0 1 1 1
> > > >
> > > >
> > > > On Tue, Jun 12, 2018 at 12:12 AM, Jose Mario Quintana <
> > > > jose.mario.quint...@gmail.com> wrote:
> > > >
> > > > > Friday night I decided to try to fall asleep by thinking about the
> > > puzzle
> > > > > and I thought I had solved it. This evening I wrote a wicked script to
> > > > > verify my thought process and I got the same result but it does not
> > > seem to
> > > > > match your conclusion.
> > > > >
> > > > > This is what I found...
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > > *** POTENTIAL SPOILER FOLLOWS ***
> > > > >
> > > > >
> > > > >
> > > > >
> > > > >
> > > > > Given the conditions of the puzzle and since the sisters' statements
> > > > > contradict each other then they have to be either both sane or both
> > > > > insane.  That leaves four possibilities:
> > > > >
> > > > > 0.  Lucy is a sane human and Mina is a sane vampire.
> > > > >     This one is inconsistent with Lucy's statement "We are both
> > > insane."
> > > > >
> > > > > 1.  Lucy is an insane human and Mina is an insane vampire.
> > > > >     This one is inconsistent with Mina's statement "of course not!"
> > > > >
> > > > > 2.  Lucy is a sane vampire and Mina is a sane human.
> > > > >     This one is consistent with both Lucy's statement and Minna's
> > > > > statement.
> > > > >
> > > > > 3.  Lucy is an insane vampire and Mina is an insane human.
> > > > >     This one is also consistent with both Lucy's statement and Minna's
> > > > > statement.
> > > > >
> > > > > However, either sane or insane, Lucy is a vampire (and Minna is a
> > > human).
> > > > >
> > > > > This is a verification in the form of a session corresponding to a
> > > wicked
> > > > > brute-force quick-and-dirty script (yet, the derived verb is not
> > > wicked)
> > > > > using the J Wicked Toolkit [0] (beware of line-wrapping)...
> > > > >
> > > > >    JVERSION
> > > > > Engine: j806/j64nonavx/windows
> > > > > Release: commercial/2017-11-06T10:01:33
> > > > > Library: 8.06.09
> > > > > Qt IDE: 1.6.2/5.6.3
> > > > > Platform: Win 64
> > > > > Installer: J806 install
> > > > > InstallPath: j:/program files/j
> > > > > Contact: www.jsoftware.com
> > > > >
> > > > >    NB. (Extra parentheses for clarity)
> > > > >
> > > > >    NB. Running the Wicked Tacit Toolkit first...
> > > > >    NB. (0!:0)<'/.../J Wicked Toolkit.ijs
> > > > >
> > > > >    'LH LS MH MS'=. 4 Fetch
> > > > >     NB. True and false are encoded as bits in the usual way (as 1 and > > > > > 0
> > > > > respectively)
> > > > >     NB. The bits are in the following order
> > > > >     NB. Lucy       Minna
> > > > >     NB. human sane human sane
> > > > >
> > > > >    'or and not'=. [:+.*.-.]sb
> > > > >
> > > > >    NB. He knew that one was a vampire and one was a human...
> > > > >    ovoh=. (LH and not o MH) or (not o LH and MH)
> > > > >
> > > > >    NB. Lucy: We are both insane...
> > > > >
> > > > >    lbit=. (((LH and       LS) or (not o LH and not o LS)) and not o LS
> > > and
> > > > > not o MS)
> > > > >      NB. Lucy is not lying
> > > > >    lbil=. (((LH and not o LS) or (not o LH and       LS)) and       LS
> > > or
> > > > >       MS)
> > > > >      NB. Lucy is     lying
> > > > >    lbi=. lbit or lbil
> > > > >
> > > > >    NB. Minna: Of course not!
> > > > >    mont=. (((MH and       MS) or (not o MH and not o MS)) and       LS
> > > or
> > > > >       MS)
> > > > >      NB. Minna is not lying
> > > > >    moni=. (((MH and not o MS) or (not o MH and       MS)) and not o LS
> > > and
> > > > > not o MS)
> > > > >      NB. Minna is     lying
> > > > >    mon=. mont or moni
> > > > >
> > > > >    find=. ((ovoh and lbi and mon)"1 # ])f. NB. Finding the consistent
> > > > > possibilities
> > > > >
> > > > >    find o #: o i. 2^4
> > > > > 0 0 1 0
> > > > > 0 1 1 1
> > > > >
> > > > >    NB. That is, Lucy (either sane or insane) is a vampire and
> > > > >    NB. Minna (either sane or insane) is a human
> > > > >
> > > > >    NB. The wrapped linear representation of find is...
> > > > >
> > > > >       66 (-@:[ ]\ 5!:5@<@:]) 'find'
> > > > > (((0&({::) *. -.@:(2&({::))) +. -.@:(0&({::)) *. 2&({::)) *. ((((0
> > > > > &({::) *. 1&({::)) +. -.@:(0&({::)) *. -.@:(1&({::))) *. -.@:(1&({
> > > > > ::)) *. -.@:(3&({::))) +. ((0&({::) *. -.@:(1&({::))) +. -.@:(0&({
> > > > > ::)) *. 1&({::)) *. 1&({::) +. 3&({::)) *. (((2&({::) *. 3&({::))
> > > > > +. -.@:(2&({::)) *. -.@:(3&({::))) *. 1&({::) +. 3&({::)) +. ((2&(
> > > > > {::) *. -.@:(3&({::))) +. -.@:(2&({::)) *. 3&({::)) *. -.@:(1&({::
> > > > > )) *. -.@:(3&({::)))"1 # ]
> > > > >
> > > > >
> > > > > PS.  There is no need to run a Toolkit for this in Jx;
> > > > >      just replace 'LH LS MH MS'=. 4 Fetch by,
> > > > >        'LH LS MH MS'=. 4 ((i.@:[ <@:(((_3?:0) (_1?:0))&)"0 _ ])(_2?:0)
> > > > > {::)
> > > > >      and 'or and not'=. [:+.*.-.]sb by,
> > > > >        'or and not'=. [:+.*.-.]:
> > > > >      and define o=. @:
> > > > >
> > > > >
> > > > > [0] J Wicked Toolkit
> > > > >     http://www.2bestsystems.com/foundation/j/Jx.zip
> > > > >     \Jx\J\J Wicked Toolkit.ijs
> > > > >
> > > > >
> > > > >
> > > > > On Sat, Jun 9, 2018 at 9:23 AM, 'Bo Jacoby' via Chat <
> > > c...@jsoftware.com>
> > > > > wrote:
> > > > >
> > > > > > The Transylvanian problem, solved using ordinal fractions.
> > > > > > sane humans and insane vampires make only true statements;
> > > > > >
> > > > > > insane humans and sane vampires make only false statements.
> > > > > > This is the coding,
> > > > > > 0001 Minna is human
> > > > > >
> > > > > > 0002 Minna is vampire
> > > > > > 0010 Minna is sane
> > > > > > 0020 Minna is insane
> > > > > > 0100 Lucy is human
> > > > > > 0200 Lucy is vampire
> > > > > > 1000 Lucy is sane
> > > > > > 2000 Lucy is insane
> > > > > > These are the possibilities: 10#.>:#:i.2 8
> > > > > >
> > > > > > 1111 1112 1121 1122 1211 1212 1221 1222
> > > > > > 2111 2112 2121 2122 2211 2212 2221 2222
> > > > > > He knew that one was a vampire and one was a human, Discard 0101 and
> > > 0202
> > > > > > leaving 8 possibilities: 1112 1122 1211 1221 2112 2122 2211 2221
> > > > > > Lucy: "We are both insane" = 2020.
> > > > > > "sane humans make only true statements"
> > > > > > If Lucy is sane the statement is false. Discard 1100, leaving 6
> > > > > > possibilities: 1211 1221 2112 2122 2211 2221
> > > > > > "insane humans make only false statements". Discard 2120, leaving 5
> > > > > > possibilities: 1211 1221 2112 2211 2221
> > > > > > "insane vampires make only true statements". Discard 2210, leaving 4
> > > > > > possibilities 1211 1221 2112 2221
> > > > > > "sane vampires make only false statements". Then "We are both
> > > insane" is
> > > > > > false in any case.
> > > > > > Minna: "We are not both insane" If Minna is a sane human then Lucy 
> > > > > > is
> > > > > > insane: Discard 1011 leaving 3 possibilities 1221 2112 2221
> > > > > > If Minna is a sane vampire then contradiction. Discard 0012 leaving 
> > > > > > 2
> > > > > > possibilities: 1221 2221
> > > > > > Now we know that Minna is an insane human, and so they are not both
> > > > > > insane,
> > > > > > and so Lucy is sane. 1221.
> > > > > > Summary:
> > > > > >
> > > > > > 1221
> > > > > >
> > > > > > 0001 Minna is human
> > > > > > 0020 Minna is insane
> > > > > > 0200 Lucy is vampire
> > > > > > 1000 Lucy is sane
> > > > > >
> > > > > >
> > > > > >     Den 17:05 fredag den 8. juni 2018 skrev Don Guinn <
> > > > > dongu...@gmail.com
> > > > > > >:
> > > > > >
> > > > > >
> > > > > >  When in elementary school there was a chart showing the numbers.
> > > But the
> > > > > > zero was to the right of the nine. That confused me then. No wonder
> > > kids
> > > > > > have difficulty grasping the concept of zero.
> > > > > >
> > > > > > On Fri, Jun 8, 2018, 8:34 AM Björn Helgason <gos...@gmail.com>
> > > wrote:
> > > > > >
> > > > > > > beenary numbers
> > > > > > >
> > > > > > > https://m.phys.org/news/2018-06-scientists-bees-concept.html
> > > > > > >
> > > > > > > On Fri, 8 Jun 2018 07:40 'Bo Jacoby' via Chat, <c...@jsoftware.com
> > > >
> > > > > > wrote:
> > > > > > >
> > > > > > > > Cardinal numbers (0, 1, 2, . . .) are  including 0 (zero).
> > > > > > > > Ordinal numbers (1, 2, 3, . . .) are  starting with 1 (first).
> > > There
> > > > > is
> > > > > > > no
> > > > > > > > "zeroth".
> > > > > > > > There is arithmetic of cardinal numbers (including the J verbs +
> > > * ^
> > > > > !
> > > > > > )
> > > > > > > ,
> > > > > > > > but there is no arithmetic of ordinal numbers.
> > > > > > > > The codes of the UDC are important numerical objects, but they
> > > are
> > > > > > > neither
> > > > > > > > integers, nor decimal fractions, nor rational numbers, nor real
> > > > > > numbers,
> > > > > > > > nor complex numbers, nor quaternions, nor vectors, nor matrices,
> > > nor
> > > > > > > > functions, nor operators. They have been neglected by
> > > mathematicians.
> > > > > > > > A new kind of numbers must be considered. I dubbed them  
> > > > > > > > 'ordinal
> > > > > > > > fractions' .
> > > > > > > > A cardinal number, such as 'one', counts a set.
> > > > > > > > An ordinal number, such as 'the first', identifies an element in
> > > a
> > > > > set.
> > > > > > > > A cardinal fraction, such as 'one half', measures a part of a
> > > > > totality.
> > > > > > > > An ordinal fraction, such as 'the first half', identifies a part
> > > of a
> > > > > > > > totality.
> > > > > > > > Consider for simplicity the binary, rather than the decimal,
> > > > > notation.
> > > > > > > > one = 1 = 0001. The digit positions, right to left, indicate
> > > ones,
> > > > > > twos,
> > > > > > > > fours, and eights, and the digit values are one-digit binary
> > > cardinal
> > > > > > > > numbers, 0 and 1.
> > > > > > > > the first = 1 = 0001. This is the cardinal number corresponding
> > > to
> > > > > the
> > > > > > > > ordinal number in question.
> > > > > > > > one half = 0.1 = 0.1000. The digit positions after the binary
> > > point
> > > > > > > > indicate halfs, fourths, eights, and sixteenths, and the digit
> > > values
> > > > > > are
> > > > > > > > one-digit binary cardinal numbers, 0 and 1.
> > > > > > > > the first half = ?????
> > > > > > > > My solution to this problem is
> > > > > > > > the first half = 1 = 1000
> > > > > > > > the second half = 2 = 2000
> > > > > > > >
> > > > > > > > the first fourth = 11 = 1100
> > > > > > > >
> > > > > > > > the second fourth = 12 = 1200
> > > > > > > >
> > > > > > > > the third fourth = 21 = 2100
> > > > > > > >
> > > > > > > > the fourth fourth = 22 = 2200
> > > > > > > >
> > > > > > > > the odd fourths = 01 = 0100
> > > > > > > > the even fourths = 02 = 0200
> > > > > > > > the sixteenth sixteenth = 2222
> > > > > > > > Note that the digit positions indicate halfs, fourths, eights,
> > > and
> > > > > > > > sixteenths, and the digit values are either 1 meaning first, and
> > > 2
> > > > > > > meaning
> > > > > > > > second, or 0 meaning both. 1000 means: first half, both fourths,
> > > both
> > > > > > > > eights, both sixteenths. 'both' goes without saying, just as 0
> > > goes
> > > > > > > without
> > > > > > > > saying. 1000 = 1 = first half. That is one reason for choosing 0
> > > for
> > > > > > > > 'both'.
> > > > > > > > I did not know the words hyponymy and hypernymy. Thanks! That is
> > > just
> > > > > > > what
> > > > > > > > I need.
> > > > > > > > In logic I let 1 and 2 represent True and False. 0 means unknown
> > > or
> > > > > > > > unimportant.
> > > > > > > >
> > > > > > > > The Transylvanian problem:
> > > > > > > > 0001 Minna is human
> > > > > > > >
> > > > > > > > 0002 Minna is vampire
> > > > > > > > 0010 Minna is sane
> > > > > > > > 0020 Minna is insane
> > > > > > > > 0100 Lucy is human
> > > > > > > > 0200 Lucy is vampire
> > > > > > > > 1000 Lucy is sane
> > > > > > > > 2000 Lucy is insane
> > > > > > > > Check the 2^4 ordinal fractions from 1111 to 2222 against the
> > > data.
> > > > > (I
> > > > > > > > have not done it)
> > > > > > > > Thanks! Bo. .
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >
> > > > > > > >    Den 5:58 fredag den 8. juni 2018 skrev Donna Y <
> > > > > dy...@sympatico.ca
> > > > > > >:
> > > > > > > >
> > > > > > > >
> > > > > > > >  Can we agree on definitions
> > > > > > > >
> > > > > > > > Ordinal numbers and Cardinal numbers are Natural numbers which
> > > do no
> > > > > > > > include the number 0. The Natural numbers are well ordered.
> > > > > > > > Whole numbers are the Natural numbers and 0. 0 is the least
> > > element
> > > > > of
> > > > > > > the
> > > > > > > > Whole numbers.
> > > > > > > > Integers are Whole numbers and Negative signed Natural numbers.
> > > (-n +
> > > > > > n=
> > > > > > > > 0  Zero is not a positive or a negative integer—0 has no sign.)
> > > The
> > > > > set
> > > > > > > of
> > > > > > > > integers has no least element.
> > > > > > > > Real numbers are continuous and complete and can be rational or
> > > > > > > > irrational—rational numbers are integers and fractions,
> > > irrational
> > > > > > > numbers
> > > > > > > > cannot be expressed as a ratio of two integers.
> > > > > > > > Imaginary numbers are not real—they exist in another
> > > dimension—root
> > > > > > > > negative 1 or i, complex numbers have real and imaginary
> > > components.
> > > > > > > >
> > > > > > > > Tables are two dimensional arrays.
> > > > > > > >
> > > > > > > > The basic structure of UDC is hierarchy but it could be viewed 
> > > > > > > > in
> > > > > other
> > > > > > > > ways—as you said yourself.
> > > > > > > >
> > > > > > > > Are you using tables where Rows are records and Columns are
> > > > > attributes?
> > > > > > > Is
> > > > > > > > there a primary key?
> > > > > > > >
> > > > > > > > I am not sure where your Ordinal Fraction comes in but a 
> > > > > > > > computer
> > > > > > > > application of UDC would need full integration of information
> > > > > retrieval
> > > > > > > > (IR) features into a database management system (DBMS).
> > > > > > > >
> > > > > > > > Right truncation specifies hypernomy (is a—as in number theory
> > > is a
> > > > > > > subset
> > > > > > > > of mathematics)—I copied this table but from my view forms of
> > > higher
> > > > > > > degree
> > > > > > > > is not a subset of diophantine equations.
> > > > > > > >
> > > > > > > > Table 1:
> > > > > > > >
> > > > > > > > 5: mathematics and natural sciences
> > > > > > > > 51: mathematics
> > > > > > > > 511: number theory
> > > > > > > > 511.5: diophantine equations
> > > > > > > > 511.57: forms of higher degree
> > > > > > > >
> > > > > > > > What is the precise reason you chose to use 0 as a wild 
> > > > > > > > card?—why
> > > > > not *
> > > > > > > or
> > > > > > > > # or & or … ? What advantages are derived by using 0?  For
> > > example
> > > > > when
> > > > > > > you
> > > > > > > > use boolean logic the 0 and 1 can represent False and True and
> > > then
> > > > > the
> > > > > > > > result vector of 0 and 1 can be used for selection.
> > > > > > > >
> > > > > > > > hat does this even mean?
> > > > > > > >
> > > > > > > > > For example: 0=0 and 0>1 and 1<0 and 10<>01 and 1><2. (meaning
> > > that
> > > > > > the
> > > > > > > > whole is equal to the whole, and the whole comprises the first
> > > part,
> > > > > > and
> > > > > > > > the first part is part of the whole, and the first half is
> > > compatible
> > > > > > > with
> > > > > > > > the odd fourths, and the first part is disjoint with the second
> > > > > part).
> > > > > > > > > The notation for ordinal fractions makes ordinal fraction
> > > > > arithmetic
> > > > > > > > easy, just as the notation for cardinal numbers makes cardinal
> > > number
> > > > > > > > arithmetic easy.
> > > > > > > > > Keep asking!
> > > > > > > >
> > > > > > > >
> > > > > > > > Maybe you can show how Ordinal Fractions can be applied to the
> > > > > problem
> > > > > > > > below:
> > > > > > > >
> > > > > > > > PUZZLE BREAK
> > > > > > > >
> > > > > > > > Inspector Craig Visits Transylvania
> > > > > > > > Inspector Craig of Scotland Yard was called to Transylvania to
> > > solve
> > > > > > some
> > > > > > > > cases of vampirism. Arriving there, he found the country
> > > inhabited
> > > > > both
> > > > > > > by
> > > > > > > > vampires and humans. Vampires always lie and humans always tell
> > > the
> > > > > > > truth.
> > > > > > > > However, half the inhabitants, both human and vampire, are
> > > insane and
> > > > > > > > totally deluded in their beliefs: all true propositions they
> > > believe
> > > > > > > false,
> > > > > > > > and all false propositions they believe true.
> > > > > > > > The other half of the inhabitants are completely sane: all true
> > > > > > > statements
> > > > > > > > they know to be true, and all false statements they know to be
> > > false.
> > > > > > > Thus
> > > > > > > > sane humans and insane vampires make only true statements; 
> > > > > > > > insane
> > > > > > humans
> > > > > > > > and sane vampires make only false statements.
> > > > > > > > Inspector Craig met two sisters, Lucy and Minna. He knew that 
> > > > > > > > one
> > > > > was a
> > > > > > > > vampire and one was a human, but knew nothing about the sanity 
> > > > > > > > of
> > > > > > either.
> > > > > > > > Here is the investigation:
> > > > > > > > Craig (to Lucy): Tell me about yourselves.
> > > > > > > > Lucy: We are both insane.
> > > > > > > > Craig (to Minna): Is that true?
> > > > > > > > Minna: Of course not!
> > > > > > > > From this, Craig was able to prove which of the sisters was the
> > > > > > vampire.
> > > > > > > > Which one was it?
> > > > > > > > — From Logician Raymond Smullyan
> > > > > > > >
> > > > > > > >
> > > > > > > > Donna Y
> > > > > > > > dy...@sympatico.ca
> > > > > > > >
> > > > > > > >
> > > > > > > > > On Jun 7, 2018, at 5:55 PM, 'Bo Jacoby' via Chat <
> > > > > c...@jsoftware.com
> > > > > > >
> > > > > > > > wrote:
> > > > > > > > >
> > > > > > > > >
> > > > > > > > > "You do not show how to access particular rows or columns or
> > > > > elements
> > > > > > > > from a table".
> > > > > > > > > The table, and the table name, is addressed by 00.
> > > > > > > > > The left column, and the left column header, is addressed by
> > > 01.
> > > > > > > > > The right column, and the right column header, is addressed by
> > > 02.
> > > > > > > > > The upper row, and the upper row header, is addressed by 10.
> > > > > > > > > The upper left table entry, and its data content, is addressed
> > > by
> > > > > 11.
> > > > > > > > > The upper right table entry, and its data content, is
> > > addressed by
> > > > > > 12.
> > > > > > > > > The lower row, and the lower row header, is addressed by 20.
> > > > > > > > > The lower left table entry, and its data content, is addressed
> > > by
> > > > > 21.
> > > > > > > > > The lower right table entry, and its data content, is
> > > addressed by
> > > > > > 22.
> > > > > > > > >
> > > > > > > > > "without knowing the number of rows or columns."
> > > > > > > > > In the example there are two rows and two columns.
> > > > > > > > > If you need a third row, call it 30.
> > > > > > > > >
> > > > > > > > > "Why not the concept of arrays with an index?"
> > > > > > > > > Arrays may have different shapes. Any ordinal fraction has the
> > > > > shape
> > > > > > > > (_$9).
> > > > > > > > > Arrays have elements. Ordinal fractions don't.
> > > > > > > > >
> > > > > > > > > Only array elements contains data. Any ordinal fraction may
> > > contain
> > > > > > > data.
> > > > > > > > >
> > > > > > > > > Arrays may have subarrays. Any ordinal fraction has 
> > > > > > > > > subordinate
> > > > > > ordinal
> > > > > > > > fractions.
> > > > > > > > > Arrays and atoms have names. Ordinal fractions don't.
> > > > > > > > >
> > > > > > > > > "the set of Natural numbers begin with 1 yet we use base 10
> > > > > > > > representation that uses 0."
> > > > > > > > >
> > > > > > > > > Cardinal numbers and ordinal fractions have similarities and
> > > > > > > > differences.
> > > > > > > > > Cardinal number 0 (meaning "nothing") is not the same thing as
> > > > > > ordinal
> > > > > > > > fraction 0 (meaning "everything").
> > > > > > > > >
> > > > > > > > > Cardinal number 1 (meaning "one") is not the same thing as
> > > ordinal
> > > > > > > > fraction 1 (meaning "first part").
> > > > > > > > >
> > > > > > > > > Using "0" for wild card character does not get along with
> > > using "0"
> > > > > > for
> > > > > > > > counting to ten.
> > > > > > > > > A cardinal number is represented by a right-justified sequence
> > > of
> > > > > > > digits
> > > > > > > > with a finite number of nonzero digits. The cardinal number 1
> > > may be
> > > > > > > > written 00001.
> > > > > > > > >
> > > > > > > > > An ordinal fraction is represented by a left-justified
> > > sequence of
> > > > > > > > digits with a finite number of nonzero digits. The ordinal
> > > fraction 1
> > > > > > may
> > > > > > > > be written 10000.
> > > > > > > > >
> > > > > > > > > "However this was not an easy system in which to do arithmetic
> > > so I
> > > > > > > > cannot see how your base 9 system could be either."
> > > > > > > > > Cardinal numbers, A and B, are ordered such that either A=B or
> > > A<B
> > > > > or
> > > > > > > > A>B. For example: 0=0 and 0<1 and 1>0 (meaning "zero is equal to
> > > > > zero"
> > > > > > ,
> > > > > > > > and "zero is fewer than one", and "one is more than zero").
> > > > > > > > >
> > > > > > > > > Ordinal fractions, A and B, are ordered such that either A=B
> > > or A<B
> > > > > > or
> > > > > > > > A>B or A<>B or A><B. For example: 0=0 and 0>1 and 1<0 and 10<>01
> > > and
> > > > > > > 1><2.
> > > > > > > > (meaning that the whole is equal to the whole, and the whole
> > > > > comprises
> > > > > > > the
> > > > > > > > first part, and the first part is part of the whole, and the
> > > first
> > > > > half
> > > > > > > is
> > > > > > > > compatible with the odd fourths, and the first part is disjoint
> > > with
> > > > > > the
> > > > > > > > second part).
> > > > > > > > > The notation for ordinal fractions makes ordinal fraction
> > > > > arithmetic
> > > > > > > > easy, just as the notation for cardinal numbers makes cardinal
> > > number
> > > > > > > > arithmetic easy.
> > > > > > > > > Keep asking!
> > > > > > > > > Bo.
> > >
> > >
> > ----------------------------------------------------------------------
> > For information about J forums see http://www.jsoftware.com/forums.htm
----------------------------------------------------------------------
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