Healthy people : These people are essentially holistic. They create unity within themselves. For example the age-old oppositions between heart and head, reason and instinct, mental and emotional, would seem to disappear in healthy people, and these two aspects become synergic - which simply means they contribute to each other - rather than antagonistic.
" The dichotomy between selfishness and unselfishness disappears altogether ... because in principle every act is both selfish and unselfish. Our subjects are simultaneously very spiritual and sensual. ... Duty cannot be contrasted with pleasure, nor work with play, when duty is pleasure, when work is play, and the person doing his duty and being virtuous is simultaneously seeking his pleasure and being happy."

The higher and lower aspects of these people are not in opposition with themselves - they are in agreement . . " and a thousand serious philosophical dilemmas are discovered to have .. no horns at all. If the war between (for example) the sexes turns out to be no war at all in mature people, but only a sign of crippling and stunting of growth, who then would wish to choose sides ? "

Maslow concludes: ".. healthy people are so different from average people, not only in degree but in kind as well, that they generate two very different kinds of psychology. It becomes more and more clear that the study of crippled, stunted, immature and unhealthy specimens can yield only a cripple psychology (*) and a cripple philosophy. The study of self-actualizing people (**) must be the basis for a more universal science of psychology."

(*) Freud vs. (**) Jung

Forum: sci.math
Subj : Re: 1/0
 Date: Thu, 11 Jan 2001 19:44:48 GMT
 From: Nico Benschop

"David W. Cantrell" wrote:
> In article <3A5DCAE5.D819314D@gte.net>, cnelson9@gte.net wrote:
> > "David W. Cantrell" wrote:
> > > In article <3A5B5CE6.C367383F@gte.net>, cnelson9@gte.net wrote:
> > > > Danny Kelly wrote:
> > > > > [...]
> > > > > ---My question is, WHY IS THERE NOT STUDY INTO A NUMBER SYSTEM
> > > > > THAT HAS AS AN ELEMENT THE NUMBER 1/0 ? -- Yours truly, Sam Kelly
> > > >
> > > > There is. See George Boole's book with the shortened title
> > > > "The Laws of Thought", 1861. --  Cliff Nelson
> > >
> > > No. This reference is surely a red herring!
> > > Boole's innovation dealt with logical, as opposed to numerical,
> > > values. In Boolean algebra, 1+1 = 1, for example.
> > > If Boole gives meaning to the expression 1/0 in his system of logic,
> > > surely 1/0 can not reasonably be descibed as "a number which is an
> > > element of the system"! (Please correct me if I am wrong.)
> > > I would be surprised if Boole does anything significant with 1/0 as
> > > an expression involving the numerical values 0 and 1, as opposed to
> > > an expression involving the logical values 0 and 1. (Again, please
> > > do correct me if I am wrong.)
> > > At Boole's time, I believe it was fairly common to regard 1/0,
> > > understood as a numerical expression, as being infinity. Boole may
> > > well have shared this view, but I'd be somewhat surprised if he
> > > gave any argument to support it in the cited text. -- David Cantrell
> > >
> > See "The Laws of Thought", 1854. -- Cliff Nelson
>
> I don't intend to do such since it would almost certainly be a waste
> of time. Unless what I said previously was incorrect (in which case,
> I would surely appreciate being corrected), let me reiterate:
> Red herring! --  David Cantrell

G.Boole: "The Laws of Thought" 1854, Dover publications, pocket edition.

Re 1/0 it certainly will be useless, it's not mentioned there by
Boole, who's binary logic is there introduced as an idempotent form of
arithmetic: x.x = x (hence x=0 or x=1), with a commutaitive calculus
x.y = y.x of binary properties x,y of objects
-- see my reply to Cliff Nelson.

On the other hand, reading Boole's treatise is definitely NOT a waste of
time. I find it still the best text on Boolean Algebra that I've seen!
The set-theoretic angle, developed much later in the 19-th century,
can be very confusing - especially if infinite sets are concerned.

The book has two parts: the first is on his arithmethmetic model (mod 2)
of Aristotelian logic (as used by Spinoza and Clark for their 'proof'
of God's existence, which Boole showed to be circular - necessarily so)

The second part treats statistics, nota bene!  Similar to Shannon's
concern with logic (structure) in his 1938 paper on Boolean algebra
as model for combinational circuits, and his statistical/entropy-based
information theory 10 years later. That balance of logic & chance
is a sign of mature science (at least to me;-)

-- NB -- http://piazza.iae.nl/users/benschop
         http://piazza.iae.nl/users/benschop/work.htm
   +---------------------------------------------------------+
   | Math = the Art of separating Necessity from Coincidence |
   | Life = making the Best of Necessity, using Coincidence  |
   |    " van de Nood een Deugd maken " ( = Engineering )    |
   +---------------------------------------------------------+

Subject:  Re: Proof that the math world is sick    (or: BALANCE
   Date:  Tue, 24 Jul 2001                           of Idea's
   From:  Nico Benschop                             and Precision)
    Org:  Digital Research
Newsgrp:  sci.math
----------------------------
Randy Poe wrote:
>
> James Harris wrote:
> > And this guy's post is a reminder of why you
> > should  NEVER bring a mathematician to a party.       ...[*]
> > They'll annoy everyone by forcing you to spell out 
> > every little petty thing in infinite detail.
>
> A mathematician, an engineer, and a physicist are 
> on a hill in Scotland looking at a herd of sheep.
> Engineer says: The sheep in Scotland are black.
> Physicist : There are at least 20 black sheep in Scotland.
> Mathematician: There are at least 20 sheep in Scotland
>                  which are black on AT LEAST ONE SIDE.  ...[*]
>
> Mathematics is precise, James. You can't be vague       ...[1]
> and say you're doing mathematics. No way around that.   - Randy

Re[*]: You see, they can even be funny at a party, James.

Re[1]: That is necessary, but NOT sufficient, for math ;-)
       The "precise part" comes AFTER the "idea part",
which latter is a bit more difficult to define precisely.
- - - Best is, if there is a BALANCE between the two. - - -

Let me compare it, not with sheep but with a TREE:
  Normally we see the trunk and the branches
        (with or without leaves, depending on the season) ...
  But we don't (normally) see the ROOTS, which are underground
           and (normally) have a shape similar to the branches.
  They feed the tree 'from the bottom' -- while the tree is fed
  'from the top' by the leaves (foto-synthesis, CO2, &c).

Legend:
  The Roots are the feeding ideas (=unseen intuition),
  the Trunk is the 'linear_sequence' proof
         (=concentrating & bringing-up distributed experience), and
  the Branches = influence of that proof & method on the rest of math
         (= producing oxygen for the environment, &c).
[ that's why in the East the Lotus is such a powerfull symbol:
  rooted in the Earth (under water) - with long stem
  (also under water) - and only the leaves & flower are seen,
  connecting to the air/sky/spirit. ]

Only the BALANCE of these three parts helps math to progress.

  The 'crank-bashing' by some mathematicians in this NG regards only
one part (usually the middle = trunk = form = linear & exact proof),
but seldom the roots (=intuition). ... Mind you, that middle part is
(very;-) necessary, but absolutely lost without the roots & leaves.

-- NB -- http://home.iae.nl/users/benschop/sgrp-flt.htm
(re: JSH's open letter to Wiles, June 1998: with good intuition, but...)