On 4/25/2014 12:01 PM, John F Sowa
It may be that we will eventually be able to
prove this. This will have to wait until we have a better grasp on
the science behind meta-grammars. It seems that these discussions
entail the need for human-like memories that record state
information. The professionals doing the discussions have similar
understanding of the foundations of their field. For example, the
discussion here on axioms should take place with one eye on
Thomas' Kuhn's view that all science comes down, as does law, to
"the reasonable man" argument. We must be able to prove to another
that our axiom is reasonable to another who can then declare that
it is a foregone conclusion. It is my observation that axioms
differ from discipline to discipline. As we know, surveyors do not
have the same axioms as cosmologists.
Kingsley and John B,
But there have been some people who claimed that you need a distinct
URI for every sense of every word.
All we can do is provide unique identifiers that denote entities
in a given world view (or situation)...
Basically, as our world view expands we discover new insights etc.
Yes. The world is a continuum. We can name some discrete points, but
we can't describe a continuum with any set of discrete identifiers.
Some insights can be described in words, but there are too many
subtle variations -- uncountably many.
Mathematicians can still read any equation over the phone to another
mathematician as a sentence in whatever NL they share.
Not just mathematicians, this is true in every profession. I am not
sure how to prove that...
There is no proof, but there is a simple explanation. In every field,
the practitioners name the things and methods they use and produce.
The novices learn and use the same words and syntax.
Agreed, and I view sketches and drawings as
another type of shorthand or markup language. And here I prefer
the definition of language and linguistics as the science that
links forms of speech to ideas. Without both of these parts we
really don't have language. One of my personal concerns is that
the use of markup languages is extending beyond internal
representations. We should always have translators to interface to
markup languages. Without this additional level of abstraction we
will not make progress toward more abstract machine reasoning. And
for all of this, we can expect to see future systems that store
much more information and knowledge than the stingy algorithms we
Two professionals discussing their fields seem to do just fine while
waiting in an airport lounge. Sure, one of them may say, "you'll need
to draw me a picture". That seems to be a call to use a shorthand
notation in the interests of time.
Symbols like '+' are abbreviations for the words or phrases. Some
diagrams are designed to be translated to and from discrete symbols.
But no words can describe a complex image -- such as a human face.
I agree, but part of an engaging discussion is
in determining where in the lattice of abstract concepts the other
person is "pointing". The "conjuring" is done in an attempt to see
if there is agreement on the specific level of abstraction that is
common in the discussion. Only after there is agreement on the
"locale" can any discussion about the specification, meaning or
extension of an entity take place.
Given enough time we humans can and must be able to conjure up an
appropriate image to get an idea across if both are professionals
in the same discipline.
There's a big difference between "conjuring up" and specifying.
Yes, I agree. My cooking is substantially
Southern because that is what I inherited from my family. I would
imagine that the same is true of practice in professions. As in
medicine's "the Science of Medicine" (SOM) and "the Art of
Medicine", we will increasingly become aware for this dichotomy in
other fields. Again, this is an under-discussed aspect of most
Just consider any profession from cooking to music to nuclear physics.
Two cooks can follow the same recipe and get wildly different results.
Jascha Heifetz and the kid next door can play the same notes, but
there's a world of difference in the results.
Gamow is a great storyteller. I wish his book
"One, Two, Three, Infinity..." got more exposure, it is one of the
best works in popular mathematics. It also has one of the best
collections of anecdotes about lightning calculators I have ever
read. I believe he also points out that Ampere and Gauss were both
lightning calculators until they developed their critical thinking
skills. He suggests there is a trade-off between these skills in
the brain's repertoire of skills.
In physics, experimenters have to deal with the full continuum of
pesky details that theoreticians ignore. George Gamow told the
following anecdote about Wolfgang Pauli:
Concord, MA USA
Pauli was such a good theoretical physicist that something usually
broke in the lab whenever he merely stepped across the threshold.
A mysterious event that did not seem at first to be connected with
Pauli presence once occurred in Professor Franck's laboratory in
Early one afternoon, without apparent cause, a complicated apparatus
for the study of atomic phenomena collapsed. Franck wrote humorously
about this to Pauli at his Zurich address and, after some delay,
received an answer in an envelope with a Danish stamp. Pauli wrote
that he had gone to visit Niels Bohr, and at the time of the mishap
in Franck's laboratory his train was stopped for a few minutes at
the Göttingen railroad station.
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