John: "...what is it about logic that leads to more great
technical innovations than other games."
Aren't those fun questions? I look at the logic operators as
a starting point. As operators, they have two inputs, A and B, which invoke 16
possible operators. The IMPLIES operator seems to be the most interesting one. It
typically interprets A to be the “before” state and B to be the “after”
state. And that’s just what we see in nature: related spatial states that
have lifetime; e.g. “the orange was on the table” and “the
orange is now on the floor”. Each state (or observation) is a static or
unchanging perception that lasts for a period of time. They are lines in
spacetime where each point on the line is the “same” as the others –
if you like that analogy. It’s more of a mental picture than actual
physics. It allows one person to say “lion!” and another to recognize
it. We all objectively see the same spatial static boundaries because we’re
mostly all copies of the same stuff.
As soon as some point changes in some significant way, we call it the
end of the first state and the beginning of the second state. We observe that
these line segments are often and predictably close to each other. For example,
one line segment might be two balls rolling toward each other. The segment
represents the “the rolling toward each other” and not any one ball
rolling. A second segment (or observation) is the two colliding. A third is a
big crashing sound.
Each of the three segments have the same spatial values and are
contiguous in time. That is, they all were observed “on the table” one
temporally after the other. So we use propositions to model the line segments
and IMPLIES to join them temporally or group them. The “composing”
operators (AND, OR, XOR, ...) are used to create complex propositions from
simpler ones. They build the statics. IMPLIES builds the dynamics. Together, we
describe observations in spacetime by noticing (1) where things do not change; sometimes
called statics, classes, noun phrases, or symmetries; and (2) where things do
change; sometimes called the dynamics, objects, or verb phrases.
So logic is a formal system (having no ambiguities) that can be functional
composed (the results of an operator is a proposition) to convey one person’s
observations and rules to another person in a manner that convinces the first
person that the second person understood.
When a person understands his or her own observations, or when people
understand each other’s observations, great technical innovations just
have to happen. It’s economics! A technical innovation is really judged
by its ability to manipulate nature to make lots of people happy. This means
understanding nature by understanding one’s observations (or drawing upon
historical observations of others); by understanding other people’s
problems and desires via statistics, marketing trends, and polls; and by
understanding the constraints of producing and delivering the innovation to
these customers. Logic does this most efficiently by eliminating contradiction
and ambiguity early in the process; hence it’s more efficient and faster
than other games in the context of technical innovations.
My thoughts, Rob
-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On Behalf Of
John Kennison
Sent: Monday, April 27, 2009 7:15 PM
To:
Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematicsin theNatural
Sciences
Robert:
As you say, logic can be viewed as a game, like chess. You also say
that "More great technical innovations result from playing the game of
logic than playing these other games." The question then is what is it
about logic that leads to more great technical innovations than other games.
--John
________________________________________
From: [hidden email] [[hidden email]] On Behalf
Of Robert Howard [[hidden email]]
Sent: Monday, April 27, 2009 2:13 PM
To: '
Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics
in theNatural Sciences
John: Why is logic valid?
For the same reason the rules of chess are valid: by definition. Its
validity is presupposed. If you don't like chess, don't play. If you do
then
you have to play by the agreed rules. Else don't call it chess (or
logic).
Make a new name for your game.
In logic, one begins with a rule that a proposition has exactly one of
two
values: true or false. Other games, like fuzzy logic, have additional
"maybe" values, but we use the adjective "fuzzy" to
distinguish these games
(or rule sets). Other rules are added to define ways to relate (or
compose)
propositions in the form of conjunctions, disjunctions, etc; to build
up
structures. All players agree to the rules and knowledge and science
progress. Some people don't like these games, so they don't play. Some
people play badly and aren't much fun. Some make mistakes (called
fallacies)
that are hard to see by other players. Some prefer other rules, like
"the
highest authority is always right" or "there is no truth;
only love".
More great technical innovations result from playing the game of logic
than
playing these other games.
John: Why is it useful to put together long strings of logical
implications?
This is probably a result of trivial observation; nature puts together
long
strings of related events of cause and effects; e.g. chemical reactions
and
planetary motions. We are merely recording what we see in the formal
language of cause and effect, namely logic. In this case, logic is more
of a
historian's tool.
--Rob Howard
-----Original Message-----
From: [hidden email] [mailto:[hidden email]] On
Behalf
Of John Kennison
Sent: Monday, April 27, 2009 5:15 AM
To: ForwNThompson; [hidden email]
Cc: Sean Moody
Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in
theNatural Sciences
Nick et al,
This is a great question, with, I think, two parts. The first
part is why
is logic valid. I am almost certainly a platonist or worse on this
point
--it's validity simply seems to be obvious. Can the proposition that
logic
is valid be supported by any argument that doesn't implicitly use
logic?
(Okay, even "implicitly" assumes logic). The argument that we
evolved to be
convinced by logical implications because it is useful for survival
suggests
that logic is, at least, approximately valid, which is a lot less of a
conclusion than what I would want, and which doesn't explain why logic
works
in modern physics.
The other part of the original question is, even if we grant that logic
is
valid (or at least approximately valid) why is it useful to put
together
long strings of logical implications? Believing that logical
implications
are trivially true, I wonder how can long chains of such implications
be
anything but trivial. (And if we believe that logic is at best
approximately
true, wouldn't long chains of implications stop being good
approximations if
each link in the chain is a little inaccurate.)
Perhaps Physics somehow restricts itself to a domain where logic works
very
well. And maybe things like consciousness are simply outside that
domain
(but I hope not).
I wonder if there is there a domain where logic is a useful
approximation,
but long chains of implications are not useful? Perhaps social
analysis?
Perhaps philosophy? Perhaps the humanities? Nick, and others,--I'd be
curious about what you think on this issue.
---John
________________________________________
From: Nicholas Thompson [
Sent: Sunday, April 26, 2009 1:40 PM
To: [hidden email]
Cc: John Kennison; Sean Moody
Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in
theNatural Sciences
Owen, et al,
Well, isn't this part of the broader mystery of why logic should get
you
anywhere in the study of nature?
Isn't logic just a language trick?
Why should nature give a fig for the tricks we play with our words?
This is all reminding me, for some reason, of the "discovery"
of the fact
that the differential of the integral is just the original
function. There
seem to be two sorts of "discovery" in our discourse:
One is the discovery
of something in nature that we did not already know. The other is
the
discovery of a new implication in what we have already said that we did
not
anticipate when we said it. I can see why mathematics can help
with the
latter sort of "discovery", but have no idea why it should
help with the
former.
In the emergence literature appears the endearing phrase "natural
reverence". The early philosophical emergentists believed
that one had to
accept emergent properties with "natural reverence," since
such properties
could not be reduced to the properties of their parts. I am
deeply
ambivalent about natural reverence: one the one hand, I believe
that there
is no point in being a scientist if you are not prepared to experience
some
natural reverence. On the other hand, I also believe that natural
reverence
is the enemy of discovery. Perhaps "natural reverence"
is a fleeting
pleasure one gets before one gets down to the dirty business of
figuring out
how things work: too little of it and one would never be inspired; too
much
of it, and one would never be curious.
Nick
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
http://home.earthlink.net/~nickthompson/naturaldesigns/
----- Original Message -----
From: Steve Smith<mailto:[hidden email]>
To: The Friday Morning Applied Complexity Coffee
Group<mailto:[hidden email]>
Sent: 4/26/2009 10:17:16 AM
Subject: Re: [FRIAM] The Unreasonable Effectiveness of Mathematics in
theNatural Sciences
Well said/observed David, I too am a Lakoff/Johnson/Nunez fan in
this
matter.
While I am quite enamored of mathematics and it's fortuitous
application to
all sorts of phenomenology, Physics being somehow the most
"pure" in an
ideological sense, I've always been suspicious of the conclusion that
"the
Universe *is* Mathematics".
This discussion also begs the age-old question of whether we are
"inventing"
or "discovering" mathematics. Similarly, it revisits the
question of whether
discoveries in mathematics portend discoveries in Physics (or other,
"messier" phenomenological observations).
- Steve
Prof David West wrote:
I'm completely of Tegmark's ilk:
I assume that means you would also adhere to the sentiment attributed
to
Einstein:
"How can it be that mathematics, being
after all a product of human
thought which is independent of experience, is
so admirably
appropriate to the objects of
reality?" Which contains the
fallacy, "independent of
experience."
Thought - and mathematics! - is but a refined metaphor of experience.
(following Lakoff)
davew
A different response, advocated by Physicist Max Tegmark
(2007), is
that physics is so successfully described by mathematics because the
physical world is completely mathematical, isomorphic to a
mathematical structure, and that we are simply uncovering this bit by
bit. In this interpretation, the various approximations that
constitute our current physics theories are successful because simple
mathematical structures can provide good approximations of certain
aspects of more complex mathematical structures. In other words, our
successful theories are not mathematics approximating physics, but
mathematics approximating mathematics.
-- Owen
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Meets Fridays 9a-11:30 at cafe at
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