The so simple natural numbers only exist within perhaps infinitely complex
individualized awarenesses that co-create within a single infinite unity -- so
naturally infinite patterns of nested recursive fractals emerge.
The natural numbers comprise a discrete infinity, which reveal a base for
I looked for it in the library, it is a huge and heavy book,
about 1034 pages. Impressive work, which covers indeed
most of mathematics as we know it. There is something
for everyone in this book, for Physicists for example the parts
about Vertex Operator Algebras and Lie Theory.
-J.
-
Good questions. You are right, a theorem
is a statement that some domain is
structured in a particular way.
The Princeton companion to mathematics
lists 35 major theorems, from the ABC
conjecture and the Atiyah-Singer Index
Theorem to the Weil Conjectures.
Theorems are based on connections in
Another reason for hidden structures is our
limited capacity for instant in-depth analysis.
They only appear to be hidden for us.
Look at this XKCD Cartoon: http://xkcd.com/731/
There seems to be nothing but flat empty
water as far as the eye can see, but there
is a large number of complex
There are theorems because systems have relationships as well as
elements, from which arise emergent properties.
Grant
Russ Abbott wrote:
I have what probably seems like a strange question: why are there
theorems? A theorem is essentially a statement to the effect that
some domain is
Russ, I apologize for being so terse. Let me try again. Here is my take
on your question...
As we know, systems are more than just components, or elements. A system
must also have relationships among its elements before they it is worthy
being called a system.
But, when you take these
BTW: there is a digital pre-print version that has some of the
publisher's marginal comments. Let me know if you'd like to have a
copy.
-- Owen
On Apr 25, 2010, at 2:23 AM, Jochen Fromm wrote:
I looked for it in the library, it is a huge and heavy book,
about 1034 pages. Impressive
Russ -
Another great question.
While Doug and I have an awful lot in common, this is probably where we
most notably diverge. You ask "why", he asks "why ask why", I ask
"why ask why ask why". ("Who dat who say who dat?" might ring a bell
for some of the other old timers here).
I don't
Grant Holland wrote circa 04/25/2010 05:42 AM:
Thus the need for theorems arises due to a system having relationships
among its components. And we haven't even mentioned emergent properties yet!
But I think Nick's answer is relevant to this point, as well. Even in a
seemingly a priori
Steve Smith wrote:
You ask why, he asks why ask why, I ask why ask why ask why.
A recursive function definition requires a base case for escape. Doug
provides that case.
Marcus
FRIAM Applied Complexity Group listserv
Meets
string why()
{
while (!why())
{
why();
}
}
(string theory search)
On Sun, Apr 25, 2010 at 10:53 AM, Marcus G. Daniels mar...@snoutfarm.comwrote:
Steve Smith wrote:
You ask why, he asks why ask why, I ask why ask why ask why.
A recursive function definition requires a base
I agree that the key has to do with relations -- and that this is related to
emergence.
Individual carbon atoms are arguably fairly simple. But carbon atoms in
relationship either with each other or with other things form extraordinary
structures. In some sense those structures were hidden from
Russ,
Bypassing all the other replies, I find this question very interesting. When
faced with questions like this I usually give an answer, am told it is not
satisfactory, give another answer, am told it is not satisfactory, etc. Then at
some point I ask the questioner to give me examples of the
The philosopher Garfinkel was fond of citing Willy Sutton on questions like
this:
REPORTER: Mr Sutton, why do you rob banks?
WILLIE: 'Cuz that's where the money is.
Without a theorem, it's impossible to to know what the question is.
Nick
Nicholas S. Thompson
Emeritus Professor of
Individual carbon atoms are arguably fairly simple.
The word *arguably* being key, I believe.
To wit:
Carbon:
*Carbon* is the chemical
elementhttp://en.wikipedia.org/wiki/Chemical_elementwith
symbol http://en.wikipedia.org/wiki/Chemical_symbol *C* and atomic
glen e. p. ropella wrote:
But I think Nick's answer is relevant to this point, as well. Even in a
seemingly a priori discrete system like that of the natural numbers,
components are psychologically induced, not necessarily embedded in
the system.
There is (actually) only *one* (closed)
In answer to Eric and lrudolph, the answer I'm looking for is not related to
epistemology. It is related to the domains to which mathematical thinking is
successfully applied, where successfully means something like produces
interesting' theorems. (Please don't quibble with me about what
If I start from the Wikipedia definition of theorem -- *In
mathematics, a theorem is a statement which has been proved on the basis of
previously established statements, such as other theorems, and previously
accepted statements, such as axioms.* I end up looking at a house of cards
which will
On Apr 24, 2010, at 11:26 PM, Nicholas Thompson wrote:
Because of the fallacy of induction?
Do you mean this induction:
http://en.wikipedia.org/wiki/Mathematical_induction#Description
I.e. are you interested in proofs over the positive integers?
-- Owen
On 25 Apr 2010 at 10:51, Russ Abbott wrote:
In answer to Eric and lrudolph, the answer I'm looking for is not related to
epistemology. It is related to the domains to which mathematical thinking is
successfully applied, where successfully means something like produces
interesting' theorems.
So, the question is not about people, nor the way people do things. But it is
something about where people have been successful, with the recognition that
success in mathematics typically involves theorems.
Would it be fair to represent your question as:
What is it about the way mathematical
No. MATHEMATICAL induction is actually serial DEduction.
I was talking about plain old vanilla philosophical induction: The fallacy is
that without deduction, induction can't get you anywhere, and that people who
think they are getting somewhere through induction alone are so caught up in
Dear Lee,
YOU ASKED: Did you read the article by Lorenz?
YOU COMPLAINED: (I wish *someone* would;
But did you actually SEND the link to the Lorenz article? It wasnt
attached to the message I got.
N
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University
(expressions of ignorance to follow:)
I wonder in all this whether there is anything interesting to be said
by looking at the relation of syntax to semantics in mathematics,
perhaps not in the sense of applying language, but rather in the
sense of recognizing that mathematics shares syntactic
Too many interesting comments to follow up. But to Lee, Friam probably
doesn't forward attachments. I didn't get the article with your earlier
message either. There is an entry in the Stanford Encyclopedia of
Philosophy on Evolutionary
Fw: [NDhighlights] #3872, Saturday - April 24, 2010: single infinite unity
sustains and is all in my awareness -- the finger that points at the Moon
is not the Moon: Rich Murray 2010.04.25
Many ways of pointing towards The Kingdom of Heaven is within you..
A Course in Miracles clarifies,
Russ,
The natural numbers can be described by listing a few axioms for the notion of
successor (or the next whole number after this one or the operation of
adding one) so, in some sense it is a very simple system. Yet all of
mathematics can, in some sense be coded into statements bout the
27 matches
Mail list logo
