two books

[Prof David West]

I just finished reading What is Real? by Adam Becker. A straightforward discussion of Quantum Physics and the "Copenhagen Interpretation," and the arguments surrounding it. it offers an indirect but scathing study of how science is really done and how far the practice of science is from the ideal of a "scientific method." Also an interesting discussion of the relationship between 'science' and 'phi8losophy'. Might be of interest to several FRIAMers.

Starting to read Roger Penrose's, The Road to Reality: a complete guide tot he laws of the universe. I would really like some advice / comments from the mathematicians in the community as to the value of the book and the likely hood that I might gain sufficient understanding of manifolds, symmetry groups, etc. etc. to understand some of the conversations on the list and at the mother church.

dave west

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Meets Fridays 9a-11:30 at cafe at St. John's College
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[Nick Thompson]

Hi, Dave,

Missed this note the first time.  Frank and Hywel had a go at this a couple
of years ago, and I bought the book and tried to join them.  Whew!  It was
at that point I gave up on the notion that I could read anything if I tried
hard enough.  Hywel has since died, but I think there was at least one other
person involved, who, with Frank, might be able to give you some guidance.

Nick

Nicholas S. Thompson
Emeritus Professor of Psychology and Biology
Clark University
http://home.earthlink.net/~nickthompson/naturaldesigns/


-----Original Message-----
From: Friam [mailto:[hidden email]] On Behalf Of Prof David West
Sent: Wednesday, November 28, 2018 10:26 AM
To: [hidden email]
Subject: [FRIAM] two books

I just finished reading What is Real? by Adam Becker. A straightforward
discussion of Quantum Physics and the "Copenhagen Interpretation," and the
arguments surrounding it. it offers an indirect but scathing study of how
science is really done and how far the practice of science is from the ideal
of a "scientific method." Also an interesting discussion of the relationship
between 'science' and 'phi8losophy'. Might be of interest to several
FRIAMers.

Starting to read Roger Penrose's, The Road to Reality: a complete guide tot
he laws of the universe. I would really like some advice / comments from the
mathematicians in the community as to the value of the book and the likely
hood that I might gain sufficient understanding of manifolds, symmetry
groups, etc. etc. to understand some of the conversations on the list and at
the mother church.

dave west

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe
http://redfish.com/mailman/listinfo/friam_redfish.com
archives back to 2003: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove


============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove

[Frank Wimberly-2]

We decided that The Road to Reality was unreadable because it's neither here nor there.  It was very Advanced without being mathematical enough.  Kind of like a long badly written Scientific American article.

To make a long story short, we finally read Gauge Fields, Knots and Gravity by John Baez more or less successfully.  The first part of the book covers manifolds, differential forms and, in general, the math you need for general relativity and quantum field theory.  If you want another opinion ask Jon Zingale or Barry Mackichan.

Frank

Or travel back in time and ask Hywel.

On Tue, Dec 4, 2018, 11:21 PM Nick Thompson <[hidden email] wrote:

Hi, Dave,

Missed this note the first time.  Frank and Hywel had a go at this a couple
of years ago, and I bought the book and tried to join them.  Whew!  It was
at that point I gave up on the notion that I could read anything if I tried
hard enough.  Hywel has since died, but I think there was at least one other
person involved, who, with Frank, might be able to give you some guidance.

Nick

Nicholas S. Thompson
Emeritus Professor of Psychology and Biology
Clark University
http://home.earthlink.net/~nickthompson/naturaldesigns/


-----Original Message-----
From: Friam [mailto:[hidden email]] On Behalf Of Prof David West
Sent: Wednesday, November 28, 2018 10:26 AM
To: [hidden email]
Subject: [FRIAM] two books

I just finished reading What is Real? by Adam Becker. A straightforward
discussion of Quantum Physics and the "Copenhagen Interpretation," and the
arguments surrounding it. it offers an indirect but scathing study of how
science is really done and how far the practice of science is from the ideal
of a "scientific method." Also an interesting discussion of the relationship
between 'science' and 'phi8losophy'. Might be of interest to several
FRIAMers.

Starting to read Roger Penrose's, The Road to Reality: a complete guide tot
he laws of the universe. I would really like some advice / comments from the
mathematicians in the community as to the value of the book and the likely
hood that I might gain sufficient understanding of manifolds, symmetry
groups, etc. etc. to understand some of the conversations on the list and at
the mother church.

dave west

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe
http://redfish.com/mailman/listinfo/friam_redfish.com
archives back to 2003: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove


============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
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archives back to 2003: http://friam.471366.n2.nabble.com/
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============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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[Ron Newman]

Frank,

And what's your view of "What is Real?", by Adam Becker?  I'm thinking of having a look at it.

Ron

On Wed, Dec 5, 2018 at 6:40 AM Frank Wimberly <[hidden email]> wrote:

We decided that The Road to Reality was unreadable because it's neither here nor there.  It was very Advanced without being mathematical enough.  Kind of like a long badly written Scientific American article.

To make a long story short, we finally read Gauge Fields, Knots and Gravity by John Baez more or less successfully.  The first part of the book covers manifolds, differential forms and, in general, the math you need for general relativity and quantum field theory.  If you want another opinion ask Jon Zingale or Barry Mackichan.

Frank

Or travel back in time and ask Hywel.

On Tue, Dec 4, 2018, 11:21 PM Nick Thompson <[hidden email] wrote:

Hi, Dave,

Missed this note the first time.  Frank and Hywel had a go at this a couple
of years ago, and I bought the book and tried to join them.  Whew!  It was
at that point I gave up on the notion that I could read anything if I tried
hard enough.  Hywel has since died, but I think there was at least one other
person involved, who, with Frank, might be able to give you some guidance.

Nick

Nicholas S. Thompson
Emeritus Professor of Psychology and Biology
Clark University
http://home.earthlink.net/~nickthompson/naturaldesigns/


-----Original Message-----
From: Friam [mailto:[hidden email]] On Behalf Of Prof David West
Sent: Wednesday, November 28, 2018 10:26 AM
To: [hidden email]
Subject: [FRIAM] two books

I just finished reading What is Real? by Adam Becker. A straightforward
discussion of Quantum Physics and the "Copenhagen Interpretation," and the
arguments surrounding it. it offers an indirect but scathing study of how
science is really done and how far the practice of science is from the ideal
of a "scientific method." Also an interesting discussion of the relationship
between 'science' and 'phi8losophy'. Might be of interest to several
FRIAMers.

Starting to read Roger Penrose's, The Road to Reality: a complete guide tot
he laws of the universe. I would really like some advice / comments from the
mathematicians in the community as to the value of the book and the likely
hood that I might gain sufficient understanding of manifolds, symmetry
groups, etc. etc. to understand some of the conversations on the list and at
the mother church.

dave west

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe
http://redfish.com/mailman/listinfo/friam_redfish.com
archives back to 2003: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove


============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
archives back to 2003: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove

============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove

[Roger Critchlow-2]

I just finished reading Philip Ball's Beyond Weird, Why Everything You Thought You Knew About Quantum Physics is Different, and while he doesn't really deliver on the book's subtitle, he does a very good job of laying out the Copenhagen Interpretation of quantum mechanics, and its discontents, and the later attempts to reformulate the question.

As one who learned quantum mechanics as a chemist, I have to say that the lack of reality that bothers the physicists never really bothers me.  I don't really care how an electron spreads itself in space to create a wave function.   I get electron densities from the wave function magnitudes, which serve to glue together nuclei of different elements into molecules, and changes of electron densities, which allow reactions to happen.  

-- rec --

On Wed, Dec 5, 2018 at 11:02 AM Ron Newman <[hidden email]> wrote:

Frank,

And what's your view of "What is Real?", by Adam Becker?  I'm thinking of having a look at it.

Ron

On Wed, Dec 5, 2018 at 6:40 AM Frank Wimberly <[hidden email]> wrote:

We decided that The Road to Reality was unreadable because it's neither here nor there.  It was very Advanced without being mathematical enough.  Kind of like a long badly written Scientific American article.

To make a long story short, we finally read Gauge Fields, Knots and Gravity by John Baez more or less successfully.  The first part of the book covers manifolds, differential forms and, in general, the math you need for general relativity and quantum field theory.  If you want another opinion ask Jon Zingale or Barry Mackichan.

Frank

Or travel back in time and ask Hywel.

On Tue, Dec 4, 2018, 11:21 PM Nick Thompson <[hidden email] wrote:

Hi, Dave,

Missed this note the first time.  Frank and Hywel had a go at this a couple
of years ago, and I bought the book and tried to join them.  Whew!  It was
at that point I gave up on the notion that I could read anything if I tried
hard enough.  Hywel has since died, but I think there was at least one other
person involved, who, with Frank, might be able to give you some guidance.

Nick

Nicholas S. Thompson
Emeritus Professor of Psychology and Biology
Clark University
http://home.earthlink.net/~nickthompson/naturaldesigns/


-----Original Message-----
From: Friam [mailto:[hidden email]] On Behalf Of Prof David West
Sent: Wednesday, November 28, 2018 10:26 AM
To: [hidden email]
Subject: [FRIAM] two books

I just finished reading What is Real? by Adam Becker. A straightforward
discussion of Quantum Physics and the "Copenhagen Interpretation," and the
arguments surrounding it. it offers an indirect but scathing study of how
science is really done and how far the practice of science is from the ideal
of a "scientific method." Also an interesting discussion of the relationship
between 'science' and 'phi8losophy'. Might be of interest to several
FRIAMers.

Starting to read Roger Penrose's, The Road to Reality: a complete guide tot
he laws of the universe. I would really like some advice / comments from the
mathematicians in the community as to the value of the book and the likely
hood that I might gain sufficient understanding of manifolds, symmetry
groups, etc. etc. to understand some of the conversations on the list and at
the mother church.

dave west

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe
http://redfish.com/mailman/listinfo/friam_redfish.com
archives back to 2003: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove


============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
archives back to 2003: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
archives back to 2003: http://friam.471366.n2.nabble.com/
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============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
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============================================================
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[Marcus G. Daniels]

Speaking as a utilitarian, what bothers me is that entanglement should be impossible.   It says something about the fabric of space time that should be impossible. 

If it is not impossible, then there must be some exploitable properties of the universe that need to be investigated because they could be very valuable to exploit them.

Just being content with math that works seems like a failure of imagination.

 

From: Friam <[hidden email]> on behalf of Roger Critchlow <[hidden email]>
Reply-To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Date: Thursday, December 6, 2018 at 3:05 PM
To: The Friday Morning Applied Complexity Coffee Group <[hidden email]>
Subject: Re: [FRIAM] two books

 

I just finished reading Philip Ball's Beyond Weird, Why Everything You Thought You Knew About Quantum Physics is Different, and while he doesn't really deliver on the book's subtitle, he does a very good job of laying out the Copenhagen Interpretation of quantum mechanics, and its discontents, and the later attempts to reformulate the question.

 

As one who learned quantum mechanics as a chemist, I have to say that the lack of reality that bothers the physicists never really bothers me.  I don't really care how an electron spreads itself in space to create a wave function.   I get electron densities from the wave function magnitudes, which serve to glue together nuclei of different elements into molecules, and changes of electron densities, which allow reactions to happen.  

 

-- rec --

 

On Wed, Dec 5, 2018 at 11:02 AM Ron Newman <[hidden email]> wrote:

Frank,

And what's your view of "What is Real?", by Adam Becker?  I'm thinking of having a look at it.

 

Ron

Ron Newman, M.S., M.M.E.

Partner, Caditz-Newman, Smart Infrastructure for Autonomous Vehicles

Founder, IdeaTreeLive.com Knowledge Modeling

Piano

Blog

 

 

On Wed, Dec 5, 2018 at 6:40 AM Frank Wimberly <[hidden email]> wrote:

We decided that The Road to Reality was unreadable because it's neither here nor there.  It was very Advanced without being mathematical enough.  Kind of like a long badly written Scientific American article.

To make a long story short, we finally read Gauge Fields, Knots and Gravity by John Baez more or less successfully.  The first part of the book covers manifolds, differential forms and, in general, the math you need for general relativity and quantum field theory.  If you want another opinion ask Jon Zingale or Barry Mackichan.

 

Frank

 

Or travel back in time and ask Hywel.

-----------------------------------
Frank Wimberly

My memoir:
https://www.amazon.com/author/frankwimberly

My scientific publications:
https://www.researchgate.net/profile/Frank_Wimberly2

Phone [phone]

 

On Tue, Dec 4, 2018, 11:21 PM Nick Thompson <[hidden email] wrote:

Hi, Dave,

Missed this note the first time.  Frank and Hywel had a go at this a couple
of years ago, and I bought the book and tried to join them.  Whew!  It was
at that point I gave up on the notion that I could read anything if I tried
hard enough.  Hywel has since died, but I think there was at least one other
person involved, who, with Frank, might be able to give you some guidance.

Nick

Nicholas S. Thompson
Emeritus Professor of Psychology and Biology
Clark University
http://home.earthlink.net/~nickthompson/naturaldesigns/


-----Original Message-----
From: Friam [mailto:[hidden email]] On Behalf Of Prof David West
Sent: Wednesday, November 28, 2018 10:26 AM
To: [hidden email]
Subject: [FRIAM] two books

I just finished reading What is Real? by Adam Becker. A straightforward
discussion of Quantum Physics and the "Copenhagen Interpretation," and the
arguments surrounding it. it offers an indirect but scathing study of how
science is really done and how far the practice of science is from the ideal
of a "scientific method." Also an interesting discussion of the relationship
between 'science' and 'phi8losophy'. Might be of interest to several
FRIAMers.

Starting to read Roger Penrose's, The Road to Reality: a complete guide tot
he laws of the universe. I would really like some advice / comments from the
mathematicians in the community as to the value of the book and the likely
hood that I might gain sufficient understanding of manifolds, symmetry
groups, etc. etc. to understand some of the conversations on the list and at
the mother church.

dave west

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College to unsubscribe
http://redfish.com/mailman/listinfo/friam_redfish.com
archives back to 2003: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove


============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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============================================================
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Meets Fridays 9a-11:30 at cafe at St. John's College
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[jon zingale]

`As one who learned quantum mechanics as a chemist, I have to say that the lack of reality that bothers the physicists never really bothers me.  I don't really care how an electron spreads itself in space to create a wave function.   I get electron densities from the wave function magnitudes, which serve to glue together nuclei of different elements into molecules, and changes of electron densities, which allow reactions to happen.`

Roger,

I tend to harbor similar feelings regarding the 'unreality'

of the wave / particle duality. Further, I tend to regard

mysticism with respect to the apparent paradox with suspicion.

Much of mechanics (classical or not) is counterintuitive

to the initiate. Generalized coordinates, deriving equations

of motion from the Hamiltonian and interpreting energy

levels on a phase space all require significant preparations,

which border on autosuggestion. Is Quantum Mechanics

really that much more counterintuitive?

In modern mathematics, one encounters categories whose

`points` have an internal structure which can be more

complicated than one's initial intuition would provide.

There is a sense that what the interested physicist is doing

by exploring the duality is attempting to understand the nature

of 'physical points'. How is a physical point like a point in

Euclidean geometry? To what extent can there be a consistent

formal description which matches our knowledge of these points?

Perhaps from some phenomenological perspective, we should

understand these physical points as founding all experience

regarding points and waves. After all, assuming the present

quantum mechanical presentation, all of the classical

experiences of  wave-like nature and particle-like nature

are derived from interactions of these underlying primitive

objects.

Cheers,

Jonathan Zingale

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[gepr]

On 12/8/18 6:09 PM, Jon Zingale wrote:
> In modern mathematics, one encounters categories whose `points` have an internal structure which can be more complicated than one's initial intuition would provide. There is a sense that what the interested physicist is doing by exploring the duality is attempting to understand the nature of 'physical points'. How is a physical point like a point in Euclidean geometry? To what extent can there be a consistent formal description which matches our knowledge of these points?
>
> Perhaps from some phenomenological perspective, we should understand these physical points as founding all experience regarding points and waves. After all, assuming the present quantum mechanical presentation, all of the classical experiences of  wave-like nature and particle-like nature are derived from interactions of these underlying primitive objects.

It boils down to semantic grounding and whether or not the derivations are truth preserving. If the math is (merely) a model of reality, then it's irrelevant whether an intermediate derivation has meaning or not.  What matters is the meaning of a given expression when we get to a "grounding point" (or in simulation a validation point). But if the math *is* reality (or maps so tightly to reality so as to be indistinguishable from reality), then each and every term of each and every expression, throughout any intermediate transformation, has physical meaning.

--
∄ uǝʃƃ

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[lrudolph]

Jon Zingale writes, in relevant part:

> In modern mathematics, one encounters categories whose
> `points` have an internal structure which can be more
> complicated than one's initial intuition would provide.
> There is a sense that what the interested physicist is doing
> by exploring the duality is attempting to understand the nature
> of 'physical points'. How is a physical point like a point in
> Euclidean geometry? To what extent can there be a consistent
> formal description which matches our knowledge of these points?
>
> Perhaps from some phenomenological perspective, we should
> understand these physical points as founding all experience
> regarding points and waves. After all, assuming the present
> quantum mechanical presentation, all of the classical
> experiences of  wave-like nature and particle-like nature
> are derived from interactions of these underlying primitive
> objects.

Here, modulo reformatting for ASCII e-mail, is part of one section of one
of my editorial chapters ("Functions of Structure in Mathematics and
Modeling") in my widely unread edited book "Qualitative Mathematics for
the Social Sciences" (Routledge, 2013; get your local libraries to order
dozens!), which (at least) obliquely talks to the issues Jon raises here,
and handles the issue of "more complicated than one's initial intuition"
somewhat head-on (though probably pitched above the head of most of the
social scientists who were the purported audience).

===begin===

ON MATHEMATICAL SPACES

The preceding discussion of projective planes provides not just explicit
examples of how set-theoretical definitions are used mathematically, but
also many examples (there not drawn explicitly to attention) of how (parts
of) such definitions can acquire or give meaning in the course of their
mathematical and para-mathematical interactions with other structures
(some mathematical but having definitions that remain out of attention,
others ‘in the world’ and defined—if at all—non-mathematically). In this
section I pick up just one of those dropped threads.

Many mathematical structures have been called ‘spaces’ (usually with some
modifier) since at least the discovery of non-Euclidean
geometries—notably, the real projective plane RP2 and the real hyperbolic
plane—early in the 19th century, and well before there were any
set-theoretical “foundations of mathematics”. By mid 20th century,
mathematical ‘spaces’ were common not only in geometry but in algebra
(‘vector spaces’), mathematical analysis (‘Hilbert spaces’, ‘Banach
spaces’, ‘Hardy spaces’, and many other kinds of vector spaces with extra
structure, as well as ‘metric spaces’ and ‘measure
spaces’), abstract algebra (‘representation spaces’, ‘prime ideal
spaces’), probability theory (‘probability spaces’), mathematical physics
(‘phase spaces’), and especially topology—the quintessential mathematics
of the 20th century—in its many manifestations: point-set, combinatorial,
algebraic, geometric, and differential. No single strictly mathematical
property is shared by these many kinds of ‘spaces’, but mathematicians in
general seem content to agree that the metaphor is broadly appropriate.

Typically, when mathematicians call some mathematical structure S a space
(here to be called a mathematical space in the hopes of averting
confusion), they understand it to share, in some sense and to some degree,
the following rather general pre-mathematical properties of the ordinary
space of our daily experience. [Footnote 15: Many presuppositions are
packed into the phrase “the ordinary space of our daily experience” and
its variants, and most if not all of them are probably unjustifiably
broad, particularly if “daily experience” is read so as to naïvely ignore
or tendentiously suppress the considerable role of linguistic framings
(cultural and sub-cultural, semi-permanent and evanescent) in that
“experience”. Still, the phrase and its variants have a reasonably well
delimited denotation that is widely understood (until it is examined
overly closely), so I take the risk of using it here.]
(1) A mathematical space is like a box that can ‘contain’ other sorts of
‘things’.
(2) A mathematical space is like a stage on which various ‘events’ can
‘happen’ (e.g., ‘things’ can ‘move’) in the course of time. [Footnote 16:
Somewhat confusingly, “time” is very often thought of as a mathematical
space by mathematicians. See Chap. 10, p. 308, and Rudolph (2006a).]
Properties (1) and (2) are essentially extrinsic to a candidate S for
‘spacehood’: they depend almost entirely not on what S is but on how S is
used.[Footnote 17: In particular, one and the same mathematical structure
S can be called a ‘space’ or not depending on the use to which it is being
put.] In contrast, a third general property is chiefly intrinsic.
(3) A mathematical space ‘has extent’, and can (usually) be ‘subdivided’;
a ‘piece’ of a mathematical space, though (usually) of smaller ‘extent’,
still has in its own right the quality of being a mathematical space.
Naturally, the interpretation of (3) depends on the meaning given to
‘extent’, ‘piece’, etc., and in that sense it is somewhat extrinsic.

What mathematicians typically try hard not to do, when calling a
mathematical structure a ‘space’, is to attribute to that structure other
properties of ordinary space that are not explicitly demanded by the
context in which the structure is being used. Model-making scientists, be
they physical, life, or social scientists, are often less fastidious when
they adopt the metaphor of ‘space’ for mathematical models in their own
disciplines: in contrast with mathematicians, they tend to incorporate
into their models not only the general properties (1)–(3) of ordinary
space, but also some or all of the following special properties.
(4) Ordinary space has (or can have imposed upon it) metric properties,
including (but not limited to) numerical measures of distance, area,
volume, and other forms of ‘extent’; a mathematical space need not.
(5) Ordinary space has (or can have imposed upon it) geometric properties,
such as notions of ‘straightness’ and ‘curvature’, ‘convexity’ and
‘concavity’, ‘collinearity’, ‘congruence’, and the like; a mathematical
space need not.
(6) Ordinary space has properties of continuity, homogeneity (i.e.,
indistinguishability among locations per se) and isotropy (i.e.,
indistinguishability among directions per se) [Footnote 18: Or, at least,
horizontal directions are (among themselves, ignoring their ‘contents’)
indistinguishable in ordinary space; as Shepard (1992, p. 500) points out,
gravity makes verticality salient for surface-dwellers (or rather, for
those surface-dwellers that live above the “nanoscale” at which van der
Waals forces, Brownian motion, etc., have effects much stronger than those
of gravity).]; a mathematical space need not. [Footnote 19: In this
connection, it is almost incredible—to a mathematician educated in the
second half of the 20th century—to read that, for instance, Bertrand
Russell (1896)
    [i]n his first published paper [...] analyses the axioms of Euclidean
    geometry [...] and finds that some of the axioms are certainly true,
    and in particular a priori true, “for their denial would involve logical
    and philosophical absurdities” (p. 3). He classifies for instance the
    homogeneity of space as a priori true, the “want of homogeneity and
    passivity is ... absurd: no philosopher has ever thrown doubt, so far
    as I know, on these two properties of empty space [...].” (Lakatos, 1962,
    p. 168; the unbracketed ellipsis points, and the italics, are Lakatos’s.)
Moreover, Russell (1896, p. 1) purports to come to his conclusions even
though
    we are not concerned with the correspondence of Geometry with fact;
    we are concerned with Geometry simply as a body of reasoning, the
    conditions of whose possibility we wish to examine [...] we have to do
    with the conception of space in its most finished and elaborated form,
    after thought has done its utmost in transforming the intuitional data.
Probably the best (though very difficult) course of action for the modern
mathematician, incredulous in the face of what appears to be such an
enormous blind spot, would be to take an appropriate modification of
Stallings’s advice (quoted on p. 64), and ‘cultivate techniques leading to
the abandonment’ of one’s own mechanisms for maintaining one’s own (surely
numerous) blind spots.]
(7) In ordinary space, a ‘point’ is atomic, with no internal structure; in
many important examples of mathematical spaces, each ‘point’ is a complex
structure in its own right.

Although the policy of endowing mathematical spaces used as models with
some or all of the special properties (4)–(7) has often been harmless, and
occasionally useful, in the natural sciences, I see no evidence that it
has often been useful (and some evidence that it has sometimes been
harmful) in the human sciences. In any case, mathematicians typically see
the denial, to a given mathematical space, of some or all of these special
properties—especially (7)—as entirely normal, and frequently commendable.
[Footnote 20: Euclid’s Definition 1 states that “a point is that which has
no parts”. But, e.g., in all the definitions of RP2, at least some
points—being sets with two elements—have non-trivial, if meager,
mereologies. A class of examples of mathematical spaces having far more
radically “non-atomic” points than those of RP2 is that of configuration
spaces of (mathematical or physical) systems of various sorts. In a
configuration space, each point is a single configuration of the entire
system. See Wehrle, Kaiser, Schmidt, and Scherer (2000) for an application
to the dynamics of human affect that—in effect—constitutes a partial
exploration of a mathematical space of “schematic facial expressions
consisting entirely of theoretically postulated facial muscle
configurations” (p. 105).]

===end===

I guess one thing not mentioned there, which occurs to me as I reread the
text I quoted from Jon, is the importance of keeping in mind (if not
necessarily always at the front of one's mind, that is, in active
attention [<---notice the metaphorical "spatialization" inherent in the
idiomatic uses of "at the front" and "in"]) that which "objects" are
"underlying primitive objects" is not necessarily, and perhaps necessarily
NOT, a fact about the system being modeled, but rather a fact about the
model.

Cheers,

Lee Rudolph


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[Marcus G. Daniels]

Well, I think there is something really surprising (unexplained) about the reality of long range communication using quantum key distribution.   There is something really surprising about the possibility of truly random numbers.  It is accepting these concepts that I see as mysticism, even if the concepts are formal, validated, and self consistent.

Sent from my iPhone

> On Dec 9, 2018, at 6:28 AM, "[hidden email]" <[hidden email]> wrote:
>
> Jon Zingale writes, in relevant part:
>
>> In modern mathematics, one encounters categories whose
>> `points` have an internal structure which can be more
>> complicated than one's initial intuition would provide.
>> There is a sense that what the interested physicist is doing
>> by exploring the duality is attempting to understand the nature
>> of 'physical points'. How is a physical point like a point in
>> Euclidean geometry? To what extent can there be a consistent
>> formal description which matches our knowledge of these points?
>>
>> Perhaps from some phenomenological perspective, we should
>> understand these physical points as founding all experience
>> regarding points and waves. After all, assuming the present
>> quantum mechanical presentation, all of the classical
>> experiences of  wave-like nature and particle-like nature
>> are derived from interactions of these underlying primitive
>> objects.
>
> Here, modulo reformatting for ASCII e-mail, is part of one section of one
> of my editorial chapters ("Functions of Structure in Mathematics and
> Modeling") in my widely unread edited book "Qualitative Mathematics for
> the Social Sciences" (Routledge, 2013; get your local libraries to order
> dozens!), which (at least) obliquely talks to the issues Jon raises here,
> and handles the issue of "more complicated than one's initial intuition"
> somewhat head-on (though probably pitched above the head of most of the
> social scientists who were the purported audience).
>
> ===begin===
>
> ON MATHEMATICAL SPACES
>
> The preceding discussion of projective planes provides not just explicit
> examples of how set-theoretical definitions are used mathematically, but
> also many examples (there not drawn explicitly to attention) of how (parts
> of) such definitions can acquire or give meaning in the course of their
> mathematical and para-mathematical interactions with other structures
> (some mathematical but having definitions that remain out of attention,
> others 'in the world' and defined-if at all-non-mathematically). In this
> section I pick up just one of those dropped threads.
>
> Many mathematical structures have been called 'spaces' (usually with some
> modifier) since at least the discovery of non-Euclidean
> geometries-notably, the real projective plane RP2 and the real hyperbolic
> plane-early in the 19th century, and well before there were any
> set-theoretical "foundations of mathematics". By mid 20th century,
> mathematical 'spaces' were common not only in geometry but in algebra
> ('vector spaces'), mathematical analysis ('Hilbert spaces', 'Banach
> spaces', 'Hardy spaces', and many other kinds of vector spaces with extra
> structure, as well as 'metric spaces' and 'measure
> spaces'), abstract algebra ('representation spaces', 'prime ideal
> spaces'), probability theory ('probability spaces'), mathematical physics
> ('phase spaces'), and especially topology-the quintessential mathematics
> of the 20th century-in its many manifestations: point-set, combinatorial,
> algebraic, geometric, and differential. No single strictly mathematical
> property is shared by these many kinds of 'spaces', but mathematicians in
> general seem content to agree that the metaphor is broadly appropriate.
>
> Typically, when mathematicians call some mathematical structure S a space
> (here to be called a mathematical space in the hopes of averting
> confusion), they understand it to share, in some sense and to some degree,
> the following rather general pre-mathematical properties of the ordinary
> space of our daily experience. [Footnote 15: Many presuppositions are
> packed into the phrase "the ordinary space of our daily experience" and
> its variants, and most if not all of them are probably unjustifiably
> broad, particularly if "daily experience" is read so as to naïvely ignore
> or tendentiously suppress the considerable role of linguistic framings
> (cultural and sub-cultural, semi-permanent and evanescent) in that
> "experience". Still, the phrase and its variants have a reasonably well
> delimited denotation that is widely understood (until it is examined
> overly closely), so I take the risk of using it here.]
> (1) A mathematical space is like a box that can 'contain' other sorts of
> 'things'.
> (2) A mathematical space is like a stage on which various 'events' can
> 'happen' (e.g., 'things' can 'move') in the course of time. [Footnote 16:
> Somewhat confusingly, "time" is very often thought of as a mathematical
> space by mathematicians. See Chap. 10, p. 308, and Rudolph (2006a).]
> Properties (1) and (2) are essentially extrinsic to a candidate S for
> 'spacehood': they depend almost entirely not on what S is but on how S is
> used.[Footnote 17: In particular, one and the same mathematical structure
> S can be called a 'space' or not depending on the use to which it is being
> put.] In contrast, a third general property is chiefly intrinsic.
> (3) A mathematical space 'has extent', and can (usually) be 'subdivided';
> a 'piece' of a mathematical space, though (usually) of smaller 'extent',
> still has in its own right the quality of being a mathematical space.
> Naturally, the interpretation of (3) depends on the meaning given to
> 'extent', 'piece', etc., and in that sense it is somewhat extrinsic.
>
> What mathematicians typically try hard not to do, when calling a
> mathematical structure a 'space', is to attribute to that structure other
> properties of ordinary space that are not explicitly demanded by the
> context in which the structure is being used. Model-making scientists, be
> they physical, life, or social scientists, are often less fastidious when
> they adopt the metaphor of 'space' for mathematical models in their own
> disciplines: in contrast with mathematicians, they tend to incorporate
> into their models not only the general properties (1)-(3) of ordinary
> space, but also some or all of the following special properties.
> (4) Ordinary space has (or can have imposed upon it) metric properties,
> including (but not limited to) numerical measures of distance, area,
> volume, and other forms of 'extent'; a mathematical space need not.
> (5) Ordinary space has (or can have imposed upon it) geometric properties,
> such as notions of 'straightness' and 'curvature', 'convexity' and
> 'concavity', 'collinearity', 'congruence', and the like; a mathematical
> space need not.
> (6) Ordinary space has properties of continuity, homogeneity (i.e.,
> indistinguishability among locations per se) and isotropy (i.e.,
> indistinguishability among directions per se) [Footnote 18: Or, at least,
> horizontal directions are (among themselves, ignoring their 'contents')
> indistinguishable in ordinary space; as Shepard (1992, p. 500) points out,
> gravity makes verticality salient for surface-dwellers (or rather, for
> those surface-dwellers that live above the "nanoscale" at which van der
> Waals forces, Brownian motion, etc., have effects much stronger than those
> of gravity).]; a mathematical space need not. [Footnote 19: In this
> connection, it is almost incredible-to a mathematician educated in the
> second half of the 20th century-to read that, for instance, Bertrand
> Russell (1896)
>    [i]n his first published paper [...] analyses the axioms of Euclidean
>    geometry [...] and finds that some of the axioms are certainly true,
>    and in particular a priori true, "for their denial would involve logical
>    and philosophical absurdities" (p. 3). He classifies for instance the
>    homogeneity of space as a priori true, the "want of homogeneity and
>    passivity is ... absurd: no philosopher has ever thrown doubt, so far
>    as I know, on these two properties of empty space [...]." (Lakatos, 1962,
>    p. 168; the unbracketed ellipsis points, and the italics, are Lakatos's.)
> Moreover, Russell (1896, p. 1) purports to come to his conclusions even
> though
>    we are not concerned with the correspondence of Geometry with fact;
>    we are concerned with Geometry simply as a body of reasoning, the
>    conditions of whose possibility we wish to examine [...] we have to do
>    with the conception of space in its most finished and elaborated form,
>    after thought has done its utmost in transforming the intuitional data.
> Probably the best (though very difficult) course of action for the modern
> mathematician, incredulous in the face of what appears to be such an
> enormous blind spot, would be to take an appropriate modification of
> Stallings's advice (quoted on p. 64), and 'cultivate techniques leading to
> the abandonment' of one's own mechanisms for maintaining one's own (surely
> numerous) blind spots.]
> (7) In ordinary space, a 'point' is atomic, with no internal structure; in
> many important examples of mathematical spaces, each 'point' is a complex
> structure in its own right.
>
> Although the policy of endowing mathematical spaces used as models with
> some or all of the special properties (4)-(7) has often been harmless, and
> occasionally useful, in the natural sciences, I see no evidence that it
> has often been useful (and some evidence that it has sometimes been
> harmful) in the human sciences. In any case, mathematicians typically see
> the denial, to a given mathematical space, of some or all of these special
> properties-especially (7)-as entirely normal, and frequently commendable.
> [Footnote 20: Euclid's Definition 1 states that "a point is that which has
> no parts". But, e.g., in all the definitions of RP2, at least some
> points-being sets with two elements-have non-trivial, if meager,
> mereologies. A class of examples of mathematical spaces having far more
> radically "non-atomic" points than those of RP2 is that of configuration
> spaces of (mathematical or physical) systems of various sorts. In a
> configuration space, each point is a single configuration of the entire
> system. See Wehrle, Kaiser, Schmidt, and Scherer (2000) for an application
> to the dynamics of human affect that-in effect-constitutes a partial
> exploration of a mathematical space of "schematic facial expressions
> consisting entirely of theoretically postulated facial muscle
> configurations" (p. 105).]
>
> ===end===
>
> I guess one thing not mentioned there, which occurs to me as I reread the
> text I quoted from Jon, is the importance of keeping in mind (if not
> necessarily always at the front of one's mind, that is, in active
> attention [<---notice the metaphorical "spatialization" inherent in the
> idiomatic uses of "at the front" and "in"]) that which "objects" are
> "underlying primitive objects" is not necessarily, and perhaps necessarily
> NOT, a fact about the system being modeled, but rather a fact about the
> model.
>
> Cheers,
>
> Lee Rudolph
>
>
> ============================================================
> FRIAM Applied Complexity Group listserv
> Meets Fridays 9a-11:30 at cafe at St. John's College
> to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
> archives back to 2003: http://friam.471366.n2.nabble.com/
> FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove

============================================================
FRIAM Applied Complexity Group listserv
Meets Fridays 9a-11:30 at cafe at St. John's College
to unsubscribe http://redfish.com/mailman/listinfo/friam_redfish.com
archives back to 2003: http://friam.471366.n2.nabble.com/
FRIAM-COMIC http://friam-comic.blogspot.com/ by Dr. Strangelove