Non-physical causation
Peter H.M. Brooks
emergence and I was wondering about the question of non-physical
causation of physical events. Clearly if you are a dualist you would
claim that the mind has some mechanism of turning mental processes into
physical events - unless you were keen on epiphenomena, which I don't
think anybody is. I was wondering, though, about the non-mental,
non-living, case. Can a non-physical thing (say the number '3' or PI, or
a program to calculate prime numbers) cause a physical event?
I can see how one can contrive that an event is decided on by something
non-physical quite easily - a program can be written to emit a sound if
it finds a certain number to be prime, it could be argued that the prime
number 'caused' the sound. Though this might appear proximally true, I
would say that the ultimate cause of the sound (or the real cause) is
the mind of the person who set up the process. So any such contrivance
or life-created event boils down to a the mental case - or at least to
case where the existence of some form of life exercises a cause.
You could say that the bark of a tree is constrained ['caused'] to be
around pi times the diameter of its branch at any particular point, but
surely this isn't really a 'cause', but simply an artefact of reality -
or a pattern that we choose to impose upon it.
So, I may well be missing a simple and obvious case, but can you suggest
something that is caused by a non-physical, non-living entity?
--
Quis custodiet ipsos custodes? - Who has custard with custard creams?
Major Molesworth Major Rtd. G&T&Bar
kames.smiths
"Peter H.M. Brooks" <pe...@new.co.za> wrote in message
news:9piejj$4e5$1...@ctb-nnrp1.saix.net...
>Can a non-physical thing (say the number '3' or PI, or
> a program to calculate prime numbers) cause a physical event?
I don't accept that the number 3 and pi are non-physical things. Are
they not just ideas (neural events) in our heads? Are you not running
into that thorny issue for dualists - how could a non-physical event
interact with a physical event?
Dave Smith
Peter H.M. Brooks
kames.smiths <kames....@ntlworld.com> wrote in message
news:DC6v7.7258$jE3.8...@news6-win.server.ntlworld.com...
abstractions, I think that pi and 3 are certainly non-physical, just as
Darcy or Frankenstein are non-physical things. I agree that they are
ideas, or neural events, but, having been exposed to maths training,
there is a certain temptation to weak platonism - that pi has a separate
existence to the neural events.
Des
"kames.smiths" <kames....@ntlworld.com> wrote in message
news:DC6v7.7258$jE3.8...@news6-win.server.ntlworld.com...
>
> news:9piejj$4e5$1...@ctb-nnrp1.saix.net...
>
> >Can a non-physical thing (say the number '3' or PI, or
> > a program to calculate prime numbers) cause a physical event?
>
> I don't accept that the number 3 and pi are non-physical things. Are
> they not just ideas (neural events) in our heads?
Is it your view then that mathematical understanding is limited to the human
brain - or at the very least to biological systems containing neurons?
> Are you not running
> into that thorny issue for dualists - how could a non-physical event
> interact with a physical event?
What about a physical event and a non-physical object conspiring to produce
a mental event?
Look at it this way, by looking at a physical object from a different
viewpoint I don't change that object but I do change my perception and hence
my experience of it.
In any case, since we can no longer view space and time as separate then we
can't talk about physical objects being changed at all. Physical objects
just are - as mathematical objects just are. Physical objects are
characterized by substance and spatio-temporal extent, mathematical objects
are characterized by logical consistency and implication.
Our minds can and do experience and explore both types of objects in a
perfectly analogous fashion - or can you demonstrate that they don't?
Des
john h brockbank
> So, I may well be missing a simple and obvious case, but can you suggest
> something that is caused by a non-physical, non-living entity?
>
Fear, caused by ghosts.
kames.smiths
"john h brockbank" <wag...@wagley.screaming.net> wrote in message
news:3bbde...@mk-nntp-1.news.uk.worldonline.com...
A man steps into a dark shed, mistakes a coiled-up rope for a snake,
leaps back, stumbles, bangs his head, and dies. Poor fellow! Killed by a
snake.
Dave Smith
kames.smiths
"Des" <DesGr...@removebtclick.com> wrote in message
news:84mv7.106208$4j4.496614@NewsReader...
>
> "kames.smiths" <kames....@ntlworld.com> wrote in message
> news:DC6v7.7258$jE3.8...@news6-win.server.ntlworld.com...
> >
> > "Peter H.M. Brooks" <pe...@new.co.za> wrote in message
> > news:9piejj$4e5$1...@ctb-nnrp1.saix.net...
> >
> > >Can a non-physical thing (say the number '3' or PI, or
> > > a program to calculate prime numbers) cause a physical event?
> >
> > I don't accept that the number 3 and pi are non-physical things. Are
> > they not just ideas (neural events) in our heads?
>
> Is it your view then that mathematical understanding is limited to the
human
> brain - or at the very least to biological systems containing neurons?
Where else could mathematical understanding take place except in brains?
> > Are you not running
> > into that thorny issue for dualists - how could a non-physical event
> > interact with a physical event?
>
> What about a physical event and a non-physical object conspiring to
produce
> a mental event?
Can you give me an example of a non-physical object?
> Look at it this way, by looking at a physical object from a different
> viewpoint I don't change that object but I do change my perception and
hence
> my experience of it.
> In any case, since we can no longer view space and time as separate
then we
> can't talk about physical objects being changed at all. Physical
objects
> just are - as mathematical objects just are. Physical objects are
> characterized by substance and spatio-temporal extent, mathematical
objects
> are characterized by logical consistency and implication.
>
> Our minds can and do experience and explore both types of objects in a
> perfectly analogous fashion - or can you demonstrate that they don't?
Again, can you explain what you mean more fully. My understanding of
mathematics is very limited, as is my understanding of physics, and your
posts tend to go over my head. It seems to me that mathematics and
physics are attempts by people to understand their world and that they
do not have any independent existence.
Dave Smith
Peter H.M. Brooks
>
> > > >Can a non-physical thing (say the number '3' or PI, or
> > > > a program to calculate prime numbers) cause a physical event?
> > >
> > > I don't accept that the number 3 and pi are non-physical things.
Are
> > > they not just ideas (neural events) in our heads?
> >
> > Is it your view then that mathematical understanding is limited to
the
> human
> > brain - or at the very least to biological systems containing
neurons?
>
> Where else could mathematical understanding take place except in
brains?
>
>
> > > Are you not running
> > > into that thorny issue for dualists - how could a non-physical
event
> > > interact with a physical event?
> >
> > What about a physical event and a non-physical object conspiring to
> produce
> > a mental event?
>
> Can you give me an example of a non-physical object?
>
>
> > Look at it this way, by looking at a physical object from a
different
> > viewpoint I don't change that object but I do change my perception
and
> hence
> > my experience of it.
>
> > In any case, since we can no longer view space and time as separate
> then we
> > can't talk about physical objects being changed at all. Physical
> objects
> > just are - as mathematical objects just are. Physical objects are
> > characterized by substance and spatio-temporal extent, mathematical
> objects
> > are characterized by logical consistency and implication.
> >
> > Our minds can and do experience and explore both types of objects in
a
> > perfectly analogous fashion - or can you demonstrate that they
don't?
>
> Again, can you explain what you mean more fully. My understanding of
> mathematics is very limited, as is my understanding of physics, and
your
> posts tend to go over my head. It seems to me that mathematics and
> physics are attempts by people to understand their world and that they
> do not have any independent existence.
>
exposed to them more tend (tend, mind you, it isn't always the case, or
absolute) to have a feeling that they have an external existance of some
sort - platonism in other words.
--
High hopes were once formed of democracy; but democracy means simply the
bludgeoning of the people by the people for the people. It has been
found out. I must say that it was high time, for all authority is quite
degrading. It degrades those who exercise it, and degrades those over
whom it is exercised.
Oscar Wilde
Peter H.M. Brooks
> news:DC6v7.7258$jE3.8...@news6-win.server.ntlworld.com...
> >
> > "Peter H.M. Brooks" <pe...@new.co.za> wrote in message
> > news:9piejj$4e5$1...@ctb-nnrp1.saix.net...
> >
> > >Can a non-physical thing (say the number '3' or PI, or
> > > a program to calculate prime numbers) cause a physical event?
> >
> > I don't accept that the number 3 and pi are non-physical things. Are
> > they not just ideas (neural events) in our heads?
>
> Is it your view then that mathematical understanding is limited to the
human
> brain - or at the very least to biological systems containing neurons?
>
>
> > Are you not running
> > into that thorny issue for dualists - how could a non-physical event
> > interact with a physical event?
>
> What about a physical event and a non-physical object conspiring to
produce
> a mental event?
>
>
> Look at it this way, by looking at a physical object from a different
> viewpoint I don't change that object but I do change my perception and
hence
> my experience of it.
>
> In any case, since we can no longer view space and time as separate
then we
> can't talk about physical objects being changed at all. Physical
objects
> just are - as mathematical objects just are. Physical objects are
> characterized by substance and spatio-temporal extent, mathematical
objects
> are characterized by logical consistency and implication.
>
and may cease to be if all minds were to disappear tomorrow.
>
> Our minds can and do experience and explore both types of objects in a
> perfectly analogous fashion - or can you demonstrate that they don't?
>
Des
>
> Where else could mathematical understanding take place except in brains?
>
a cloud of gas
a hot cup of tea
a house brick
a computer
Though personally I can't imagine what it would mean for such things to have
any sense of understanding
>
> Can you give me an example of a non-physical object?
Concepts such as truth, beauty and love, or the axioms of some formal
mathematical system.
>
> Again, can you explain what you mean more fully.
Well, both physical and mathematical environments can be explored
independently by different conscious beings and those beings will experience
the same facts/truths about those environments. Does this not suggest that
those truths are external to the beings doing the exploring.
> My understanding of
> mathematics is very limited, as is my understanding of physics, and your
> posts tend to go over my head. It seems to me that mathematics and
> physics are attempts by people to understand their world and that they
> do not have any independent existence.
>
Well I would certainly agree that any form of understanding cannot have a
detached existance from a conscious being. But I would also argue that the
human experience rests equally on non-physical or atemporal aspects of
reality as it does on physical aspects.
My point is that unless you can make a testable case for assigning a
different level of ontology to logical/mathematical truths than to physical
ones then I would prefer to keep them at the same level. This is also in
line with my intuitive feelings and my belief that understanding and mental
events in general cannot be adequately explained by a purely materialistic
model of reality.
Des
Des
> >
> > In any case, since we can no longer view space and time as separate
> then we
> > can't talk about physical objects being changed at all. Physical
> objects
> > just are - as mathematical objects just are. Physical objects are
> > characterized by substance and spatio-temporal extent, mathematical
> objects
> > are characterized by logical consistency and implication.
> >
> Indeed, but the latter is a considerably less concrete sort of existance
Well this is certainly true if by concrete you mean having physical
substance and spatio-temporal extent.
Iow, I agree that you can't stub your toe on a mathematical truth, but that
doesn't make it any less real.
> and may cease to be if all minds were to disappear tomorrow.
Not really, only the perception of those objects would disappear - as would
the perception of physical objects.
In any case, mathematical objects, being atemporal, cannot cease - they just
are.
Des
Peter H.M. Brooks
>
> > >
>
> > Indeed, but the latter is a considerably less concrete sort of
existance
>
> Well this is certainly true if by concrete you mean having physical
> substance and spatio-temporal extent.
> Iow, I agree that you can't stub your toe on a mathematical truth, but
that
> doesn't make it any less real.
>
>
> > and may cease to be if all minds were to disappear tomorrow.
>
> Not really, only the perception of those objects would disappear - as
would
> the perception of physical objects.
> In any case, mathematical objects, being atemporal, cannot cease -
they just
> are.
>
somewhere?
kames.smiths
> > Can you give me an example of a non-physical object?
> Concepts such as truth, beauty and love, or the axioms of some formal
> mathematical system.
You are talking about thoughts and feelings. I would tend to classify
these as processes or events rather than objects (though I suppose they
can be said to be 'objects' of thought, in that metaphorical sense of
the word object). Whether ideas and feelings are physical or
non-physical is not clear. My own guess is that some physical processes
have a subjective as well as an objective component - it feels like
something to be them.
> Well, both physical and mathematical environments can be explored
> independently by different conscious beings and those beings will
experience
> the same facts/truths about those environments. Does this not suggest
that
> those truths are external to the beings doing the exploring.
Not necessarily. Perhaps beings with similar perceptual and conceptual
mechanisms will tend to reach similar conclusions. However, I would
argue that the 'mathematical environment' is primarily constructed by
exploring the physical environment and that the two environments are not
as distinct as you seem to imply. Attributes of the physical world such
as number and shape are focused upon, and rules of arithmetic and
geometry are derived therefrom. I believe there are historical accounts
of the development of counting and so forth, but I can't claim any
familiarity with these.
> >It seems to me that mathematics and
> > physics are attempts by people to understand their world and that
they
> > do not have any independent existence.
> >
> Well I would certainly agree that any form of understanding cannot
have a
> detached existance from a conscious being. But I would also argue that
the
> human experience rests equally on non-physical or atemporal aspects of
> reality as it does on physical aspects.
Would you mind explaining what you mean by 'atemporal aspects of
reality'?
> My point is that unless you can make a testable case for assigning a
> different level of ontology to logical/mathematical truths than to
physical
> ones then I would prefer to keep them at the same level.
Can you have different levels of ontology?
> This is also in
> line with my intuitive feelings and my belief that understanding and
mental
> events in general cannot be adequately explained by a purely
materialistic
> model of reality.
I agree. I don't think the traditional materialistic model of reality is
tenable. However, it may be possible to widen our understanding of
physical processes so that they can be regarded as including both
experiential and material aspects.
Dave Smith
wamccabe
1. The creation of the universe. No matter how it is defined / described,
the cause must somehow be outside of the experience of the universe itself
or there must be no cause at all. It seems that all that we consider
physical is within the scope of our universe so this event (if caused) must
have a non-physical cause.
2. Entropy. Time. Any form of degradation. The cause is often stated but it
is definitely not physical. This is not an external force / object acting
upon the subject it is the nature of reality that this happens.
3. The "random" event. There are doubts about whether or not this can
happen.
"Peter H.M. Brooks" <pe...@new.co.za> wrote in message
news:9piejj$4e5$1...@ctb-nnrp1.saix.net...
> So, I may well be missing a simple and obvious case, but can you suggest
> something that is caused by a non-physical, non-living entity?
>
> --
> Quis custodiet ipsos custodes? - Who has custard with custard creams?
> Major Molesworth Major Rtd. G&T&Bar
>
>
---
Outgoing mail is certified Virus Free.
Checked by AVG anti-virus system (http://www.grisoft.com).
Version: 6.0.280 / Virus Database: 147 - Release Date: 11/09/2001
Peter H.M. Brooks
wamccabe <wamc...@ic24.net> wrote in message
news:Kr1w7.19220$Bp3.292134@news2-hme0...
> Best guesses
> 1. The creation of the universe. No matter how it is defined /
described,
> the cause must somehow be outside of the experience of the universe
itself
> or there must be no cause at all. It seems that all that we consider
> physical is within the scope of our universe so this event (if caused)
must
> have a non-physical cause.
>
example, the implosion of one universe led to the explosion of another
both would be physical events.
>
> 2. Entropy. Time. Any form of degradation. The cause is often stated
but it
> is definitely not physical. This is not an external force / object
acting
> upon the subject it is the nature of reality that this happens.
>
from the gas laws.
>
> 3. The "random" event. There are doubts about whether or not this can
> happen.
>
that there are multiple definitions. I would imagine that, however,
random events are as physical as non-random ones if either sort exist.
Des
>
> > Concepts such as truth, beauty and love, or the axioms of some formal
> > mathematical system.
>
> You are talking about thoughts and feelings. I would tend to classify
> these as processes or events rather than objects (though I suppose they
> can be said to be 'objects' of thought, in that metaphorical sense of
> the word object). Whether ideas and feelings are physical or
> non-physical is not clear.
I think it is only the perception or understanding of those objects which
can be described as a process.
Since abstract objects such as mathematical truths are not characterised by
a temporal extent then they cannot themselves be described in terms of
processes - which implicitly have a dynamic.
>My own guess is that some physical processes
> have a subjective as well as an objective component - it feels like
> something to be them.
That is my own starting point - it would seem to be irrefutable and in need
of some form of explanation.
Our current physical models do not provide any such explanation.
>
> > Well, both physical and mathematical environments can be explored
> > independently by different conscious beings and those beings will
> experience
> > the same facts/truths about those environments. Does this not suggest
> that
> > those truths are external to the beings doing the exploring.
>
> Not necessarily. Perhaps beings with similar perceptual and conceptual
> mechanisms will tend to reach similar conclusions. However, I would
> argue that the 'mathematical environment' is primarily constructed by
> exploring the physical environment and that the two environments are not
> as distinct as you seem to imply.
I agree that it is primarilly the manifestation of mathematical truths in
our physical environment which allows us to explore those truths. But that
is because we are (at least in part) physical beings and because the mental
process of understanding seems to represent some form of connection between
the concrete and the abstract.
>Attributes of the physical world such
> as number and shape are focused upon, and rules of arithmetic and
> geometry are derived therefrom. I believe there are historical accounts
> of the development of counting and so forth, but I can't claim any
> familiarity with these.
Yes, it is clear that there is some form of evolutionary history to the
development of mathematical understanding. It's also interesting to note
that most of this evolution would appear to have happened later and quite
separately from any significant biological evolution.
>
> Would you mind explaining what you mean by 'atemporal aspects of
> reality'?
Simply that mathematical truths are not characterised by time or space. It
makes no sense to ask where a mathematical truth resides or when it came
into being. Such truths are nevertheless an essential part of the fabric of
reality.
>
> > My point is that unless you can make a testable case for assigning a
> > different level of ontology to logical/mathematical truths than to
> physical
> > ones then I would prefer to keep them at the same level.
>
> Can you have different levels of ontology?
I guess that's more a matter of definition and interpretation and I'm happy
to defer to trained philosophers in such matters of usage. The phrase
"levels of ontology" certainly has some currency - as a quick google search
will show. However what I mean is that there are no grounds for believing
that we can explain the mathematical in terms of the material - or vice
versa. We need to add both of these as distinct irreducible elements to our
explanatory framework.
>
> > This is also in
> > line with my intuitive feelings and my belief that understanding and
> mental
> > events in general cannot be adequately explained by a purely
> materialistic
> > model of reality.
>
> I agree. I don't think the traditional materialistic model of reality is
> tenable. However, it may be possible to widen our understanding of
> physical processes so that they can be regarded as including both
> experiential and material aspects.
>
That's rather what I'm hoping will be possible.
I don't have a problem with describing understanding as physical if physical
is defined broadly enough to encompass the entire human experience and not
just those aspects which can be measured directly or empirically.
I still hold to the view that a sensible explanatory framework for the human
experience should incude material, logical and mental.
Des
Des
>
> Des <DesGr...@removebtclick.com> wrote in message
> news:eFCv7.636$sI1.4722@NewsReader...
> >
> > > >
> >
> > > Indeed, but the latter is a considerably less concrete sort of
> existance
> >
> > Well this is certainly true if by concrete you mean having physical
> > substance and spatio-temporal extent.
> > Iow, I agree that you can't stub your toe on a mathematical truth, but
> that
> > doesn't make it any less real.
> >
> If it requires minds to exist then it is less real.
On which basis the material and mathematical are equally real.
> >
> > > and may cease to be if all minds were to disappear tomorrow.
> >
> > Not really, only the perception of those objects would disappear - as
> would
> > the perception of physical objects.
> > In any case, mathematical objects, being atemporal, cannot cease -
> they just
> > are.
> >
> So you are claiming that undescovered mathematical truths already exist
> somewhere?
>
I've tried to stress that mathematical truths are not characterised by time
or space. So it makes no sense at all to use the words already or somewhere
in relation to them.
You need to distinguish between mathematical truths and the perception of
those truths. Just as you need to distinguish between the complete material
world and the partial and classical views of that world which we experience.
Des
Peter H.M. Brooks
human
> experience should incude material, logical and mental.
>
actually understand anything and everything, must remain only mental -
even if it were to be completely described materially. The material
world, despite being so described, must remain material, even if the
material being described gives rise to (through supervenience or
emergence) our subjective selves. I think that the logical must be part
of the mental, despite the platonic temptation to see it separate. I
think that our view of maths, physics and logic has, as in Hopkins
metaphor, become a cage of sand that seems to us composed of steel
cable. Its apparent external existence simply proves what a powerful
model of the objective world we have built, not that this apparently
separate existence is real in the same sense as the physical world.
If it were real then we would have to accept, for example, that the
separate geometries that arise from making the three possible fifth
postulates all existed, and exist, all the time in contradiction to each
other. I know that this appears to be the case in space, but, again,
this, counter intuitively, suggests that all three can't be real at the
same time - reality really isn't consistent in the way our minds would
like it to be.
I am also interested, though not enough yet to explore the matter
properly, in what happens in the nexus between the two non-Euclidean
worlds and the Euclidean. It seems to me that this may be more than just
a metaphorical comparison between the meeting of mind and the material
world, but might contain some seeds of the explanation. It does truly
puzzle me, too, as I can see how a singularity can be constructed to
take care of this in a continuous world, but we know that space, at
least, is discrete, so there isn't really a place for two smeared
singularities between Euclidean and non Euclidean space - there appears
that there has to be a particular physical point where the axiom system
moves from one to another. To me this seems even more disturbing than a
smeared singularity.
Peter H.M. Brooks
>
> > So you are claiming that undescovered mathematical truths already
exist
> > somewhere?
> >
>
> I've tried to stress that mathematical truths are not characterised by
time
> or space. So it makes no sense at all to use the words already or
somewhere
> in relation to them.
>
The problem is that some constructions appear not to be necessary
truths. In other words, it may seem reasonable that, at time t, before
somebody made the construction, it is unreasonable to suggest that they
already exist somewhere. So, like a painiting (and you could argue that
there was a space filled with all possible paintings with them just
waiting for a painter to come along and realise them) the mathematician
has created a new mathematical truth. If such constructions of novel,
non-necessary truths are possible, then there will be a time before they
exist and a time after they have become to exist.
>
> You need to distinguish between mathematical truths and the perception
of
> those truths. Just as you need to distinguish between the complete
material
> world and the partial and classical views of that world which we
experience.
>
I agree that that distinction is important. The question is if a truth
that hasn't yet been perceived currently exists in some sense - as I say
above, I can imagine how this would be necessary of many things, but it
stretches credulity for it to be true of everything.
Peter Ashby
"Des" <DesGr...@removebtclick.com> wrote:
> "Peter H.M. Brooks" <pe...@new.co.za> wrote in message
> news:9pn7rd$ssp$1...@ctb-nnrp2.saix.net...
> > If it requires minds to exist then it is less real.
>
> On which basis the material and mathematical are equally real.
On which basis neither of the above existed prior to minds which is
absurd and in contravention to observations. That is unless you wish to
postulate some form of god or some sort of alien consciousness which
formed in the Big Bang.
Peter
--
Peter Ashby
Wellcome Trust Biocentre
University of Dundee
Dundee, Scotland
Reverse the spam and remove to email me.
Des
"Peter Ashby" <p.r....@dundee.MAPS.ac.uk> wrote in message
news:p.r.ashby-935C6...@dux.dundee.ac.uk...
> In article <yTew7.7869$sI1.34965@NewsReader>,
> "Des" <DesGr...@removebtclick.com> wrote:
>
> > "Peter H.M. Brooks" <pe...@new.co.za> wrote in message
> > news:9pn7rd$ssp$1...@ctb-nnrp2.saix.net...
>
> > > If it requires minds to exist then it is less real.
> >
> > On which basis the material and mathematical are equally real.
>
> On which basis neither of the above existed prior to minds which is
> absurd and in contravention to observations. That is unless you wish to
> postulate some form of god or some sort of alien consciousness which
> formed in the Big Bang.
>
You need to understand that mathematical objects are not characterised by
spatio-temporal extent. Therefore it makes no sense to talk about a time
before they existed. You are confusing the objects themselves with their
pereception.
By the same token however, if you remove the subjective (ie mental) element
from the world then it is difficult to describe any form of dynamic in the
universe at all - iow, it is difficult to make an objective distinction
between space and time.
But before we go off into some meaningless and fruitless argument about what
is real and what is subordinate, let me say that in this context I am
talking about the elements of an explanatory framework whose purpose is to
produce an explanatory model of the complete human experience. What I am
saying is that such a framework requires (at least) material and
mathematical components and that both of those components must be distinct
and irreducible.
Des
Peter H.M. Brooks
about what
> is real and what is subordinate, let me say that in this context I am
> talking about the elements of an explanatory framework whose purpose
is to
> produce an explanatory model of the complete human experience. What I
am
> saying is that such a framework requires (at least) material and
> mathematical components and that both of those components must be
distinct
> and irreducible.
>
description is required to do the reduction from a neurone firing to the
physics of the cell. However, I would have thought it possible to
describe the world without mathematics - historians do it all the time.
Des
>
>........................................I think that the logical must be
part
> of the mental, despite the platonic temptation to see it separate. I
> think that our view of maths, physics and logic has, as in Hopkins
> metaphor, become a cage of sand that seems to us composed of steel
> cable. Its apparent external existence simply proves what a powerful
> model of the objective world we have built, not that this apparently
> separate existence is real in the same sense as the physical world.
I'm begining to think that the problems that people have with accepting the
independent existence of mathematics, stem from a natural attempt to assign
a time and a space to mathematical objects. In my case I seek to isolate the
components that are required to create a complete explanation of the human
experience and in doing so I come to the conclusion that an essential
ingredient is not only the language of logic and mathematics but the
independent existance of such objects. The relationship between an
explanation of our experience and the relaity of our experience is a rather
subtle one and I would expect different people to have different takes on
that. However, if it is a good explanation then it should tell the story not
just of what we do expereince but also of what we might experience - and of
course it should be testable.
>
> If it were real then we would have to accept, for example, that the
> separate geometries that arise from making the three possible fifth
> postulates all existed, and exist, all the time in contradiction to each
> other. I know that this appears to be the case in space, but, again,
> this, counter intuitively, suggests that all three can't be real at the
> same time - reality really isn't consistent in the way our minds would
> like it to be.
Euclidian geometry is a strange example to chose if you are arguing that
mathematics is subordinate to the physical, since nowhere in nature is it
actually realised. In fact it would seem that the 2 dimensions of Euclidian
geometry are insufficent for any interesting physics since we need at least
3 spatial dimensions to allow the symmetries behind the standard model which
results in the beautiful balance of the known forces. Indeed, if we want to
unify these forces then we need to look at structures in even higher
dimensions.
Even if we extend Euclidian geometry to 3 spatial dimensions then we are
struggling to realise most of the postulates due to relativity and the need
for an infinite space. As a mathematical tool however, the notion of a 3+1
Euclidian space time allows us to extend our ordinary calculus to deal with
more realistic space times - space times in which the (equivalent of) the
5th postulate can take on all of its possible values.
So it would seem that Euclidian geometry is an entirely abstract object, the
truth of which has allowed us to greatly extend our explanations of the
realtionship between space, time and matter. Iow, a perfect example of the
interplay between mind, matter and maths (TM).
>
> I am also interested, though not enough yet to explore the matter
> properly, in what happens in the nexus between the two non-Euclidean
> worlds and the Euclidean. It seems to me that this may be more than just
> a metaphorical comparison between the meeting of mind and the material
> world, but might contain some seeds of the explanation. It does truly
> puzzle me, too, as I can see how a singularity can be constructed to
> take care of this in a continuous world, but we know that space, at
> least, is discrete, so there isn't really a place for two smeared
> singularities between Euclidean and non Euclidean space - there appears
> that there has to be a particular physical point where the axiom system
> moves from one to another. To me this seems even more disturbing than a
> smeared singularity.
>
I'm not sure I understand the point you are making here.
However it is true that our current best model of space, time and matter
(General Relativity) can only be a large scale approximation. A number of
models are competing to bridge the gap between the discrete quantum world
and the large scale world of the cosmos. The chief contenders are string
theory and quantum gravity. I won't pretend to understand these to any great
extent but I will say that they are in large part geometric in nature, with
the basic elements of space-time being topological entities.
One thing I have found is that the more closely you examine the material
world, the more mathematical its structure begins to look.
Des
Des
>
> Des <DesGr...@removebtclick.com> wrote in message
> >
> >
> > But before we go off into some meaningless and fruitless argument
> about what
> > is real and what is subordinate, let me say that in this context I am
> > talking about the elements of an explanatory framework whose purpose
> is to
> > produce an explanatory model of the complete human experience. What I
> am
> > saying is that such a framework requires (at least) material and
> > mathematical components and that both of those components must be
> distinct
> > and irreducible.
> >
> I am not sure about that. Surely, I agree that a mathematical
> description is required to do the reduction from a neurone firing to the
> physics of the cell. However, I would have thought it possible to
> describe the world without mathematics - historians do it all the time.
>
Mathematics is surely just a particularly pure form of language. If one told
the story of the physics of a neuron in a human language then the basic
truths of that story (or explanation) would remain the same subject to the
inaccuracies of that language. In particualr, any predictions that were made
should still be testable.
Des
Peter H.M. Brooks
accepting mathematics as a separate space, platonism is instinctively,
apparently, desireable to me. I am concerned that my instinctive feeling
doesn't have a proper grounding, though. Not because of the non-temporal
question, but by the reification of maths not having any justification.
>
> >
> > If it were real then we would have to accept, for example, that the
> > separate geometries that arise from making the three possible fifth
> > postulates all existed, and exist, all the time in contradiction to
each
> > other. I know that this appears to be the case in space, but, again,
> > this, counter intuitively, suggests that all three can't be real at
the
> > same time - reality really isn't consistent in the way our minds
would
> > like it to be.
>
> Euclidian geometry is a strange example to chose if you are arguing
that
> mathematics is subordinate to the physical, since nowhere in nature is
it
> actually realised. In fact it would seem that the 2 dimensions of
Euclidian
> geometry are insufficent for any interesting physics since we need at
least
> 3 spatial dimensions to allow the symmetries behind the standard model
which
> results in the beautiful balance of the known forces. Indeed, if we
want to
> unify these forces then we need to look at structures in even higher
> dimensions.
>
On billiard tables Euclidian geometry applies as closely as anybody
would wish to measure.
>
> Even if we extend Euclidian geometry to 3 spatial dimensions then we
are
> struggling to realise most of the postulates due to relativity and the
need
> for an infinite space. As a mathematical tool however, the notion of a
3+1
> Euclidian space time allows us to extend our ordinary calculus to deal
with
> more realistic space times - space times in which the (equivalent of)
the
> 5th postulate can take on all of its possible values.
>
> So it would seem that Euclidian geometry is an entirely abstract
object, the
> truth of which has allowed us to greatly extend our explanations of
the
> realtionship between space, time and matter. Iow, a perfect example of
the
> interplay between mind, matter and maths (TM).
>
any essential way.
euclidean geometry works. If you measure sub-atomic distances on
non-euclidean geometry works - if you measure inter-galactic distances
the other. Space is discrete, so where does a sub-atomic distance turn
into a macroscopic one and where does a macoscopic distance turn into a
megascopic one, to use an ugly neolgism.
>
> One thing I have found is that the more closely you examine the
material
> world, the more mathematical its structure begins to look.
>
the more the patterns you are using appear to fit, because you get more
used to the patterns, not necessarily because they actually fit better.
Peter H.M. Brooks
>
> > > But before we go off into some meaningless and fruitless argument
> > about what
> > > is real and what is subordinate, let me say that in this context I
am
> > > talking about the elements of an explanatory framework whose
purpose
> > is to
> > > produce an explanatory model of the complete human experience.
What I
> > am
> > > saying is that such a framework requires (at least) material and
> > > mathematical components and that both of those components must be
> > distinct
> > > and irreducible.
> > >
> > I am not sure about that. Surely, I agree that a mathematical
> > description is required to do the reduction from a neurone firing to
the
> > physics of the cell. However, I would have thought it possible to
> > describe the world without mathematics - historians do it all the
time.
> >
>
> Mathematics is surely just a particularly pure form of language.
>
separate existance any more than Moby Dick does.
>
> If one told
> the story of the physics of a neuron in a human language then the
basic
> truths of that story (or explanation) would remain the same subject to
the
> inaccuracies of that language. In particualr, any predictions that
were made
> should still be testable.
>
result of ambiguity, mathematics, through being tautologous and, as you
say, a simplified language, removes ambiguity. Sadly, in interpreting
mathematics, people often add the ambiguity again.
Des
> >
> > If one told
> > the story of the physics of a neuron in a human language then the
> basic
> > truths of that story (or explanation) would remain the same subject to
> the
> > inaccuracies of that language. In particualr, any predictions that
> were made
> > should still be testable.
> >
> Indeed, no argument there! Most of the inaccuracies in language are a
> result of ambiguity, mathematics, through being tautologous and, as you
> say, a simplified language, removes ambiguity. Sadly, in interpreting
> mathematics, people often add the ambiguity again.
>
Yes I would agree with this too.
History is littered with examples of people who have failed to take the
implications of mathematical models seriously
One thinks of Einstein's cosmological constant and attempts to cherry pick
from quantum mechanics.
It is interesting to note that high energy theoretical physicists have
currently (at least in some cases) exceeded the ability of experiments to
test their predictions. In the absence of such experiments, the development
of those models is being driven largely by mathematical completeness and
elegance considerations - one thinks of string theory and super symmetry
theories. It will be interesting to see if nature complies with these
notions of mathematical beauty - if she does then it will certainly not be
the first time.
Des
Peter H.M. Brooks
edifices - if she doesn't. One thinks of Aristotle.
Des
> > It is interesting to note that high energy theoretical physicists have
> > currently (at least in some cases) exceeded the ability of experiments
> to
> > test their predictions. In the absence of such experiments, the
> development
> > of those models is being driven largely by mathematical completeness
> and
> > elegance considerations - one thinks of string theory and super
> symmetry
> > theories. It will be interesting to see if nature complies with these
> > notions of mathematical beauty - if she does then it will certainly
> not be
> > the first time.
> >
> Nor would it be the first time nature didn't comply with theoretical
> edifices - if she doesn't. One thinks of Aristotle.
>
Aristotle didn't destroy any notion that there was a close connection
between mathematics and nature he merely shifted the balance back to
observation based science - a balance which I think we retain today.
Nevertheless it would stretch the imagination beyond breaking point to
believe that each time a new fundamental particle is created (and consider
the number of times that happens) it's structure is somehow randomly
reinvented. Far more sensible to believe that these patterns and symmetries
exist as atemporal components of the fabric of reality.
Des
Peter H.M. Brooks
>
>
> Nevertheless it would stretch the imagination beyond breaking point to
> believe that each time a new fundamental particle is created (and
consider
> the number of times that happens) it's structure is somehow randomly
> reinvented. Far more sensible to believe that these patterns and
symmetries
> exist as atemporal components of the fabric of reality.
>
material. I have no problem accepting that they existed long before they
were discovered - and I think that the term 'discovered' is the correct
one.
If mathematical objects existed in some platonic space having picnics
together etc. waiting for people to discover them like some tribe in the
upper reaches of the Amazon, then I would feel the same way about them.
I also feel happy that some patterns (the circumference of a circle
being pi times the diameter) are part of the structure of fabric of
reality, as are many symmetries [which are really just one form of
pattern]. However, I am not sure that all mathematics is reflected in
the fabric of reality, or, if it is, that this reflection is
consistent - I mentioned Euclidean and non-Euclidean geometries as an
example of observed inconsistency which I think points this matter up.
Des
>
> You are shifting the goal posts rather here. Fundamental particles are
> material. I have no problem accepting that they existed long before they
> were discovered - and I think that the term 'discovered' is the correct
> one.
The particles were discovered in the same way that the mathematical
symmetries that underly them were.
But my point was not whether or not these particles existed before they were
discovered. My point was that these particles can be created (including
ex-nihil - or at least ex-vacuo) so that the space-time symmetries which
they represent must in some sense exist in readiness for these particles to
instantiate them.
>
> If mathematical objects existed in some platonic space having picnics
> together etc. waiting for people to discover them like some tribe in the
> upper reaches of the Amazon, then I would feel the same way about them.
I don't think mathematical objects have picnics.
> I also feel happy that some patterns (the circumference of a circle
> being pi times the diameter) are part of the structure of fabric of
> reality, as are many symmetries [which are really just one form of
> pattern].
Well that's a start.
But having started why not go all the way and accept that all abstract or
non-material objects have the same type of existence?
>However, I am not sure that all mathematics is reflected in
> the fabric of reality, or, if it is, that this reflection is
> consistent - I mentioned Euclidean and non-Euclidean geometries as an
> example of observed inconsistency which I think points this matter up.
>
I'm probably being a bit slow here but I still don't "grok" your example of
Euclidean and non-Euclidean geometries.
Surely these are just different geometries that arise from different sets of
axioms?
Maybe you could elaborate for my benefit?
Truth in relation to mathematical objects can either take the form of
consistency with other mathematical objects or consistency with some mapping
to the material world. Your examples are each true in terms of their
mathematical consistency but it would seem that they are only approximately
true in terms of their consistency with the material world.
Des
Peter H.M. Brooks
>
> "Peter H.M. Brooks" <pe...@new.co.za> wrote in message
> news:9pue79$re8$1...@ctb-nnrp1.saix.net...
> >
> > You are shifting the goal posts rather here. Fundamental particles
are
> > material. I have no problem accepting that they existed long before
they
> > were discovered - and I think that the term 'discovered' is the
correct
> > one.
>
> The particles were discovered in the same way that the mathematical
> symmetries that underly them were.
>
physical prediction which can then be tested - the positive result of
the testing of the physical prediction is the actual discovery. However
neat the maths, if its predictions are false, then it isn't a material
discovery - though it remains a mathematical one.
>
> But my point was not whether or not these particles existed before
they were
> discovered. My point was that these particles can be created
(including
> ex-nihil - or at least ex-vacuo) so that the space-time symmetries
which
> they represent must in some sense exist in readiness for these
particles to
> instantiate them.
>
unstable atom to a lower one in a nuclear reactor or bomb, you turn
matter into energy, so we are familiar with matter existing and not
existing at different times.
>
> >
> > If mathematical objects existed in some platonic space having
picnics
> > together etc. waiting for people to discover them like some tribe in
the
> > upper reaches of the Amazon, then I would feel the same way about
them.
>
> I don't think mathematical objects have picnics.
>
A 'picnic' is defined as a function P, that maps a set O of mathematical
objects (o0..oN) onto a set B (b0..bN) where for any arbirary distance
metric m, m(oi,oj) < m(bi,bj) and there exists a distance known as
'blanket' for which |m(bi,bj) - m(oi,oj)| <= |blanket| after the
application of P.
Now, after mid-day on the 9th October 2001, it can be said that some
mathematical objects have picnics on blankets.
You may argue now, that I have simply, through making the above
definition, discovered mathematical objects at their picnic and that you
were retrospectivly wrong in saying that they don't have picnics.
However, I would say that I have invented mathematical picnics [unless,
of course, Torkel, or some other kind soul, can point to an earlier
definition of a mathematical picnic {maybe, if you class mathematicians
as mathematical objects (in some sense) a departmental outing could be a
mathematical picnic}].
>
>
> > I also feel happy that some patterns (the circumference of a circle
> > being pi times the diameter) are part of the structure of fabric of
> > reality, as are many symmetries [which are really just one form of
> > pattern].
>
> Well that's a start.
> But having started why not go all the way and accept that all abstract
or
> non-material objects have the same type of existence?
>
Because I would have to argue that my abstract painting 'Chaos I - 1996'
http://www.psyche.demon.co.uk/tone.jpg existed before I painted it. I
have great difficulty accepting that as true. Mind you, I know you are
not arguing that the paint itself, in that configuration, existed, but
the mental structure of that painting as, possibly, represented by a
relation existed.
>
> >However, I am not sure that all mathematics is reflected in
> > the fabric of reality, or, if it is, that this reflection is
> > consistent - I mentioned Euclidean and non-Euclidean geometries as
an
> > example of observed inconsistency which I think points this matter
up.
> >
>
> I'm probably being a bit slow here but I still don't "grok" your
example of
> Euclidean and non-Euclidean geometries.
> Surely these are just different geometries that arise from different
sets of
> axioms?
> Maybe you could elaborate for my benefit?
>
Yes, they are different geometries. For example, in this web-page
http://darc.obspm.fr/~luminet/etopo.html the following paragraph occurs:
"
The question of the extension of space is perfectly well put within the
framework of the Friedmann-Lemaître models, called more commonly
"big-bang models". These ones assume that
the universe has the same properties everywhere (space is known as "
homogeneous and isotropic "). The geometrical properties of space are of
two kinds only: the curvature, constant in
space when matter is uniformly distributed, and the topology. Regarding
the curvature, three families of spaces can be considered: Euclidean
space (zero curvature), spherical space
(positive curvature) and hyperbolic space (negative curvature).
Spherical space is, in all the cases, finite (it is one of the reasons
for which Einstein, in the spirit of Parmenides, choose it
initially). For spaces belonging to the two other families, the finite
or infinite character depends on topology. In the simplest versions
however (simply-connected topologies), they are
infinite.
"
Now it is my understanding that real space exhibits, depending on scale,
all three curvatures. As I said, billiard ball space [everyday human
distances] show zero curvature, the other two are found at
inter-galactic distances or microscopic distances.
This article at http://www.unesco.org/courier/2001_05/uk/doss14.htm
makes the point that the curvature of space has changed over time, but
also mentions the scale of observation (something that would be
unnecessary if curvature was constant over all scales):
"Now if we turn to the universe as a whole-by which we mean huge scales
of over 1025 metres-it appears that the virtually uniform
distribution of galaxies throughout the cosmos
must curve space in a likewise uniform fashion. Aside from this constant
curvature, the
universe should also have an underlying dynamic:
in other words, it can either be expanding or contracting.
On the basis of Einstein's equations, Alexander
Friedmann and Georges Lemaître discovered in the 1920s a set of models
for such curved
space. The most simple version points to so-called
positive curvature, resembling a simple sphere that dilates from the big
bang onwards to
reach a maximum size before contracting back into
a final "big crunch." Space could also have no curvature or a negative
curvature (forming
a "hyperbolic" shape that resembles a saddle). In
both of these cases, the universe expands forever, though the rate of
expansion slows
over time.
Recent observations have suggested that cosmic
space is in fact close to the "no curvature" model-in other words it is
flat and almost
Euclidean, like our normal understanding of space.
But the data also indicates that the universe is expanding at an
increasing rate,
suggesting that some kind of "cosmological
constant" is accelerating the expansion rate.
"
>
> Truth in relation to mathematical objects can either take the form of
> consistency with other mathematical objects or consistency with some
mapping
> to the material world. Your examples are each true in terms of their
> mathematical consistency but it would seem that they are only
approximately
> true in terms of their consistency with the material world.
>
Yes. I would say that truth only applies to internal consistency.
Mappings to the real world are useful, accurate to some extent or
currently the best we have, I doubt that 'true' is a possible thing for
them to be. At least not in the same way that mathematical truth is
true.
Des
> > symmetries that underly them were.
> >
> Up to a point. The mathematical 'finding' of a particle is linked to a
> physical prediction which can then be tested - the positive result of
> the testing of the physical prediction is the actual discovery. However
> neat the maths, if its predictions are false, then it isn't a material
> discovery - though it remains a mathematical one.
I would say that physical and mathematical detection in modern high energy
colliders are inseperable.
Sub atomic particles are rarely seen directly and these days they are only
"seen" at all by means of very the powerful numerical analyses of associated
reactions.
> >
> > But my point was not whether or not these particles existed before
> they were
> > discovered. My point was that these particles can be created
> (including
> > ex-nihil - or at least ex-vacuo) so that the space-time symmetries
> which
> > they represent must in some sense exist in readiness for these
> particles to
> > instantiate them.
> >
> Indeed, but I don't see this as a problem. If you convert a high weight
> unstable atom to a lower one in a nuclear reactor or bomb, you turn
> matter into energy, so we are familiar with matter existing and not
> existing at different times.
Right, but before the particle existed - where did it's pattern or structure
exist?
>
> Now, after mid-day on the 9th October 2001, it can be said that some
> mathematical objects have picnics on blankets.
This is indeed the sort of connection between the mathematical and the
physical that I had in mind.
>
> You may argue now, that I have simply, through making the above
> definition, discovered mathematical objects at their picnic and that you
> were retrospectivly wrong in saying that they don't have picnics.
No, the mathematical objects don't have picnics - they just are.
But those objects have combined with your vivid imagination to produce a
mental process in which they are perceived as having picnics.
> However, I would say that I have invented mathematical picnics [unless,
> of course, Torkel, or some other kind soul, can point to an earlier
> definition of a mathematical picnic {maybe, if you class mathematicians
> as mathematical objects (in some sense) a departmental outing could be a
> mathematical picnic}].
I think that you have indeed invented the mathematical picnic.
But as I said earlier, your mathematical picnic is a mental construct
produced by mapping a particular set of mathematical abstractions onto a
particular set of physical circumstances. You illustrate the power of my
proposed explanatory framework very well.
> > I'm probably being a bit slow here but I still don't "grok" your
> example of
> > Euclidean and non-Euclidean geometries.
> > Surely these are just different geometries that arise from different
> sets of
> > axioms?
> > Maybe you could elaborate for my benefit?
> >
> Yes, they are different geometries. For example, in this web-page
> http://darc.obspm.fr/~luminet/etopo.html the following paragraph occurs:
>
> "
> "
> Now it is my understanding that real space exhibits, depending on scale,
> all three curvatures. As I said, billiard ball space [everyday human
> distances] show zero curvature, the other two are found at
> inter-galactic distances or microscopic distances.
>
Firstly, it's not so easy to separate space and time in this context, one
normally thinks of the curvature and topology of the space-time manifold -
there being no simple global foliation of a general manifold into purely
spacelike hypersurfaces.
You should also note that the latest findings show that space appears to be
extremely flat on an inter-galactic scale. However significant positive
space-space curvature is found here on Earth and is responsible for the
tides. It is also necessary to account for this curvature when using GPS
systems - though fortunately it is built into the circuitry. I'm not sure
whether we ever see any negative space-space curvature in traditional 3D
space - although the string theoreticians require every possible variation
in the smallest of volumes.
And don't forget the much more significant space-time curvature which is
what causes an inertial body to appear to fall downwards. It would be
foolish to neglect this particular component of curvature even (in fact
especially) on a billiard table since without it you would risk losing your
balls!
But if your point is that we can approximate a non zero curvature locally
(ie within an arbitrarily small element of space-time) by a flat space
model - then yes that would be true outside a singularity. In fact this
really just amounts to a generalisation of Taylor's theorem and was the key
to formulating the original field equations.
> > Truth in relation to mathematical objects can either take the form of
> > consistency with other mathematical objects or consistency with some
> mapping
> > to the material world. Your examples are each true in terms of their
> > mathematical consistency but it would seem that they are only
> approximately
> > true in terms of their consistency with the material world.
> >
> Yes. I would say that truth only applies to internal consistency.
> Mappings to the real world are useful, accurate to some extent or
> currently the best we have, I doubt that 'true' is a possible thing for
> them to be. At least not in the same way that mathematical truth is
> true.
>
In his book "The Fabric of Reality" David Deutsch makes a powerful argument
for both material and mathematical aspects of reality being identical in
this respect. Effectively, he argues that mathematical truths are subject to
the same type of uncertainties as those relating to physics.
Des
Peter H.M. Brooks
>
> "Peter H.M. Brooks" <pe...@new.co.za> wrote in message
> news:9pum9d$sp6$1...@ctb-nnrp1.saix.net...
> >
> > Des <DesGr...@removebtclick.com> wrote in message
> > news:hUzw7.347$qg3.3755@NewsReader...
> > >
> > >
> > > The particles were discovered in the same way that the
mathematical
> > > symmetries that underly them were.
> > >
> > Up to a point. The mathematical 'finding' of a particle is linked to
a
> > physical prediction which can then be tested - the positive result
of
> > the testing of the physical prediction is the actual discovery.
However
> > neat the maths, if its predictions are false, then it isn't a
material
> > discovery - though it remains a mathematical one.
>
> I would say that physical and mathematical detection in modern high
energy
> colliders are inseperable.
>
there is a place for a philosophical separation, though.
>
> Sub atomic particles are rarely seen directly and these days they are
only
> "seen" at all by means of very the powerful numerical analyses of
associated
> reactions.
>
things - though you could argue that everything you see is a result of
'seeing' photons.
>
>
> > >
> > > But my point was not whether or not these particles existed before
> > they were
> > > discovered. My point was that these particles can be created
> > (including
> > > ex-nihil - or at least ex-vacuo) so that the space-time
symmetries
> > which
> > > they represent must in some sense exist in readiness for these
> > particles to
> > > instantiate them.
> > >
> > Indeed, but I don't see this as a problem. If you convert a high
weight
> > unstable atom to a lower one in a nuclear reactor or bomb, you turn
> > matter into energy, so we are familiar with matter existing and not
> > existing at different times.
>
> Right, but before the particle existed - where did it's pattern or
structure
> exist?
>
from different parts of the galaxy, the pattern they make in the pond is
something that simply happens as a result of their three separate wave
creations - it didn't have to exist in some separate space. Ditto for
the pattern of three frogs jumping into a pond.
>
>
> >
> > Now, after mid-day on the 9th October 2001, it can be said that some
> > mathematical objects have picnics on blankets.
>
> This is indeed the sort of connection between the mathematical and the
> physical that I had in mind.
>
> >
> > You may argue now, that I have simply, through making the above
> > definition, discovered mathematical objects at their picnic and that
you
> > were retrospectivly wrong in saying that they don't have picnics.
>
> No, the mathematical objects don't have picnics - they just are.
> But those objects have combined with your vivid imagination to produce
a
> mental process in which they are perceived as having picnics.
>
process.
>
> > However, I would say that I have invented mathematical picnics
[unless,
> > of course, Torkel, or some other kind soul, can point to an earlier
> > definition of a mathematical picnic {maybe, if you class
mathematicians
> > as mathematical objects (in some sense) a departmental outing could
be a
> > mathematical picnic}].
>
> I think that you have indeed invented the mathematical picnic.
>
>
> But as I said earlier, your mathematical picnic is a mental construct
> produced by mapping a particular set of mathematical abstractions onto
a
> particular set of physical circumstances. You illustrate the power of
my
> proposed explanatory framework very well.
>
like the others? Can't one now have a picnic of picnics?
low flying aircraft anyway.
>
> And don't forget the much more significant space-time curvature which
is
> what causes an inertial body to appear to fall downwards. It would be
> foolish to neglect this particular component of curvature even (in
fact
> especially) on a billiard table since without it you would risk losing
your
> balls!
>
two-dimensional thing (even though we know it isn't).
>
> But if your point is that we can approximate a non zero curvature
locally
> (ie within an arbitrarily small element of space-time) by a flat space
> model - then yes that would be true outside a singularity. In fact
this
> really just amounts to a generalisation of Taylor's theorem and was
the key
> to formulating the original field equations.
>
>
>
> > > Truth in relation to mathematical objects can either take the form
of
> > > consistency with other mathematical objects or consistency with
some
> > mapping
> > > to the material world. Your examples are each true in terms of
their
> > > mathematical consistency but it would seem that they are only
> > approximately
> > > true in terms of their consistency with the material world.
> > >
> > Yes. I would say that truth only applies to internal consistency.
> > Mappings to the real world are useful, accurate to some extent or
> > currently the best we have, I doubt that 'true' is a possible thing
for
> > them to be. At least not in the same way that mathematical truth is
> > true.
> >
>
> In his book "The Fabric of Reality" David Deutsch makes a powerful
argument
> for both material and mathematical aspects of reality being identical
in
> this respect. Effectively, he argues that mathematical truths are
subject to
> the same type of uncertainties as those relating to physics.
>
reference.
Des
> > Right, but before the particle existed - where did it's pattern or
>> structure
> > exist?
> >
> I don't see that it has to. If three micro-metiorites fall into a pond
> from different parts of the galaxy, the pattern they make in the pond is
> something that simply happens as a result of their three separate wave
> creations - it didn't have to exist in some separate space. Ditto for
> the pattern of three frogs jumping into a pond.
The difference is that the pattern for the electrons is always exactly the
same and is not encoded anywhere within the initial ingredients - unlike the
examples you cite where the patterns are determined in principle by the
intital conditions.
> > And don't forget the much more significant space-time curvature which
> is
> > what causes an inertial body to appear to fall downwards. It would be
> > foolish to neglect this particular component of curvature even (in
> fact
> > especially) on a billiard table since without it you would risk losing
> your
> > balls!
> >
> I am looking at the billiard table, as is conventional, as a
> two-dimensional thing (even though we know it isn't).
Yes, but even so you still require your flat 2D space to be curved wrt time
in order to keep the balls pinned to the table.
I only labour this point because people often forget this very important
component.
Des
Peter H.M. Brooks
>
> "Peter H.M. Brooks" <pe...@new.co.za> wrote in message
> news:9pv7hp$68h$1...@ctb-nnrp2.saix.net...
> >
> > Des <DesGr...@removebtclick.com> wrote in message
>
> > > Right, but before the particle existed - where did it's pattern or
> >> structure
> > > exist?
> > >
> > I don't see that it has to. If three micro-metiorites fall into a
pond
> > from different parts of the galaxy, the pattern they make in the
pond is
> > something that simply happens as a result of their three separate
wave
> > creations - it didn't have to exist in some separate space. Ditto
for
> > the pattern of three frogs jumping into a pond.
>
> The difference is that the pattern for the electrons is always exactly
the
> same and is not encoded anywhere within the initial ingredients -
unlike the
> examples you cite where the patterns are determined in principle by
the
> intital conditions.
>
they existed as a probability function between the nucleus and infinity
with a bump in a region determined by where they were in the valency
shell. Or were you talking about them when they are stripped from their
home and sent through slits?
>
>
> > > And don't forget the much more significant space-time curvature
which
> > is
> > > what causes an inertial body to appear to fall downwards. It would
be
> > > foolish to neglect this particular component of curvature even (in
> > fact
> > > especially) on a billiard table since without it you would risk
losing
> > your
> > > balls!
> > >
> > I am looking at the billiard table, as is conventional, as a
> > two-dimensional thing (even though we know it isn't).
>
> Yes, but even so you still require your flat 2D space to be curved wrt
time
> in order to keep the balls pinned to the table.
> I only labour this point because people often forget this very
important
> component.
>
necessary to be that complicated.
Des
>
> I am not sure that electrons are always the same. I rather thought that
> they existed as a probability function between the nucleus and infinity
> with a bump in a region determined by where they were in the valency
> shell. Or were you talking about them when they are stripped from their
> home and sent through slits?
No, what we measure (directly and indirectly) as an electron always has
precisely the same fundamental characteristics (within the accuracy to which
they can be measured - which is very accurate). These characterstics are
mass, charge and spin and these latter two explain the reason why the
electron can exist as either a free wave or a localised standing wave (as in
a hydrogen atome frx). Both of these charectersitics can be explained very
well in terms of multi-dimensional transformational symmetries. The question
is, where do the specifications for these symetries exist before our
brand-new electron instantiates them?
> > Yes, but even so you still require your flat 2D space to be curved wrt
> time
> > in order to keep the balls pinned to the table.
> > I only labour this point because people often forget this very
> important
> > component.
> >
> True, though, using Euclidean geometry and Newtonian mechanics it isn't
> necessary to be that complicated.
>
>
It does if you are looking for an explanation rather than just doing curve
fitting
Des
Peter H.M. Brooks
as classes, as in object orientated programming, that define the nature
of instances.
This may be a good analogy, I would see a more fitting one being the
bark of a tree and the trunk - all tree bark, to a high degree of
accuracy ends up around pi times as long as the trunk at the same point
of measurement - where do the specifications for this symetry exist
before each tree and branch instantiates it?
>
>
>
> > > Yes, but even so you still require your flat 2D space to be curved
wrt
> > time
> > > in order to keep the balls pinned to the table.
> > > I only labour this point because people often forget this very
> > important
> > > component.
> > >
> > True, though, using Euclidean geometry and Newtonian mechanics it
isn't
> > necessary to be that complicated.
> >
> >
> It does if you are looking for an explanation rather than just doing
curve
> fitting
>
Well, then, lay on Macduff.. If this helps explain why differerent
geometries exist at different scales I am happy to hear more.