Not sure whether this is (still?) an appropriate forum for these kinds of
questions, but I'll give it a whirl. Please note that I've also posted
this on the "other" newsgroup.
I've been tripped up in class by teaching some of the "rules" of article
usage. My first mistake was saying that one should use "the" when the noun
is followed by a non-partitive of-phrase, eg:
"the behaviour of monkeys"
"the growth of the plants"
vs
"a bottle of beer" (partitive)
"a number of questions"
However, this does not hold true. So why do we say:
"the behaviour of monkeys"
but
"a knowledge of physics (is necessary)"
"an understanding of the factors which..."
and
"Computer-support can provide ease of diagram generation"
Is it to do with qualities of the noun?
My second mistake was saying that we use "the" with second mention.
However, it's context-dependent of course. In the passage below, 2nd & 3rd
mentions use "a". Presumably this is to do with specificity - ie, the
questionnaire is not specified at any point.
"In Case Study 1, which acted as a pilot study, three types of questionnaire
were tried: a self-completion questionnaire, an interview-based
questionnaire and a questionnaire plus a group discussion. An
interview-based questionnaire was considered most appropriate for rich
qualitative feedback along with obtaining an unbiased rating of each
diagram. Consequently, Case Study 2 and 3 adopted only an interview-based
questionnaire."
Does it all come down to some hard-to-pin-down notion of definiteness, or
are there some useful guidelines I can give to my students?
Thanks,
Helen
> However, this does not hold true. So why do we say:
>
> "the behaviour of monkeys"
> but
> "a knowledge of physics (is necessary)"
"The behaviour of monkeys" refers to the behaviour of monkeys in
general.
"The knowledge of physics" would refer to knowledge of physics in
general, that is, the world's complete knowlegde of physics, the sum
of the knowledge of all physicists.
"A knowledge of physics" refers to one person's knowledge of
physics. It is unspecific as the knowledge different people will have
of physics will be different, some may have more detailed knowledge
than others, some will have knowledge of different aspects than others.
To say "I have a knowledge of physics" is to accept that knowledge is
necessarily incomplete. If physics were a closed and limited topic,
such that one person might be able to know all there was of it, then
"I have the knowledge of physics" might be an acceptable statement, but it
isn't and so it isn't.
Matthew Huntbach
"A knowledge of physics" refers to one person's knowledge of
> physics. It is unspecific as the knowledge different people will have
> of physics will be different, some may have more detailed knowledge
> than others, some will have knowledge of different aspects than others.
> To say "I have a knowledge of physics" is to accept that knowledge is
> necessarily incomplete. If physics were a closed and limited topic,
> such that one person might be able to know all there was of it, then
> "I have the knowledge of physics" might be an acceptable statement, but it
> isn't and so it isn't.
>
'Knowledge' in these contexts is usually replaced by 'understanding'
by most moderns. But I like 'knowledge' better -- has more old-world
charm.
I have the knowledge of physics necessary to this job.
> Physicists being thoroughgoing materialists of course insist that
> knowledge exists independently of themselves; that it doesn't have to
> be known to be knowledge, notwithstanding the quite just protestations
> of philosophers.
What physicist ever claimed that?
I don't think anyone with an idea of what the word "knowledge" means
would insist that it exists outside of knowing beings. You might claim
that facts exist before they are known, but not knowledge.
> Philosophically, I agree with the previous poster on what 'the
> knowledge of physics' should mean, but that is not what physicists
> mean by it.
Do you have a citation for that?
{snipped}
--
John
The change is significant, and the distinction is useful. It's possible to
know much and understand little.
Adrian
Whatever that word is that you were looking for in another thread,
you're doing it. Probably the majority of physicists are
materialists, though I've known some who were faithful to various non-
materialist religions. And probably most believe that the laws of
physics and the appropriate calculational methods to use with them,
not to mention other physical facts, exist in some sense independently
of knowledge of them. Contrary to your "of course", I think some
might argue that this is an idealist position not easily combined with
materialism.
I liked Matthew's position better because he said, "'The knowledge of
physics' /would/ refer" (my emphasis). I don't think the phrase is
used much. One can say, as Helen did, "A knowledge of physics is
necessary". Here I think "a" means the same thing as "some".
Otherwise the phrase works for me with specifying adjectives: at least
slight knowledge of physics, detailed knowledge of physics, etc.
Another version with "the" has a restrictive clause: the knowledge of
physics that was available to So-and-so, etc.
> Philosophically, I agree with the previous poster on what 'the
> knowledge of physics' should mean, but that is not what physicists
> mean by it.
>
> "A knowledge of physics" refers to one person's knowledge of> physics. It is unspecific as the knowledge different people will have
> > of physics will be different, some may have more detailed knowledge
> > than others, some will have knowledge of different aspects than others.
> > To say "I have a knowledge of physics" is to accept that knowledge is
> > necessarily incomplete. If physics were a closed and limited topic,
> > such that one person might be able to know all there was of it, then
> > "I have the knowledge of physics" might be an acceptable statement, but it
> > isn't and so it isn't.
Does anyone say "I have a knowledge of physics"?
How about "I have the knowledge of how to get around London"?
> 'Knowledge' in these contexts is usually replaced by 'understanding'
> by most moderns. But I like 'knowledge' better -- has more old-world
> charm.
To get back to Helen's question, I think an important difference
between "knowledge" and "behavior" here is that "knowledge" is a mass
noun--you can have some, more, less, a lot, a little.... However,
"behavior" in her example is whatever you call a noun that can't be
quantified.
--
Jerry Friedman is a materialist who thinks true laws of physics
probably exist.
No. Believing that anything at all exists outside human experience is
something an idealist would neither contend nor hold with. An idealist
is someone who argues that the stuff of human perception and thought
is all there is to the universe. But I agree, of course, that I ought
not to generalize to all physicists. But you would have a tough time
being interested in the universe if you didn't believe it existed
independently of us. Most physicists believe not only that the
universe exists independently of us but that there is an ideal
perception of it, 'God's design of the universe', which they can
unlock, if they really tried. You wouldn't have terms like 'theories
of everything' otherwise. Philosophers might suggest that the universe
is a bunch of things flying around at random, occasionally in patterns
we can mathematically model; that no one of these models is the
correct one; that different models merely rival each other in their
fidelity of approximation. But few physicists, I think, hold with
this, at least in their private hearts. They are wont to believe that
there is a true model that they can 'discover' (not 'develop' ).
Physicists always talk about discovering new laws rather than
developing newer, better models. They seem to think that these laws,
which are merely an idea, have always, in some sense, existed even
before anyone thought of them. They are apt to think that their best
ideas existed independently of them; that they merely discovered them,
not developed them. That is what I meant when I said that physicists
think that 'knowledge' is independent of us.
But even in former times, belief that God was a being and that he
was omniscient probably meant that 'the knowledge of physics' still
referred to everything God knew, viz.everything there was to know.
Thank you Matthew, that's very helpful.
Helen
<snip>
> I liked Matthew's position better because he said, "'The knowledge of
> physics' /would/ refer" (my emphasis). I don't think the phrase is
> used much. One can say, as Helen did, "A knowledge of physics is
> necessary". Here I think "a" means the same thing as "some".
> Otherwise the phrase works for me with specifying adjectives: at least
> slight knowledge of physics, detailed knowledge of physics, etc.
Yes, that helps. On AEU it was suggested that "a knowledge of physics" is
in fact partitive, in the same way as "a number of questions".
> Another version with "the" has a restrictive clause: the knowledge of
> physics that was available to So-and-so, etc.
Yes, this makes it much more specific such that both the speaker & the
listener understand the referent. I think this has something to do with
article usage though it's hard to discuss without sounding woolly.
<snip>
> To get back to Helen's question, I think an important difference
> between "knowledge" and "behavior" here is that "knowledge" is a mass
> noun--you can have some, more, less, a lot, a little....
While "knowledge" is usually used as a mass noun, I think in these examples
it's actually being used as a countable noun: "a knowledge". Same with
understanding. You can get away with a little more with understanding (!)
eg:
I have an understanding.
*I have a knowledge.
I have a knowledge of geometry.
But you can't make them plural.
Anyway, correct me if I'm wrong, and many thanks for your help.
Helen
I see that "idealist" has more meanings than I knew. I was thinking
of Platonic idealism.
However, as you note below, few or no physicists deny material
reality, as Plato did.
> But I agree, of course, that I ought
> not to generalize to all physicists. But you would have a tough time
> being interested in the universe if you didn't believe it existed
> independently of us. Most physicists believe not only that the
> universe exists independently of us but that there is an ideal
> perception of it, 'God's design of the universe', which they can
> unlock, if they really tried.
Platonic idealism.
> You wouldn't have terms like 'theories
> of everything' otherwise.
Keep in mind that a large number of physicists aren't tremendously
interested in a "theory of everything" and the vast majority aren't
engaged in looking for it. The ones who are get the most publicity,
though.
> Philosophers might suggest that the universe
> is a bunch of things flying around at random, occasionally in patterns
> we can mathematically model; that no one of these models is the
> correct one; that different models merely rival each other in their
> fidelity of approximation. But few physicists, I think, hold with
> this, at least in their private hearts. They are wont to believe that
> there is a true model
I'd agree with that, though there are exceptions. A friend of mine
quoted a distinguished experimental physicist as saying, "Experiment
talks--theory is bullshit."
> that they can 'discover' (not 'develop' ).
I'd say the number who believe the true model can be known is somewhat
smaller, though still a majority.
> Physicists always talk about discovering new laws rather than
> developing newer, better models. They seem to think that these laws,
> which are merely an idea, have always, in some sense, existed even
> before anyone thought of them.
That's why I called the position "idealist" and said it was hard to
reconcile with materialism. If only material things exist, what does
it mean to say the true laws of physics exist? (I don't think most
physicists worry about such questions. I don't even remember them
from my undergrad days.)
> They are apt to think that their best
> ideas existed independently of them; that they merely discovered them,
> not developed them.
Well... most physicists' best ideas are gizmos for making difficult
measurements, tricks for speeding up computer programs, ways to apply
known methods to new problems, etc. I don't think they spend much
thought on whether they discovered such ideas or developed them.
In my physics days, two of my three best ideas (keeping in mind that
"best" doesn't imply "good") involved noticing that people were
arguing about a word that they were using with different meanings.
I'm still trying to do it.
> That is what I meant when I said that physicists
> think that 'knowledge' is independent of us.
I wouldn't use "knowledge" for something that no human being knows.
> But even in former times, belief that God was a being and that he
> was omniscient probably meant that 'the knowledge of physics' still
> referred to everything God knew, viz.everything there was to know.
I don't remember seeing such a phrase in that sense. I'd expect
something more like "the laws of nature".
--
Jerry Friedman
>> Philosophers might suggest that the universe is a bunch of things
>> flying around at random, occasionally in patterns we can
>> mathematically model; that no one of these models is the correct
>> one; that different models merely rival each other in their
>> fidelity of approximation. But few physicists, I think, hold with
>> this, at least in their private hearts. They are wont to believe
>> that there is a true model
>
> I'd agree with that, though there are exceptions. A friend of mine
> quoted a distinguished experimental physicist as saying, "Experiment
> talks--theory is bullshit."
Theoretical and experimental physicists have a long history of putting
each other down.
Theoretical physicist, n. Someone who is never observed in the
laboratory, but whose existence is postulated in order to make the
numbers balance.
--
Peter Moylan http://www.pmoylan.org
Please note the changed e-mail and web addresses. The domain
eepjm.newcastle.edu.au no longer exists, and I can no longer
receive mail at my newcastle.edu.au addresses. The optusnet
address could disappear at any time.
> On AEU it was suggested that "a knowledge of physics" is
> in fact partitive, in the same way as "a number of questions".
...
Well, it's certainly not possessive/genitive, but I don't know that
it's the same as "a number of questions."
> > To get back to Helen's question, I think an important difference
> > between "knowledge" and "behavior" here is that "knowledge" is a mass
> > noun--you can have some, more, less, a lot, a little....
>
> While "knowledge" is usually used as a mass noun, I think in these examples
> it's actually being used as a countable noun: "a knowledge". Same with
> understanding. You can get away with a little more with understanding (!)
> eg:
>
> I have an understanding.
> *I have a knowledge.
> I have a knowledge of geometry.
>
> But you can't make them plural.
...
To me, "a knowledge" is somewhat anomalous. It means something like
"an amount of knowledge" or "a kind of knowledge" that changes the
mass noun into a count noun.
But my point was that "behavior" in "the behavior of monkeys" is
neither mass nor count. Nobody jumped up to tell me what the word for
that kind of noun is. Does anyone know?
--
Jerry Friedman
Won't "abstract noun" do? . . No, I suppose not, since some of them are
countable and some are not. So I don't know, either. But actually
"abstract" and "concrete" have no grammatical significance that I can
think of: don't they just represent a semantic distinction?
--
Mike.
--
Posted via a free Usenet account from http://www.teranews.com
I don't, but it seems almost perfectly replaceable by a verb phrase,
'how monkeys behave'. Maybe it's a reification.
--
John
> >> But few physicists, I think, hold with
> >> this, at least in their private hearts. They are wont to believe
> >> that there is a true model
>
> > I'd agree with that, though there are exceptions. A friend of mine
> > quoted a distinguished experimental physicist as saying, "Experiment
> > talks--theory is bullshit."
>
> Theoretical and experimental physicists have a long history of putting
> each other down.
>
> Theoretical physicist, n. Someone who is never observed in the
> laboratory, but whose existence is postulated in order to make the
> numbers balance.
Entry number 29 in this exchange:
The Experimenter to the Theorist
When in disgrace with chairs' and students' eyes,
I at department teas beweep my state,
And trouble deaf deans with my bootless cries,
And look through my CV, and curse my fate,
Wishing me like one with non-zero hope,
Equipped like him, like him with grants possessed,
Desiring this man's amp and that man's scope,
With what I built myself contented least,
Yet in these thoughts myself almost despising,
Haply I think on thee! My eigenstate,
Like to the tenured prof at noon arising
In suburbs nice, whistles though running late,
For thy dull work forgotten stinks so foully
That I would scorn exchange terms e'en with Pauli.
--
Jerry Friedman studied theoretical physics.
Only at a stretch. Plato actually thought that reality was a base
model of a perfect transcendental divine model which alone was worth
knowing; that actual reality is a mere contemptible and untrustworthy
illusion.
>
>
>
> > Physicists always talk about discovering new laws rather than
> > developing newer, better models. They seem to think that these laws,
> > which are merely an idea, have always, in some sense, existed even
> > before anyone thought of them.
>
> That's why I called the position "idealist" and said it was hard to
> reconcile with materialism. If only material things exist, what does
> it mean to say the true laws of physics exist? (I don't think most
> physicists worry about such questions. I don't even remember them
> from my undergrad days.)
>
No. A thing doesn't have to be concrete to be material. Most
materialists have no problems believing that abstract entities such as
the natural numbers exist for example. Indeed, it is the idealists
who will object if you tell them that numbers no-one has ever thought
of exist. 'Material' refers to anything that is not mental and is
independent of perception.
What I'm referring to here is the fact that physicists are still apt
to say that Newton discovered the law of gravitation. Actually the
inverse square law is merely an approximation. Yet physicists and
mathematicians too believe not only that knowledge but mistaken ideas
exist independently of them.
> > They are apt to think that their best
> > ideas existed independently of them; that they merely discovered them,
> > not developed them.
>
> Well... most physicists' best ideas are gizmos for making difficult
> measurements, tricks for speeding up computer programs, ways to apply
> known methods to new problems, etc. I don't think they spend much
> thought on whether they discovered such ideas or developed them.
>
> In my physics days, two of my three best ideas (keeping in mind that
> "best" doesn't imply "good") involved noticing that people were
> arguing about a word that they were using with different meanings.
> I'm still trying to do it.
>
>
I think you are thinking too much of experimental physicists. I was
mostly referring to theoritical physicists.
> That is what I meant when I said that physicists
> > think that 'knowledge' is independent of us.
>
> I wouldn't use "knowledge" for something that no human being knows.
>
No more I. But I'm quite sure that I've seen constructs like
'Knowledge is extraordinarily vast' where what seemed meant was not
merely human knowledge but all there is to know; all the stock of
potential human knowledge, as it were. But I must own that I have
never had grounds for ever thinking these advertent, or that
physicists are particularly prone to this sentiment, above other
classes of people writing on scientific subjects.
I said that earlier--but I didn't say it again here. The position you
describe above has resemblances to Platonic idealism in seeing the
laws as real, but it leaves out Plato's belief that material things
were an illusion. How's that?
> > > Physicists always talk about discovering new laws rather than
> > > developing newer, better models. They seem to think that these laws,
> > > which are merely an idea, have always, in some sense, existed even
> > > before anyone thought of them.
>
> > That's why I called the position "idealist" and said it was hard to
> > reconcile with materialism. If only material things exist, what does
> > it mean to say the true laws of physics exist? (I don't think most
> > physicists worry about such questions. I don't even remember them
> > from my undergrad days.)
>
> No. A thing doesn't have to be concrete to be material.
Okay, apparently "material" has more meanings than I suspected too.
> Most
> materialists have no problems believing that abstract entities such as
> the natural numbers exist for example. Indeed, it is the idealists
> who will object if you tell them that numbers no-one has ever thought
> of exist. 'Material' refers to anything that is not mental and is
> independent of perception.
> What I'm referring to here is the fact that physicists are still apt
> to say that Newton discovered the law of gravitation. Actually the
> inverse square law is merely an approximation. Yet physicists and
> mathematicians too believe not only that knowledge but mistaken ideas
> exist independently of them.
I think lots of physicists would say Newton discovered a good
approximation (which he naturally thought was the true law). Heck,
I'd say that.
> > > They are apt to think that their best
> > > ideas existed independently of them; that they merely discovered them,
> > > not developed them.
>
> > Well... most physicists' best ideas are gizmos for making difficult
> > measurements, tricks for speeding up computer programs, ways to apply
> > known methods to new problems, etc. I don't think they spend much
> > thought on whether they discovered such ideas or developed them.
>
> > In my physics days, two of my three best ideas (keeping in mind that
> > "best" doesn't imply "good") involved noticing that people were
> > arguing about a word that they were using with different meanings.
> > I'm still trying to do it.
>
> I think you are thinking too much of experimental physicists. I was
> mostly referring to theoritical physicists.
I couldn't tell, because you just said "physicists".
> > That is what I meant when I said that physicists
>
> > > think that 'knowledge' is independent of us.
>
> > I wouldn't use "knowledge" for something that no human being knows.
>
> No more I. But I'm quite sure that I've seen constructs like
> 'Knowledge is extraordinarily vast' where what seemed meant was not
> merely human knowledge but all there is to know; all the stock of
> potential human knowledge, as it were. But I must own that I have
> never had grounds for ever thinking these advertent, or that
> physicists are particularly prone to this sentiment, above other
> classes of people writing on scientific subjects.
Okay again. I don't remember seeing anything like that, but there's a
great deal of the world's prose, including almost of of philosophy,
that I haven't read.
--
Jerry Friedman
>> What I'm referring to here is the fact that physicists are still
>> apt to say that Newton discovered the law of gravitation. Actually
>> the inverse square law is merely an approximation. Yet physicists
>> and mathematicians too believe not only that knowledge but mistaken
>> ideas exist independently of them.
>
> I think lots of physicists would say Newton discovered a good
> approximation (which he naturally thought was the true law). Heck,
> I'd say that.
It is entirely possible that there are no true laws in physics; only
better and better approximations to the truth. And what is "truth" in
this context? Generally, we accept a physical law as true if the results
it predicts match up with what is measured in reality. (With a few side
provisos: the theory should be able to predict results before the
measurements are made, rather than postdict after the event as most
clairvoyants do; the experiments should be repeatable; etc.). If two or
more different theories produce the same correct predictions then
strictly speaking they are all correct theories; although in practice,
for convenience, we have a tendency to choose the simplest explanation.
We accept that physical theories might need revisions as experimental
science advances and allows for more precise measurements.
Newton gets the credit for his theory of gravitation on several grounds:
1. There was no conceivable way in Newton's time to design an experiment
that would show a departure between his theory and practice. Even with
today's better equipment, we need the utmost precision to detect any
departures from his theory. His theory gives not merely a good
approximation, but an outstandingly close approximation.
2. Even today, most calculations related to motion under gravitational
forces use Newton's equations as the preferred calculation, because they
give the right answer, to sufficiently high precision, in all but the
most extreme and unusual cases. They can even handle situations, such as
the gravitational effects of black holes, that nobody had thought
of in Newton's time.
3. The more sophisticated approach of General Relativity could not have
been developed, I believe, without taking advantage of a great deal of
prior theory, including in particular Newtonian Relativity.
Anti-science people, such as the self-styled "Creation scientists", like
to point to the difference between Newton's theories and Einstein's
theories as evidence for the "fact" that scientists keep changing their
minds. Let us pass lightly over the fact that a gap of more than two
centuries represents a rather slow rate of mind-changing. The essential
point is that the later theories are refinements and improvements of the
earlier ones, not complete replacements.
Even the long-ago theory that everything was made from four elements was
correct in essence. Its main failings were an inaccurate count of the
number of elements, and a lack of understanding of the finer details of
how elements combine.
Isn't it more or less true that any law of physics these days seems to
boil down to "this always happens except when it doesn't"? "It's a
particle except when it's a wave" (photon)... "it's infinitely
massive yet infinitely tiny" (singularity)... "it's doesn't exist
except when you see it" (quantum mechanics)..."it's finite but has no
boundaries...." (the Big Bang)....
Science is Zen. Discuss.
--
Archie Valparaiso
Tunbridge Wells borough residents are the
second best recyclers in Kent.
Newton's work is still, I think, the most prodigious achievement of
human intellect ever.
> Anti-science people, such as the self-styled "Creation scientists", like
> to point to the difference between Newton's theories and Einstein's
> theories as evidence for the "fact" that scientists keep changing their
> minds. Let us pass lightly over the fact that a gap of more than two
> centuries represents a rather slow rate of mind-changing. The essential
> point is that the later theories are refinements and improvements of the
> earlier ones, not complete replacements.
>
The anti-science people, however stupid, are right about one thing. It
is dangerous to make sweeping qualitative assertions in physics. It is
true that theories originate by scientists assuming such assertions
and building a mathematical theory around it, but experiment only
vindicates the mathematical theory, and that only approximately. It
doesn't at all follow that the absolute and sweeping qualitative
assertions assuming which the theory has been erected are absolutely
true. But physicists have historically been particularly prone to this
superstition.
> Even the long-ago theory that everything was made from four elements was
> correct in essence. Its main failings were an inaccurate count of the
> number of elements, and a lack of understanding of the finer details of
> how elements combine.
>
But that age-old theory was a theory strictly out of people's heads,
concieved at a time when 'intellectuals'(see Plato) were mad enough to
think that philosophers could produce the laws of nature out of their
head and aberrations observed in practice were a base illusion.
Besides, no-one had taken any care in defining 'element'. They also
thought that fire was an element which we are wont to call a process.
> Science is Zen. Discuss.
Okay.
Science is also Not-Zen.
--
Roland Hutchinson              Will play viola da gamba for food.
NB mail to my.spamtrap [at] verizon.net is heavily filtered to
remove spam.  If your message looks like spam I may not see it.
>Archie Valparaiso wrote:
>
>> Science is Zen. Discuss.
>
>Okay.
>
>Science is also Not-Zen.
[applause]
>On Tue, 20 Feb 2007 16:31:20 GMT, Roland Hutchinson
><my.sp...@verizon.net> wrought:
>
>>Archie Valparaiso wrote:
>>
>>> Science is Zen. Discuss.
>>
>>Okay.
>>
>>Science is also Not-Zen.
>
>[applause]
One-handed, please.
It's true with the "seems to". The theories are clear and free of
paradoxes (though all you can calculate with the quantum ones is
probabilities), but they sound strange in English and are strange to
think about.
For two cents I'd give my famous off-topic explanation of wave-
particle duality. *draws line in dust with toe*
What would be finite with no boundaries is the universe (if it's
closed, which they're now saying it probably isn't). But the same is
true of the rim of a circle or the surface of a sphere. It's just a
little harder to imagine about the universe.
> Science is Zen. Discuss.
Ask the neurologist who shared the 1986 Nobel for discovering nerve
growth factor.
--
Jerry Friedman
Okay, it was Stanley Cohen.
What do you think of "Newton discovered the fact that F = GMm/r^2 is
an outstandingly close approximation"?
By the way, you should be careful about inferring what physicists (and
other people) "inadvertently" think about these matters from what they
say. The same physicist might say both that Newton discovered his
theory and that he developed it. The physicist's real underlying
philosophical view may be that the distinction doesn't matter
(possibly expressed with such terms as "meaningless").
--
Jerry Friedman
[appl
(The emoticon of one hand clapping.)
>>[applause]
>
>One-handed, please.
[applau]
David
A little harder, he says. Ha! It's not a little harder for some of us;
it's much, much, much, much, much, much, much, much, much, much, much,
much, much, much, much, much, much, much, much, much harder.
Please bear with me and I'll try and explain why. (Although it's not
easy trying to make why something is incomprehensible comprehensible.)
On the surface of that sphere, although a caterpillar may be
physically limited to that surface, it is -- if it's a smart
caterpillar -- aware that there is somewhere else to go: off the
sphere. Or on a big sphere, like the surface of the earth, even before
rockets and planes existed we knew all about treetops, soaring eagles
(hi, Rey!) the clouds, the moon, the sun and the stars. We couldn't
reach them but we knew where they were in relation to us.
Now let's go to the outer limits of the universe. Let's say there's a
star there, right on the edge. From our star we can go anwhere we like
-- back towards the inner areas of the universe or over to a
neighbouring star or anywhere else, like us, right on the edge. But we
can't go forwards.
WHY NOT?
See? It's not at all like the surface of a sphere. Not even a tiny
bit!
And that's the problem for us cosmoduffers. We just cannot conceive of
an explosion, which is what we're told the Big Bang was, expanding
without spreading out into some previously unoccupied space. The edge
of the universe must be its edge because certain material would be the
first to be thrown out by that explosion. It moves away from the
nucleus of the explosion -- into what? Into where? And, as I tried
(and probably failed) to say above, why can't a spaceship lift off
from a planet of one of those "scout" stars go faster in the same
direction as the explosion, extending the boundary of the universe as
it goes. Or is -- in a quantummy sort of way -- that exactly what
happens, with the boundary only existing when there's something there
pushing it further outwards?
> See? It's not at all like the surface of a sphere. Not even a tiny
> bit!
>
> And that's the problem for us cosmoduffers. We just cannot conceive
> of an explosion, which is what we're told the Big Bang was, expanding
> without spreading out into some previously unoccupied space. The
> edge of the universe must be its edge because certain material would
> be the first to be thrown out by that explosion. It moves away from
> the nucleus of the explosion -- into what? Into where? And, as I
> tried (and probably failed) to say above, why can't a spaceship lift
> off from a planet of one of those "scout" stars go faster in the same
> direction as the explosion, extending the boundary of the universe
> as it goes.
An essential part of the Big Bang theory is that the initial expansion
happened at a speed faster than the speed of light. This is possible,
apparently, because it was a case of space itself expanding, rather than
matter expanding through a pre-existing space. (But don't ask me more
about that, because that is where my head starts to hurt.)
Now, if you think about it, the speed of light limits how far away we
can see, no matter how much we improve our telescopes. The "visible
universe" or "reachable universe" grows with time (because then light
from remote places has had more time to reach us here on Earth), but the
growth rate is limited by the speed of light. That means that there is
no way we will ever be able to see the edge of the universe. It is
always over the horizon for us, and will forever remain so unless we
invent faster-than-light travel.
If I may be permitted to make your head hurt too, I can add that this is
so not only for observers on Earth, but also for observers anywhere
else. (Because Earth doesn't occupy a privileged position. No matter
where you are, you'll feel as if you're at the centre of the universe.)
Therefore the edge of the universe is "over the horizon" _for any
observer anywhere in the universe_. You can't stand at the edge of the
universe and try to look out, because you can't get there from here. And
you can't get there from anywhere else, either. For all practical
purposes, the universe doesn't have an edge. We know that it's finite,
but no matter how far you travel you'll never find an edge, no matter
where you started from.
Which means ... actually, it means that you're right. The human mind
can't help but be boggled by the concepts involved.
>Archie Valparaiso wrote:
Oh, goody. Someone bit.
Perhaps the problem is the explosion analogy itself. It makes me think
that some bits would be the first to fly out in all directions,
followed by all the rest, and those first bits together would form the
"edge", or outer membrane of a big, expanding balloon seen from the
inside. If it's not like that at all, as you suggest, then I feel a
bit conned by the pop scientists.
[ ppl u ]
--
SML
The name "Big Bang" was first used by Fred Hoyle as a disparaging
nickname for what is now known as the standard cosmological model.
He was a proponent of the rival steady state theory.
The nickname was adopted by the big-bangers in much the same spirit
as that of the Quakers and Methodists who adopted those disparaging
nicknames by which their detractors referred to them.
My (extremely limited) understanding of the Big Bang is that nothing
went flying through space. Space expanded resulting in the contents
being spread out but with each "item" of the contents pretty much
stationary in its local bit of space.
(The nature of the contents changed as time went by, but that is a
whole 'mother story, as is the question of whether such a clear
distinction can be made between space and contents.)
[Is there a doctor in the house? The AUE physicists look as though
they might need CPR.]
--
Peter Duncanson, UK
(in alt.usage.english)
Isn't there a stereotype that Americans like overstatement and the
British like understatement?
> Please bear with me and I'll try and explain why. (Although it's not
> easy trying to make why something is incomprehensible comprehensible.)
>
> On the surface of that sphere, although a caterpillar may be
> physically limited to that surface, it is -- if it's a smart
> caterpillar -- aware that there is somewhere else to go: off the
> sphere. Or on a big sphere, like the surface of the earth, even before
> rockets and planes existed we knew all about treetops, soaring eagles
> (hi, Rey!) the clouds, the moon, the sun and the stars. We couldn't
> reach them but we knew where they were in relation to us.
This is the misconception. The analogy is not to a caterpillar /on/ a
sphere. It's to a Flatlander /in/ the surface. Mr. Square isn't
aware that there's a third dimension, can't go in those directions,
needs a lot of help even to accept such a hypothesis.
Flatland mathematicians develop geometry, and some genius (Gauss,
Bolyai, Lobachevsky) realizes that one can imagine geometry in which
Mr. Triangle's angles don't add up to 180 degrees. One possibility
for the shape of their universe would be something unimaginable like a
circle (I mean just the rim), it would be a wrapped-around two-
diemnsional surface, and you could actually go in one direction and
come back to your starting point. They make the note (which I'll
return to below), that in principle, such a hypercircle would have an
inside and an outside as a circle does, and could be imagined as being
"embedded" in three dimensions the way a circle is a one-dimensional
figure embedded in Flatland. However, you can completely understand
its mathematics from a two-dimensional point of view, without ever
imagining taking shortcuts through that unimaginable inside.
Another Flatland genius notices that if you and your friend walk (they
don't see it as crawling) in parallel, you get closer together. He
says some force must be acting (only on moving objects) and works out
the equations for it.
Now we get to the Flatland Einstein, who realizes that this "force"
has a simple explanation if the space Flatlanders live in is actually
that hypercircle or sphere hypothesized by the mathematicians. If you
and your friend go north, you get closer till you meet at the North
Pole, and the same is true for any attempt to go in the same
direction. This exactly reproduces the equations that were already
known. Physics has determined that the universe is curved!
Still, though, there's no edge, and no way to get to any inside or
outside of their universe, even though Mr. Abbott might see such a
thing.
> Now let's go to the outer limits of the universe. Let's say there's a
> star there, right on the edge. From our star we can go anwhere we like
> -- back towards the inner areas of the universe or over to a
> neighbouring star or anywhere else, like us, right on the edge. But we
> can't go forwards.
There's no edge. We can go any of our three familiar directions from
any star. We can't go in the fourth direction for the same reason Mr.
Square can't go into the third.
And we can do all our mathematics without having to think about a
higher-dimensional space that our curved universe is embedded in. We
know nothing about whether such a space exists or not.
> WHY NOT?
>
> See? It's not at all like the surface of a sphere. Not even a tiny
> bit!
It's exactly like it (almost).
> And that's the problem for us cosmoduffers. We just cannot conceive of
> an explosion, which is what we're told the Big Bang was, expanding
> without spreading out into some previously unoccupied space. The edge
> of the universe must be its edge because certain material would be the
> first to be thrown out by that explosion. It moves away from the
> nucleus of the explosion -- into what? Into where?
You're supposed to imagine Flatland as a balloon blowing up. From A.
Square's point of view, everything in the rubber surface is getting
farther away, and the farther it is, the faster it's moving. From our
point of view, the balloon is expanding into the embedding space, but
he can know nothing about that.
> And, as I tried
> (and probably failed) to say above, why can't a spaceship lift off
> from a planet of one of those "scout" stars go faster in the same
> direction as the explosion, extending the boundary of the universe as
> it goes.
Because--if we imagine a space in which our universe is embedded,
which I think most physicists would prefer not to do--the direction of
the explosion is not a direction we can go. Such a direction may not
exist.
> Or is -- in a quantummy sort of way -- that exactly what
> happens, with the boundary only existing when there's something there
> pushing it further outwards?
Definitely in the spirit of quantum mechanics, but unfortunately based
on the wrong picture.
Now I may have given some false impressions here. As I said in an
earlier post, current observations suggest that our universe is flat
on large scales. So the analogy for the expansion is an infinite
plane expanding. Into what? Sorry, it's infinite. If you look at
any region, you see points getting farther apart--that's what I mean
(or what Hubble means) by "expanding". If it's marked like graph
paper, then yesterday it was an infinite plane with squares 1 meter
wide, and today the squares are 1.1 meter wide.
Also, the force that the Flatland physicist discovered is not gravity,
and (since our universe seems to be flat on large scales) has no
detectable analogue for us. I brought it up to illustrate how spatial
curvature could be interpreted as a force. If Flatland has gravity--
any two objects attract each other--what the Flatland Einstein
discovered is that you can understand this force by saying that mass
causes a local curvature of space, strongest near the mass, and then
two masses curve each other's paths. Thus it looks like they exert a
force on each other.
Finally, for anyone returning to this post with bleary eyes after the
nap induced above, our Einstein (or "our Albert", as he's called in
northern England) showed that we have to think of the universe as a
four-dimensional "surface", with the fourth dimension being time.
Thus gravity is a curvature of four-dimensional spacetime. If we want
to think of our locally curved universe as embedded in a higher-
dimensional space, we'd need at least five dimensions, probably more.
--
Jerry Friedman can't really picture any of this.
I managed to work up to visualizing six dimensions...they tell me there are
actually ten, but I didn't need the rest for the sort of idle musing I was
doing....
But yes, an extra dimension (or more) *is* quite enough to make the whole thing
work....r
--
"You got Schadenfreude on my Weltanschauung!"
"You got Weltanschauung in my Schadenfreude!"
As I understand it, this isn't quite right. The expansion obeys
Hubble's Law: the speed of recession (seen from any point) is
proportional to the distance. So at any time in the history of the
universe, nearby points are moving slower than c and distant points
are moving faster, which means you can't see them.
> This is possible,
> apparently, because it was a case of space itself expanding, rather than
> matter expanding through a pre-existing space. (But don't ask me more
> about that, because that is where my head starts to hurt.)
There's that.
> Now, if you think about it, the speed of light limits how far away we
> can see, no matter how much we improve our telescopes. The "visible
> universe" or "reachable universe" grows with time (because then light
> from remote places has had more time to reach us here on Earth), but the
> growth rate is limited by the speed of light. That means that there is
> no way we will ever be able to see the edge of the universe. It is
> always over the horizon for us, and will forever remain so unless we
> invent faster-than-light travel.
> If I may be permitted to make your head hurt too, I can add that this is
> so not only for observers on Earth, but also for observers anywhere
> else. (Because Earth doesn't occupy a privileged position. No matter
> where you are, you'll feel as if you're at the centre of the universe.)
> Therefore the edge of the universe is "over the horizon" _for any
> observer anywhere in the universe_. You can't stand at the edge of the
> universe and try to look out, because you can't get there from here. And
> you can't get there from anywhere else, either. For all practical
> purposes, the universe doesn't have an edge. We know that it's finite,
> but no matter how far you travel you'll never find an edge, no matter
> where you started from.
If the universe is finite, it still doesn't have an edge in any sense
(though the visible universe does, as you noted).
But it doesn't seem to be finite, they're saying now.
> Which means ... actually, it means that you're right. The human mind
> can't help but be boggled by the concepts involved.
That too.
--
Jerry Friedman likes to have his mind boggled at times.
>On Feb 21, 7:55 am, Peter Moylan <p...@ozebelgDieSpammers.org> wrote:
>> Archie Valparaiso wrote:
>> > See? It's not at all like the surface of a sphere. Not even a tiny
>> > bit!
>>
>> > And that's the problem for us cosmoduffers. We just cannot conceive
>> > of an explosion, which is what we're told the Big Bang was, expanding
>> > without spreading out into some previously unoccupied space. The
>> > edge of the universe must be its edge because certain material would
>> > be the first to be thrown out by that explosion. It moves away from
>> > the nucleus of the explosion -- into what? Into where? And, as I
>> > tried (and probably failed) to say above, why can't a spaceship lift
>> > off from a planet of one of those "scout" stars go faster in the same
>> > direction as the explosion, extending the boundary of the universe
>> > as it goes.
>>
>> An essential part of the Big Bang theory is that the initial expansion
>> happened at a speed faster than the speed of light.
>
>As I understand it, this isn't quite right. The expansion obeys
>Hubble's Law: the speed of recession (seen from any point) is
>proportional to the distance. So at any time in the history of the
>universe, nearby points are moving slower than c and distant points
>are moving faster, which means you can't see them.
>
I think that Hubble's Law describes the universe after it had settled
down for a while, but a fraction of a second after the universe was
created inflation took place, during which it expanded much faster
than the speed of light. Inflation started at the Planck time (10^-43
secs) and lasted until 10^-33 secs, but the universe expanded 10^35
times during that brief period. There's a diagram on Ned Wright's
cosmology pages at
http://www.astro.ucla.edu/~wright/BBhistory.html
The temperature during this inflation fell from 10^32 K to 10^27-28 K,
and this was the time during which the Grand Unified Theory was
broken. This is the theory that at these temperatures there was only
one force in the universe, and as it cooled, the four forces that we
know today (gravity, electromagnetic, weak force between electrons and
the nucleus, and the strong force within the nucleus) separated out.
In one of his books Steven Weinberg suggested that even if we could
build a particle accelerator as big as our galaxy, it would not be big
enough to enable particles to reach these energy levels, so I'm not
sure that GUT can be proved by direct experiment. (Weinberg and his
co-workers won the Nobel Prize for showing that the weak and
electromagnetic forces were essentially identical.)
Incidentally, he, and most other physicists and astronomers who have
written books for laymen, admit that they cannot visualise a
four-dimensional space-time continuum any better than the rest of us
can, except by maths, of course.
--
Robin Bignall
Herts, England
No. Time is a logical fiction. It's just put in there to help build
the model. Physics does not assume the existence of time(though
physicists might)
As you say, the idea that time proceeds at a constant rate is merely
an assumption. Indeed it isn't even the most appropriate logical form
of the actual assumption which is broadly,too muddle-headed to couch
better. Roughly, the idea is the ratio of the durations of two events,
not too far away fom each other in space time is a constant. i.e even
if caesium transitions 'took longer' way back, a tea break in the
vicinity (in space-time) would take correspondingly longer, so you
couldn't tell. And a tacit and very useful assumption is epitemology
is that if you can't percieve it, you can't even have a word for it
and so it is nonsense. Time, philosophically, just helps arrange our
perception of the universe, rather as in the Kantian view, but
somewhat more sophisticatedly.
I made a mistake. The critrion isn't proximity in space-time as much
as that the venues of the two events should not be moving very quickly
relative to each other. But perhaps, from common sense considerations,
you might also want to urge that they are not not far apart in space-
time so that comparison makes sense.
[ ... ]
> Time is a logical fiction. It's just put in there to help build
> the model. Physics does not assume the existence of time(though
> physicists might)
Time is what keeps everything from happening all at once.
[ ... ]
--
Bob Lieblich
Not original with me, but I don't know the source (I think it's that
prolific writer Anonymous)
> I see - broadly. Not that that advances my thinking much. I shall
> continue to think, off aue. Though I'd just like to add that the
> intense concentration of mass in the initial universe may (why not?)
> have given corresponding gravitational effects, and those should
> have (?) slowed all clocks to a crawl. So the big bang may have been
> rather more slo-mo in God's eyes than it looks like from here.
IIRC, the early universe didn't have any mass. It was all energy, until
the whole mess cooled down enough to allow massive (in the literal
sense) particles to form.
Still, you've raised a disturbing question. In a static space, the speed
of a photon can, I suppose, be used to define time. In fact, I think
that that's part of what Special Relativity does. If space itself is
expanding, there doesn't seem to be anything that can be used as a
clock, unless you somehow postulate an observer outside the universe.
(Who had to have something to do while waiting for the tree in
Berkeley's quad to grow.) Without a clock of some sort, time is meaningless.
No doubt someone has already figured this out; but it's not me.
>Paul Wolff wrote:
>
>> I see - broadly. Not that that advances my thinking much. I shall
>> continue to think, off aue. Though I'd just like to add that the
>> intense concentration of mass in the initial universe may (why not?)
>> have given corresponding gravitational effects, and those should
>> have (?) slowed all clocks to a crawl. So the big bang may have been
>> rather more slo-mo in God's eyes than it looks like from here.
>
>IIRC, the early universe didn't have any mass. It was all energy, until
>the whole mess cooled down enough to allow massive (in the literal
>sense) particles to form.
>
Energy has mass, so the mass of the universe at its creation was
exactly whatever its mass is now, but rather more concentrated.
>Still, you've raised a disturbing question. In a static space, the speed
>of a photon can, I suppose, be used to define time. In fact, I think
>that that's part of what Special Relativity does. If space itself is
>expanding, there doesn't seem to be anything that can be used as a
>clock, unless you somehow postulate an observer outside the universe.
>(Who had to have something to do while waiting for the tree in
>Berkeley's quad to grow.) Without a clock of some sort, time is meaningless.
>
>No doubt someone has already figured this out; but it's not me.
Nor me. But there was nowhere outside the universe as it was being
created where a clock could be located. The expansion of the embryo
universe created spacetime. Everywhere there was and is is inside the
universe: literally nothing is or can be outside it. (Multiverse
theories are a different matter.)
Bob Lieblich
Not original with me, but I don't know the source (I think it's that
prolific writer Anonymous)
No guarantees of accuracy, but Peter Coffee (eWeek.com) wrote:
Albert Einstein famously said time is what keeps everything from
happening all at once; his collaborator John Wheeler is less well-known
for adding, "and space is what keeps everything from happening to me."
--
Maria
I have seen the attribution to Einstein elsewhere, but I assumed it
was like that approving comment about astrology that the likes of "Dr.
Jay Stevens" attribute to him. Still, it's such a good line that I
think he deserves to be credited for it, along with Wheeler for the
topper. Kudos to both (one kudo each).
--
Bob Lieblich
His own space-time event