Binswanger's Spherical Universe

[dondigitalia 0]

I've listened to Harry Binswanger's lecture course on Philosophy of Science a couple of times this week, and one of the things he said in the section on Physics has really been bugging me.

In his answer to the problem of an infinite universe, he posited a universe that was arranged "as if it were a sphere." That the reason one could never reach an edge is that it is impossible to travel in a straight line over such cosmic distances; that the forces at work in the universe would cause one to travel on a curve, almost as though it were on the surface of a sphere. He hints, but doesn't say straight out, that one might end up right back at one's starting point, similar to travel here on Earth.

I understand that the path of light gets bent over large distances, but wouldn't it be possible for humans to compensate for those forces and veer in the opposite direction, so that the end result was, in fact a straight line? I don't see how his model alleviates the problem of infinity.

It all seems rather fantastical to me. On the other hand, Alex's idea of an asizal universe seems much more realistic. I'm wondering what others' thoughts are on Binswanger's solution, and how it might integrate with Alex's (if at all)

[Carlos 0]

I don't understand why there would have to be a difference between Harry Binswanger's and Alex S's Universe.

Personally that sounds almost like a "gravitationally-closed" universe, which I rather like! I don't mean gravitationally-closed in the sense of "warped space-time", but rather as in one can't escape the gravitational-field of the known universe forever; I think eventually you would have to stall-out and get drug back.

[Carlos 0]

...and I just referred to the past tense of drag as "drug"

"The past tense of drag is actually dragged, not drug. This error is particularly common in speech...."

[dondigitalia 0]

The way he described it in the lecture was more along the lines of a warped space-time, than a closed gravitational field, although he made it very clear that he did not regard space itself as being curved. He said, instead, that any linear path through space is curved.

[ADS 0]

Hi Dave,

I'm off to bed, but I did want to write you quick response. Please feel free to follow up with anything you want me to expand on.

I've listened to Harry Binswanger's lecture course on Philosophy of Science a couple of times this week ...

This very lecture of Dr. Binswanger's ("Selected Topics in the Philosophy of Science," given in 1987) was the main impetus for my essay. And you're quite right to contrast my position with the position that he takes in this lecture, because they definitely are irreconcilable.

In his lecture, Dr. Binswanger puts forth/relies on three ideas that I argue against in my essay: 1) the universe has a size, 2) the universe has a finite number of entities, and 3) the universe must be sphere-like (in some way) because otherwise it would be infinite. (The first of these premises is not stated explicitly, I don't think, although in my view it is lurking in the background.) Given this, there is no getting around my disagreement with Dr. Binswanger's view as expressed in this lecture.

That being said, I do want to point out that we should not necessarily assume that Dr. Binswanger has not modified his views in some way. In 2002, Dr. Binswanger read my essay, and stated publicly on his e-mail list that he agreed with me that the universe has neither a size nor a finite number of entities. He also said that he agreed with the analogy I drew between time and space.

[dondigitalia 0]

This very lecture of Dr. Binswanger's ("Selected Topics in the Philosophy of Science," given in 1987) was the main impetus for my essay.

I had a feeling it might have been. As soon as he started in on this subject, I started making all kinds of connections between your paper and this lecture.

In his lecture, Dr. Binswanger puts forth/relies on three ideas that I argue against in my essay:...(The first of these premises is not stated explicitly, I don't think, although in my view it is lurking in the background.)  Given this, there is no getting around my disagreement with Dr. Binswanger's view as expressed in this lecture.

You're remembering correctly. He never specifically ascribes a size to the universe, but everything he's says presupposes a size. That was the main reason I posted about it here, for you to respond to, since it is in direct contradiction with what you've written.

That being said, I do want to point out that we should not necessarily assume that Dr. Binswanger has not modified his views in some way.  In 2002, Dr. Binswanger read my essay, and stated publicly on his e-mail list that he agreed with me that the universe has neither a size nor a finite number of entities.  He also said that he agreed with the analogy I drew between time and space.

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Hey, when you're right, you're right.

He did make it clear that his position in that lecture was not a final position, and is properly viewed as a work in progress. I'm glad to see that he has since expressed agreement with your view (which I also agree with).

I don't really have any other questions. I mainly wanted to find out if I was missing something, or misinterpretting him, or if he was just wrong on that point.

[Stephen Speicher 0]

That being said, I do want to point out that we should not necessarily assume that Dr. Binswanger has not modified his views in some way.  In 2002, Dr. Binswanger read my essay, and stated publicly on his e-mail list that he agreed with me that the universe has neither a size nor a finite number of entities.  He also said that he agreed with the analogy I drew between time and space.

←

Hey, when you're right, you're right.

He did make it clear that his position in that lecture was not a final position, and is properly viewed as a work in progress. I'm glad to see that he has since expressed agreement with your view (which I also agree with).

←

Just for the record, and for clarity, Harry agreed that is wrong to assume that the universe has a size or that its contents can quantified, and he agreed that the same principles that solve the "time problem" also solve the "size problem," but he did not necessarily agree with some of the formulations and arguments presented in that behalf. Also, for the record, personally I do agree with those formulations and arguments.

[dondigitalia 0]

Hmm... do either of you have a record of what exactly it was he said? I don't know what the rules are for quoting from HBL, but if such a record does exist, could you quote it here?

[Stephen Speicher 0]

Hmm... do either of you have a record of what exactly it was he said?

Yes, I have a record of the post and my summary accurately reflects the relevant portion from the post.

I don't know what the rules are for quoting from HBL, but if such a record does exist, could you quote it here?

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If a member wants a post forwarded elsewhere, HBL asks that you request permission and they will forward the post. I have asked Harry if I can post the relevant portion here. If not, I will ask that the post be forwarded to you.

[dondigitalia 0]

Yes, I have a record of the post and my summary accurately reflects the relevant portion from the post.

If a member wants a post forwarded elsewhere, HBL asks that you request permission and they will forward the post. I have asked Harry if I can post the relevant portion here. If not, I will ask that the post be forwarded to you.

←

Thank you.

[Stephen Speicher 0]

I have asked Harry if I can post the relevant portion here.

←

Here is the post in its entirety, reprinted by permission.

*********************************************************

Date: Sat, 07 Sep 2002 01:05:38 -0400

From: Harry Binswanger <hblist@hblist.com>

Subject: HBL Comments on the unbounded finite universe

From Harry Binswanger

I have rejected several posts commenting on Alex S........'s very

intelligent essay on the unbounded finite universe, so I should make some

comments of my own.

I have not studied Mr. S........'s essay thoroughly, but I have read it

once and gone over it lightly a second time.

I agree with Mr. S........'s general intent: to show that the paradoxes

that arise regarding the size of the universe and the number of entities in

it are based on the wrong assumption that the universe has a size or is the

kind of thing whose contents can be quantified.

I also agree with his parallel between time and space--the universe is not

in time or in space, and just as it is wrong to say "an infinite time has

passed before now" so it is wrong to say "an infinite number of entities

exist extending out from here." (And, by the same token, it is wrong to say

that time or distance is finite.)

He is right that the same principles that solve the "time problem" solve

the "size problem."

I don't think I agree, however, with a few of his formulations or

arguments. At the risk of seeming over-critical, I will cover my

disagreements briefly. (By the way, he attributes a phrase to me that I did

not originate and is a standard Objectivist formulation: "The universe is

not in time; time is in the universe.")

1. A small point: He writes:

"If everything that exists must be finite, then *everything that exists*

(i.e., existence) *must be finite*."

That could be read as committing the fallacy of composition. It does not

follow from the finiteness of each thing that the totality of all things

must be finite. But I think his argument is actually: If to exist is to be

finite, then since the universe exists, it must be finite.

2. He writes:

"Thus, the two questions, 'Have a finite number of events transpired

throughout the entire history of the universe?' and 'Are there a finite

number of entities in the universe?' are essentially the same:"

I agree that far, but then he says:

"they both steal the concept of number from the concept of quantity."

I don't see the issue as stealing the concept of "number," and I don't

follow his argument about the relation of number to quantity as being

relevant here. My point would be: there is no such thing as "the entire

history of the universe." And the parallel for number would be: there is no

such thing as "the entire extent of the universe."

Why not?

For one thing, since the universe is not "in time," it is at least very

unclear that there is one "now" for the whole universe. Ayn Rand held that

time was "local"--i.e., a single time does not apply to the whole universe.

At least that's what she said to me in conversation--maybe it was only a

hypothesis on her part, I didn't ask her how certain she was of that.

If there is no one "now" for the whole universe, how do we talk about the

number of things in the universe? This is another aspect of the general

fact, that Mr. S........ points out, that the universe is not a "bounded"

set of things. In this case, the lack of bounds is temporal.

(You might argue that since the ultimate constituents of the universe do

not come into existence or go out of existence, we can get around this

temporal problem by counting just the ultimate constituents. But I don't

think this is possible either--I don't know how you'd ever be able to

determine if you'd counted them all once and only once. And what if there

are ultimately only four kinds of ultimate constituents, which

interpenetrate or are goo-like? We can't assume that the ultimate

constituents are physical objects in the perceptual-level sense.)

The second reason why I think that size and number of components do not

apply to the universe is the issue of spatial boundedness. Here I would go

farther, or deeper, than Mr. S......... The ideas of space and of

*direction* only apply *within* the universe. For this reason, as I've

argued in lectures, it makes no sense to talk about going *out*

indefinitely "in a straight line" from somewhere. "Out"--in relation to

what? "In a straight line"--as determined how?

If a super-fast spaceship moves out from the earth, we cannot forget that

the earth moves. Eventually, the earth disintegrates and its elements

disperse. We can't mark a static X in empty space and move "out" from that.

There is no cosmic graph paper to chart our distance or our direction.

Position is a concept that depends upon entities, and all entities move.

So, I hold that it is an error to even in imagination survey the entire

universe, considering it a collection existing at one moment, as if one

were outside of it looking at it. You can't consistently think about the

"spread" of it and draw, in thought, a diameter across it.

In general, I think the concept of "direction" is fundamental, and it

depends on the faculty of sight. It is probably a concept formed from the

visual form of perception. I have argued that "direction" is an axiomatic

concept for geometry, and I think more thought needs to be given to that

concept.

Also, I oppose the concept "infinity," even in mathematics. I think the

origins of the concept lie in mysticism. (What is called "infinite" in

mathematics can be re-defined in terms that are non-mystical, such as

"considering this sequence in so far as it continues, abstracting from its

end," or by other devices).

If this is correct, then the proper statement is not really "the universe

is finite" but "the universe is not infinite." Here I may be in

disagreement with Ayn Rand. She said in one Q&A when asked what it means to

say that the universe is finite: "It means: there is only so much of it."

(That's from memory, but I'm fairly sure I have it verbatim; if anyone has

the actual Q&A, I'd appreciate getting her whole answer.)

But, at any rate, it makes no sense to ask: if the universe is not

infinite, what happens when you get to the end of it? There's no such thing

as getting to the end of it. Neither the spatial concepts nor the

directional concepts apply.

After a while, this kind of cosmological discussion gets rather tedious, so

please try not to reply. And I will apply severe standards for posting any

replies that people can't resist making.

Harry Binswanger

hblist@hblist.com

*********************************************************

[dondigitalia 0]

Thanks again, Stephen. I think his point #1 is just nit-picking; I think it's very clear that *everything that exists* is intended to be taken as a single existent, rather than a sum of parts, and there is no fallacy of composition.

I'm a little confused as to how he doesn't see the concept "number" as being stolen from quantity, especially considering his discussion of "number" and it's relationship to quantity in the very lecture that led to Alex's essay and this thread.

I don't see his argument about the earth moving or ceasing to exist as relevant, since typically, when taking spacial measurements, we take measurements of things as they are at a particular point in time, rather than throughout all of time. I think he's mistakenly bringing an epistemological difficulty into a metaphysical issue.

All that said, I'm still in agreement with "The Unbounded, Finite Universe."

[Stephen Speicher 0]

I don't see his argument about the earth moving or ceasing to exist as relevant, since typically, when taking spacial measurements, we take measurements of things as they are at a particular point in time, rather than throughout all of time.

←

As I understand HB's argument on this point, we can only measure on a local spatial and temporal scale. There is no "particular point in time" that spans the entire universe, and "spacial measurements" lose all meaning on a large-enough cosmological scale. The argument about the Earth assumes Earth to be an origin, and HB argues that even straight-line motion as a direction loses meaning beyond some cosmological level. You may question the relevance of this argument, but not validly on the basis of "we take measurements of things as they are at a particular point in time."

[dondigitalia 0]

As I understand HB's argument on this point, we can only measure on a local spatial and temporal scale. There is no "particular point in time" that spans the entire universe, and "spacial measurements" lose all meaning on a large-enough cosmological scale. The argument about the Earth assumes Earth to be an origin, and HB argues that even straight-line motion as a direction loses meaning beyond some cosmological level. You may question the relevance of this argument, but not validly on the basis of "we take measurements of things as they are at a particular point in time."

←

I didn't mean to give the impression that I was trying to ascribe a particular point in time to the entire universe--I'm not.

What I'm rejecting is the idea that planetary motion has any metaphysical significance to heading out in a straight line. I would regard that as a difficulty in measuring the direction of the spaceship, but not any indication that travelling out in a straight line is impossible.

He says, "'Out'--in relation to what? 'In a straight line'--as determined how?" My answer to those questions would be: in relation to and as determined by the position of things at the beginning of the trip (that's what I meant when I said "a particular point in time"). How do you make that measurement a million years from now, when things have moved? I don't know, but I don't see the difficulty in measuring the direction as relevant at all to whether or not the spaceship is actually travelling in a straight line.

[Stephen Speicher 0]

I didn't mean to give the impression that I was trying to ascribe a particular point in time to the entire universe--I'm not.

What I'm rejecting is the idea that planetary motion has any metaphysical significance to heading out in a straight line. I would regard that as a difficulty in measuring the direction of the spaceship, but not any indication that travelling out in a straight line is impossible.

He says, "'Out'--in relation to what? 'In a straight line'--as determined how?" My answer to those questions would be: in relation to and as determined by the position of things at the beginning of the trip (that's what I meant when I said "a particular point in time"). How do you make that measurement a million years from now, when things have moved? I don't know, but I don't see the difficulty in measuring the direction as relevant at all to whether or not the spaceship is actually travelling in a straight line.

←

Dave, how do you determine straight-line motion in space? (Ask one of your physics professors about the most sophisticated gyroscopically-controlled inertial stellar compass system.) Wherever you are is "here," and wherever you are going is "there," and guidance for the straight-line direction between "here" and "there" depends on "fixed" points in the cosmos. Local measurements and guidance corrections work because the distance the "fixed stars" actually move is small-enough to be discounted. Over long-enough cosmological distances, and over long-enough cosmological times, the fixed references not only have moved but, as HB pointed out, have "disintegrate[d] and its elements disperse."

As presented this is not simply a practical problem to be solved, but rather a consequence of what is meant by "direction" on sufficient cosmological scales. As I said in my last post, HB's argument amounts to saying that eventually straight-line motion as a direction loses all meaning.

[dondigitalia 0]

As presented this is not simply a practical problem to be solved, but rather a consequence of what is meant by "direction" on sufficient cosmological scales. As I said in my last post, HB's argument amounts to saying that eventually straight-line motion as a direction loses all meaning.

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But is that relevant on a metaphysical level?

Not to say that I disagree that on very large scales, such measurements lose meaning, because of the nature of the physical universe, but whether or not that is something that is inherent in existence as such. What I'm questioning is whether or not we can make such a statement philosophically, or if it is a matter of science.

I'm usually very hesitant to posit hypothetical universes (for reasons I hope are obvious), but sometimes I do find it helpful to keep a distinction between philosophic and scientific knowledge. Suppose a universe where cosmic bodies were fixed and eternal; in such a situation, straight-line motion would not lose all meaning.

Since the motion of planets, stars, galaxies, what-have-you is discovered scientifically, rather than philosophically, then where does Binswanger's statement fit into the hierarchy? Is it properly a matter of metaphysics, or of science? Or is it a little of both?

[Stephen Speicher 0]

But is that relevant on a metaphysical level?

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That is a separate issue from the one I addressed. My point to you was to challenge the basis on which you questioned the relevance of HB's argument.

[dondigitalia 0]

That is a separate issue from the one I addressed. My point to you was to challenge the basis on which you questioned the relevance of HB's argument.

←

Initially, I communicated my question rather unclearly. This was, in part, due to the fact that I was package-dealing a number of issues together in my own mind (some of which have no relevance), which I think I've untangled now.

My last post most clearly states my actual concerns over the relvancy of that particular point.

[Stephen Speicher 0]

Initially, I communicated my question rather unclearly. This was, in part, due to the fact that I was package-dealing a number of issues together in my own mind (some of which have no relevance), which I think I've untangled now.

My last post most clearly states my actual concerns over the relvancy of that particular point.

←

Okay.

I'm usually very hesitant to posit hypothetical universes (for reasons I hope are obvious), but sometimes I do find it helpful to keep a distinction between philosophic and scientific knowledge. Suppose a universe where cosmic bodies were fixed and eternal; in such a situation, straight-line motion would not lose all meaning.

That's like saying "Suppose a universe where identity is other than it is." Such a statement is arbitrary and meaningless. Motion is a relative concept.

Since the motion of planets, stars, galaxies, what-have-you is discovered scientifically, rather than philosophically, then where does  Binswanger's statement fit into the hierarchy? Is it properly a matter of metaphysics, or of science? Or is it a little of both?

←

As presented, I would say primarily philosophical.

[dondigitalia 0]

That's like saying "Suppose a universe where identity is other than it is." Such a statement is arbitrary and meaningless. Motion is a relative concept.

That's why I'm usually very hesitant to posit fictional universes. The reason I'm trying to do so here is to remove the scientific aspects from the argument and determine exactly what can be said philosophically, without any appeal to science.

Perhaps I'm making a mistake in being too strict about the admitting scientifically discovered facts into philosophic problems, but I don't think so. I think this separation is supported by Ayn Rand's own statements on philosophic vs. scientific issues.

Here is my breakdown of how I understand what he is saying:

- Position is a relationship between entities which are "fixed" in space.

- Direction is a relationship between an entity in motion and other entities which are "fixed" in space.

- Both direction and position are dependent on the continued existence and spacial "fixation" of entities.

- Since, in the universe, all entities are either are in motion and none are eternal, then it is meaningless to talk about direction and position on very large, cosmological scales, both spacially and temporally.

(Note: In my use of "space" above, I don't mean to imply that I or Binswanger regard space as something independent existent which holds entities. It was just the easiest way I could think of to communicate my point.)

The first three points I see as philosophical. It's the last one that I'm calling into question as admissable. It relies on scientific knowledge. Doesn't an appeal to that knowledge take us out of metaphysics? Of course, it's true, but I'm confused as to why you say his view is primarily philosophical. Or were you not referring to that point?

[ELS 0]

Stephen Speicher,Feb 18 2006, 09:58 PM]

Dave...Wherever you are is "here," and wherever you are going is "there," and guidance for the straight-line direction between "here" and "there" depends on "fixed" points in the cosmos. Local measurements and guidance corrections work because the distance the "fixed stars" actually move is small-enough to be discounted. Over long-enough cosmological distances, and over long-enough cosmological times, the fixed references not only have moved but, as HB pointed out, have "disintegrate[d] and its elements disperse."

Stephen's (and HB's) observations are key to understanding the epistemological nature of the problem of scale in the reference points of a constantly changing universe.

Any measurement system has a definite scale - a specific range beyond which it cannot be applied. Whatever the standard of measurement, the range is decided objectively by how well and long the standard can be applied, i.e., at what point the measurement process ceases to to be valid. Any standard of measurement ceases to be epistemologically valid when it doesn't cover the range of what it purports to measure.

Add continuously (eternally) changing reference points outside the range, beyond the scale of any existing measurements, or the measurement system, and you have the problem of universal measurement.

It's the problem of reduction to the perceptual level given a range of measurement whose reference points are continuously changing. The existents are not as fixed as on the (local) perceptual level. And as you expand the measurement into continuously changing existents - i.e., reference points - you lose all referents - and all reference.

To lose, on a given scale, for a specific range, all referents - and all reference points - is the problem.

For details, I'll soon answer Harry Binswanger's observations - and perhaps, indirectly, Alex S's observations.

ELS(Edward L. Scheiderer)

[Stephen Speicher 0]

Here is my breakdown of how I understand what he is saying:

- Position is a relationship between entities which are "fixed" in space.

No. The entities are at rest relative to each other.

I think that the rest are your own formulations that do not necessarily reflect what I understood HB to write. As to the issue of philosophical/scientific, I said that the arguments were "primarily" philosophical.

Dave, I am not sure where these arguments are going anymore. Anyway, my own view is in accord with Alex's arguments, as detailed in his essay.

[Stephen Speicher 0]

Stephen's (and HB's) observations are key to understanding the epistemological nature of the problem of scale in the reference points of a constantly changing universe.

←

Perhaps, but more relevant to the question "Are all the entities in the universe a quantity?", I think the principles that Alex identifies (and chews) in his essay are more fundamental and certainly sufficient to answer the question.

[dondigitalia 0]

No. The entities are at rest relative to each other.

I don't see how that is different from what I said (other than being more clear), if you take into account the note I inserted at the end. My use of "fixed" can be taken as meaning "at rest."

I think that the rest are your own formulations that do not necessarily reflect what I understood HB to write.

They are my own formulations, but they are drawn from both what you reposted from HBL, and his discussion of the concept of "direction" in "Selected Topics in The Philosophy of Science."

Dave, I am not sure where these arguments are going anymore. Anyway, my own view is in accord with Alex's arguments, as detailed in his essay.

My own purpose in the last half of this thread was not really to argue anything, but rather sort through the scientific points vs. the philosophic points, with the aim of determining their relevance.

[Carlos 0]

I don't see how that is different from what I said (other than being more clear), if you take into account the note I inserted at the end. My use of "fixed" can be taken as meaning "at rest."

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But at-rest with respect to what? The universe is not laid out on graph paper, with ordered lines in a grid to tell us where we are without looking in relation to other entities. This is stressed hugely by the fact that when outside of the presence of a gravitational field, it is impossible for an individual to distinguish whether he is traveling in constant straight-line motion or is completely at rest. So to say that we determine position by judging the relation between a "fixed" entity doesn't make sense; because sometimes in my Classical Mechanics course, for example, an object in motion would be chosen as the mathematical origin-point for all the calculations that would describe the system!

To absolutely describe an entity as being at-rest or fixed would require us to be able to distinguish between a "here" and a "there" in space outside of the presence of any objects; but that's impossible because there isn't any"thing" to judge the relation of your position by.