Argument by analogy

[Catastrophe]

I would be very pleased to receive any comment on the strength of an analogy, described (inter alia) as:

Logic
a process of arguing from similarity in known respects to similarity in other respects.

The analogy in question is my posting in respect of the perspective of a "flatlander".

To clarify the terms of the first analogy, by 'flatlander' I am following in principle the use of the term by Edwin A Abbott (originally anonymously) in the book "Flatland - The Classic Speculation on Life in Four Dimensions". In a Preface (entitled "Limitations") Isaac Asimov describes the book as "probably the best introduction one can find into the manner of perceiving dimensions" although I have seen some comment also from Google:

What is Flatland a satire of?

In 1884, the English minister, headmaster, and biblical and Shakespearean scholar Edwin Abbott Abbott produced a thin volume titled Flatland: A Romance of Many Dimensions. It was both an introduction to the notion of higher dimensions and a satire of Victorian society and norms.

My use of the idea is not to repeat or criticise the idea, but to try to extract some "similarity in known respects to similarity in other respects"; viz., analogy.

By flatlander, I mean a 2-D being living in a 2-D 'universe'. By consulting mathematical sources, I was able to confirm that a sphere is actually a 2-D surface existing in 3-D. It is similar to the idea that, inhabiting (at least, historically) only a tiny portion of the Earth's surface, mankind once thought the Earth to be flat. There is, of course, the difference that we are a 3-D (spatial) lifeform inhabiting a 3-D (spatial) 'universe'.

The first analogy considers our simplistic view that we inhabit a 3-D space 'universe' travelling through a 4th dimension, which is how time is commonly considered. (Spacetime will be considered later).

To the flatlander, there is no 3rd spatial dimension, no 'up' or 'down', although these are, of course, apparent to us.
Thus, his 'universe' is bounded by the surface of the sphere. If his 'universe' is to be perceived as expanding, this would be viewed as increase in surface area with time, and his spherical surface would be judged as expanding by increasing distance between points on the surface. Of course, radius of a sphere has no meaning for him.

If we now change perspective to what our own would be, if we were able to view flatland, we would see his 'universe', his curved 2-D surface, increasing in radius, and his "time axis" would be the increase in radius of this sphere. Whilst we might (but not necessarily) relate flatland 'time' to our time, it is easy to see it as akin to a linear dimension to us.

The points I wish to draw from this analogy, are:
That the flatlander's 'universe' is limited to that spherical surface existing in his 'time. For us, as a D+ being, meaning a being able to perceive and process at least one more dimension than the flatlander, it is simply akin to an expanding soap bubble. Note that this is a common analogy for us, but not so in the later example. We should at least be prepared for some differences. Thus a D+ being (e.g., us) could observe a million or more of what a flatlander considers to be 'his' 'universe'. Hence my use of 'around' the word universe. That means that 'universe' is no longer "all there is", but "all that can be perceived or generally recognised by the entity owning that 'universe'.
"Universe" is a relative term, which may be replaced by "observed universe".


The second analogy follows directly from the first. The difference is that, in distinction to our "natural" viewpoint of dividing space from time, we simply ( ) substitute spacetime as the spherical surface (or 'bubble' if you will). This means that what we (D+) observe as radius no longer corresponds to time, whether 'our time' or 'flatlander time', but to something akin to time for a D++. It means that we understand our (D+) "expansion of the universe" into what?, we need perception of an additional dimension, which we do not have. If a comprehension of "universe" needs perception of an additional dimension, why not also comprehension of an "additional time" dimension, which, after all, is only part of comprehension of "universe"?

What do you think? It is not a proof, but might it help conceptualisation?

Cat

 

[Helio]

The points I wish to draw from this analogy, are:
That the flatlander's 'universe' is limited to that spherical surface existing in his 'time. For us, as a D+ being, meaning a being able to perceive and process at least one more dimension than the flatlander, it is simply akin to an expanding soap bubble. Note that this is a common analogy for us, but not so in the later example. We should at least be prepared for some differences. Thus a D+ being (e.g., us) could observe a million or more of what a flatlander considers to be 'his' 'universe'. Hence my use of 'around' the word universe. That means that 'universe' is no longer "all there is", but "all that can be perceived or generally recognised by the entity owning that 'universe'.
"Universe" is a relative term, which may be replaced by "observed universe".

Yes. The analogy is about the best there is for describing today's view of our universe based on GR. The current model shows that the universe is very close to being "flat", but in a 3D sense. In your soap bubble analogy, two parallel rays that run along the surface will return to the point of emittance. This surface uniformity is a 2D example of 3D space, both considered to be "flat". At least this is my understanding of it. A distorted bubble would render the rays unparallel.

The "universe" relates to observable science, even in principle, and seems to be "flat". The "Universe" allows for what else may be there, so things like more dimensions are fodder for those discussions.

The second analogy follows directly from the first. The difference is that, in distinction to our "natural" viewpoint of dividing space from time, we simply ( ) substitute spacetime as the spherical surface (or 'bubble' if you will). This means that what we (D+) observe as radius no longer corresponds to time, whether 'our time' or 'flatlander time', but to something akin to time for a D++. It means that we understand our (D+) "expansion of the universe" into what?, we need perception of an additional dimension, which we do not have. If a comprehension of "universe" needs perception of an additional dimension, why not also comprehension of an "additional time" dimension, which, after all, is only part of comprehension of "universe"?

If I understand what you're saying, analogies help support the idea that we need more fodder for discussion. We are likely too limited since we are limited in both observational and imaginative capability.

One interesting thing I read about was Lemaitre's initial work with GR where he saw a serious flaw in de Sitter's GR model, namely that it violated the axiom of homogeneity. Lemaitre also saw how de Sitter's geodesics would require an absolute center for the universe -- the point of the observer.

Lemaitre's model, using Einstein's homogeneity, allowed him to separate 3D space from time. Time, of course, was critical to his expansion model since more time gave more expansion. I don't, however, see other books and articles mention this, so I could be repeating an error one respectable scientist made.

 

[billslugg]

I've shied away from using analogies when it was pointed out that analogies are imperfect by definition. This means a guaranteed objection.

The only one I can't dispense with is the use of the surface of a sphere as a 2D analogy to explain "finite but unbounded" to people who are having trouble with the 3D version.

 

[Catastrophe]

Yes. The analogy is about the best there is for describing today's view of our universe based on GR. The current model shows that the universe is very close to being "flat", but in a 3D sense. In your soap bubble analogy, two parallel rays that run along the surface will return to the point of emittance. This surface uniformity is a 2D example of 3D space, both considered to be "flat". At least this is my understanding of it. A distorted bubble would render the rays unparallel.

The "universe" relates to observable science, even in principle, and seems to be "flat". The "Universe" allows for what else may be there, so things like more dimensions are fodder for those discussions.


If I understand what you're saying, analogies help support the idea that we need more fodder for discussion. We are likely too limited since we are limited in both observational and imaginative capability.

One interesting thing I read about was Lemaitre's initial work with GR where he saw a serious flaw in de Sitter's GR model, namely that it violated the axiom of homogeneity. Lemaitre also saw how de Sitter's geodesics would require an absolute center for the universe -- the point of the observer.

Lemaitre's model, using Einstein's homogeneity, allowed him to separate 3D space from time. Time, of course, was critical to his expansion model since more time gave more expansion. I don't, however, see other books and articles mention this, so I could be repeating an error one respectable scientist made.

Helio, thank you for your excellent comments.

My present post represents some time considering my original posts, where I was (and still am) a little unhappy with the bubble question. However, it is well known and easily understood, so I relented. I was fully leaning towards the 2-D mathematical sphere ("That the flatlander's 'universe' is limited to that spherical surface existing in his 'time."). I took a risk - possibly unwise.

Lemaitre also saw how de Sitter's geodesics would require an absolute center for the universe -- the point of the observer.

Yes, but an observable universe, not the Universe. There are trillions of observable universes.
But that was not his point.

If I understand what you're saying, analogies help support the idea that we need more fodder for discussion. We are likely too limited since we are limited in both observational and imaginative capability.

True. But for me, the unsupported "extra dimension" is verbal garbage. The analogy, for me at least, provides some (albeit conditional) rationale for D+. We see the problem for the flatlander and, for me, there is a possible solution (though suggested, not proven). There is, at least, a supportable, but not provable, route towards D(n) and D(n + 1).

Lemaitre's model, using Einstein's homogeneity, allowed him to separate 3D space from time.

I tried to cover both eventualities.

Cat

 

[Catastrophe]

Billslugg. Thank you for your response.

The only one I can't dispense with is the use of the surface of a sphere as a 2D analogy to explain "finite but unbounded" to people who are having trouble with the 3D version.

I share your worry about analogies (remember Korzybski), but there are good/bad, useful/useless analogies. At least, in my honest opinion. I always attempt to seek the "map" which is closest to the "territory".

Cat

 

[Catastrophe]

Let me throw a spanner in the works . . . . . . . . .

At least it might be a spanner.

It depends on the current status of string theory.
But Ars technica comments as follows:

But that was almost 30 years ago, and we still don’t know what M-theory is. We still haven’t figured out a solution for string theory.

If string theory were on firmer ground, I would have been happy to point out the following, which appears in "Understanding Astrophysics", Issue 145, Future, 2023:

String Theory, a potential Grand Unified Theory . . . . . . suggests that spacetime has at least 10 dimensions . . . . . . This theory of eternal inflation gives rise to a potentially infinite number of bubble universes with different dimensions and laws of physics.

Now, I am not suggesting that this proves anything - indeed the basis of this suggestion may prove to be unfounded. But I find it interesting that something sounding like the consequences of the second analogy seem to be suggested.

Cat

 

[Atlan0001]

In String Theory, I've read, the inhabitants of a 2-dimensional Flatland Universe (U) are 1-dimensional string-stick life who look to 0-dimensional points as being the resident possibility of all higher (or omni) dimensionality.

We relate to that 1-dimensional string-stick life, and omni-dimensional 0-point possible infinity of higher (in this case of Flatland, situated lower as the higher!) dimensionalities, via my many posts' describing "entangled, entangling, spontaneously concurrent (t=0) REALTIME NOW (t=0) instant moment." You can't get anymore 2-dimensional Flatland Universe (U) -- and 1-dimensional string-stick life Flatlander in it -- than a universally flat "(t=0) REALTIME NOW (t=0)" 'time front'! Nor deal in any higher (omni) dimensionality than a 0-dimensional point of and in such a "Mandelbrot Set"!

R. I. P. Kurt Godel!

 

[Catastrophe]

Helio, you stated:

Lemaitre's model, using Einstein's homogeneity, allowed him to separate 3D space from time. Time, of course, was critical to his expansion model since more time gave more expansion. I don't, however, see other books and articles mention this, so I could be repeating an error one respectable scientist made.

Using Britannica for background:

The big-bang model is based on two assumptions. The first is that Albert Einstein’s general theory of relativity correctly describes the gravitational interaction of all matter. The second assumption, called the cosmological principle, states that an observer’s view of the universe depends neither on the direction in which he looks nor on his location. This principle applies only to the large-scale properties of the universe, but it does imply that the universe has no edge, so that the big-bang origin occurred not at a particular point in space but rather throughout space at the same time. These two assumptions make it possible to calculate the history of the cosmos after a certain epoch called the Planck time. Scientists have yet to determine what prevailed before Planck time.

Would this be a fair starting place to clarify your post?

My first point here would be that it "allowed him to separate 3D space from time".
This is what I followed in the first analogy.
I did not separate them in the second analogy.
I do not wish to fall into the trap that I have described myself elsewhere, re wandering off or overcomplicating, so please point this out, if I do.

My thought here is that we are not (or should not be) thinking in terms of our current human experience of time. In terms of a so-called Big Bang (or t = 0, if you prefer) (I am referring to the metaphysical element before BBT begins) and to the immediate follow up (inflation, et cetera), there is no "tea at 4 pm" element, there is only expansion i.e., change.

Timing the expansion by change (or rate of change) seems to be a cyclic process. Expansion is change. Change denotes expansion. "Time" is measured by change in 3D. There is no external possibility of measurement.

I start from already being worried about how these time intervals arise. There were no seconds to measure by, so they must obviously be based on assumptions about 3D measurements, or, rather, just guesses. Can you offer me any reassurance?

And what grounds do be have to make assumptions about temperatures and times? I recall the remark quoted above "gives rise to a potentially infinite number of bubble universes with different dimensions and laws of physics."
How do we "know" that our current physics apply to BB and BBT?
Falling back on my 'mentor', Korzybski, the map seems separated from the territory by many billions of years of ignorance of the events, or even any basic confidence in our ability to understand them at all. Do we have a vocabulary to match the events, so remote from our experience. Are we 'flatlanders' just unable to understand expansion as D+ understands.

I am certainly not trying to be difficult here, but I have very great respect for your knowledge in this area and would really like to understand your point of view. And why " This principle applies only to the large-scale properties of the universe" when the "universe" was small? Is this not fundamental?

Cat

 

[Helio]

Helio, you stated:



Using Britannica for background:
....
Would this be a fair starting place to clarify your post?

Not that much, surprisingly. Yes, GR does describe "the gravitational interaction with matter", but this doesn't address the greater dance between space and matter. As Wheeler said, "Space tells matter how to move. Matter tells space how to curve."

But first once has to recognize that space isn't the emptiness we thought it was. "It's really somethin' that space ain't nuthin'!" [This could be original given its corniness. ]

As for their tossing in the cosmological principle, I personally don't find it all that helpful. I don't recall seeing Einstein using it explicitly, but I could easily be wrong. What I do see asserted is his assumption of homogeneity, which says no location is unique. Of course, SR also showed only realtive motions, no absolutes for spacetime.

It was over a year after introducing GR (1915) before he applied his theory to the cosmos (1917).

As for the use of the "Planck time", at least they are showing some limits to science. The delineation, however, between science and metaphysics seems to be at near t=1E-12 seconds, not t=1E-43 sec (Planck unit of time). This is according, as you know, to what we learn from the CERN scientists who are the only ones able to reach such energy levels.

My thought here is that we are not (or should not be) thinking in terms of our current human experience of time. In terms of a so-called Big Bang (or t = 0, if you prefer) (I am referring to the metaphysical element before BBT begins) and to the immediate follow up (inflation, et cetera), there is no "tea at 4 pm" element, there is only expansion i.e., change.

Timing the expansion by change (or rate of change) seems to be a cyclic process. Expansion is change. Change denotes expansion. "Time" is measured by change in 3D. There is no external possibility of measurement.

I start from already being worried about how these time intervals arise. There were no seconds to measure by, so they must obviously be based on assumptions about 3D measurements, or, rather, just guesses. Can you offer me any reassurance?

Measurements are a human convention. Nature does find without them.

But, yes, the 3D space as a function of time for the cosmos was actually the breakthrough that Lemaitre introduced. [Friedman (1922) was the first to see this in the math, but he never proposed a physics theory for it. Einstein was quick to tell him his physics was wrong, but he used "abominable" for Lemaitre's model. ]

And what grounds do be have to make assumptions about temperatures and times? I recall the remark quoted above "gives rise to a potentially infinite number of bubble universes with different dimensions and laws of physics."

Like Friedman, the mathematical elegance for string theory and, to a lesser degree, multi-universes should be seen as Einstein saw both Friedman's and Lemaitre's work -- "your math is fine but your physics is" wrong. Friedman is recognized only because his math eventually matched the hard observations, which is lacking greatly for string theory, so far.

Einstein was very excited when his GR model solved the very troubling Mercury anomaly, which ended the search for Vulcan. But, before heavily promoting his model, he felt he needed a couple more independent lines of evidence to bolster his theory. The other two I've mentioned, though the small solar redshift was already known in measurements, as I understand. Edington's 1919 solar eclipse study not only was the additional evidence Einstein needed, but it was the event that made him world famous. It made from page news all over the world, apparently.

How do we "know" that our current physics apply to BB and BBT?
Falling back on my 'mentor', Korzybski, the map seems separated from the territory by many billions of years of ignorance of the events, or even any basic confidence in our ability to understand them at all. Do we have a vocabulary to match the events, so remote from our experience. Are we 'flatlanders' just unable to understand expansion as D+ understands.

This is why I like science so much. Objective-based models are the ones that will work far better than the ones heavily subjective-base. This sounds too obvious, perhaps, but recall that in Galileo's day, it was the philosopher that was at the top of the totem pole; mathematicians, like him originally, were near the bottom. The BBT Bullets thread lists most of the separate lines of evidence that all support the BBT. The discovery of the predicted CMBR was even greater than Edington's solar results. Hawking said it was likely the greatest discovery of mankind.

The number of predictions for any model for the entire universe will never be few in number, of course. Any failed, unambiguous prediction, however, could end or greatly alter the theory. Recall that Galileo's discovery of both crescent and gibbous phases for Venus quickly was recognized, even by the Jesuits, as falsifying the long-established model of Aristotle/Ptolemy/Aquinas. Facts are facts.

I am certainly not trying to be difficult here, but I have very great respect for your knowledge in this area and would really like to understand your point of view. And why " This principle applies only to the large-scale properties of the universe" when the "universe" was small? Is this not fundamental?

I'm unclear what this is trying to say. Homogeneity would have been extremely obvious, in theory, subsequent to the Inflation period, when the universe was perhaps smaller than a grapefruit. This fast expansion, hypothetically, established the isotropy and tiny (1 part per 100,000) of anisotropy found in the CMBR. Isotropy, of course, is a given for a homogeneous universe. But it wasn't at all obvious in the early 1900s. The view was that the MW was the universe and one can easily see a lack of uniformity (isotropy). Discovering that the spiral nebulae were other "island universes" didn't improve the isotropy. But, today, we see a uniform distribution of galaxies the farther we look. The CMBR demands no less.

 

[billslugg]

Space tells matter how to move, matter tells space how to curve.
There is an absolute velocity in space, referenced to CMBR.

 

[Helio]

Space tells matter how to move, matter tells space how to curve.

Oops, thanks. [I knew better.]

There is an absolute velocity in space, referenced to CMBR.

Are you referring to the Hubble Flow?

 

[Catastrophe]

Helio, thank you greatly for such a comprehensive reply. I appreciate it very much.

There is a lot there for me to think about. I will revert on individual issues.
However, much of my problem may come from this.

I'm unclear what this is trying to say. Homogeneity would have been extremely obvious, in theory, subsequent to the Inflation period, when the universe was perhaps smaller than a grapefruit. This fast expansion, hypothetically, established the isotropy and tiny (1 part per 100,000) of anisotropy found in the CMBR. Isotropy, of course, is a given for a homogeneous universe.

As I think you may have noticed, I am a great fan of Korzybski.
"The map is not the territory". This has become my life credo.
"A life credo is a statement of your core values and beliefs, and how you intend to incorporate them into your life."

This has led me to distinguish between two main divisions of language.
1. "Common parlance" is a phrase that refers to a style of speaking or a group of words that are used by many people in everyday conversation.
The word "parlance" is a formal noun that means a particular way of expressing oneself or using words, especially by a specific group of people. (Google parlance/common parlance).
This may include, or not, literary language involving aesthetics.
2. Accurate (hopefully scientific) parlance. Here I hope to be able to avoid ambiguity.
Unfortunately, a dictionary will have several, (very often) strongly conflicting entries.
This naturally results in confusion when people in a discussion are are assuming different meanings for the same words. This is not for "everyday use".

To get to the point of this monologue - homogeneity.

Oxford languages gives:
noun: homogeneity

the quality or state of being all the same or all of the same kind.

Similar: uniformity, homogeneousness, similarity, similar nature, similitude.

Note: no synonyms, just similar.
Merriam-Webster is much less specific.
It seems, therefore, that we are using different definitions.
I am intending: "the quality or state of being all the same or all of the same kind."
There is absolutely no way that I could accept:

Outer space (or simply space) is the expanse that exists beyond Earth's atmosphere and between celestial bodies. It contains ultra-low levels of particle ...

and

The brain is the central organ of the human nervous system, and with the spinal cord makes up the central nervous system. It consists of the cerebrum, ...

as being "all the same or all of the same kind".

Cat

 

[billslugg]

Oops, thanks. [I knew better.]


Are you referring to the Hubble Flow?

No, I am referring to the Earth's abolute velocity being meaureable in magnitude and direction. There is one direction blue shifted, and the rearward direction red shifted. We are going 500 or so km per second in absolute terms in the direction of Vega IIRC.

 

[Helio]

Helio, thank you greatly for such a comprehensive reply. I appreciate it very much.

You're always welcome, Cat. Your professional touch is appreciated, as well as you patience. I'm neither an astronomer nor a physicist, but I have enjoyed reading the history and learning most of the terms. If one learns the terms in any science field then the rest is understandable at least.

As I think you may have noticed, I am a great fan of Korzybski.
"The map is not the territory". This has become my life credo.

Yes. I like that expression. GR is the map and it has been found to juxtapose nicely over the territory.

This has led me to distinguish between two main divisions of language.
1. "Common parlance" is a phrase that refers to a style of speaking or a group of words that are used by many people in everyday conversation.
The word "parlance" is a formal noun that means a particular way of expressing oneself or using words, especially by a specific group of people. (Google parlance/common parlance).
This may include, or not, literary language involving aesthetics.
2. Accurate (hopefully scientific) parlance. Here I hope to be able to avoid ambiguity.
Unfortunately, a dictionary will have several, (very often) strongly conflicting entries.
This naturally results in confusion when people in a discussion are are assuming different meanings for the same words. This is not for "everyday use".

Yes. Some have the talent to accomplish both regularly, but that happens when it is clear what level of knowledge both parties have in a discourse.

To get to the point of this monologue - homogeneity.

Yes. When I think of homogeneity I think about a bottle of milk. No matter where you magically look within the bottle it is certain that the white view will be no different than anywhere else. It's perfectly uniform without magnification.

The universe isn't quite like that, but no matter where one magically travels the overall view will be essentially unchanged. This is guaranteed thanks to the CMBR, which reveals just how homogenous the universe was at the time of Recombination. The subsequent expansion certainly changed things as far as GMCs and galaxies, but the overall large-scale average density from region to region would be unchanged.

Isotropy is often used in lieu of homogeneity. This is logical since we can only see the universe from a single point (Earth). It avoids the question of homogeneity since things that are isotropic aren't necessarily homogeneous, but things that are homogeneous necessarily are isotropic. [If I'm wrong, I'd appreciate a correction.]

When I see "outer space", I quickly revert to the old sci-fy books, which meets that definition you gave. If one wants to be serious, then "spacetime" is the better word to use, I think. This makes the leap into the theory of GR.

 

[Catastrophe]

Billslugg, the definition I have is:

Absolute velocity is the velocity of an object or fluid particle relative to a stationary space that is independent of the physical objects in it:

also: does the Earth have absolute velocity (Google)

No, the Earth does not have absolute velocity because there is no universal velocity. This is because there is no universal stationary reference frame against which all other reference frames can be measured.

Can absolute velocity be relative to CMB?

No, there are no absolute velocities in the universe, so absolute velocity cannot be relative to the cosmic microwave background (CMB). All velocities in the universe are relative.

Cat

 

[Helio]

No, I am referring to the Earth's abolute velocity being meaureable in magnitude and direction. There is one direction blue shifted, and the rearward direction red shifted. We are going 500 or so km per second in absolute terms in the direction of Vega IIRC.

Yes, the dipole. But, I assume this dipole is a direct result of our movement in the Hubble Flow, so the CMBR is static (co-moving) within this flow. I also assume the HF (Hubble Flow; or is it the Hubble-Lemaitre Flow?) is determined by the CMBR.

 

[Catastrophe]

Helio, you have chosen a complicated example! But you are correct.

Whether milk is homogeneous or heterogeneous depends on the type of milk and how it's processed:

• Whole milk from the cow
  A heterogeneous mixture because the fat globules are not evenly distributed and can be seen under a microscope.
  
  
  
• Skim milk
  A homogeneous mixture because the fat globules have been removed.
  
  
  
• Store-bought milk
  A homogeneous mixture because it's been homogenized, a process that breaks down and distributes the fat globules evenly.
  
  
  
• Raw milk
  A heterogeneous mixture because it will separate into layers if left to stand.

Homogenization is a process that gives milk its smooth texture and rich white color. It prevents cream from rising to the top, so there's no need to mix it back in before drinking.

(Google)

Cat

 

[Helio]

Helio, you have chosen a complicated example! But you are correct.

Don't milk cartons still say "homogeneous" ? Perhaps not. I should look.

If I see heterogeneous milk, then I know to toss it out quickly and not open the lid.

 

[Catastrophe]

Fat globules of milk are coated with a membrane composed of lipids and proteins. This membrane acts as an emulsifier and keeps the globules separated as an oil-in-water emul- sion. However, the emulsion lacks physical stability, and creaming occurs.

I seem to remember being taught about 70 years ago that no emulsion is permanently stable.
Most (if not all) emulsions can be broken e.g., by heat. Natural milk, if left alone, seems stable, but, even so, it can lose water by evaporation and break.

To be strictly technical, emulsions containing (as they do) dispersed 'water insoluble' components are not homogeneous. Solutions containing (as they do) dissolved components are 'more homogeneous'. Nice examples of how tricky words can be.

Cat

 

[Catastrophe]

Don't milk cartons still say "homogeneous" ? Perhaps not. I should look.

If I see heterogeneous milk, then I know to toss it out quickly and not open the lid.

See #17, which is from Google.

 

[billslugg]

I have never read anything about CMBR having an inherent dipole for a motionless observer, the anisotropy being due to a non-homogenious expansion. How to know which it is? Don't know.

 

[Helio]

I have never read anything about CMBR having an inherent dipole for a motionless observer,

Right, the dipole applies to your point — our net motion relative to the CMBR, which is, I think, the same motion relative to the Hubble Flow.

the anisotropy being due to a non-homogenious expansion.

Right. An early criticism of BBT was the lack of anisotropy and, also, the extreme “flatness” of space time. Inflation theory came in and fixed both of these, but some see it as ad hoc since it lacks stability, so far.

 

[billslugg]

All inflation means is the universe had to be smaller than we thought at the start in order to explain the observed low degree of variability today. The variability comes from quantum fluctuations. We know how big they were. To make smooth CMBR today we must put the quantum fluctuations into a smaller universe at the very start. We are simply picking a smaller starting point.

 

[Helio]

All inflation means is the universe had to be smaller than we thought at the start in order to explain the observed low degree of variability today. The variability comes from quantum fluctuations. We know how big they were. To make smooth CMBR today we must put the quantum fluctuations into a smaller universe at the very start. We are simply picking a smaller starting point.

I don't really understand how Inflation actually helps. The idea is that two points in space that is expanding away from each other much faster than c will not be able to ever share information with one another. This, somehow, smooths the quantum effects to give us the isotropy found in the CMBR.

But if a very smooth temperature gradient is desired, don't points need to share information to keep such equilibrium. Perhaps the ongoing quantum fluctuations would never allow such smoothness. So I'm a little puzzled how it all stretches quickly and smooths itself.

 

[billslugg]

I recall two mechanisms for the benefits of inflation.
1) Starting out smaller allows information to be moved brfore it gets too big.
2) Expanding more allows bumps to even out more.