The Universe can be geometrically flat, but topologically finite and closed!

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The Universe can be geometrically flat, but topologically finite and closed!

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Post by WilliamPaolini »

This is an interesting article I just came across. Authors showing how just because our observations may show that the observable universe is geometrically flat, that does not mean it is infinite as its topology can be cylindrical or donut shaped as example and still show un-diverging and un-converging parallel lines when examining it.

https://www.livescience.com/universe-th ... donut.html
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by SpyderwerX »

An interesting concept. I'm curious about the possibility of "looking at yourself from behind" in an extremely 'deep field' image.
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by helicon »

FWIW, I came across an article posted on Facebook this morning espousing the donut shape of the universe.
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by pakarinen »

helicon wrote: Mon Jul 19, 2021 9:42 pm FWIW, I came across an article posted on Facebook this morning espousing the donut shape of the universe.
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by notFritzArgelander »

Color me extremely skeptical. A doughnut would not obey the cosmological principles of spatial uniformity and homogeneity and so would require large exceptions to Noether's Theorem and perhaps small violations of conservation of momentum and angular momentum. The more mundane explanation of the absence of large scale fluctuations as due to instrumental selection effects is much more likely.

This is another case of theorists looking for complicated but headline grabbing explanations without adequate observational evidence that such complications are necessary. :)
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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notFritzArgelander wrote: Tue Jul 20, 2021 12:01 am ...

This is another case of theorists looking for complicated but headline grabbing explanations without adequate observational evidence that such complications are necessary. :)

And web publications that emphasize more over better.
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by notFritzArgelander »

GCoyote wrote: Tue Jul 20, 2021 12:08 am
notFritzArgelander wrote: Tue Jul 20, 2021 12:01 am ...

This is another case of theorists looking for complicated but headline grabbing explanations without adequate observational evidence that such complications are necessary. :)

And web publications that emphasize more over better.
I welcome the OP, BTW, it's just that "extraordinary claims require extraordinary evidence" as Carl Sagan said improving on Laplace.
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by Thomas_M44 »

WilliamPaolini wrote: Mon Jul 19, 2021 7:11 pm This is an interesting article I just came across. Authors showing how just because our observations may show that the observable universe is geometrically flat, that does not mean it is infinite as its topology can be cylindrical or donut shaped as example and still show un-diverging and un-converging parallel lines when examining it.

https://www.livescience.com/universe-th ... donut.html
You know, I recall conjecture of the universe being toroidal as going back to at least the mid 1980’s.

It would be fascinating should this in fact prove true.
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by notFritzArgelander »

Thomas_M44 wrote: Tue Jul 20, 2021 3:12 am
WilliamPaolini wrote: Mon Jul 19, 2021 7:11 pm This is an interesting article I just came across. Authors showing how just because our observations may show that the observable universe is geometrically flat, that does not mean it is infinite as its topology can be cylindrical or donut shaped as example and still show un-diverging and un-converging parallel lines when examining it.

https://www.livescience.com/universe-th ... donut.html
You know, I recall conjecture of the universe being toroidal as going back to at least the mid 1980’s.

It would be fascinating should this in fact prove true.
You're right. I'd also be interested, of course. There's just not enough evidence for throwing over an infinite flat universe.
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by turboscrew »

I recall talks of universe being finite but boundless. That was some decades ago.
Probably different stuff...
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by notFritzArgelander »

turboscrew wrote: Tue Jul 20, 2021 10:35 pm I recall talks of universe being finite but boundless. That was some decades ago.
Probably different stuff...
Most of that was about spherical spacetime with negative total energy. Indeed different.
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by pakarinen »

GCoyote wrote: Tue Jul 20, 2021 12:08 am And web publications that emphasize more over better.
But mo' be mo' bettah!
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by WilliamPaolini »

notFritzArgelander wrote: Tue Jul 20, 2021 6:30 am There's just not enough evidence for throwing over an infinite flat universe.
A point the authors brought out though was that given the expansion of the universe since the CBR survey was taken, that indeed it might be impossible to tell now (given current technology)! So not sure we really have any highly reliable evidence one way or another given the nature of the measurement problem. I would more say that what we have today from the data we have that universe "seems" infinite and flat. I would say the even "likely" is too strong of a word. Of course this is standard for cosmological theories IMO. It is all just theoretical and as experience has shown over time the understandings inevitably change. Nature of the beast that the best that can be done is to say that we think we might know :lol: I give noting in cosmology more credence than that.
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by notFritzArgelander »

WilliamPaolini wrote: Thu Jul 22, 2021 2:54 am
notFritzArgelander wrote: Tue Jul 20, 2021 6:30 am There's just not enough evidence for throwing over an infinite flat universe.
A point the authors brought out though was that given the expansion of the universe since the CBR survey was taken, that indeed it might be impossible to tell now (given current technology)! So not sure we really have any highly reliable evidence one way or another given the nature of the measurement problem. I would more say that what we have today from the data we have that universe "seems" infinite and flat. I would say the even "likely" is too strong of a word. Of course this is standard for cosmological theories IMO. It is all just theoretical and as experience has shown over time the understandings inevitably change. Nature of the beast that the best that can be done is to say that we think we might know :lol: I give noting in cosmology more credence than that.
Still Will Ockham’s bright and shiny razor slices (in the absence of the requisite evidence) in favor of flat and infinite. A toroidal topology requires more epicycles… er…. parameters. ;)
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by WilliamPaolini »

There are a number of articles out there pointing out that Ockham's razor is indeed not a general principle in science but instead Ockham's razor is more accurately a popularized myth. There are oodles of examples in science where Ockham's razor is entirely not the case. So that razor is really not sharp at all.

As one scientist put it, "It has approximately zero real-world applications, so please, stop using it as part of your arguments."

--> https://www.theatlantic.com/science/arc ... or/495332/

--> https://towardsdatascience.com/stop-usi ... 81d143f9e6

--> https://nesslabs.com/occams-razor

And the list goes on and on and on!
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by notFritzArgelander »

WilliamPaolini wrote: Thu Jul 22, 2021 3:10 am There are a number of articles out there pointing out that Ockham's razor is indeed not a general principle in science but instead Ockham's razor is more accurately a popularized myth. There are oodles of examples in science where Ockham's razor is entirely not the case. So that razor is really not sharp at all.
We’ll have agree to disagree on that. I never claimed that the razor was a scientific principle. It’s a logical principle. All evidence being equal, the simplest hypothesis in a parametric sense is to be preferred.

Initially that’s how Copernicus was beating Ptolemy until the latter system was falsified. It’s still how QM beats Bohm-de Broglie pilot wave mechanics.

So while Ockham’s principle is logical, not scientific, scientists who score low on WQ (wackadoodle quotient) use it freely to evaluate hypotheses unjustified by evidence.
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by WilliamPaolini »

Yup, we will definitely have to agree to disagree. I would never consider offering the "razor" as a point in a debate as having any worth at all as it has been wrong many-a-time. Sure examples can be shown where it was so, just as there are examples to the contrary for it. Not a good track record. It is NOT an axiom, just a low-rigor rule of thumb, and as another has said, "no substitute for insight, logic and the scientific method". I guess it is something to say though when one has run out of pertinent points though ;->
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by notFritzArgelander »

WilliamPaolini wrote: Thu Jul 22, 2021 8:03 pm Yup, we will definitely have to agree to disagree. I would never consider offering the "razor" as a point in a debate as having any worth at all as it has been wrong many-a-time. Sure examples can be shown where it was so, just as there are examples to the contrary for it. Not a good track record. It is NOT an axiom, just a low-rigor rule of thumb, and as another has said, "no substitute for insight, logic and the scientific method". I guess it is something to say though when one has run out of pertinent points though ;->
So this particular topic, where there is absolutely no data supporting the universe being finite and closed, but an abundance of data supporting infinite, flat, and open is the perfect place for Ockham's bright and shiny razor to cut off the metaphysical (as far as we know) speculation as adding complexity with no added value in explanatory power! :)

The pertinent points include:
1) all data support flat, infinite, open
2) all data (within error limits) support zero average energy density which also supports flat, infinite, open since any finite universe would have negative average energy density
3) a finite doughnut universe needs additional cosmological parameters which are parametrically a more complex model unjustified by the data (this is where Ockham comes in in). There is no data to fix these free parameters so the proponents can keep hiding their idea from testing.

I detest "maybe it could be this" science that hides behind lack of data to create PR for ill considered ideas. It's the same intellectually dishonest salesmanship that is found among proponents of MOND and is a discredit to honest science.
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by WilliamPaolini »

notFritzArgelander wrote: Thu Jul 22, 2021 9:37 pm
I detest "maybe it could be this" science that hides behind lack of data to create PR for ill considered ideas. It's the same intellectually dishonest salesmanship that is found among proponents of MOND and is a discredit to honest science.
Like you said and I repeated, agree to disagree. And I understand your detestation, but also remember that other have the same detestation when all these "theories" are treated like they are facts of the universe. They are not. Once cannot say that it is a fact that the universe is flat and infinite. It just looks that way now with the capabilities we have, that's all. All any theory is is a best understanding that can be mustered and deduced given the "limited" data we have collected from our "limited" current day technologies. As time has always shown in science, as technology progresses then the theories refine and change and sometimes get turned on their heads. So no discrediting in the second view, just a taking of the long view. As far as I am concerned, the jury is always out on any cosmological theory in the light of future capabilities. So I take them all with a very large grain of salt. I periodically read science books from 100+ years in the past and it is humorous in light of what we know today. And of course, everything from today will similarly look the same to the reader 100+ years from now. As I always tell the younger folks who read what is really many times a misrepresentation of the facts in so many articles on theories, no, what you read is NOT a fact of the matter, it is just our best guess or most likely probability given the data in hand. It is never more than that and anyone characterizing it as more, is simply overstating things. So is the universe flat and infinite? Best answer is looks that way right now, but things might change in that view especially given that the observable universe is just a tiny fraction of infinite. Is the universe 13+ billion years old? Best answer is looks that way at the moment, but things might change in that view. IMO it is a discredit to science that so many folks characterize things as "is" when in fact that is not the case.
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Re: The Universe can be geometrically flat, but topologically finite and closed!

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Post by notFritzArgelander »

WilliamPaolini wrote: Fri Jul 23, 2021 2:15 am
notFritzArgelander wrote: Thu Jul 22, 2021 9:37 pm
I detest "maybe it could be this" science that hides behind lack of data to create PR for ill considered ideas. It's the same intellectually dishonest salesmanship that is found among proponents of MOND and is a discredit to honest science.
Like you said and I repeated, agree to disagree. And I understand your detestation, but also remember that other have the same detestation when all these "theories" are treated like they are facts of the universe. They are not. Once cannot say that it is a fact that the universe is flat and infinite. It just looks that way now with the capabilities we have, that's all.
So far we are in agreement.
All any theory is is a best understanding that can be mustered and deduced given the "limited" data we have collected from our "limited" current day technologies. As time has always shown in science, as technology progresses then the theories refine and change and sometimes get turned on their heads.
Still no disagreement.
So no discrediting in the second view, just a taking of the long view. As far as I am concerned, the jury is always out on any cosmological theory in the light of future capabilities.


Still no disagreement.
So I take them all with a very large grain of salt.
There is no harm in taking the best that we know as the best that we know at present. Cynical skepticism about the current state of theory is unwholesome. That is one place we disagree.
I periodically read science books from 100+ years in the past and it is humorous in light of what we know today.


And I have read science going back to antiquity. More recent offerings I've read include Newton's Principia. One other difference is that I don't ridicule past knowledge. To do so is to profoundly misunderstand the scientific enterprise. I don't find Aristotle or Newton or Tycho laughable.
And of course, everything from today will similarly look the same to the reader 100+ years from now.
Of course that statement is only plausible to the those who believe in continued exponential growth in knowledge while avoiding the clear evidence that progress is slowing down. It is an unscientific belief. Nature habitually saturates exponential growth. ;)
As I always tell the younger folks who read what is really many times a misrepresentation of the facts in so many articles on theories, no, what you read is NOT a fact of the matter, it is just our best guess or most likely probability given the data in hand.
But there are facts of the matter, i.e. data. Theories are subject to change. Although substantial change is coming a lot more slowly than in the first half of the 20th century.
It is never more than that and anyone characterizing it as more, is simply overstating things. So is the universe flat and infinite? Best answer is looks that way right now, but things might change in that view especially given that the observable universe is just a tiny fraction of infinite. Is the universe 13+ billion years old? Best answer is looks that way at the moment, but things might change in that view. IMO it is a discredit to science that so many folks characterize things as "is" when in fact that is not the case.
It is indeed a discredit to science when folks characterize things as "is" without acknowledging the errors in measurement and the significance of differences in various theoretical approaches. I am quite comfortable that I haven't done that. So on that point we agree again.

However it is a sign of the slowing of of real progress and a great discredit to science the part of folks, usually mediocre theorists, who get some wild idea that has no, zero, zilch, nada data supporting it and have built in mathematical devices to avoid falsification by data so they can continue to tinker with their pet idea without making a concrete prediction that can be shown wrong. That's what the MOND folks do and from reading the article on finite toroidal universes that's what those folks have done. They've added parameters that can be tuned so that they never have to admit the idea is bad. THAT is the greatest possible discredit to science. "Maybe some day...." is not an adequate defense to an hypothesis that by construction evades falsification. That is not interesting science. It's not astrophysics. It's PR.
Scopes: Refs: Orion ST80, SV 80EDA f7, TS 102ED f11 Newts: Z12 f5; Cats: VMC110L, Intes MK66,VMC200L f9.75 EPs: KK Fujiyama Orthoscopics, 2x Vixen NPLs (40-6mm) and BCOs, Baader Mark IV zooms, TV Panoptics, Delos, Plossl 32-8mm. Mixed brand Masuyama/Astroplans Binoculars: Nikon Aculon 10x50, Celestron 15x70, Baader Maxbright. Mounts: Star Seeker III, Vixen Porta II, Celestron CG5, Orion Sirius EQG
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