What Is the Geometry of the Universe?

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space.

more…

Tau.Neutrino said:

What Is the Geometry of the Universe?

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space.

more…

There was a time, after all, when everyone thought the Earth was flat, because our planet’s curvature was too subtle to detect and a spherical Earth was unfathomable.

No.

I’ll continue past the first para now.

JudgeMental said:

Tau.Neutrino said:

What Is the Geometry of the Universe?

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space.

more…

There was a time, after all, when everyone thought the Earth was flat, because our planet’s curvature was too subtle to detect and a spherical Earth was unfathomable.

No.

I’ll continue past the first para now.

So you are saying there was no time when everybody thought the Earth was flat?

The Rev Dodgson said:

JudgeMental said:

Tau.Neutrino said:

What Is the Geometry of the Universe?

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space.

more…

There was a time, after all, when everyone thought the Earth was flat, because our planet’s curvature was too subtle to detect and a spherical Earth was unfathomable.

No.

I’ll continue past the first para now.

So you are saying there was no time when everybody thought the Earth was flat?

No, I’m saying you can’t make the first statement.

JudgeMental said:

The Rev Dodgson said:

JudgeMental said:

There was a time, after all, when everyone thought the Earth was flat, because our planet’s curvature was too subtle to detect and a spherical Earth was unfathomable.

No.

I’ll continue past the first para now.

So you are saying there was no time when everybody thought the Earth was flat?

No, I’m saying you can’t make the first statement.

In our mind’s eye, the universe seems to go on forever.?

Well to be pedantic, it is possible to make that statement.

But I agree it isn’t true.

Not for my mind’s eye anyway.

The Rev Dodgson said:

JudgeMental said:

The Rev Dodgson said:

So you are saying there was no time when everybody thought the Earth was flat?

No, I’m saying you can’t make the first statement.

In our mind’s eye, the universe seems to go on forever.?

Well to be pedantic, it is possible to make that statement.

But I agree it isn’t true.

Not for my mind’s eye anyway.

no more possible than the quote. can’t have it both ways.

JudgeMental said:

The Rev Dodgson said:

JudgeMental said:

No, I’m saying you can’t make the first statement.

In our mind’s eye, the universe seems to go on forever.?

Well to be pedantic, it is possible to make that statement.

But I agree it isn’t true.

Not for my mind’s eye anyway.

no more possible than the quote. can’t have it both ways.

I have no idea what you mean.

The Rev Dodgson said:

JudgeMental said:

The Rev Dodgson said:

In our mind’s eye, the universe seems to go on forever.?

Well to be pedantic, it is possible to make that statement.

But I agree it isn’t true.

Not for my mind’s eye anyway.

no more possible than the quote. can’t have it both ways.

I have no idea what you mean.

He might mean that it’s not true there was a time when “our planet’s curvature was too subtle to detect and a spherical Earth was unfathomable.”

…given that the ancient Greeks knew the Earth was a sphere, on the basis of fairly simple observations.

Nonetheless those observations were quite ingenious and one can imagine a time when nobody was clever enough to conduct them.

Bubblecar said:

The Rev Dodgson said:

JudgeMental said:

no more possible than the quote. can’t have it both ways.

I have no idea what you mean.

He might mean that it’s not true there was a time when “our planet’s curvature was too subtle to detect and a spherical Earth was unfathomable.”

…given that the ancient Greeks knew the Earth was a sphere, on the basis of fairly simple observations.

Nonetheless those observations were quite ingenious and one can imagine a time when nobody was clever enough to conduct them.

or they just didn’t think about it.

JudgeMental said:

Bubblecar said:

The Rev Dodgson said:

I have no idea what you mean.

He might mean that it’s not true there was a time when “our planet’s curvature was too subtle to detect and a spherical Earth was unfathomable.”

…given that the ancient Greeks knew the Earth was a sphere, on the basis of fairly simple observations.

Nonetheless those observations were quite ingenious and one can imagine a time when nobody was clever enough to conduct them.

or they just didn’t think about it.

Doubtless many people never conceived of such questions.

Bubblecar said:

JudgeMental said:

Bubblecar said:

He might mean that it’s not true there was a time when “our planet’s curvature was too subtle to detect and a spherical Earth was unfathomable.”

…given that the ancient Greeks knew the Earth was a sphere, on the basis of fairly simple observations.

Nonetheless those observations were quite ingenious and one can imagine a time when nobody was clever enough to conduct them.

or they just didn’t think about it.

Doubtless many people never conceived of such questions.

The autrakian aboriginals did a fair bit of astronomy but did they also realise the earth was a sphere?

JudgeMental said:

Bubblecar said:

JudgeMental said:

or they just didn’t think about it.

Doubtless many people never conceived of such questions.

The autrakian aboriginals did a fair bit of astronomy but did they also realise the earth was a sphere?

According to the ABC they did:

The Earth is round: Indigenous astronomers were able to track the way that the night sky shifts as their relative latitude would change. This indicated the spherical, curved nature of the planet and its sky, understanding the connection between latitude on the ground and declination in the sky

https://www.abc.net.au/news/2019-07-15/indigenous-astronomy-discoveries-that-preceded-modern-science/11308924

Bubblecar said:

JudgeMental said:

Bubblecar said:

Doubtless many people never conceived of such questions.

The autrakian aboriginals did a fair bit of astronomy but did they also realise the earth was a sphere?

According to the ABC they did:

The Earth is round: Indigenous astronomers were able to track the way that the night sky shifts as their relative latitude would change. This indicated the spherical, curved nature of the planet and its sky, understanding the connection between latitude on the ground and declination in the sky

https://www.abc.net.au/news/2019-07-15/indigenous-astronomy-discoveries-that-preceded-modern-science/11308924

Hmmmmm might be a long bow there. Did they move far enough distances to see that effect rather than just a change in the earth’s orbit?

JudgeMental said:

Bubblecar said:

JudgeMental said:

The autrakian aboriginals did a fair bit of astronomy but did they also realise the earth was a sphere?

According to the ABC they did:

The Earth is round: Indigenous astronomers were able to track the way that the night sky shifts as their relative latitude would change. This indicated the spherical, curved nature of the planet and its sky, understanding the connection between latitude on the ground and declination in the sky

https://www.abc.net.au/news/2019-07-15/indigenous-astronomy-discoveries-that-preceded-modern-science/11308924

Hmmmmm might be a long bow there. Did they move far enough distances to see that effect rather than just a change in the earth’s orbit?

That’s what I thought.

Bubblecar said:

JudgeMental said:

Bubblecar said:

Doubtless many people never conceived of such questions.

The autrakian aboriginals did a fair bit of astronomy but did they also realise the earth was a sphere?

According to the ABC they did:

The Earth is round: Indigenous astronomers were able to track the way that the night sky shifts as their relative latitude would change. This indicated the spherical, curved nature of the planet and its sky, understanding the connection between latitude on the ground and declination in the sky

https://www.abc.net.au/news/2019-07-15/indigenous-astronomy-discoveries-that-preceded-modern-science/11308924

That article doesn’t seem to say anything about indigenous astronomers knowing the Earth is round.

The Rev Dodgson said:

JudgeMental said:

Bubblecar said:

According to the ABC they did:

The Earth is round: Indigenous astronomers were able to track the way that the night sky shifts as their relative latitude would change. This indicated the spherical, curved nature of the planet and its sky, understanding the connection between latitude on the ground and declination in the sky

https://www.abc.net.au/news/2019-07-15/indigenous-astronomy-discoveries-that-preceded-modern-science/11308924

Hmmmmm might be a long bow there. Did they move far enough distances to see that effect rather than just a change in the earth’s orbit?

That’s what I thought.

In more arid areas where tribal ranges were larger I imagine they might move 100kms in a week or so. Would that be enough?

Witty Rejoinder said:

The Rev Dodgson said:

JudgeMental said:

Hmmmmm might be a long bow there. Did they move far enough distances to see that effect rather than just a change in the earth’s orbit?

That’s what I thought.

In more arid areas where tribal ranges were larger I imagine they might move 100kms in a week or so. Would that be enough?

100 km N/S is 0.9 degrees. Without accurate angle measuring instruments I’d say it was nowhere near enough.

The examples given in the article were all based on observation with the naked eye, without measurement, which is a different thing altogether.

The Rev Dodgson said:

Witty Rejoinder said:

The Rev Dodgson said:

That’s what I thought.

In more arid areas where tribal ranges were larger I imagine they might move 100kms in a week or so. Would that be enough?

100 km N/S is 0.9 degrees. Without accurate angle measuring instruments I’d say it was nowhere near enough.

The examples given in the article were all based on observation with the naked eye, without measurement, which is a different thing altogether.

just looked up sun angle sydney and melbourne 12 noon wa time. difference is 2°

The Rev Dodgson said:

Bubblecar said:

JudgeMental said:

The autrakian aboriginals did a fair bit of astronomy but did they also realise the earth was a sphere?

According to the ABC they did:

The Earth is round: Indigenous astronomers were able to track the way that the night sky shifts as their relative latitude would change. This indicated the spherical, curved nature of the planet and its sky, understanding the connection between latitude on the ground and declination in the sky

https://www.abc.net.au/news/2019-07-15/indigenous-astronomy-discoveries-that-preceded-modern-science/11308924

That article doesn’t seem to say anything about indigenous astronomers knowing the Earth is round.

Very few people ever twigged that the world was round.

Its unlikely that a culture that no written language, no maths, no science, built little to nothing and were still in the stone age in 1770 knew the world was round.

True knowledge can only come from a written language as a way to pass that knowledge on.

wookiemeister said:

The Rev Dodgson said:

Bubblecar said:

According to the ABC they did:

The Earth is round: Indigenous astronomers were able to track the way that the night sky shifts as their relative latitude would change. This indicated the spherical, curved nature of the planet and its sky, understanding the connection between latitude on the ground and declination in the sky

https://www.abc.net.au/news/2019-07-15/indigenous-astronomy-discoveries-that-preceded-modern-science/11308924

That article doesn’t seem to say anything about indigenous astronomers knowing the Earth is round.

Very few people ever twigged that the world was round.

Its unlikely that a culture that no written language, no maths, no science, built little to nothing and were still in the stone age in 1770 knew the world was round.

True knowledge can only come from a written language as a way to pass that knowledge on.

Pacific Islanders were celestial navigators par excellence and didn’t have written language.

Tau.Neutrino said:

What Is the Geometry of the Universe?

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space.

more…

Immediate reaction. Is this article a rehash of the topological multiverse?

> The other is about its topology: how these local pieces are stitched together into an overarching shape.

Yep. Old news. The topological multiverse is already ruled out within the visible universe. I can direct you to a paper by the Planck telescope on the topic if you like.

> In 2015, astronomers performed just such a search using data from the Planck space telescope. They combed the data for the kinds of matching circles we would expect to see inside a flat three-dimensional torus or one other flat three-dimensional shape called a slab, but they failed to find them. That means that if we do live in a torus, it’s probably such a large one that any repeating patterns lie beyond the observable universe.

Good. They already know that a topological multiverse is ruled out within the observable universe.

> Is Our Universe Spherical?

An old question, going way back to the 1930s if not earlier.

According to observations from Planck and elsewhere, our universe is not statistically different from flat.

> Most such tests, along with other curvature measurements, suggest that the universe is either flat or very close to flat.

Good. So the writers of the article already know that as well. They’re really well informed.

> Is Our Universe Hyperbolic?

See above.

> so far most cosmological measurements seem to favor a flat universe. But we can’t rule out the possibility that we live in either a spherical or a hyperbolic world, because small pieces of both of these worlds look nearly flat.

Occam’s razor.

mollwollfumble said:

Tau.Neutrino said:

What Is the Geometry of the Universe?

In our mind’s eye, the universe seems to go on forever. But using geometry we can explore a variety of three-dimensional shapes that offer alternatives to “ordinary” infinite space.

more…

Immediate reaction. Is this article a rehash of the topological multiverse?

> The other is about its topology: how these local pieces are stitched together into an overarching shape.

Yep. Old news. The topological multiverse is already ruled out within the visible universe. I can direct you to a paper by the Planck telescope on the topic if you like.

> In 2015, astronomers performed just such a search using data from the Planck space telescope. They combed the data for the kinds of matching circles we would expect to see inside a flat three-dimensional torus or one other flat three-dimensional shape called a slab, but they failed to find them. That means that if we do live in a torus, it’s probably such a large one that any repeating patterns lie beyond the observable universe.

Good. They already know that a topological multiverse is ruled out within the observable universe.

> Is Our Universe Spherical?

An old question, going way back to the 1930s if not earlier.

According to observations from Planck and elsewhere, our universe is not statistically different from flat.

> Most such tests, along with other curvature measurements, suggest that the universe is either flat or very close to flat.

Good. So the writers of the article already know that as well. They’re really well informed.

> Is Our Universe Hyperbolic?

See above.

> so far most cosmological measurements seem to favor a flat universe. But we can’t rule out the possibility that we live in either a spherical or a hyperbolic world, because small pieces of both of these worlds look nearly flat.

Occam’s razor.

Since there are an infinite number of very large finite sizes for the Universe, surely it would be very surprising if the local little bit looked anything other than flat, whatever the shape of the whole thing.

Occam’s razor is way over-used, and this question is a good example of where it is totally inapplicable.

The Rev Dodgson said:

Since there are an infinite number of very large finite sizes for the Universe, surely it would be very surprising if the local little bit looked anything other than flat, whatever the shape of the whole thing.

Occam’s razor is way over-used, and this question is a good example of where it is totally inapplicable.

> An infinite number of finite sizes.

OK.

> very surprising if the local little bit looked anything other than flat, whatever the shape of the whole thing.

Definitely not. There’s no reason that a universe can’t be strongly curved, if non-flat is allowed. To put it more succinctly, a curved universe aught not to look locally flat at all, according to theory. By rights it ought to look curved even on scales as small as a galaxy. To force a curved universe to have a radius big enough to look locally flat was a huge challenge for cosmology.

> Occam’s razor is way over-used

Both over-used and under-used. There is absolutely no reason to expect a universe to be anything other than cartesian.

Just like Occam’s razor says that my keyboard is unlikely to turn into a lathe in the next few seconds. See, it didn’t. Occam’s razor is confirmed yet again.

mollwollfumble said:

The Rev Dodgson said:

Since there are an infinite number of very large finite sizes for the Universe, surely it would be very surprising if the local little bit looked anything other than flat, whatever the shape of the whole thing.

Occam’s razor is way over-used, and this question is a good example of where it is totally inapplicable.

> An infinite number of finite sizes.

OK.

> very surprising if the local little bit looked anything other than flat, whatever the shape of the whole thing.

Definitely not. There’s no reason that a universe can’t be strongly curved, if non-flat is allowed. To put it more succinctly, a curved universe aught not to look locally flat at all, according to theory. By rights it ought to look curved even on scales as small as a galaxy. To force a curved universe to have a radius big enough to look locally flat was a huge challenge for cosmology.

> Occam’s razor is way over-used

Both over-used and under-used. There is absolutely no reason to expect a universe to be anything other than cartesian.

Just like Occam’s razor says that my keyboard is unlikely to turn into a lathe in the next few seconds. See, it didn’t. Occam’s razor is confirmed yet again.

I didn’t say a universe can’t be strongly curved. I’m just saying that if you take a random selection from a hypothetical infinite collection of finite sized universes (and this collection has a lower limit on size, but no upper limit), then the probability that your selection will have a measurable radius is very close to zero.

As for Occam’s razor, cherry picking an example where it works does not make it applicable in this case.

A better example would be that given time it is certain that your keyboard will no longer be recognisable as a keyboard, in spite of Occam claiming that it will remain a keyboard.

The late Gene Rodenberry described the edge of the universe as Th Barrier but he didn’t expand on that.

Peak Warming Man said:

The late Gene Rodenberry described the edge of the universe as Th Barrier but he didn’t expand on that.

Maybe he didn’t have the dark energy for it.

The Rev Dodgson said:

mollwollfumble said:

The Rev Dodgson said:

Since there are an infinite number of very large finite sizes for the Universe, surely it would be very surprising if the local little bit looked anything other than flat, whatever the shape of the whole thing.

Occam’s razor is way over-used, and this question is a good example of where it is totally inapplicable.

> An infinite number of finite sizes.

OK.

> very surprising if the local little bit looked anything other than flat, whatever the shape of the whole thing.

Definitely not. There’s no reason that a universe can’t be strongly curved, if non-flat is allowed. To put it more succinctly, a curved universe aught not to look locally flat at all, according to theory. By rights it ought to look curved even on scales as small as a galaxy. To force a curved universe to have a radius big enough to look locally flat was a huge challenge for cosmology.

> Occam’s razor is way over-used

Both over-used and under-used. There is absolutely no reason to expect a universe to be anything other than cartesian.

Just like Occam’s razor says that my keyboard is unlikely to turn into a lathe in the next few seconds. See, it didn’t. Occam’s razor is confirmed yet again.

I didn’t say a universe can’t be strongly curved. I’m just saying that if you take a random selection from a hypothetical infinite collection of finite sized universes (and this collection has a lower limit on size, but no upper limit), then the probability that your selection will have a measurable radius is very close to zero.

As for Occam’s razor, cherry picking an example where it works does not make it applicable in this case.

A better example would be that given time it is certain that your keyboard will no longer be recognisable as a keyboard, in spite of Occam claiming that it will remain a keyboard.

> I didn’t say a universe can’t be strongly curved. I’m just saying that if you take a random selection from a hypothetical infinite collection of finite sized universes (and this collection has a lower limit on size, but no upper limit), then the probability that your selection will have a measurable radius is very close to zero.

Cosmology doesn’t work quite that way.

Cosmology says we have to “you take a random selection from a hypothetical infinite collection of finite” curvature “universes (and this collection has a lower limit on” curvature, “but no upper limit”.

So what cosmology expects (on the tentative assumption that a non-flat universe is possible) is lots of universes with arbitrarily high curvature. As curvature is the inverse of radius, all these universes will be very small. Universes with near-zero nonzero curvature (ie. large finite universes and near-flat hyperbolic universes, just as you’re describing) would be exceedingly rare. So rare that cosmologists have to invent a new force of nature (in addition to the familiar five of strong, weak, electromagnetic, gravity and dark energy) to make them even possible at all.