[Longtitube]

You could have just googled it instead of writing us an essay about how you don't think Hipparchus believed in infinitely distant stars.

https://www.quora.com/What-is-open-space-in-outer-space

Thank you for the Quora link; reading the further remarks from Dr Nazarro was quite enlightening. Unfortunately, he doesn't substantiate his remarks on Hipparchus with a reference of any sort, so it's of no use in verifying anything.

Aristarchus believed that the stars were infinitely distant too:

https://books.google.com/books?id=LE1HDwAAQBAJ&newbks=1&newbks_redir=0&lpg=PT78&pg=PT78#v=onepage&f=false

I'm aware of Aristarchus's belief, but he doesn't feature in Kings Dethroned. Sorry.

[Longtitube]

Incorrect, Longitude clearly argues that Hipparchus believed in a small universe like Ptolemy. He states at the end of his second post: -

" Instead of astronomers originally thinking the stars were infinitely distant or unthinkingly accepting the opinion of their predecessors, the impression from reading their works is a growing understanding of how much bigger they each realise the universe is than previously thought; "

He suggests that astronomers did not originally think the stars were infinitely distant and eventually realized that it was enormous. This is clearly wrong.

Incorrect. Hickson maintains Hipparchus believed the "heavenly bodies are infinitely distant" but never substantiates this. Having checked the works of Ptolemy and the few other secondhand records of Hipparchus's writings, I cannot find anything to substantiate this either. I don't know what Hipparchus believed about the distance to the stars, but if you know of a citation or reference which clearly tells us, I'd be obliged if you shared it.

[Tom Bishop]

Yes, sources were also provided showing that Hipparchus believed in an infinitely distant sun. If he treated the sun as infinitely distant it is difficult to argue that he never treated he stars as infinitely distant.

Your argument is that you do not personally believe that Hipparchus believed in infinitely distant stars, and do not actually have a source on that except for your own opinion, which is a poor argument to say the least.

[AATW]

Yes, sources were also provided showing that Hipparchus believed in an infinitely distant sun. If he treated the sun as infinitely distant it is difficult to argue that he never treated he stars as infinitely distant.

Your argument is that you do not personally believe that Hipparchus believed in infinitely distant stars, and do not actually have a source on that except for your own opinion, which is a poor argument to say the least.

What is the significance of him believing that?
The ancients believed in 4 elements, water, air, earth, fire, that everything was made out of. They were wrong. What of it?
Our knowledge about and understanding of of the world and universe has developed over time and continues to as we have better instruments to observe things.

[Action80]

Chapters 1 & 2

After describing triangulation, as used by surveyors and on which the author is particularly keen, he introduces the astronomers Hipparchus of Nicaea, Claudius Ptolemy of Alexandria, Nicolas Copernicus, Tycho Brahe, Johannes Kepler and Galileo Galilei. As astronomers, their opinions and theories formed the standard views of astronomy in their times and Copernicus and Kepler especially laid the foundations of modern astronomy, but the author believes they all made a fundamental mistake: beginning at Hipparchus they all held that “the heavenly bodies (the stars) are infinitely distant.” (page 3)

The author never says where this saying is recorded; he only insists it was Hipparchus’s conviction and that the others accepted it at face value. We can’t check Hipparchus’s own writings, they’re lost; we mostly know them from Ptolemy. So, if Ptolemy, author of the standard text on geocentric astronomy used for 1400 years (the famous Almagest), built his theory of the universe while accepting this, you’d expect to find it in his writings, but you’d be disappointed – the Almagest doesn’t mention it. In fact, Ptolemy claims the stars are just beyond the orbit of Saturn, 20,000 earth radii from Earth (from Ptolemy’s Planetary Hypotheses, Hamm, 2011, p202).

I find it amusing that you fail to point to a direct reference to Ptolemy when laying claim as to what he believed, instead relying on the hearsay of others "to speak the truth," "you can trust us, this is what Ptolemy believed."

Nah, doesn't fly.

Yet when Hickson claims a direct quote of Hipparchus (i.e., "the heavenly bodies are infinitely distant," you offer nothing more than a statement a direct quote of Hipparchus or his work would be impossible, because we cannot check Hipparchus' writings.

You know you do not have access to them.

That's all.

Spare us the rest of the writing as it is rendered totally useless by this demonstration of your bias.

This demonstration indicates an inability to assess the printed material on a toothpaste tube, let alone a written work by a scientist.

[BillO]

Yes, sources were also provided showing that Hipparchus believed in an infinitely distant sun.

Who Nazzaro?  Are we to take his account of this seriously?  He's a carpenter with a PhD in philosophy and psychology from Whales and he did his undergraduate work in theology.  Sure sounds like an expert on the cosmos.

Hipparchus was at the very beginning of real scientific inquiry into the nature of the cosmos.  His beliefs were likely to alter over time as he worked through answering the questions of the day.  It's the same with science today, the inquiry continues and our understanding of the universe changes.  I'm honestly not sure what the significance is of his at one point thinking the sun was infinitely far away though, if indeed he ever did.  He would soon become aware that was not possible given his model had it orbiting the earth once a year.  If I'm not mistaken he put the sun somewhere between Venus and Mars.  Does not sound infinite to me.

See this excerpt form the Encyclopedia Britannica: http://abyss.uoregon.edu/~js/glossary/hipparchus.html

[Tom Bishop]

Who Nazzaro?  Are we to take his account of this seriously?  He's a carpenter from Whales with a PhD in philosophy and psychology and he did his undergraduate work in theology.  Sure sounds like an expert on the cosmos.

Actually if you have a PhD in Philosophy that does usually involve becoming an expert in the Ancient Greeks. Philosophy curriculums place heavy emphasis on the Ancient Greeks. This would involve knowledge of their interpretation about the world in which they lived and the philosophies surrounding that.

But no, I cited a NASA website on that:

https://sunearthday.nasa.gov/2009eclipse/amateur.php - "Hipparchus assumed that the sun was at an infinite distance."

[AATW]

https://sunearthday.nasa.gov/2009eclipse/amateur.php - "Hipparchus assumed that the sun was at an infinite distance."

Ok. And so what?

[stack]

Who Nazzaro?  Are we to take his account of this seriously?  He's a carpenter from Whales with a PhD in philosophy and psychology and he did his undergraduate work in theology.  Sure sounds like an expert on the cosmos.

Actually if you have a PhD in Philosophy that does usually involve becoming an expert in the Ancient Greeks. Philosophy curriculums place heavy emphasis on the Ancient Greeks.

But no, I cited a NASA website on that:

https://sunearthday.nasa.gov/2009eclipse/amateur.php - "Hipparchus assumed that the sun was at an infinite distance."

Yes, that was book #1. However, you're ignoring his book #2...

His second book came after the first:

"In the second book, Hipparchus started from the opposite extreme assumption: he assigned a (minimum) distance to the Sun of 470 Earth radii."
https://www.newworldencyclopedia.org/entry/hipparchus_(astronomer)

[Tom Bishop]

https://sunearthday.nasa.gov/2009eclipse/amateur.php - "Hipparchus assumed that the sun was at an infinite distance."

Ok. And so what?

So if he thought the Sun was an infinite distance then it is difficult to argue that he didn't think the stars were as well. This makes Longitude wrong in his assessment.

Yes, that was book #1. However, you're ignoring his book #2...

His second book came after the first:

"In the second book, Hipparchus started from the opposite extreme assumption: he assigned a (minimum) distance to the Sun of 470 Earth radii."
https://www.newworldencyclopedia.org/entry/hipparchus_(astronomer)

Actually NASA mainly cites him as asserting that the Sun was at an infinite distance.

He clearly treated the Sun as at an infinite distance at some point. Therefore he likely thought that the stars were also at infinite distance. Hence, Longitude is wrong to assert that he never thought that.

[stack]

https://sunearthday.nasa.gov/2009eclipse/amateur.php - "Hipparchus assumed that the sun was at an infinite distance."

Ok. And so what?

So if he thought the Sun was an infinite distance then it is difficult to argue that he didn't think the stars were as well. This makes Longitude wrong in his assessment.

Yes, that was book #1. However, you're ignoring his book #2...

His second book came after the first:

"In the second book, Hipparchus started from the opposite extreme assumption: he assigned a (minimum) distance to the Sun of 470 Earth radii."
https://www.newworldencyclopedia.org/entry/hipparchus_(astronomer)

Actually NASA mainly cites him as asserting that the Sun was at an infinite distance.

He clearly treated the Sun as at an infinite distance at some point. Therefore he likely thought that the stars were also at infinite distance. Hence, Longitude is wrong to assert that he never thought that.

Yes, NASA mainly does cite that. But the fact remains that Hipparchus revised his thinking and calculated the sun's distance to be a min of 470 Earth radii in book #2. Which came after book #1.

I'm not seeing where Longitude claimed Hipparchus never thought the sun was near infinitely far away. Hickson's claim is that Hipparchus said it was without taking into consideration book #2. Which again, came after book #1.

[Pete Svarrior]

Ok. And so what?

C'mon. It was Longitube who started this pointless line of inquiry (which, for stack's benefit, can be found early in this post). If you're gonna "so what?" someone repeatedly, at least pick the right target.

[Longtitube]

Yes, sources were also provided showing that Hipparchus believed in an infinitely distant sun. If he treated the sun as infinitely distant it is difficult to argue that he never treated he stars as infinitely distant.

Your argument is that you do not personally believe that Hipparchus believed in infinitely distant stars, and do not actually have a source on that except for your own opinion, which is a poor argument to say the least.

You provided a selective quotation from one website. I'll offer in return a link to a paper examining accounts of Hipparchus's On Sizes and Distances (as reconstructed from the extant quotations in Ptolemy, Pappus etc) which considers the substance of Book 1 (which assumes an imperceptible parallax for the Sun) and the contents of Book 2 (which considers a minimum distance to the Sun). You'll doubtless be pleased this is from New York University instead of NASA.

https://archive.nyu.edu/bitstream/2451/61288/56/11.%20Carman.pdf

Nowhere in this comprehensive examination of the subject of both books (determining the size of the Moon) does it indicate Hipparchus believed the Sun or any other stars to be infinitely distant.

You also offered a quotation from some random guy on Quora. Random guy doesn't substantiate his opinion with a reference or a citation and may have been quoting Gerrard Hickson's book for all we know.

Kings Dethroned doesn't substantiate its claim either. That's the point.

[Longtitube]

Chapters 1 & 2

After describing triangulation, as used by surveyors and on which the author is particularly keen, he introduces the astronomers Hipparchus of Nicaea, Claudius Ptolemy of Alexandria, Nicolas Copernicus, Tycho Brahe, Johannes Kepler and Galileo Galilei. As astronomers, their opinions and theories formed the standard views of astronomy in their times and Copernicus and Kepler especially laid the foundations of modern astronomy, but the author believes they all made a fundamental mistake: beginning at Hipparchus they all held that “the heavenly bodies (the stars) are infinitely distant.” (page 3)

The author never says where this saying is recorded; he only insists it was Hipparchus’s conviction and that the others accepted it at face value. We can’t check Hipparchus’s own writings, they’re lost; we mostly know them from Ptolemy. So, if Ptolemy, author of the standard text on geocentric astronomy used for 1400 years (the famous Almagest), built his theory of the universe while accepting this, you’d expect to find it in his writings, but you’d be disappointed – the Almagest doesn’t mention it. In fact, Ptolemy claims the stars are just beyond the orbit of Saturn, 20,000 earth radii from Earth (from Ptolemy’s Planetary Hypotheses, Hamm, 2011, p202).

I find it amusing that you fail to point to a direct reference to Ptolemy when laying claim as to what he believed, instead relying on the hearsay of others "to speak the truth," "you can trust us, this is what Ptolemy believed."

Nah, doesn't fly.

Yet when Hickson claims a direct quote of Hipparchus (i.e., "the heavenly bodies are infinitely distant," you offer nothing more than a statement a direct quote of Hipparchus or his work would be impossible, because we cannot check Hipparchus' writings.

You know you do not have access to them.

That's all.

Spare us the rest of the writing as it is rendered totally useless by this demonstration of your bias.

This demonstration indicates an inability to assess the printed material on a toothpaste tube, let alone a written work by a scientist.

I do beg your pardon, how remiss of me.

Therefore, the greatest distance of Saturn, which is adjacent to the sphere of the fixed stars, is 19,865 earth radii, and its least distance is 14,187 earth radii.
…
If all the diameters subtended the same apparent angle at their mean distances, the ratio of one diameter to another would equal the ratio of their distances, because the ratio of the circumferences of circles, as well as of similar arcs, one to another, is equal to the ratio of their radii. In the measure in which the diameter of the Sun is 1,210, the diameter of the Moon is 48; the diameter of Mercury 115 the diameter of Venus 622½; the diameter of Mars 5,040; the diameter of Jupiter 11,504; and the diameter of Saturn 17,026. The diameter of the first magnitude stars in this measure, assuming that their (sphere) is adjacent to the furthest distance of Saturn, is 19,865, or about 20,000; and the amount is surely not less than 20,000. But the diameters do not subtend equal angles, for the diameter of the Moon subtends an angle 1 1/3 times that of the Sun, and the diameters of the planets subtend angles smaller than the Sun in the ratios mentioned. It is clear that in the measure where the diameter of the Sun is 1,210, the diameter of the Moon is 64 because it is 1⅓ times 48; the diameter of Mercury is 8 because it is about 1/15 of 115; the diameter of Venus is 62 which is about of 622½; the diameter of Mars is 252 which is 1/20 of 5,040; the diameter of Jupiter is 959 which is about 1/12 of 11,504; the diameter of Saturn is 946 which is about 1/18 of 17,026; the diameters of the first magnitude stars is 1,000 which is 1/20 of 20,000, and they are certainly not smaller.

Planetary Hypotheses Book 1, part 2 by Claudius Ptolemy

https://pdfcoffee.com/download/goldstein-the-arabic-version-of-ptolemyx27s-planetary-hypotheses-2-pdf-free.html

Now perhaps you know of where Hickson gets his quotation, with a direct citation or reference? In turn, I find it slightly amusing Kings Dethroned is accepted as the trustworthy work of a scientist.

[AATW]

Ok. And so what?

C'mon. It was Longitube who started this pointless line of inquiry (which, for stack's benefit, can be found early in this post). If you're gonna "so what?" someone repeatedly, at least pick the right target.

I mean, in my first "so what" I did elaborate somewhat. Let's concede that this dude did believe that the stars were infinitely distant. I don't see why that it's claimed in Kings Dethroned to be such a "gotcha". Didn't Newton believe in alchemy? (I might have made that up, pretty sure one of the scientific big guns did and have a feeling it was him). OK, so he was wrong about that. What of it? Most of old science was wrong, heck even Newton was wrong although his theories are still useful in most circumstances. That's what science is about, "standing on the shoulders of giants", but also correcting and updating things as you go to improve and refine models.

[Pete Svarrior]

I mean, in my first "so what" I did elaborate somewhat. Let's concede that this dude did believe that the stars were infinitely distant. I don't see why that it's claimed in Kings Dethroned to be such a "gotcha".

What is proposed in Kings Dethroned is that a substantial portion of science was directly based on this misunderstanding, rather than that it existed coincidentally, and that the misconceptions stemming from this were never corrected. That's why Longitube wanted to "nuh uh" his way out of it early.

Longitube's claim is not the most important claim in the world, but he did make it, and truth is good.

[BillO]

But no, I cited a NASA website on that:

https://sunearthday.nasa.gov/2009eclipse/amateur.php - "Hipparchus assumed that the sun was at an infinite distance."

Okay.  Perhaps the assumption of infinite distance was to simplify the problem in light of him not knowing exactly how far the sun was actually away.  Such methods have been in practice since the beginning and are still used.  Once he had studied the seasons and rationalized the sun must be in orbit around the earth he had no problems placing it between Mars and Venus.  It is still interesting to see the progress he made given the limited knowledge and tools of the time.  The model he eventually decided on lasted virtually unchanged for over 1600 years.

[Action80]

Chapters 1 & 2

After describing triangulation, as used by surveyors and on which the author is particularly keen, he introduces the astronomers Hipparchus of Nicaea, Claudius Ptolemy of Alexandria, Nicolas Copernicus, Tycho Brahe, Johannes Kepler and Galileo Galilei. As astronomers, their opinions and theories formed the standard views of astronomy in their times and Copernicus and Kepler especially laid the foundations of modern astronomy, but the author believes they all made a fundamental mistake: beginning at Hipparchus they all held that “the heavenly bodies (the stars) are infinitely distant.” (page 3)

The author never says where this saying is recorded; he only insists it was Hipparchus’s conviction and that the others accepted it at face value. We can’t check Hipparchus’s own writings, they’re lost; we mostly know them from Ptolemy. So, if Ptolemy, author of the standard text on geocentric astronomy used for 1400 years (the famous Almagest), built his theory of the universe while accepting this, you’d expect to find it in his writings, but you’d be disappointed – the Almagest doesn’t mention it. In fact, Ptolemy claims the stars are just beyond the orbit of Saturn, 20,000 earth radii from Earth (from Ptolemy’s Planetary Hypotheses, Hamm, 2011, p202).

I find it amusing that you fail to point to a direct reference to Ptolemy when laying claim as to what he believed, instead relying on the hearsay of others "to speak the truth," "you can trust us, this is what Ptolemy believed."

Nah, doesn't fly.

Yet when Hickson claims a direct quote of Hipparchus (i.e., "the heavenly bodies are infinitely distant," you offer nothing more than a statement a direct quote of Hipparchus or his work would be impossible, because we cannot check Hipparchus' writings.

You know you do not have access to them.

That's all.

Spare us the rest of the writing as it is rendered totally useless by this demonstration of your bias.

This demonstration indicates an inability to assess the printed material on a toothpaste tube, let alone a written work by a scientist.

I do beg your pardon, how remiss of me.

Therefore, the greatest distance of Saturn, which is adjacent to the sphere of the fixed stars, is 19,865 earth radii, and its least distance is 14,187 earth radii.
…
If all the diameters subtended the same apparent angle at their mean distances, the ratio of one diameter to another would equal the ratio of their distances, because the ratio of the circumferences of circles, as well as of similar arcs, one to another, is equal to the ratio of their radii. In the measure in which the diameter of the Sun is 1,210, the diameter of the Moon is 48; the diameter of Mercury 115 the diameter of Venus 622½; the diameter of Mars 5,040; the diameter of Jupiter 11,504; and the diameter of Saturn 17,026. The diameter of the first magnitude stars in this measure, assuming that their (sphere) is adjacent to the furthest distance of Saturn, is 19,865, or about 20,000; and the amount is surely not less than 20,000. But the diameters do not subtend equal angles, for the diameter of the Moon subtends an angle 1 1/3 times that of the Sun, and the diameters of the planets subtend angles smaller than the Sun in the ratios mentioned. It is clear that in the measure where the diameter of the Sun is 1,210, the diameter of the Moon is 64 because it is 1⅓ times 48; the diameter of Mercury is 8 because it is about 1/15 of 115; the diameter of Venus is 62 which is about of 622½; the diameter of Mars is 252 which is 1/20 of 5,040; the diameter of Jupiter is 959 which is about 1/12 of 11,504; the diameter of Saturn is 946 which is about 1/18 of 17,026; the diameters of the first magnitude stars is 1,000 which is 1/20 of 20,000, and they are certainly not smaller.

Planetary Hypotheses Book 1, part 2 by Claudius Ptolemy

https://pdfcoffee.com/download/goldstein-the-arabic-version-of-ptolemyx27s-planetary-hypotheses-2-pdf-free.html

Now perhaps you know of where Hickson gets his quotation, with a direct citation or reference? In turn, I find it slightly amusing Kings Dethroned is accepted as the trustworthy work of a scientist.

Yeah, I am wondering how you claim that something cannot be adjacent to the infinite.

Finite is adjacent to infinite.

So, Ptolemy made no claim resembling your analysis.

[BillO]

Finite is adjacent to infinite.

What?  Not to take this topic off course too much, but no, this is not true at all.  There is no point between a given point of origin and infinity where you can say "One step closer to the origin and you are a finite distance away, but one step further and you are an infinite distance away".  Nor could you find a scale between two given points where you divide the scale one more time and now you can say there are an infinite number of positions between those two points on this scale.  Infinity is not a place, or a quantity, it is the conceptualization of the uncountably large.  It does not exist any where near the finite.

[Longtitube]

Finite is adjacent to infinite.

Wow.    You need to consult a dictionary.