The Flat Earth Society
Flat Earth Discussion Boards => Flat Earth Community => Topic started by: Longtitube on June 16, 2022, 08:22:04 PM

“Kings Dethroned” by Gerrard Hickson, first published in 1922, is listed in the wiki under FE Literature, and I’m grateful to the member who mentioned it recently, although slightly amused by the presumed globe Earth referred to throughout.
Hickson makes some bold claims for his book, especially to have made a “remarkable discovery” and found a “catalogue of blunders”, stemming from an ancient error, which will presumably ‘dethrone’ the ‘kings’ of astronomy; but a hundred years after publication, do his “new and startling theories” stack up? Does he have important contributions to understanding the cosmos?
Let’s have a look.

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).
https://classicalliberalarts.com/resources/PTOLEMY_ALMAGEST_ENGLISH.pdf (https://classicalliberalarts.com/resources/PTOLEMY_ALMAGEST_ENGLISH.pdf)
https://tspace.library.utoronto.ca/bitstream/1807/32069/1/Hamm_Elizabeth_A_201111_PhD_Thesis.pdf (https://tspace.library.utoronto.ca/bitstream/1807/32069/1/Hamm_Elizabeth_A_201111_PhD_Thesis.pdf)
Perhaps Copernicus, whose De Revolutionibus changed astronomy’s view of the universe from geocentric to heliocentric (although Aristarchus of Samos held this opinion in the 3rd century BC), uses this infinitelydistant idea for the stars? No: –
“…the chief contention by which it is sought to prove that the universe is finite is its motion. Let us therefore leave the question whether the universe is finite or infinite to be discussed by the natural philosophers.” (Copernicus: De Revolutionibus Book 1, chapter 8 )
Disappointingly, this is just the first example of carelessness with both historical accounts and facts to be met throughout Hickson’s book.
Tycho Brahe “differed with some of the details of the Prussian doctor's theory (Copernicus), but accepted it in the main; and took no account whatever of the question of the distance of the stars.” So says our author on page 7, but Tycho in fact devised his own theory of the universe, with Sun and Moon orbiting the Earth, all the other planets orbiting the Sun and the stars on a sphere surrounding them all: this Tychonic theory was the main rival to Copernicus for around two hundred years. He gave no figure for the distance to the stars.
Kepler was a gifted mathematician who developed his laws of planetary motion to explain the planets’ behaviour better than Copernicus, Ptolemy or anyone else had. The ancient theory of epicycles and all the other compensations previously used were done away with, replaced by elliptical orbits, but he doesn’t mention the distance of the stars either.
The author says of Galileo: “In the year 1642 he invented the telescope, and so may be said to have founded the modern method of observing the heavens.” (page 8 ) Galileo died in 1642 and didn’t invent the telescope, but he did start the modern method of observing the heavens – in 1609. Through his selfbuilt telescopes, he saw the craters on the Moon’s surface, was astonished to see far more stars than can be seen by the unaided eye, discovered Venus has phases like the Moon and discovered the four largest moons of Jupiter. After watching these moons for a long time, he came up with an idea for using one of them to accurately tell the time – the constant problem for ship’s navigators out of sight of land: we’ll look at this in Chapter 3.
From observing the stars by telescope, Galileo calculated the distance to the stars was from hundreds to thousands of times the earthsun distance. (Galileo: Dialogue, p359360)
https://rauterberg.employee.id.tue.nl/lecturenotes/DDM110%20CAS/Galilei1632%20Dialogue%20Concerning%20the%20Two%20Chief%20World%20Systems.pdf (https://rauterberg.employee.id.tue.nl/lecturenotes/DDM110%20CAS/Galilei1632%20Dialogue%20Concerning%20the%20Two%20Chief%20World%20Systems.pdf)
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; but you’d never know this from Hickson’s book.

Chapter 3
The author now gets to the meat of his case by first examining the observations of Ole Rømer the Danish astronomer.
“Ole Romer [sic] observed that in the case of the eclipses of the satellites, or moons, of Jupiter, the period of time between them was not always the same, for they occurred 16½ minutes later on some occasions than on others. He therefore tried to account for this slight difference in time, and was led to some strange conclusions.
These eclipses occur at different seasons of the year, so that sometimes they can be seen when the earth is at A (see dia. 3), and at other times when the earth is at B, on the opposite side of the sun and the orbit, {according to Copernican Astronomy).” (Hickson page 10)
Let’s get a few facts clear. As suggested by Galileo, Rømer was taking observations of Jupiter’s moon Io, which Galileo discovered in 1610. Its orbit around Jupiter takes about 42½ hours and it passes through the shadow of Jupiter every orbit, therefore it is eclipsed about every 42½ hours. Galileo’s idea was to accurately record the time of Io’s eclipses to be used by navigators as a reliable way to tell the time and thus find their longitude. For some months an observer will see Io disappear as it is eclipsed by Jupiter’s shadow, for some months Io is seen reappearing as it emerges from Jupiter’s shadow. In between these months either the sun hides both Jupiter and its moons or Io cannot be clearly seen entering or leaving eclipse because Jupiter’s bulk hides it.
At this time the speed of light was unknown and was often thought of as infinite. Rømer discovered the time of the eclipse varied by a small amount through the year and the differences accumulated. Over months the differences amounted to minutes, but while Io’s eclipse timing got slower over some months, for others it speeded up. Rømer realised this coincided with Earth moving away from and then moving towards Jupiter in the course of Earth’s annual orbit and deduced light therefore had a finite speed.
The author explains this difference by differences in angle of view of Io at different times (page 12), but he has forgotten an important detail: Io is seen either disappearing or reappearing as it moves into or out of Jupiter’s shadow, just as someone stepping into a spotlight’s lit area is seen at one time from across the street, or from two hundred yards along the street. Viewpoint has nothing to do with it.
The author also carelessly states Rømer measured the maximum difference in time as 16½ minutes and so claimed light would take 8¼ minutes to travel from the Sun to Earth. This is not true: Rømer estimated the maximum difference in eclipse time at about 22 minutes: Hickson has substituted the answer an astronomer might give nowadays. His dismissal of Rømer’s discovery is invalid and can be ignored.
https://en.wikipedia.org/wiki/R%C3%B8mer%27s_determination_of_the_speed_of_light (https://en.wikipedia.org/wiki/R%C3%B8mer%27s_determination_of_the_speed_of_light)

Chapter 4
The author spends some pages on gravity, but this has been argued over in these fora so often and Hickson has nothing new to say, so I’ll pass it by.
He then speaks of Edmond Halley “…it is to him that we owe nearly all the methods of measuring distance which are used in astronomy at the present day. So far no one had seriously considered the possibility of measuring the distance to the sun, planets or stars since Hipparchus had failed away back in the second century B.C. but now, since the science had made great strides, it occurred to Dr Halley that it might be possible at least to find the distance from the earth to the sun, or to the nearest planet.” (page 16)
Hickson is referring to the diurnal, or geocentric parallax method and claims Halley invented it. This is fiction: Halley’s predecessor, the first Astronomer Royal John Flamsteed had already used the method to measure the distance to Mars in October 1672, the year before a young Halley even started his studies at Oxford. Hickson freely criticises the method and says it will be dealt with in due course (in chapter 8 ). We’ll leave his points until then, but readers are asked to carefully note diagram 6 on page 20: –
(https://i.imgur.com/uqCPGyu.jpg?1)
The author concludes this chapter with comments on James Bradley’s theory of the aberration of light. “If Bradley intended to prove anything by this theory it was that the apparent movement of the stars proves that the earth is in motion; which surely is begging the question.” (page 21)
What is the aberration of light?
“It was in 1727 that Bradley began the series of observations which resulted in his discovery and interpretation of the aberration of the fixed stars. The general law of aberration, to which the apparent annual motions of the stars are subjected, is this: Every star in the heavens … travels once a year in a minute ellipse, whose major axis is somewhat more than twothirds of an arcminute in length, while its minor axis depends on the position of the star with reference to that great circle on the heavens in which the sun seems annually to travel. A star close by the pole of this circle the ecliptic has an almost circular aberrationellipse; one near the ecliptic itself has an aberrationellipse so eccentric as to be almost a straight line. But every star has an aberration ellipse of the same major axis. And that major axis, though minute, belongs to the order of magnitudes which are obvious to the telescopist palpable, unmistakable, clear as the sun at noon, to the worker in a wellappointed observatory.” (Old and New Astronomy: Proctor & Ranyard, p2378)
https://archive.org/details/oldnewastronomy00procuoft (https://archive.org/details/oldnewastronomy00procuoft)
As telescopes and other instruments were refined and observing techniques grew more precise, astronomers were searching the sky for signs of parallax among the stars and Bradley thought he had found it in a regular, predictable movement of every star in the course of each year. Unfortunately, that movement is at right angles to the hopedfor direction of stellar parallax. Bradley finally realised what he was seeing was due to the finite speed of light and the movement of Earth in its orbit. Hickson doesn’t like this and tries to dismiss it in theoretical terms, but the movement is real and measurable by astronomers each year.
Bradley’s discovery killed off the Tychonic system as a competitor to modern astronomy. Hickson’s objections are overruled.

Chapter 5
The author is very keen on triangulation, used by surveyors, to measure how far away a distant object is: he spends chapter 5 dissecting the measurement of the distance from Earth to the Moon by “direct triangulation” as done by Lalande and Lacaille, a pair of French astronomers, in 175152.
He goes on: – “…in making the final computations they made "allowances" in order to conform to certain of the established false theories of astronomy.” These “allowances” are first for atmospheric refraction which Hickson claims doesn’t exist. Plainly the man has never seen a mirage.
The second “allowance” he decries is for equatorial parallax, but equatorial parallax is allowed for only after the distance from observer to moon has been calculated. Astronomers want to know the distance between the centre of the Earth and the centre of the Moon, not just between the Earth and Moon’s surfaces. Equatorial parallax is no “false theory”, even if Hickson is unfamiliar with its use and ignorant of its purpose.
The author’s biggest mistake here is his imagining what these two astronomers actually did. “The moon was at a low altitude away in the west, the two observers took the angles with extreme care, and at a later date they met, compared notes, and made the necessary calculations.” (page 23) This is nonsense, they did not take their observations with the Moon low in the west but on the meridian: at the Moon’s highest elevation from the horizon. A surveyor may make most of his measurements in horizontal angles – which is what the author has mistakenly assumed happened – but astronomers also look up and measure vertical angles. Direct triangulation has been used, but in the vertical plane.
The author tries to cover for himself with an illustration in his book, but advises us to ignore diagrams such as one in a wellknown book on astronomy from his day: –
“I have occasion to call the reader's attention to the fact that some books, Proctor's "Old and New Astronomy" for example, in describing the principle of how to measure to the moon, illustrate it by a diagram which differs from our diagram 8. Though the principle as it is explained in those books seems plausible enough, it would be impossible in practice, for the diagram they use clearly shows the moon to be near the zenith.” (pages 2324)
Here's the diagram from page 23: you can see the presumed position of the Moon near the horizon in the west: –
(https://i.imgur.com/aSf41l3.jpg)
Now compare the diagram from p246 of Proctor’s book showing the vertical angles actually measured: –
(https://i.imgur.com/kWG59QI.jpg)
Lalande measured from Berlin, not Greenwich, but the method is the same. The vertical angle between the moon and a plumbline is carefully measured at both locations and the distance to the Moon calculated. There’s nothing impossible involved: the author merely demonstrates ignorance. His claim “the distance of the moon is no more known today than it was at the time of the flood” (page 26) is only bluster.
He also seems to think this was the first time measuring the distance to the Moon had been attempted, but it wasn’t. It was tried, successfully, by none other than Hipparchus in the 2nd century BC.
https://www.britannica.com/biography/HipparchusGreekastronomer (https://www.britannica.com/biography/HipparchusGreekastronomer)

Chapter 6
The author mocks ideas about the formation of the universe and atomic theory, but we’ll skip all that as irrelevant blather. Hopefully he didn’t live to see the bombing of Hiroshima and Nagasaki.
He returns to facts and figures (page 29) discussing the work of Johann Franz Encke of the Berlin Observatory, who collected many observations of the 1761 and 1769 transits of Venus – where Venus crosses the face of the Sun as seen from Earth – to produce a calculation of the distance between Earth and Sun. The author claims Encke’s figures were accepted without question, but he is mistaken – there was a good deal of argument over his calculations and as a result the transits of 1874 and 1882 were eagerly anticipated for more rigorous measurements.
What the author does get right is that Halley proposed (in 1716) the method of observing the transit, and from places as far apart as possible, but because Hickson insists the observers must be placed at the poles (because he has seen diagrams apparently showing this) – and weren’t – there must be “allowances” made which make the measurements invalid in his eyes. This quibbling does not help his case: if the baseline for a measurement is 6,200 instead of 7,900 miles or so, that doesn’t make the measurement invalid. Halley himself didn’t insist on polar observations, but suggested observing from Hudson Bay, Canada and Pondicherry (Puducherry) in Tamil Nadu, India. We’ll return to this with discussion of the 19th century transits of Venus.
https://www.nature.com/articles/010027a0.pdf (https://www.nature.com/articles/010027a0.pdf)
https://www.jstor.org/stable/44860644?seq=1 (https://www.jstor.org/stable/44860644?seq=1)
https://eclipse.gsfc.nasa.gov/transit/HalleyParallax.html (https://eclipse.gsfc.nasa.gov/transit/HalleyParallax.html)

Chapter 7
Heading this chapter “A Galaxy of Blunders”, the author boldly states the following on page 32: –
“I respectfully call the attention of the responsible authorities of astronomy to this chapter, for it is probable that I shall here shatter some of their most cherished theories, and complete the overthrow of the Copernican astronomy they represent.”
Hickson has turned his attention to the discovery of stellar parallax and the measurement of the distance to “the star known as "61 Cygni"” by F.W. Bessel in 1838.
Before examining the author’s comments, it would help to know that astronomers had known about parallax for many hundreds of years: Hipparchus, Ptolemy and others observed and measured lunar parallax and attempted to measure that of the Sun and the planets Mars and Venus, but no nakedeye observations of stellar parallax were ever made. Astronomers including Tycho objected to a heliocentric universe because it implied the stars must be at huge distances if no stellar parallax could be seen from a moving Earth (how curious –supposedly Tycho “unquestioningly” believes the stars are “infinitely distant” but objects to them being enormously distant? Hickson doesn’t address this). The arrival of the telescope began to change that: Bradley mistakenly thought he had found parallax, as previously discussed, but as telescopes and associated instruments got better, they greatly increased the precision of the measurements possible.
Bessel, among others, had been observing 61 Cygni (which Bradley discovered was a double star) from 1812 onwards. The reason for the interest? 61 Cygni moves across the background stars, indicating it is nearer to Earth than those background stars: astronomers nicknamed it the ‘Flying Star’. This isn’t some abstract theory; it’s been measured and photographed for many years. This animated image is a sequence of nine photographs of 61 Cygni at oneyear intervals from 2012 to 2020: –
(https://i.imgur.com/qbHfDTz.gif)
Various astronomers tried to measure its distance, including Bessel, who used a heliometer to measure 61 Cygni’s stellar parallax for some years, but when he received a more accurate instrument he made his best measurements to date in 1837 and 1838. This time the error range was smaller than the measurement made and the result was publicised. Shortly afterwards others published parallax measurements of Alpha Centauri and Vega.
The author introduces objections to these measurements in terms of theories he claims all astronomers believe: the “Theory of Parallax”, the “Theory of Perpendicularity” and the “Theory of Geocentric Parallax”. Parallax is described clearly (page 35) and he “leave(s) the reader to make his own comments upon it.” – in other words he can’t think of a reason to fault this.
The ”Theory of Perpendicularity” (page 35) on the other hand is an invention of the author, because no amount of searching textbooks, encyclopedias and general works on astronomy has shown a mention of any such theory in relation to astronomy. He then reckons geocentric (or diurnal) parallax theory says the line from the centre of the Earth to a star is absolutely parallel to the line of sight from an observer on the Earth to the same star (page 36). It does not: –
geocentric parallax: the difference in the apparent direction or position of a celestial body as observed from the centre of the earth and from a point on the surface of the earth (MerriamWebster dictionary)
The author maintains the imaginary “theory of perpendicularity” together with geocentric parallax (which he misunderstands) mean a parallax measurement is impossible, but if a measurement is possible then the theories must be wrong. Since one of these theories is the author’s invention his argument is groundless. He would also be wrong in supposing Bessel measured an angle between 61 Cygni and one other star: he actually measured between the Flying Star and six others.
The author then introduces an extraordinary argument in terms of sidereal time, apparently unaware that we have kept time by the heavens for hundreds of years. He thinks that if an astronomer waited until the exact moment Earth is at the opposite side of its orbit from a previous observation of parallax, then the line of sight will be exactly parallel to that of the previous observation and no parallax measurement will be possible (page 37). He is still thinking in terms of surveyors measuring horizontal angles, not astronomers observing a star actually changing position against the background stars and his argument is lost in theoretical confusion.
Although difficult to measure, astronomers contemporary with Hickson were already calculating stellar parallax by making photographic records to more easily measure it: the number of stars measured would shortly reach a couple of thousand. When the theories don’t fit the facts, it’s time to check the author actually understands the theories.
Unbelievably, Hickson now states, “my case is now really won…” and goes on to claim this silly theoretical puffery means Earth does not in fact orbit anything. Since his arguments have been found to be groundless, we can ignore this too.
https://en.wikipedia.org/wiki/61_Cygni#Parallax_measurement (https://en.wikipedia.org/wiki/61_Cygni#Parallax_measurement)

Chapter 8
After revisiting refraction – and showing no more understanding of it than in chapter 5 – the author fully considers diurnal parallax, as used to measure the distance to Mars in 1877 and thence calculate the parallax of the Sun.
The author seems to think Gill the astronomer only measured angles from Mars to a star in the evening and morning on Ascension Island and thereby calculated his result. The author repeats his confused contention that no angle could be measured because of his muddled ideas about astronomical theory. He is again mistaken in a number of important ways.
Back in chapter 4, Hickson made the important point, repeated here, that in the time between evening and morning observations, Earth is presumed to be moving through space in its orbit, as is Mars, so angles from a presumed baseline are changing in that time. He illustrates this with diagram 20 (page 46) showing his presumed scenario: –
(https://i.imgur.com/k0Muj5U.jpg)
Notice how Mars (M) has moved further in its orbit than Earth, in accordance with Hickson’s argument, but he previously illustrated this same problem with diagram 6 (page 20): –
(https://i.imgur.com/uqCPGyu.jpg?1)
Which scenario does the author mean us to use? Is Mars moving across the sky faster or slower than Earth? They can’t both be right. This poses serious problems for his argument.
However, the author seems to have settled diagram 20 in his mind, because he goes on to explain why he thinks that scenario, with Mars moving further across the sky in a night than Earth, is correct, because Mars moves east across the sky in its orbit anyway, according to Mr Hickson. Here he displays his ignorance to the world.
The casual stargazer will notice planets like Mars generally drift east in the sky from night to night, but the observant stargazer will eventually notice the planets change this direction and drift west for a while: this is known as retrograde motion. This has fascinated astronomers for millennia: all the astronomers from the ancient Babylonians to the present day know about retrograde motion and Ptolemy’s epicycles were introduced to account for it. In the course of an orbit, Jupiter and Saturn will show retrograde motion several times and Mars only once, but this happens when Earth is closest to the planet in question.
Gill made his measurements when Mars was at opposition, which is when Earth is closest to Mars, which is also when Mars is seen in retrograde motion. Had the author bothered to check Gill’s detailed reports to the Royal Astronomical Society he would have discovered this and saved himself a great deal of embarrassment.
Gill includes a chart of Mars’s position in the sky during his observations. I say observations because Gill spent months at Mars Bay, Ascension, observing and recording the planet’s position. The observations detailed start on July 31 and the last is in early October: –
(https://i.imgur.com/PZ7tEWz.jpg)
There are more than two dozen stars in that chart, used over the two months plus to measure the position of Mars in the sky, not the angle of Mars from a baseline on the ground. So many are used because, as the author says, Mars is in motion during the period of observations, but while he thinks this makes the diurnal parallax method invalid, the astronomer is actually gathering data on Mars’s orbital movement so as to separate the diurnal parallax from the orbital movement. This is standard practice in parallax measurements.
From the chart, you can clearly see Mars entering retrograde motion in early August. The scale of Right Ascension along the top and Declination on the right edge clearly show the chart top is North and right is West. When Gill made his last observation in October, Mars was about to end its retrograde motion and return to the more usual eastward drift until its next opposition, about two years later.
Gill’s report shows that the author is wrong to maintain no angles can be measured, wrong to complain the motion of Mars makes parallax measurements impossible and utterly wrong in his understanding of planetary motion. Far from “exploded” (page 44), the “theory of parallactic angles” is vindicated.
And the author’s cheap (and unsubstantiated) crack about there being only 7½ hours between the evening and morning observations also overlooks practical reality: there are less than 10 hours of full darkness for observations at Ascension in August, September and October, so if Mars rises later than the sun sets, there will be less than 10 hours available for two full sets of observations before the next day.
https://academic.oup.com/mnras/article/39/2/98/1018889 (https://academic.oup.com/mnras/article/39/2/98/1018889)

Chapter 9
We return to the transits of Venus across the sun’s face, this time in 1874 and 1882. As the author says, 1874 was not a great success, in some cases because observers were clouded out. He then claims that of the many measurements in 1882, only two were deemed especially fit for purpose: those from Bermuda and from Sabrina Land.
The observations made from Bermuda by astronomer John Isaac Plummer are easily found, but Sabrina Land? This is a section of the Antarctic coast almost due south of Perth, Western Australia, and the author dismisses the site as being unable to see the 1882 transit properly. That may be, but where are these observations supposedly from Sabrina Land? Who made them? They are not to be found.
The reason none are to be found is because they never happened: Sir George Airey apparently advocated sending an expedition to Antarctica but dropped the idea before plans for expeditions were finalised: Proctor relates this in Old and New Astronomy p262 and following. Hickson’s shoddy case collapses.
The author spends the rest of the chapter recapping the methods and results he vainly hopes he has debunked, but he has no more proved his case than when he started, nor has he even explained how Hipparchus et al were mistaken about the stars. There remains only his proposition for a “new” astronomy – can he finally redeem himself with a solid alternative to the astronomers’ methods and theories?

Chapter 10 – THE BIRTH OF A NEW ASTRONOMY
“It is for me, now, to show how the distance to the sun is really to be ascertained, and this may indicate the way to a new astronomy, and a saner conception of the universe.” (page 57)
With this introduction, the author outlines his “remarkable discovery” of 1907, mentioned in the preface.
“Let two observers be placed on the same meridian; A in the northern hemisphere at about Mansfield, Nova Scotia, for example, 60 N, 74 W., and B in the southern hemisphere at Tierra del Fuego, Cape Horn, 55 S. 74 W., as shown in diagram 23. As the two observers are on the same meridian, they use the same north and south, while all lines which cross that meridian at right angles indicate east and west, and are parallel to each other; so that A's east is parallel to B's, and to the equator, as in diagram 24. The chord that is a straight line connecting the two points of observation A, B, will give them a baseline 6,900 miles in length, which runs in a direction due north and south…
(https://i.imgur.com/O7iHtvX.jpg)
…Now let our observers take their places at about 8 o'clock local time (1 p.m. Greenwich Mean Time) on a morning within a week or so of Christmas … The observer at A in Nova Scotia will see the sun, blood red, just rising above the horizon to his eastsoutheast, while the observer at Tierra del Fuego will see the sun at the same time, about eight degrees to the northward of his east (east by north) ; and so the two lines of sight from A and B converge so as to meet at the sun, which is between the two easts, a little to the southward of A and to the northward of B.”
Let’s imagine following the author’s prescription and see what might happen. As above, we’ll send observer A to 60°N, 74°W for 18th December 2021 and at the same time send observer B to 55°S, 74°W. Each observer has modern communications and the necessary instruments to measure the direction to the rising sun. At 1pm GMT, we call A for his measurements: it is difficult to hear what he’s saying since his teeth are chattering uncontrollably, but the sun hasn’t risen yet – it won’t rise for another hour. B is difficult to reach, but we eventually get through and hear that his equipment is lost in the ocean and he has been swimming since arriving at 55°S, 74°W: he’s nearly 70 miles offshore in the Southern Ocean and over 250 miles westward from Cape Horn.
(https://i.imgur.com/EzKmLUe.jpg)
(https://i.imgur.com/Ea3T3Mg.jpg)
Trying again the following day (19th December), A (‘Cold feet’ on the map) reports he was rescued from hypothermia by a passing Inuit, who lent him warmer clothing. Mansfield, Nova Scotia is in fact over a thousand miles away; he is instead in Nunavik, northern Quebec, about midway between Puvirnituq and Kangirsuk and the temperature is minus 30°C. Sunrise is at 14:07 GMT and the sun rises at bearing 142°. Our reequipped B (‘Wet feet’ on the map) is much more comfortable on the big life–raft and reports the Sun at 61° at the same time, but remarks that sunrise was about 8:20 GMT, almost six hours ago – the sun is now 46° above the horizon.
(https://i.imgur.com/H7H9FZC.jpg)
This is a shambles. Not only does the author not know where Mansfield, Nova Scotia or Cape Horn are, he has forgotten the day is much longer for southern latitudes in December than for northern latitudes. His planned scenario of noting the bearing of the rising sun from two widely–separated locations at the same time fails because he has confused the solstice with the equinox: the 2021 winter solstice was December 21st – midsummer in the southern latitudes, winter in the northern ones.
So, let’s instead try the same experimental observation at the next vernal equinox, 20th March 2022, when the sun should rise at the same time at both locations, as it should between A and B all along the 74°W meridian. When we call observer A, he reports the sun rising over the Nunavik landscape at 11:04 GMT and observer B reports that sunrise in the Southern Ocean is at the same time. What is the sun’s bearing? A reports just a tiny bit over 90° and B reckons just a fraction less than 90°. The lines of sight will definitely converge, but at a very large distance indeed and many, many times more than Hickson’s claimed 13,000 miles.
So much for his “remarkable discovery.”

But there is another glaring error in the author’s method: he claims the bearing of the Sun from A and B is all that’s needed, but has forgotten a globe is presumed. The difference in latitude between A and B is 115°, so A and B are 115° different in orientation relative to each other. The two observers’ north and south are in very different directions in 3D space. For all bearings other than directly east or west (which are parallel), finding the angle between bearings is not simple arithmetic. His claim that the planets and stars will be found to be no more than 20,000 miles away (page 59) is spectacularly wrong.
(https://i.imgur.com/V8xP7HG.jpg)
Hickson has only confirmed the findings of the first nine chapters. His “new astronomy” is as unconvincing as his previous incompetence.
Should anyone like to check these bearings for the rising sun, all you need are astronomical tables like Hickson (mis)used, or perhaps the stargazing program Stellarium, which incorporates them.

Chapter 11
The author, like some of his contemporaries, tries to pick apart the Michelson–Morley experiment findings, but the existence of the Aether has been argued over in these fora at least as often as gravity and Hickson has nothing new to add, least of all an explanation of what the Aether might be. We’ll leave that there, as he has nothing else worth saying in the chapter.
Chapters 12 & 13
Hickson now turns his attention to Einsteinian relativity and holds forth for two chapters on his opinion of it. This is both tedious and ignorant, but if he argued about frames of reference in these fora, using the street vs wagon example on page 65, the regular members would make mincemeat of his lack of understanding.
https://forum.tfes.org/index.php?topic=10576.20 (https://forum.tfes.org/index.php?topic=10576.20)
https://forum.tfes.org/index.php?topic=10576.0 (https://forum.tfes.org/index.php?topic=10576.0)
Hickson’s opinion of the nature of light is similarly laughable: –
“…we find that Light is not a material thing, that it is not subject to gravitation, that it has no weight and does not bend, and that it does not describe any kind of curve; but that it is "an expression," in the same sense as sound is an expression, and that as such its velocity varies according to the density of the medium through which it passes; and that therefore the Velocity of Light is not constant, and Einstein's Second [sic] Law is entirely wrong!” (page 73)
Einstein’s law is about the constant speed of light regardless of the speed of its source, not its speed through different things like water, etc. The author is shouting at the wrong bus driver.

Chapter 14
The author sets out three tests of Einstein’s theories (page 79): –
“1. That certain irregularities in the movements of the planet Mercury would be accounted for by Einstein's geometry.
2. That because light has weight it would bend by gravitation as it passed near another body on its way to the earth, and that this could be verified by observations taken at the time of a solar eclipse.
3. That certain lines in the spectrum would be found to shift.
The author dismisses test no.1 by quoting a newspaper article: – “The "proof" he adduces from the aberration of the orbit of Mercury can be disposed of in a sentence. [Einstein] has made the elementary blunder of regarding Mercury as globular instead of spheroidal.” (page 80) This is gibberish: as an explanation it explains nothing.
Test no.2 was proved by the eclipse observations from 1919 referred to in the book and further supported by observations of the 1922 eclipse by Dodwell and Davidson (too late for Hickson’s book).
https://academic.oup.com/mnras/article/84/3/150/1014643?login=true (https://academic.oup.com/mnras/article/84/3/150/1014643?login=true)
The author however believes the results are the exact opposite of what Einstein’s theory predicted.: “…if light was matter, and was affected by the gravitation of the sun, the stars would be seen nearer to the sun; and not as stated by the lecturer and illustrated on the slide. ... If Einstein's theories had been right the stars would be seen nearer to the sun than the crosses, but the Astronomer Royal demonstrated the fact that they were actually further away!” (page 83)
Practical astronomers need some knowledge of optics in the course of their work, for example, the refracting effect of a convex lens on light passing through it. From viewing the object through a convex lens, in other words through a magnifying glass, the original object is seen as covering a larger area than it really does.
(https://i.imgur.com/iloPpFT.jpg)
The effect of light passing the Sun is predicted by Einstein to be similar, where instead of light passing through a lens and being refracted, the light is instead bent by gravitational effect: –
(https://i.imgur.com/qvRMj6J.jpg)
The stars are seen over a larger area than previously, so they are seen farther from the sun than would be expected without the effect. This is what Eddington (1919 eclipse) and Dodwell and Davidson (1922 eclipse) reported.
So, despite the author’s confidence, he is wrong again. It might also be noted that light has no mass, but it does have momentum, as proved by the photoelectric effect, which is why general relativity predicted light being affected by gravity. The person who developed the theoretical explanation of the photoelectric effect was a German physicist – Albert Einstein. It won him a Nobel Prize.
https://en.wikipedia.org/wiki/Photoelectric_effect (https://en.wikipedia.org/wiki/Photoelectric_effect)
“…Of [3.] it is said by the Authorities of Astronomy that the observations necessary to prove or disprove such a shifting of the lines in the spectrum would be so extremely difficult that it is practically impossible ever to do it, and therefore it is set aside.”
The PoundRebka experiment of 1959 measured the effect described in test no.3 – it was later improved in accuracy by Pound and Snider in 1964 and you can read an FE view of this proof of General Relativity in the wiki. Hickson is very unlikely to have lived to see this evidence, but evidence it is.

Chapter 15
This is the last chapter and appears to be about various newspaper reports from Hickson's time and about as credible as sensational articles from Twitter, Facebook or the current popular press. The tone is very like an elderly uncle shaking his morning newspaper in irritation while harrumphing about The State Of The World. We won’t waste time on it.

Conclusion
No kings were dethroned in writing this book. The author has entirely failed to demonstrate how his erroneous opening premise – that beginning with Hipparchus, astronomers believed the stars to be infinitely distant – has ruined modern astronomy. He has demonstrated extremely poor understanding and almost no practical knowledge of his subject as well as hopelessly muddled theoretical misunderstandings. His proposed method of measuring the distance from Earth to the Sun, Moon, planets and stars is wretchedly incompetent and his resulting claim for the Sun’s true distance from Earth is not even in the wrong ballpark – it's in the wrong continent. His book changes nothing of, and adds nothing to our understanding of the cosmos.
Rather wonder why he bothered.

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/Whatisopenspaceinouterspace
(https://i.imgur.com/JfGQ1in.png)
He also assumed that the Sun was infinitely distant:
https://sunearthday.nasa.gov/2009eclipse/amateur.php  "Hipparchus assumed that the sun was at an infinite distance."
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
(https://i.imgur.com/vrvx5IM.png)
A reference to the beliefs of the ancient greeks and romans:
Astrology and Religion Among the Greeks and Romans, by Franz Cumont, [1912] 
https://www.sacredtexts.com/astro/argr/argr11.htm
2. This brings us to the second question which we have set before ourselves: How did souls rise to the stars?
"It may be said that originally they made use of every method of locomotion: they ascended to heaven on foot, on horseback, in carriages, and they even had recourse to aviation. Among the ancient Egyptians the firmament was conceived as being so close to the mountains of the earth that it was possible to climb up to it with the aid of a ladder. Although the stars had been relegated to an infinite distance in space, the ladder still survived in Roman paganism as an amulet and as a symbol. Many people continued to place in tombs a small bronze ladder which recalled the naive beliefs of distant ages; and in the mysteries of Mithra a ladder of seven steps, made of seven different metals, still symbolised the passage of the soul across the planetary spheres."

He also assumed that the Sun was infinitely distant:
https://sunearthday.nasa.gov/2009eclipse/amateur.php  "Hipparchus assumed that the sun was at an infinite distance."
Nice cherrypicking, but you left out some context...
"In the first book, Hipparchus assumed that the parallax of the Sun was 0, as if it is at infinite distance."
Notice:
"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)
Aristarchus believed that the stars were infinitely distant too:
As for Aristarchus it's not clear cut that he believed stars were infinitely far away...
"Aristarchus' heliocentric theory, as reported by Archimedes, namely, that not just the earth but the circle in which the earth moves around the sun is as a point in relation to the sphere of the fixed stars (see Figure 2).[82] Archimedes' own comment is that that is, strictly speaking, impossible, since a point has zero magnitude and the fixed stars would then be at infinite distance[83] (a similar point applies, of course, to the first type of parallax case as well). What Aristarchus needs is not that the stars be infinitely, only that they be indefinitely, far away."
https://publishing.cdlib.org/ucpressebooks/view?docId=ft8h4nb53w&chunk.id=d0e17813&toc.depth=1&toc.id=d0e16804&brand=ucpress
More that they are so far away a distance couldn't be determined. "Near infinitely away", "immeasurable distance" is what keeps coming up.

He also assumed that the Sun was infinitely distant:
https://sunearthday.nasa.gov/2009eclipse/amateur.php  "Hipparchus assumed that the sun was at an infinite distance."
Nice cherrypicking, but you left out some context...
"In the first book, Hipparchus assumed that the parallax of the Sun was 0, as if it is at infinite distance."
Notice:
"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)
His beliefs in other parts of his life does not negate his treatment of the Sun as if it was infinitely distant. Most articles about Hipparchus prominently show his treatment of the Sun as infinitely distant and laugh at him for it, and don't even bring up his later work.
Other Greeks argue that an infinitely distant sun was illogical if it moved across the sky and around the earth, or vice versa. This sort of criticism is probably why he came up with a minimum distance in his second book.
If he thought the Sun was infinitely distant it is also difficult to argue that he never thought that the stars were infinitely distant. He clearly did.
As for Aristarchus it's not clear cut that he believed stars were infinitely far away...
"Aristarchus' heliocentric theory, as reported by Archimedes, namely, that not just the earth but the circle in which the earth moves around the sun is as a point in relation to the sphere of the fixed stars (see Figure 2).[82] Archimedes' own comment is that that is, strictly speaking, impossible, since a point has zero magnitude and the fixed stars would then be at infinite distance[83] (a similar point applies, of course, to the first type of parallax case as well). What Aristarchus needs is not that the stars be infinitely, only that they be indefinitely, far away."
https://publishing.cdlib.org/ucpressebooks/view?docId=ft8h4nb53w&chunk.id=d0e17813&toc.depth=1&toc.id=d0e16804&brand=ucpress
More that they are so far away a distance couldn't be determined. "Near infinitely away", "immeasurable distance" is what keeps coming up.
Yes, it could be a synonym for immeasurably large. The point in the Kings Dethroned book is that the Ancient Greeks assumed a very large universe.
Longitude appears to argue that Hipparchus thought the universe ended just past the orbit of Saturn, which is incorrect. Ptolemy believed that. It wasn't Hipparchus' belief, and may not have been the general belief.

He also assumed that the Sun was infinitely distant:
https://sunearthday.nasa.gov/2009eclipse/amateur.php  "Hipparchus assumed that the sun was at an infinite distance."
Nice cherrypicking, but you left out some context...
"In the first book, Hipparchus assumed that the parallax of the Sun was 0, as if it is at infinite distance."
Notice:
"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)
His beliefs in other parts of his life does not negate his treatment of the Sun as if it was infinitely distant. Most articles about Hipparchus prominently show his treatment of the Sun as infinitely distant and laugh at him for it, and don't even bring up his later work.
I'm not saying I don't believe you, but citation requested.
And no, 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)
Other Greeks argue that an infinitely distant sun was illogical if it moved across the sky and around the earth, or vice versa. This sort of criticism is probably why he came up with a minimum distance in his second book.
Speculation much? Citation requested. This sort of criticism led to...You're really trying to read the mind of someone from thousands of years ago?
If he thought the Sun was infinitely distant it is also difficult to argue that he never thought that the stars were infinitely distant. He clearly did.
He did not. As far as the sun goes. As for stars, perhaps. There was no way to measure parallax thousands of years ago to the accuracy required.
As for Aristarchus it's not clear cut that he believed stars were infinitely far away...
"Aristarchus' heliocentric theory, as reported by Archimedes, namely, that not just the earth but the circle in which the earth moves around the sun is as a point in relation to the sphere of the fixed stars (see Figure 2).[82] Archimedes' own comment is that that is, strictly speaking, impossible, since a point has zero magnitude and the fixed stars would then be at infinite distance[83] (a similar point applies, of course, to the first type of parallax case as well). What Aristarchus needs is not that the stars be infinitely, only that they be indefinitely, far away."
https://publishing.cdlib.org/ucpressebooks/view?docId=ft8h4nb53w&chunk.id=d0e17813&toc.depth=1&toc.id=d0e16804&brand=ucpress
More that they are so far away a distance couldn't be determined. "Near infinitely away", "immeasurable distance" is what keeps coming up.
Yes, it could be a synonym for immeasurably large. The point in the Kings Dethroned book is that the Ancient Greeks assumed a very large universe.
Yes, so do we today. The Universe is very large indeed.
Longitude appears to argue that Hipparchus thought the universe ended just past the orbit of Saturn, which is incorrect. Ptolemy believed that. It wasn't Hipparchus' belief, and may not have been the general belief.
I might have missed this, but I'm not seeing where exactly "Longitude appears to argue that Hipparchus thought the universe ended just past the orbit of Saturn"
All I found was, "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)."
Not Hipparchus.
But even if so, so what?

Incorrect, Longitude clearly argues that Hipparchus believed in a small universe like Ptolemy. He states at the end of his second post (https://forum.tfes.org/index.php?topic=19422.msg266530#msg266530): 
" 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.

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/Whatisopenspaceinouterspace
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.

Incorrect, Longitude clearly argues that Hipparchus believed in a small universe like Ptolemy. He states at the end of his second post (https://forum.tfes.org/index.php?topic=19422.msg266530#msg266530): 
" 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.

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.

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.

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.

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 (http://abyss.uoregon.edu/~js/glossary/hipparchus.html)

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."

https://sunearthday.nasa.gov/2009eclipse/amateur.php  "Hipparchus assumed that the sun was at an infinite distance."
Ok. And so what?

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)

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.

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.

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 (https://forum.tfes.org/index.php?topic=19422.msg266530#msg266530)). If you're gonna "so what?" someone repeatedly, at least pick the right target.

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.

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/goldsteinthearabicversionofptolemyx27splanetaryhypotheses2pdffree.html (https://pdfcoffee.com/download/goldsteinthearabicversionofptolemyx27splanetaryhypotheses2pdffree.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.

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 (https://forum.tfes.org/index.php?topic=19422.msg266530#msg266530)). 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.

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.

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.

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/goldsteinthearabicversionofptolemyx27splanetaryhypotheses2pdffree.html (https://pdfcoffee.com/download/goldsteinthearabicversionofptolemyx27splanetaryhypotheses2pdffree.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.

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.

Finite is adjacent to infinite.
Wow. :o You need to consult a dictionary.

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.
Finite is adjacent to infinite.
Wow. :o You need to consult a dictionary.
Yeah, you can measure something, and then?
You cannot.
They are adjacent.

They are adjacent.
You keep using that word. I do not think it means what you think it means.
They're opposites.

Yeah, you can measure something, and then?
You cannot.
They are adjacent.
Can you provide a single reference for this?

They are adjacent.
You keep using that word. I do not think it means what you think it means.
They're opposites.
Adjacent most certainly does not mean "opposites."
It means next to each other.
Yeah, you can measure something, and then?
You cannot.
They are adjacent.
Can you provide a single reference for this?
Yes.
The reference is this.
There is a point in time when things are no longer able to be measured.
It is then you label that point as infinite.

There is a point in time when things are no longer able to be measured.
It is then you label that point as infinite.
Why would you no longer be able to measure something? Do you eventually run out of numbers?

Adjacent most certainly does not mean "opposites."
It means next to each other.
Correct.
Adjacent means “next to each other”.
But finite and infinite are not next to each other, they are opposites. Hence the prefix “in”, which means “not”. See?

There is a point in time when things are no longer able to be measured.
It is then you label that point as infinite.
Why would you no longer be able to measure something? Do you eventually run out of numbers?
You believe all things are measurable, evidently?

Adjacent most certainly does not mean "opposites."
It means next to each other.
Correct.
Adjacent means “next to each other”.
But finite and infinite are not next to each other, they are opposites. Hence the prefix “in”, which means “not”. See?
So, you want to engage in the process proposed by Copernicus.
Well, I understand the need for some to hold fast to the idea that nothing could possibly be immeasurable.

Adjacent most certainly does not mean "opposites."
It means next to each other.
Correct.
Adjacent means “next to each other”.
But finite and infinite are not next to each other, they are opposites. Hence the prefix “in”, which means “not”. See?
So, you want to engage in the process proposed by Copernicus.
Well, I understand the need for some to hold fast to the idea that nothing could possibly be immeasurable.
Talk about marching out the straw men.
So, you made the bold (and quite ridiculous) claim that finite is adjacent to infinite. Instead of the strawman, can you provide us with the mathematical proof of this? Or even a mathematical discussion around it other than you just saying it's so? There must be one around and you must have seen it in order to make your claim. I (and others here) would love to see it.

There is a point in time when things are no longer able to be measured.
It is then you label that point as infinite.
Why would you no longer be able to measure something? Do you eventually run out of numbers?
You believe all things are measurable, evidently?
Not sure where you got that impression. I'm just asking, at what point does something become too big (or small) to measure? Even then, "too big to measure" and "infinite" are not necessarily the same thing.

There is a point in time when things are no longer able to be measured.
It is then you label that point as infinite.
No there isn't. There isn't a point.
Numbers don't just run out. It doesn't go 1  2  3 .... 999,999  1,000,000 ... oh we've run out of numbers...infinity!
Infinity is a concept. Infinity  1 is still infinity. Infinity divided by 2 is still infinity. There are as many even numbers as there are numbers.
Infinity is counterintuitive and there is no "point" at which the finite becomes infinite.
Infinite simply means "not finite". Y'know, like incompetent or incapable...

There is a point in time when things are no longer able to be measured.
It is then you label that point as infinite.
No there isn't. There isn't a point.
Numbers don't just run out. It doesn't go 1  2  3 .... 999,999  1,000,000 ... oh we've run out of numbers...infinity!
Yeah..you are just flat out wrong.
Worse yet, you know what you are writing is wrong and wrote it anyway.
Infinity is a concept.
It is certainly more than a concept.
A purely vertical line has infinite slope. Any vertical line can be found adjacent to multitudes of other lines of various slope anywhere. anyplace, or anytime.
It really would be best for you to stop posting in threads having anything to do with math.

A purely vertical line has infinite slope.
Incorrect. It's undefined.
https://tutorme.com/blog/post/whatistheslopeofaverticalline/
Because you can't divide by 0.

Numbers don't just run out. It doesn't go 1  2  3 .... 999,999  1,000,000 ... oh we've run out of numbers...infinity!
Yeah..you are just flat out wrong.
Ahhh.. that would be you.
No matter which number set you use  the natural, whole, integer, rational, real and complex number sets are all closed under addition. That means AATW is right, you are wrong.
That also means you can take any number you like in any of those sets, and add any other number you like and the answer will still be a finite number in that set. That also means there is no point where it becomes infinity.
Why are you arguing this position? This is grade 9 or 10 math. Go look it up or provide a proof for your assertion.
It really would be best for you to stop posting in threads having anything to do with math.
Fucking priceless!!!!!

A purely vertical line has infinite slope.
Incorrect. It's undefined.
https://tutorme.com/blog/post/whatistheslopeofaverticalline/
Because you can't divide by 0.
Infinity is "undefined." And the symbol given is: ∞
Infinity.

Infinity is "undefined." And the symbol given is: ∞
Infinity.
Infinity may have no set value, but it is defined:https://www.britannica.com/science/infinitymathematics (https://www.britannica.com/science/infinitymathematics)

Infinity is "undefined." And the symbol given is: ∞
Infinity.
Infinity may have no set value, but it is defined:https://www.britannica.com/science/infinitymathematics (https://www.britannica.com/science/infinitymathematics)
"Mathematical infinities
The ancient Greeks expressed infinity by the word apeiron, which had connotations of being unbounded, indefinite, undefined, and formless."

The ancient Greeks expressed infinity by the word apeiron, which had connotations of being unbounded, indefinite, undefined, and formless."
The ancient Greeks, eh? Nice cherry. You should have read a bit further. I think you'd have found mathematics has come a long way since then. Like I said, infinity is well defined, but not as a value. We (us that know some math anyway) know exactly what is meant by infinity. Where is the proof the finite is adjacent to infinite? Still waiting...
BTW, here is proof that the sum of two real numbers (no matter what they are) is a real number (the set of real numbers is closed under addition). :https://proofwiki.org/wiki/Real_Addition_is_Closed (https://proofwiki.org/wiki/Real_Addition_is_Closed) So good luck finding a disproof.

The ancient Greeks expressed infinity by the word apeiron, which had connotations of being unbounded, indefinite, undefined, and formless."
The ancient Greeks, eh? Nice cherry. You should have read a bit further. I think you'd have found mathematics has come a long way since then. Like I said, infinity is well defined, but not as a value. We (us that know some math anyway) know exactly what is meant by infinity. Where is the proof the finite is adjacent to infinite? Still waiting...
BTW, here is proof that the sum of two real numbers (no matter what they are) is a real number (the set of real numbers is closed under addition). :https://proofwiki.org/wiki/Real_Addition_is_Closed (https://proofwiki.org/wiki/Real_Addition_is_Closed) So good luck finding a disproof.
Nice cherry?
It was quoted directly from your own source.
Funny your source offers absolutely nothing in regard to counter that infinity is, in fact, undefined.
As for your real numbers...
Irrelevant to the discussion.
Toodle pip.

The ancient Greeks expressed infinity by the word apeiron, which had connotations of being unbounded, indefinite, undefined, and formless."
The ancient Greeks, eh? Nice cherry. You should have read a bit further. I think you'd have found mathematics has come a long way since then. Like I said, infinity is well defined, but not as a value. We (us that know some math anyway) know exactly what is meant by infinity. Where is the proof the finite is adjacent to infinite? Still waiting...
BTW, here is proof that the sum of two real numbers (no matter what they are) is a real number (the set of real numbers is closed under addition). :https://proofwiki.org/wiki/Real_Addition_is_Closed (https://proofwiki.org/wiki/Real_Addition_is_Closed) So good luck finding a disproof.
Nice cherry?
It was quoted directly from your own source.
Funny your source offers absolutely nothing in regard to counter that infinity is, in fact, undefined.
As for your real numbers...
Irrelevant to the discussion.
Toodle pip.
Yeah, they are 100% relevant, you are just not able to understand that.
Sad.
I'll leave you to your strange universe. I've tried as hard as I want to on this. I've given you everything you need. Maybe go back to school?
Until next time..

Any vertical line can be found adjacent to multitudes of other lines of various slope anywhere. anyplace, or anytime.
Are you referring to the asymptote (https://en.wikipedia.org/wiki/Asymptote)? Apparently you don't seem to understand that there are an infinite number of numbers between 89 and 90 degrees.
It really would be best for you to stop posting in threads having anything to do with math.
You may want to consider taking your own advice.

The ancient Greeks expressed infinity by the word apeiron, which had connotations of being unbounded, indefinite, undefined, and formless."
The ancient Greeks, eh? Nice cherry. You should have read a bit further. I think you'd have found mathematics has come a long way since then. Like I said, infinity is well defined, but not as a value. We (us that know some math anyway) know exactly what is meant by infinity. Where is the proof the finite is adjacent to infinite? Still waiting...
BTW, here is proof that the sum of two real numbers (no matter what they are) is a real number (the set of real numbers is closed under addition). :https://proofwiki.org/wiki/Real_Addition_is_Closed (https://proofwiki.org/wiki/Real_Addition_is_Closed) So good luck finding a disproof.
Nice cherry?
It was quoted directly from your own source.
Funny your source offers absolutely nothing in regard to counter that infinity is, in fact, undefined.
As for your real numbers...
Irrelevant to the discussion.
Toodle pip.
Yeah, they are 100% relevant, you are just not able to understand that.
Sad.
I'll leave you to your strange universe. I've tried as hard as I want to on this. I've given you everything you need. Maybe go back to school?
Until next time..
Yes.
Until next time, when I expose your constant gaslighting and irrelevant commentary, as usual.

The ancient Greeks expressed infinity by the word apeiron, which had connotations of being unbounded, indefinite, undefined, and formless."
The ancient Greeks, eh? Nice cherry. You should have read a bit further. I think you'd have found mathematics has come a long way since then. Like I said, infinity is well defined, but not as a value. We (us that know some math anyway) know exactly what is meant by infinity. Where is the proof the finite is adjacent to infinite? Still waiting...
BTW, here is proof that the sum of two real numbers (no matter what they are) is a real number (the set of real numbers is closed under addition). :https://proofwiki.org/wiki/Real_Addition_is_Closed (https://proofwiki.org/wiki/Real_Addition_is_Closed) So good luck finding a disproof.
Nice cherry?
It was quoted directly from your own source.
Funny your source offers absolutely nothing in regard to counter that infinity is, in fact, undefined.
As for your real numbers...
Irrelevant to the discussion.
Toodle pip.
Yeah, they are 100% relevant, you are just not able to understand that.
Sad.
I'll leave you to your strange universe. I've tried as hard as I want to on this. I've given you everything you need. Maybe go back to school?
Until next time..
Yes.
Until next time, when I expose your constant gaslighting and irrelevant commentary, as usual.
Gaslighting??!! Okay, so now I understand.
Peace dude. Be happy.

Yeah, that's an Action 80 (Lackey) thing  Just rants and never provides any evidence to back up his rants. Comes with the territory. Definitely gives FE a bad rap.
I mean seriously, just because something is currently (or in the past) unmeasurable doesn't defacto mean that the unmeasurable thing is (was) infinite. That's just daft. It just means we didn't know how to and/or lacked the proper gear to measure it.
And to trot out an ancient greek term like it blanket applies to current weights and measures tech is equally daft. I mean the last time I checked it's 2022, not 7th century BC.

Definitely gives FE a bad rap.
Imagine how bad RE's "rap" would be if we were as intellectually dishonest as you are and judged a group by its worst representatives.

Yeah, that's an Action 80 (Lackey) thing  Just rants and never provides any evidence to back up his rants. Comes with the territory. Definitely gives FE a bad rap.
I mean seriously, just because something is currently (or in the past) unmeasurable doesn't defacto mean that the unmeasurable thing is (was) infinite. That's just daft. It just means we didn't know how to and/or lacked the proper gear to measure it.
And to trot out an ancient greek term like it blanket applies to current weights and measures tech is equally daft. I mean the last time I checked it's 2022, not 7th century BC.
Hey, if you can trot out anything that states infinity is not undefined or has otherwise negated what the Greeks had to say about it being undefined, by all means, go ahead.
But I already see you don't, as you admit anything that cannot be measured remains undefined, or infinite.

Hey, if you can trot out anything that states infinity is not undefined or has otherwise negated what the Greeks had to say about it being undefined, by all means, go ahead.
Sure.
Wikipedia has it right and goes into interpretations of it in some detail: https://en.wikipedia.org/wiki/Infinity (https://en.wikipedia.org/wiki/Infinity)
Infinity is that which is boundless, endless, or larger than any natural number.
Every dictionary on the web states the same thing in as many ways as you might fancy.
https://www.mathsisfun.com/definitions/infinite.html (https://www.mathsisfun.com/definitions/infinite.html)
https://www.merriamwebster.com/dictionary/infinite (https://www.merriamwebster.com/dictionary/infinite)
https://dictionary.cambridge.org/dictionary/english/infinite (https://dictionary.cambridge.org/dictionary/english/infinite)
https://www.lexico.com/definition/infinite (https://www.lexico.com/definition/infinite)
I could go on...
Here are 59 synonyms for "infinite". You'll notice that none of them are "undefined": https://www.thesaurus.com/browse/infinite (https://www.thesaurus.com/browse/infinite)
Maybe a short video on the matter?

Hey, if you can trot out anything that states infinity is not undefined or has otherwise negated what the Greeks had to say about it being undefined, by all means, go ahead.
Sure.
Wikipedia has it right and goes into interpretations of it in some detail: https://en.wikipedia.org/wiki/Infinity (https://en.wikipedia.org/wiki/Infinity)
Infinity is that which is boundless, endless, or larger than any natural number.
Every dictionary on the web states the same thing in as many ways as you might fancy.
https://www.mathsisfun.com/definitions/infinite.html (https://www.mathsisfun.com/definitions/infinite.html)
https://www.merriamwebster.com/dictionary/infinite (https://www.merriamwebster.com/dictionary/infinite)
https://dictionary.cambridge.org/dictionary/english/infinite (https://dictionary.cambridge.org/dictionary/english/infinite)
https://www.lexico.com/definition/infinite (https://www.lexico.com/definition/infinite)
I could go on...
Here are 59 synonyms for "infinite". You'll notice that none of them are "undefined": https://www.thesaurus.com/browse/infinite (https://www.thesaurus.com/browse/infinite)
Maybe a short video on the matter?
The lack of the word "undefined," in your examples in that it offers nothing contrary to what I have written.

Hey, if you can trot out anything that states infinity is not undefined or has otherwise negated what the Greeks had to say about it being undefined, by all means, go ahead.
*sigh*
What is the difference between Infinity and Undefined?
• Undefined means, it is impossible to solve.
• Infinity means, it is without bound.

The lack of the word "undefined," in your examples in that it offers nothing contrary to what I have written.
They were definitions of infinite/infinity. That might explain why the word "undefined" did not get mentioned.

Hey, if you can trot out anything that states infinity is not undefined or has otherwise negated what the Greeks had to say about it being undefined, by all means, go ahead.
*sigh*
What is the difference between Infinity and Undefined?
• Undefined means, it is impossible to solve.
• Infinity means, it is without bound.
"The value of infinity is also undefined."

"The value of infinity is also undefined."
Correct. Just like pigeon or scourge, infinity is not a value. So, one more time, the definition of infinity is: Infinity is that which is boundless, endless, or larger than any natural number.

Definitely gives FE a bad rap.
Imagine how bad RE's "rap" would be if we were as intellectually dishonest as you are and judged a group by its worst representatives.
I imagine it would be pretty bad if that were the case. Fortunately, I'm not intellectually dishonest. But thanks for backing me up and agreeing that I was right about who is one of the worst representatives of FE.

I imagine it would be pretty bad if that were the case.
Indeed. Will that perhaps trigger a little bit of selfreflection for the future?
Fortunately, I'm not intellectually dishonest.
That remains to be seen. The question above could be a good start. Unfortunately, the statement below is a terrible start.
But thanks for backing me up and agreeing that I was right about who is one of the worst representatives of FE.
I didn't back you up on anything. More intellectual dishonesty, I guess it's a habit.
To clarify: it is you who thinks Action80 is a representative of FE at all. I make no judgement on the matter, but I think it's extremely poor of you to take one member of a group (as per your perception) and decide that the whole group should be judged by their behaviour.
Do better. Be better. Introspect.

I imagine it would be pretty bad if that were the case.
Indeed. Will that perhaps trigger a little bit of selfreflection for the future?
Sure, if it's a valid perspective from a respected individual it would trigger selfreflection.
Do better. Be better. Introspect.
Words everyone should abide by including yourself.

Sure, if it's a valid perspective from a respected individual it would trigger selfreflection.
I see. So, even though you've immediately conceded my perspective, you will not reflect on it, because of the individual who made you aware of it  me.
That's terrible. You've definitely cemented yourself as intellectually dishonest.

Sure, if it's a valid perspective from a respected individual it would trigger selfreflection.
I see. So, even though you've immediately conceded my perspective, you will not reflect on it, because of the individual who made you aware of it  me.
That's terrible. You've definitely cemented yourself as intellectually dishonest.
It's not conceding "your" perspective. I was previously aware of the existence and benefits of selfreflection before you mentioned it. I'm pretty sure you didn't come up with the concept. And like I wrote, a valid perspective from a respected individual would trigger selfreflection. You missed the bit about a "valid perspective". It's not just about the respectability of the individual who delivered the perspective.

You missed the bit about a "valid perspective".
I didn't miss it at all  in fact, I addressed it directly. Did you misread, or are you just really driving the point that you don't have an ounce of honesty in you home?
I was previously aware of the existence and benefits of selfreflection before you mentioned it. I'm pretty sure you didn't come up with the concept.
What on Earth does this have to do with anything? Have you already forgotten what you're being chastised for? Impressive!

You missed the bit about a "valid perspective".
I didn't miss it at all  in fact, I addressed it directly. Did you misread, or are you just really driving the point that you don't have an ounce of honesty in you home?
It’s unclear what my dwelling has to do with anything.
I was previously aware of the existence and benefits of selfreflection before you mentioned it. I'm pretty sure you didn't come up with the concept.
What on Earth does this have to do with anything? Have you already forgotten what you're being chastised for? Impressive!
I guess I wrongfully assumed you were simply offering your brand of what you perceive to be sage advice. And advice is usually welcomed when delivered from a valid perspective and by a respected voice.
So yes, self reflection is a good thing for everyone. I think most would agree and are probably aware of the concept prior to you feeling compelled to introduce it here.

self reflection is a good thing for everyone. I think most would agree and are probably aware of the concept prior to you feeling compelled to introduce it here.
Feel free to start a thread on the process when you have a bit of time. Perhaps it may be a topic for you that allows for some personal growth.

"The value of infinity is also undefined."
Correct. Just like pigeon or scourge, infinity is not a value. So, one more time, the definition of infinity is: Infinity is that which is boundless, endless, or larger than any natural number.
Well, pigeon is singular.
One is defined.
Scourge is also singular.
One is defined.
Infinity, being boundless, remains undefined.

Infinity, being boundless, remains undefined.
Infinity is defined as boundless.
Regardless, being boundless means that there is no boundary between infinite and finite.

This thing, being thusly defined, remains undefined.
Selfawareness issues?
Infinity is singular. No sure WTF that has to do with anything. It's not a value, never was and was never meant to be. You seem awfully confused.

It’s unclear what my dwelling has to do with anything.
Right. Now that you've confirmed you're trolling, let me make one thing clear: If you're not ready to be sincere in the upper fora, please be ready not to be in the upper fora at all. If you do not make the decision by yourself, one will be made for you.
Have a splendiferous day!