Haven't slept for more than two hours in last few days

Maia · August 16, 2016, 7:49pm

Turd Ferguson:

That’s great. How well does this work in calculating yields of grain for taxation?

Yeah… that’s the original issue with π, back in Egyptian times. You can get away with rope techniques when the yield is low, but that can be deceiving when it is large, and your assigning bushels to long term storage for famine (Joshep and the coat of many colors) as well as paying wages to administrators, and setting a grain to gold and silver exchange rate for trade.

The rope has to be exactlingly regulated, and farmers get clever after a while and learn how to make it seem more or less, as well as the tax collectors.

If your building with monolithic stone slabs, not hard. If your building something like the pantheon’s dome roof, harder.

I’ve had a nightmare just trying to get a radius establish, the Pythagorean Table of Opposites run amok when I try to do it. I don’t think we’ve really proven π is irrational if we haven’t fully explained the varient calculations that result form different kinds of diameters possible. I’m not as accepting of Zenodorus’ definition of a circle anymore.

I doubt they had taxation in that way in Neolithic Britain. They did, however, have a very sophisticated knowledge of subjects such as astronomy.

MagsJ · August 16, 2016, 8:33pm

Did you now?

You crack me up Iam… you really do.

The_Golden_Turd · August 16, 2016, 9:37pm

I wouldn’t call the small underground observatories scattered around the isles a sophisticated knowledge.

(Thunder woke me up, can’t sleep)

I can’t recall what they are called, but the little Neolithic to Bronze Age short tunnels… they figured out if you sat in one, a tunneling effect with light would occur, allowing you to see more light, and therefore increased magnification of one spot.

Great for timing a exact approach of one star to a fixed observational point, but I wouldn’t call that advanced astronomy.

I will give you a basic example of what advanced astronomy looked like.

The earliest Assyrian and Babylonian philosophers were astronomers (I will explain the terminology later, I simply can’t recall it, starts with an I)… they would lay on their backs, with straight plains of wood above them, and would just watch the stars pass.

They had small round clay tablets, a line on the stick above represented a line on the tablet, and they would simply transcribe the movement of the stars to this, looking at the distance of the stars on the edge of the stick above.

This allowed them to create remarkably accurate starmaps, in clay, some which we still have. They even did pretty advance work calculating and explaining the trajectory of planetary movement, which us hard as hell to express mathematically, I have a thread on this site somewhere on both the philosophers being philosophers, as well as how they observed the stars somewhere on the sight.

Iapetas? Iapetus? Ah… both words probably jibberish popping in my head. They sell pretty decent fascimilies of they star maps.

Germans had something far more rudimentry, small disks with a few stars on them.

members.westnet.com.au/gary-davi … e11-9.html

Ohhh… just found this quote I made from wiki in a unfinished Diocles thread I was making, not finished for reasons I don’t know why, deals with our topic:

Latitude by the altitude of the sun Edit
In discussing the work of Pytheas, Strabo typically uses direct discourse: “Pytheas says …” In presenting his astronomical observations, he changes to indirect discourse: “Hipparchus says that Pytheas says …” either because he never read Pytheas’ manuscript (because it was not available to him) or in deference to Hipparchus, who appears to have been the first to apply the Babylonian system of representing the sphere of the earth by 360°.[53]

Strabo uses the degrees, based on Hipparchus.[54] Neither say that Pytheas did. Nevertheless, Pytheas did obtain latitudes, which, according to Strabo, he expressed in proportions of the gnōmōn (“index”), or trigonometric tangents of angles of elevation to celestial bodies. They were measured on the gnōmōn, the vertical leg of a right triangle, and the flat leg of the triangle. The imaginary hypotenuse looked along the line of sight to the celestial body or marked the edge of a shadow cast by the vertical leg on the horizontal leg.

Pytheas took the altitude of the sun at Massalia at noon on the longest day of the year and found that the tangent was the proportion of 120 (the length of the gnōmōn) to 1/5 less than 42 (the length of the shadow).[55] Hipparchus, relying on the authority of Pytheas (says Strabo[56]), states that the ratio is the same as for Byzantium and that the two therefore are on the same parallel. Nansen and others prefer to give the cotangent 209/600,[57] which is the inverse of the tangent, but the angle is greater than 45° and it is the tangent that Strabo states. His number system did not permit him to express it as a decimal but the tangent is about 2.87.

It is unlikely that any of the geographers could compute the arctangent, or angle of that tangent. Moderns look it up in a table. Hipparchos is said to have had a table of some angles. The altitude, or angle of elevation, is 70° 47’ 50″[57] but that is not the latitude.

At noon on the longest day the plane of longitude passing through Marseilles is exactly on edge to the sun. If the Earth’s axis were not tilted toward the sun, a vertical rod at the equator would have no shadow. A rod further north would have a north-south shadow, and as an elevation of 90° would be a zero latitude, the complement of the elevation gives the latitude. The sun is even higher in the sky due to the tilt. The angle added to the elevation by the tilt is known as the obliquity of the ecliptic and at that time was 23° 44′ 40″.[57] The complement of the elevation less the obliquity is 43° 13′, only 5′ in error from Marseilles’s latitude, 43° 18′.[58]

Latitude by the elevation of the north pole Edit
A second method of determining the latitude of the observer measures the angle of elevation of a celestial pole, north in the northern hemisphere. Seen from zero latitude the north pole’s elevation is zero; that is, it is a point on the horizon. The declination of the observer’s zenith also is zero and therefore so is his latitude.

As the observer’s latitude increases (he travels north) so does the declination. The pole rises over the horizon by an angle of the same amount. The elevation at the terrestrial North Pole is 90° (straight up) and the celestial pole has a declination of the same value. The latitude also is 90.[59]

Moderns have Polaris to mark the approximate location of the North celestial pole, which it does nearly exactly, but this position of Polaris was not available in Pytheas’ time, due to changes in the positions of the stars. Pytheas reported that the pole was an empty space at the corner of a quadrangle, the other three sides of which were marked by stars.[60] Their identity has not survived but based on calculations these are believed to have been α and κ in Draco and β in Ursa Minor.[61]

Pytheas sailed northward with the intent of locating the Arctic Circle and exploring the “frigid zone” to the north of it at the extreme of the earth. He did not know the latitude of the circle in degrees. All he had to go by was the definition of the frigid zone as the latitudes north of the line where the celestial arctic circle was equal to the celestial Tropic of Cancer, the tropikos kuklos (refer to the next subsection). Strabo’s angular report of this line as being at 24° may well be based on a tangent known to Pytheas, but he does not say that. In whatever mathematical form Pytheas knew the location, he could only have determined when he was there by taking periodic readings of the elevation of the pole (eksarma tou polou in Strabo and others).

Today the elevation can be obtained easily on ship with a quadrant. Electronic navigational systems have made even this simple measure unnecessary. Longitude was beyond Pytheas and his peers, but it was not of as great a consequence, because ships seldom strayed out of sight of land. East-west distance was a matter of contention to the geographers; they are one of Strabo’s most frequent topics. Because of the gnōmōn north-south distances were accurate often to within a degree.

It is unlikely that any gnōmōn could be read accurately on the pitching deck of a small vessel at night. Pytheas must have made frequent overnight stops to use his gnōmōn and talk to the natives, which would have required interpreters, probably acquired along the way. The few fragments that have survived indicate that this material was a significant part of the periplus, possibly kept as the ship’s log. There is little hint of native hostility; the Celts and the Germans appear to have helped him, which suggests that the expedition was put forward as purely scientific. In any case all voyages required stops for food, water and repairs; the treatment of voyagers fell under the special “guest” ethic for visitors.

Location of the Arctic Circle Edit
The ancient Greek view of the heavenly bodies on which their navigation was imported from Babylonia by the Ionian Greeks, who used it to become a seafaring nation of merchants and colonists during the Archaic period in Greece. Massalia was an Ionian colony. The first Ionian philosopher, Thales, was known for his ability to measure the distance of a ship at sea from a cliff by the very method Pytheas used to determine the latitude of Massalia, the trigonometric ratios.

The astronomic model on which ancient Greek navigation was based, which is still in place today, was already extant in the time of Pytheas, the concept of the degrees only being missing. The model[62] divided the universe into a celestial and an earthly sphere pierced by the same poles. Each of the spheres were divided into zones (zonai) by circles (kukloi) in planes at right angles to the poles. The zones of the celestial sphere repeated on a larger scale those of the terrestrial sphere.

The basis for division into zones was the two distinct paths of the heavenly bodies: that of the stars and that of the sun and moon. Astronomers know today that the Earth revolving around the sun is tilted on its axis, bringing each hemisphere now closer to the sun, now further away. The Greeks had the opposite model, that the stars and the sun rotated around the earth. The stars moved in fixed circles around the poles. The sun moved at an oblique angle to the circles, which obliquity brought it now to the north, now to the south. The circle of the sun was the ecliptic. It was the center of a band called the zodiac on which various constellations were located.

The shadow cast by a vertical rod at noon was the basis for defining zonation. The intersection of the northernmost or southernmost points of the ecliptic defined the axial circles passing through those points as the two tropics (tropikoi kukloi, “circles at the turning points”) later named for the zodiacal constellations found there, Cancer and Capricorn. During noon of the summer solstice (therinē tropē) rods there cast no shadow.[63] The latitudes between the tropics were called the torrid zone (diakekaumenē, “burned up”).

Based on their experience of the Torrid Zone south of Egypt and Libya, the Greek geographers judged it uninhabitable. Symmetry requires that there be an uninhabitable Frigid Zone (katepsugmenē, “frozen”) to the north and reports from there since the time of Homer seemed to confirm it. The edge of the Frigid Zone ought to be as far south from the North Pole in latitude as the Summer Tropic is from the Equator. Strabo gives it as 24°, which may be based on a previous tangent of Pytheas, but he does not say. The Arctic Circle would then be at 66°, accurate to within a degree.[64]

Seen from the equator the celestial North Pole (boreios polos) is a point on the horizon. As the observer moves northward the pole rises and the circumpolar stars appear, now unblocked by the Earth. At the Tropic of Cancer the radius of the circumpolar stars reaches 24°. The edge stands on the horizon. The constellation of mikra arktos (Ursa Minor, “little bear”) was entirely contained within the circumpolar region. The latitude was therefore called the arktikos kuklos, “circle of the bear”. The terrestrial Arctic Circle was regarded as fixed at this latitude. The celestial Arctic Circle was regarded as identical to the circumference of the circumpolar stars and therefore a variable.

When the observer is on the terrestrial Arctic Circle and the radius of the circumpolar stars is 66° the celestial Arctic Circle is identical to the celestial Tropic of Cancer.[65] That is what Pytheas means when he says that Thule is located at the place where the Arctic Circle is identical to the Tropic of Cancer.[27] At that point, on the day of the Summer Solstice, the vertical rod of the gnōmōn casts a shadow extending in theory to the horizon over 360° as the sun does not set. Under the pole the Arctic Circle is identical to the Equator and the sun never sets but rises and falls on the horizon. The shadow of the gnōmōn winds perpetually around it.

Latitude by longest day and shortest solar elevation Edit
Strabo uses the astronomical cubit (pēchus, the length of the forearm from the elbow to the tip of the little finger) as a measure of the elevation of the sun. The term “cubit” in this context is obscure; it has nothing to do with distance along either a straight line or an arc, does not apply to celestial distances, and has nothing to do with the gnōmōn. Hipparchus borrowed this term from Babylonia, where it meant 2°. They in turn took it from ancient Sumer so long ago that if the connection between cubits and degrees was known in either Babylonia or Ionia it did not survive. Strabo states degrees in either cubits or as a proportion of a great circle. The Greeks also used the length of day at the summer solstice as a measure of latitude. It is stated in equinoctial hours (hōrai isēmerinai), one being 1/12 of the time between sunrise and sunset on an equinox.

Based partly on data taken from Pytheas, Hipparchus correlated cubits of the sun’s elevation at noon on the winter solstice, latitudes in hours of a day on the summer solstice, and distances between latitudes in stadia for some locations.[66] Pytheas had proved that Marseilles and Byzantium were on the same parallel (see above). Hipparchus, through Strabo,[67] adds that Byzantium and the mouth of the Borysthenes, today’s Dnepr river, were on the same meridian and were separated by 3700 stadia, 5.3° at Strabo’s 700 stadia per a degree of meridian arc. As the parallel through the river-mouth also crossed the coast of “Celtica”, the distance due north from Marseilles to Celtica was 3700 stadia, a baseline from which Pytheas seems to have calculated latitude and distance.[68]

Strabo says that Ierne (Ireland) is under 5000 stadia (7.1°) north of this line. These figures place Celtica around the mouth of the Loire river, an emporium for the trading of British tin. The part of Ireland referenced is the vicinity of Belfast. Pytheas then would either have crossed the Bay of Biscay from the coast of Spain to the mouth of the Loire, or reached it along the coast, crossed the English channel from the vicinity of Brest, France to Cornwall, and traversed the Irish Sea to reach the Orkney Islands. A statement of Eratosthenes attributed by Strabo to Pytheas, that the north of the Iberian Peninsula was an easier passage to Celtica than across the Ocean,[69] is somewhat ambiguous: apparently he knew or knew of both routes, but he does not say which he took.

At noon on the winter solstice the sun stands at 9 cubits and the longest day on the summer solstice is 16 hours at the baseline through Celtica.[70] At 2500 stadia, approximately 283 miles, or 3.6°, north of Celtica, are a people Hipparchus called Celtic, but whom Strabo thinks are the British, a discrepancy he might not have noted if he had known that the British were also Celtic. The location is Cornwall. The sun stands at 6 cubits and the longest day is 17 hours. At 9100 stadia, approximately 1032 miles, north of Marseilles, 5400 or 7.7° north of Celtica, the elevation is 4 cubits and the longest day is 18 hours. This location is in the vicinity of the Firth of Clyde.

Here Strabo launches another quibble. Hipparchus, relying on Pytheas, according to Strabo, places this area south of Britain, but he, Strabo, calculates that it is north of Ierne. Pytheas, however, rightly knows what is now Scotland as part of Britain, land of the Picts, even though north of Ierne. North of southern Scotland the longest day is 19 hours. Strabo, based on theory alone, states that Ierne is so cold[27] that any lands north of it must be uninhabited. In the hindsight given to moderns Pytheas, in relying on observation in the field, appears more scientific than Strabo, who discounted the findings of others merely because of their strangeness to him. The ultimate cause of his skepticism is simply that he did not believe Scandinavia could exist. This disbelief may also be the cause of alteration of Pytheas’ data.

en.m.wikipedia.org/wiki/Apollonius_of_Perga

viewtopic.php?f=4&t=189657&p=2586137&hilit=Babylonian+philosopher#p2586137

Where are those two stinking threads already?

I was fairly certain I posted both on this site.

Damn frustrating.

Maia · August 16, 2016, 9:46pm

Turd Ferguson:

I wouldn’t call the small underground observatories scattered around the isles a sophisticated knowledge.

(Thunder woke me up, can’t sleep)

I can’t recall what they are called, but the little Neolithic to Bronze Age short tunnels… they figured out if you sat in one, a tunneling effect with light would occur, allowing you to see more light, and therefore increased magnification of one spot.

Great for timing a exact approach of one star to a fixed observational point, but I wouldn’t call that advanced astronomy.

I will give you a basic example of what advanced astronomy looked like.

The earliest Assyrian and Babylonian philosophers were astronomers (I will explain the terminology later, I simply can’t recall it, starts with an I)… they would lay on their backs, with straight plains of wood above them, and would just watch the stars pass.

They had small round clay tablets, a line on the stick above represented a line on the tablet, and they would simply transcribe the movement of the stars to this, looking at the distance of the stars on the edge of the stick above.

This allowed them to create remarkably accurate starmaps, in clay, some which we still have. They even did pretty advance work calculating and explaining the trajectory of planetary movement, which us hard as hell to express mathematically, I have a thread on this site somewhere on both the philosophers being philosophers, as well as how they observed the stars somewhere on the sight.

Iapetas? Iapetus? Ah… both words probably jibberish popping in my head. They sell pretty decent fascimilies of they star maps.

Germans had something far more rudimentry, small disks with a few stars on them.

members.westnet.com.au/gary-davi … e11-9.html

Ohhh… just found this quote I made from wiki in a unfinished Diocles thread I was making, not finished for reasons I don’t know why, deals with our topic:

Latitude by the altitude of the sun Edit
In discussing the work of Pytheas, Strabo typically uses direct discourse: “Pytheas says …” In presenting his astronomical observations, he changes to indirect discourse: “Hipparchus says that Pytheas says …” either because he never read Pytheas’ manuscript (because it was not available to him) or in deference to Hipparchus, who appears to have been the first to apply the Babylonian system of representing the sphere of the earth by 360°.[53]

Strabo uses the degrees, based on Hipparchus.[54] Neither say that Pytheas did. Nevertheless, Pytheas did obtain latitudes, which, according to Strabo, he expressed in proportions of the gnōmōn (“index”), or trigonometric tangents of angles of elevation to celestial bodies. They were measured on the gnōmōn, the vertical leg of a right triangle, and the flat leg of the triangle. The imaginary hypotenuse looked along the line of sight to the celestial body or marked the edge of a shadow cast by the vertical leg on the horizontal leg.

Pytheas took the altitude of the sun at Massalia at noon on the longest day of the year and found that the tangent was the proportion of 120 (the length of the gnōmōn) to 1/5 less than 42 (the length of the shadow).[55] Hipparchus, relying on the authority of Pytheas (says Strabo[56]), states that the ratio is the same as for Byzantium and that the two therefore are on the same parallel. Nansen and others prefer to give the cotangent 209/600,[57] which is the inverse of the tangent, but the angle is greater than 45° and it is the tangent that Strabo states. His number system did not permit him to express it as a decimal but the tangent is about 2.87.

It is unlikely that any of the geographers could compute the arctangent, or angle of that tangent. Moderns look it up in a table. Hipparchos is said to have had a table of some angles. The altitude, or angle of elevation, is 70° 47’ 50″[57] but that is not the latitude.

At noon on the longest day the plane of longitude passing through Marseilles is exactly on edge to the sun. If the Earth’s axis were not tilted toward the sun, a vertical rod at the equator would have no shadow. A rod further north would have a north-south shadow, and as an elevation of 90° would be a zero latitude, the complement of the elevation gives the latitude. The sun is even higher in the sky due to the tilt. The angle added to the elevation by the tilt is known as the obliquity of the ecliptic and at that time was 23° 44′ 40″.[57] The complement of the elevation less the obliquity is 43° 13′, only 5′ in error from Marseilles’s latitude, 43° 18′.[58]

Latitude by the elevation of the north pole Edit
A second method of determining the latitude of the observer measures the angle of elevation of a celestial pole, north in the northern hemisphere. Seen from zero latitude the north pole’s elevation is zero; that is, it is a point on the horizon. The declination of the observer’s zenith also is zero and therefore so is his latitude.

As the observer’s latitude increases (he travels north) so does the declination. The pole rises over the horizon by an angle of the same amount. The elevation at the terrestrial North Pole is 90° (straight up) and the celestial pole has a declination of the same value. The latitude also is 90.[59]

Moderns have Polaris to mark the approximate location of the North celestial pole, which it does nearly exactly, but this position of Polaris was not available in Pytheas’ time, due to changes in the positions of the stars. Pytheas reported that the pole was an empty space at the corner of a quadrangle, the other three sides of which were marked by stars.[60] Their identity has not survived but based on calculations these are believed to have been α and κ in Draco and β in Ursa Minor.[61]

Pytheas sailed northward with the intent of locating the Arctic Circle and exploring the “frigid zone” to the north of it at the extreme of the earth. He did not know the latitude of the circle in degrees. All he had to go by was the definition of the frigid zone as the latitudes north of the line where the celestial arctic circle was equal to the celestial Tropic of Cancer, the tropikos kuklos (refer to the next subsection). Strabo’s angular report of this line as being at 24° may well be based on a tangent known to Pytheas, but he does not say that. In whatever mathematical form Pytheas knew the location, he could only have determined when he was there by taking periodic readings of the elevation of the pole (eksarma tou polou in Strabo and others).

Today the elevation can be obtained easily on ship with a quadrant. Electronic navigational systems have made even this simple measure unnecessary. Longitude was beyond Pytheas and his peers, but it was not of as great a consequence, because ships seldom strayed out of sight of land. East-west distance was a matter of contention to the geographers; they are one of Strabo’s most frequent topics. Because of the gnōmōn north-south distances were accurate often to within a degree.

It is unlikely that any gnōmōn could be read accurately on the pitching deck of a small vessel at night. Pytheas must have made frequent overnight stops to use his gnōmōn and talk to the natives, which would have required interpreters, probably acquired along the way. The few fragments that have survived indicate that this material was a significant part of the periplus, possibly kept as the ship’s log. There is little hint of native hostility; the Celts and the Germans appear to have helped him, which suggests that the expedition was put forward as purely scientific. In any case all voyages required stops for food, water and repairs; the treatment of voyagers fell under the special “guest” ethic for visitors.

Location of the Arctic Circle Edit
The ancient Greek view of the heavenly bodies on which their navigation was imported from Babylonia by the Ionian Greeks, who used it to become a seafaring nation of merchants and colonists during the Archaic period in Greece. Massalia was an Ionian colony. The first Ionian philosopher, Thales, was known for his ability to measure the distance of a ship at sea from a cliff by the very method Pytheas used to determine the latitude of Massalia, the trigonometric ratios.

The astronomic model on which ancient Greek navigation was based, which is still in place today, was already extant in the time of Pytheas, the concept of the degrees only being missing. The model[62] divided the universe into a celestial and an earthly sphere pierced by the same poles. Each of the spheres were divided into zones (zonai) by circles (kukloi) in planes at right angles to the poles. The zones of the celestial sphere repeated on a larger scale those of the terrestrial sphere.

The basis for division into zones was the two distinct paths of the heavenly bodies: that of the stars and that of the sun and moon. Astronomers know today that the Earth revolving around the sun is tilted on its axis, bringing each hemisphere now closer to the sun, now further away. The Greeks had the opposite model, that the stars and the sun rotated around the earth. The stars moved in fixed circles around the poles. The sun moved at an oblique angle to the circles, which obliquity brought it now to the north, now to the south. The circle of the sun was the ecliptic. It was the center of a band called the zodiac on which various constellations were located.

The shadow cast by a vertical rod at noon was the basis for defining zonation. The intersection of the northernmost or southernmost points of the ecliptic defined the axial circles passing through those points as the two tropics (tropikoi kukloi, “circles at the turning points”) later named for the zodiacal constellations found there, Cancer and Capricorn. During noon of the summer solstice (therinē tropē) rods there cast no shadow.[63] The latitudes between the tropics were called the torrid zone (diakekaumenē, “burned up”).

Based on their experience of the Torrid Zone south of Egypt and Libya, the Greek geographers judged it uninhabitable. Symmetry requires that there be an uninhabitable Frigid Zone (katepsugmenē, “frozen”) to the north and reports from there since the time of Homer seemed to confirm it. The edge of the Frigid Zone ought to be as far south from the North Pole in latitude as the Summer Tropic is from the Equator. Strabo gives it as 24°, which may be based on a previous tangent of Pytheas, but he does not say. The Arctic Circle would then be at 66°, accurate to within a degree.[64]

Seen from the equator the celestial North Pole (boreios polos) is a point on the horizon. As the observer moves northward the pole rises and the circumpolar stars appear, now unblocked by the Earth. At the Tropic of Cancer the radius of the circumpolar stars reaches 24°. The edge stands on the horizon. The constellation of mikra arktos (Ursa Minor, “little bear”) was entirely contained within the circumpolar region. The latitude was therefore called the arktikos kuklos, “circle of the bear”. The terrestrial Arctic Circle was regarded as fixed at this latitude. The celestial Arctic Circle was regarded as identical to the circumference of the circumpolar stars and therefore a variable.

When the observer is on the terrestrial Arctic Circle and the radius of the circumpolar stars is 66° the celestial Arctic Circle is identical to the celestial Tropic of Cancer.[65] That is what Pytheas means when he says that Thule is located at the place where the Arctic Circle is identical to the Tropic of Cancer.[27] At that point, on the day of the Summer Solstice, the vertical rod of the gnōmōn casts a shadow extending in theory to the horizon over 360° as the sun does not set. Under the pole the Arctic Circle is identical to the Equator and the sun never sets but rises and falls on the horizon. The shadow of the gnōmōn winds perpetually around it.

Latitude by longest day and shortest solar elevation Edit
Strabo uses the astronomical cubit (pēchus, the length of the forearm from the elbow to the tip of the little finger) as a measure of the elevation of the sun. The term “cubit” in this context is obscure; it has nothing to do with distance along either a straight line or an arc, does not apply to celestial distances, and has nothing to do with the gnōmōn. Hipparchus borrowed this term from Babylonia, where it meant 2°. They in turn took it from ancient Sumer so long ago that if the connection between cubits and degrees was known in either Babylonia or Ionia it did not survive. Strabo states degrees in either cubits or as a proportion of a great circle. The Greeks also used the length of day at the summer solstice as a measure of latitude. It is stated in equinoctial hours (hōrai isēmerinai), one being 1/12 of the time between sunrise and sunset on an equinox.

Based partly on data taken from Pytheas, Hipparchus correlated cubits of the sun’s elevation at noon on the winter solstice, latitudes in hours of a day on the summer solstice, and distances between latitudes in stadia for some locations.[66] Pytheas had proved that Marseilles and Byzantium were on the same parallel (see above). Hipparchus, through Strabo,[67] adds that Byzantium and the mouth of the Borysthenes, today’s Dnepr river, were on the same meridian and were separated by 3700 stadia, 5.3° at Strabo’s 700 stadia per a degree of meridian arc. As the parallel through the river-mouth also crossed the coast of “Celtica”, the distance due north from Marseilles to Celtica was 3700 stadia, a baseline from which Pytheas seems to have calculated latitude and distance.[68]

Strabo says that Ierne (Ireland) is under 5000 stadia (7.1°) north of this line. These figures place Celtica around the mouth of the Loire river, an emporium for the trading of British tin. The part of Ireland referenced is the vicinity of Belfast. Pytheas then would either have crossed the Bay of Biscay from the coast of Spain to the mouth of the Loire, or reached it along the coast, crossed the English channel from the vicinity of Brest, France to Cornwall, and traversed the Irish Sea to reach the Orkney Islands. A statement of Eratosthenes attributed by Strabo to Pytheas, that the north of the Iberian Peninsula was an easier passage to Celtica than across the Ocean,[69] is somewhat ambiguous: apparently he knew or knew of both routes, but he does not say which he took.

At noon on the winter solstice the sun stands at 9 cubits and the longest day on the summer solstice is 16 hours at the baseline through Celtica.[70] At 2500 stadia, approximately 283 miles, or 3.6°, north of Celtica, are a people Hipparchus called Celtic, but whom Strabo thinks are the British, a discrepancy he might not have noted if he had known that the British were also Celtic. The location is Cornwall. The sun stands at 6 cubits and the longest day is 17 hours. At 9100 stadia, approximately 1032 miles, north of Marseilles, 5400 or 7.7° north of Celtica, the elevation is 4 cubits and the longest day is 18 hours. This location is in the vicinity of the Firth of Clyde.

Here Strabo launches another quibble. Hipparchus, relying on Pytheas, according to Strabo, places this area south of Britain, but he, Strabo, calculates that it is north of Ierne. Pytheas, however, rightly knows what is now Scotland as part of Britain, land of the Picts, even though north of Ierne. North of southern Scotland the longest day is 19 hours. Strabo, based on theory alone, states that Ierne is so cold[27] that any lands north of it must be uninhabited. In the hindsight given to moderns Pytheas, in relying on observation in the field, appears more scientific than Strabo, who discounted the findings of others merely because of their strangeness to him. The ultimate cause of his skepticism is simply that he did not believe Scandinavia could exist. This disbelief may also be the cause of alteration of Pytheas’ data.

en.m.wikipedia.org/wiki/Apollonius_of_Perga

ilovephilosophy.com/viewtopi … r#p2586137

Where are those two stinking threads already?

I was fairly certain I posted both on this site.

Damn frustrating.

Well, ok, and while I certainly don’t claim to be an expert on astronomy, what I can say is that the megalith builders of the British Isles were building their circles, aligned to all sorts of different celestial events, about two milliennia before Pytheas and Greek astronomy.

The_Golden_Turd · August 16, 2016, 10:06pm

I’m not talking about the circles, your country has actual underground observatories. They look like tombs, were mistaken as granieries. Tab lost his virginity in one.

I can’t recall their name. Gotta go look them up.

The_Golden_Turd · August 16, 2016, 10:08pm

The_Golden_Turd · August 16, 2016, 10:10pm

biztekmojo.com/002342/ancien … telescopes

Maia · August 16, 2016, 10:12pm

Maybe cromlechs?

The_Golden_Turd · August 16, 2016, 11:22pm

bbc.com/news/uk-wales-22109262

Not the circles, not like Stonehenge, the long underground passages. I know you got a fixation on the circular passages, I’m not talking about those.

Maia · August 17, 2016, 6:49am

A cromlech is a chambered tomb, usually a group of stones with a larger, flat stone on top. Not a circle, and in fact they predate all known circles by about a millennium, sometimes two millennia in the very earliest examples. I told you about the one where I found some old coins in a small hole in one of the stones.

The_Golden_Turd · August 17, 2016, 7:25am

See, the problem is, when I type in the term, about 1/3rd of the images are what I’m looking for, two thirds are not, and nothing is labeled right.

It is a mostly underground tunnel, not a Stonehenge, not a tomb as far as anyone has figured out, not a grainery as once thought. It is roofed.

Be a lot easier if the spelling of pre-angle Saxon sites in the UK had easier spellings. I can’t figure out these Welsh like crazy words.

I know a lot more about the fortifications used in England, especially during the Roman and Alfred the Great era, and Norman times, but I know little in terminology or use of these kinds of structures period, outside a half dozen documentaries I’ve seen over the years.

It would be awesome if you could see, I could just give a pic for confirmation.

Maia · August 17, 2016, 7:33am

Turd Ferguson:

See, the problem is, when I type in the term, about 1/3rd of the images are what I’m looking for, two thirds are not, and nothing is labeled right.

It is a mostly underground tunnel, not a Stonehenge, not a tomb as far as anyone has figured out, not a grainery as once thought. It is roofed.

Be a lot easier if the spelling of pre-angle Saxon sites in the UK had easier spellings. I can’t figure out these Welsh like crazy words.

I know a lot more about the fortifications used in England, especially during the Roman and Alfred the Great era, and Norman times, but I know little in terminology or use of these kinds of structures period, outside a half dozen documentaries I’ve seen over the years.

It would be awesome if you could see, I could just give a pic for confirmation.

There are passage graves, but they are definitely tombs as bones have been found. These are larger than the cromlechs, within which, as you say, no bodies have usually been discovered, but the supposition that they must be tombs is very old. All these structures are roofed and at least partially underground.

The_Golden_Turd · August 17, 2016, 8:05am

Might be cromlechs, the name tingles every time I see it.

I have a rather flat, tone,death voice, as I rarely talk, and when I do, it is usually softly. I honestly can’t imagine trying to say that word out load and expect a computer to accurately understand what I said so as to spell it correctly. I would just break under the pain of having to say all those weird Welsh like terms.

I know some of Welsh history, but would never verbally discuss it, for that reason. I haven’t the slightest clue how those words are to be pronounced.

I found with middle to early modern English, I can’t always read it, but if I say it out loud, it sometimes makes sense, but Dutch, Irish, and Scottish words… I just hate those Saxons for dragging ass and stopping their westward advance. Wish the place names were simpler. I honestly have a much easier time with Chinese sites than I do with English sites. Once Alfred’s burgs come about, I start getting tongue tied. It is a logical system, but the names for places are rude and obscene.

Maia · August 17, 2016, 8:09am

Turd Ferguson:

Might be cromlechs, the name tingles every time I see it.

I have a rather flat, tone,death voice, as I rarely talk, and when I do, it is usually softly. I honestly can’t imagine trying to say that word out load and expect a computer to accurately understand what I said so as to spell it correctly. I would just break under the pain of having to say all those weird Welsh like terms.

I know some of Welsh history, but would never verbally discuss it, for that reason. I haven’t the slightest clue how those words are to be pronounced.

I found with middle to early modern English, I can’t always read it, but if I say it out loud, it sometimes makes sense, but Dutch, Irish, and Scottish words… I just hate those Saxons for dragging ass and stopping their westward advance. Wish the place names were simpler. I honestly have a much easier time with Chinese sites than I do with English sites. Once Alfred’s burgs come about, I start getting tongue tied. It is a logical system, but the names for places are rude and obscene.

You think you’ve got it bad? Imagine how my screen reader reads a word like Llanfairpwllgwyngyllgogerychwyrndrobwllllantysiliogogogoch.

The_Golden_Turd · August 17, 2016, 8:20am

It is odd how English comes from the british isles, but those languages are the hardest for me to grasp.

Half the reason I want to go to England and walk around honestly is just to get the names right. I’m honestly not too inspired by the culture or “foreigness” of the locals… I’m just one of those people who can’t figure our how to pronounce a word unless he hears it first. I had a bad speech problem growing up, I got over it, but learned I was pronouncing names and philosophical terms wrong… so whenever I hosted a philosophy ground discussion, I would spend a few hours before hand showing up, watching videos discussing the topic, less for the information and much more for the pronunciation.

Chinese and Korean is easy given the number of historical dramas… especially Romance of the Three Kingdoms… the fansubs hit the notes of the opera to the english words exactly, and if you just say it at a certain pitch, the tones come out right mostly. I have a lot more confidence saying a Chinese place name. But british ones, I gotta look it up, and hear it repeated. I like a lot of Irish sagas, but you will never hear a beep out of my mouth about them. Anyone speaking Gaelic would just ask me not to try to pronounce it.

Maia · August 17, 2016, 8:25am

Turd Ferguson:

It is odd how English comes from the british isles, but those languages are the hardest for me to grasp.

Half the reason I want to go to England and walk around honestly is just to get the names right. I’m honestly not too inspired by the culture or “foreigness” of the locals… I’m just one of those people who can’t figure our how to pronounce a word unless he hears it first. I had a bad speech problem growing up, I got over it, but learned I was pronouncing names and philosophical terms wrong… so whenever I hosted a philosophy ground discussion, I would spend a few hours before hand showing up, watching videos discussing the topic, less for the information and much more for the pronunciation.

Chinese and Korean is easy given the number of historical dramas… especially Romance of the Three Kingdoms… the fansubs hit the notes of the opera to the english words exactly, and if you just say it at a certain pitch, the tones come out right mostly. I have a lot more confidence saying a Chinese place name. But british ones, I gotta look it up, and hear it repeated. I like a lot of Irish sagas, but you will never hear a beep out of my mouth about them. Anyone speaking Gaelic would just ask me not to try to pronounce it.

It’s always best to hear a native saying something. And there are regional variations too. For example, Newcastle and Carlisle, to name just two, are pronounced differently by the locals than in the standard BBC pronunciation. I think Welsh is really cool though, and have been to north Wales many, many times, where Welsh is still the first language.

The_Golden_Turd · August 17, 2016, 8:47am

You know what… I watch a lot of Doctor Who. Had a bit of a crush on Clara, but couldn’t understand a damn thing she said in the 50th anniversary special. I could make the individual words out, but the pattern was bizarre.

Since I deal with a wide range of history… for example I’m interested in all Greek history, but as a philosopher only care about Ancient to Byzantine Greek (hence Koine)… I don’t want to pronounce it like a modern Greek… but pronouncing it like in ancient times, not as appealing. I just want to say it in as close to a standard American accent as I can, as the word is commonly said in philosophy circles. It always bother me when I see someone talk in English change their accent to speak another language. I gotta do it for Chinese, but not as much for Japanese (I did have one semester of Japanese).

I’m not certain I can come back and say the names with a American accent.

Maia · August 17, 2016, 8:54am

Turd Ferguson:

You know what… I watch a lot of Doctor Who. Had a bit of a crush on Clara, but couldn’t understand a damn thing she said in the 50th anniversary special. I could make the individual words out, but the pattern was bizarre.

Since I deal with a wide range of history… for example I’m interested in all Greek history, but as a philosopher only care about Ancient to Byzantine Greek (hence Koine)… I don’t want to pronounce it like a modern Greek… but pronouncing it like in ancient times, not as appealing. I just want to say it in as close to a standard American accent as I can, as the word is commonly said in philosophy circles. It always bother me when I see someone talk in English change their accent to speak another language. I gotta do it for Chinese, but not as much for Japanese (I did have one semester of Japanese).

I’m not certain I can come back and say the names with a American accent.

Clara, that is, Jenna Coleman, has a Lancashire accent. It’s not especially strong though and I’m surprised you found the pattern bizarre. I do find though, and this isn’t intended as a criticism, that the American accent is fairly monotone, so to you, British accents must sound all over the place, in pitch and tone, that is.

The_Golden_Turd · August 17, 2016, 9:08am

Some I can’t understand. Sounds like someone in Boston talking through a snorkle.

And I knew the location too… yeah, I as a INTJ fall for FPs rather easily. I try not to. I just see her and go mushy. I’m a deeply disturbed MSN, saw all sorts of hate articles by women saying they hate men who are attracted to her, as a one dimensional character.

Maia · August 17, 2016, 9:18am

Not sure I fully understand all those abbreviations… But I do happen to know that Jenna Coleman is playing Queen Victoria in a TV series soon.