Tuesday, April 27, 2004

A Day's Walk, the Horizon and Astronomy - LexiLine Journal 270

A reader sent some interesting questions concerning astronomical and geodetic measure as follows:

>Actually this is an inquiry.
>However, your website appears to have many nooks and crannys worth

>I have no nomenclature for the measurements that interest me
>at the moment.
>What is the distance in miles or kilometers from an adult standing
>to the average horizon?
>Do you have any names the ancients used for this distance?
>How does this compare to the distance a person can walk in a day?
>Not a forced march.

Here are my answers:


The height of the observer and the distance to the horizon can be calculated at:

I do not know what the ancients called this distance.


In ancient days, a day's walk without a load to carry was about 24 miles as we can see from the Gemara Pesachim.

As noted at

"The wind brought the quails from the sea, dropping them around the perimeter of the camp (11:31). The Israelite camp was three parsah square (Berachot 54b). A parsah is equal to 4 mil (a mil is approximately 3160 feet), and according to the Gemara (Pesachim 94a) an average person is able to walk ten parsah - 40 mil - during a twelve-hour day (approximately 126,000 feet - 24 miles)."

As we can see from
the ancient Hebrews were astronomers and utilized a hermetic system in which time and measurement of the heavens and the world were related to measuring distances on earth. It is written at that website:

[beginning of long section of quoted material]

"prepared by Rabbi Eliezer Chrysler, Kollel Iyun Hadaf, Jerusalem
Pesachim 94



2)(a) According to Rava, the world (from east where the sun rises, to the west, where it sets) is six thousand Parsah - twenty-four thousand Mil (kilometers) wide, and the thickness of the sky, one thousand Parsah.

(b) We know from Rebbi Yochanan that a person walks ten Parsah a day, and from Rava's tradition that the width of the world is six thousand Parsah. Considering that one walks five Mil from dawn-break until sunrise, and the same distance from sunset until nightfall, this leaves a person to walk thirty Mil between sunrise and sunset. In other words, he walks one sixth of the distance during the period between dawn-break and sunrise, that he walks from sunrise until sunset. In that case, the sun too, must travel during that period (between dawn-break and sunrise), one sixth of the distance that it travels between sunrise and sunset - i.e. one thousand Parsah.

(c) The sun travels one thousand Parsah (from dawn-break until sunrise) during the time it takes an average person to walk five Mil.

3)(a) The Gemara proves Ula and Rava both wrong from Rebbi Yehudah, who says in a Beraisa that a person walks ten Parsah a day, but that, between dawn- break and sunrise he walks, not *five* Mil (a *sixth* of the day's total), but *four* (a *tenth*).

(b) Rebbi Yochanan, on whose statement both Amora'im based their reckonings, is vindicated - because he only made the statement that a person walks ten Parsah daily, and it was other Amora'im who split the day into three as above, not Rebbi Yochanan himself.

4)(a) Rebbi Chanina (who says that from Sedom to Tzo'ar is *five* Mil) will also agree that between dawn-break and sunrise a person walks *four* Milin; However, the angels who accompanied Lot were rushing from the stricken Sedom, so they managed to travel *five* Mil in the time that a walking person would only have walked *four*.

(b) If Egypt is 400 Parsah by 400 Parsah, and Kush, the world, Gan Eden and Gehinom, each one, sixty times larger than the previous one - then the world is clearly more than 6,000 Parsah wide.

(c) We see with our own eyes that the inhabited world is at least one thousand Parsah. So, if as the Beraisa says, 'the inhabited world (Earth) is situated underneath one star', then had there been just six stars in the sky, then the entire world from East to West (including the section that is outside Earth) would already be six thousand Parsah - but there are far more than six stars side by side in the sky! So how can Rava give the size of the world as six thousand Parsah?

5)(a) Nimrod was responsible for the entire world rebelling against G-d - by proposing the building of the Tower of Bavel.

(b) When Hashem reminded Nevuchadnetzar of his ancestry after he tried to emulate G-d Himself, by flying into the air on a thick cloud (similar to the sin of his ancestor Nimrod).

(c) The distance from ...

... the earth to the first of the seven heavens - is five hundred years (walking distance) - over nine million miles.

... one heaven to the next is the same.

... the east, where the sunrises, to the west, where it sets - is the same - five hundred years distance from the earth.

(d) But didn't Rava say earlier that the world is only six thousand Parsah wide?

6)(a) Rebbi attempted to prove the gentile sages, who maintain that the Mazalos remain static, and it is Galgal that turns, wrong, from the fact that Taurus is never seen in the south, or Scorpio in the north.

(b) Rav Acha bar Ya'akov answers the question by comparing it to the metal that is stuck in the middle of the wide hole of the mill - which moves on its own axis, and not together with the mill-stone. So too, are the Mazalos placed in their own wheel within that of Galgal, and they do not move together with Galgal.

(c) In his second answer, he compares the Galgal and the Mazalos to a door- socket and the lintel. Like the metal in the hole of the mill-wheel, the door-socket does not swivel together with the door, and if one were to swivel it, the door would not swing with it.

(d) The Jewish sages contend that it is the Mazalos that move, and that the Galgal remains static. They do not however, move full circle, only slightly, to the next Mazel and back, as they serve the sun.

7)(a) According to the non-Jewish sages, the sun travels below the earth during the night. Rebbi conceded that the non-Jewish sages were right - because by day the water-springs are cold (when the sun is far away from them), and by night (when the sun is close to them) they are hot.

(b) The river-water nevertheless becomes warm by day, due to the fact that it has flowed far from its source, and has had a chance to become heated from the general warmth that pervades during the day.

(c) According to Rebbi Nasan, the world is hot in the summer, and the fountains cold, because the sun shines in the middle of the sky (far from the fountain-water and close to the earth); whereas in the winter, when the sun shines at the side of the world (close to the fountain-water, and far from the earth) it is the other way round, the world is cold and the fountain-water, hot.

8) The sun's strength is directed ...

... towards the mountains in Nisan, Iyar and Sivan - in order to melt the snow.

... through inhabited country in Tamuz, Av and Elul - to ripen the fruit.

... over the sea in Tishri, Mar-cheshvan and Kislev - to dry up the rivers.

... across the desert in Teves, Shevat and Adar - to dry the seeds.

Note: these four correspond to the four seasons (Agados Maharsha).

9)(a) Abaye reconciles Rebbi Eliezer in our Mishnah (who says that anyone who is not inside the Azarah during the entire period of Shechitas ha'Pesach, is Patur from Kares, in spite of the fact that he is able to enter) with his own statement, that a grown-up Areil who is able to circumcise, and who fails to do so on Erev Pesach, is Chayav Kares for not bringing the Korban Pesach (since he could have done so) - by differentiating between the Derech Rechokah of a Tahor (whom the Torah exempts) and that of a Tamei (or of an Areil) which it does not - see end of 93b.

(b) The Tana Kama of Rebbi Yossi bar Rebbi Yehudah learns Pesach from a Gezeirah Shavah "Richuk Makom" "Richuk Makom" from Ma'aser Sheini - that Richuk Makom by Pesach means outside the walls of Yerushalayim).

(c) Rav Yitzchak bar Rav Yosef, who says that in order to become a Pesach ha'Ba b'Tum'ah, one requires a majority of those standing *in the Azarah* to be Tamei (and does not contend with those standing outside), holds like Rebbi Eliezer in our Mishnah it is not clear though, how Temei'im are permitted to enter the Azarah in the first place).

(d) Rebbi Yossi Hagelili learns from the Pasuk in Beha'aloscha "u'va'Derech Lo Hayah" that (since the word Rechokah is omitted here) any Derech is sufficient to be called a Derech Rechokah, even just outside the Azarah - like Rebbi Eliezer.

[end of long section of quoted material]


The following link


seems to indicate that the ancient Hebrews understood the problems related to refraction,
seeing it as a "passage through the firmament" - measuring it as the time it takes to walk 3/4 mil
so that "the terrestrial horizon", the point at which "sunset occurs" and the point at which "night
begins", i.e. when the first stars can be seen in terms of the sun's passage, for example, were all recognized to be different by the ancients.

There is also a discussion here of the length of the "day" referred to since 40 Mil is generally
thought to cover a 12-hour period from sunrise to sunset, and this of course also depends upon the time of year involved and the period between dawn and sunrise.

It is a complicated matter and as we can see, the ancients understood these astronomical difficulties.

Interesting for astronomy and geodetics is that astronomical time was measured in terms of the distance covered by an average person walking on earth, i.e. a principally hermetic principle.


The parsah as a length of measurement may in some historical manner correspond to the Russian versta of 3500 feet (500 sazheni, 1.067 km, .66288 miles) inasmuch as 126,000 feet (10 parsah) divided by 3500 = 36, an exact multiple in the duodecimal and decimal systems.

Note that a day's walk with a load to carry is of course less than 24 miles, and may have been calculated as something like 10 or 11 kilometers.

for the statement that the Latvian verste - as opposed to the Russian versta - "was an old Latvian distance measure equivalent to approximately 10 kilometers".


See https://listhost.uchicago.edu/pipermail/ane/2002-June/001877.html

"If by circuit of 60 stadia is meant a circle drawn around a radius of 60 stadia of 185 m then it looks like the radius is 11.1 km or 1/10 degree which would be 7.5 Roman miles. 7.5 Roman miles sounds like about the right distance apart for villages or hamlets, that they would be about a day's walk for a person carrying produce or some other burden to market.""

Note that 1 Roman mile = 1618 yards as compared to the modern mile of 1760 yards so that 7.5 Roman miles is approximately 6.9 modern miles or ca. 11.1 kilometers. Note that these distances were correlated to geodetic measure, i.e. 1/10 of 1 degree. Peter Tompkins in his Secrets of the Great Pyramid discusses these matters at length.

Note also that the above is the same system of way stations as is found in ancient Latvia: http://snipurl.com/5zdp

"in the Piltene region at the beginning of the l9th century, there were seven inns along a stretch of road covering 7 verstis (verste - an old Latvian distance measure equivalent to approximately 10 kilometers)".

Re: 30 LexiLine Newsletter 2004 A Day's Walk and the Horizon

From Rebecca Turner:

Subj: Re: [LexiLine] 30 LexiLine Newsletter 2004 A Day's Walk and
the Horizon
Date: 4/27/2004 4:48:37 PM Eastern Daylight Time
From: Rebecca tURNER <scooter_4851@yahoo.com>
To: LexiLine-owner@yahoogroups.com

A day's walk--a moment in eternity, or less:>

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