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Thank you for that interesting article. That is something that had puzzled me as well, and my own opinion has always been that it signifies an accurate way of determining the length of a cubit. Anybody who is involved in any kind of serious measurement knows having an accurate unit of measurement is important. If you are building Pyramids, having an accurate unit of measure becomes important. When the French invented the Meter, the determined it by the astronomical measure of 1⁄10,000,000 part of the quarter of a meridian, assuming that to be an unchangeable constant which could always be referenced should doubts arise. Since then more “unchangeable constants” have been devised to determine accurately the length of a Meter, including one based on the speed of light (see “Metre” and “History of the Metre” in Wikipedia). I am guessing that the Egyptians had figured some astronomical fixed measurement (like the French) with which to determine the length of the cubit, and that is what is meant in the Book of Abraham by “one day to a cubit”.
I like the cubit notion. It would certainly be interesting to have more attestations that suggest that a finger-at-arms-length was commonly referred to as an angular cubit, but it’s a slick explanation of something that is otherwise obscure. And sounds plausible enough to be going on with.
With regard to the issues related to Kolob (somewhat off Prof. Johnson’s point but raised by some other responders), and what the information about it in the text of Abraham and the facsimile mean (in modern astronomical terms), I think we’re trying to fit a square peg into a round hole. As John Gee has argued (to me persuasively) here:
http://maxwellinstitute.byu.edu/publications/books/?bookid=40&chapid=161
and in the latter third of this FAIR presentation:
http://www.fairlds.org/fair-conferences/2009-fair-conference/2009-the-larger-issue
we simply cannot justify assuming that the Book of Abraham is a treatise on astronomy, as we understand it (any more than the Genesis creation account is, to paraphrase Elder Talmage, a scientific explanation.)
The relevant portion of Dr. Gee’s FAIR presentation begins with this rather pointed intro: “[The astronomical discussion in Abraham] chapter [3] has never made much sense to Latter-day Saints. There is a good reason it makes no sense to us. It is not meant for us. The Lord shows all this to Abraham with a specific purpose: ‘I show these things unto thee before ye go into Egypt, that ye may declare all these words’ (Abraham 3:15). ”
In short, Dr. Gee describes neatly why Abraham 3 was meant to be of relevance to ancient Egyptians; not modern students of astronomy (whether at the accuracy level Newtonian physics or with the adjustments of relativity fully considered). If you haven’t read it, I recommend it (and the other book chapter as well).
Thanks to all who have read and commented on this article; they all add to the interest and they seem to indicate the Interpreter has found a good niche in the LDS community. Let’s go forward.
Comments on the article: One Day to a Cubit
Let’s consider the size of the cubit used in the sources quoted. The latitudes of the places mentioned by Marco Polo, which are extended areas, seems to indicate that the word ‘cubit’ was used by Marco Polo and his translators for an angle of about 4-6 degrees – called anciently a palm, or the width of the four fingers of one’s hand.
A study of the moon’s path through the stars in the passage quoted from 331 BC shows that the word ‘cubit’ was used in this source to describe a much smaller angle, either two and a half degrees, as was sometimes used, or one degree, which is conveniently a finger’s width at arm’s length. The idea of a day to a cubit fits exactly for the sun if Joseph Smith chose one degree for his cubit.
Hi John,
I don’t believe Dr. Johnson misunderstood what you said—he was just being polite in response to a post that, frankly, doesn’t make sense. First, note that Einstein’s “Theory of Relativity” entails both the Special Theory and the General Theory. Second, the famous transformation in the Special Theory of relativity is called the “Lorentz” transformation, not “Lawrence”. Third, the Lorentz transformation doesn’t transform speed into distance—it transforms length as observed near the speed of light to length as observed at rest, and it transforms the passage of time as observed near the speed of light to the passage of time as observed at rest.
Melvin Cook had the unrivaled mental-gymnastic ability to radically twist scientific understanding to support his preconceived notions of how the world works, and he was certainly capable of coming to the unique interpretation that the reason why the Lorentz transformation takes place is because length somehow equals time. But Einstein certainly didn’t interpret it that way.
Fascinating article. You cited ancient sources using “cubit” as an angular measurement (such as Marco Polo) and Marco Polo’s quote makes clear that his “cubit” was not a very big angle, but do any of the sources specifically define this angular cubit as the width of the finger on the outstretched arm?
I have not found a definitive statement to that effect although texts hint at that correspondance. Certainly I have not examined every ancient text. Furthermore, a cubit is a natural unit defined by the body itself and the accord with a degree is very good,..
The Marco Polo quotes effectively determine his definition of an angular cubit. As Marco Polo sailed from Sumatra to Comorin to Malabar to Gujarat, the Pole Star “rose” by one cubit, then two cubits and finally by six cubits. A good geographer/astronomer (i.e. not me!) can calculate the angular changes in the Pole Star over this journey, thus confirming what constituted a “cubit” for Marco Polo. It wasn’t clear to me from the article whether these calculations have been done and whether “cubit” does correspond to “degree”.
A span with outspread fingers, from the tip of the thumb to the tip of the little finger, covers approximately 18 degrees, or roughly the size (height) of the constellation.Orion. However, in this context, Isaiah is praising the power and greatness of God (Isaiah 40:12), and its use may be entirely poetic.
Isaiah 40 is much more then just poetic and I am certain is very deeply related to Facsimile 2. I am not sure how much of that I can describe in detail but perhaps if one considers both after getting oneself to a high mountain and considering the works of God and the steps of creation and being called by name by the Lord, as it says in Isaiah 40, that one might gain a better understanding of what is being talked about. In fact that is pretty much the only place that I would attempt to imitate the actions of vs. 10-12.
Thanks for your comment. The poetic praise of God by Isaiah is lovely, and I agree fully with the value of the perspective from a mountain peak. Our extended family climbed Willard Peak in northern Utah several times, and I have climbed Timpanogos three times. My highest climb was Long’s Peak in Colorado. I have also stood on the Aereopagus (Mars Hill) in Greece and the mount in Israel said in legend to be the spot where Elijah challenged the priests of Baal. All were wonderful and powerfully evocative in several different ways.
Back in the late 1950s, University of Utah Prof. Melvin Cook noted that the “one day to a cubit” of Abraham Fac. 1 Fig. 1 made sense in Einsteinian terms. I.e., as one approaches the speed of light, time becomes distance and vice-versa. Hence, God, who must travel faster than the speed of light (not possible according to Einstein) would experience such a shift and could therefore be, during his travels, everywhere at the same time, and see past, present, and future (D&C 38:2; 88:41; 130:6-7). Using the Lawrence-Fitzgerald transformation formula (intended to explain how much distance equates to how much time & vice-versa), Cook noted that the 1,000 years of a Kolob day came to 18 cm., a handspan. He discussed this in his 1967 book, Science and Mormonism.
John A. Tvedtnes
Thanks for the note about Dr. Cook and relativity. Relativity theory is indeed needed to describe many objects and events in the universe, such as the big bang, supernovas, black holes, neutron stars, and other phenomena where very high velocities and very values of gravity are involved. Indeed, relartivity has been invoked to show how the 15 billion years since the big bang can agree with the six days earthly days of creation, but this involves considerable extrapolation. I cannot see how this helps to solve the time difference of a thousand celestial years and a terrestrial day. Furthermore, phenomena in most stellar systems can be explained without recourse to relativity.
A better explanation is to suppose that Kolob is a rotating planet in orbit about a star, and its period of rotation (spin period) could be any value, including a thousand terrestrial years.
You misunderstood my comment. I was not referring to Einstein’s Theory of Relativity, but to his Special Theory of Relativity, which is tied to the Lawrence-Fitzgerald transforrmation formula. I was not suggesting that Kolob’s day wasn’t 1,000 earth years. I suggest you re-read my original posting and check on the ST and its assertion that time becomes distance and vice-versa as one approaches the speec of light. BTW, Kolob may not be a planet as we know them, since it is said to govern various planets. Nor is it, as many believe, the residence of God, but only “nigh unto the throne of God.”
Sorry if I misunderstood your original posting. Thanks for bringing the Cook work to our attention. You seem to imply that Cook has properly shown accord between a Kolobian day and a thousand terrestrail years by the special theory of relativity. If so, that is fine. However, there may also be a simpler way of obtaining agreement: by imaging that Kolob has a planet with the correct period. Of course, some speculation is involved in any case.
Pres. Packer teaches that the scriptures are like an onion with layer after layer of meaning. There is rarely only one correct interpretation of a scripture passage. Your simple explanation and Cook’s more esoteric one are likely both correct.
ASTROPHYSICS:
• Fac.2, Fig.1 The Celestial = the planet on which God resides.
• Fac.2, Fig.1; Abr. 3:2-4 Kolob = a star.
• Presumably, The Celestial orbits around Kolob (planets usually orbit stars) yet The Celestial is the frame of reference (about which Einstein had so much to say) from which Kolob (and by extension, all created things) measures its time and motion, not vice versa.
• Kolob, in relation to our planet, Earth, either
• rotates on its axis once in a 1,000 earth-years, or
• The Celestial revolves around Kolob once in a 1,000 earth-years (in context this seems the more likely; also given the use of the word “revolves”).
• God, being infinite and eternal, possesses infinite energy and according to relativity, would therefore be described (from our earthly frame of reference) as having no time and no distance (rather in accord with D&C 88:41).
• Starting at the center place, The Celestial, there is no time. Moving outward, time is reckoned ever faster (which according to relativity equates with less energy) as the distance from God or The Celestial increases.
• Fac.2, Fig.2,4 Oliblish = a star, which because of its proximity to The Celestial and Kolob, also shares Kolob’s measurement of time.
• Fac.2, Fig.5 Enish-go-on-dosh = our Sun, one of 15 planets/stars which are governed by Kolob. A thousand of our years is but a day on Kolob.
TYPOLOGY:
• Moses 6:63 All things bear witness of Christ.
• Fac.2, Fig.1; Abr. 3:2-3 Kolob = Christ because they, Kolob and Christ, are nearest unto the throne of God. Kolob is the first and the last—the first creation, the first in government (see Fac.2, Fig.5), the last in its time measurement.
• Fac.2, Fig.2,4 Oliblish = Michael (HEB = “one like unto God”) equal in its time measurement with that of Kolob.
• Fac.2, Fig.5 Enish-go-on-dosh = our Sun, which along with 15 other stars/planets is governed by Kolob. These 15 are representative of the First Presidency and Quorum of the Twelve.
• Fac.2, Fig.5 Kae-e-vanrash = the light of Christ, the power of God.
According to Einstein, there is a speed at which God could travel that would cause 1,000 years to us to appear as one day to Him. Specifically, that speed is 99.9999999992494% of the speed of light.
Of course, there is a speed at which the Kolobian day and one thousand terrestrial years are in accord. But what is the meaing of that unusual speed? Would you claim to have discovered thet speed of God? There are much simpler ways of achieving such an accord.
How does this relate to “Meted out the Heavens with the span”? Does the span then become 1/2 a degree as it is 1/2 a cubit or is the measure of a span perhaps 12 degrees from the tip of the thumb to the tip of the little finger?
Thanks for your comment. A span of the hand with outstretched arms covers appriximately 18 degrees from the tip of the thumb to the tip of the little finger, and this is indeed related to the cubit’s use as a measure of angle. For comparison, this is roughly the height of the constellation Orion. However in this chapter (Isaiah 40) the prophet is praising the majesty and power of God, and he may be speaking poetically rather than literally since he also asks. “who has measured the waters in the hollos of his hand?”.
A span of the hand, from the tip of the thumb to the tip of the little finger is apporximately 18 degrees. For comparison, this is about the height of the constellation Orion and slightly less than the length of the Big Dipper. You might try these in the sky.
Whether the comment of Isaiah 40 has a direct relevance to a cubit as a measure of angle, I do not know. If one extends the hand in a span with outstretched arm, the span from the tip of the thumb to the tip of the litte finger is about 18 degrees. By comparison, this is about the vertical height of Orion and nearly as large as the Big Dipper. However since Isaiah is here praising the power of God, his comment may be meant figuratively,