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Sagan, Stars and Grains of Sand

Monday, February 23, 2015 @ 02:02 PM
posted by Roger Price
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Pandora’s Cluster

Credit: NASA/JPL-Caltech

Who could look at the stars and yawn? Certainly not astronomer Carl Sagan.  Sagan, a serious scientist, popularized a journey though the universe just over a third of a century ago with his award winning TV series, Cosmos. To impress upon his viewers how many stars existed, Sagan would enthusiastically assert that there were “billions and billions” of them, stressing and drawing out the first syllable each time.

As he acknowledged at the outset, however, the “size and age of the Cosmos are beyond ordinary human understanding.” So, to try to make such an enormous quantity understandable, he said that “the total number of stars in the universe is larger than all the grains of sand on all the beaches of the planet Earth.” (Watch here; see also, Sagan, Cosmos (Random House 1980) at 4, 196.) It was a wonderful reference.

We may sense that there are a lot of stars in the sky, but with the naked eye it is hard to pinpoint and count them, even or maybe especially on a clear night. Sand is somewhat different. We can take a fistful of it at a beach, survey the area, think about the coast lines of the various continents, and then factor in countless interior beaches. Sagan says that our hand will hold about 10,000 grains of sand. (Cosmos, at 196.) Without help, we may not be able to do the math or know the result of the equation, but we can understand that the beaches hold an enormous number of grains of sand.

What Sagan did not say is that his two subjects, stars and sand, were invoked long ago in the Hebrew Bible as metaphors for abundance. They appear first in the book of Genesis, each separately and once together.

In the very first instance, God is assuring Abram that although he is of advanced age and without heirs, he will, nevertheless, have many descendants. “Look toward heaven and count the stars, if you are able to count them.  . . . So shall your offspring be.” (See Gen. 15:5.) Shortly later, we are told that Abram’s concubine Hagar has borne him a son, Ishmael, and not long after that Abram, now called Abraham, and his wife Sarah become the parents of Isaac. (See Gen. 16:1-16, 21:1-3.)

The second reference — the joint reference — follows Abraham’s test on the mountain where he goes with Isaac to present a burnt offering for God. According to the story, an angel of God calls to Abraham, stops the proceedings before the sacrifice of Isaac and relates God’s declaration: “I will bestow My blessing upon you and make your descendants as numerous as the stars of heaven and the sands on the seashore . . . .” (See Gen. 22:17.)

The third mention in Genesis arises in the context of Jacob meeting with his estranged brother Esau after many years. Here Jacob expresses his fear that Esau may kill him and his family and prays that God remember his prior promise which Jacob casts as follows: “Yet You have said, ‘I will deal bountifully with you and make your offspring as the sands of the sea, which are too numerous to count.’” (See Gen. 32:4-13.)

Of course, the authors of these biblical passages were exercising poetic license to make a point, partly social, partly political, partly theological. Each had seen the evening sky dotted with distant lights. Even if they could see no more than a few thousand points, such lights must have seemed to be beyond measure. The authors may even have been familiar with the eastern shores of the Mediterranean Sea along the north coast of Egypt or the western areas of Canaan. The numbers of grains of sand would also surely have seemed limitless. So the authors and the final editors of the text made sure to stress that each of the three prime patriarchs of the Jewish People was present to witness a divine promise of fertility and demographic strength.

Not surprisingly, the metaphors had rhetorical legs, especially at times of great social stress, as can be seen in other biblical invocations.

  • The setting for Hosea’s prophecy — the dissolution of the Northern Kingdom of Israel due to internal corruption and external military forces — is among the earliest of preserved writings of its kind. After expressing God’s disenchantment with the House of Israel, Hosea consoled with a prediction that the people of Israel and of the Southern Kingdom of Judah would be reunited: “The number of the people of Israel shall be like the sands of the sea, which cannot be measured and counted . . . .“ (See Hos. 2:1-2.)
  • The Northern Kingdom was destroyed by the Assyrians around 722 BCE, and a number of northerners did migrate south. But a century plus afterwards, the Kingdom of Judah came under attack by the Babylonians. As he sat in prison contemplating the destruction of Judah, Jeremiah revived the ancient metaphors and conveyed God’s assurance that the kingship of David’s family and the centrality of the priests would continue. “Like the host of heaven which cannot be counted, and the sand of the sea which cannot be measured, so will I multiply the offspring of my servant David, and of the Levites who minister to Me.” (See Jer. 33:1, 22.)
  • Still later, writing in the name of Isaiah, but centuries following the original prophet of that name, a second Isaiah chastised now exiled Judahites but also promised them that they will, through the success of God’s servant Cyrus, be free. He urged them to return from Babylonia to Judea and heed God’s commands. If they did, said Deutero-Isaiah in God’s name, then “your prosperity would be like a river, your triumph like the waves of the sea. Your offspring would be as many as the sand, their issue as many as its grains.” (See Is. 48:18-19.)

These words, must have been encouraging, as well as comforting, to those who first heard and later read them, and understood their roots in the tales of the patriarchs.

The authors of the Hebrew Bible would have be shocked to learn that today there are about six million Jews in modern Israel.  To them, 6,000,000 would seem to fulfill the ancient promises. Imagine their surprise if they learned that there are almost six million more Jews in a place called the United States of America, across a sea even greater than the great sea with which they may have been somewhat familiar.   Add to those communities other Jews in North America, South America, Africa, Asia, Australia and Europe and you have a world population of Jews totaling just under 14,000,000.

Perspective is important, however, and those 14,000,000 collectively do not exceed two-tenths of one per-cent of the planet’s more than 7,000,000,000 human inhabitants. Even if each and every person on Earth were Jewish, they still would not be as numerous as the stars in heaven or the grains of sand on the seashore.

The biblical authors did not know, and could not have known, how far their metaphor really reached. Nor could they reasonably have anticipated that even though those grains and stars are too numerous to count, there would  be efforts later to estimate the numbers involved.

Let’s start with sand. Conceptually, the problem is not too difficult, especially if you stick with the biblical formulation and exclude inland beaches. All you need to know is the volume of sand on the world’s coastal beaches and divide that number by the volume of an average grain of sand.

Sand particles, like the quartz grains that permeate the Mediterranean coast of Israel today, range between 0.05 and 2mm in diameter. For purposes of our calculation, a cubic millimeter of sand will serve as the volume of an average grain of sand.

The volume of sand on the world’s coastal beaches is a product of the length, width and depth of those beaches. The length of coasts can be determined reasonably well by modern technology, but not all coasts have beaches. Most estimates of the fraction of beach shore to coast range from about one-fifth to two-fifths. The length but especially the width of a beach varies throughout the day as tides ebb and flow. Naturally, the depth of the beach will then vary as well. One good effort to solve this problem was developed by physics professor Howard McAllister of the University of Hawaii, based on work done by Judaism and Science contributor Ludwik Kowalski. Prof. McAllister calculated the total length of the earth’s beach shores at around 50,000 kilometers (about 31,000 miles) and set the average width at 30 meters (just under 100 feet) and the average depth at 5 meters (just over 16 feet).

If you accept these parameters, then the number of grains of sand on the beaches of the seashores of the world total 7.5 x 1018, or 7.5 billion billion. Vary the coastal length, the percentage of beach shore, or the average width or the average depth and the estimated volume of sand will change. Of course, while this is educated conjecture, it is still conjecture. Another approach puts the number of grains at 5 billion billion, including those on inland beaches. Either way, the result is more than a few sextillion (a billion billion) grains of sand.

Calculating the number of stars in the sky presents different challenges than counting the grains of sand on the Earth’s seashores. Instead of having a reasonably fixed parameter with which to work, like the number of miles of seashore, the stars are set in a universe which is not only expanding, but expanding at an accelerated rate.

On the other hand, we are not concerned with the size of an average star, in the way we were with an average grain of sand. We will include the yellow stars like our Sun, but also all of the stars along the spectrum from red to blue, and even brown and white stars, too.  And we will include stars smaller than our Sun, the dwarfs and the neutron stars, and stars larger, the giants, and much larger, the supergiants.

The practical problem is that we can only include stars that we can see and we can only see a star if the radiation it emits, in the form of visible light or other electromagnetic waves, reaches our measuring devices. Even with NASA’s relatively new Hubble Space Telescope and the other, newer space observatories, our vision is limited to a discrete portion of the universe.

Moreover, some of what we do and do not detect presents a false picture. Our universe is about 13.7 billion years old. A few years ago, Hubble received light from a galaxy 13.2 billion light years way. We do not know, of course, and cannot know, if that star system has survived. We may be seeing stars that no longer exist. Conversely, stars are being born all the time. The light from some of these young stars may not have had time to reach us yet. If it takes 5 billion more years to get here, we will never see it as our Sun will die by then, and take us with it.

What we can say is that our Sun is one of over one hundred billion stars in its galaxy, the Milky Way. The star count is made by estimating the mass of the galaxy. Adjustments are then made to account for the fact that most of the stars in our galaxy are red dwarfs, each of which is smaller than one solar mass, the mass of our Sun. Some estimate the total number of stars in our galaxy to be 400 billion. [Ed. update: For more on the Milky Way, see “What is the Milky Way“]

As Hubble and other observatories probe deeper and deeper into space, they see farther and farther back in time. Astronomers now believe that there may be 100 to 500 billion galaxies in the known universe. The majority of these galaxies, including the Andromeda galaxy located only 2.5 light years  (15 trillion miles) from us, are shaped in a spiral like the Milky Way. But not all are. Some, like the much more distant M13 galaxy found in the constellation Hercules, are rounder and are known as globular clusters. The most massive galaxies, the largest known one of which is the IC 1101, may be flat or round but are more elliptical.

Similarly, the number of stars may vary greatly from galaxy to galaxy. For instance, according to the Jet Propulsion Laboratory, Andromeda may contain a trillion stars. It is far from the largest galaxy, however. IC 1101, a billion light years away, may hold a hundred trillion stars. Conversely, dwarf galaxy may hold just one to ten million stars. Consequently, a reasonable range of the possible number of stars in the known universe is quite large and extends from 10 billion billion to 200 billion billion.

Even at the low end of the estimated range, the number of stars seems to exceed the number of sands of grain on the seashores of the Earth, and the inland beaches, too. (For a different set of numbers, but with the same relative results, see here.) So Carl Sagan was right.

Now some folks may conclude from all of this that the Hebrew Bible has been proven, once again, to be a faulty guide. The reported promise from God that the number of descendants of the Jewish patriarchs would exceed the number of stars in heaven or grains of sand on the seashore has not come true. Moreover, science through Sagan and others has shown definitively that the promise will never be fulfilled.

The literalists would be literally correct, of course.  But, as they often do, they miss the greater messages of biblical literature. First, the recorders of the patriarchal legends and the prophets cited above were not seeking to make a scientific point, or a mathematical statement about demography. They were, rather, expressing their faith in their social and political future. They were asserting, even as Americans echoed a similar assertion over two millennia later, a mixture of confidence and hope in a doctrine of manifest destiny, a conviction that the descendants of Abraham, as a people and a nation, had a mission to fulfill and would, in time, fulfill it. The belief was surely related to a belief in God, but it was grounded in quite natural human concerns and desires.

Second, in focusing on the number of stars or grains, the literalists would, to mix the metaphor, miss the forest for the trees. The biblical authors were not concerned with tallying the precise number of stars or grains. They did not care whether the sums were in the millions or billions or, as it turns out, the sextillions. Indeed, they had no concept of such numbers. What they thought, and correctly so at the time and to a considerable degree even today, was that the numbers were so huge as to be uncountable.  And they were expressing their awe at the wonder of it all.

Here Sagan and the authors of biblical authors are on the same page. For all of his disdain at the mythology of religion, and especially in instances which he saw as the intrusion of religion on the turf of science, in 1990 Sagan joined in an open letter which acknowledged: “As scientists, many of us have had profound experiences of awe and reverence before the universe.” Five years later, and just one year before he died, Sagan contended that “science is not only compatible with spirituality; it is a profound source of spirituality.” Summarizing Sagan’s approach to the sacred, Dartmouth religion professor Nancy Frankenberry has written that he was “utterly imbued with  . . . a marvelous sense of belonging to a planet, a galaxy, a cosmos that inspires devotion as much as discovery.” (See Frankenberry, The Faith of Scientists (Princeton 2008), at 222-24.)

So we should not be surprised to learn that Sagan, like the author of the second creation story in Genesis, addressed the same, age old questions asking who we are, where we came from (and when) and what our place is in the universe.   That biblical author described the first human as being fashioned out of the dust of the ground. In the Hebrew text, the connection of humanity to the soil is made starkly clear by the use of a pun: “ha-adam” (the human) is formed from “ha-adamah” (the ground). (See Gen. 2:7.)

What that author did not realize was that the dust of the Earth was stardust, forged in the furnaces of untold stars, spewed into space, moved along with intersteller winds and, ultimately, bound together on our home planet. Sagan, with such knowledge, wrote that humankind is “the local embodiment of a Cosmos grown to self-awareness.”  We are, he said, “starstuff pondering stars; organized assemblages of ten billion billion billion atoms considering he evolution of atoms; tracing the long journey by which, here at least, consciousness arose.”  (See Cosmos, above, at 345.)

The late poet Aaron Zeitlin once wrote:

Praise Me, says God, and I will know that you love Me.

Curse Me, says God, and I will know that you love Me.

Praise Me or curse Me, and I will know that you love Me.  . . .

But if you sit fenced off in your apathy, says God,

If you sit entrenched in, “I couldn’t care less,” says God,

If you look at the stars and yawn, . . .

Then I created you in vain, says God.

Both Carl Sagan and the authors of the Hebrew Bible would ask the same question: How can you look at the stars and yawn?

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2 Responses to “Sagan, Stars and Grains of Sand”

  1. Bob Magrisso says:

    “What they thought, and correctly so at the time and to a considerable degree even today, was that the numbers were so huge as to be uncountable. And they were expressing their awe at the wonder of it all.”

    I really appreciate your bringing together the two world views of the Torah and modern science, in this blog post, and ending in “awe and wonder”. I might add mystery as well.

    The more we have learned through science, the greater, vaster and more magnificent Creation appears. The insights from the ancient sages expressed through these metaphors have even more power to move us when we look into what has been discovered in the intervening thousands of years.

    At the heart of it all, is still the great Mystery. Science recognizes the Unknown and mystery and, at best, so does Judaism.

  2. Daniel Shoe says:

    A billion billion is a quintillion, not a sextillion. A quintillion is 10^18 and a sextillion is 10^21.

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