Scientific Perspectives on the Scriptures: Genesis Day Two – Expansion
Summary: The first chapter of Genesis reveals remarkable insights into the origins of the universe. Scientific discoveries are only today beginning to reveal the extent of those insights. The key to understanding Genesis is to recognize the methodology employed by its author/s. Applying that methodology, early Jewish scholars like Nahmanides (1194 – 1270 AD) accurately described cosmic phenomena which scientists now theorize were crucial for the creation of the universe. Day Two addresses two such phenomena – expansion, and the density variations of matter and energy in the early universe. Like modern cosmologists, Genesis recognized that these two cosmic phenomena were a prerequisite for the creation of heavier elements in the stars, and ultimately life itself. The analysis in these articles may not accord with current scientific, theological or philosophical interpretations of science and the Scriptures, but to ignore or dismiss it, without further investigation or reflection, would be a disservice to our understanding of our cosmic origins and our cosmic destiny.
Before addressing Day Two, we should recall the methodology employed by the author/s of Genesis in Day One.
Day One starts with “the heaven and the earth”, which are then re-described collectively as “the waters”. The “waters” are then ‘converted’ into “light”. According to science, this transformation occurred following the Big Bang, when matter and antimatter interacted to create photons of light. But because there was a slight excess of matter over antimatter, some matter was not converted into light. That excess matter accounts for the universe we see all around us. Genesis refers to this excess matter as “the darkness”, which was separated from the “light”.
The same methodology is applied in Day Two.
At the start of Day Two, “light and darkness” are collectively re-described as “the waters” again. And as in Day One, water symbolizes life-giving properties; in this case, the life-giving properties of “light and darkness”.
Accordingly, Day Two starts with this:
“And God said, Let there be a firmament in the midst of the waters, and let it divide the waters from the waters.” Genesis 1: 6
The first thing to establish in this verse is what is meant by the word “firmament”. It is a new concept that does not feature in Day One. In my King James Version of the Bible, the reference relating to the word “firmament” says “Heb. [Hebrew] expansion”. I never paid much attention to it until I started researching the science in more detail for my latest book, A ‘Final Theory’ of God. The reference to “expansion” then began to make a lot more sense.
With that more accurate translation, verse 6 reads, “And God said, Let there be an EXPANSION in the midst of the waters …” This verse then takes on a very different meaning.
But what did ‘expansion’ mean in the original Hebrew? The Hebrew word is raqiya`, which loosely translated, means to hammer out something small into something large. But it still seemed highly improbable that it could mean expansion in the scientific sense, although it did seem to be an unusual word to use. There has been a lot of debate about whether the word refers to the scientific concept of expansion and, of course, the answer depends on the objective of those making the argument.
But there is a more reliable way to determine what it means. And that is to see what Jewish scholars of the Torah thought it meant before there was any inkling in the scientific community about the importance of expansion in the ‘creation’ of the universe and life. And for that we need to return to Nahmanides (1194 – 1270 AD), to whom we referred in Day One.
We should remind ourselves of what Nahmanides said in his commentary on Day One:
And know that the heavens and all that is in them are one material, and the earth and all that is within it is [another] material; and the Holy One, blessed be He, created both of them from nothing – and the two of them alone were created, and everything was made from them.
This is what Nahmanides then says about “the firmament” in Day Two:
He [God] said about the material that existed at the beginning when He created it from nothing, that it should be stretched out like a tent in the midst of the water and separate the waters from the waters.”
Since Nahmanides lived some 700 years before the scientific concept of expansion was proposed by Alan Guth and Henry Tye in the late 1970’s, he could hardly have been trying to fit his translation of Genesis to science. For all the debate about what the word means, this evidence is by far the most reliable and compelling.
What are “the waters”?
With that in mind, we can now consider what constituted “the waters”. As we have already seen, the word is used as a collective description of “light and darkness”, which includes visible matter and energy, as well as dark matter. Of visible energy, it includes energy in the form of photons; and of visible matter, it comprises fundamental particles like electrons, protons and neutrons, the latter two of which are composed of 3 quarks each. Although scientists still know little about dark matter, they do know that it has an effect on visible matter and energy.
Of the visible matter that was ‘created’ by the Big Bang, the electrons, protons and neutrons combined to form the first basic elements (atoms). Greene says this: “Our most refined theories of the origin of the universe – our most refined cosmological theories – tell us that by the time the universe was a couple of minutes old, it was filled with a nearly uniform hot gas composed of roughly 75 percent hydrogen, 23 percent helium, and small amounts of deuterium and lithium.”
Weinberg says that the Big Bang theory enables scientists to calculate that “the matter formed in the first few minutes of the universe was about three-quarters hydrogen and one-quarter helium, with only a trace of other elements, chiefly very light ones like lithium. This is the raw material out of which heavier elements were later formed in stars.”
Martin Rees adds that, at this stage, the universe would have been “dense and opaque, like the glowing gas inside a star.”
Michio Kaku explains why that should be. He says that “for years after the big bang, the temperature of the universe was so hot that anytime an atom formed, it would be ripped apart; hence there were many free electrons that could scatter light. Thus, the universe was opaque, not transparent. Any light beam moving in this super-hot universe would be absorbed after travelling a short distance, so the universe looked cloudy.”
This was the state of the universe at the end of Day One, and the start of Day Two. There were “the waters” – “light and darkness” – which were called “Day” and “Night”. As we have already noted, this naming is to highlight permanent changes to the state of the universe as the original matter and energy are ‘processed’ through the first three ‘days’ (this naming only appears in the first three days).
Day Two tells us that it is into this state of the early universe, described as “the waters”, that God is said to have inserted an “expansion” to separate some parts of “the waters” from other parts of “the waters” – “to divide the waters from the waters.”
When God is said to put this plan into effect, this is what happens:
“And God made the firmament (expansion,) and divided the waters which were under the firmament (expansion) from the waters which were above the firmament (expansion): and it was so.” Genesis 1:7
The underlined emphasis of the words “were” are the original, suggesting a pre-existing state in which certain parts of “the waters” were in different places – “under” or “above”. That would have been a consequence of what happened in Day One. And Day One was about inflationary cosmology.
Greene identifies one specific consequence of inflationary cosmology which was crucial to the formation of the universe as we see it today.
Why some of “the waters” were “under”, and others “above”, the “Firmament”
According to Greene, “the initial nonuniformity that ultimately resulted in the formation of stars and galaxies came from quantum mechanics.” Like particles, fields are also subject to quantum phenomena, so the “rate of change” of a field is not uniform but “will undulate up or down” at various speeds, or “assume a strange mixture of many different rates of change, and hence its value will undergo a frenzied, fuzzy, random jitter.” This means that the “amount of energy in one location would have been a bit different to what it was in another.”
These small differences in the quantum world of the pre-inflationary universe were then amplified by inflationary expansion, causing certain areas of the expanding universe to be more ‘dense’ in particles and energy than others. This has been confirmed by measurements of the temperature differences of microwave photons arriving from space. Greene says that “observations have shown that … tiny temperature differences fill out a particular pattern on the sky …,” confirming slight differences in the density of matter and energy in different locations in the universe. And these variations were “set down nearly 14 billion years ago … [and arose] from quantum uncertainty.”
Greene attributes these variations to the inflaton (Higgs) field, to which we referred in Day One. Scientists believe that this field was the engine for inflationary expansion in the earliest moments of the universe. According to Greene, the inflaton field “reached the value of lowest energy at different places at slightly different moments. In turn, inflationary expansion shut off at slightly different times at different locations in space, so that the amount of spatial expansion at different locations varied slightly …”
This resulted in different densities of matter and energy in different regions of space, or more accurately, the expanding universe. According to Rees, “slightly overdense regions, expanding slower than average, were destined to become galaxies and clusters; others, slightly underdense, were destined to become voids.”
It seems then, that describing some of ‘the waters’ as being in different places – “under” or “above” – in relation to the “expansion”, is quite accurate, according to inflationary cosmology. Without it, the universe as we know it, and life itself, would not exist.
Why no mention in Day Two of the words “And God saw …”?
We should recall that there is a subtle but crucial difference between the explanation of what takes place on Day Two, and what takes place on all the other ‘days’. After God is said to have ‘instructed’ that there be an “expansion”, He then “made the expansion”; but there is no ‘observation’; that is, the words “And God saw …” are absent from Day Two.
However, if Greene is right about how expansion works in scientific terms, then it seems that the author/s of Genesis must have had some understanding of the need and effect of expansion in creating the universe as we know it.
Nahmanides certainly recognized the omission, and identified a reason for it.
He asks the question, “Why does it not say, ‘And God saw that it was good,’ on the second [day]?” And he answers, “Since the work of the water was not finished – therefore, it is written twice on the third [day]; once for the work of the water and once for the work of the day.”
The question then is, what “work” did “the waters” still have to do, and why was expansion important to that work?
As we have already seen, by the beginning of Day Two, the Big Bang had only created the lighter elements of hydrogen, helium, deuterium and lithium. The Big Bang did not generate sufficient heat to produce the heavier elements needed to create the universe and life as we know it. That is because “… elements with 5 and 8 neutrons and protons are extremely unstable and hence cannot act as a ‘bridge’ to create elements that have a greater number of protons and neutrons.”
That required a different cosmic phenomenon.
In the 1950’s, Fred Hoyle, an English physicist at Cambridge University, had a moment of ‘insight’ which went some way to resolving how the heavier elements could have been created. As Kaku says, “in a stroke of genius, Hoyle realized that IF there were a previously unnoticed unstable form of carbon, created out of three helium nuclei, it might last just long enough to act as a ‘bridge,’ allowing for the creation of higher elements. … When this unstable form of carbon was actually found, it brilliantly demonstrated that nucleosynthesis could take place in the stars, rather than the big bang.”
However, not all stars are heavy enough to produce the heat necessary to create the heavier elements. That would require heavier stars with greater gravity. According to Rees, such stars can reach a “billion degrees” and thus “release further energy via the build-up of carbon (six protons), and by a chain of transmutations into progressively heavier nuclei.” But once we get to iron, which has the most “tightly bound” nucleus, “energy must be added” to create the even heavier elements beyond iron. And so, says Rees, “a star therefore faces an energy crisis when its core is transmuted into iron … [and] …the consequences are dramatic.”
The intense gravity causes the core of the star to implode which “releases enough energy to blow off the overlying material in a colossal explosion – creating a supernova.”
The supernova then ‘fertilizes’, so to speak, the universe by blasting its mix of elements into space. “The debris thrown back into space contains this mix of elements. Oxygen is the most common, followed by carbon, nitrogen, silicon and iron. The calculated proportions … [depend on the] … types of stars and the various evolutionary paths they take …”
This mix of elements was a pre-requisite for life. As Kaku says, “our true ‘mother’ sun was actually an unnamed star or collection of stars that died billions of years ago in a supernova, which then seeded nearby nebulae with the higher elements beyond iron that make up our body.”
Calibrating Cosmic Forces for the Creation of Life
However, all this chemistry in the stars depends on a precise balance between the expansion force and the density variations of matter and energy in space, which Genesis symbolizes by referring to some of “the waters” being “under the expansion” and others being “over the expansion”.
But for this balance to be effective in creating a universe capable of spawning and sustaining life, certain cosmic forces and factors also had to be calibrated to very precise values. In his book Just Six Numbers, Martin Rees identifies six numbers whose values had to be “finely tuned” for our universe to exist in its present form. And according to Rees, these numbers were “imprinted into [the universe] at the time of the initial Big Bang.”
In Nahmanides’ terminology, the “work” that “the waters” still had to do required that the quantities and properties of the matter and energy created in Day One had to be precisely calibrated for the “expansion” force to finish the “work”.
- First, the ‘creation’ of “light and darkness” in Day One resulted in the creation of fundamental particles with the ability to bind together to form atoms (elements). For that to happen, the number ε had to be tuned to the correct value. This number, “whose value is 0.007, defines how firmly atomic nuclei bind together and how all the atoms on earth were made. … If ε were 0.006 or 0.008, we could not exist.”
The number ε is important in relation to expansion, because it is the effect of expansion, in conjunction with the ‘balancing’ of the other numbers, that enables the first atoms (elements) to build more complex and heavier atoms. But again, for expansion to bring that about, “the waters” needed different densities in different locations in the expanding universe, otherwise the ‘fine tuning’ of the number ε would have been powerless to create heavier elements.
- The ‘creation’ of “light and darkness” also resulted in the ‘fine tuning’ of another of Rees’ numbers. That number is N, which “measures the strength of the electrical forces that hold atoms together, divided by the force of gravitybetween them.” However, it is only when the density discrepancies in different parts of the expanding universe are subjected to the effects of expansion that the ‘fine tuning’ of N can finish its “work” by creating heavier elements.
- Thirdly, the transformation of initial matter and space, which were “without form, and void,” into “light and darkness,” also produced three dimensions, and the expansion (motion) of matter and energy through space as a consequence of that transformation, created the concept of time, which Genesis refers to as “the evening and the morning.” That satisfies another of Rees’ six numbers, the number D, which “… is the number of spatial dimensions in our world, D, and equals three. Life couldn’t exist if D were two or four. Time is a fourth dimension … [which] … has a built in arrow: we move only towards the future.” Expansion is crucial to ensure that time continues to move towards the future.
The next three of Rees’ numbers are particularly relevant to Day Two. They relate to the effect of expansion on the density variations of matter and energy. Rees explains it this way: “The starting point is an expanding universe, described by Ω, λ and Q. The outcome depends sensitively on these three key numbers, imprinted (we are not sure how) in the very early universe.”
- The first is Ω (omega). This number relates to the density of matter in the universe (both visible matter and dark matter). If the density was too great in relation to the expansion force and gravity, the early universe would have collapsed in on itself. If the density in relation to expansion and gravity was too sparse, the universe would have expanded at such a quick rate that no galaxies and stars could have formed, and the universe would have become a dark, empty place. Given the counterforces of expansion and gravity, scientists have calculated a critical density within which the actual density should fall for the universe to have emerged in the form we see it. Rees explains that “the ratio of the actual density to the critical density is a crucial number. Cosmologists denote it by the Greek letter Ω (omega). The fate of the universe depends on whether or not Ω exceeds one.” But Rees also notes that Ω must have been “tuned amazingly close to unity in the early universe.” This means that at the start of Day Two “the waters” contained exactly the right density of matter necessary to create the universe, and thus life. But in order to do so, a precisely calibrated rate of expansion was required to finish the “work”. As Rees says, “only a ‘finely tuned’ expansion rate can provide the arena for these processes to unfold.”
- The rate of expansion is denoted by λ (lambda). It is the weakest force in the universe, and the most mysterious. But it is a crucial force. It acts as a counter-force to gravity, thus ensuring that gravity doesn’t cause all the matter and energy in the universe to collapse in on itself. However, for expansion to ensure that “the waters” could finish their “work”, it had to be “finely tuned”. But it also required one further cosmic phenomenon to be precisely calibrated – the density variations of matter and energy.
- And that brings us to the last of Rees’ six numbers, the number Q. This number is a measure of the density differences which are the “initial irregularities [that] ‘seed’ the growth of structure[s]” like stars and galaxies. According to Rees, “the number Q measures the amplitude of these irregularities or ‘ripples’. Why Q is about 10-5 is still a mystery.” Genesis symbolizes these density variations by describing some of “the waters” as being “under the expansion” and others being “above the expansion.” These density differences in “the waters” were crucial for expansion to finish the “work”. And that “work” was to prepare the early universe for the creation of heavier elements in stars. As Rees says, “slightly overdense regions, expanding slower than average, were destined to become galaxies and clusters; others, slightly underdense, were destined to become voids.”
How Expansion enables “the waters” to do its “work”
Greene explains the process as follows: “as the universe expands, matter and radiation lose energy to gravity while an inflaton field gains energy from gravity.” The “total energy carried by ordinary particles of matter and radiation drops because it is continually transferred to gravity as the universe expands. … gravity depletes the energy in fast moving particles of matter and radiation as space swells.” On the other hand, “a uniform inflaton field exerts a negative pressure within an expanding universe. … [thus] the total energy embodied in the inflaton field increases as the universe expands because it extracts energy from gravity.”
However, this ‘exchange’ of energy away from gravity, and to expansion, is dependent on very precise variations of the matter density in the expanding universe. If the density of energy and matter were absolutely uniform, this exchange would be uniform, and no stars and galaxies could form. If the densities of matter and energy in certain regions of space were too great, expansion would cause a greater transfer of energy to gravity than in less dense regions, and that increased gravity would attract other nearby matter, thus preventing the formation of galaxies and stars with the right density to be the engines for creating heavier elements.
As Rees says, “the dominant gravitational stuff is … ‘dark matter’ … [which is] … influenced by gravity. … Swarms of dark matter on subgalactic scales condense out first; these merge into galactic-mass objects, which then form clusters.”
But this clustering of dark matter also needs atoms. According to Rees, the atoms “ride along passively [on the dark matter], constituting a dilute gas that ‘feels’ the dark matter’s gravity.” And this ‘gas’ of atoms “exerts a pressure as well … [which] … prevents the gas from being pulled by gravity into very small ‘clumps’ of dark matter.”
This process of matter ‘clustering’ into galaxies and stars was playing out across the universe; and it was a consequence of expansion amplifying the density variations in matter and energy. It was the process that would create the conditions for the ‘manufacture’ of heavier elements, the elements needed to create life.
That was the “work” that “the waters” had to finish. And that is why there is no observation in Day Two, hence the omission of the words “And God saw …”.
Manipulating probabilities – “And God made the firmament” Genesis 1:7
For our consideration of the lack of an ‘observation’ in Day Two, it is important to understand, as Rees says, that “[w]hen the universe was a million years old, everything was still expanding almost uniformly.”
However, “if our universe had started off completely smooth and uniform, it would have remained so throughout its expansion … It would [have been] cold and dull: no galaxies, therefore no stars, no periodic table, no complexity, certainly no people.”
The expansion force needed something to bring together all the other forces (numbers) that had been ‘imprinted’ on Day One. And that something was the slight density differences of matter and energy in space. As we have seen, Genesis describes these density differences as some of “the waters” being “under the expansion”, and others being “above the expansion”.
Scientists calculate the length of the events recorded in Day One as about 300,000 years of Earth time. That would have meant there was a near uniform density of matter, energy and forces throughout the universe at the start of Day Two.
However, at about this time, the universe began to cool from the extreme temperatures following the Big Bang. Kaku explains it this way: “After 380,000 years … the temperature dropped to 3,000 degrees. Below that temperature, atoms were no longer ripped apart … [and] … stable atoms could form, and light beams could now travel for light-years without being absorbed.”
Rees says that “after half a million years of expansion, the temperature dropped to around 3,000 degrees … As the universe cooled further, it literally entered a dark age … [which] persisted until the first protogalaxies formed and lit it up again.”
According to Greene, in the “early history of the universe, matter was spread uniformly throughout space.” Furthermore, “although attractive gravity causes clumps of matter and creases of space to grow, repulsive gravity (expansion) does the opposite: it causes them to diminish, leading to an ever smoother, ever more uniform outcome.”
At this point, we should remind ourselves of what Kaku said regarding quantum theory: “The quantum theory is based on the idea that there is a probability that all possible events … might occur. This, in turn, lies at the heart of inflationary universe theory …”
However, Kaku also acknowledges that “physicists realize that if we could somehow control these probabilities” then anything “is possible.”
The description of Day Two then starts to make sense. The scientific consensus is that the matter and energy density in the early universe was almost perfectly uniform. Gravity and expansion were evenly balanced, thus tending to “an ever smoother, ever more uniform outcome.”
However, since there is a probability that all “possible events … might occur”, at this early stage of the universe there must have been a probability that the almost perfect uniformity could have become perfectly uniform, in terms of both matter and energy density, as well as the balance of the gravitational and expansionary forces. That would have meant that no universe as we know it would have formed, and thus no life.
The use of the words “And God said, Let there be an expansion …” suggests a manipulation of probabilities. It suggests the exclusion of the probability of perfect uniformity, or the probability of under-density or over-density. And that is important, because otherwise, as Rees says, either the “universe would be inert and structureless”, or “it would have been a violent place in which no stars or solar systems could survive …”
Day Two was a bridge to Day Three. Therefore, no reference to “And God saw …” was necessary. The slight density variations which existed at the start of Day Two, symbolized by “the waters” being in different locations – “under” or “above”, needed only to be amplified by the effects of a precisely calibrated rate of expansion to prepare the early universe for the next intended steps in constructing a universe capable of spawning and sustaining life. The important thing was to ensure that other probabilities did not intervene to disturb that ‘fine-tuning’.
The omission of the words “And God saw that it was good” suggests that the author/s of Genesis understood that, as did Nahmanides.
“And God called the firmament Heaven.” Genesis 1:8
Day Two concludes its account of the division of “the waters” with this: “And God called the firmament Heaven.” As we have already noted, this naming at the end of the “day” (always with a capital letter), signifies a permanent change from the state of the universe at the start of the ‘day’. At the start of Day Two there were “the waters” into which was inserted an “expansion”. At the end of Day Two the “expansion” had divided “the waters”, resulting in what God is said to call “Heaven”.
We should now recall what Rees said about the effect of the density differences in matter and energy in different parts of space: “slightly overdense regions, expanding slower than average, were destined to become galaxies and clusters; others, slightly underdense, were destined to become voids’.
Genesis calls these voids “Heaven” – those areas of space that were left ‘free’ of matter. When we look up at the night sky, it is those areas that are not lit up by stars. As Greene says, “according to inflation, the more than 100 billion galaxies, sparkling throughout space like heavenly diamonds, are nothing but quantum mechanics writ large across the sky.”
“And the evening and the morning were the second day.” Genesis 1:8
Day Two ends at just about the time Rees says the “first protogalaxies formed” which lit up the universe again following the “dark age”. According to Rees’ depiction of the time-line of the universe, that would have been about 1 billion years after the Big Bang. Thus “the evening and the morning” of Day Two were approximately one billion years, less the 300,000 years for Day One.
However, as already noted, it was important that the effect of the “expansion” up to this time should not yet be made “irreversible”, hence there is no reference to “And God saw …” in Day Two. That only comes halfway through Day Three. In the language of the delayed-choice experiments, the effect of the density differences should not be “fully settled” by an observation (measurement) until all the elements had been created, ‘fertilizing’ the universe with their life-creating, and life-sustaining, properties.
That leaves just one final point to make regarding Day Two. What makes the Genesis account of “expansion” so remarkable is that it does separate, so to speak, the initial “inflation” in Day One, from the “expansion” which is said to start in Day Two. And that perfectly corresponds to Rees’ description of the process up to this point: “The fierce repulsion that drove inflation must have switched off, allowing the universe, having by then enlarged enough to encompass everything that we now see, to embark on its more leisurely expansion.”
The expansion which divides “the waters” causes matter and energy to concentrate into dense clusters, ready to form stars, from which the heavier elements necessary for the creation of life can be ‘manufactured’.
The expanding universe is thus ready for its next major transformation.
The next article will address the even more remarkable insights in Day Three.
Joseph BH McMillan. This article is an abridged extract from A ‘Final Theory’ of God.
Copyright © Joseph BH McMillan 2017 All Rights Reserved
 I make no judgment on the author or authors of Genesis.
 The Big Bang also created dark matter, but for the sake of simplicity, I have not addressed it here, although it is addressed in the book.
 Nahmanides, Commentary on Genesis 1:1 at Para 3 . Retrieved from http://www.sefaria.org/Ramban_on_Genesis.1.1.3?lang=en
 Nahmanides, Commentary of Genesis 1:6, Retrieved from http://www.sefaria.org/Ramban_on_Genesis.1.6.1?lang=en
 Greene, Brian. The Fabric of the Cosmos, Penguin, London, 2005 (paperback), page 171 (emphasis in bold is Greene’s).
 Weinberg, Steven. Dreams of a Final Theory, Vintage, New York, 1994 (paperback), pages 33 – 34.
 Rees, Martin. Just Six Numbers, Phoenix, London, 1999 (paperback), page 119.
 Kaku, Michio. Parallel Worlds, Penguin, London, 2006 (paperback), pages 57 – 58.
 Greene, page 305.
 Greene, page 306.
 Greene, page 306.
 Greene, page 311.
 Greene, page 311 – 312.
 Greene, page 307 – my emphasis in bold.
 Rees, page 119.
 Nahmanides, Commentary on Genesis 1:11. Retrieved from http://www.sefaria.org/Ramban_on_Genesis.1.11.1?lang=en
 Kaku, page 56.
 Kaku, page 62 – emphasis on IF is mine.
 Rees, page 50.
 Rees, page 50.
 Rees, page 50.
 Rees, page 50.
 Kaku, page 67.
 Rees, page 1.
 Rees, page 2.
 Rees, page 2.
 Rees, page 3.
 Rees, page 82.
 Rees, page 100
 Rees, page 99.
 Rees, page 127.
 Rees, page 128.
 Rees, page 119.
 Greene, page 312.
 Greene, page 311 – bold emphasis is Greene’s.
 Greene, pages 311 to 322 – bold emphasis is Greene’s.
 Rees, page 119 – 120.
 Rees, page 122.
 Rees, page 122.
 Rees, page 121.
 Rees, page 117.
 Kaku, page 58.
 Rees, page 119.
 Greene, page 314.
 Greene, page 315.
 Kaku, page 147.
 Kaku, pages 147 and 146 respectively.
 Rees, page 3.
 Genesis 1: 7.
 Rees, page 119 – emphasis in bold is mine.
 Greene, page 308.
 Rees, page 119.
 Rees, illustration at page 132.
 Rees, page 139 – emphasis in bold is mine.