There can be neither works nor words without number. We can understand how man can act and speak without design or significance, but we cannot imagine that the great and infinite Creator and Redeemer could either work or speak without both His words and His works being absolutely perfect in every particular.
"As for God His WAY is perfect" (Psa 18:30). "The Law of the LORD is perfect" (Psa 19:7). They are both perfect in power, perfect in holiness and righteousness, perfect in design, perfect in execution, perfect in their object and end, and, may we not say, perfect in number.
"The LORD is righteous in all His ways: and holy in all His works" (Psa 145:17).
All His works were (and are) done, and all His words were spoken and written, in the right way, at the right time, in the right order, and in the right number. "He telleth the number of the stars" (Psa 147:4). He "bringeth out their host by number" (Isa 40:26). "He weigheth the waters by measure" (Job 28:25).
We may, therefore, say with David: "I meditate on all Thy works; I muse on the work of Thy hands" (Psa 143:5).
In all the works of God we find not only what we call "Law," and a Law-maker, but we observe a Law enforcer. We speak of laws, but they are nothing in themselves. They have no being; they possess no power; they cannot make themselves, or carry themselves out. What we mean when we speak of law in nature is simply this: God in action; God not merely giving or making laws, but carrying them out and enforcing them.
As He is perfect, so His works and His words also must be perfect. And when we see number used not by chance, but by design; not at haphazard, but with significance; then we see not merely so many works and words, but the Living God working and speaking.
In this first part of our subject we are to speak only of design in the use of number; and in the second part, of significance. In this first chapter we will confine our thoughts to design as it is seen in the works of God; and in the second, as it is seen in the Word of God.
When we see the same design in each; the same laws at work; the same mysterious principles being carried out in each, the conviction is overwhelming that we have the same great Designer, the same Author; and we see the same Hand, the same seal stamped on all His works, and the same signature or autograph, as it were, upon every page of His Word. And that, not an autograph which may be torn off or obliterated, but indelible, like the water-mark in the paper; so impressed upon and interwoven with it that no power on earth can blot it out.
Here we see number displayed in a remarkable manner. The 12 signs of the Zodiac, each with three constellations, making 36 in all, which together with the 12 signs make a total of 48. There must be a reason, therefore, why the number 12 should thus pervade the heavens. Why should 12 be the predominating factor? Why should it not be 11, or 13, or 7, or 20?
Because 12 is one of the four perfect numbers, the number of governmental perfection; hence it is associated with the rule of the heavens, for the sun is given "to rule the day," and the moon "to govern the night." The significance of this, however, must be deferred till we come to consider the number "twelve" under this head. It is enough for us now to notice the fact here, upon the threshold of our subject, that we have one common measure, or factor, which is seen in the 12 signs of the Zodiac, the 36 (3x12) constellations,* the total 48 (4x12); the 360 (12x30) degrees, into which the great circle of the heavens is divided. No one can tell us why the number of degrees was first fixed at 360. It has come down to us from ancient times, and is used universally without a question.** And it is this division of the Zodiac which gives us the 12 months of the Zodiacal year. This is called also the Prophetic year, for it is the year which is used in the prophecies of the Bible.***
Here, then, is an example of number as it is used in the heavens. Twelve is the pervading factor.
It is not necessary to go into the intricacies of this vast part of our subject. Notwithstanding the fact that God gave to man these heavenly time-keepers, he has so misused the gift (as he has every other gift which God has ever given him) that he cannot tell you now what year it really is! No subject is in more hopeless confusion, made worse by those who desire the dates to fit in with their theories of numbers, instead of with the facts of history.
We shall, therefore, avoid man's use of numbers. Our only concern in this work is with God's use of them. Here we shall find both design and significance. Here, therefore, we shall find that which is certain and full of interest.
The first natural division of time is stamped by the Number seven. On the seventh day God rested from His work of Creation.
When He ordained the ritual for Israel which should show forth His work of Redemption, seven is again stamped upon it in all its times and seasons. The seventh day was the holy day; the seventh month was specially hallowed by its number of sacred festivals; the seventh year was the Sabbatic year of rest for the land: while 7 x 7 years marked the year of Jubilee (Lev 25:4,8).
Thirty jubilees bring us from the Exodus to the opening of Christ's ministry, when, opening Isaiah 61:2, He proclaimed "the acceptable year of the Lord" in a seven-fold prophecy (see Luke 4:18-21).
The great symbolical divisions of Israel's history, or rather of the times of God's dealings with them, are marked by the same number; and if we confine ourselves to duration of years rather than to the succession of years and chronological dates; with kairoV (kairos), season, a definitely limited portion of time, rather than with cronoV (chronos), time, the course of time in general* (hence our word "chronology"), we shall have no difficulty.
God's dealings with His people have to do with actual duration of time rather than with specific dates; and we find that His dealings with Israel were measured out into four periods, each consisting of 490 (70 times 7) years. Thus:
It is clear that these are periods of duration having regard only to Israel, and to Jehovah's immediate dealings with them. For in each one there is a period of time during which He was not immediately governing them, but in which His hand was removed, and His people were without visible tokens of His presence with them.
Thus the number seven is stamped on "the times and seasons" of Scripture, marking the spiritual perfection of the Divine Prophecies.
We see the same law at work in various departments of nature. Sometimes
one number is the dominant factor, sometimes another. In nature seven
is found to mark the only possible mode of classification of the mass
of individuals which constitutes the special department called science.
We give the seven divisions, with examples from the animal and
vegetable kingdoms. The one specimen of an animal (the dog) and
one specimen of a flower (the rose).
Here all is law and order. Number comes in, in many cases determining various classifications. In the Endogens (or inside-growing plants) three is a prevailing number; while in Exogens (or outside-growing plants) five is a prevailing number.
The grains in Indian corn, or maize, are set in rows, generally straight, but in some cases spirally. These rows are always arranged in an even number. Never odd! They range from 8, 10, 12, 14, 16, and sometimes as high as 24. But never in 5, 7, 9, 11, 13, or any odd number of rows. The even number is permanent. Mr. H. L. Hastings tells of one farmer who looked for 27 years and could not find a "cob" with an odd number of rows. A slave was once offered his freedom if he found a corn-cob with an odd number, and one day he found one! But he had found it also some time before, when it was young; carefully cut out one row, and bound it up, so that the parts grew together as the corn-cob developed, and finally presented the phenomenon of having an odd number of rows. This exception proves the rule in an interesting manner.
If we notice how the leaves grow upon the stem of a plant, not only is law seen in classifying their nature and character, but number is observed in their arrangement and disposition. Some are placed alternately, some opposite, while others are arranged spirally. But in each case all is in perfect order. After a certain number of leaves one will come immediately over and in the same line with the first:
offers a vast field for illustration, but here again the grand impress is seen to be the number seven. The days of man's years are "Three-score years and ten" (7x10). In seven years the whole structure of his body changes: and we are all familiar with "the seven ages of man."
There are seven Greek words used to describe these seven ages, according to Philo:
The various periods of gestation also are commonly a multiple of seven, either of days or weeks.
With INSECTS the ova are hatched from seven half-days (as the wasp, bee, etc.); while with others it is seven whole days. The majority of insects require from 14 (2x7) to 42 (6x7) days; the same applies to the larva state.
With ANIMALS the period of gestation of
With BIRDS, the gestation of
With the Human species it is 280 days (or 40x7).
Moreover, man appears to be made on what we may call the seven-day principle. In various diseases the seventh, fourteenth, and twenty-first are critical days; and in others seven or 14 half-days. Man's pulse beats on the seven-day principle, for Dr. Stratton points out that for six days out of the seven it beats faster in the morning than in the evening, while on the seventh day it beats slower. Thus the number seven is stamped upon physiology, and he is thus admonished, as man, to rest one day in seven. He cannot violate this law with impunity, for it is interwoven with his very being. He may say "I will rest when I please," one day in ten, or irregularly, or not at all. He might as well say of his eight-day clock, "It is mine, and I will wind it up when I please." Unless he wound it at least once in eight days, according to the principle on which it was made, it would be worthless as a clock. So with man's body. If he rests not according to the Divine law, he will, sooner or later, be compelled to "keep his sabbaths," and the rest which he would not take at regular intervals, at God's command, he has to take at the command of man all at once! Even in this case God gives him more rest than he can get for himself; for God would have him take 52 days' rest in the year, and the few days' "change" he is able to get for himself is a poor substitute for this. It is like all man's attempts to improve on God's way.
It is not always seven, however, which is the predominant factor in physiology or natural history.
In the case of the BEE, it is the number three which pervades its phenomena
Here we are met with a field of research in which constant discoveries are being made. Chemistry is worthy of the name Science. Here are no theories and hypotheses, which deprive other so-called sciences of all title to the name. Science is Scientia, knowledge, that which we know, and what we know is truth which can never alter. Chemistry, for example, is not like geology, whose old theories are constantly being superseded by new ones. If we know the action of a certain substance, then our knowledge never changes. But side by side with this unchangeable truth there is the constant discovery of new truths.
All matter is made up of certain combinations of various elements, which are its ultimate, indecomposable constituents. Not that these elements are absolutely simple, but that hitherto they have not been decomposed. Some of these have been known from the most ancient times, while others are of quite recent discovery. Hence their number is slowly being increased. In 1874 there were 64; now there are about 70.
But though their total number cannot yet be known, the law by which they are arranged has been discovered. This law is complex, but perfect.
1. All the elements when magnetized fall into two classes. One class immediately ranges itself east and west, at right angles to the line of magnetic force (which is north and south), and is hence called Diamagnetic (i.e. through or across the magnet); while the other immediately ranges itself by the side of and parallel to the magnetic pole (i.e. north and south), and is called Paramagnetic (i.e. by the side of the magnet).
2. Further, it is observed that these elements have other properties. Some combine with only one atom of another element, and are called Monads; some combine with only two atoms of another element, and are called Diads; some combine with only three, and are called Triads: while those that combine with four are called Tetrads, etc.
3. Now when the elements are arranged, first on the two sides of the dividing line, according to their Diamagnetic and Paramagnetic characters; and then placed on lines according to their properties as Monads, Diads, etc.; and further, are arranged in the order of their atomic weights,* the result is seen in the accompanying illustration [Reynold's Curve of the Elements according to the Newlands-Mendelejeff Periodic Law], which exhibits the presence and working of a wonderful law.
On carefully examining this table it will be seen,
1. That on either side of the central or neutral line, there are alternate groups of seven elements, and that these seven fall into the form of an introversion, Monad answering to Monad, Diad to Diad, etc., thus:
Thus we have an introversion of seven elements alternated throughout the entire series.
2. Next observe that each time the line crosses upward from right to left there is a group of three neutral elements that occur together, near the atomic weights of 60, 100, and 190. So perfect is the law that the discoverers believe that about the points 20 and 155 there are yet two sets of three elements to be discovered...
3. Also observe that when the lines pass upward from left to right there are no elements whatever on this neutral line, and therefore we do not expect any to be discovered.
4. Further, that there are others which will yet be discovered to fill in the gaps that are left vacant, above the weights 145. A few years ago the number stood at 64. The present list contains 69. Some newly-discovered elements have been brought under notice while writing these words. They are Cerium, 141.5; Neodymium, 140.8; Praseodunium, 143.6; and "Ytterbium," 173. These with others that may yet be discovered will fill up some of the gaps that remain.
5. There is an element whose atomic weight is a multiple of 7 (or very nearly so) for every multiple up to 147, while the majority of the others are either square numbers (or multiples of a square number), multiples of 11, or cube numbers. Indeed we may say that every important element is a multiple of either 4 or 7; gold, the most valuable, for example, being 196 (4x72); iron, the most useful, 56 (7x23); silver being 108 (4x27, or 22x33), copper 63 (7x9), carbon 12 (3x4), mercury 200 (4x50), bismuth 208 (4x52), etc.*
6. Note that all the parts of the image which Nebuchadnezzar saw in his dream are here, and they are all on the left or diamagnetic side; that is to say, they are at cross purposes with the line of Divine government! The three which are pure and unmixed are all on the same line of monads"gold," "silver," and "copper,"while the fourth, "iron," is neutral, neither for nor against, like the fourth power, which is both religious and at the same time antichristian. The heaviest is at the top and the lightest at the bottom, as though to show us that the image being top-heavy is not destined to stand. Three have already passed away; the fourth is approaching its end; and presently, the "power" which was committed to the Gentiles shall be given to Him "whose right it is," and the fifth monarchy (illustrated by the Rock out of which all the others proceed) shall swallow all up when the kingdoms of this world shall become the kingdom of our Lord and of His Christ.
Thus the very elements of matter are all arranged according to number and law. When this law was first spoken of, it appeared to some chemists to be as absurd as suggesting that the alphabetical arrangement could be the scientific or natural order.
But here we have a natural, or rather, we should say, a Divine order.
For the elements, when arranged according to the weights and properties
which God has given to them, are found to fall into this wondrous order.
Here there can be no room for human fancy, but all is the result of knowledge,
or science truly so called.
Sound is the impression produced on the ear by the vibrations of air. The pitch of the musical note is higher or lower according as these vibrations are faster or slower. When they are too slow, or not sufficiently regular and continuous to make a musical sound, we call it noise.
Experiments have long been completed which fix the number of vibrations for each musical note; by which, of course, we may easily calculate the difference between the number of vibrations between each note.
These were finally settled at Stuttgart in 1834. They were adopted by the Paris Conservatoire in 1859, but it was not till 1869 that they were adopted in England by the Society of Arts. The following is the scale of Do showing the number of vibrations in a second under each note and the differences between them:
In the upper row of figures, those immediately under each note are the number of vibrations producing such note. The figures in brackets, between these numbers, show the difference between these vibrations. The figures in the lower line are merely the factors of the respective numbers.
On examining the above it will be at once seen that the number eleven is stamped upon music; and we may say seven also, for there are seven notes of the scale (the eighth being the repetition of the first).
The number of vibrations in a second, for each note, is a multiple of eleven, and the difference in the number of vibrations between each note is also a multiple of eleven. These differences are not always the same. We speak of tones and semitones, as though all tones were alike, and all semitones were alike; but this is not the case. The difference between the semitone Mi and Fa* is 22; while between the other semitone, Si and Do, it is 33. So with the tones: the difference between the tone Do and Re, for example, is 33; while between Fa and Sol it is 44; between Sol and La it is 44; and between La and Si it is 55.
The ear can detect and convey these vibrations to the brain only within certain limits. Each ear has within it a minute organ, like a little harp, with about ten thousand strings. These organs were discovered by an Italian named Corti, and hence have been named "the organs of Corti." When a sound is made, the corresponding string of this little harp vibrates in sympathy, and conveys the impression to the brain. The immense number of these little strings provides for the conveyance of every conceivable sound within certain limits. In the scale, as we have seen, there is a range of 264 vibrations. There is a difference between each one, so that there are practically 264 notes in the scale, but the ear cannot detect them. The ear of a skilled violinist can detect many more than an ordinary untrained ear. The mechanical action of a pianoforte can record only twelve of these notes. The violin can be made to produce a much larger number, and is therefore more perfect as an instrument, but not equal in this respect to the human voice. The wonderful mechanism of the human voice, being created by God, far excels every instrument that man can make.
There are vibrations which the ear cannot detect, so slow as to make no audible sound, but there are contrivances by which they can be made visible to the eye. When sand is thrown upon a thin metal disc, to which a chord is attached and caused to vibrate, the sand will immediately arrange itself in a perfect geometrical pattern. The pattern will vary with the number of the vibrations. These are called "Chladni's figures." Moist plaster on glass or moist water-colour on rigid surfaces will vibrate at the sound, say, of the human voice, or of a cornet, and will assume forms of various kindsgeometrical, vegetable and floral; some resembling ferns, others resembling leaves and shells, according to the pitch of the note.
The "Pendulograph" is another contrivance for rendering these vibrations visible to the eye; and for exhibiting depths of sound which are totally inaudible to the ear. The pen is attached to one pendulum and the paper to the other, and these are made to oscillate at right angles with each other. When each pendulum is set at the same length (making the same number of vibrations in the same time), the figure made by the pen will be a perfect circle. But when these lengths (or vibrations) vary, the patterns that are described are as exquisite as they are marvelous, and almost infinite in their variety and design.
Even the organs of Corti are limited in their perception, notwithstanding the many thousands of minute vibrating chords. When these organs are perfect or well formed there is what is called "an ear for music." But in many cases there is "no ear for music." This means that these organs are defective, not fully developed, or malformed, in the case of such persons; and that the sounds are not accurately conveyed to the brain.
There is a solemn and important truth therefore in the words, "He that planted the ear"! (Psa 94:9). What wondrous planting!
Not every one has this peculiar (musical) "ear." And no one has by nature that ear which can distinguish the things of God. The spiritual ear is the direct gift and planting of God. Hence it is written, "He that hath an ear," i.e., only he that hath that divinely-planted, God-given ear can hear the things of the Spirit of God. "An ear to hear" those spiritual things is a far greater reality, and an infinitely greater gift, than an ear for music! Oh wondrous ear! It is the Lord that gives "the hearing ear" (Prov 20:12). He wakeneth the ear to hear (Isa 50:4); It is the Lord that openeth the ear (Isa 50:5). The natural ear does not hear spiritual sounds; it cannot discern them (Isa 64:4 and 1 Cor 2:9). Thus nature and grace illustrate each other, and reveal the great fact that there is a secret ear, more delicate than any "organs of Corti," that can detect sounds invisible as well as inaudible to the senses, and which enables those who possess it to say:
One more step brings us to colour, which is caused by the vibrations of light, as sound is caused by the vibrations of air. There is a relation between the two, so that a particular colour corresponds to a particular note in music.
Hence there are seven colours answering to the seven musical sounds, and it is found that sounds which harmonize, correspond with colours that harmonize. While discords in colour correspond with discords in music.
The seven, both in music and colour, are divided into three and four. Three primary colours and four secondary, from which all others proceed, answer to the three primary sounds called the Tri-chord, or common chord, and four secondary.
The subject is too abstruse to enlarge further upon here. Sufficient has been said to show that in the works of God all is perfect harmony, order and symmetry, both in number and design; and one corresponds with the other in a real and wonderful manner.
The one great question now is, May we not expect to find the same phenomena in that greatest of all God's works, viz., His Word? If not the greatest in some senses, yet it is the greatest in its importance to us. For if we find in it the same corresponding perfection in design, then we see throughout the whole of it the same mysterious autograph. And its truths, and promises, and precepts come to us with increased solemnity and power; for the words of the book say with the stars of heaven