THE BASES OF MATHEMATICS ARE INTELLIGENTLY DESIGNED
O. R. Adams Jr.
© O. R. Adams Jr. 2006
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Much has been written in recent years about Intelligent Design in nature, particularly in biology. The evolutionists in each case, especially where plant and animal life is involved, come up with some theory to explain it all by evolution; although the explanations, in my opinion, are often not based on good reason. But there are some things in nature that cannot possibly be explained by Darwinian Evolution, could not reasonably be considered as happening by accident; and that are clearly intelligently designed. These are the bases of mathematics.
By bases of mathematics, I mean the natural things that mathematics are used to determine. These things of nature were not invented by man, cannot be changed by man, and did not evolve. Insofar as the human mind can determine, they have existed forever.
In a discussion of this nature, we have a problem of separating provable facts from spiritual concepts concerning God. For example, known facts are subject to proof, whereas, in my opinion the existence of God can neither be proved nor disproved. Nevertheless, throughout our history, great minds have recognized intelligent design in the world and in the universe, and considered this a proof of God. In this paper, I take the position that evidence of intelligent design is not proof of the existence of God, because the evidence does not indicate any particular designer, or the number of the designers. The evidence merely supports the logical conclusion that certain things were intelligently designed. This same principle can also be applied to the things that humans have designed. For example, examination of a camera, and its operation, presents evidence that it was intelligently designed. But that alone is no evidence of who designed it, or how many designers there may have been working together on it. In this regard, when I refer to what someone has said about mathematics and God, or other natural things and God, I am doing so only to support the facts of Intelligent Design.
Euclid, who lived about 325 BC to about 265 BC, and is called the father of geometry, said:
"The laws of nature are but the mathematical thoughts of God."
I think that it is clear from this statement that
The online encyclopedia, Wikipedia, states:
mathematicians have expressed the view that God is in some way responsible for
the rational order described so successfully by mathematics.
Wikipedia gives a number of examples, including one from Pythagoras:
rule the Universe."
Pythagoras (582 B.C. – about 507 B.C.) was an ancient Greek mathematician and philosopher. He was the father of the Pythagoras Theorem so important to trigonometry (a˛ + b˛ = c˛). (http://en.wikipedia.org/wiki/Pythagoras) His theorem, which I consider to now be a natural law, is a prime example of the intelligent design of one very important basis of mathematics.
The following is from Johannes Kepler:
chief aim of all investigations of the external world should be to discover the
rational order and harmony which has been imposed on it by God and which He
revealed to us in the language of mathematics. (Wikipedia)
Johannes Kepler was a noted
mathematician and astronomer, who lived form 1571 to 1630.
This rational order and harmony most certainly shows intelligent design, although, as stated above, I do not think that it shows the existence of any particular god.
Sir Isaac Newton (1643 – 1727) was a great mathematician and a great
scientist, and one of his many accomplishments was his significant contribution
to the development of calculus. He said:
most beautiful system of the sun, planets, and comets, could only proceed from
the counsel and dominion of an intelligent Being.
Leonhard Euler. (1707-1783) I consider Euler to probably be the greatest scientific genius of all time. He greatly advanced calculus, and he derived several direct formulas for determining Pi (the relationship between the circumference and the diameter of a circle).
"According to math professor Howard Anton, he 'made major contributions to virtually every branch of mathematics as well as to the theory of optics, planetary motion, electricity, magnetism, and general mechanics.'" "Euler was so smart it’s almost scary. In his thick textbook Calculus, Howard Anton includes brief biographies of famous mathematicians; his entry on Euler sounds like an episode from Ripley’s 'Believe It or Not' –
Euler was probably the most prolific mathematician who ever lived. It has been said that, “Euler wrote mathematics as effortlessly as most men breathe.” .... Euler’s energy and capacity for work were virtually boundless. His collected works form about 60 to 80 quarto sized volumes and it is believed that much of his work has been lost. What is particularly astonishing is that Euler was blind for the last 17 years of his life, and this was one of his most productive periods! Euler’s flawless memory was phenomenal. Early in his life he memorized the entire Aeneid by Virgil and at age 70 could not only recite the entire work, but could also state the first and last sentence on each page of the book from which he memorized the work. His ability to solve problems in his head was beyond belief. He worked out in his head major problems of lunar motion that baffled Isaac Newton and once did a complicated calculation in his head to settle an argument between two students whose computations differed in the fiftieth decimal place."
In his later life, Euler became blind. "Undeterred by misfortune, upheaval
and disability, Euler continued his work. With only his mind’s eye, he worked
through detailed algorithms and dictated them to his sons. Dan Graves said
that his work actually became clearer and more concise. An online
biography at Ryerson Polytechnic Institute states that 'He was apparently able
to do extensive and complex calculations in his head, remembering every step so
that he could recite them for his sons to record. ... he published more than 500
books and papers during his lifetime, with another 400 appearing posthumously'.
Another online biography claims that his death in 1783 left a vast backlog of
articles that the St. Petersburg
The following are quotations from the online book on Euler,
Leonhard Euler – His Life and His Faith,
by Dr. George W. Benthien, who has a Ph.D. in mathematics from
Euler was a committed Christian and frequently expressed awe at the works of the Creator. Euler was particularly impressed by the design of the eye. Here is one statement that he made concerning the eye:
though we are very far short of perfect knowledge of the subject, the little we do know of it is more than sufficient to convince us of the power and wisdom of the Creator. We discover in the structure of the eye perfections that the most exalted genius could not have imagined.
Concerning the calculus of variations he wrote:
for the fabric of the universe is most perfect and the work of a most wise creator, nothing at all takes place in the universe in which some rule of the maximum or minimum does not appear. – Leonhard Euler, Methodist Inveniendi Unius Curvus, 1st Addition, Art. 1 (1744).
Einstein, in more modern times, recognized this rational order and harmony of intelligent design in nature, and the mathematical aspects of it.
As to mathematics and nature, Einstein stated in a
lecture, "Geometry and Experience," before the
One reason why mathematics
enjoys special esteem, above all other sciences, is that its propositions
are absolutely certain and indisputable,
while those of all other sciences are to some extent debatable and in
constant danger of being overthrown by newly
discovered facts. ... But there is another
reason for the high repute of mathematics, in that it
is mathematics, which affords the exact natural sciences a certain
measure of certainty, to which without mathematics they
could not attain.
Einstein also said:
Our experience up to date justifies us in feeling sure that in nature is actualized the idea of mathematical simplicity. (Albert Einstein, Le Matin, March 29,1922, quoted in Abraham Pais, Einstein Lived Here, 1994)
In his essay, "The World as I See It," Einstein
wrote "of the Reason that manifests itself in nature." (Albert
Einstein, Ideas and Opinions, New York, 1954, p. 11.)
That Einstein clearly considered these aspects of nature to be of intelligent design is shown by his following statement:
You will hardly find one among the profounder sort of scientific minds without a peculiar religious feeling of his own . . . . His religious feeling takes the form of a rapturous amazement at the harmony of natural law, which reveals an intelligence of such superiority that, compared with it, all the systematic thinking and acting of human beings is an utterly insignificant reflection. (Albert Einstein, Ideas and Opinions, New York, 1954, p. 40.)
I agree with Einstein that "the harmony of natural law," including the bases of mathematics, "reveals an intelligence" superior to those geniuses who invented the tools of mathematics by which many of these natural laws may be determined. Consider Einstein's equation on energy and matter, E = m c˛ (E is energy, m is mass, and c is speed of light). If this equation is true, it represents a mathematical balance in nature, in relation to matter and energy, which reflects a design of enormous implications. In the equation, mass is not limited, and it could therefore mean that any mass in the world contains the possibility of enormous amounts of energy. Think of the implications this concept could have on our present crisis of the environment and energy needs of the world. We are already seeing possibilities of the use of new and different sources of energy.
The following are some of the many statements concerning
God of a world renowned mathematician of our current times, Gregory Chaitin,
from his book,
Mathematics is a way of characterizing or expressing structure. And the universe seems to be built, at some fundamental level, out of mathematical structure. To speak metaphorically, it appears that God is a mathematician and that the structure of the world―God's thoughts!―are mathematical, that is the cloth out of which the world is woven, the wood out of which the world is built. (p. xii) ...
Leibniz's God was a logical necessity to provide the initial complexity to create the world ... . (p. 59)
The way that Leibniz summarizes his view of what precisely it is that makes the scientific enterprise possible is this: "God has chosen that which is the most perfect, that is to say, in which at the same time the hypotheses are as simple as possible, and the phenomena are as rich as possible." ... (p. 63)
could not have failed to be aware that in using this term [relating to p
and a circle, and "the calculus of transcendentals"] he was evoking
the notion of God's transcendence of all things human, of human limitations, of
human finiteness. (Emphasis in book)... (p. 95)
Similarly, it was Cantor's obsession with God's infiniteness and transcendence that led him to create his spectacularly successful but extremely controversial theory of infinite sets of infinite numbers. ... (p. 96)
This intellectual journey actually begins, as is often the case, with ancient Greeks. Pythagoras is credited with naming both mathematics and philosophy. And the Pythagoreans believed that number―whole numbers―rule the universe, and that God is a mathematician, a point of view largely vindicated by modern science, especially quantum mechanics, in which the hydrogen atom is modeled as a musical instrument that produces a discrete scale of notes. Although, as we saw in Chapter Three, perhaps God is actually a computer programmer! (p. 97)
Kronecker's best known statement is, "God created the integers, all the rest is the work of man!" (p. 100)
As my friend Jacob
T. Schwartz once told me, the medieval cathedrals were the work of anonymous
hands, and took lifetimes to build. And Schwartz delighted in quoting a
celebrated doctor from that period, who said about a patient, "I treated
him and God cured him!" I think that is also the right attitude to have in
science and mathematics. (p. 143)
Throughout history, many, if not all, of the world's greatest minds have recognized the intelligent design of nature, of the world, and of the universe. Many were not mathematicians, or even renowned scientists. An example was Thomas Jefferson, our third president, who was a great thinker and had considerable scientific knowledge, but I would not classify him as either a mathematician or a scientist. In 1823, near the end of his life, he wrote a letter to John Adams, in which he stated:
... I hold (without appeal to revelation) that when we take a view of the Universe, in it's parts general or particular, it is impossible for the human mind not to perceive and feel a conviction of design, consummate skill, and indefinite power in every atom of it's composition. The movements of the heavenly bodies, so exactly held in their course by the balance of centrifugal and centripetal forces, the structure of our earth itself, with it's distribution of lands, waters and atmosphere, animal and vegetable bodies, examined in all their minutest particles, insects mere atoms of life, yet as perfectly organised as man or mammoth, the mineral substances, their generation and uses, it is impossible, I say, for the human mind not to believe that there is, in all this, design, cause and effect, up to an ultimate cause, a fabricator of all things from matter and motion, their preserver and regulator while permitted to exist in their present forms, and their regenerator into new and other forms. We see, too, evident proofs of the necessity of a superintending power to maintain the Universe in it's course and order. ...
Now let us consider the most simple of mathematics, the arithmetic of addition. Observe the simple equation: 2 + 2 = 4. It is rational, balanced, and useful; and the intelligence of the equation cannot be denied. Is the intelligence reflected the result of nature, humans, or both? Certainly intelligent people developed the tools and the language used in this simple equation. But the basic facts are the important things behind it, and without which it would be of no use. The basic facts are that if you take two objects and add two more such objects to the group, you then have four. This was undoubtedly discovered by early man, but no man invented these facts, nor can any man change them.
The same basic principles of nature apply to multiplication and division. If you have twelve sets of two items each, you can easily count them and prove that they amount to twenty-four. If you then divide the group of twenty-four into three equal groups, then each group will have eight.
Now let us add the elements of motion, velocity, time and distance. With simple mathematics we can determine that if an object travels at a certain velocity for a certain period of time, it will travel a certain distance. These are balanced facts of nature that work together in a harmony that reflects an intelligence beyond that of any human, as has been recognized by many great mathematicians.
It should be clear that the design of nature, that results in these basic facts, reflects much more intelligence than the intelligent humans who invented (or perhaps a more appropriate word would be discovered) the mathematical tools to arrive at the answer of these facts of nature. Certainly the tools were designed by people using their intelligence, but they would be useless without the basic rational, harmonious, and useful facts of nature to which they are applied. So which is the most important, and which reflects the most intelligent design?
In many fields of mathematics, including calculus, a historical study will show that many principles were worked out independently by different people, and different people contributed to and expanded the concepts. The underlying facts were always there, and it was only a matter of time until experience and knowledge evolved to the extent that people would figure out the tools that could be applied to determining the facts in such complicated problems.
Let us move on to the consideration of geometry and trigonometry. These fields deal with straight lines, curves, round objects, solids, flat objects, rectangles, squares, and angles. Again, each of these things is a fact of nature, and the facts and relationships relating to them were not invented by man, nor can he change any of them. Although, he has certainly invented some intelligent tools to apply to them and get the answers of nature in regard to them.
In the eighteenth century, Leonhard Euler, one of the greatest mathematical geniuses of all time, developed several direct formulas for determining pi. From my testing, it appears that one or more of his formulas for determining pi are used in electronic calculators, and mathematical software programs for computers, such as Mathematica and Derive. But no one invented pi. It is merely an immutable physical relationship between the diameter and circumference of a circle, as well as the relationship between the area of a circle, and its radius. The knowledge and use of pi is indispensable to the solving of many problems necessary in the fields of such things as astronomy, physics, navigation, surveying, and the various fields of engineering, as well as most other fields of science. These fields all deal with natural laws that existed prior to the time any human worked in any of the fields. And as intelligent as mathematical principles are, they are merely tools which we use in working with these natural laws.
With calculus we can determine the shape of a curve, and its slope at different points; the area under a defined curve; and the length of a curve between particular points. All of these relationships existed before there were any people.
Now to our elements of motion, velocity, time and distance, let us add power and acceleration. None of these were invented by man and they could not have resulted from evolution. They are far too balanced, interrelated, consistent, harmonious, and intelligently designed to have resulted by accident. When we consider together all of these interrelated laws of nature, the design is evident, and accident must be eliminated.
The elements which are our sources of power in the world were neither invented by man, nor can he add to them. He must work with what he has. It is true that man has invented ways to reform and combine different elements and use them for power for our various kinds of vehicles and power plants. But these elements existed before man. For example, Benjamin Franklin did not invent electricity; he merely discovered it and made use of it.
With the tool of calculus, developed by mathematical
geniuses such as
Since man did not invent either magnetism or electricity, he did not invent radio waves. But he certainly has invented ways to put to use these phenomena of nature in connection with many others. Consider one of our modern instruments, the GPS. They are used to guide our missiles in warfare with great accuracy. We can use them in a boat or a ship to navigate. You can put in routes, and they will give you the distance between programmed waypoints, and the estimated times of arrival based on the average time you are traveling – all calculated in the instrument. We have them in cars that can guide us both visibly and orally to a destination. Think of all of the different elements of nature involved. First we have to have satellites put into orbit to send radio signals which the receiver in the GPS can pick up, so that its mathematical "brain" can use triangulation and timing to calculate present position, and destination positions. Information had to have been programmed in from charts and maps, originally obtained from some kind of surveying. It would seem to me that in the design and production of the instrument, all fields of mathematics, and a number of fields of engineering would have been used. The number of natural laws and elements used are phenomenal, and their harmonious working together, and the consistency and integrity of all of them are necessary to the working of the instrument. But all of them have been waiting for man to use in this manner since before there was man. And after man came upon the earth, and the evolution of his knowledge and experience began, it was only a matter of time until he would develop tools such as the GPS to make use of these relevant laws of nature.
Consider what the future may hold as our knowledge and experience evolve further.
I have covered a very few of the many and varied examples of the intelligent working together of the natural laws that constitute the bases of mathematics. Most anyone can come up with additional examples, and I would encourage them to do so.
In conclusion, I can do no better than repeat the words of Albert Einstein, on "the harmony of natural law, which reveals an intelligence of such superiority that, compared with it, all the systematic thinking and acting of human beings is an utterly insignificant reflection."
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