Mathematics was a subject I resented throughout my school years. Beyond additions, subtractions and multiplications nothing made any sense to me. The geometry, triangles, their angles, the algebra, its symbols, equations, operations, trigonometry consistently irked me through my school years. There was mathematics in my preschool, school, high school and college and all along the way it had been an arduous task to get a grip on mathematical theorems. When I got admission into a medical school, I felt that finally the tyranny of mathematics over my life was over. Then came the rude awakening. When I sat down for the very first lecture in medical school, the professor of Biochemistry started to talk about probability and statistics. He went on to elaborate how probability and statistics play a vital role in the modern medical practice. That was not it. There was mathematics in medical physiology as you study the blood pressure across a vessel, there was mathematics in pharmacology as you study the metabolism of drugs, there was mathematics even in treatment plan as you describe prognosis in terms of mean, median and average. It did not take me long to realize that whereever I go, I am surrounded by mathematics. There is mathematics in biology, chemistry, physics, astronomy, geology, forensic science, you name it, it is there. Looking around now I realized that the most common language in the universe is the language of mathematics.
Mathematics is everywhere
First of all, I want to make one fact clear before we go further. That is, Mathematics is not just in the books of mathematics or in the department of mathematics in the college. It is not just limited to additions, subtractions or multiplications. It is around you, whether you see it or not. Every time you use a cell phone or a computer you are unleashing the power of mathematics to do your work at the speed of light. For example, when you download a song from the computer, you are downloading a string of millions of numbers, 0s and 1s. Whether you download a song or a sermon or a picture, it is transmitted in the form of binary numbers.
When Sir Isaac Newton published his groundbreaking textbook of science in 1687, he titled it, Principia, ‘the Mathematical Principles of Natural Philosophy’. Scientific method started with a foundational conviction, which is all regularity of nature can be expressed in terms of mathematics. Galileo affirmed: ‘the book of Nature is written in the language of mathematics” Eighteenth-century English poet Alexander Pope said, ‘Nature and Nature’s laws lay hid in night, God said, ‘Let Newton be!’ And all was light”. Nature and Nature’s laws………When we look around we just see the nature but it takes a thinking mind like that of Newton to see the laws embedded in nature.
Use of Mathematics throughout History
Mathematics is everywhere in the universe. This is not a realization that dawned upon us in recent times. Even philosophers in the ancient times realized it. Today, we are seeing a modern resurgence of the idea that unity of the universe can be explained in terms of mathematics. We have u pluribus unum on our coins, out of many one. Such a quest for seeing unity in diversity is not new. Ancient Greek philosophers strove to discover the single explanatory principle underlying the complex nature of the universe. For Thales, everything is water, For Anaxemedes, everything is air, for Democritus, everything is atoms, and for Pythagoras, everything is number. So, there has been attempts to explain the unity in diversity in terms of mathematics. We should also note how mathematics has been a foundation for the study of logic. When you construct a logical argument you put your propositions brick by brick. Three hundred years before Christ, Euclid wrote the most influential work in the history of mathematics, ‘Elements’. It is a treatise consisting of 13 books that constructs mathematical theorems based on simple axioms and propositions. If you analyze the work of Euclid you would notice how Euclid builds his mathematical theorems starting with simple axioms. Such an approach gave us profound philosophical insights into the nature of truth. Over the last two thousand years, Euclidean geometry gave credibility to the belief that truth and certainty can be achieved by human thought.
|Another interesting thing is mathematics can give us appearance of simplicity on the surface while hiding mind bending complexities in its tummy. For example, triangle looks so simple on the surface but volumes upon volumes of mathematical theorems have been published just describing the nature of a triangle|
Blackhole on the Blackboard
You don’t need me to tell you that universe and its sheer size is just mind boggling. Pascal said ‘the eternal silence of the those infinite spaces’ terrified him. Physics of black holes uses information theory mathematics. So the good news is that things like black holes that stretch infinite space in the universe can be explained in terms of mathematical equations that stretch only a classroom blackboard. And all those mathematical laws are consistent with each other.
One of the most influential mathematicians of 20th century, Andre Weil said, ‘God exists since mathematics is consistent’. His point is that the consistency of mathematics is an evidence for God’s existence. This morning I want to show that mathematics provides one of the most profound evidences for the existence of God.
First the Origin of Mathematics Point us to God
Stephen Hawkings, in his latest book, The Grand Design, argues, I quote, “Because there is a law such as gravity, the Universe can and will create itself from nothing. Spontaneous creation is the reason there is something rather than nothing, why the Universe exists, why we exist”. When I heard this, I thought what a transformation! When Sir Isaac Newton, the discoverer of the law of gravity, wrote Principia, describing the mathematical nature of the law of gravity, he added General Scholium to it, as a doxology to praise God as the Creator of all laws in the universe. And here comes, Stephen Hawkings, who once held the Lucian chair, which was held by Newton more than three hundred years ago, and says the law of gravity can explain the orgin of the universe and the existence of mankind. The greatest bluder committed by Hawkings here is to ignore the boundaries of science. A physical law such as the law of gravity cannot explain itself. It needs an explanation for its own origin and existence. Even if we propose another law to explain the existence of the law of gravity, that law needs an explanation. Besides, no physical law can exist independent of matter. So, to propose that the law of gravity preceded the origin of universe is pure speculation, not science. Before the universe, what was there? If you say, there was God, that is called religion. If you say, there was the law of gravity, that was called science. In reality, that should be called scientism.
Making a Religion Out of Science
What was there before the creation of the universe? That is a metaphysical question, not a question in the purview of science because science deals with what is observable and testable. For metaphysical questions, most people look to religion for answers. People like Stephen Hawkings want us to rely on science for answers to those metaphysical questions. But we got to realize that when they do that, they are not doing science. They are making a religion out of science. That sounds absurd, but that is exactly what they are doing. When you try to use science to answer metaphysical questions, you are making a religion out of science. And that is called scientism. Scientism violates the very nature of scientific method.
Throughout history, philosophers tried to give an explanation for the mathematical nature of the world. Classical Greek philosopher Plato (427 BC – 347 BC) helped to lay the foundations of Western philosophy and science. In one of his dialogues, Timaeus, Plato tells us how God created the physical world based on an Ideal world of mathematics. He says how every temporary thing has an eternal form and every physical thing has a trascendental form. For example, if you see an orange, it points to a perfect sphere that exists in the transcendental world. If you look at a basket ball, it points to a perfect circle. In Plato’s view, the physical world is an image of the mathematical reality. We call it Platonic Realm.
Plato developed the idea that the natural laws must be mathematical. For Plato, the certainty of geometry arises from eternal, unchanging perfection of the objects of mathematics. Remember Plato’s allegory of cave. The prisoners inside the cave can see only the shadows of the things passing by. They can see at least the shadows because of the sun shining over the cave. They are not able to see the sun, yet the sun is the source of all visibility in the cave. It is the sun that renders visible all the objects of the world of sense experience. These Platonic ideas did not sound foreign to scientists worked in the Christian West. They believed that a rational God created this universe on mathematical ideas. Johannes Kepler in 17th century believed that God is a geometer and that the beauty of mathematics must be reflected in the heavens in the way the planets are organized. He predicted that the orbit of every planet had to be one, single, purely geometric curve and he found that. He was convinced that it was there and it would be worth looking for. Kepler said, “I believe the geometric proportion served the creator as an idea when He introduced the continuous generation of similar objects from similar objects”.
Similary, Newton started the search for a single mathematical law that governed all motions in the universe because he assumed that God must have built a natural law in the language of mathematics. Father of modern taxonomy, biologist Carl Linnaeus believed plants as ideas in the mind of God. He saw mathematical symmetry even in the anatomy of plants. Swiss biologist Louis Agassiz (1807-1873) believed that animals started as ideas in the mind of God. They started with a basic metaphysical assumption. So, you see, either a theist or atheist, has to start with metaphysical assumptions for the mathematical nature of universe. Whether you say it is God or Gravity at the beginning, you are doing metaphysics.
Mathematics is not just used to study the nature, but also to form the foundation of logic. Mathematics and Logic go hand in hand and it has been like that for thousands of years. Take Euclid for example. Euclid’s Elements has 4 key components. The first component is Basic Assumptions, then comes Definitions, then comes Proofs and finally, Logical structure of proved propositions.
Premises/Conclusion and Causes/Effects
Plato’s disciple Aristotle worked extensively on Logic and demonstrative science. In Logic, the premises of the syllogism are related to the conclusion. In demonstrative science, causes of a phenomenon are related to the effects. So, the nature of a conclusion depends on the nature of the premises and the nature of the effects depend on the nature of the causes.
ARISTOTLE & SPINOZA
Aristotle explained causality in terms of four different kinds of causes – material cause, efficient cause, formal cause and final cause. For example, why does it rain?
Material cause is water droplets
Efficient cause is what prompts the water vapor to condense into droplets
Formal cause is what makes the droplets fall to Earth’s surface
Most important is the Final cause. For Aristotle, the drops fall to Earth because plants and animals need water to live and grow. The final cause explains the larger purpose of the origin of rain. So, there got to be final cause to explain the origin of a thing or person. That is true for everything, what is the purpose for the origin of the universe? There got to be a final cause. What is the purpose for the origin of man? There got to be final cause. The tragedy of the modern science and modern society is we forgot the importance of final cause. Take human beings, we can explain human beings in terms of material cause, efficient cause and Formal cause. But we just don’t bother to explain human life in terms of final cause. A little bit lewd example is sex. We treat sex and explain it in terms of material cause, efficient cause and formal cause, and there is no final purpose to sex. But, for Aristotle, causality should never be explained without a final cause. For him, everything has a ‘teleological behavior’. Every thing has a purpose and goal. Every thing has a cause and in the beginning there was that Uncaused Cause. Aristotle applied the idea of universality of cause and effect to every thing he studied.
In 17th century, Dutch philosopher Baruch Spinoza (1632 – 1677) used this idea of cause and effect to demonstrate the existence of God.
Spinoza thought we could prove the existence of God by the same methods we use in geometry.
Spinoza structured his Ethics exactly like Euclid’s Elements, and he named Part 1 of his work, ‘Of God’ and worked on proving the existence of God using mathematical examples. He says that for the existence or nonexistence of everything, there must be a reason or cause. Now, where is the cause? the cause for something’s existence or nonexistence can be within the things of nature or can be outside of its nature.
- The cause within the things of nature: a square can happen, a circle can happen, but a square circle cannot exist, because, then, its nature would involve contradiction, that cant happen.
- The cause outside the things of nature: whether a particular square or a particular circle exists or not depends on the order of physical nature. If there is no cause or reason that hinders a thing from existing, it exists necessarily. So, if there is no cause or reason to stop God from existing, God must exist.
- Is there a cause that stops God from existing? If there is a cause that stops God from existing is within God’s nature, then there would be a contradiction in God’s nature, which is absurd, because God by definition is absolutely infinite and perfect
- If there is a cause out side of God that stops God from existing, then, that cause would be just as powerful as we claim God to be, and then that would be God. For example, if x is god, but y can stop x, then we cannot call x as god anymore, because y is more powerful than x. In that instance, y becomes god.
So, only God can stop God from existing, Spinoza ends by saying that there is no existence we can be more sure of than the existence of God. So, Spinoza used the same methods we use in geometry to prove the existence of God. Spinoza was not alone to make such declarations.
When modern science began, the founding fathers of science started with a basic assumption that God created this universe on mathematical foundations. They argued about how God did it, how God sustains it, how God ends it, but they never doubted that God did it.
Newton and Leibniz
Newton’s Interventionist God in Astronomy
Sir Isaac Newton (1643 – 1727) was an English physicist and one of the most influential people in human history. His contemporary, Gottfried Leibniz was a German mathematician and philosopher. Both were devout Christians but they had major differences on how God runs the universe. Newton said, look at the solar system. All its planets orbit in nearly circles, all plantes revolving in virtually same plane, in the same direction. Such regularity could not have come about by chance. Random motion of the particles would not have created a solar system like ours. Newton said, God chose it, because it was good and suitable for human habitation. God could have created a universe with matter and particles of random motion, but that is not what God chose to do. Newton thought of the universe as a clock that God wound up at the beginning of the creation. But, Newton thought that the clock could not run forever, and it needs some attention from time to time and God intervenes to set things back in order as needed.
Leibniz: God is Not a Cosmic Plumber
But, Leibniz did not agree with Newton. He thought that the idea of God as an astronomical maintenance man as absurd. He believed that God had carefully chosen the most suitable world among an infinity of possible worlds. He coined that famous phrase, ‘best of all possible worlds’ because although it is not a perfect world, it is the best possible world God had chosen for us. Leibniz believed that God had to set up the universe to be the best possible because God is good. He said that God made the universe to run on mathematical natural laws, which can sustain the universe with out God’s maintenance from time to time. That is how we got the Principle of Sufficient Reason, which states, that, ‘For every possible event, there is a reason why it happens the way it does and not otherwise’. To summarize, Leibniz said that God made the universe on rational, mathematical laws and those laws explain it completely. Leibniz felt that Newton had insulted God by suggesting that God’s handwork was in need of repair. Leibniz said that Newton portrayed God as a ‘cosmic plumber’. Lebniz said that God did not need to intervene in nature because God perfectly anticipated every contingency from the beginning.
You remember the famous conversation between French mathematician Pierre-Simon Laplace and Napolean Bonaparte. The famous encounter happened in 1802. Napolean asks Laplace why God is not mentioned in his scientific treatise, Celestial Mechanics. To that, Laplace, answers, ‘Sir, I have no need of that hypothesis’. Now, many atheists use this Laplace’s reply to Napolean as an evidence of Laplace’s atheism. But, the fact is, Laplace is simply subscribing to the Leibniz’s view of the universe rather than Newton’s view. For Leibniz, God made the laws of nature and every natural system is a consequence of those laws. But, sadly, as science becomes more secular, God has been removed even as the author of natural laws. If you ask a modern secular scientist about the existence of laws of nature, you would get the goofy reply, ‘there are just there’.
But the origin of mathematical laws of nature needs an explanation. Even if all the best scientists around the world sit in a big hall and come up with a big equation which explains every other law in the universe, that does not solve the problem. Because that Big Equation needs an explanation for its origin. As Leibniz said, only a rational God could have produced a rational universe built on rational laws. To suggest that such rational laws came out without a rational being is irrational.
- Existence of Mathematical laws point us to God
Do they really exist or just our mental constructs?
Do they really exist or are they just our mental constructs? On one hand, there are people who believe that mathematical laws are just mental constructs without any real existence outside of us. Prominent figure in this group is famous atheist and Scottish philosopher David Hume (1711 – 1776) maintained that ‘all our ideas are merely copies of our impressions’, and that only experiences based on the senses have any reality. For instance, geometrical shapes would have a reality only to the extent that they are found in Nature. On the other hand, there are people who maintain that mathematical laws exist in nature whether human beings are conscious of them or not. A prominent figure in this group is Rene Descartes. In his Meditations on First Philosophy, Descartes wrote, I quote, “
“When I imagine a triangle, even though such a figure may exist nowhere in the world except in my thoughts, indeed may never have existed, there is nonethelesss a certain nature or form, or particular essence, of this figure that is immutable and eternal, which I did not invent, and which in no way depends on my mind’ English mathematical physicist, Roger Penrose, who is an atheist by the way, wrote these words, I quote, “There often does appear to be some profound reality about mathematical concepts, going quite beyond the mental deliberations of any particular mathematician. It is as though human thought is, instead, being guided towards some external truth – a truth which has a reality of its own, and which is revealed only partially to any one of us’
Note those words: A truth which has a reality of its own
The mathematical laws are out there with real existence. German physicist Heinrich Hertz (1857-1894) described it this way, I quote, “We cannot help but think that mathematical formulas have a life of their own, that they know more than their discoverers do, and that they return more to us than we have invested in them”
How do we know that mathematical laws have their own existence?
Srinivasa Ramanujan was an indian mathematician who lived a short life, between 1887 – 1920. He once said, ‘an equation means nothing to me unless it expresses a thought of God’. He was an autodidact, a self-taught person in pure mathematics and workingly independently, he made substantial contributions to the field of mathematics. He lived in a radically different society, he had no formal training in academic mathematics, yet he tackled same mathematical problems encountered by other mathematicians and came up with his own solutions. What he discovered through his deductions a century ago are being independently verified today as mathematicians work in fields like crystallography and string theory. No matter where you live, regardless of your cultural and traditional background, you can objectively do mathematical deductions and verifications. Why is that possible? Because mathematics has a universal character and they exist independently of our mind. Ramanujan’s work is a proof that mathematics has independent existence.
Albert Einstein said, ‘Subtle is the Lord, but malicious He is not”. The mathematical ideas and laws are subtle and secretive, but not malicious, there is no illusion, there is no maya, human mind can decipher those laws by rational thinking.
So, mathematical laws, out there, have objective reality. Otherwise, the very idea of science would be in peril. Suppose there are three scientists A,B and C. They start with an idea that mathematical laws are objective and they are indepently verifiable. Without that starting point, they cannot even start working. A comes back with his own discoveries, B comes with his own discoveries and C comes with his own discoveries. When they analyze the results between them, they assume that if their results are contradictory to each other about a same physical phenomenon their findings are not valid? Why do they start with such an assumption? Because they believe that natural laws are objective and independently verifiable no matter who is doing the experiment.
Mathematical laws do exist, whether you believe them or not.
But how can be certain that they are really out there? The only tool we have to access the mathematical realm is our mind. But, the question is, can we trust our mind?
If you take three 3 calculators and give them a problem of addition, they gave you same results. You assume they are functioning on same operating mechanism using same mathematical laws. Otherwise, they would have yielded different results. If three different minds worked on same objective experiment, and came up with same results, then there must be something objective even about human mind’s thinking mechanisms. That search for objectivity or certainty within one self has been a great passion for many philosophers of science.
How can I prove that I exist?
Before we subtract any certainty from things external to us, we should have some certainty about our own existence. Many years ago, American philosopher Morris Raphael Cohen was teaching a class to a group of students. A student stood up and asked him, ‘Professor Cohen, can you prove me that I exist?’ Cohen, replied, ‘Certainly, to whom shall I address the proof?’ The story sounds funny, but that explains the core of a philosophical quest for certainty. How can I prove that I exist? Are you certain about your own existence? You cannot say that you doubt everything. If that is your argument, I need to introduce you to Michel de Montaigne (1533 – 1592), considered as the father of Modern Skepticism. Montaigne says, that when a skeptic says, ‘I doubt everything, I doubt everything’ the argument takes him by the throat and forces him to affirm one thing, that is, he does doubt. Even when you say that you doubt everything, you are certain about one thing, that is, you are doubting. You got to be certain about at least one thing before you start doubting things.
Remember your analytic geometry class, when the teacher writes on the black board, for a principal unknown, say is x, say it y. But if you see it, the teacher always has certain things which he is certain about before looking for principal unknowns. Where did we get this method? It started with Descartes. Descartes (1596 – 1650) was the most famous French philosopher and mathematician. Descartes had experienced same question what baffled the student in Mr.Cohen’s class: How can I prove my own existence. That question puzzled and perplexed Descartes.
In 1629, he retreated to a Dutch inn and started to question everything. He questioned the room he was in, the chair he was sitting on, the bed he was lying on, even the physical body his mind residing in? Descartes is doubting, and doubting and doubting, the only thing he cannot doubt is that that he is doubting. He is certain that he is doubting. When he is doubting, he is thinking, when he is thinking, he is existing. Descartes realized there is a thinking entity within his body which is distinct from everything else.
You know, Descartes was the first philosopher to make mind-body distinction. We call it Cartesian dualism. Cartesian dualism professes that mind and matter are distinct but coexist. Neither Aristotle nor Plato made a distinction between the mind and the body. Rene Descartes (1596-1650) was the first to explicitly formulate this division.
For D, reality had two distinct forms: That of the mind (or thought) and that of the material world. In Cartesian method, the mind uses deductive logic to understand the matter.
A Certainty without and a Certainty within
A Certainty without: We can be certain that mathematical laws outside of us have their own existence
A Certainty Within: We can be certain that mind is equipped with deductive logic to understand the laws of mathematics.
These two certainties have to meet in every scientists work. Otherwise, there is no science. Why they are meeting like that is the greatest mystery of science. Physicist and mathematician Eugene Wigner was awarded Nobel Prize in Physics in 1963. The Nobel statement said he was awarded the Prize, ‘for his contributions to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles’. He discovered fundamental symmetry principles through deductive reasoning and applied them to find amazing discoveries through induction. Eugene Wigner himself called it, ‘the unreasonable effectiveness of mathematics’.
Pure Thought in Symbiosis with the Concrete
Mathematical deductive thinking has produced amazing discoveries about the nature, and why it works is a profound mystery of science. Vietnamese professor of astronomy at the University of Virginia, Trinh Xuan Thuan asked these questions about this, ‘Why this synergy between the world and mathematics? Why do do abstract entities, forged in the minds of mathematicians, and generally of no use in ordinary life, turn out to be in concordance with natural phenomena? Why is pure thought in symbiosis with the concrete?’
You see, there is a surprising consonance between mathematics and reality.
New Realities Need New Mathematics
In 1920s, Albert Einstein told us new things about physical world. He said gravity warps space. But to prove his theory, he could no longer use Euclidean geometry, which describes only flat space. Einstein was thrilled when he realized that he could use non-Euclidean geometry. So, what did Einstien do? He found a new dimension to reality and he had to use new type of mathematics to describe that reality. What do we learn from this? There is a grand coherence between human mind and mathematical laws in nature. This grand coherence needs an explanation.
Let us start like this. On one hand, let us take Mind and Body. On the other hand, let us take Mathematical laws and the universe. In other words, what mind is to the body, the mathematical laws are like that to the universe.
First, let us take Mind and Body. Here the brain as an organ is part of the body, not mind. To illustrate this, the mind is like software and the brain is like hardware. If you open a computer, you will see hardware inside it, but you cannot see the software that operates the computer. Similarly, if you open human skull, you can see the brain, the hardware, but you cannot see, the mind which is the software. You can see the anatomical parts of the brain which are used to do analytical thinking but you cannot see how, for example, ‘the laws of logic’ operate in those regions. The same concept applies to the universe and mathematical laws. You can see planets, stars and galaxies but you cannot see the laws of physics that operate them. They are there, but you cannot see them. The law of logic is there in your brain, but you cannot see it. In the same way, the laws of mathematics are there in the universe but you cannot see them. The most surprising thing is, the laws of logic that operate in human mind have the grand coherence with the laws of mathematics that operate in the universe.
Two Softwares: Their Existence needs an Explanation
In a computer, the software exists independently of the computer’s electronic circuits. Similarly, mathematical laws have their own existence independent of matter they act upon. Laws of logic have their own existence independent of physical brain. According to Darwinian evolution, from a primitive pond scum, human beings evolved. With human body, human brain evolved, and mind is a product of brain. In fact, most evolutionists do not even make the distinction between mind and body. But, overall, according to Darwinian evolution, this software that operates human mind is a product of interactions of blind mutations over millions of years.
Three Fundamental Questions
According to Darwinian naturalism, blind mutations produced human mind and blind processes produced mathematical laws in the nature. There comes the first question, how can this software arise from blind mutations? Do mutations gather for yearly conference to talk about their movements that give precise rational thinking to human mind?
Then the second question is, how can universe, which was born out of Big Bang and operate on blind processes without any intelligent guidance can come up with mathematical laws?
The third question should disturb any intellectually honest atheist in this world? How is the software in human being, who is a product of blind mutations over millions of years is in exact sync with the software in the universe, which is a product of blind processes over billions of years? This should boggle every thinking person’s mind.
Mathematical Argument Against Evolution
Now can an evolutionist describe this amazing coincidence between the properties of the brain and those of the universe? He would say, they are simply the outcome of natural selection. They talk about natural selection as though it has some intelligence on its own. But we need to ask more questions, what drives natural selection? Instincts. Natural selection operates on instincts, for example, if you are hungry, look for food; if you are thirsty, look for water, if you are hunted, run for your life, if you are cold, cover your skin. That is how natural selection works, it is about survival. You do not need to understand the laws of mathematics for your survival. You do not need to understand the laws of symmetry that helps you discover the structure of atom in order to survive. An evolutionist might say that human beings developed analytical thinking as a survival tool. But, most scientists and philosophers use thier analytical thinking tools just for the sheer pleasure of intellectual quest, not as a tool for survival. For example, when Einstein told us E = mc2, at that instance, he had no idea that his equation could be used to build a nuclear weapon, which nations could use for their survival against enemy nations. Darwinian natural selection cannot explain the deductive logic of human mind.
There are two softwares and their existence needs an explanation. Naturalism and darwinian evolution does not explain their existence. Common sense says that no software can be created without a being with intelligent mind. To say that a software can come out of rocks and ponds if you give millions of years is just ridiculous. In evolution and naturalism, hardware precedes software. But we know from experience that software always needs an intelligent mind to frame it.
Descartes tried to explain the origin and existence of these two softwares. How can Descartes explain the origin and existence of logical thinking of human mind and mathematical laws of the nature? Descartes knew the unreasonable effectiveness of mathematics, he tasted the joy of it. We know Newton’s first law, A body at rest with nothing acting on it stays in its state of rest, and a body with nothing acting on it, moving in a straight line at a constant speed, continues to do so. Newton wrote it in 1687. But, using his deductive method, Descartes already published that law, forty years before Newton, in 1644.
How did mind get this capacity to understand the mathematical nature of the universe?
Descartes described himself as a being that doubts. It does not mean that he enjoys that state of being a being of doubting. Quite contrary. He says it would be better to know everything, than to doubt. Knowing is more perfect than doubting. So, there are two ideas. Idea of doubting, and the more perfect, the idea of knowing. The question is, where does he get the idea of something more perfect than himself? He says it has to be from some nature which was itself more perfect, that has all possible perfections, that is God. Mind becomes more perfect as it stays near God, who is absolutely perfect. Let me use an illustration. Suppose you are walking on a hot, dusty road in the midsummer. You felt thirsty, and you wanted to drink a ice cold soda. Somebody gave you an ice cold soda. What do you assume? Everything around you is hot and dusty. That could not be the source of your soda. You assume that ice cold soda came from a refrigerator or from a box of ice cubes. The coldness of soda could have come only being around an object which is colder than it is. That is what Descartes saying about the perfection of human mind. It is almost perfect because it came from a being who is more perfect than human mind, that is, God.
Here Descartes uses mathematical examples to prove the existence of God. He says that existence is included in the idea of a perfect being in the same way the idea of a triangle includes that its angles add up to the sum of two right angles or the idea of a sphere includes that all its its parts are equidistant from its center. “It is at least as certain that God, who is this perfect Being, exists, as any theorem of geometry could possibly be.
God is the starting point for Descartes.
Both Spinoza and Descartes tried to prove existence of God through mathematical arguments. Let me explain the difference. Take iPad for example. What Spinoza is saying is, if you look at the iPad, its structure proves that it might have been designed by an intelligent being. See the nature of iPad, contradicting itself is not in its nature, it must have been designed by a being who has no contradiction in His nature. What Descrates is saying is, he can trust iPad for his work because he believes it is made by an intelligent and good being (Steve Jobs). I can trust my iPad because it was created by Steve Jobs, a good human being. I can trust my mind, because it was created by a Good God.
Descartes believed that God is the one who guarantees that our clear and distinct ideas are true. God is the source of all our clear, and distinct ideas. Since God is good, he does not deceive us and we can trust the ideas that come from him as true Descartes said that he can use his mind because a Rational God has built it and he can trust his mind because Good God made it. Folks, this is the reason that explains why modern science emerged in Christian West, rather than in Confucian China or Hindu India or Islamic Middle East?
Modern science was born in Christian West because it believed that a rational God built a universe with rational laws, and he imbued human mind with rational faculties which, when properly used, would help him decipher the mathematical codes underlying the nature. Scientific method did not arise in China because Confucianism revolves around yin and yang, two forces which act differently at different times, and the philosopher’s quest is to understand how these two forces act with each other. Chinese has always been smart people, for thousands of years they were technologically ahead of the West and made such inventions like paper, compass, gunpowder etc. But still, they could not invent scientific method because they did not believe that the natural world came from a God who decreed mathematical laws. They were in quest to understand yin and yang, the two opposite forces. The Chinese did not look for the laws in nature because they had no concept of a God who decreed rational laws.
Similarly, scientific method did not arise in Hindu India because Hinduism describes nature as maya, the one big illusion and the philosopher’s quest is to break that illusion. When you think that everything around you is an illusion, looking for objectivity is futile.
Why didn’t scientific method born in Islamic Middles East, which shares the idea of monotheism with Judaism and Christianity. I can explain that to you using a quotation from Descartes’ 1637 book, Discourse on the Method of Rightly Conducting the Reason to Find the Truth in the Sciences. This is what he says “Those long chains of reasoning, so simple and easy, which enabled the geometricians to reach the most difficult demonstrations, made me wonder whether all things knowable to man might not fall into a similar logical sequence” Then he goes on to say, “If so, we need only refrain from accepting as true that which is not true, and carefully follow the order necessary to deduce each one from the others, and there cannot be any propositions so abstruse that we cannot prove them, nor so obscure that we cannot discover them”
Note those words carefully, whether all things knowable to man might not fall into a similar logical sequence. Western skepticism born out of this sentence. The West allowed skepticism of all most everything. It allowed even Biblical criticism. The Bible proved its reliability after careful scrutiny by everyone who engaged to critically examine it. But, there is no such thing as Quranic criticism. If you criticise Quran in Middle Eastern nations, you will be a dead man. So, Muslim nations never developed the art of critical examination that is fundamental to scientific method and as a result, the scientific contributions of Muslims to the world are not significant. Also,
Quran boasts as it says everything about nature we can know of. Bible never makes such boastful statements. Scientists like Robert Boyle developed the idea of two books, the book of Scripture, which is the Bible and the book of nature, which is science.
So, Descartes developed the idea of mind-body distinction and told us that we can be certain that the tools of reason given to human mind are trust worthy because they came from a God, whose nature is Good. There is no maya, there is no illusion, there is no yin and yang. There are only mathematical laws which can be grasped with mind built with rational faculties by its Creator.
Thus, Descartes idea of mind-body distinction gave us scientific certainity. Now, let me tell you one other interesting thing. It also gave us sexual equality. Scientific certainty and sexual equality. For example, French philosopher Francois Poullain de la Barre (1647 – 1723), he wrote in 1673, ‘The Mind has No Sex’. A female brain structurally differs from a male brain. But, there is no such thing as female mind or male mind, or in religious terms, there is no such thing as female soul or male soul. Darwinism does not make the mind-body distinction, that is why, it puts male sex and female sex in perpetual warfare.
Descartes’s skepticism is anchored in God. The father of modern skepticism stated that his certainty is rooted in God. Look at the modern day skeptics who reject God, yet describe themselves as followers of Descartes. That is not just limited to skepticism folks,
Empiricism started with devout Christians like John Locke, where is God among today’s empiricists?
Existentialism started with devout Christians like Soren Kirkgaard, where is God among today’s existentialists?
Rationalism started with devout Christians like Leibniz, where is God among today’s rationlists?
Scientific method started with devout Christians like Bacon, where is God among today’s scientists?
Descartes believed that mathematical laws in nature can be studied and understood using the rational tools of human mind because those laws owe their existence to God. When we see the mathematical nature of natural laws that pervade universe on one hand, and the mathematical nature of logical laws that pervade the human mind on the other hand and when you find out that there is a perfect synchrony between them, it points us to a rational Creator who created both of them. You cannot say that nature itself can explain this great mystery.
The first paragraph of the Declaration of Independence has a remarkable phrase: Laws of Nature and of Nature’s God. You cannot just say, Laws of nature, thats all there to it. You cannot separate the two, because Laws of Nature owe their existence to God of Nature.
You cannot say, the mathematical laws just came from Nature,
you cannot say, the moral laws just came from nature,
the laws of nature came from God of nature. So, the very existence of mathematical laws point us to God.
- Nature of mathematical laws point us to God:
Finally, I think the very nature of mathematical laws point us to God.
The properties of mathematical laws reflect the very nature of God.
- Like God, mathematical laws have existence without physical substance
The Bible tells us that God is a Spirit. That means God does not have a physical body. He exists as a Spirit. Mathematical laws have similar existence. You cannot bind the law of gravity in a jar and study its atomic structure because it does not have any. It is there, but you cannot catch it. Like God, mathematical laws have existence without physical substance.
- Like God, mathematical laws are omnipresent, they are everywhere. They are true on earth, as much as as on the moon, or on the sun or in a distant galaxy.
- Like God, mathematical laws are omniscient, they know you before you act. You don’t have to tell the law of gravity ahead of time to act in a certain way at a certain distance for certain purpose. If you embark on a spaceship and planning to go to a distant galaxy and you need the laws of motion to act at that particular space, you dont have to inform them ahead of time. They will deliver their action without you telling them how to act. In this respect, they are omniscient, like God.
- Like God, mathematical laws are omnipotent. There is absolutely nothing in our universe which can escape the effect of mathematical laws, from the tiniest atom to the largest galaxy, from babies to dinosaurs, from tress to animals, no one can escape their dominance.
- Like God, there is no contradiction in the laws of mathematics. Laws of motion do not contradict the laws of thermodynamics, and the laws of thermodynamics do not contradict the laws of electromagnetism. They all act in cohesion fulfilling their purposes in the universe.
- Like God, mathematical laws are absolute. They do not depend on person, place or time. Whether you work individually or in a group, whether you work in America or India or Europe. They are absolute. They are not relative to place, person or time.
- Like God, there are intemporal. Like God, they do not change with time. The mathematical laws do not change tomorrow, or next month or next year.
USE OF MATHEMATICS:
I believe that every Christian should be familiar with foundational mathematics. Boethius (480 – 524) was a Christian mathematician and theologian who lived in early 6th century. He stressed teaching quadrivium, which consisted of arithmetic, geometry, astronomy and music. Bernard Riemann, whose geometry, Albert Einstein used in his theory of relativity, was a devout Christian. Reimann tried to prove mathematically the correctness of the Book of Genesis.
Applied Mathematics is everywhere. Personally I am surprised how mathematics made its way into logic, and from there, into ethics. Spinoza titled his book, ‘Ethics demonstrated in Geometrical Order’. In classical logic, every thing starts with a set of premises. Euclid started his Elements with axioms, which are self-evident propositions. Euclid wrote his book Elements starting with axioms, Newton wrote Principia starting with axioms or self-evident truth The United States Declaration of Independence was written in a geometric form with a logical structure. We hold these truths to be self-evident, that all men are created equal, that they are endowed by their Creator with certain unalienable Rights, that among these are Life, Liberty and the pursuit of Happiness. We hold these truths to be self-evident. Remember, Euclid’s Elements starts with self-evident axioms, Newton’s Principia starts with self-evident axioms. that all men are created equal, that they are endowed by their Creator with certain unalienable Rights. Jefferson wrote it in the form of the most basic formula of logic: If p, then q, p, therefore, q. If we all men are created equal, they deserve equal rights. All men are created equal, so, they deserve equal rights.Great men and women of history, they did not just study the structure of a logical argument, they pinned those arguments with God as their Creator. Seneca Falls Convention, which heralded women’s rights, starts with these words, ‘We hold these truths to be self-evident: That all men and women are created equal”.
LIMITS OF MATHEMATICS:
Carl Gauss, the Prince of mathematicians, referred to mathematics as ‘the queen of the sciences’. But the queen has her own limitations. Mathematics has been abused throughout history. The Nazis formulated their projects in mathematical language, ‘Jewish Problem and Final Solution’, Philosopher Francis Hutcheson used mathematics to support his ruthless utilitarianism and Jonathan Swift used mathematical rationality to justify parents eating their infants in his book ‘Modest Proposal’.
Even Mathematics is Not Complete Revelation
Kurt Godel (1906-1978). He is author of a famous mathematical theorem named after him, which is widely regarded as the most important logic discovery in the twentieth century. Godel’s theorem states that any arithmetic system contains undecidable propositions, whose truth cannot be decided on the basis of the axioms contained within that system alone. Those propositions can be proved only by adding axioms external to the system. In other words, total truth cannot be contained within a finite system. Any finite system is incomplete. This ‘incompleteness’ theorem implies that rational thought has inherent limitations and cannot attain absolute truth.
So, what is the point? Today we have mathematical theorems informing that mathematical systems cannot attain absolute truth. That is why God gave us revelation. God spoke His mind through His word, informing us what is right and what is wrong. God manifested Himself to us in the Person of Lord Jesus Christ. He lived in this world as a sinless human being and finally died on the cross to redeem us from our sins. He rose again from dead to give us the hope of eternal life. He left us so many infallible evidences for any one who wants to verify and choice is your to make.
So many infallible proofs are pointing us to the existence of God
So many infallible proofs are pointing us the supernatural life of Lord Jesus Christ
So many infallible proofs are pointing us to the divine origin of the Bible
Spinoza saw the work of God in the harmony of the universe, but he died a lost soul without coming to the saving knowledge of the cross of Lord Jesus Christ. Albert Einstein said, ‘I believe in Spinoza’s God, who reveals himself in the orderly harmony of what exists’. Albert Einstein died without the saving knowledge of the gospel. You may be a mathematical genius but if you do not put your faith in Lord Jesus Christ, you are a lost man on your way to an eternity in hell fire.
Pascal was considered the father of cost-benefit analysis, he used the first cost benefit argument in history and along with Pierre de Fermat, was also one of the founders of probability theory. Pascal, in his book Pensees uses a Wager and recommends us to bet on God because that is where the available evidence points us.
In this game which involves life and eternity, bet on God, you would not be disappointed.