God and Math

Discussion in 'Apologetical Methods' started by Scott, Oct 26, 2005.

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  1. Scott

    Scott Puritan Board Graduate

    How would one make a short, positive case that a presuppositional perspective is necessary to support the use of math? I am not asking for internal critiques of other views, but how to Christian worldview positively supports math. Thanks
  2. Jeff_Bartel

    Jeff_Bartel Puritan Board Graduate

  3. Contra_Mundum

    Contra_Mundum Pilgrim, Alien, Stranger Staff Member

  4. Scott

    Scott Puritan Board Graduate

    I have read Nickel and listend to Bahnsen's tape. I was wondering if anyone would be able to briefly set out a positive argument, of the sort that you would make to a co-worker who would not be willing to read a book.
  5. Me Died Blue

    Me Died Blue Puritan Board Post-Graduate

    Could you elaborate on this a bit?
  6. Scott

    Scott Puritan Board Graduate

    I don't follow. Say that we are discussing with an atheist who ends up admitting that the atheistic view cannot support math. He says, "how does the Christian view make math possible?" What do you say?
  7. Civbert

    Civbert Puritan Board Junior

    How about this - find one example of the application of addition.


    I think one also must presuppose the validity of the laws of logic. First because no intelligent conversation can happen without it, second because all mathematics presuppose the basic law of contradiction. 1 = 1 is true and 1 =/= 1 is false.

    Calculus is like multiplication and multiplication is just addition. It all builds on this and additional axioms.

    Geometry is based on axioms, and one must assume axioms in all systems if they are rational, including Christianity.
  8. SRoper

    SRoper Puritan Board Graduate

    "Geometry is based on axioms, and one must assume axioms in all systems if they are rational, including Christianity."

    So which axioms do you assume? For example, do you assume that Euclid's Fifth Postulate (the Parallel Postulate) is true?
  9. Vytautas

    Vytautas Puritan Board Freshman

    If Calculus is like multiplication and multiplication is just addition and addition is found in the Bible, can you deduce Calculus from the Bible?
  10. Civbert

    Civbert Puritan Board Junior

    It is true for euclidean geometry and false for hyperbolic geometry. That does not mean either is "truth".

    What you can not do is assume Euclid's 5th and the hyperbolic's alternative postulate are true at the same time (not rationally anyhow). But you are free to assume either and work within that system - and switch to the other later.

    That is a difference in the axiom of Christianity and mathematical axioms. The axiom of Christianity can only be "chosen" if you are "chosen" to believe it is true, and once you have the faith of the Christian axiom, you can not switch. Geometric axioms can be switched at any time. And you can switch geometry axioms without violating the axiom of Christianity since neither contradict Christianity.
  11. Civbert

    Civbert Puritan Board Junior

    Once you deduce the validity of addition, then it's only a matter of mental work to deduce Calculus. I suppose you will need to adopt some additional mathematical axioms, but that's OK as long as they are not contrary or contradictory to Scripture.
  12. VirginiaHuguenot

    VirginiaHuguenot Puritanboard Librarian

  13. caddy

    caddy Puritan Board Senior

  14. WrittenFromUtopia

    WrittenFromUtopia Puritan Board Graduate

    What about Non-Euclidean geometry?
  15. BobVigneault

    BobVigneault Bawberator

  16. tewilder

    tewilder Puritan Board Freshman

    I don't get the argument here.

    If the point is to support the idea that knowledge must be based on the "axiom of Scripture", what good is Godel's proof the truth in arithmetic can't be reduced to an axiomatic system? Godel himself thought that it supported the idea of a sort of Platonic rational intuition that transcended proof methods.
  17. caddy

    caddy Puritan Board Senior

    God by the Numbers

    [SIZE=+1]God by the Numbers: Coincidence and random mutation[/SIZE]
    Christianity Today ^| 3/10/06 | Charles Edward White

    God by the Numbers
    Coincidence and random mutation are not the most likely explanations for some things.
    by Charles Edward White

    Math and theology have had a long and checkered relationship. The Babylonians and Mayans both associated numbers with God. In fact, both societies named their gods with numbers. The Mayans used 13 and the Babylonians used 60. In the Greek world, followers of Pythagoras prayed to the first 4 numbers and thought they were the creator. On the other hand, in the 18th century, the French mathematician Laplace told Napoleon he had no need of God even as a hypothesis, and in 1744, John Wesley confessed: "I am convinced, from many experiments, I could not study either mathematics, arithmetic, or algebra … without being a deist, if not an atheist."

    No one knows what Wesley saw in 18th-century mathematics that he feared would lead him away from the God of the Bible, but today, many Christian mathematicians think that numbers point to God. Three numbers in particular suggest evidence for God's existence. They are 1/1010123, 10162, and eπi.

    Fine-tuning the universe
    The first recent number that points to God is 1 in 10 to the 10 to the 123. This number comes from astronomy. Oxford professor Roger Penrose discusses it in his book The Large, the Small, and the Human Mind. It derives from a formula by Jacob Beckenstein and Stephen Hawking and describes the chances of our universe being created at random. Penrose spoofs this view by picturing God throwing a dart at all the possible space-time continua and hitting the universe we inhabit. The Beckenstein-Hawking formula is too complicated to discuss here, but another approach to the same problem involves the fine-tuning of the universe and the existence of habitable planets.

    The fine-tuning of the universe is shown in the precise strengths of four basic forces. Gravity is the best known of these forces and is the weakest, with a relative strength of 1. Next comes the weak nuclear force that holds the neutron together. It is 1034 times stronger than gravity but works only at subatomic distances. Electromagnetism is 1,000 times stronger than the weak nuclear force, and the strong nuclear force, which keeps protons together in the nucleus of an atom, is 100 times stronger yet. If even one of these forces had a slightly different strength, the life-sustaining universe we know would be impossible.

    If gravity were slightly stronger, all stars would be large, like the ones that produce iron and other heavier elements, but they would burn out too rapidly for the development of life. On the other hand, if gravity were weaker, the stars would endure, but none would produce the heavier elements necessary to form planets.

    The weak nuclear force controls the decay of neutrons. If it were stronger, neutrons would decay more rapidly, and there would be nothing in the universe but hydrogen. However, if this force were weaker, all the hydrogen would turn into helium and other elements.

    The electromagnetic force binds atoms to one another to form molecules. If it were either weaker or stronger, no chemical bonds would form, so no life could exist.

    Finally, the strong nuclear force overcomes the electromagnetic force and allows the atomic nucleus to exist. Like the weak nuclear force, changing it would produce a universe with only hydrogen or with no hydrogen.

    In sum, without planets, hydrogen, and chemical bonds, there would be no life as we know it.

    Besides these 4 factors, there are at least 25 others that require pinpoint precision to produce a universe that contains life. Getting each of them exactly right suggests the presence of an Intelligent Designer.

    The second component to be considered when calculating the likelihood of this life-supporting universe is the presence of habitable planets. In addition to the fine-tuning of the whole universe, there needs to be a carefully specified place where life can reside. Life as we know it can only exist within certain limits. There are at least 45 parameters, from the size of our galaxy to the mass of the moon, which permit the presence of life on a planet. A huge galaxy erupts with too many stars and thus disturbs planetary orbits, but a tiny galaxy does not produce enough heavy elements for a planet to form. At the other end of the spectrum, too large a moon destabilizes a planet's orbit, while having no moon or one that is too small permits a planet to wobble as it spins and disrupts the planet's climate.

    From these 45 planetary characteristics alone, Hugh Ross, in his chapter in Mere Creation, calculates there is less than 1 chance in 1069 of habitable planets occurring at random.

    The fine-tuning of the four physical forces and the presence of one habitable planet are just two of the components that would go into a formula to predict the probability of a life-supporting universe. The first one to try to calculate this number was Frank Drake in 1961, when he listed fewer than ten factors. Coming at the same problem from a different direction by calculating the entropy of black holes, Penrose says the number is 1 in 10 to the 10 to the 123. This number is beyond human comprehension. 10 to the 10 to the 3 would be written as 10 followed by 999 zeros.

    To write 10 to the 10 to the 123 in one line would extend beyond the bounds of the universe. If Penrose is right in calculating the odds of a life-supporting universe at 1 in 10 to the 10 to the 123, then a strong case for a Creator emerges.

    Not enough time
    The second number that points to God comes from the field of biology. William Dembski, in The Creation Hypothesis, suggests the following argument.

    Darwin thought that all life, including humans, arose from a one-celled organism. But to get from a one-celled organism to a human being with a least a trillion cells, there would have to be many changes. Darwin says these changes were produced at random, but they would have had to occur in the right order. It doesn't do any good to give an organism a leg until it has a nervous system to control it. Even if we limit the number of necessary mutations to 1,000 and argue that half of these mutations are beneficial, the odds against getting 1,000 beneficial mutations in the proper order is 21000. Expressed in decimal form, this number is about 10301.

    10301 mutations is a number far beyond the capacity of the universe to generate. Even if every particle in the universe mutated at the fastest possible rate and had done so since the Big Bang, there still would not be enough mutations.

    There are about 1080 elementary particles in the universe. The fastest they could mutate would be Planck time, or 10-42 seconds. Planck time is the smallest unit of time and can be approximated as the time it would take two photons traveling at 186,000 miles per second to pass each other. If every particle in the universe (1080) had been mutating at the fastest possible rate (1042) since the Big Bang about 15 billion years ago, or 1017 seconds ago, it would produce 1080 x 1042 x 1017 or 10139 mutations. But to have a chance at even 1,000 beneficial mutations takes 10301 tries. Thus, the chance of getting 1,000 beneficial mutations out of all the mutations the universe can generate is 10139 divided by 10301, or 1 chance in 10162.

    For Darwin's theory to have a chance of being right, the universe would have to be a trillion quadrillion quadrillion quadrillion quadrillion quadrillion quadrillion quadrillion quadrillion quadrillion quadrillion times older than it is. Because the universe is so young, Darwin's argument fails, and William Paley's contention that design presupposes a designer becomes more persuasive.

    Connecting the constants
    The final number comes from theoretical mathematics. It is Euler's (pronounced "Oiler's") number: eπi. This number is equal to -1, so when the formula is written eπi+1 = 0, it connects the five most important constants in mathematics (e, π, i, 0, and 1) along with three of the most important mathematical operations (addition, multiplication, and exponentiation).

    These five constants symbolize the four major branches of classical mathematics: arithmetic, represented by 1 and 0; algebra, by i; geometry, by π; and analysis, by e, the base of the natural log. eπi+1 = 0 has been called "the most famous of all formulas," because, as one textbook says, "It appeals equally to the mystic, the scientist, the philosopher, and the mathematician."

    The reason for this wide-ranging appeal is its utter serendipity. First, there is the ubiquitous number e, which pops up in the most unexpected places. It was first discovered in an attempt to make multiplication easier. In 1614, John Napier figured that adding exponents was easier than multiplying multi-digit numbers, so he (and others) calculated the logarithms of all integers from 1 to 100,000, expressing these numbers as powers of 10. Later mathematicians found it more convenient to express logarithms as powers of the natural log e, a number close to 2.71828.

    This number also appears in banking, because it is the limit for growth of compound interest. Let's say one invested $1,000 in a very generous bank that paid an annual interest of 100%. If interest were compounded annually, at the end of the year, the money would have grown to $2,000. If, however, the bank compounded interest four times a year, the money would grow to $2,441.41. If the bank compounded interest continually, the deposit could grow to $2,718.28, which just happens to be the value of e times the original investment.

    Finally, e turns up at the origin of calculus, where it is the function equal to its own derivative (if y = ex then dy/dx = ex), and it equals the limit of (1+ 1/n)n as n approaches infinity. e is irrational, so it can never be written exactly in decimal form, but it is a very useful and fascinating number in its own right.

    When we combine e with π, we are introducing the oldest irrational number. Two thousand years before Christ, the Greeks knew that π was the ratio of the circumference of a circle to its diameter and that it could not be expressed as the ratio of any two integers. It is essential in geometry, but it also turns up in waves of air, water, electricity, and light, and it even helps actuaries calculate how many 50-year-old men will die this year.

    The number i is a relative latecomer, proposed in the 1600s as an imaginary number and defined as the square root of -1. It was proposed to help solve equations like x2+ 1 = 0, but today it is useful in science and engineering. George Gamow, in his book One, Two, Three … Infinity, even uses i to locate buried treasure with an outdated map.

    The idea that these two irrational numbers should combine with an imaginary one to yield so utilitarian a result is breathtaking. It is like deconstructing a chemical necessary for life (salt) and finding that it consists of two deadly poisons (sodium and chlorine). That these three strange numbers with such diverse origins should work together to produce a result so basic to mathematics argues that there is a profound elegance or beauty built into the system.

    The discovery of this number gave mathematicians the same sense of delight and wonder that would come from the discovery that three broken pieces of pottery, each made in different countries, could be fitted together to make a perfect sphere. It seemed to argue that there was a plan where no plan should be.

    Because of the serendipitous elegance of this formula, a mathematics professor at MIT, an atheist, once wrote this formula on the blackboard, saying, "There is no God, but if there were, this formula would be proof of his existence."

    Today, numbers from astronomy, biology, and theoretical mathematics point to a rational mind behind the universe. To be sure, they do not point to the personal God of the Bible as such. Yet they are not inimical to the biblical God, either. The apostle John prepared the way for this conclusion when he used the word for logic, reason, and rationality—logos—to describe Christ at the beginning of his Gospel: "In the beginning was the logos, and the logos was with God, and the logos was God." When we think logically, which is the goal of mathematics, we are led to think of God.

    Charles Edward White is professor of Christian thought and history at Spring Arbor University in Michigan.

    Related Elsewhere:


    "Three numbers in particular suggest evidence for God's existence."

    Well, I do suppose some are quite comfortable with all this scientific evidence and such. And that leads them to believe a creator is responsible for everything, instead of thinking we came from a rock, some slime or some other such thing. But, all that is really necessary is for one to look around and see a multitude of different things. Then peruse the Bible, online or your own copy, and there's the proof...

    FreeRepublic.com is powered by software copyright 2000-2003 Robinson-DeFehr Consulting, LLC.

  18. greenbaggins

    greenbaggins Administrator Staff Member

    Hey, Tim! This is my father's article, in case you didn't know.

  19. tewilder

    tewilder Puritan Board Freshman

    Yes. I met him once or twice at dinner at someone's house but decided not to raise the topic of the article.
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