Of math and theology
01/03/15 05:09
Mathematics wasn’t one of my strong suits during my educational career. I did family well with algebra and a little better with geometry. I learned some practical mathematical skills that I use in my daily life. These days the computers do more of the math for us than used to be the case, but I still am able to compute the area of geometric shapes and understand of reducing and enlarging things by percentages. I am reasonably skilled at basic math functions and can add, subtract, multiply and divide in my head well enough to figure change when making a purchase or estimate sales tax or a tip at a restaurant.
I was really focused on philosophy and theology during my college years, with just enough French thrown in to accomplish a minor in that subject. Truth be told, I was reading French in part because it gave me original language access to some existential philosophers. Two fields of study in one book - not bad. But our college required at least one math course for a degree and the fit for me was logic. Logic was offered as a math course and taught by a mathematics professor. It was a small class, which meant that I got individualized instruction and I could follow the study easily. Being a mathematics professor, the teacher used standardized tests, mostly multiple choice, so that she could compare her students from one year to another. I learned the material and easily passed the tests.
There was little actual manipulation of numbers in the course and in a way it was a study in the history and philosophy of science as much as it was a course in mathematics. That part of the course was very interesting to me. What are the classical forms of argument? How can we spot an error in reasoning? What are typical fallacies that are presented in arguments and how are these fallacies countered?
Since those days, I have come to understand and appreciate more about the study of math and although I am certainly still rather weak in that area of my education, I am less intimidated by math than once was the case.
Along the way, I had a close friend who was a double major: Christian Thought and Mathematics. He would frequently espouse the similarities of the two disciplines. In both disciplines he was most drawn to the sides of the disciplines that study entirely abstract concepts. He was good at abstract thought. He was less interested in how mathematical concepts applied in the real world, and more interested in the intrinsic nature of numbers and how they interacted. In those days, there was a bit of a division between “pure” mathematics and “applied” mathematics. These are not concepts that I fully understand, but I think that “pure” is generally an unfortunate choice of a moniker.Actually numbers can be as abstract as nearly any other form of thought.
Yes, I know the argument that mathematics are constant, that numbers follow set rules and that when applied correctly, answers are uniformly consistent. Therefore mathematics can be used to study the ancient past, as in astronomy, or predict the future. Since one plus one is always two, we know that this will be the case in the future as well.
The problem, of course is that not all math is as simple as one plus one. Ten times ten is one hundred, of course, but that is assuming that you are using a base ten system. And it assumes that you are using the Hindu-Arabic numeral system that is common in our part of the world. If you use an alphabetic numeral system, such as ancient Hebrew, or a base twelve system favored by some because it is a more interesting composite number, the results vary. Well, that isn’t completely true. The results are consistent within the system, but challenging to compare between different systems.
And we haven’t even begun to discuss imaginary numbers, which are not fantasies at all, but rather numbers that produce “real” negative numbers when squared.
It would be better if the person writing this blog were a mathematician who really knows what he or she is talking about. Alas, you’re stuck with me. And I really wanted to talk about theology anyway. What is clear to me is that the desire for a completely logical universe where the same rules apply in every situation has uniformly lead physicists and astronomers to areas a great speculation. “If we could see a distant planet, that would explain the slight dimming of the star that we can see. Therefore we assume that there is a planet in that particular solar system.” “If we build a particle accelerator that is large enough we might be able to prove or disprove the existence of the Higgs-Boson particle.” Sometimes, as with the Higgs-Boson, the theory proves to be correct. Technically we haven’t proven the existence of those distance planets, but it appears that scientists are likely correct with that theory as well. There are plenty of other scientific theories that don’t pan out as successfully. Sometimes these theories are off base because of mistakes in mathematics or the inability to accurately measure very large or very small parts of the universe.
They may have proven the existence of the Higgs-Boson, but it isn’t “the god particle,” and no, they haven’t provided evidence, either pro or con about the existence of God.
What I am saying is that even with all of the imprecision and limits of language, mathematics, while more precise on some levels, is filled with as many untested assumptions and speculative theories as any other field of study. Mathematicians and some of us lay people like, on occasion, to speak of math as being very consistent and logical and universal, but that is hardly the case. It is common, these days, to hear scientists talk about the limits of thinking of a universe, since current theory supports the existence of many universes - or a multiverse. There is even speculation about universes where mathematics operate by different sets of rules.
It is all very confusing.
I think I’ll stick to the study of God, which, from my point of view, is far less speculative. At least in theology we can come to limited agreement about what previous generations said and believed.
No, I’m just kidding, we have little common agreement. Still the pursuit of understanding others is a worthy enterprise.
Maybe my friend had it right: theology and mathematics are very similar fields of study.
I was really focused on philosophy and theology during my college years, with just enough French thrown in to accomplish a minor in that subject. Truth be told, I was reading French in part because it gave me original language access to some existential philosophers. Two fields of study in one book - not bad. But our college required at least one math course for a degree and the fit for me was logic. Logic was offered as a math course and taught by a mathematics professor. It was a small class, which meant that I got individualized instruction and I could follow the study easily. Being a mathematics professor, the teacher used standardized tests, mostly multiple choice, so that she could compare her students from one year to another. I learned the material and easily passed the tests.
There was little actual manipulation of numbers in the course and in a way it was a study in the history and philosophy of science as much as it was a course in mathematics. That part of the course was very interesting to me. What are the classical forms of argument? How can we spot an error in reasoning? What are typical fallacies that are presented in arguments and how are these fallacies countered?
Since those days, I have come to understand and appreciate more about the study of math and although I am certainly still rather weak in that area of my education, I am less intimidated by math than once was the case.
Along the way, I had a close friend who was a double major: Christian Thought and Mathematics. He would frequently espouse the similarities of the two disciplines. In both disciplines he was most drawn to the sides of the disciplines that study entirely abstract concepts. He was good at abstract thought. He was less interested in how mathematical concepts applied in the real world, and more interested in the intrinsic nature of numbers and how they interacted. In those days, there was a bit of a division between “pure” mathematics and “applied” mathematics. These are not concepts that I fully understand, but I think that “pure” is generally an unfortunate choice of a moniker.Actually numbers can be as abstract as nearly any other form of thought.
Yes, I know the argument that mathematics are constant, that numbers follow set rules and that when applied correctly, answers are uniformly consistent. Therefore mathematics can be used to study the ancient past, as in astronomy, or predict the future. Since one plus one is always two, we know that this will be the case in the future as well.
The problem, of course is that not all math is as simple as one plus one. Ten times ten is one hundred, of course, but that is assuming that you are using a base ten system. And it assumes that you are using the Hindu-Arabic numeral system that is common in our part of the world. If you use an alphabetic numeral system, such as ancient Hebrew, or a base twelve system favored by some because it is a more interesting composite number, the results vary. Well, that isn’t completely true. The results are consistent within the system, but challenging to compare between different systems.
And we haven’t even begun to discuss imaginary numbers, which are not fantasies at all, but rather numbers that produce “real” negative numbers when squared.
It would be better if the person writing this blog were a mathematician who really knows what he or she is talking about. Alas, you’re stuck with me. And I really wanted to talk about theology anyway. What is clear to me is that the desire for a completely logical universe where the same rules apply in every situation has uniformly lead physicists and astronomers to areas a great speculation. “If we could see a distant planet, that would explain the slight dimming of the star that we can see. Therefore we assume that there is a planet in that particular solar system.” “If we build a particle accelerator that is large enough we might be able to prove or disprove the existence of the Higgs-Boson particle.” Sometimes, as with the Higgs-Boson, the theory proves to be correct. Technically we haven’t proven the existence of those distance planets, but it appears that scientists are likely correct with that theory as well. There are plenty of other scientific theories that don’t pan out as successfully. Sometimes these theories are off base because of mistakes in mathematics or the inability to accurately measure very large or very small parts of the universe.
They may have proven the existence of the Higgs-Boson, but it isn’t “the god particle,” and no, they haven’t provided evidence, either pro or con about the existence of God.
What I am saying is that even with all of the imprecision and limits of language, mathematics, while more precise on some levels, is filled with as many untested assumptions and speculative theories as any other field of study. Mathematicians and some of us lay people like, on occasion, to speak of math as being very consistent and logical and universal, but that is hardly the case. It is common, these days, to hear scientists talk about the limits of thinking of a universe, since current theory supports the existence of many universes - or a multiverse. There is even speculation about universes where mathematics operate by different sets of rules.
It is all very confusing.
I think I’ll stick to the study of God, which, from my point of view, is far less speculative. At least in theology we can come to limited agreement about what previous generations said and believed.
No, I’m just kidding, we have little common agreement. Still the pursuit of understanding others is a worthy enterprise.
Maybe my friend had it right: theology and mathematics are very similar fields of study.