Moral Relativism, Absolute Truth, and Pi December 11, 2006
Posted by TimTheFoolMan in absolute truth, moral relativism, Morality, Parenting/Children, Pi, Religion, Religion, Philosophy, and Science, Science & Technology.trackback
It’s been a long time coming, and I suppose I should have stated this clearly earlier. I have a confession to make. I don’t know the exact value of Pi.
Oh, sure. I know an “approximate” value: 3.1415926535. I know that from memory. But I have to confess that I don’t know the exact value.
Relative Knowledge
In science, most things are exact. I suppose this is why Pi sets on edge, the teeth of any serious student of math at one point or another in their careers.
I suppose the most frustrating thing about Pi is, you can get pretty close, without a lot of education. My oldest son, when he was in pre-school, once guessed “pi” when the teacher asked how many jelly beans were in the jar. The other kids laughed and said “That’s not a number!”
My 5 year-old son quickly responded “Yes it is. It’s more than three but not four.” (An exasperated teacher was then left the interesting chore of teaching fractional numbers to a handful of confused preschoolers.) My son was wrong about the number of jelly beans (it was several hundred), but he had already developed a basic understanding of Pi.
Unfortunately, he didn’t know the true value of Pi, and he still doesn’t. Have I failed him as a father because I don’t know it either?
Pi, Any Way You Slice It
Most children are introduced to Pi as “3.14.” In school, I determined to get a bit more exact, and learn it to ten decimal places. Unfortunately, in the black and white of math, neither of those answers are strictly correct.
At the tender age of 5, my son was able to wrap his brain around the notion of fractional values. (My example was “You have three apples, and then I give you part of another. Do you have four apples yet? Do you have more than three?”). Now a freshman in college, he has a much deeper understanding of numbers and math, but he still has much to learn. When I look at research that documents thousands of digits of this confounding number, I realize that I have much to learn too.
Interestingly, there are people who have devoted their careers to studying Pi. They develop exotic proofs, study and learn ways to understand more and more clearly exactly what Pi is. There are countless web sites devoted to the search for the exact value of Pi, but as far as I can determine, none of them have it… yet.
Clearly, the simple logic of geometry suggests that there is, in fact, one and only one “true” value of Pi. We can pretend that it’s 3.14 or 3.1415926535, but we will be wrong. We can claim the moral high ground of our value being “true for me,” but that doesn’t make it true in all cases, everywhere, for everyone.
Only the true value of Pi (the value that, to this day, remains unknown), is always true, everywhere. To suggest otherwise is to be ridiculous.
Knowing the Unknowable
However, until the actual value is known and proven, people of various educational levels can engage in debates over this, sometimes expending huge amounts of energy in the process, and frequently accomplishing very little. Such is the case with subjects that we “split hairs” over.
At this stage, some scientists have abandoned their personal search for the “true” value of Pi, and are left to deal with the unsatisfying sense of there being a truth, out in the distance somewhere, that they cannot yet grasp or know or understand. How incredibly frustrating.
Interesting isn’t it, how closely this parallels the search for theological truth? The endless frustration of feeling that you’ve almost got it, and then finding out that you’re nowhere near knowing everything that there is to know, and that the “mind of God” seems to extend on to several more decimal places than you imagined. It seems so simple at first, and then you realize that what you “knew” and what you understood as “the truth” is merely an approximation, and that God has an infinitely rich and non-repeating pattern out there for you to discover.
Someday (though not, scripture says, in this life), I will see face to face, and know as I am known. Someday (though not, scientists say, anytime soon), I may see the exact value of Pi, and not just an approximation. Until then, I’ll just have to learn to live with the unknown, tell people the “best approximation” of the truth that my brain is currently able to comprehend, and hope for the day of complete understanding.
A Fool and his Words are Soon Parted 
This post didn’t even touch on moral relativism. As for philosophizing the existence of objective reality (therefore inducing the existence of “absolute truth”, to contrast with “relative truth” as in subjective reality), you have not presented anything of intellectual value to the table, in my opinion. You did show a general understanding of pi, but even this didn’t go so far as to talk about transcendence (in mathematics, not theology) and irrationality, finite and infinite (in terms of symbolic representability), expression and ideal concept, constructivism and other philosophies in mathematics.
You touched on three major notions: (1) approximation as a method of understanding in the face of uncertainty (“Relative Knowledge”), (2) the number Pi in conventional understanding in society (“Pi, Any Way You Slice It”), and (3) recognition of incomprehensibilities (“Knowing the Unknowable”).
“Only the true value of Pi (the value that, to this day, remains unknown), is always true, everywhere. To suggest otherwise is to be ridiculous.” After this statement, you go on to claim that there is some kind of controversy over pi. This may be the case with friends and math-enthusiasts, but there are no big mainstream controversies regarding pi (except for the transcendence of pi^e, and the normality of its digits, but these are merely wondered about and not argued about in mathematics). I think it is ridiculous to state that scientists (mathematicians, more to the point) cannot fully know, understand, grasp etc. that there is some “true” value of pi. Empirically, we cannot find the exact value of pi or prove its uniqueness, properties, etc. But, mathematically, this can be rigorously defined and proven. Empirical research by computers (and some measuring real life objects) can scientifically evidence this claim.
Although theological and mathematical assertions can only be evidenced scientifically, and not proved empirically to the degree of the certainty of abstractions in modern mathematics, it is still too weak of an analogy to make any sort of conclusions (like that the many theological positions can be reasonably taken on faith, kind of “like” mathematics as you seem to argue).
I still think you could have strengthened the power of your case, though, if you invoked the concept of infinity. Our representation is only finite (in the case of Pi and theology such as God, dualism, creation, eschatology, revelation, omnimax, etc.), but in the case of mathematics, what we speak of sometimes entails infinite information with respect to our representations. You could try and show that this is also the case for theological principles, as well. Then you would be saying something.
Re: Moral relativism from Wikipedia:
I was simply stating that incomplete knowledge (such as my son’s incomplete understanding of Pi) naturally leads us to make distinct claims that are relative to our intellectual framework. Without knowledge of any number of absolutes, assessments that I make about moral issues are correspondingly suspect.
For example, the simple lesson for my son is that killing someone else is wrong. If he were to then see me shoot someone threatening us, and kill him, the “moral equivalent to Pi as 3” didn’t hold, and he’s going to want to understand why, in that case, killing someone else might not be wrong. In the same way that we simplify our description of Pi’s value based on someone’s intellectual capability, we tend to teach moral values and theological things in simplistic ways, ignoring the circumstances that force our understanding to be inherently relative to our own experience/knowledge.
That issue aside, you stated (or restated) in your closing paragraph what I was intending to state with the article, namely:
– Pi has a value, and one that transcends our ability to understand it or state it
– Our lack of ability to understand or state that value accurately in no way changes what Pi means, regardless of the context
– My experience with theological issues is such that I see the same kind of variance in understanding leading to debates that would parallel people arguing if 22/7, 3.14, or 3 were actually the correct value of Pi
I wasn’t claiming that there was some kind of international debate about Pi’s value, as much as there has been (and will continue to be) further and further research into a more exact understanding of its nature and “true value.” In the same way, I think it’s just as silly for people of faith (or non-faith) to treat “unknowable” theological issues as closed issues. – Tim
Okay, I see where you are going with this. I was reacting too much to your little story of smart people trying to get closer to pi, but you were using it as an analogy of theologians and the like figuring out, or simplistically explaining, morality.
I think the entire issue is grounded in definitions. If a concept is clearly and unambiguously defined, like pi (a circle is defined, its circumference can be rigorously defined by arc-length and calculus, and its diameter is defined, so we can divide them to define pi). And if there were some moral descriptor that we unambiguously defined (like “x is good” is equivalent to “x gives some person A happiness”), it would be objective and therefore invariant, or not relative to any of our opinions. This is because for any person A, they did or did not attain some happiness from x, regardless of what others think.
Suppose “x is bad” means that “x causes some person B to suffer”. Then something can be both bad and good at the same time, which is paradoxical (but not contradictory in the way I defined “good” and “bad” here). What would one do in this case? Probably try and make amends to the definitions so that they are the negations of each other. Here’s my point: towards what meaningful system do we keep redefining, if only slightly, our moral descriptions and theories? I think it is your point that just like people approximating pi, a real number regardless of our never expressing it finitely in our number system, we are approximating some kind of objective morality, independent of ourselves.
(I might add here that this is only descriptive morality we are talking about, not prescriptive morality as in “you should/should not do x”. There is an “Is/Ought” problem in trying to logically conclude a prescriptive claim from objective descriptions of reality unless personal values are taken into account.)
Unlike pi, the number we can approximate, this “transcending” morality that I think you are hinting at is not clearly defined by us. With pi, we have defined something but can only approximate it. We have not defined what it means to be a perfect morality. Perhaps, even, you have only percieved large amounts of agreement on moral issues in the schools of thought you have looked at in the world. There are numerous distinct mindsets about what is moral and not, I would assume.
But here is where I think moral relativism has a point: anything that is true independent of what we think is objective, and so prescriptive morality is subjective because it has no other ground than our thoughts of what it is exactly we are talking about. (And prescriptive morality, what we would be talking about it such a case, depends on our own will and volition.)
Lastly, I would like to concede my lack of knowledge of _theological_ arguments for objective morality. My guess would be that it goes something like this (under assumption that God, as in an entity that explains why there is a universe and which is capable of thought): God’s thinking corresponds to objective reality; God’s thinking is objective; God’s prescriptions to humans are objective; God-commanded morality is objective. But if you know any arguments that are interesting, please point me in the right direction.
Hi,
Hope you don’t mind, but I invited my students to visit this thread, as we are broaching some of this content in our Philosophy Club.
BTW, have you read any of John D. Barrow’s work? Seems up your alley…
MrB,
I don’t mind a bit, and welcome to all!
I’ve only scanned bits and pieces surrounding the Anthropic Principle… enough for me to sit squarely on the fence over it. However, from what I can discern, Barrow himself was a bit on the fence about it too.
Please feel free to comment, and I encourage your students to do the same. – Tim
Hi Tim,
Thank you for the nice entry. It was a pleasure to read.
I only have one thing to add: If we are one day allowed to discover the exact value of Pi, I guess we will still not be fully able to grasp God. Pi is a transcendental number, but to God even transcendence must be immanent, for he made it. Or in other words: The transcendence of God must transcend even the transcendental numbers, because he made them.
Sincerely,
Selwyn
I don’t believe in God.
Cinamon, I’m completely OK with that. I have many friend that share the same feelings you have, so I hope you won’t “throw the baby out with the bathwater,” and discard everything else I say here based upon disagreement on that point. – Tim
There is a true value of pie that scientists discovered, but I don’t think you’ll ever be writing it in Math class lol. I am defietly one of those people who HATES when teachers tell yo to use 3.14. Math should be exact, not kinda close. I find a different way to the solution of the problem, if I have a choice. I use 22/7, its exact and it works for me, because I love fractions.
Don’t use 22/7 I was jk. Lol, but its close enough, right? lmao.