“For I the LORD do not change….” (Malachi 3:6a, ESV)
Last night Robin and I had the privilege along with our kids of eating dinner with a group of our brothers and sisters in Christ (other Christians). At the table were several math teachers. When it came time to ask about dessert our daughter (Beth) chimed in that she would like some. To this we offered to get her some for later, which we did and even stopped to enjoy on our way home. Where we were was a place known for its desserts, and when the question was asked one of those at the table made the comment that you can’t square pie (pi or π), which is a math joke based upon mathematical definition. In response, one from my family (I don’t know which one exactly) responded by asking if they knew the square root of pi (π). No one came up with an answer, and the conversation moved on.
This morning, while in my shower where I often think of strange things, including illustrations, I thought again of this conversation. Following is a note that I sent to one of those at the table. I have included it as a response and have not reworded it really for sake of time but also to keep it in context.
“I know we had some mathematicians at our table last night and one of my family threw out the question about the square root of π in response to a statement about squaring π as being something that we cannot do. For me, mathematics did not make sense until I took calculus and moved from memorizing a bunch of formulas to understanding how these formulas were derived, and that when it comes from curves they could only find their answers in accepting some constants that could not be fully defined and using approximations which bring you close but never get you there.
I quickly thought about going further with it, but decided not to. But as I sat thinking about it this morning I realized where there was a gap between the understanding of a child and the understanding of the educated mind.
By definition π is an irrational or transcendent number. It cannot be represented accurately in fractional form, nor is it the root of others. By definition, based upon observation and calculation, it is a constant—a non-varying existent number which can never be fully represented even with the best computers which man has invented. It goes on and on and on without end or ever repeating itself in an endless cycle of numbers. It is totally unique to itself as is another famous constant e (Euler’s number or constant used in logarithmic equations).
[In response] a mathematician will resort to [this] definition and base all of his assumptions on [the] definition leading to the fact that [no] product of that number cannot accurately be [deduced] either. This would make deriving a square root impossible just as it would make squaring a circle impossible because you can always go a step further.
But from a child’s or non-mathematician viewpoint there is a limit to the number. It only extends as far as they can know it and as such they then can square or even square root that number. In doing this they remove the irrational and make it seemingly rational. They remove the transcendence and make it something they can wrap their hands around. And having reduced it to a limited number which they can plug it into their calculators, and using limited decimal spaces they can then manipulate it. Thus where the mathematician would say by definition that there can be no square root of π the non-mathematician would say that 1.772 is close enough for them.
In a sense isn’t what the non-mathematician does with π similar to what man does with our God who he does not understand. Sure they might make some sense out of it that they can work with, but in the end they have done nothing more than taken that which they cannot fully see and rationalized it into that which they can see, after all their calculators let them do it. And on an opposite side, there are also those who because they cannot fully grasp the limitless nature of something kept them always questioning. In that sense I am glad that at some point in time men discovered constants, and because of those constants he could move forward. He doesn’t have to fully grasp them though much has been revealed. He doesn’t have to know their exact end but trust that the results are dependable. He can move forward knowing that some things do not change, and because of that he finds stability.
I am so thankful that our constant is not found in a number, but in our God who created everything and even demonstrated for us in His creation that some things just have to be accepted as true for things to make sense."
“For I the LORD do not change….” (Malachi 3:6a, ESV)
“Every good gift and every perfect gift is from above, coming down from the Father of lights with whom there is no variation or shadow due to change.” (James 1:17, ESV)
“For by him all things were created, in heaven and on earth, visible and invisible, whether thrones or dominions or rulers or authorities—all things were created through him and for him. And he is before all things, and in him all things hold together. And he is the head of the body, the church. He is the beginning, the firstborn from the dead, that in everything he might be preeminent. For in him all the fullness of God was pleased to dwell, and through him to reconcile to himself all things, whether on earth or in heaven, making peace by the blood of his cross.” (Colossians 1:16–20, ESV)