Hello Blog Readers,
I apologize for the hiatus in posts to this math blog. That’s kind of the way my mind works: periods of frantic genius and creativity followed by periods of brief stagnation. If you’re the type of person who can keep up with the math in this blog, I’m sure you can relate. Us mathematicians all seem to have a bit of bipolar to us when it comes to work product.
So where were we? The last four blogs focused on some of the few remaining big conjectures in prime number theory. They proved Brocard’s and Legendre’s conjectures using a technique that I’m calling Accommodation Theory (some recognition for those proofs at some point from the math world would be nice…). They took a look at Goldbach’s conjecture and explained how Goldbach’s relates to RSA encryption. Above all, the work in the blogs sought to create some ordering system to the distribution of the prime numbers. It’s worth pointing out that this ordering system was obtained not by studying where the primes were located, but instead by studying where and how a finite set of composite numbers could behave. I love the prime numbers, and I’m sure at some point in the future I will be revisiting the subjects along with my beloved Accommodation Theory. However, for now, if you wish to visit or revisit the subject, please, take a look at my prior blog entries.
So let’s move forward with this math blog. In the near future, I will be making some calculus-related posts as I gear up to teach the subject starting in August. Today though, I want to focus on a philosophical issue relating to math. That is, the question of whether the mathematical rules and principles we as humans create and observe in our natural universe actually exist in our natural universe. In some ways the question is like the old riddle, “If a tree falls in the forest and no one is there to hear it, does it make a sound?” Here though, the questions take on mathematical tones. “If no one is there to count the sheep in the field, how many sheep are in the field?” Or, “Do the physics equations on the chalkboard (say for gravity or relativity) exist absent the mind devising the equations?” Topics like these are explored in a book called Are Numbers Real? by Brian Clegg. It’s a very fascinating topic when you start diving into it, and you start to learn that some of the mathematical techniques we take for granted in our world are not nearly as based in ‘common sense’ as we would like to believe. Many of these techniques (for example, fractions) took hundreds if not thousands of years to create and understand. That does not necessarily mean that the concept of 1/2 does not exist outside the human mind, but that the language of math is often a language of “revealed truths,” rather than of intuition.
Personally, I like to believe that the universe does in fact have an internal mathematical language governing its existence. And here is where the faith comes into play, for if we are living in a universe whose existence is dictated by a language, and if that language is offered to us by way of revealed truth, then my mind immediately turns to the question of who is speaking this language to us, i.e. who originally wrote this language? When I ponder that question, the answer that best makes sense to me is that a creator or architect of this language, and therefore the universe, must exist. For me personally, in my Catholic faith, that architect is God.
Being a Catholic in the Millennial generation is not the easiest thing in the world. There is a lot of criticism in the modern age claiming that science and the Bible are incompatible. For some time in my youth, I too felt that this must be true, but the more I studied both the sciences and my religion, the less I saw the contradictions. Also, where there are contradictions I’ve always considered it to be a matter of revealed truth – where the story and mythos gives way to the larger truths of the universe which could not have been understood 1000s of years ago. Anyways, I hope to address one of these claimed contradictions here, and show that it is not a contradiction at all. That is the claimed contradiction of the age of the universe.
We’ve heard the adage: the Bible states that the Universe, Earth, and all life on it was created in 7 days, but science tells us that the Earth alone is billions of years old, and the universe even older. Can the paradox be rectified, or is the Bible already wrong with its first sentence? In fact, the paradox can be rectified. The answer is simple: relativity and the ability to exist outside our universe.
Our vantage of time and space comes from within our universe. Yet, if a creator of the universe exists, then that creator exists outside our universe. The creator’s vantage of time and space can and would be entirely different from our own vantage. And whose vantage is the Bible talking about when discussing creation? God’s vantage. As a result, what is perceived as a 7 day feat outside of the universe could indeed be billions of years inside creation. That is the power of relativity, the power of existence beyond our universe, and the power of science. It also gives credence to the Bible’s claim that everything we know, all of existence, is but a moment in God’s time.
Perhaps a few pop culture references can solidify what I am trying to say. In the movie Interstellar, the main character goes on a journey through space that eventually takes him through a worm hole, and then near and eventually into a black hole. As he goes into the black hole, he starts experiencing new dimensions that briefly give him the ability to manipulate both time and gravity. As he comes out of the ordeal, his entire journey, which from his vantage lasts maybe a couple of months, ends up taking nearly 100 years from earth’s vantage. He looks exactly as he looked when he left, but his daughter has aged and lived her entire life. So it is here. From God’s vantage, all of time and existence as we know it may be occurring in the blink of an eye.
Another reference for those who prefer the idea that we are not living in a physical universe, but a computer simulated universe. In the television show Black Mirror, computers have become advanced enough to have artificial intelligence and perceive time. Yet, the programmer can set the computer’s perception of time, such that weeks, months, even years can pass inside the computer simulation while only seconds pass on the outside. While the show exploits these techniques to some pretty sinister ends, it is clear that the idea could also be used in the area of universe creation, with entire universes being created and existing for billions of years on the inside, while only for a moment on the outside.
What’s my point with all of this? I don’t know. Just maybe that our modern society is too quick to write off religion as antiquated, and that the often purported defense of “but, science!” is generally not enough to wash away the high probability of the existence of God. For if you accept that the laws of the universe are governed by a mathematical language, then at some point you need to step back and ask yourself, who or what is writing the math? And as you delve deeper into the subject, you may come to learn the joy that many of us as mathematicians already know and experience: that learning to speak the language of math is learning to speak the language of God.