I have learned that God is the Master Physicist, Master Mathematician, and the Master of any good discipline you may think of. We worship an awesome God. I believe God smiles as we uncover His majesty.
If you know someone who has lost faith or is an agnostic or an atheist, here is your answer for them. Dr. Jason Lisle Ph.D. is a devoted Christian and astrophysicist and founder of the Biblical Science Institute. He has a most remarkable video with detailed pictures demonstrating the beauty of the mathematics of the mind of God. There is no secular or atheistic explanation for these—showing a touch of the beauty of God’s mathematics.
The Mathematics of God
Let me explain a couple of terms in lay person’s language to better understand the marvelous nature of the omniscient mind of God. We can think of mathematics as an abstract way to quantify things. For example, I have three apples; the quantity is three.
Fellow of the Royal Society, and Fellow of Trinity College, Cambridge, Srinivasa Ramanujan (Ra-ma-mu”-dzen) from Madrasa, India, was a deeply religious Hindu who credited his world-renown mathematical capacities to divinity – revealed to him by a family goddess. “An equation for me has no meaning,” he once said, “unless it expresses a thought of God.” A movie has been made of him, “The Man Who Knew Infinity.” I also mention him in a former blog post, “Remarkable Angel Assistance Stories”. We see numbers all over nature as part of God’s “creation mathematics”,
Different Colors of Noise
Next, we usually think of noise as being acoustic—something we hear or don’t want to hear. But in general terms, we can think of noise as the variability of any quantity. For example, the numbers describing the height of the flood stage of the Nile River each year when analyzed over the 2,000 years of recorded data have a variability called flicker noise–sometimes called pink noise. We can think of white noise like a flip of a coin—heads or tails are equally probable. With each flip, we have no memory of the past flips. Random-walk noise on the other hand can be modeled by taking one step forward if the flip of the coin is positive and one step backward if the flip is tails. In this case, your position has a perfect memory of all the past flips.
Flicker Noise or Pink noise
Flicker noise has a spectral noise behavior halfway between white noise and random walk noise. Flicker noise tends to lose the memory of past flips but retains a good memory of recent flips. Flicker noise is ubiquitous in nature; everything from resting neuron voltage to the scintillation variations in the starlight; “Twinkle, twinkle little star, how I wonder what you are?” You are flickering like flicker noise! Further, flicker noise is self-similar; in other words, if you analyze a section of a flicker-noise data set, the section looks very much like the whole data set with similar spectral noise-color properties and amplitude.
God’s Pictorial Beauty
Dr. Benoit Mandelbrot first discovered some of the beauty in God’s mathematics back in the 1980s. Click the link “Mandelbrot set”. At the bottom of the page, you will see pictures like the few we have shared here. These images from God’s mathematics have always existed, but Mandelbrot’s insights with the availability of the digital computer revealed them to us:
These detailed images have infinite depth—showing the infinite mind of God and the beauty we see in nature because of His creation mathematics, and the images are self-similar. AMAZING! Enjoy a touch of God’s mathematics.
As Dr. Lisle shares the beauty of these self-similar fractal processes coming from a mathematical equation, one comes to know a touch of the beauty that the Master Mathematician uses in creation. It demonstrates that God’s mind is infinite. His love for us, His children, is infinite. It is fascinating that the beauty in the Mandelbrot set has always been there as part of God’s infinite mind in His Creations, and if we look closely, we will see them all over in natural processes. Like flicker-noise they are self-similar and ubiquitous in nature.
Flicker Noise is a Limiting Noise in Atomic Clocks
Because flicker noise is also a self-similar process, this made Mandelbrot’s work extremely interesting to us, because flicker noise is a limiting noise process in precision clocks—like atomic clocks needed for GPS. Back in the 1960s, Jim’s and my theses had demonstrated how to characterize flicker noise. The spectral density of flicker noise is proportional to 1/f, where f is the Fourier frequency used to model a data set. Characterizing flicker noise is mathematically a challenge because the integral of 1/f (flicker-noise) blows up mathematically at both integration limits. This means that both the average value for a flicker noise process and its classical variance don’t mathematically exist –do not converge to meaningful values.
It reminds me of agency (free choice). We can choose the right or we can choose the wrong. The good Lord gave us all a conscience to do so–the light of Christ–and we are most grateful for our individual sovereignty “to choose our life and what it will be.”
Because of Flicker Noise in Atomic Clocks
In 1977, I was invited to Tokyo, Japan, to give a talk on my research on the presence of flicker-noise in atomic clocks at an International Flicker-noise Symposium. There, I met Dr. Voss, who demonstrated how flicker-noise describes music variations—a fascinating talk.
Later, I invited him to give a talk at a Frequency Control Symposium in Philadelphia, PA. Again, it was a fascinating talk. Using computer simulations of noise, he shared the sound of music made from white noise. It sounded horrible—drive you crazy. Then he shared some music made from computer-generated random-walk noise–it put you to sleep. Then he shared some computer-simulated music made from flicker-noise, and it was very pleasing to listen to. Remember flicker noise is halfway between these two noise processes in terms of its spectral properties.
Because, flicker-noise processes are ubiquitous in nature, the Allan variance is used across the globe to characterize and identify these flicker-noise processes. The Allan variance, the Modified Allan variance, and the Time variance, which my colleagues and I developed at the lab in Boulder, nicely differentiate flicker noise from the several other kinds and colors of noise that are invariably present in nature and are commonly present in any time-series data set.
The Secret Code Seen in Creation
So, for all you non-believers out there, in this link Dr. Jason Lisle shares with the world a piece of the infinite beauty and depth of the mathematical Mind of God. Secular folks and atheists simply cannot explain how this could be. Our second daughter, Karie Allan Clingo, shared this link with us. Thank you, Karie, for sharing this inspiring talk–amazing insights into the mathematical mind of God.
David W. Allan
P.S. Since July 2022, Dr. Lisle has shared recent data about the new James Webb Space Telescope, which shows agreement with the Bible creation model and not with the “Big Bang.”
Fractals
A fractal is a never-ending complex pattern. They are created by repeating a simple process over and over you will get an amazing number of beautiful images, as offspring from Mandelbrot’s work. He has a fun TEDx talk.
Natures Fractal: Natural beauty in nature.
Heavenly Fractals: Zoom into the infinite.
Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences,… Benoit Mandelbrot – Wikipedia
Thank you, Lord, for your inspiring mathematics and for everything else—making our trip here on Earth so beautiful.
David W. Allan
Photos: CC Pixabay – CC Public Domain Pictures