Discovering G64
by Mike McFerron
Location: Lewis University - Oremus Fine Arts Building
Deployed: March 24, 2025; 8:53am
Status: searching
Deployed: March 24, 2025; 8:53am
Status: searching
As we search for meanings of existence in the cosmos, what may at first appear to be relationships built upon isolation are instead entanglements of blurred boundaries that oscillate with and for each other.
Discovering G64 uses Per Nørgård's infinity series as basis for pitch material in this work, and it also acts as an exploratory device to identify the last 500 digits of Graham’s Number (G64). The length of Discovering G64 is, to date, unknown.
Named for the famous mathematician, Ronald Graham, Graham's Number is one of the largest numbers ever used in a mathematical proof. It's so large, in fact, that a digital representation of this number, where each digit was the size of an atom, would be too large to fit in our universe!
Graham’s Number is so large that we don’t know the first number; however, mathematicians know how the number ends. Discovering G64 deploys Nørgård's infinity sequence to identify and sonically represent those last 500 digits. It does this by searching for sets of three numbers from that 500-digit list. Throughout this search, the value of each step from the infinity sequence is also mapped to a pitch class and sonically presented to the listener.
At the bottom of the interface's screen are three larger musical elements: melody, bass, texture, and nature. When a 3-digit set from G64 is discovered, one of these larger sonic elements becomes available to the audience to place into the sonic mix.
Discovering G64 uses Per Nørgård's infinity series as basis for pitch material in this work, and it also acts as an exploratory device to identify the last 500 digits of Graham’s Number (G64). The length of Discovering G64 is, to date, unknown.
Named for the famous mathematician, Ronald Graham, Graham's Number is one of the largest numbers ever used in a mathematical proof. It's so large, in fact, that a digital representation of this number, where each digit was the size of an atom, would be too large to fit in our universe!
Graham’s Number is so large that we don’t know the first number; however, mathematicians know how the number ends. Discovering G64 deploys Nørgård's infinity sequence to identify and sonically represent those last 500 digits. It does this by searching for sets of three numbers from that 500-digit list. Throughout this search, the value of each step from the infinity sequence is also mapped to a pitch class and sonically presented to the listener.
At the bottom of the interface's screen are three larger musical elements: melody, bass, texture, and nature. When a 3-digit set from G64 is discovered, one of these larger sonic elements becomes available to the audience to place into the sonic mix.
Interface Description
The interface has three primary sections:
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1. Main volume control for the installation. Users are invited to freely raise and lower the volume to suit their preference.
2. The Infinite Melody section displays the current index (a.k.a "step") and its value of the infinity sequence. Each value is sonically represented with a bell-like sound and users may change the octave and volume of these sounds.
3. The Discovering section displays the 3-digit set from Graham's Number that is currently being sought. The "current box" indicates the current value and the previous two values from the infinity indices. Once a 3-digit set matches the current box, the set is considered "found" and a new sonic theme (melody, bass, texture, nature). Users are also invited to adjust the volume of these sonic themes if they are available.
History of this Installation: Infinity Sequence
During 2015, I became interested in using Per Nørgård's infinity sequence in my compositions. Since then, I've used the sequence in nearly every one of my compositions at varying degrees. As I was first learning about the sequence, I came across lists of indices/values of the sequence. Some were short intended to illustrate the sequence's formula while a few would list 10,000 or so indices/values. You can view the first 10,000 numbers that the infinite sequence generates by clicking the button on the right. I was fascinated by these lists, and so I decided to write a little script to linearly generate the infinity sequence...infinitely, or at least as long as the computer stayed alive. This was my first experiment with the infinity sequence and it became an installation that came to mean a great deal to me.
This first application did not produce sound. It only displayed an index, or step, and the value of that step. The application was installed on a very old laptop in my office and I started it running on April 2, 2016. Even though I built an option to change the speed at which it would choose a value, for nearly the entire life of the application it calculated a step each quarter of a second. The application didn't save the indices and values or write those numbers to a computer file. Instead, it simply displayed each step and its value and moved on to the next step/value combination. It continued unobtrusively in my office, and each day that I arrived on campus I would take a moment to enjoy the numbers pass by. I became quite attached to this ritual, and when someone would stop by and ask me about the program, I would blather on and on about it. This computer program welcomed me to work each day, and in some ways, it became my daily meditation.
After more than a year of displaying values for each step, I was showing the application to a colleague of mine, David, who was visiting from New York. As I was explaining the application to him, the number 18 suddenly appeared. I surprised David with my excitement of seeing this number. I explained to him that I had never seen a number that high. In fact, in the first 10,000 steps of the sequence, the highest value for a step is 13. As I continued to be excited about this new "discovery," showing David spreadsheets where I had done my "I'm not a mathematician" analysis on the sequence, I soon realized that David was also excited. Of course, he and I had only seen the number 18, but for a quarter of a second we shared that number -- a number that we discovered together.
After generating the infinity sequence for nearly six years, cleaning staff accidentally unplugged the laptop on which the application was running. After what was likely several hours over a long weekend, the laptop's battery drained and the computer shut down bringing the installation to an end. At the time of its death, the application had found the values for over 625,000,000 steps. The last screenshot taken on April 2, 2021 is on the right.
This first application did not produce sound. It only displayed an index, or step, and the value of that step. The application was installed on a very old laptop in my office and I started it running on April 2, 2016. Even though I built an option to change the speed at which it would choose a value, for nearly the entire life of the application it calculated a step each quarter of a second. The application didn't save the indices and values or write those numbers to a computer file. Instead, it simply displayed each step and its value and moved on to the next step/value combination. It continued unobtrusively in my office, and each day that I arrived on campus I would take a moment to enjoy the numbers pass by. I became quite attached to this ritual, and when someone would stop by and ask me about the program, I would blather on and on about it. This computer program welcomed me to work each day, and in some ways, it became my daily meditation.
After more than a year of displaying values for each step, I was showing the application to a colleague of mine, David, who was visiting from New York. As I was explaining the application to him, the number 18 suddenly appeared. I surprised David with my excitement of seeing this number. I explained to him that I had never seen a number that high. In fact, in the first 10,000 steps of the sequence, the highest value for a step is 13. As I continued to be excited about this new "discovery," showing David spreadsheets where I had done my "I'm not a mathematician" analysis on the sequence, I soon realized that David was also excited. Of course, he and I had only seen the number 18, but for a quarter of a second we shared that number -- a number that we discovered together.
After generating the infinity sequence for nearly six years, cleaning staff accidentally unplugged the laptop on which the application was running. After what was likely several hours over a long weekend, the laptop's battery drained and the computer shut down bringing the installation to an end. At the time of its death, the application had found the values for over 625,000,000 steps. The last screenshot taken on April 2, 2021 is on the right.
Graham's Number
Below are the last 500 digits of Graham's Number:
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0 2 4 2 5 9 5 0 6 9 5 0 6 4 7 3 8 3 9 5 6 5 7 4 7 9 1 3 6 5 1 9 3 5 1 7 9 8 3 3 4 5 3 5 3 6 2 5 2 1 4 3 0 0 3 5 4 0 1 2 6 0 2 6 7 7 1 6 2 2 6 7 2 1 6 0 4 1 9 8 1 0 6 5 2 2 6 3 1 6 9 3 5 5 1 8 8 7 8 0 3 8 8 1 4 4 8 3 1 4 0 6 5 2 5 2 6 1 6 8 7 8 5 0 9 5 5 5 2 6 4 6 0 5 1 0 7 1 1 7 2 0 0 0 9 9 7 0 9 2 9 1 2 4 9 5 4 4 3 7 8 8 8 7 4 9 6 0 6 2 8 8 2 9 1 1 7 2 5 0 6 3 0 0 1 3 0 3 6 2 2 9 3 4 9 1 6 0 8 0 2 5 4 5 9 4 6 1 4 9 4 5 7 8 8 7 1 4 2 7 8 3 2 3 5 0 8 2 9 2 4 2 1 0 2 0 9 1 8 2 5 8 9 6 7 5 3 5 6 0 4 3 0 8 6 9 9 3 8 0 1 6 8 9 2 4 9 8 8 9 2 6 8 0 9 9 5 1 0 1 6 9 0 5 5 9 1 9 9 5 1 1 9 5 0 2 7 8 8 7 1 7 8 3 0 8 3 7 0 1 8 3 4 0 2 3 6 4 7 4 5 4 8 8 8 2 2 2 2 1 6 1 5 7 3 2 2 8 0 1 0 1 3 2 9 7 4 5 0 9 2 7 3 4 4 5 9 4 5 0 4 3 4 3 3 0 0 9 0 1 0 9 6 9 2 8 0 2 5 3 5 2 7 5 1 8 3 3 2 8 9 8 8 4 4 6 1 5 0 8 9 4 0 4 2 4 8 2 6 5 0 1 8 1 9 3 8 5 1 5 6 2 5 3 5 7 9 6 3 9 9 6 1 8 9 9 3 9 6 7 9 0 5 4 9 6 6 3 8 0 0 3 2 2 2 3 4 8 7 2 3 9 6 7 0 1 8 4 8 5 1 8 6 4 3 9 0 5 9 1 0 4 5 7 5 6 2 7 2 6 2 4 6 4 1 9 5 3 8 7
Installation History
Location: Lewis University - Oremus Fine Arts Building
Deployed: December 31, 2024; 3:11pm
Status: Dead.
Cause of death: power outage due to weather. Last known step: 2,000,000+
Deployed: December 31, 2024; 3:11pm
Status: Dead.
Cause of death: power outage due to weather. Last known step: 2,000,000+