Numbers Game

“They are encrypted messages to somebody. We think it’s to spies, we hope it’s just a spy and nothing more sinister than that. A numbers station is defined as any of several hundred short wave radio broadcasters all of which are using high power, big transmitters, large antennas, global coverage of the entire planet, which do nothing except broadcast meaningless strings of numbers. They never say why they are doing it. They never say who they are.”1

I first heard a numbers station in my grandfather’s basement at the age of 13. I spent one summer living with my grandpa when my parents were going through a particularly messy divorce. The one thing they could agree on was that I should not be anywhere near them for a while. I was shipped off to Warrington, VA with a suitcase and a few vague promises that one of them would be back for me before the next school year started.

Papa Jack was unusual. Before that summer I had only met him once at the age of six. I barely remembered him but did recall his intense gaze and strange, stilted, manner of speech. Mom said her dad was always odd but had been kind and loving. He had raised her on his own since the death of his wife during my mom’s birth. She said that the lack of a mother was only bearable because of his attentiveness and care for her. “Dad felt that because I had no mom he would have to be twice the parent. He would do anything for me and I never wanted for anything.”  My mother’s high regard and obvious love for him greatly lessened the fear I had about living with someone who was a complete stranger for the next three months. The last words she said to me before loading me into the car that would take me on the six hour drive to Virginia were puzzling. “Your grandfather is very fond of numbers. Remember that. I love you son.” I took a seat in the back of the battered Ford Focus. She smiled sweetly and waved as we pulled away. It would be the last I time I saw my mother.

Only a few moments after grandpa met me at the door with a big hug and luminous smile he led me to what would be my room. It was small but comfortable. There was a large bed, a dresser, and a desk. The hardwood floor glowed as if it had been newly polished. A pleasant smell drifted in through the open window which looked out on the tidy garden that made up most of the narrow back yard. It was all so bucolic that it took me a moment to notice the strange markings that covered all of the walls from top to bottom. They were numbers. They were of different shapes; different sizes, different fonts and colors, but they were all clearly numbers. Positive, negative, rational, irrational, and complex, all were represented. Not truly comprehending what I was seeing, I simply gazed, slack-jawed at the walls. After what felt like an eternity I took a seat on the edge of the bed and looked back at my grandfather. His eyes had taken on a feverish tint and a soft yellow glow seemed to emanate from the top of his head giving the strange markings on the wall an ominous tone.

“Yes they are all numbers son. Do you want to know what they mean?”  His pupils darkened measurably as he spoke and the room suddenly felt cramped and hot. I shrank back into the bed as he continued. “Do you know that the world is composed of numbers? Yes. Every molecule, every atom, every subatomic particle, can ultimately be described by a number or series of numbers. There is one very special number however.” He appeared to shrink into the shadows as he spoke and a small bead of sweat was visible across his brow.

“Can you guess what that number might be?” Now I was afraid. Of course I had no idea what he was asking but in my confusion and terror I somehow managed to squeak out a pitiful reply. “No.” A look of apprehension flashed briefly across the face of my granddad. He whipped his head from side to side as if he was trying to shake something off. The moment of uncertainty was gone quickly. His neck stiffened and his jaw clenched as he fixed me with an intense stare. Confusion, and fear were reflected in his eyes. My mind raced as I tried to comprehend what was happening. One very special number? It did not make sense.

“Mathematics has determined this number” he continued. My curiosity was beginning to overcome my fear. I leaned in closer and held my breath slightly as I waited for the answer. “The number is negative one-twelfth (-1/12).”  It took a moment for me to come to my senses as I tried to register exactly what I just heard. “Im sorry grandpa, but did you just say negative one-twelfth, the fraction negative one-twelfth.” He laughed slightly and continued. “The sum of all integers continued to infinity can be calculated. When the calculation is complete, using certain assumptions, and within a strict and defined mathematical framework, the answer is negative one-twelfth.” 2

No doubt my grandfather was losing it. It was obvious that senility was setting in. Suddenly I relaxed as the realization that my papa Jack was simply suffering from the depredations of old age sank in. He could sense the change in my demeanor and became enraged. “ You think I’m crazy don’t you? I can assure you I am not. There is a short wave radio in the basement. Go down there this evening before you go to bed and turn it on. It is already tuned to a very special station, a numbers station. Listen for a while and then you will understand.” Suddenly all the emotion in his eyes and face and tone of voice were gone, replaced by a kind of emptiness. He stared at the walls of the room for a brief moment then turned and left.

An hour or two later I set off for the basement. The short wave radio sat alone on a large oak table in the corner. I could tell it was old by the analog dials and switches that adorned the front and top of the large square box. A long wire which must have been an antenna spiraled out of the back and into the wall, no doubt emerging at the roof where a strangely shaped contraption of tubes and metal rods protruded at least 10 feet into the sky.

My granddad said that the radio was already set to the appropriate station so I simply turned on the power. It took me a few moments to identify the appropriate switch but once flipped I immediately heard a strange buzzing. Within seconds a voice could be heard just above the scratchy static and white noise. “one plus two plus three plus four plus five….” The voice went on and on, slowly, rhythmically summing the rational integers. As I listened to the seemingly endless, hypnotic recitation of numbers eventually I must have fallen asleep. I woke up in a daze not sure of exactly where I was or what I was doing.

My hearing returned first and I became aware of the numbers station droning on in the background. “twenty one thousand two hundred and two plus twenty one thousand two hundred and three plus….” Next I began to notice a bright light and realized that my sight was being restored. As full clarity of vision returned I saw before me a strange being, enshrined in a brilliant bright, white light. It sat at a screen of some sort, with what looked to be a keyboard like device in its lap. It was typing. Typing an endless stream of numbers. Suddenly it turned and looked my way. I could see surprise?, fear?, confusion?, reflected in its eyes?. Instantly a wall seemed to slam shut before me. All the light was extinguished. The numbers station had ceased to broadcast and only a faint hissing sound was left. I sat alone in the dark and began to cry. “Negative one-twelfth. Its not possible that that’s all we are, is it?”

“Mathematical knowledge is unlike any other knowledge. Its truths are objective, necessary and timeless. What kinds of things are mathematical entities and theorems, that they are knowable in this way? Do they exist somewhere, a set of immaterial objects in the enchanted gardens of the Platonic world, waiting to be discovered? Or are they mere creations of the human mind? This question has divided thinkers for centuries. It seems spooky to suggest that mathematical entities actually exist in and of themselves. But if math is only a product of the human imagination, how do we all end up agreeing on exactly the same math? Some might argue that mathematical entities are like chess pieces, elaborate fictions in a game invented by humans. But unlike chess, mathematics is indispensable to scientific theories describing our universe. And yet there are many mathematical concepts — from esoteric numerical systems to infinite-dimensional spaces — that we don’t currently find in the world around us. In what sense do they exist? Many mathematicians, when pressed, admit to being Platonists. The great logician Kurt Gödel argued that mathematical concepts and ideas “form an objective reality of their own, which we cannot create or change, but only perceive and describe.” But if this is true, how do humans manage to access this hidden reality? We don’t know. But one fanciful possibility is that we live in a computer simulation based on the laws of mathematics — not in what we commonly take to be the real world. According to this theory, some highly advanced computer programmer of the future has devised this simulation, and we are unknowingly part of it. Thus when we discover a mathematical truth, we are simply discovering aspects of the code that the programmer used. This may strike you as very unlikely. But the Oxford philosopher Nick Bostrom has argued that we are more likely to be in such a simulation than not. If such simulations are possible in theory, he reasons, then eventually humans will create them — presumably many of them. If this is so, in time there will be many more simulated worlds than nonsimulated ones. Statistically speaking, therefore, we are more likely to be living in a simulated world than the real one. Very clever. But is there any way to empirically test this hypothesis? Indeed, there may be. In a recent paper, “Constraints on the Universe as a Numerical Simulation,” the physicists Silas R. Beane, Zohreh Davoudi and Martin J. Savage outline a possible method for detecting that our world is actually a computer simulation. Physicists have been creating their own computer simulations of the forces of nature for years — on a tiny scale, the size of an atomic nucleus. They use a three-dimensional grid to model a little chunk of the universe; then they run the program to see what happens. This way, they have been able to simulate the motion and collisions of elementary particles. But these computer simulations, Professor Beane and his colleagues observe, generate slight but distinctive anomalies — certain kinds of asymmetries. Might we be able to detect these same distinctive anomalies in the actual universe, they wondered? In their paper, they suggest that a closer look at cosmic rays, those high-energy particles coming to Earth’s atmosphere from outside the solar system, may reveal similar asymmetries. If so, this would indicate that we might — just might — ourselves be in someone else’s computer simulation. Are we prepared to take the “red pill,” as Neo did in “The Matrix,” to see the truth behind the illusion — to see “how deep the rabbit hole goes”? Perhaps not yet. The jury is still out on the simulation hypothesis. But even if it proves too far-fetched, the possibility of the Platonic nature of mathematical ideas remains — and may hold the key to understanding our own reality.”3

199% Invisible podcast. Episode 97. Numbers Stations. Dec. 2000.

2http://www.slate.com/blogs/bad_astronomy/2014/01/17/infinite_series_when_the_sum_of_all_positive_integers_is_a_small_negative.html

3New York Times. Feb. 2014. Op-Ed. Edward Frenkel, professor of mathematics at the University of California, Berkeley. A version of this op-ed appears in print on February 16, 2014, on page SR12 of the National edition with the headline: Is the Universe a Simulation?

Notes:

The boardman, bulgerian betty They follow an old school 1 time pad – only used once by recipient and receiver.

A perfect cryptography system. Some broadcasts are jammed.

Most in the US come from Cuba Govt. transmitter site in warrington VA (Cynthia) Havana Moon – William Godbey – retired navy.

John Fulford (ex-police intelligence officer) – roamed around florida looking for transmitter sites. Military transmitter site at an airport in south florida. West Palm Beach International airport. John R. Winston – FCC.

Will not discuss these stations. Location of transmitter not a secret but receiver is European Gongs in England over shortwave radios – 5 months after fall of berlin wall gong station stopped transmitting Taiwain – New Star broadcasting.

Everybody sounds the same on shortwave Few strange stations.

Buzzer on 4625 kilohertz Shortwave is dying but the number stations persist.