When Randomness Starts to Look Like a Message
Is it random or is it a coincidence?
There is something unsettling about the possibility that the universe might be trying to tell us something.
Imagine sitting in front of a screen, watching data arrive from a radio telescope pointed towards a distant region of space. Most of what you see is noise. Random fluctuations, scattered signals, and measurements that seem to mean very little.
Then something catches your attention.
A signal appears at remarkably regular intervals. You examine it more closely and notice that it seems to follow a mathematical pattern. You try different ways of analysing the data, and the pattern continues to emerge.
For a moment, you wonder whether you have discovered something extraordinary. Could this be evidence of an unknown physical process? Could it even be a signal from another civilisation?
But then comes the more uncomfortable question.
What if the pattern is real, but the explanation you have attached to it is completely wrong?
I find this fascinating because we often treat mathematical patterns as though they carry meaning in themselves. If something fits an equation, repeats at regular intervals, or resembles a familiar sequence, we instinctively search for an explanation.
Usually, that instinct is useful. Sometimes, however, it leads us somewhere unexpected.
The signal that seemed almost too regular
In 1967, astronomer Jocelyn Bell Burnell noticed an unusual recurring signal in radio telescope data at the University of Cambridge. The signal appeared to come from a particular region of the sky, and its regularity was unlike anything the researchers had previously encountered.
Further observations revealed pulses arriving approximately every 1.337 seconds.
The signal was so unusual that the researchers jokingly labelled the source LGM-1, short for “Little Green Men”. An artificial transmission from an extraterrestrial civilisation was one possibility they considered.
The explanation turned out to be something else entirely.
The source was a pulsar, a rapidly rotating neutron star that emits beams of radiation. As the star rotates, its radiation sweeps past Earth at regular intervals, producing the pulses detected by the telescope.
The signal really was regular. The pattern was not an illusion. What changed was our understanding of what had produced it.
This is an important distinction. The researchers were right to investigate an unusual pattern, but the pattern alone could not establish its cause.
A signal can look artificial without being artificial. A sequence can look deliberate without having been deliberately created.
Finding a pattern is one achievement. Understanding why it exists is another.
Mathematics can find patterns almost anywhere
Consider a sequence of random digits:
7, 2, 9, 4, 1, 8, 3, 6, 0, 5
At first glance, there is nothing particularly interesting about it. But suppose you are allowed to rearrange the digits, examine different sections, compare them with mathematical constants, and test various possible relationships.
Eventually, you might find something that looks remarkable.
Perhaps a section resembles a familiar sequence. Perhaps a few numbers match the decimal expansion of a mathematical constant. Perhaps you discover a relationship that appears too precise to be accidental.
Does that mean the sequence was not random?
Not necessarily.
The important detail is that you searched for the pattern after seeing the data. You did not make a specific prediction and then test it. You explored many possible relationships until one caught your attention.
This changes how surprising the result really is.
Imagine predicting in advance that the next ten coin flips will all be heads. The probability of that particular sequence, assuming a fair coin, is 1 in 1,024.
Now imagine flipping the coin ten times and examining the result afterwards. You could look for repeated pairs, runs of heads, alternating sequences, or many other patterns.
The more possibilities you consider, the more opportunities you have to discover something that seems unusual.
This is related to a statistical concept called the look-elsewhere effect. When we examine enough possible patterns, at least one may appear significant simply by chance.
The same problem arises when scientists search large datasets for unusual signals. If researchers examine millions of frequencies, time intervals, and possible relationships, some results may look extraordinary even when no meaningful signal is present.
The mathematics may be perfectly correct. The pattern may genuinely fit the data.
The mistake is forgetting how many other patterns could have been found.
When a mathematical model becomes a trap
One of the most powerful things mathematics allows us to do is describe complicated observations using relatively simple rules.
An equation can describe a curve. A statistical model can identify relationships in thousands of measurements. A mathematical function can predict how a system might behave under different conditions.
But there is a subtle danger in this process.
Given enough flexibility, a model can fit data that it has little real explanatory power over.
Imagine plotting ten measurements on a graph. You could draw a straight line that captures the general trend, even if it does not pass through every point. Alternatively, you could construct a complicated curve that passes through all ten measurements exactly.
The second curve fits the observed data perfectly.
Is it therefore the better model?
Not necessarily.
If the measurements contain random fluctuations, the complicated curve may simply reproduce those fluctuations. When new measurements arrive, its predictions might be far less accurate.
This is known as overfitting. A model captures not only the underlying relationship we want to understand, but also accidental features of the particular data we happened to observe.
This problem appears in machine learning, scientific research, economics, and many other fields. A model can describe the past extremely well while failing to predict what happens next.
Get Jishnu Teja Yogesh’s stories in your inbox
Join Medium for free to get updates from this writer.
The distinction matters because the purpose of a mathematical model is not merely to reproduce what we have already seen. It is to help us understand the process behind those observations.
A model that fits every detail is not automatically a model that explains every detail.
The difference between finding a pattern and predicting one
There is a useful way to distinguish an interesting coincidence from a convincing scientific explanation.
Ask whether the pattern could have been predicted before the data were observed.
Suppose I give you a long sequence of numbers and ask you to discover a mathematical rule that reproduces it. You might eventually find one that works remarkably well.
Now suppose I give you the rule first and ask you to predict the next hundred numbers before revealing them.
These are very different tasks.
In the first case, you can use the observed data to guide your search. In the second, the rule must make predictions that can be tested independently.
This is why scientists value replication and independent observations.
A candidate signal that appears once might be a genuine discovery, but it might also be instrumental error, interference from human technology, or a random fluctuation. If the signal appears again under conditions that rule out these alternatives, the evidence becomes much stronger.
The SETI@home project, which analysed radio telescope data in the search for extraterrestrial intelligence, illustrates this challenge. Searching large volumes of data can produce many candidate signals, but identifying an unusual result is only the beginning. Researchers must investigate whether it has a natural explanation, comes from human interference, or warrants further study.
The absence of an immediate explanation does not establish an extraordinary one.
This is not a reason to dismiss unusual observations. It is a reason to investigate them carefully.
A discovery becomes convincing when the evidence distinguishes it from competing explanations, not merely when one explanation seems to fit.
Why our brains are so good at seeing patterns
There is a reason this problem extends beyond science.
Human beings are exceptionally good at recognising patterns. We notice familiar faces in crowds, detect changes in someone’s voice, remember repeated experiences, and learn relationships between events.
This ability is essential to how we understand the world.
But our minds do not approach every observation as though it were a completely new statistical experiment. We bring expectations, memories, and assumptions with us.
If we expect a pattern to exist, we may pay more attention to evidence that supports it. Once we have noticed a particular coincidence, we may remember every time it happens while forgetting the many occasions when it does not.
A familiar example is thinking about a person and then unexpectedly receiving a message from them. The timing feels remarkable because we notice the connection. We rarely count all the times we thought about someone and nothing followed.
The event itself may be genuinely surprising. But our judgement of how surprising it is can be distorted by the way we remember and interpret it.
This does not mean that every pattern we notice is imaginary. It means that noticing a pattern and establishing its significance require different kinds of reasoning.
Our instincts can help us identify what deserves investigation. They cannot replace the investigation itself.
So, is the universe full of patterns?
In a sense, yes.
The physical world contains genuine mathematical regularities. Planetary motion follows gravitational laws. Sound can be analysed through its frequencies. Pulsars produce periodic signals because of their physical properties.
Mathematics is extraordinarily successful at describing these relationships.
But the existence of genuine patterns does not mean every apparent pattern reveals a hidden law.
A natural process can produce an unexpected signal. Random data can produce an arrangement that looks highly structured. A flexible model can make an accidental arrangement appear even more convincing.
We cannot reliably distinguish these possibilities by asking only how impressive the pattern looks.
We must consider how the data were collected, what assumptions the model makes, how many possible patterns were examined, and whether the result survives independent testing.
The pattern is the beginning of the investigation, not its conclusion.
Perhaps the most interesting question is why we believe the pattern
I think there is something deeply human about our desire to find structure in the world.
When we encounter something unfamiliar, we search for relationships that might make it understandable. When an event repeats, we look for a rule. When a mathematical model fits an observation, we begin to wonder what else it might explain.
This instinct is responsible for some of our greatest discoveries. Without the willingness to investigate unusual observations, the first pulsars might have remained unnoticed in the data.
But the same instinct can lead us to see meaning where the evidence does not support it.
The answer cannot be to distrust every pattern. That would be just as unreasonable as believing every pattern must have a deeper explanation.
Instead, we need to separate the excitement of finding a pattern from the discipline required to explain it.
A strange signal deserves investigation. An unexpected relationship deserves testing. A mathematical model that fits the data deserves scrutiny, especially when the fit seems almost too good to be true.
Sometimes, the explanation will be extraordinary. Other times, the apparent mystery will dissolve into chance, noise, or a natural process we did not previously understand.
Both outcomes teach us something.
The universe does not owe us an explanation that matches our first interpretation. And mathematics, powerful as it is, cannot tell us what a pattern means without evidence about the world that produced it.
Perhaps that is what makes these discoveries so fascinating.
Not that randomness can sometimes look like order, but that the difference between an accidental pattern and a genuine discovery is rarely visible in the pattern alone.
We have to learn how to tell them apart.
Further Reading
- NASA. Information about pulsars and neutron stars. https://science.nasa.gov/universe/stars/neutron-stars/
- Gross, E. and Vitells, O. (2010). Trial factors for the look elsewhere effect in high energy physics. European Physical Journal C. https://doi.org/10.1140/epjc/s10052-010-1470-8
- SETI@home. An overview of the distributed computing project that searched radio telescope data for possible extraterrestrial signals. https://setiathome.berkeley.edu/
