We tend to think of ourselves as observers of the world.
Something happens outside us. Our senses receive it. We see it, hear it, understand it, and respond.
It feels almost immediate.
But perhaps the process is much more interesting than that.
The world is full of information. Light reaches our eyes. Sound reaches our ears. Our bodies constantly receive signals about temperature, movement, pressure and balance.
Yet we don't experience all of it.
We experience a selection.
We notice some things and ignore others. We recognize patterns. We fill gaps. We interpret ambiguity. We remember certain events and forget others.
Two people can experience the same event and walk away with very different understandings of what happened.
So perhaps perception is not simply about receiving information.
Perhaps it is also about building a representation of it.
From biology and chemistry
At the physical level, cognition begins with living matter.
Neurons are excitable cells. Their membranes maintain differences in electrical potential through the movement of ions such as sodium, potassium, calcium and chloride. When a neuron receives sufficient input, changes in membrane potential can produce an action potential - an electrical signal that propagates along the axon.
Communication between neurons largely occurs at synapses.
When an action potential reaches a presynaptic terminal, it can trigger the release of neurotransmitters into the synaptic cleft. These molecules bind to receptors on another cell and alter its electrical or biochemical state.
But neurotransmission is not simply an on/off mechanism.
Different neurotransmitters, receptors and neuromodulatory systems can influence neural circuits in different ways. Dopamine, serotonin, acetylcholine, glutamate, GABA and many other chemical systems participate in regulating neural activity, learning, motivation, attention, memory and behaviour.
At the same time, neurons are not isolated.
They form extraordinarily complex networks, constantly changing through mechanisms of synaptic plasticity and other forms of cellular and network adaptation.
So what we casually call “brain activity” is actually a dynamic interaction between:
electrical signals + chemical signalling + cellular biology + network connectivity + plasticity.
There is no single molecule called a thought, nor a single neuron containing a memory.
Mental processes emerge from activity distributed across biological systems operating at multiple scales.
This makes the brain fundamentally different from the simplified neural networks we build in software.
Yet the analogy remains useful.
Both involve networks whose connections and parameters determine how signals are transformed.
The difference is that the biological system is a living, chemically active, self-regulating system shaped by evolution, development and continuous interaction with the body and environment.
From psychology
At another level, we encounter the phenomena we describe as perception, attention, memory, learning, language, emotion and decision-making.
Psychology asks questions that cannot be reduced to simply observing individual neurons.
How does attention select information?
How does working memory maintain information temporarily?
How are long-term memories formed and retrieved?
How does prior experience influence perception?
How do humans learn from incomplete and uncertain information?
How do emotions influence decisions?
These processes interact continuously.
What we perceive can influence what we remember.
What we remember can influence what we expect.
What we expect can influence what we notice.
What we attend to can influence what we learn.
Rather than a collection of independent mental functions, cognition appears to be a highly interconnected system.
This also complicates our understanding of the self.
Our memories, bodily states, perceptions, emotions, beliefs and social experiences contribute to an evolving representation of who we are.
The feeling of being a continuous “self” may therefore depend, at least partly, on processes that integrate information across time.
That does not settle the philosophical question of what the self ultimately is.
It simply gives us another way to investigate it.
From mathematics
At the foundation of modern AI, information is ultimately represented numerically.
An image can be represented as an array of numbers. Words can be represented as vectors - points in a high-dimensional mathematical space. These representations can then be transformed using matrices and other mathematical operations.
A matrix can be thought of, very roughly, as a structured transformation.
It can change one representation into another while preserving or modifying particular relationships between its components.
A neural network applies many such transformations, together with nonlinear functions, to convert an input into increasingly useful representations.
But mathematics alone does not tell the system what is useful.
This is where statistics and optimization enter.
During training, a model produces predictions from data. Those predictions are compared with a target or objective through a loss function. An optimization procedure then adjusts the model's parameters to reduce that loss.
Repeated across large amounts of data, this process allows the model to learn statistical regularities.
In simplified form:
data → numerical representation → mathematical transformations → prediction → error measurement → parameter adjustment → improved prediction.
Matrices provide much of the computational machinery for transforming representations.
Statistics provides the framework for reasoning about patterns and uncertainty.
Optimization provides a mechanism for changing the parameters of the model.
Together, they allow relatively simple mathematical operations to produce highly complex learned behaviour.
The mathematics does not prove that a machine understands.
It gives us a formal system through which we can construct, analyse and test models of information processing.
And that distinction matters.
From engineering and AI
Engineers build models because reality is often too complicated to work with directly.
We simplify.
We abstract.
We represent.
A software system represents a process.
A simulation represents a physical system.
A machine-learning model represents statistical relationships found in data.
But the model is never the thing itself.
A weather simulation is not the atmosphere.
A neural network is not a biological brain.
A map is not the territory.
The usefulness of a model comes from how well it captures the relationships that matter for the problem we are trying to understand.
Artificial intelligence makes this especially interesting because we are now building systems that learn internal representations from enormous quantities of data.
They can recognize patterns, generate language, make predictions and transform one representation into another.
The engineering question is:
How can we build systems that perform these functions?
But underneath it is a deeper scientific question:
What does it mean for a physical or computational system to represent something?
And then there is the universe
The idea of models becomes even more interesting when we move in the opposite direction - from the microscopic to the cosmic.
We cannot hold a galaxy in our hands.
We cannot travel to the edge of the observable universe and look back.
We cannot directly observe every process that shaped the universe.
Instead, we observe measurable phenomena and construct mathematical models.
From light, motion, radiation and other observations, we build models of stars, galaxies, black holes, spacetime and cosmic evolution.
Our equations are not the universe.
They are mathematical descriptions of relationships that appear to correspond to what we observe.
When observations disagree with a model, the model must be revised, extended or replaced.
There is something striking about this across such different scales.
A nervous system receives physical signals and constructs representations of its environment.
A scientist receives observations and constructs a mathematical model of a physical system.
An engineer receives a problem and constructs an abstraction that can be manipulated.
In each case, we are trying to understand something more complex than the representation itself.
The strange part
This leads to a question that sits somewhere between biology, mathematics, psychology, physics and philosophy.
If our brains construct representations of the world, then the reality we experience is mediated by a biological system that is constantly transforming physical signals.
We don't experience the universe in its entirety.
We experience what our sensory and nervous systems can detect, what our brains process, and what our cognitive systems make of it.
And yet, using these biological systems, humans have developed mathematics, microscopes, particle detectors, computers and telescopes capable of revealing structures far beyond ordinary perception.
A biological system that evolved on one planet can construct mathematical representations of objects billions of light-years away.
That is remarkable.
Perhaps one of the most interesting things we can study, therefore, is not only the world outside us, but the system that allows us to construct models of that world.
And that brings me back to a simple question:
When we think we are looking at reality, how much of what we experience comes from the world - and how much comes from the model through which our nervous system allows us to experience it?