The ways of knowing

Image by Eli Digital Creative from Pixabay

When trying to understand the nature of reality, we have to grapple with the question of how it is that we can know something of it. As we are limited to view the universe through a human lens, it is not clear how our mental constructs correspond to reality. To explore this, we should look at our lens in detail, refine its shape, polish out any scratches and understand its limitations.

In this article I want to introduce and explore the implications of the two fundamental ways in which we understand the world, through our intuition and models. This leads us to the conclusion that, due to the limitations of our brains and the experiences we have with them, we can never be sure exactly how our view of the world corresponds to reality itself...

Intuition

The experience of just knowing something, without being able to explain the reasoning behind it, is the essence of intuition. When your gut tells you to take that new job, or you have an uneasy feeling about someone, intuition is at play. Even when differentiating between pictures of cats and dogs, you can tell the difference immediately, without having to think. You have this intuitive knowledge of many objects in the world.

Intuitions go right to the core of the human experience. To be able to move around, you need to have a basic intuition of what three dimensional space is. Imagine catching a ball that has been thrown to you. You spontaneously move your arm and hand to coincide with the ball and close your fingers around it. You do this without knowing the details of what you just did, or how you just did it. You don’t calculate the trajectory of the ball and work out the exact order in which to tense and relax your muscles. You just do it. Most experience of moving around in space is intuitive in this way. Unless you are learning an advanced or intricate task, you just set the intention to do something and your body obliges. At some basic level, your brain has a way to immediately make sense of where you and other objects are in space. The intuitions of three dimensional space are so basic that it is impossible to imagine what it would mean not to have them. If you are not convinced by this, try to visualise a ten dimensional object. You will quickly realise what it is to not have intuitions about something.

There are a whole host of other intuitions that come with being human. Take the concept of time. It is intuitively obvious what it means for something to have happened in the past, or to be going to happen in the future. However, it is impossible to imagine what it would mean to live outside of time. Other examples are evident when using language or interacting socially. The fact that we have these intuitions is no accident, they are necessary to be able to make quick decisions and survive as a complex being in the world.

These fundamental intuitions have been built into how the brain works by evolution. They give us a basis for all human understanding. However, we can reason in more detail. No one is born with knowledge of quantum mechanics, but we are still able to make use of it to build the device you are using to read this blog. To do this we have another way in which we can know things, we build models.

Models of reality

A model is a way of representing something out there in the world. Along with a simplified representation of the system that is modelled, it includes the rules that govern how it behaves. A model car has all the components of a car, assembled in the same configuration, but with the real components replaced with smaller plastic representations. Another example is a mathematical model of a physical system, such as a pendulum. The properties of the system, the position and velocity of the pendulum, are represented as mathematical variables and the relationships between them are encoded in equations.

Models are useful, as they allow one to experiment on a system without having to manipulate the system itself. By manipulating the representations within the framework of a model, one can learn about a system and anticipate how it will behave. You can open the doors of the model car and see how it would look, or start the pendulum with a specific velocity and see how it swings.

A model also simplifies a real system by removing irrelevant factors. If we wanted to understand how a pendulum swings, but also take account of all the properties of a real pendulum, the way the light reflects off its surface, the exact swooshing sound it makes, we would be faced with an impossible task. Instead, a model allows us to describe the dynamics of the system, in a satisfactory level of detail, with a much simpler calculation. We just have to ensure we use a model of sufficient complexity.

Explicit models

The models considered so far are what I will call explicit models. Explicit models are not intuitive in themselves, but are built from fundamental concepts that we have intuitions about. We do not immediately know the specific velocity of the pendulum after a certain time period has passed, but we are able to use mathematical tools, which are built on intuitive logical axioms, to calculate it.

Building an explicit model is a way of reducing complex systems into intuitive building blocks. Thinking with our intuitions is automatic, so when we reduce a problem in this way we can effectively reason out an answer. Consider plotting out a mathematical function on a piece of paper, it becomes much easier to understand the behaviour contained within it. Our intuitions about how things move in space can be commandeered to reason about the abstract notion of a mathematical function.

Explicit models can be things of exquisite detail and boundless complexity, allowing them to go beyond and contradict our intuitive knowledge. Science is full of such unintuitive findings. We intuitively believe, for example, that spending money on ourselves will make us happiest. However, psychological experiments show we are better off spending it on others. When presented with such a conflict, we can usually choose to trust the explicit model, as it is built on more fundamental intuitions. How we make this choice is not always obvious though, it is a topic I hope to explore more in the future.

Brains automatically build models of the world

When interpreting the world, brains think in representations. When you see a round green coffee table, you do not think of it as the collection of visual excitations caused by the light reflecting off the different components of the table. You think of it as a singular representation, in this case, a table. On top of this, you keep track of the particular characteristics of this object: it is green, it has a round top and is close to the ground.

Breaking down objects in the world into such representations allows us to think about them efficiently. It is much easier to mentally manipulate a simplified representation than all the detailed properties of the object. When you remember the green coffee table, storing an exact image would contain a lot of irrelevant information. You would need to keep track of the changing shades of green caused by different shadows falling across the table; the visual interaction of the edges of the table with the background; and so on. It is much easier to remember that it is a table with a few specific characteristics. As you already have significant prior knowledge of tables, you can use this limited information to reconstruct an image of the object in your mind at the moment you wish to recall it.

Another huge advantage of thinking with representations comes in our ability to communicate. We know that other people also know the general properties of tables. We can therefore convey information about the object we just saw with a very short description: it is a green coffee table. If we could not represent the table so simply, we would have to give an excruciating description of what we saw when we looked at the table for them to understand.

Implicit models

When we are making mental representations of objects in the world, we are automatically using our own personal implicit models. The prior knowledge that describes how to represent the world and how it should behave is encoded into our brains.

To get a feel for an implicit model, consider walking down the side of the road. As you do this, your brain takes in a vast quantity of sensory information and condenses it into the representations that make up a mental model of the street. You know where the other pedestrians are, how many cars there are and how fast they’re moving. You may notice trees on the side of the road, but you will likely not notice the shape of the foliage. You have a model of the world that serves for moving down the street, avoiding other pedestrians and not getting hit by a car, but you do not waste brain power on irrelevant details. In every part of our life, consciously or unconsciously, we are making use of such implicit models. We convert the vast stream of sensory information into important representations and discard irrelevant information. This allows us to think, communicate and remember quickly and efficiently.

Given this concept, we can see that we are actually making use of implicit models when we are thinking intuitively. Fundamental intuitions are built into the structure of the brain by evolution. Your intuition of where you are in space, for example, comes from certain neurons in the brain, grid cells, which are specifically designed for this task.

Our brains also have the ability to learn. One way that this manifests itself is in the power to turn explicit models implicit, allowing them to then feed directly into our intuitions. Pianists start by learning an explicit model of a piano. However, with practice, they encode an implicit model of it into their brains, allowing them to play through feeling rather than reasoning.

Our models and intuitions can never fully represent reality

We are now left with a nice map of how we can understand the world around us. However, the question remains, how does this understanding correspond to reality itself? On this topic, recent work by Donald Hoffman in the field of evolutionary game theory dropped a bombshell...

The power of evolution to give us useful intuitions via implicit models of the world has an overriding characteristic: it tries to be as efficient as possible. This leads to implicit models that are as simple as they can be, containing only the details required for us to thrive as organisms. If the complexity of a model can be reduced, it will be. When taken to its logical conclusion, this statement can shake the very foundation of what we can know about what is real. There is no reason evolution should have provided us with a good representation of reality. On the contrary, it would be inefficient and selectively unfavourable to do so. Even our most fundamental intuitions cannot be trusted. Although this appears discouraging, by using these intuitions, we do seem able to build descriptive models of staggering beauty and complexity through the application of the scientific method.

Science as a series of emergent models

The pursuit of science is one of building progressively better explicit models of the world. Each field of science offers self consistent frameworks, containing representations of reality and rules about they interact. These frameworks are refined and merged as science progresses. At the turn of the 20th century, molecular chemistry and physics were completely independent. Classical physics could not hope to provide a theory of molecular dynamics. However, with the development of quantum mechanics, the models of reality provided by physics could suddenly describe the laws of chemistry.

Despite physics offering a conceptual framework that contains the laws of chemistry, calculating molecular dynamics from first principles is impossible in practice. We cannot just do away with chemistry in favour of a more fundamental model, as it still offers the most utility when trying to understand chemical reactions. It removes the unnecessary complications of physics with higher level laws that serve as a good enough approximation.

Chemistry emerges from physics as a series of assumptions are made that transform the rules of quantum mechanics into the rules that govern chemical reactions. This emergence occurs across the sciences: biology emerges from chemistry; psychology from biology; and economics from collective human psychology. As we try to explain more complex phenomena with our models, we find we need coarser descriptions of reality to be able to make useful predictions. The level of simplification we require is one that makes use of representations and rules that can be manipulated by our intuitions, or through tools that are built from intuitive building blocks. The tools provided by mathematics offer a potent example of this. Their limitations feed into how we must separate our bodies of knowledge. It is our inability to solve complex non-linear differential equations that ultimately leads to the separation of chemistry from physics.

There is a commonly held belief amongst physicists that the search for a unified physical theory, a model built on one mathematical framework, is the pursuit of reality itself. This quest is currently stuck on the incompatibility of gravity with quantum field theory, but a final theory may well be possible. However, given the argument made so far, I think it is worth pondering whether the rules of physics can be anything other than a model that gives us a way of making predictions about the world. As any final theory would be based on mathematics, there are a series of blindspots. There is no way of conveying conscious experience with mathematics, the qualia of the colour blue can not be conveyed with symbols and equations. Maybe this is what Stephen Hawkins was considering when he asked: What is it that breathes fire into the equations and makes a universe for them to govern?

Photo by Greg Rakozy on Unsplash

A synthesis of knowing and being

Our knowledge of reality comes from the lived experience of our models and intuitions. Evolution starts us off with fundamental intuitions, implicit models baked into our very being. We then use these intuitions to build powerful explicit models, allowing us a huge breadth of understanding of the universe in which we find ourselves.

However, due to the limitations of our physical manifestation, we cannot allow ourselves to believe that our models correspond to reality itself. Instead, we should hold them lightly, treating them as tools that can help us to reach our goals. Even as the austere power of science continues to expand our understanding, we should not be seduced into a dogmatic scientific materialism. This then gives us the freedom to open our mind to other ways of thinking about the world, for the utility rather than verity. We can open ourselves up to the more subtle understanding conveyed in ancient wisdom or through non-conceptual emotional experience.

It is also powerful to remember that the models other people are using, implicit or explicit, may not line up with our own. We tend to behave as if our own models really represent the world as it is. Realising that this cannot be true can help us all to understand one another and communicate better.

At first glance, the fact that we may never know reality as it is may seem a defeatist and depressing statement. Instead, I see it as an uplifting one. We can stop worrying about having absolute knowledge of the world and focus on what we are presented with right now. The direct experience of the present moment is as close to reality as we can get.