by Russell Newton

The Nature of Uncertainty

Uncertainty is a very uncomfortable concept to wrap our minds around. The human brain highly prefers a concrete answer, thought, or even guess. It’s why we jump to conclusions and prioritize speed over accuracy. Learning to thrive in the limbo of uncertainty can greatly benefit your thinking skills because it teaches you to slow down, check your assumptions, put away your ego, and embrace the ultimate version of “I have no idea.” Once you can accept this starting point, the world will suddenly open up—because you are listening and observing.

We kick off with a thought experiment dubbed Plato’s Cave. It tells the tale of prisoners shackled in a dark cave facing inside, so the only thing they can see is a series of shadows from people, animals, and events going on outside. Of course, this is not the real world—from our vantage point. But to them, these shadows are everything, and it is unthinkable that anything else exists. So the question comes—how can we ever know if what we are seeing is merely a shadow, or the true form and nature of the thing? Of people? Of ourselves? Accept that perception is necessarily flawed, and attempt to think from the ground up.

The Nature of Uncertainty

Thought alone can take us to new and surprising places. We’ve seen with Schrodinger’s cat that thought experiments allow us to grapple with phenomena in the natural world that simply can’t be measured in the ordinary ways. Let’s now turn to how thought experiments can be used to help us tackle ideas from an entirely different realm of knowledge. What can thought experiments teach us about the nature of reality itself, as well as our ability to access and understand it?


The early philosophers didn’t take long to paint themselves into a corner. As they used their powers of logic and reasoning to fashion a picture of the world and their place in it, they inevitably came to ask: what about our thought itself? What are the differences between what we think we know and what we do actually know—and how could we ever measure the distance between the two?

Shadows Vs. Reality

The next thought experiment is again a fictitious, allegorical situation designed to draw attention to the nature of our perception, the ways we can be ignorant and not know it, what it means to be educated, and our own intrinsic capacity for expanding our conscious awareness. The thought experiment is Plato’s “allegory of the cave” and is essentially concerned with the branch of philosophy called epistemology. Very simply, this branch includes those theories and models concerning knowledge of reality itself. What is knowledge (or beliefs, theories, ideas, even truth), can humans be said to have knowledge, and if so, how?
A very simple thought experiment will quickly show you how far-reaching these questions can be: Right now, try to think of something you know. Now, ask yourself, how do you know it? If you “know” that the sky is blue, well, have you literally checked today? Or are you simply expecting it to be blue because it was yesterday when you looked? And if you looked, are you really sure it is in fact blue, and not some other color, like white? What does it even mean for something to be blue anyway, and if both you and your friend believe you’ve seen blue, how could you ever be sure that you were both alluding to the same set of neural impulses in your respective visual cortices? Really, do you “know” the sky is blue just because you’ve been told it is?

It might interest you to know that certain cultures have wildly different color-naming conventions (the Russians have two distinct words for two distinct colors that Americans simply call blue), and the Candushi tribe in Peru don’t even bother having words for colors.
These questions may seem a little circular or redundant, but in asking them we’re warming up our brains to tackle others like them. What’s the best way to think about the things you can’t think about? Consider the world you live in and you’re sure to see how valuable a skill this is! Mental flexibility, critical thinking, the ability to reflexively see yourself think and adjust given incomplete information—these are the things that make a person intelligent.


On to Plato’s cave allegory. The setup is as follows. Imagine a dark cave where some prisoners are held captive for their entire lives, and cannot turn their heads around to look behind them. They are chained so as to look straight ahead to the cave wall in front of them. Behind them is a fire. Between the prisoners and the fire is a pathway, along which people can walk—“puppeteers”—and the things they carry will naturally cast a shadow on the wall in front of the prisoners.


So, the prisoners never see the real items passing behind them; they only see the elaborate shadows cast on the wall. Perhaps they also hear echoes of whatever is passing by. Plato then asks, what would the experience and reality of these prisoners be? He said they would take the shadows for reality itself, thinking them real and not just reflections of the real. They would not understand the cause of the shadows, they would merely see the end result and mistakenly believe it to be reality.


An object would pass behind them and cast a shadow—maybe a book, in the allegory (a symbol for learning and wisdom)—and the prisoners would say “I see a book.” However, we, knowing better, would know that the prisoner is wrong—he sees a shadow of a book, but doesn’t know it. Plato then asks us, What is the nature of the claim this prisoner makes? When he uses the word “book,” what is he actually talking about?
Plato says that, not knowing any better, the prisoners would completely believe that the word “book” referred to the particular shadow they saw on the walls. Without being able to turn around, they would never know what a “real” book is. They’d use their language as we all do—to point to things in their experience. Importantly, they would not feel as though they were wrong. They would have no idea that they were mistaken. In fact, it would be akin to esteemed scientists of days gone by who claimed resolutely that the earth was the center of the universe, or that the body was ruled over by four humors. The claim “I see a book” is exactly like their claim, “I have knowledge. I know this.”
Now, as we’ve seen before, thought experiments are typically used to make some point the author wants to emphasize in a particular context. In this case, Plato had a theory of “Forms” he wished to draw attention to with this allegory. Though this classical view of Forms is only of historical interest today, Plato hoped the allegory would help people better grasp his unusual ideas. To him, language doesn’t refer to the literal things in front of us, but to Forms, i.e., abstractions that are physically incarnated in the real world but exist primarily in the mind.
In other words, there can exist a form called “blue” on its own, independent of any material manifestation. For Plato, being ignorant of the world of Forms was like being the prisoner who didn’t know about real objects except for the shadows they cast. In Plato’s conception, the things we see around us are mere shadows of the unseen, abstract Forms. We don’t need to follow along with this particular argument to derive value from Plato’s allegory.


For Plato, being able to turn your head and educate yourself on the real sources of your immediate experience is akin to learning about his Forms. (He was, ironically and unfortunately, rather wedded to his ideas and took pity on those who didn’t agree with him!) Though there are many problems with Plato’s conception, the cave allegory is nevertheless a useful exercise. It shines a light on the way we use language, how we pattern our experience and the consequences it might have for ever grasping the “real world”—if that’s possible.


It’s a simple yet powerful thought: what we see might not be the same as what is, and in fact what we see has as much to do with what’s in front of us as our own nature as observers. Plato believed fervently that education and intellectual refinement were humankind’s highest virtue and redeemer. But it all begins with the ability to recognize your own potential ignorance—via doubt.


How many of us go about life as though there was nothing in our world that we didn’t fully grasp? When was the last time you truly considered your alternatives, or any potential gaps or errors in your thinking? It can be one of the most difficult but also most illuminating exercises: What if you’re wrong, or only seeing a tiny part of the truth? What if your ideal solution is invisible to you right now?


Plato likened a philosopher to a prisoner who has managed to escape, and who perhaps has the task of trying to explain what he’s seen. He believed the ordinary public to be ignorant and resistant to education. The allegory also draws neat lines between two modes of gaining knowledge: direct experience through the senses, or via reason and argument that is independent of the senses.


Like the prisoners, we only know the world through the narrow aperture of our own limited sensory experience. If we were to figuratively rise from our imprisonment and see the world from a higher realm, would we even comprehend it? Thought experiments that ask us to imagine life in six dimensions or worlds where time doesn’t exist can perhaps give us a sense of what Plato was getting at.


There are many questions that come from Plato’s allegory. What is truly accessible through human senses and intellect? Is it even possible to go beyond those limits? Is there a world outside of our experience of it, neutral and abstract, and is it possible to access it beyond our ordinary perceptions? In a way, each of us is in our own private cave, unable even to accurately confirm that our neighbor is using the same rules for assigning words to shadows. The glaring of the sun on eyes that have never seen it before could be damaging—a prisoner returning from the outside world would not be able to communicate what he’d seen, and would be temporarily blinded. Would the other prisoners even want to follow his lead?


Without getting embroiled in the finer details of Plato’s philosophy (of which there are many), we can see the spirit of the enquiry: the big deal here is that, like the prisoners, we too could be laboring under a falsehood and never know it. Right now, at this moment, what are you ignorant of?
By design, an impossible question to answer!
When was the last time you even entertained the possibility that what you think is completely, utterly wrong? It might be anyone’s guess just how much we can educate ourselves and expand our minds, but one thing is true: none of it is possible unless we are willing to first acknowledge the possibility of being wrong. Nobody walks around consciously making room for the fact that they may be operating in ignorance. But what if we did?
The first step—perhaps the biggest step—is to really internalize the idea that our perceptions of things and the things themselves are not necessarily identical. The objects that created our sense perceptions are distinct from the perceptions themselves. It’s easy to get comfy inside our own sense-caves, but we can always peek out periodically. Even if we can’t literally turn our heads and take in reality “for real,” we can use our minds, logic, and rational thought to help us get a little closer.
How can this thought experiment improve the quality of our own thinking?
Plato’s experiment connects closely with the age-old maxim that “the map is not the territory.” We can use maps (ideas and symbols) to helps us navigate reality, but the correspondence is never perfect, and we should be careful not to forget that we have made an analogy at all—our conceptions of reality are not identical with reality.
Maps are, necessarily, simplified abstractions that omit plenty of key information. They are like models of the world, mere sketched outlines to help us better understand reality. If you forget that you are using a map at all, you may overlook these inherent limitations and weaknesses, and be tripped up by them as a result. The map is always going to be a best guess, a snapshot, a simplification. These maps need to evolve, and this isn’t possible if you are never truly cognizant of the fact that you are using one in the first place.