If something is impossible, it can’t be done. Seems straightforward enough. But what makes the difference between whether something is possible or impossible? In asking this question, we find there is not one single answer, but several tiers, each nested within the one before.
Logically impossible
At the most bedrock level, we have logical impossibilities. These are things that cannot exist or cannot be done because they contradict themselves. These include mathematical contradictions, as well as things that contradict their own definitions.
For example, suppose among the men in a certain town, there is a barber who shaves those, and only those, who do not shave themselves. Does the barber shave himself? If so, he is not the barber. Does he not shave himself? If so, then he shaves himself. Therefore, a barber who fits this description cannot exist.
Other things that are logically impossible: A square circle in cartesian coordinates. A solution to a 2x2 sudoku puzzle with a 1 in the top left and a 2 in the bottom right. A legal crime. A dry ocean.
Physically impossible
We don’t live in a universe where everything logically consistent is possible. Everything that exists has a nature, described by laws of physics, and these natures render a whole host of things impossible.
I should pause to mention the distinction between the true nature of reality and our current theoretical understanding of it. Science is very much a work in progress, so there are many things we don’t know yet, and many we think we know but are wrong about. Nevertheless, there are things that are logically possible, but impossible within the true laws of physics, whatever they turn out to be at perfect resolution.
With that in mind, we can talk about what would be impossible if our current understanding were correct, and let it be a proof of concept. Some things that are impossible in our universe, but logically acceptable, are perpetual motion, going faster than light or backward in time, getting out of a black hole, and reducing the total entropy of a closed system.
Technologically impossible
Even within the laws of physics, many things are not possible to us yet, because we do not have the technology to do them. This tier is vast and rich, and in considering what is inside it, we can imagine mind-bogglingly bizarre futures.
In the near term, we have things like mind-computer interfaces, autonomous cars, and quantum computers. A little further out, we might expect to invent nuclear fusion power plants, space elevators, superconducting power lines, weather control, conscious artificial intelligence, biological immortality, revival of extinct species, human colonies all over the solar system, and so much more.
These may seem like science fiction magic to untrained ears, but the difference between them and magic is that people can envision a path toward inventing them that makes sense in the context of modern science.
Economically impossible
Even when we know how to do things, we still need the will and the resources for them. As humanity finds new ways to harness energy and resources, especially in space, more and more things become possible. These include things like space ships with spin gravity, particle accelerators that dwarf CERN, interferometer telescopes the size of the solar system, and buildings tens of thousands of meters high.
But when we’re talking about the merely economically impossible, we don’t have to limit ourselves to such small scales. We could build an orbital ring around the Earth’s equator, orbiting just outside the atmosphere, with launch platforms for shuttles and rockets. We could mine asteroids and use their materials to build giant ships in space. We could envelop the sun entirely in solar energy collectors, a Dyson sphere. We could build giant reflectors to direct all of the sun’s light in one direction, effectively a rocket thruster that could move the solar system. All under known science, and with technology that has already been invented.
Cognitively impossible
Here we come to the last, most easily surpassed level of impossibility. These are things which are impossible only because people believe they are. As soon as people put their minds and efforts toward it, it becomes possible. Many of the great inventions of history came about because someone or some group of people decided they were going to do what everyone else assumed to be impossible, from the Wright brothers inventing the airplane, to the USSR sending a man to space, to the US putting boot prints on the moon.
Today, the biggest example of someone challenging the cognitively impossible is Elon Musk. From SpaceX building bigger and better rockets, to the Boring Company digging tunnels under Los Angeles to solve traffic congestion, to Neuralink connecting people’s brains with computers. He, those who work for him, and many other entrepreneurs, bring the cognitively impossible into existence.
Other things that seem cognitively impossible: World peace. Meeting the basic needs of everyone on Earth. Tolerance and good will across political and religious divides. Governments that work for everyone. A business culture that cares about the poor, the workers, and the environment. Cultures where there are no social minorities or majorities. Cities floating on the ocean. Powering civilization and the global economy with sustainable resources.
All of these things are possible and doable given the technology and economic infrastructure we have now. Why don’t we? Well, there are a million reasons, all of which are unique to their particular challenge. But many of them can be overcome if enough people or the right few see through the curtain of the way things are, and aim their sights on achieving what many brush off as impossible. Not everything is possible. But the number of things that are is vast.
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