Magic, tricks, and high-dimensional configuration spaces


What is a magic trick? Any complex system, such as our world, may be described in terms of its numerous degrees of freedom, each designated along its own configuration dimension. As such, the configuration of such a system may be captured by a long list of numbers – or, equivalently, by a point in a high-dimensional configuration space. In this post, I want to entertain the idea that magic tricks are just exploiting these “extra-dimensions” to do the “impossible” - leading to some broad implications!


How can extra dimensions help to do magic? Think of shadow theater: a stick can cast a line-shadow on my screen – which looks like a wall to my little shadow character. If I move my character past that stick, on the screen it will appear that they moved “through the wall.” So something that looks impossible in 2D space, was easily accomplished with the help of an extra dimension. Just so, when a magician apparently “teleports a coin from a matchbox to behind my ear,” they actually do something quite simple, but using extra dimensions - ones that I did not notice were there, like their sleeve. The art of the magician, in this case, is to manipulate my attention in such a way that out of all the myriads of the degrees of freedom describing our complex world, I only pay attention to a few, and in particular that I miss the ones actually being used to do the trick.


This simple idea seems quite universal to me – and perhaps can fruitfully explain many things we consider wonderous in the world, like technology, genius, or "real" magic. Computers work because of the hidden electronic degrees of freedom that have been carefully engineered for the task. A brilliant diplomat might find a collaborative dimension between two enemies that no one else noticed. In all cases, the game is about “finding a way to walk around the wall, when others may have tried to walk through it.” I.e., for a task that seems hard or impossible according to the familiar dimensions of the world, try to find a new dimension that might make the task easy.


As such, it seems to me that what we might call “real" magic is just another example of this, where the extra dimension being utilized is entirely new and unfamiliar to us – something we have never seen or experienced before, and thus something we can never guess at. Thus, a computer will be truly magical to someone who has never heard of electricity, as will global cooperation to someone who knows nothing of the market forces.


Let’s now finally circle back to the start of the article and remember that the full description of our complex world is extremely high-dimensional. With this, we may arrive at a fun conclusion that for almost any "wall" we might want to walk through, there is most likely at least some dimension that would allow us to walk around it. In other words, we might guess that most impossible things only look so within our familiar dimension - our familiar set of degrees of freedom. And so, just as growing up we stop being shocked by magic tricks - knowing that there is probably just some dimension there that we didn’t notice - we could similarly grow to believe that, one way or another, anything is possible.

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