Four-dimensional surgery of a three-dimensional patient

In the last visit to the dentist, it was thought, how difficult it is for surgeons to live in three-dimensional space. The sore is inside the body (in the case of a dentist - inside the tooth), but to get to it, you have to dig deep and destroy (and then restore) significant body volumes from the surface itself - until you get to the actual sore.

Now, if there was a four-dimensional surgeon, then it would be much easier for him to treat a three-dimensional patient. In the three-dimensional world, the three-dimensional body is limited on all sides. Those. everywhere there is a border - from which side do not approach, you will see only her, this border. But in the four-dimensional world, the three-dimensional body will have no border from the fourth dimension - and the surgeon will be able to see the entire thickness of the three-dimensional body and act directly on the sore, without affecting anything around.

The four-dimensional situation is hard to imagine.

But there is a simple metaphor for understanding - let's imagine a two-dimensional world and look at it from the side of the three-dimensional world. Take a piece of paper and draw a tooth silhouette on it. In a two-dimensional world, teeth, perhaps, would be no less useful - to crush other two-dimensional creatures between two opposite teeth for the purpose of subsequent eating. So two-dimensional creatures, too, would probably have developed teeth and would have to treat them. I'll draw such a tooth by hand - and a sore inside. We abstract that the sore develops, having rotted from somewhere from the surface. Let it have arisen in our group - for clarity of example.
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So, our two-dimensional patient goes to a two-dimensional dentist. And the one, having illumined a tooth on a two-dimensional X-ray machine, determines which side needs to be drilled into a tooth in order to get to caries. By the way, there are problems with drilling in the two-dimensional world - it will be extremely difficult to make a rotating tool, because it will rotate from all sides — you will not catch it. A circular disk or chainsaw can be made - but they will be surrounded on all sides by teeth and you cannot hold them in two-dimensional hands, and you can’t unwind too much. So there will be our two-dimensional dentist armed with something like a micro-excavator.


We see that the problem with a two-dimensional dentist is the same as with a three-dimensional one - you need to dig a tooth, destroying part of the enamel and dentin, cure the sore, and then fill it with artificial substitutes for enamel and dentin.

And now let's take and imagine a three-dimensional dentist who has taken to cure a two-dimensional patient. Imagine this picture is much easier than in the four-dimensional case. Three-dimensional dentist picks up a sheet of paper and ... drills right into the sore, without touching anything around. He doesn’t even need an x-ray - he sees the entire thickness of the two-dimensional body in full view. This is a two-dimensional surgeon, from which side you don’t come up, sees only the border of the tooth - and in the third dimension such a tooth is defenseless, it has no border - and all of it is perfectly visible. I will not draw the third dimension - here is a picture of you with a drill (albeit not from a medical one), drilling right into the sore inside the tooth.


So, a four-dimensional dentist could very similarly stick his four-dimensional boron directly into any point of three-dimensional space - in the form of a three-dimensional projection of the corresponding part of four-dimensional boron. In the simplest case - a rotating gear ball, hanging in space, not relying on anything. Actually, relying on the adjacent parts of boron in the neighboring three-dimensional spaces, which are separated from ours by the Planck length in the fourth dimension - and thus forming a four-dimensional tool. Also, our hyper-surgeon would be able to see the entire three-dimensional thickness with his four-dimensional eye. Provided, of course, that the three-dimensional spaces next to ours turned out to be transparent - so I would not be able to see the insides of a two-dimensional tooth on a piece of paper if there were a stack of other sheets on top of it.

True, they should be almost completely transparent - otherwise our world would experience the strongest impact from these neighboring worlds - and no stable three-dimensional structures could be formed. A two-dimensional leaf of some ether of Planck thickness, suspended in a vacuum and screened from external influences, could behave like a full-fledged two-dimensional world in a three-dimensional environment. But place this piece in the thickness of the tree - and the deformations scatter two-dimensional bodies into adjacent planes (deformation is enough not by millimeters, but to a negligible Planck length), and pervopendicularly digging loggers will crack the remaining atomized two-dimensional ones. So for the survival of three-dimensionality within the four-dimensional world, it is necessary to start an isolated three-dimensional volume (analogue of a leaf) from some ether (or something else, not material in itself, but capable of generating material elementary particles, standing three-dimensional waves interacting only within this three-dimensional volume without flowing into the fourth dimension - otherwise we would immediately notice a violation of the law of conservation). And with this volume once someone four-dimensional wanted to interact.

However, it is good if our 3D patient is met by a 4-D surgeon, and not a 4-D bully. After all, the defenselessness of three-dimensional creatures has the reverse side of the four-dimensional impunity. Moral: you want to survive in the four-dimensional world, provide protection in the fourth dimension.

And it's easy to see - taking the metaphor of the state leading the arms race. Suppose we had only ground weapons. And we surrounded the country around the perimeter of the appropriate armed frontier. We get a two-dimensional border. And here as a result of scientific and technical progress, whipped up by this very arms race, the neighboring country invented airplanes. And that's all - our country is completely defenseless (for example, our weapons do not fire up to them - for the sake of abstract example). Aircraft can fly to any point of our country, see everything from above that they want, and bomb any point inside the country without affecting the borders. Here they are - three-dimensional hooligans (if not worse), beating the two-dimensional lad with impunity.

Of course, in reality everything is somewhat more complicated. The arms race is not in the usual, but in the phase space. The range of the weapon, the speed of the projectile, the accuracy of the hit are all separate measurements in the phase space. Do the enemy tanks shoot for a kilometer, and you have two? You got a decisive advantage in the war. However, with the complication of space before the phase, visibility is lost, therefore we will not go this way in our metaphors.

The best example of the fourth dimension is an informational, ideological weapon. You defended the borders, built a mighty air dome from the air defense and missile defense - would it seem like you are afraid? But all your soldiers read the news and write in the social network. Whose news do they read, who for them seems more convincing? How are they united? Do they understand what they are protecting? What makes them go forward, what is their very meaning of life - what is the thought of a bright future that protects them from the consciousness of inevitable mortality? If all this is not the ideas of your country, if the enemy has achieved a decisive advantage in explaining the image of the future, in its attractiveness, then everything, three-dimensional soldiers are totally vulnerable in the fourth dimension.

Are your top-secret objects safely hidden from the eyes of the enemy? But your people will blab everything about them in social networks, mark them up on wikis and google cards or report them more confidentially to outsiders. The four-dimensional enemy will only see the big picture (and it’s not bad in social networks on a semi-automatic basis). Do you think that your soldiers, in which case, will bring their weapons to the enemy? But this enemy has long been for them the best friend, with whom they connect all thoughts about their own future. No, the weapon will be pointed at you.

I quote the poem "The Idea" by Pierre Beranger (1870):

People's sorrow aching,
I fell into a reverie - and suddenly
An idea passes before me.
Idea? Yes, sneaky friend.
Still weak, but beautiful;
The sound of speech is hard, the look childishly simple.
Nobody is like a god - we'll see alive
Its development and growth.

One towards brute force!
I shout to her: “Child! fear yourself:
Spies ears pricked up,
The gendarmes gathered menacingly. "
- “In my favor their persecution.
Going forward with hope.
Now all my meaning
Perhaps the people will understand. ”

"Fear, child, the earth is shaking
Under the weight of thick columns,
And, saber bald, rushing
For squadron squadron.
- “I, without trumpeting, without drumming,
I wake the words asleep
And for recruiting in their own camp
I will go alone among the bayonets. "

"Fear not to be destroyed."
Here on earth is your very footprint.
Run: wick in the gun nested,
A minute - and there is no salvation. "
- “And tomorrow kernels and grapeshot
In my defense fuse
His oratorical speeches;
After all, the gun is the same lawyer. ”

"You are annoyed by the deputies."
- "My strength will humble them."
“This force will bend in the dungeon.”
- "The dungeon spirits my spirit."
“The clerics curse thunder.”
- "And tomorrow I will go for a censer."
- "Already the vassals conspired."
“I will find shelter in their ranks.”

And suddenly a terrible picture:
Blood streams, the sea of ​​evil,
Wreath victory discipline
With prostrate courage took off.
But defeated with a new force
The idea of ​​laurels distributes
And being touched by their grave,
Flies forward with their banner.

In the world that our metaphorical optics painted, the only protection against a four-dimensional enemy is protection in the world of ideas. Only the desire to achieve a bright tomorrow, where a person is waiting for not bestial consumer vegetation, but a combined creative impulse forward, into deep space, into thermonuclear energy, into great art, into a genuine future, where tomorrow differs from yesterday not with the new iPhone model, but with a spaceship, sent to Alpha Centauri is the only defense against defeat in this four-dimensional world.