Four-dimensional surgery of a three-dimensional patient

    Salvador Dali, “Crucifixion (hypercubic body)”

    In the last visit to the dentist I thought how difficult it is for surgeons to live in three-dimensional space. The sore is inside the body (in the case of the dentist, inside the tooth), but in order to get to it, you have to dig deep into 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 a three-dimensional world, a three-dimensional body is bounded on all sides. Those. everywhere there is a border - from which side do not go, you will see only it, this border. But in the four-dimensional world, the three-dimensional body will not have a border from the side of 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.

    It is hard to imagine a four-dimensional situation.

    But there is a simple metaphor for understanding - imagine a two-dimensional world and look at it from the side of a three-dimensional world. Take a sheet of paper and draw a tooth silhouette on it. In the two-dimensional world, teeth would probably be no less useful - to split other two-dimensional creatures between two opposite teeth for the purpose of subsequent eating. So two-dimensional creatures would also develop teeth and probably have to be treated. 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 thickness - for illustration purposes.

    Two-dimensional tooth - 1

    So, our two-dimensional patient goes to a two-dimensional dentist. And he, having enlightened the tooth on a two-dimensional X-ray machine, is determined on which side you need to drill into the 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 won’t grab it. A circular disk or a chainsaw can be made - but they will be surrounded by teeth on all sides and you won’t hold them in two-dimensional hands, and you won’t especially unwind them. So there will be our two-dimensional dentist armed with something like a micro-excavator.

    Two-dimensional tooth - 2

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

    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. A three-dimensional dentist picks up a sheet of paper and ... drills it straight into a sore without touching anything around. He doesn’t even need an x-ray - he sees the entire thickness of a two-dimensional body in full view. This is a two-dimensional surgeon, from which side do not go, he sees only the border of the tooth - and in the third dimension such a tooth is defenseless, it has no border - and it is perfectly visible to the whole. I will not draw the third dimension - here is a photograph with a drill (albeit not a medical one) drilling directly into a sore inside a tooth.

    Two-dimensional tooth - 3

    So, a four-dimensional dentist could very similarly stick his four-dimensional boron directly at any point in three-dimensional space - in the form of a three-dimensional projection of the corresponding part of the four-dimensional boron. In the simplest case - a rotating toothed ball hanging in space without relying on anything. But in reality, relying on the neighboring parts of the boron in neighboring three-dimensional spaces that are far from ours by the Planck length in the fourth dimension - and thus forming a four-dimensional tool. Also, our hypersurgeon could 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 - even I would not be able to see the inside of the 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 have experienced the strongest influence from these neighboring worlds - and no stable three-dimensional structures could have formed. A two-dimensional sheet of some ether of Planck thickness, suspended in a vacuum and shielded from external influences - could behave like a full-fledged two-dimensional world in a three-dimensional environment. But put this leaf in the thickness of the tree - and deformations scatter two-dimensional bodies into adjacent planes (deformation is not enough for millimeters, but for an insignificant Planck length), and perpendicular burrowing woodworms will gnaw on the remaining atomized two-dimensional. So for the survival of three-dimensionality inside the four-dimensional world, you need to create an isolated three-dimensional volume (analogue of the sheet) 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, not flowing into the fourth dimension - otherwise we would immediately notice a violation of the conservation law). And with this volume once someone wanted to interact with someone four-dimensional.

    However, it is good if our three-dimensional patient encounters precisely a four-dimensional surgeon, and not a four-dimensional bully. Indeed, the defenselessness of three-dimensional creatures has the reverse side of four-dimensional impunity. Moral: if you want to survive in a four-dimensional world, provide protection in the fourth dimension.

    And this is easy to see - taking the metaphor of a state leading an arms race. Suppose we had only ground weapons. And we surrounded the country along the perimeter with appropriately armed border posts. We get a two-dimensional border. And here, as a result of scientific and technological progress, spurred on 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 penetrate them - for the most abstract example). Airplanes are able to fly anywhere in our country, see from above everything they want, and bomb any point within the country without affecting the border. Here they are - three-dimensional hooligans (if not worse), who beat a two-dimensional guy with impunity.

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

    The best example of the fourth dimension is informational, ideological weapons. You defended the borders, built a mighty air dome from air defense and missile defense - it would seem, what should you be afraid of? But all your soldiers read the news and write on social networks. Whose news are they reading, who seems more convincing to them? How are they united? Do they understand what they protect? What makes them move forward, what makes up their very meaning of life - what kind of thought about a bright future protects them from the consciousness of imminent mortality? If all this is not the idea of ​​your country, if the enemy has gained 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 securely hidden from the enemy’s eyes? But your people will chat everything about them on social networks, mark them on wikis and google maps, or report them more privately to prying ears. The four-dimensional enemy will only have to see the big picture (and it’s pretty good for social networks in semi-automatic mode). Do you think that your soldiers, if something happens, will point their weapons at the enemy? But this enemy has long been their best friend, with whom they associate all thoughts about their own future. No, weapons will be pointed at you.

    I will quote the poem “Idea” by Pierre Beranger (1870):

    I was ill with people's sorrow,
    I fell into a dreaminess - and suddenly an
    idea passes before me.
    Idea? Yes, a cowardly friend.
    Still weak, but already beautiful;
    The sound of speech is solid, the look is childishly simple.
    Nobody is like a god - we will see vividly
    Her development and growth.

    One towards brute force!
    I shout to her: “Child! Fearing:
    Spies ears pricked up,
    Gendarmes menacingly gathered. "
    - “In my favor, their persecution.
    I am going forward with hope.
    Now, all my significance
    will probably be understood by the people. ”

    "Fear, child, the earth is shaking.
    Under the weight of the thick columns,
    And, with sabers, headless, the
    squadron rushes behind the squadron."
    - "I, without trumpeting, without drumming, I wake
    up the words asleep by force
    And for recruitment in their own camp
    I will pass one among the bayonets."

    “Fear not to be destroyed
    Here on earth is your very footprint.
    Run: the wick is put into the gun,
    Minute - and there is no salvation. ”
    - “And tomorrow kernels and
    My oratory speeches will burn in my defense ;
    After all, the gun is the same lawyer. "

    "You annoyed the deputies."
    “My strength will humble them.”
    “This power will bend in prison.”
    “The dungeon inspires my spirit.”
    “The curses of the clerics are booming.”
    “And tomorrow they’ll go censer me.”
    - "Already took up arms of the vassals."
    “I will find shelter in their ranks.”

    And suddenly a terrible picture:
    Streams of blood, a sea of ​​evil, a
    wreath of victory discipline
    With an open bravery removed.
    But to the vanquished with a new force, the
    idea of ​​laurels distributes
    And, touching before their grave,
    Flies with their banner forward.

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

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