4D swordfighting

[quickfur]

The recent discussion about hooks and ropes have suddenly made me realize that in 4D, swordfighting is ... basically impossible, except in a very strangely modified form (which is totally impractical in a real fight).

The bottom line is this: for maximum maneuverability, 4D swords will have to be essentially 1D sticks (well, slightly widened and sharpened for piercing, of course). But due to the extra dimension, this means that it's basically impossible to parry. Trying to block an incoming 4D sword blow with another 4D sword is like trying to shoot down a bullet in midair -- it's so unlikely that it's essentially impossible.

Also, 4D shields will need a 3D surface area in order to stand any chance of blocking an incoming 1D sword blow. Even if your shield is extended in 2 dimensions, trying to block a 4D sword with it is like trying to block a bullet with a stick in the 3D world. It's a little more likely than shooting down a bullet in midair, but still so unlikely that it's just not practical in any real sense. This means that shields are bulky and cumbersome in 4D.

The only thing that remotely resembles parrying in 4D would be if both combatants wield weapons that are extended in 2 dimensions. Such things act as intermediates between swords and shields: you can still cut with the 2D "swordshield", and you can also parry your opponent's swordshield blows. But if your opponent wields a 1D sword, then you're out of luck: your "swordshield" is pretty much defenseless against it. Plus, a 2D swordshield is much bulkier than a 1D sword, which means it will be harder to handle in an agile way. All of this means that 2D swordshields are worthless in a real fight, and the only likely place you'll see 4D parrying is at the circus where 2D swordshields are used for comic effect.

So basically, there is no 4D swordfighting in any practical sense; there's only armed combat where combatants wield both a sword and a shield (with 3D surface area).

Having said all that, though, the real situation is a bit more complicated. For one thing, it's awfully hard to hit anything with a 1D sword: the 3 degrees of freedom (assuming you stand on the ground and don't jump) means that it's very easy to dodge incoming blows. Given this fact, it would seem that 4D fighters would be chosen for their dodging skills, and that dodging would play a much more important role than in 3D. This also lends some credence to the 2D swordshield, since with those things, it's easier to actually hit something even if they are more cumbersome to handle. Also, you won't be able to cut things effectively with a 1D sword: even if you hit your target, it would only amount to a piercing blow rather than a severing blow. You don't stand a chance of cutting off limbs with a 1D sword; you need a 2D swordshield for that. Still, if you strike in the right spot, you can probably hit some vital organs and disable your opponent, perhaps for just long enough that you can move in with the cumbersome 2D swordshield to sever some limbs without the risk of getting hit yourself.

[mr_e_man]

Also, you won't be able to cut things effectively with a 1D sword: even if you hit your target, it would only amount to a piercing blow rather than a severing blow. You don't stand a chance of cutting off limbs with a 1D sword; you need a 2D swordshield for that.

True.

In 3D, a sword can be used in two ways: slashing, making a 2D cut through the body; and stabbing, making a 1D cut. Stabbing is essentially making the sword (a 1D object) act like a bullet (a 0D object) by matching its direction of motion with its geometric direction. Likewise, a shield with sharp edges could be "stabbed" with, making 2D cuts, by moving it in one of the directions that it spans.

With a k-dimensional weapon, slashing makes a (k+1)-dimensional cut, and stabbing makes a k-dimensional cut.

Also, 4D shields will need a 3D surface area in order to stand any chance of blocking an incoming 1D sword blow. Even if your shield is extended in 2 dimensions, trying to block a 4D sword with it is like trying to block a bullet with a stick in the 3D world. It's a little more likely than shooting down a bullet in midair, but still so unlikely that it's just not practical in any real sense. This means that shields are bulky and cumbersome in 4D.

The only thing that remotely resembles parrying in 4D would be if both combatants wield weapons that are extended in 2 dimensions. Such things act as intermediates between swords and shields: you can still cut with the 2D "swordshield", and you can also parry your opponent's swordshield blows. But if your opponent wields a 1D sword, then you're out of luck: your "swordshield" is pretty much defenseless against it.

False.

It helps to think in terms of spacetime, adding 1 to all the dimensions.
A swinging sword (1D) and a parrying swield (2D) thus become (respectively) 2D and 3D objects in 5D spacetime. Since 2+3=5, these objects are likely to intersect in a point, which means the parry is successful.
Two swields, being two 3D objects in 5D spacetime, are likely to intersect in a line. But that's just geometry. Physically, one point on this line will occur first, and that is when and where the blades clash.

A bullet and a sword/stick, in 3D space, become 1D and 2D objects in 4D spacetime. Since 1+2<4, there is likely no intersection. Indeed you can't block a bullet with a stick.


So, in 4D space, I think the swield would be quite useful. (Still a proper shield would be needed to block a bullet.)

[PatrickPowers]

Thanks for such a stimulating topic. In 4D world a sword can't parry a blow, nor can a saber or katana cut anything in two.

The swordsman will also be 4D. I like to imagine that he has the same number of atoms as a 3D swordsman, and these atoms are the same size and mass we enjoy. Then the 4D swordsman has a height of about one centimeter. I say that he is compact. Compactness increases with the number of atoms and depends on the shape of the object. The more dimensions an object has the more compact it is. So a 3D shield is less compact than the swordsman, hence is somewhat easier to wield than the equivalent shield in our world. A 2D shield is even less compact and easier to wield, while a 1D sword is the easiest of all. The 1D sword can take advantage of this by being made longer and/or heavier relative to the swordsman.

I had to resort to math to convince myself that there is no way to cut any object in two. To me this is amazing. I can show you the math but the idea is that all cutting is 2D planar so it can't partition a 4D object, and cutting edges are always approx. 1D, even things like chain saws. It's certainly possible to separate a solid into two parts, but I couldn't think of any method that had any elegance.

I suppose a 2D sword would be something like a 2D disc with the edge sharpened so that one has a circular edge, which is then a 1D edge embedded into a 2D space.

I'd go with a long 1D sword -- one body length? two? three? -- with a body width 2D gauntlet perpendicular to the sword for parrying. A two-handed grip might be the way to go. But that's just a guess/interesting possibility.

A thought provoking idea with some surprises along the way.

[quickfur]

A 3d-cube-shaped object in 4D is razor-thin and can definitely cut 4D objects in two. In 3D, a cutting instrument like a knife or sword is basically a longish segment of a 2D plane, with minimal 3D thickness along the edge and a thin 3D thickness for support behind the edge. So in 4D you could take a (3D) cube and taper it similarly along one face. Or, if it helps you visualize it, attach two cubes to each other at one face and fold them in on each other such that they make a very small angle (say 1° or so). The shared square face then would function as your cutting edge. Basically, this is a wedge shape.

So if you boil it all down, in 4D a severing instrument has a 2D edge, and a piercing instrument has a 0D point.

That leaves the in-between case of an instrument with a 1D edge. In 3D, a 1D edge functions as the edge of a cutting instrument, but in 4D a 1D edge can no longer cut an object into two pieces. It can give you a nasty gash, of course, but no matter how deep the gash is, it will never be able to sever anything.

So what you have in 4D is a differentiation between severing (cutting an object into two or more pieces), cutting (etching an object but not cutting it into two), and piercing (drilling a hole into an object). In 3D severing and cutting are the same thing, but in 4D they are different.

[PatrickPowers]

Aha. So to make such a thing, start with metal with two long dimensions and two short. Hammer on the two small dimensions to make a triangular cross section. The two long dimensions don't have to be equal. One is the reach of the weapon, the other has to be at least as wide as whatever it is you want to sever.

[PatrickPowers]

So how about cutting an apple in half. Will that be easier in 4D or harder? It depends on the number of molecules the edge intersects

Solve for the number of water molecules n in the radius of a 3D apple. With N being the number of molecules in the apple, n₃= N^1/3.
Solve for the number of water molecules in a cross section of a 3D apple. c₃ = N^2/3

Solve for the number of water molecules n in the radius of a 4D apple. With N being the number of molecules in the apple, n₄ = N^1/4.
Solve for the number of water molecules in a cross section of a 3D apple. c₄ = N^3/4

c₄/c₃ = N^3/4 divided by N^2/3 = N^1/12 more atoms to separate. That's the compactness formula for a 4D sold again. I estimate the compactness of an apple is about 140 , so the 4D apple is 140 times harder to sever. But the cross section of a muscle is also much larger in 4D, so maybe people are 140 times stronger.