A geometric puzzle based on the Thing movies

James Arness was not a scientist, but was an actor who is best known for having played Marshall Dillon in the long-running TV series “Gunsmoke.” This series had a 20-year run, unheard of nowadays for scripted shows with actors that are animate, as opposed to animated.

Today I wish to raise a puzzle about an earlier movie that he starred in called The Thing.

The full title of the movie is: The Thing from Another World. Arness played a creature who was discovered by scientists at the North Pole embedded in the ice. It is one of the great science-fiction movies of all times, in my opinion. It is filled with wonderful dialogue and scary scenes. The leader of the scientific group is Dr. Arthur Carrington, who at one point says:

There are no enemies in science, only phenomena to be studied.

Not sure I agree with this statement, especially when the phenomenon is an eight foot creature who is really frosted about being defrosted. Okay maybe this is too much, but anyway Arness’s creature is pretty upset.

Later there were two further Thing movies, both directed by John Carpenter and both named “The Thing.” As part of Hollywood’s approach to originality these movies take place at the south pole. One stars Kurt Russell, and the other stars Mary Elizabeth Winstead, and the latter is the prequel to Russell’s movie. Let’s use the terminology Thing I for the original, Thing II for Kurt Russell’s movie, and Thing III for the most recent movie.

## Goofs and Setups

As with many movies there are errors, goofs, and continuity mistakes in these movies. See this for a list of them for the movie Thing I. Here is one:

At the end, the co-pilot throws his tool to force the thing up on the walkway, but immediately after electrocuting the monster the co-pilot is seen holding the same instrument.

My problem is not a simple error or goof. What I am puzzled about in the Thing movies, all three of them, is more fundamental. It is part of the setup of the whole story.

It comes down to a geometric problem, and I am terrible at geometry. So my hope is that you will be able to explain how do they get the creature out of the ice? Let’s get started explaining the situation.

## The Ice Puzzle

Long before there were refrigerators there were ice boxes. People collected ice from rivers or frozen lakes during the winter—harvested it—and then stored it for the summer months. Cutting out the blocks of ice is straightforward: drill a hole through the ice, which was usually a foot or two thick, then use a saw to cut out a block. Since ice floats the block does not sink and it can be pulled out of the river or harvested. There was a whole industry based on harvesting ice in this way. Here is a quote to further explain how the procedure worked:

Ice harvesting generally involved waiting until approximately a foot of ice had built up on the water surface in the winter. The ice would then be cut with either a handsaw or a powered saw blade into long continuous strips and then cut into large individual blocks for transport by wagon back to the icehouse.

My puzzle is based on cutting out blocks of ice in very different situation. In Thing I and Thing III the scientists discover a creature that is just below the surface of the ice. They can see through the ice a vague outline of the creature, and see that it is frozen in solid ice. The size of the creature is large, so it is about 4 by 4 by 8 feet in dimensions. In both movies they decide to remove the creature encased in the ice. In a later scene we see the huge block of ice—an almost perfect rectangular block—placed on a table somewhere back at their base. Of course there is the small issue that the block would weigh about six thousand pounds, but that is not what I am puzzled about.

What I am puzzled about is, how did they cut out the block? The problem is the ice where the creature is has essentially infinite depth. It is not frozen over a riverr—no, the ice extends down at least hundreds of feet. So removing the block is quite different than removing a block of ice from a river. The issue to me is a geometric one: I see how they can cut down the sides of the block with saws or some other tools. What I do not see is how can they cut the bottom out? In the river case there is no need to cut the bottom, since the bottom is bounded by the unfrozen river water. There is no such interface in this case. So how in the world can they cut out the bottom of the block?

I am puzzled. How can they do this?

## The Ice Puzzle: More Details

Let me try and make the puzzle into a more precise math problem. Here is the block of ice that you want to remove:

You can cut from the surface down with a saw. So you can make this into:

where the black arrows are cuts your saw can make. The problem is how do you get a cut that goes in the horizontal direction? I see in real life that one could dig up a huge trench around the whole area and then proceed to cut out the block. That would be extremely time consuming and certainly there seems to be no way that could be done in the Thing I and probably not in Thing III.

Is there a trick I am missing? The best I can see is to do the following:

Dig down the extra on each side and remove the two triangular pieces L and R, then one could get down to cut across. Is this how they did it? It is, however, awfully difficult to cut at an angle.

## A Way Out, and Some Problems?

Ken suggests that perhaps the monster was encased in a glacier flowing down at an angle. Then a cut at an angle to the glacier can be made by a Pendulum saw, also called a “swing saw.” Pendulum saws use gravity to guide the blade, and are used to cut ice from rivers even today. This helps if we also suppose that the other methods can be used to make cuts that are normal to the glacier’s surface.

Another possibility is that there were fault planes beneath the ice, say parallel to the surface. Then we only need four normal cuts that intersect with the hidden plane, whose presence we have detected perhaps by ultrasound. If this were the idea, would it be worth five seconds of movie time to show it?

This last idea suggests some computational problems. You are given a known arrangement of bounded fault planes beneath the surface, at various depths or maybe even all at the same depth. How many blocks of ice, or how much volume of ice, can you obtain with ${k}$ cuts that are normal to the surface? Can such a problem be NP-hard?

## Open Problems

So how did they get the creature out of the frozen ice? Or is it just movie magic that should not be looked at too carefully?

1. October 12, 2012 9:05 am

How about the same way you cut notches in wood or similar? Do the vertical cuts. Then use a lever of some kind — a jack, I guess, for large pieces like this — to push the block horizontally near the top. With enough force the block will crack along the bottom, guided by the four cuts, and come loose, ina vaguely rectangular shape.

October 12, 2012 10:08 am

Janne

Not sure would work, but sounds interesting. The ice block might be heavy and also could crack. But like the idea.

Dick

October 12, 2012 10:35 am

In the beginning (1938), there was the novella “Who Goes There?” by John Campbell, which was set in Antarctica. The first film adaptation (Thing I) moved it to the Arctic among other changes, and the second adaptation (Thing II) went back to the original for inspiration (including leaving the action in Antarctica). The third adaptation (Thing III) was conceived as a direct prequel to Thing II, but had none of the creative staff from Thing II (specifically, John Carpenter was not involved in Thing III).

If you don’t care about preserving the block, traditional techniques for cutting mortises would work well. Cutting 4 “mortises”, one on each side of the creature, would be relatively easy, providing access to the bottom of the block for horizontal cutting.

Another option would be to dig deep notches around the block, then flood the bottom couple of inches with hot water/brine to melt the ice at that level. By recycling and reheating the melt-water, it might be possible to “cut” the block free, so it’s floating in a pool of melt.

3. October 12, 2012 10:39 am

U-shaped pipe which drags behind it a sheet of plastic or some other divider. Pump warm water through the pipe, drag it underneath, plastic keeps ice from re-melting to ice. More than 30 seconds of thought would probably let us engineer something better. Maybe something that carries a roll of plastic so you wouldn’t have to slide the trailing plastic under the block. Come in from both sides, use the material you used to separate as a lift point…

October 12, 2012 11:14 am

I would use a rectangular, rigid metal frame, made by a highly resistive material, and heat it by electric current. The vertically oriented frame should be lowered, until the lower edge is beneath the creature’s lowest part; and then, it could be moved slowly horizontally (by its rigidity), essentially extruding the block of ice. The applied current should keep the frame hot enough during the process to melt its way through the ice.

October 12, 2012 11:18 am

I think by this method, any shape of ice could be cut, provided its cross section is invariant under translation or rotation.

October 12, 2012 11:27 am

A bit off topic, but still about the movie. You mention the great dialogue and I agree. The key was the ensemble nature of the conversations among the characters. Interrupting each other, stepping on each other’s lines, mumbled wisecracks, etc. Many movies back in the day had this more “social” character. A similar approach can be seen in “His Girl Friday” (a very funny movie from 1940) — the conversations among the beat reporters sitting around playing cards and waiting for a story to break are priceless. I don’t know what accounts for today’s almost universal change in approach. The remake of “The Thing” from 1982 had none of the originals’ camaraderie. You get the sense that the earlier version reflected the interpersonal relationships that arose during the war years, but this wouldn’t necessarily account for the same writing in HIs Girl Friday or earlier movies. Sorry, nothing to contribute to the real point of your post.

October 12, 2012 12:57 pm

Mike Bacon,

Great point. You are exactly right. Appart from the sci-fi part the dialogue was special.

October 12, 2012 12:38 pm

LOL … At least part of the answer has been known since 1917: a rotary bit that drills perfectly square holes! 🙂

October 12, 2012 12:50 pm

… and once all four sides of the rectilinear trench have been cut, cut the back plane with hot wire ice-cutter (more familiar to model-plane builders as a hot-wire foam-cutter). Simple! 🙂

October 13, 2012 12:42 am

From memory, in the novella, they use thermite. It turns out that the crashed alien spaceship is made of magnesium alloy or similar, so this is not such a good idea.

More generally, they might extract the body from the ice using some technique (thermite, explosives, or a v-shaped or cone-shaped trench) which extracts the body but within an excessively large and inconveniently shaped chunk of ice, and then trim that trunk to a convenient rectangle to transport it back to their huts.

8. October 13, 2012 2:31 am

” Is this how they did it? It is, however, awfully difficult to cut at an angle.”

Not ice. Just use a long, straight, taut, filament heated by an electric current running through it. It would act like a cheese knife cutting through butter

9. October 13, 2012 2:35 am

Oops. Looks like John Sidles already suggested the same thing as me

October 13, 2012 6:02 am

No need to cut a trench as deep as you indicate. Just crop a prism from the bottom of it (the red arrow) – after pulling it out, to reduce the weight for transport.
The sport of answering goof questions reminds me of how in Nethack some bugs are fixed by explanations.

11. October 13, 2012 11:35 am

A slight modification of the hot wire idea.
Use a hot wire shaped like a U. Place plane of U normal to ice surface. Move plane of U down, then move it parallel to ice surface, then move it up

October 13, 2012 12:09 pm

No need to cut at an angle. Cut stairs with that have points that touch your angled line. If you can determine how deep you want to cut, you can divide that into n equal parts. Measure from the edge of the block you’re removing straigt out in each direction, equal to the distance you’re cutting down. You can then make “Stairs” of height and lenth n down to the point you wish to cut the bottom. It would look something like an upside-down Incan Pyramid. Strap the block up and smooth one side of your “Pyramid” and you can drag it out by hand or snowmobile. Preferably snowmobile!

October 13, 2012 12:43 pm

Hard to type when the thing asking for the e-mail is hovering over the text box, think I figured out how to stop that now.

Anyway, the height and length of the stairs wouldn’t be equal to n, they’d be equal to the length of an individual equal part n.

Hope that sounds a bit more rational.

October 13, 2012 12:18 pm

Law and Order ran for 20 seasons, ending in 2010.

14. October 15, 2012 6:21 am

How about a circular saw? In fact, even a semicircular saw that goes backwards and forwards very rapidly could in principle do the job. Just start it going downwards and then gradually rotate it to cut out a semi-cylinder under the Thing, before rotating back upwards again. (Whether the material of the saw could be strong enough is another question.)

15. October 15, 2012 12:00 pm

If you weren’t worried about the size of the trenches, then perhaps really big blow torches could open them up quickly, and you could shape the rest of it with John’s hot wire ice-cutters.

October 15, 2012 12:27 pm

It is a remarkable fact of solid-matter engineering, that even the highest-precision optical mirrors (for example) are produced by chemical-bond-disrupting processes that — when visualized at the atomic level — are comparably unsubtle to a thermal lance and/or a sledgehammer.

October 15, 2012 12:57 pm

And to complete the cycle, the quartz spheres of Gravity Probe B — the highest-precision macroscopic objects ever fabricated — were the result of a grinding process that is simultaneously geometrically elegant yet physically violent.

Needless to say, the various mirrors, chambers, diodes, wires, and substances of quantum computers are necessarily fabricated by similarly gross processes, from similarly gross atomic materials. Whether the dynamics of these devices can be entirely free of quantenfeldtheoretisch Dreckeffecten is (in essence) the physical question that is at-issue in the Harrow/Kalai debate.

A Literary Aside  Phillip Pullman’s His Dark Materials trilogy is concerned with the spiritual analog of this same question. The title is a reference to a verse by Milton:

Into this wilde Abyss,
The Womb of nature and perhaps her Grave,
Of neither Sea, nor Shore, nor Air, nor Fire,
But all these in their pregnant causes mixt
Confus’dly, and which thus must ever fight,
Unless th’ Almighty Maker them ordain
His dark materials to create more Worlds,
Into this wilde Abyss the warie fiend
Stood on the brink of Hell and look’d a while,
Pondering his Voyage; for no narrow frith