2009.03.12 in uncategorized

Galaxy Sized Spoon: A Problem for the Ages

I got to wondering again about the greatest engineering problem we could ever face: the challenge of constructing a galaxy size spoon.  Forget Dyson spheres, those things are useless and easy. What we need is a galaxy size spoon. Clearly the most useful goal we should have as a race. It will likely take many generations, much patience and there will be many challenges, but I think the end result will be well worth it. There are many questions and challenging relating to the construction of this super spoon, which I hope someday to have answers to.

So what challenges are faced in the construction of this greatest of spoons? Well the first problem I've thought of is simply if there is enough material in the universe to do it. Furthermore, what is this spoon going to be made of?

A metal spoon? A plastic spoon? Aluminum? Iron? Copper? All of the above? Now I think a metal spoon would really be ideal. Now if we had a plastic spoon, we could use some of the hydrogen in addition to the carbon, although the mass of the carbon is much more significant, and really all these numbers are fairly arbitrary so I'll just say a plastic spoon is composed of pure carbon. Actually a pure carbon spoon would be really cool too. Then we could experiment with different allotropes of carbon. A diamond spoon! Graphite! Buckyballs?

Now the total mass of the universe is not really known for many obvious reasons, but I've seen estimates ranging from on the order of 10⁵⁰ to 10⁶⁰ kg. I'll say 10⁵⁵ kg because it's the first number I saw when using duck duck go to find the mass of the universe. This is clearly flawless reasoning in choosing a number.

So suppose the mass of the universe is 10⁵⁵ kg. Now of this, we only want the non-hydrogen/helium components. Now of the total mass, it's estimated only about 4% is normal matter, with the rest being the mysterious dark energy and dark matter and what not. Of that remaining normal matter, about 99% is hydrogen and helium, which aren't good spoon building materials. So about 1% of 4%, so I'll say that the amount of potentially usable material is on the order of 10⁵⁵ * 10⁻⁴ = 10⁵¹ kg. Now this includes all the elements. Most of this is going to be the more common fusion products, such as carbon, oxygen, and nitrogen, with diminishing amounts as you approach and pass iron with the whole belt of nuclear stability with the binding energy and all that, but whatever. You have 10⁵¹ kg of potentially usable material in total to use for the spoon. Now how much material do we need for such a spoon? When we say galaxy sized spoon, what do we mean? Do we mean the bowl, actual spoon part is capable of engulfing the milky way? Or do we mean from tip of the spoon to the tip of the handle is about 1 galactic diameter? I'll arbitrarily choose the second option, and say the spoon is 100,000 light years from tip of the handle to the other end.

Now we need to estimate the volume of the spoon. So I have a spoon here I'll use as an example. I measured it to be about 15.5 cm long. The spoon part is sort of elliptical shaped, 3.2 cm and 5 cm on each axis, and about 8mm deep. The spoon is about 1mm thick in the spoon part, and 2 mm in the handle, although this varies a lot in different places, like it's 'bubbly' in the center where it kind of hollows in the bottom. The handle varies in width, from ~5mm to 1.6 cm. So the spoon is a somewhat complex shape, at least this spoon. So I'll just take ratios derived from these numbers, and assume the spoon is composed of a rectangular handle attached to a hollowed half ellipsoid, where the rectangle I'll say is 3 cm x 10.5 cm x 2 mm.

The handle's length is then 15.5 cm - 5 cm = 10.5 cm. By calculating the volume of the volume of the half ellipsoid, and subtracting the hollow part, and adding the handle (and of course scaling up in the ratio 15.5cm:100,000 ly), I find that this crude estimate of the spoon's volume to be about 2 * 10⁶⁰ m³ of physical parts of the spoon.

This is indeed a large spoon. Now using some density figure we can find the mass of the spoon. The question of the density is another tricky one, as it varies with temperature and pressure. What would these be in this galaxy sized spoon? The issue of pressure on different parts of the spoon is another issue to be addressed later, and temperature is another tricky one. Because I'm lazy and also have no idea what kind of things happen when you have a mass of this magnitude, I'll just say the densities of the materials are the standard ones we use under earthy conditions.

Now calculating for different materials, I get for the mass of the spoon to be:

  • Iron (ρ = 7870 kg/m³) = 1.6 * 10⁶⁴ kg
  • Gold (for the lulz) (ρ = 19,300 kg/m³) = 4.0 * 10⁶⁴ kg
  • Copper (ρ = 8960 kg/m³) = 1.9 * 10⁶⁴ kg
  • Nickel (ρ = 8900 kg/m³) =  1.8 * 10⁶⁴ kg
  • Silicon (ρ = 2330 kg/m³) = 4.8*10⁶³ kg
  • Corn Syrup (ρ = 1380 kg/m³) = 2.8*10⁶³ kg
  • Ice (ρ = 927 kg/m³) =  1.9 * 10⁶³ kg
  • Lard (ρ = 919 kg/m³) = 1.9 * 10⁶³ kg
  • Plastics (850 < ρ < 1400 kg/m³) = 1.8*10⁶³ - 2.9*10⁶³ kg
  • Diamond (ρ = 3500 kg/m³) = 7.2 * 10⁶³ kg
  • Graphite (ρ = 2090 kg/m³) = 4.3 * 10⁶³ kg
So we are looking at a range from 1.8*10⁶³ to 2 * 10⁶⁴ kg of material for the spoon. This is larger than even the largest figure for the total mass of the universe by several orders of magnitude, much less the figure for material we could potentially use as normal matter that isn't H or He. This is a very sad result. I’m a bit disappointed. Actually I should have realized the magnitude would be too large just from the volume before even calculating the actual mass, but I’m rather dumb so I went through all that for almost no reason. But I’m not giving up that easily. We could try refining the spoon parameters, maybe save some mass. Maybe make this a galaxy sized SPORK instead. Everyone loves sporks. Could make this a hollow spoon, or shorten the handle and change the proportions a bit. My example spoon may not have been very good.

We could make it a mesh spoon, although that’s sort of cheating. Is it really a spoon if it’s meshed? Well probably not in the actual spoon part, but I think a "mesh" handle if feasible would work, and would save considerable mass. Also making the surface of the spoon ’pitted’ could help save mass, in a similar way to how in Hadrian’s Pantheon has the tessellated coffers to reduce the mass so building the dome was possible.

I remember being there and there construction or something going on which was funny because it’s an ancient building, now with scaffolding and plastic sheets being worked on.

A smaller spoon compromise might be needed, maybe a dwarf galaxy sized spoon or something. So let us assume that we can get this spoon down to a reasonable mass. And by reasonable mass I mean a mass less than the total mass in the universe. I will arbitrarily decide this to be 1/2 of the total non-H/He matter. Or could just take the whole thing. I mean at this level of technology you probably have synthesis of any element thing from anything taken care of. Now it doesn't really matter because I’m too lazy to calculate how big of a spoon this would produce either way right now, so now the other issues should be considered.

Next there are the obvious issues of the simple size of the spoon and delivering materials to areas being worked on. The speed of light limit when constructing a multi-lightyear ultrastructure must really be inconvenient. How would you move along the spoon? How would you navigate it? It would take many years from any given point on the spoon to see the progress on the construction of a relatively ’nearby’ part of the spoon. Obviously most of the construction would have to be taken care of by robots. These would have to be quite the robots. They would have to last for a very long time, and be able to handle the construction, and be able to supply themselves with the power. There would have to be 'gatherer' robots to acquire material and convert it into spoon construction material.

What’s the surface of the spoon like? On one hand I envision giant bubbles holding entire civilizations that are somehow there and somehow producing energy and surviving there on the surface. Actually, they could be inside the spoon, which also may be hollow anyway to save the tons of mass necessary to make any of it possible. Now that I think of it, this is thinking of the spoon too much as an artificial planet, which it is not. It’s far too large and massive.

The gravity problem is quite the problem. Could anything survive near it, or in it? Maybe inside the surface at certain points to have nice cancellation of forces so you don’t die. Although moving around near portions of the spoon, the tidal forces I would think would be terrible. With all this mass, could the spoon even survive? Well anyways, that’s a separate issue to think about...what about random surface features like you might see on the death star or something, but that would be an unnecessary decoration and would take a lot of extra mass. There was a name for that which was on reddit not too long ago that I don’t remember.  So from very close, the spoon’s surface would be very smooth, unless it’s easier to produce a rough, jagged surfaced spoon. Although if you’re going through all the trouble of producing this great spoon you might as well make it nice and produce a nice clean, smooth surface.

So gravity…it’s a problem. This spoon is huge and heavy. I think it’s likely to collapse, at least without some kind of special structure or shape, which may vary considerably from my model spoon. I don’t really know how I could try calculating this. I don’t know much about structure. However, this is not your typical engineering structure problem. Instead of building some structure where the gravity of the earth is your concern, in this extraordinary case, the gravity of the structure itself is the only concern. I have very little idea how to begin calculating this. I should think about this some more. I’m not sure anyone has considered such an issue before.

What about moving the spoon? Rotating it? With it’s huge mass, the amount of energy required to accelerate it is obviously huge as well. With a structure on the scale of thousands of light years, how does the motion propagate? What does motion even mean for a structure this big? I mean this really becomes a strange question if you have consumed all the mass and energy producing the spoon, and then there is nothing left to measure your velocity relative to, just the 1 enormous spoon that is what’s left of the universe. Would it just snap? Parts shear off? I assume it isn't a truly solid mass. We have these hollow parts now.

However, at this point the technology to produce the spoon is such that we might as well assume the construction is perfect doesn't have any weak points or anything like that which could cause problems. I feel like the whole thing would just collapse in on itself. It’s just too massive. However, the mass is rather spread out over a large area. However, a considerable portion of the mass of the universe concentrated into the area of a small galaxy is very dense. Could this mass actually collapse to form a black hole? Is this the cycle of the universe? Civilizations form to produce a giant spoon that collapses in on itself to form a new universe?

Now assume you can somehow generate the energy to move it. What do you do with it? Well it’s so massive, it probably pulls in stars and things into it over huge amounts of time with the whole gravity thing. You could scoop stars I guess? What would that mean? The time it takes you to move the spoon may be longer than the lifetime of the stars.

What happens if a star or something else hits the spoon? Would it be disastrous to the integrity of the spoon? What kind of crater in the surface would it produce? I don’t think it could penetrate. There’s still a great many light years through to the other side of the spoon from any point on the surface. Although, if it is hollow, how thick are the walls? What kind of space is inside? Is this a vacuous hollow, or more of a honeycomb type of thing? Are there even stars, galaxies or other items left to scoop with so much mass incorporated into the spoon?

Here I have a picture of what I think the spoon would look like from a very far distance. Notice you can’t see it. This is probably because you've put most of the energy of the universe into the material of the spoon, and also tapped whatever photons were flying around too. Also you've used all the nearby stars and galaxies in producing the spoon, so there’s no light sources. The spoon doesn't glow. Well if you really wanted you might try, but this brings a whole new level to the problem, bringing issues such as what parts glow, and generating power for it. You might need to do something like recapture the lost energy of the emitted light to continue emitting or something crazy if there’s nothing left.

Galaxy Sized Spoon

Artist's Rendition of what the spoon might look like when completed. (Whale is from open clip art)

(The accompanying spacewhale oversees the construction of the spoon and also may be the vessel containing remaining civilization. The reason it is visible is not known. It also isn't clear why it's so big next to the spoon. It is a very large spacewhale. However, it could be very close. It probably isn't to scale. Although the spoon definitely is in this picture.)

Or does the spoon glow? It should be a blackbody. But what is the temperature of the spoon? I think all this madness, between bringing all this mass together, along with all the manipulations going on it would heat up. Now heating up where? I think if it’s heated up in the portion of the spoon currently being worked on, you've got this huge surface with a heterogeneous temperature distribution, and this I think would have consequences on the structure of the spoon. You may need to take measures to keep the temperature approximately constant over the entirety of the spoon to prevent bad things from happening.

With all these challenges, the ambition may need to be scaled down to something less impressive like a star or planet sized spoon, which is far more manageable, although all the same issues apply but many orders of magnitude less.

So those are some of the issues I've thought of for the spoon in a somewhat random order. There are probably many more issues, some of which I've just not remembered right now. I hope to develop more thoughts on these issues, figure out how to calculate some of them and try to imagine solutions. Also there’s probably a lot of problems with my thinking about these problems and just wrong things. It’s not like I’m actually going to proofread any of this or try to make it coherent or anything.

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