This letter is a commentary on this post, which was subsequently revised in my Sapphire Mansions paper.

From rfreitas@calweb.com Wed Oct 31 07:36:21 2001
Date: Thu, 4 May 2000 06:06:36 -0700 (PDT)
From: Robert Freitas <rfreitas@calweb.com>
To: Robert J. Bradbury <bradbury@aeiveos.com>
Subject: Sapphire Mansions

[Original letter text].

I'm sending this to both your U.S. addresses because in the last two weeks I've gotten mail from you than had both addresses, and I keep getting confused which is the one you want me to use. (Right now your address in my online address book is the "@www.aeiveos.com" -- shall I keep using this, or should I switch to the "@aeiveos.com" version? I think you've told me before; sorry to be so thick, I just can't remember....)

Also, I'm finishing this up at ~6AM this morning, so please forgive any typos -- hope they aren't too bad.

> Now, where does the mass for nanotech come from: O/N/C - from air

Also H -- not a LOT of mass, but a lot of atoms! Air can be up to 3% water by weight.

> Si/Al/Ca/Mg/Ca/Fe/Na/K/P - from dirt/rocks

There's actually ~1000× more oxygen atoms per unit volume, and about 2× more oxygen atoms per unit mass, in rocks than in air!

> Almost everything else - from seawater

Yes. But the problem here is that the energy costs for extracting rare elements from seawater are nontrivial. A lot of people are pretty cavalier about this, but it is a significant problem. Nanotech is not magic.

Back in January I wrote a 50KB+ article on "nanomoney" for Gina Miller's newsletter, which has yet to be published :>(, in which I pointed out that chemical element scarcity may hold true even in a world of abundant nanotechnology. Consider: One of every 3 billion atoms in ordinary crustal rock is a gold atom, or 3.1 ppb (parts-per-billion) by weight. All natural gold atoms are of one isotope, Au¹⁹⁷. A ~10 kg nanotech desktop refinery wholly dedicated to sorting gold atoms from crustal rock, perhaps employing ~1 kg of the input ordering and reagent preparation subsystems found in Drexler's original manufacturing appliance, could in theory sort ~10²⁵ crustal atoms per second, extracting ~3 ×10¹⁵ gold atoms/sec or ~1 microgram/sec, which is a net output of about 1 troy ounce of gold per year. To achieve this paltry output, the desktop refinery must process 16,000 tons/yr of rock (~100 cm³/sec) and the unit draws about 1 megawatt of continuous power assuming a minimum waste heat generation of 3 MJ/kg of input materials. So you get about $300/yr worth of gold, but the energy costs you $900,000/yr at today's $0.10/Kw-hr electric rates. Cost breakeven occurs if the crustal rock can be ~3,000× preconcentrated in gold content, using bulk chemical processes, but this may be uneconomical and hardly seems worth the trouble.

As for seawater extraction using self-replicating machine systems, which Moore [Edward F. Moore, "Artificial Living Plants," Scientific American195(October 1956):118-126] talked about back in the 1950s, note that gold is ~100 times less plentiful in seawater than in the crust -- though gross filtration and bulk preprocessing might improve throughput. And in case you're interested in making nukes, U²³⁵ is about as rare in the crust and in seawater as is gold.

> So, where does the energy come from? The sun obviously.

Seems most convenient. However, as I think I've pointed out before, if you are absorbing high quality photons for your mansion-building etc., then these photons are not available to drive photosynthesis in the ecology. Even if the heat flux is nearly the same, the entropy flux is not, and so the ecosphere starves. In the deserts you can get away with this to some degree, but anywhere else this is going to be a problem if you are using up more than, say, 1% of the incident visible flux. If you block, say, >10%, the plants and the soil phytos are probably going to suffer. And the Greenies are going to string you up by your thumbs. :>)

> Where do the designs come from? Open source one would hope.

Well, you could be right. A good case can be made that in a nano-abundant era, people will tend to compete for prestige and glory rather than food and shelter. OTOH, will mature nanotech make money and intellectual capital/property obsolete? I don't know. Seems to me that human wants are infinite, but the physically accessible universe is finite, and therefore as long as these two things remain true, then scarcity will by definition exist, at some level, which means that money and capitalism may not just "go away" as many have hoped. And if money and capitalism are still needed to efficiently allocate scarcity, then the world may not go completely "open source" as some seem to hope/expect.

Of course, it is (very) possible I'm wrong about this. Who knows? My opinion on this seems to oscillate back and forth. But this is where I'm at today....

> It is worth noting that over the history of civilizations we have put 185 petagrams of carbon into the atmosphere [1]. Not so. That 185 Pg C release you've been citing is NOT the total amount of C that humanity has put into the atmosphere, as you claimed. If you read the discussion in Science carefully, you'll see that this figure refers only to the amount of extra C put into the air as a result of land conversion by humans. It does not include, for instance, C emissions due to factory/automotive burning of petroleum-related fuels. You'd have to add those emissions to the 185 Pg to get the total you are seeking.

How much would this be? Well, I found one estimate (see references [23] in my Ecophagy paper) that since the beginning of the Industrial Age humanity has consumed ~1 × 10¹⁴ kg of petroleum, most of which is carbon atoms because petroleum (by weight) is mostly just hydrocarbons. So that's another ~100 Pg of released C that you must add to your total. So 300 Pg would probably be a closer estimate to the truth.

> That works out to about 31,000 kg/person. We probably don't want to remove more carbon than that from the atmosphere.

Perhaps you can explain to me why the historical anthropogenic carbon emission is a logical or reasonable limit on the total we might want to remove? I just can't see any logical nexus between the two. I mean, most of this C has been recycled or buried by now anyway, so it is basically irrelevant.

The first and obviously most relevant number, as a limit to atmospheric removal, is the current carbon inventory in the atmosphere, which is 5.2 ×10¹⁴ kg (520 Pg), mostly as CO₂ (Ref.[22] in Ecophagy paper). CO₂ concentration is 362 ppm today, and apparently was somewhere in the low 200's back before 1800, so we probably could cause the planet to start cooling if we pull out more than maybe 200 ppm of the CO₂, which would be about 290 Pg, or ~50,000 kg/person. A reference in Ecophagy [43] claims that changes of only 100 Pg over a 600-year period were associated with three minor ice ages, so maybe the limit is only 50-100 Pg, or 8,000-16,000 kg/person.

However, this is the rapacious techno-geek upper limit. The Greenies will probably want to restrict you to some fraction of the natural turnover rate in the global carbon cycle. Global net primary production of biomass C is ~115 Pg/yr; however, most of this is just turnover in place. The net new biomass C fixed globally is somewhere around 5 ×10¹² kg/yr or ~5 Pg/yr, a mere 800 kg/person-year of C. The Greenies will argue that this appears to be the most new C that Mother Nature can absorb, and thus if you try to remove more than this, you could disequilibrate the global carbon cycle in the other direction.

The next thing I question is why you care so much about carbon anyway, since later on you talk about building everything out sapphire, and you never really talk much about what you're using the carbon for. So, I guess I expected more discussion of the sapphire materials budget in here somewhere.

Oxygen is 46.6% of crustal rocks by weight, and Al is 8.13% of crustal rocks by weight, compared to sapphire which is 52.9% Al by weight. So you must process at least 6.5 kg of crustal rock for every 1 kg of stoichiometric sapphire that you can extract. Now, I haven't done a comprehensive study of the geographical distribution of Al-rich minerals, but you can bet they are not uniformly distributed. For example, check out Tables 1 & 2 of http://www.science.smith.edu/sem/pages/Lindsey/bauxite.html -- Table 1 gives one Arkansas sample with alumina content as high as 48.46%; Table 2 gives another sample from a different area in Arkansas with an alumina content of only 0.8%. Somehow, these all average out to 8.13% in the crust, but the high/low range is a factor of 60×, or ~8× above and below the mean. So I think you should assume that you aren't going to be able to pull 1 kg of sapphire out of every random 6.5 kg of crust that you hunker down onto. You've got to assume at least 50 kg, and a wonderfully conservative figure to use would be 100 kg.

Since you are going to have to rip apart lots of weird aluminomagnesiosilicates and other strange and complex minerals to extract the Al to build the sapphire, this will take a lot of energy. I'm not sure where your 15.9 MJ/mole for sapphire (see below) came from, though I checked the DH's on some minerals and compared them to alumina and your figure looks a bit high as a thermodynamic limit. How did you compute it? Simple siliceous minerals whose DH's I could find in my reference books were like Na₂SiO₃^.9H₂O at -4.2 MJ/mole, Mg₂SiO₄ (forsterite) at -2.0 MJ/mole, and Ca₃SiO₅ at -2.9 MJ/mole, vs. alumina at -1.7 MJ/mole. Pretty thin data, but 15 MJ/mole sounds very high. It works out to ~156 MJ/kg, because Al₂O₃ is 0.102 kg/mole.

As noted in the Ecophagy paper (and you more or less agreed), we are probably not going to be able to maximally efficient with our extraction energetics, so even if I'm right that your number is a bit too high, your analysis would be more plausible if you take a conservative approach and claim a production cost of, say, ~100 MJ/kg to produce sapphire widgets from raw crustal rock. Unless, that is, you can provide some hard numbers to explain to me why the figure should be 156 MJ/kg.

So if I were doing this analysis, I would start with the conservative assumptions that you will have to process perhaps up to ~100 kg of crust to get 1 kg of sapphire, and that you can pull at most 160,000 kg/sec of C out of the air worldwide (this means you plus everyone else combined); and that building diamond or sapphire is probably going to cost you ~100 MJ/kg in energy consumed and thermal pollution generated.

(Hmmm, C is ~250× less abundant by weight than Al in crustal rock, but maybe you could get more C from this source than from the air. Somebody should put a pencil to this...)

> First, you spend $2,200 and go buy yourself an acre of land in Arizona. For those textropian readers, you probably have that much already so you don't have to go anywhere :-). For the latecomers, you will simply have to buy more land in a less sunny area (like North Dakota). Yeah, I remember driving through northern AZ and seeing a sign touting land for $100/acre, back in the mid-1980s.

I wonder how many people would really want to live in Arizona or NDak, even if they could have a mansion there. Real estate prices are pretty cheap in both places already (meaning, a Californian or Seattlean with big winnings from his appreciated home can already move to these places and buy a mansion) -- so why don't they? A few years ago I read a book by hard-money investment guru Doug Casey, in which he said you could still buy Australian desert land for $1/acre. Of course, you have to buy 500,000+ acres at a pop, and there's no water or infrastructure anywhere nearby, but what the heck! The price includes mile after mile of beachfront! (I can get you the book ref if you want it.)

I suppose if you can become self-sufficient, and do a nanotech simulation of Shangri-la out in the desert (kind of like Las Vegas? :>) ), you'll attract more people. But there are limits to the maximum number density of personal Shangri-las, which is actually what you should be calculating here, IMHO.

> Then you get your open-source nanoseed to assemble solar collectors over most of the property. At an insolation of ~1000 W/m² and 0.2 conversion efficiencies (pretty conservative), that gives you 400,000 watts of power during the day.

OK, I've already sent you some material on why this number you are using is NOT conservative, but actually unrealistically high. I've already sent you a bunch of references that show that the amount of energy reaching the ground in the visible portion of the spectrum is at best 400 W/m². If you somehow feel that you can build solar energy collectors that have good efficiency over the entire spectrum, from IR to UV, then at most you could extract ~600 W/m² at ground level. But this assumes perpendicular incidence on a cloudless dust-free day. And you'll get a fair number of days like this in AZ and Australia, though not in NDak. But realistically , even with solar tracking collectors, you can't collect this maximum for more than maybe 8 hours/day. On average, you have 12 hours of nighttime darkness, during which time you are collecting zero W/m². And in the two hours near sunset/sunrise, the sun is low in the sky that the rays are heavily extincted, you are going through as much as 6 zenith optical depths of atmosphere, so power is very low. So even in the most optimistic scenario, using perfectly efficient all-frequency collectors on a 24-hour basis, you are down to maybe 200-300 W/m². It is basically as I asserted in NM -- the range of what is reasonable under typical conditions is probably 100-400 W/m². You apply your 30% efficiency figure to that, and now you're down to 30-133 W/m². So if you used 50 W/m² as your realistic power input after efficiency losses, I'd call that reasonable, maybe very slightly conservative, but certainly not very conservative. The net figure you used, 200 W/m², is not conservative, and especially not for 24 hour operation.

The other thing that's unrealistic here is that you take your acre of land and 100% cover it with collectors. I would specify that percentage covered by collectors as a variable, and then select some reasonable value for the variable, perhaps 25% or 50%.

So your usable power input from your one acre would be, say:

(4047 m²/acre) × (50% in collectors) × (250 W/m² ground insolation) × (30% efficient collectors) × (8 hrs/24 hrs duty cycle) ~ 50 kW/acre on a 24-hour basis.

And this is assuming cloudless conditions during the daylight hours. Ref #585 in NMI claims that on a hazy day, sunlight power intensity can drop by a factor of 10, and on cloudy or rainy days it can go even lower. That tracking flat-plate-collector URL I gave you last time that had average insolation for Sacramento, CA at 71-475 W/m², gives 33-345 W/m² for Seattle and 125-483 W/m² for Phoenix, so in the winter, on average, Seattle gets 4× less power than Phoenix per m². All this is another reason to be very conservative with your power figures.

> Assuming a mass manipulation cost of ~15,900 kJ/mol of sapphire (perhaps the highest cost), that lets you nanoassemble ~10 kg of nanomaterial per hour. Doing it my way, I use 100 MJ/kg to make diamond or sapphire and 50 KW of power and come up with 50,000 W / (100 MJ/kg) ~ 0.5 gm/sec or ~1.8 kg/hour.

Using your numbers, I get 400,000 W / (156 MJ/kg) = 9 kg/hr during daylight, so your 10 kg/hr figure is for daylight hours only, and is not a 24-hour basis. Taking day/night duty cycle into account, you're down to 4.5 kg/hr or 3.3 kg/hr, depending on which way you want to go.

But I think your numbers are a bit too liberal, so I want to continue using my figure of ~2 kg/hr. If this is sapphire, then you are going to be producing a slag heap of ~200 kg/hr of "used" crustal rock. It will be rock that has much of its aluminum extracted, so it will not look like normal rock; it will look and feel quite different. Also, almost certainly this slag will no longer be large chunks of rock, but rather will be finely powered dust, or whatever comes out of your extraction system. So, in goes nice weathered rocks, sand, dirt, etc., and outcomes finely powdered de-aluminized material that will blow away in the wind (onto your neighbor's mansion, causing him to sue you). SO, you'd better may sure you repackage your slag as replacement rocks or gravel that you can pack back into the hole you're digging in your backyard, so the Greenies won't come after you.

Let's see, a 420,000 kg mansion would require 42 million kg of rock to be processed, which at the average crustal density of 2670 kg/m³ is a ~16,000 m³ hole; if we allocate 0.05 acre for this (e.g., a 10 m × 20 m swimming pool), then the diggings must go down about 16,000m³ / 200 m² ~ 80 meters, or nearly one football field deep. OK, I can buy that. Then, after the aluminum is extracted, we rebuild the slag into something environmentalle responsible and stick it back into the hole, and we have removed 420,000 kg of sapphire of volume 420,000 kg / (3970 kg/m³) ~ 106 m³, which, assuming 100% packing density of the slag material, gives you a 0.05 acre pool hole that averages 106 m³ / 200 m² = 0.5 m deep. OK, we probably want to leave ~200 m³ of slag up top somewhere, to make the depth come out right.

> For this you will need ~10 kg of nanoassemblers, since they have a mass doubling time of ~1 hr [2]. This could be quibbled with, because Drexler boxes are not made entirely of sapphire. They will have other rarer elements in them, which may slow the box-self-replication time (using a crustal substrate) by a factor of 10 or more.

But if the substrate is perfectly materials-matched to the box composition, then Drexler's 1 kg box produces 1 kg of output in 1 hour. So to produce 2 kg/hr, you need 2 kg of assemblers.

But I'll admit, if at the end of the day we only disagree by a factor of 5×, then that's not too shabby. What is the materials cost? $0 because you are taking it out of the air or the ground (except in the case of some rare materials that you have some friend take out of the seawater and FedEx to you).

Well, if a 420,000 kr mansion is 1% rare elements, that's a 4-ton shipment from the coast -- roughly the mass of 2-4 cars. I don't think I'd choose FedEx for this, but I guess if you were in a big hurry....

> Now, what can you do with this. First you spend about 13 minutes of each day to replicate ~2kg of food. With the time left over (on the first day) you assemble your 100 kg air car (10 hours). This is so you can fly back and forth from Seattle or San Francisco every weekend to check on the progress. Now, you start on your 2600 square foot house (34,000 kg). That takes 5 months to grow. Then you've made a deal with your friend who lives by the ocean to construct a dock for you, so you go to work on your 150' yacht (~225,000 kg). That takes 2.8 years. [Air freight to deliver the yacht to the ocean is extra unless you want to take the time to build a big helicopter.] By now you've had enough time to get your design completed for your new "I too can live like Bill Gates" 40,000 sq ft. mansion so your crew of hardworking nanoassemblers goes to work on that. For ~420,000 kg, that takes 5.1 years. An acre is 43,560 ft², so at 2 stories the 40,000 ft² manse would just fit on the 0.5 acre not covered by solar cells. I guess youd build the roof of the manse first, with solar cells on top of it, and then you literally "raise the roof" as it grows up out of the ground.

I think your mass estimate is way high. If you assume 4 m × 4 m rooms that are 3 m high, and walls (suing traditional building materials) that are an average thickness of 4 cm (yes, your walls are 6 inches thick, but most of that is empty space or lightweight fiberglass insulation), assuming 2000 kg/m³ for building materials, and taking the shared-wall effect into account, I get ~10 kg/ft². But the typical load-bearing building material is mainly wood, with a failure strength ~10⁸ N/m². By contrast, the failure strength of sapphire is ~2 × 10¹⁰ N/m², and perhaps 5 × 10¹⁰ N/m² for diamond. So in theory you can make all your walls and floors and ceilings anywhere from 100-500 times less massive if you build with diamondoid materials rather than with wood. This means you can cut your house and yacht masses (and thus the construction times) by anywhere from 10× (if you're feeling REALLY conservative) to 100× (if you're feeling really brave). A factor of 100× is about as far as I'd take it, though. The subjective impression will be that houses are like eggshells, because the walls can be so thin -- but very very strong eggshells. They will have a compacted thickness of 0.4-4 millimeters, which may mean there are girders a couple of cm thick every foot or two apart, and cardboard-thin walls. Actually, you could construct the walls as two thin parallel plates, with vacuum between them, which would provide excellent thermal insulation (just ask your favorite thermos bottle). You could use active surfaces programmed with sound cancellation routines to simulate acoustic insulation, and of course the vacuum will help a bit here, too.

So, the bottom line is that a 40,000 ft² manse is only going to weigh 4,000-40,000 kg, and assuming my conservative figure of 2 kg/hr manufacturing capacity, can be built in 2000-20,000 hours, or 3 months to 2.3 years; using your 10 kg/hr figure, the manse gets built in 400-4000 hrs, or 17 days to 6 months.

> Then I guess you rest. Maybe rent out your nanoassemblers for someone else to build something interesting. So the total time required to live like Bill Gates and never have to work again (i.e. all of your "survival" needs are met) is ~8.3 years.

Well, I think we can get this down to 1 year or less. :>)

> Now the only problem with this seems to be that you use up your global atmospheric carbon allocation by the time you finish your small house.

Huh? This is the first time you've mentioned carbon. The last thing you mentioned was sapphire, and it would be most logical to build the house etc out of sapphire, though I'd give the exterior surface a thin diamond coating because it is a bit harder and is completely impervious to chemical attack -- unlike sapphire, which, under the right conditions, can dissolve away.

I think you want to build these heavy objects out of material that is plentiful in the ground, rather than out of relatively rare carbon. After all, if your carbon allocation is only ~800 kg/person-year, you have to watch out -- diamond will still be "scarce". For instance, a coating of 10 micron diamond on the 3000 m² exterior surface of your 40,000 ft² manse requires ~100 kg of diamond, a healthy chunk of you annual allocation. Indeed, 800 kg is a cube of diamond 61 cm on an edge (about beachball-sized) -- your entirely yearly allocation. (Well, I guess you could give the missus a 4 million carat diamond ring on every anniversary, but I doubt she'd be impressed.)

> So the yacht and mansion are probably going to have to be built out of sapphire instead of diamond.

Nothing wrong with this. The materials are more plentiful hence cheaper, and sapphire is only very slightly more dense than diamond and nearly as strong.

> That means that while building your mansion, its a requirement to build a very big swimming pool as well (7% of the crust is Al). I suppose if you really want, you build the mansion first because then you can build the yacht in the pool.

You can rethink this, in light of the above. (e.g., I already did the pool calc.)

BTW, the idea that you'd park a yacht in a pool is silly. There are two reasons why people own yachts -- (1) the freedom to travel by water whenver and wherever they want to go, and (2) showing all their friends how filthy rich they are. Putting your yacht in your pool certainly satisfies (2) but not (1); berthing it on a waterway or body of water accomplishes both.

If you really want an "indoor yacht" (which I think would be really impressive), then you're going to need a lot more acreage and a bigger house an pool. You'll need something on the order of a 0.4 million ft² shopping mall -- you know, with a train to take you from one end to the other, a moat with real crocodiles, etc. At ~1 kg/ft² and ~10 kg/hr, the mall-manse would take ~50 years to build. Now this is a project more worthy of someone who is planning to live 1000+ years, right? :>)

For comparison, the largest residential palace in the world is the Vatican Palace, which covers 13.5 acres (0.6 million ft²) and has 1400 rooms, chapels and halls.

Note that the Earth's land surface area is ~30% of 5.1 ×10¹⁴ m², which if evenly divided amongst, say, 7 billion people gives you 20,000 m² or ~5 acres/person. You and your wife would have 10 acres to play with. (I've already got my 10 acres, here on a hilltop in Pilot Hill, CA, so I'm already set! You go somewhere else. Like the Arizona desert. ;>) ) (BTW, I lived in AZ for 10 years when I was a kid. I'd rather live in Pilot Hill.) Or, were you to attract 19 willing females to live in your manse, you could control 100 acres....

If we can count the oceans (some people want to live on/under exotic locales), we can get it up to ~15 acres/person. And if we can carve out huge underground domes, perhaps with grand 100 meter high ceilings and diamond-reinforced walls, then the personal acreage numbers can go a lothigher, eh? And then there's space. Or population control

> Since you've got about 4x as much Si as Al in the crust, its likely that buried in your basement is a 1.3 Mkg supercomputer.

I don't get the necessary connection to Si and Al in the crust, since we already know your net hole depth isn't even deep enough (after Al extraction) to make a decent pool, let alone a good-sized basement under your manse. But I imagine that regardless, you will indeed have a large computer in the basement, where you can let the earth's thermal mass assist you with the cooling perhaps?

> The architecture is presumably a lot of ROM or suspend-RAM, since you don't have enough power to use it all as a computer and you certainly don't have enough surface area to cool it even if you did. But you can allocate 1/4 of your power grid to a 1 cm³ nanocomputer (at 10⁵ W). That gives you about 10²¹ instructions per second to work on the problem of how you upload yourself into it. More than likely the ROM holds partial-upload backups (yours and others, since you want yours distributed around the planet in case a meteor hits your mansion). Also, don't forget, after a long day, you should go outside in soak in that enormous jacuzzi that the computer has been heating up for you all day.

Ah, an excellent suggestion for the waste heat!

> If someone can figure out what a Castle weighs I'd love to add that to the list!

Not sure why you'd want to build a castle (e.g., a large structure built out of stone blocks), but....

The largest inhabited castle in the world is Windsor Castle (U.K.), which is laid out as a parallelogram measuring 540 ft × 1890 ft. From photos it appears to average ~ 50 ft tall and would compact to ~200 ft wide if the interior courtyards were squeezed out; assuming the compacted form is ~0.1% structure by volume (e.g., 1 meter wall per 10 meters interior span; outer castle walls are typically ~2 meters thick), and is constructed of stone of mean crustal rock density ~2670 kg/m³, then the mass of Windsor Castle is ~1.4 million kg.

The mass of Coral Castle in Miami, FL, is given as ~1.1 million kg at http://www.biblebelievers.org.au/great.htm and at http://www.flinet.com/~labyrinthina/coral.htm, the credibility of both sources being questionable however.

The weight of the Great Pyramid at Giza is given as ~6300 million kg by http://www.andyland.demon.co.uk/pyramid/ and by http://members.tripodasia.com.my/tarung/historyofpyramid.htm.

Hope this helps a little.
Rob Freitas