Sapphire Mansions

(Understanding the Real Impact of Molecular Nanotechnology)

Robert J. Bradbury
© October 2001, All Rights Reserved

Version 0.6 - June 2003

This paper is derived from a post that I made to the Extropian Mailing List in August 1999.  It has been updated to correct minor errors in the original post and improved to incorporate comments made by reviewers.

Understanding the full impact Molecular Nanotechnology, as defined by Eric Drexler, will have on our lives is quite difficult for most people.  The big picture involves the realization that Molecular Nanotechnology can be distilled down to 3 essential things: mass, energy and designs.  We will examine each of these to determine what the limits are once we have the ability to manufacture things with robust Molecular Nanotechnology.
 

Mass

Where does the mass for building designs of molecular nanotechnology come from?  One gets the gaseous elements, oxygen and nitrogen directly from the atmosphere.  Carbon, which is one of the primary building blocks for molecular nanotechnology, utilized in everything from buckytubes to diamond, can be extracted from the carbon dioxide in the atmosphere. In regions where relative humidity is high, one can also easily extract hydrogen from the water vapor in the atmosphere.  One gets the heavier elements, Aluminum, Silicon, Calcium, Magnesium, Iron, Sodium, Potassium, Phosphorus, etc. from the Earth (soil & rocks).  Any elements of low abundance in the Earth one would get from seawater.  The rarest elements will not come cheaply [Fre00b] but fortunately it appears they will rarely be required for most molecular machinery and structures.1

Because carbon is an essential component for the strongest materials, it is useful to know the carbon budget per person.  The current atmospheric CO2 level is ~362 parts per million (0.036%) which is equivalent to 5.2×1014 kg (520 Pg) of carbon [Vit97].  The pre-industrial level of atmospheric CO2 was 280 parts per million (or 0.028% of the atmosphere).  Reducing our current CO2 levels to a pre-industrial state would involve the extraction of ~118 Pg of carbon.  Assuming a world population of 6.2×109 people, each person has a carbon budget of ~20,000 kg.  During civilized history land conversion has put 185 Pg of carbon into the atmosphere [DeF00].  This would optimistically allow ~31,000 kg/person but much of this carbon may have already been removed and sequestered in oceanic or land sinks.  Conservatively, there is evidence that changes of only 100 Pg over a 600 year period can produce minor ice ages [Fis99], so one might be limited to carbon extraction of less than 27 kg/person/yr unless one can provide offsetting increases in other greenhouse gases such as N2O, assorted CFCs or SF6.  This is potentially a workable approach since some of these molecules have global warming potentials hundreds to thousands of times greater than CO2 [EPA-IPCC96] and remain in the atmosphere for much longer periods [Las90].

Energy

Where do we get the energy for putting molecular machinery or molecular structures together?  The sun obviously.  Though the solar insolation in the Earth's orbit is ~1370 W/m2 [Wil97], the amount reaching the surface of the earth varies from ~150-300 W/m2 [Dal93, Ram91].  Commonly used solar cells for residential applications typically have efficiencies from 12-28% [CAD00, Gre01, Fab01], though with concentrators can achieve ~34% with predictions that 4 layer stacked cells could soon allow efficiencies as high as 40% [Dim00].  These are not however the limits.  Solar cells have the advantage that they can still harvest light energy even on cloudy days.  Heliostats [Sti01] in contrast require direct sunlight to focus direct sunlight but may offset this by being better able to utilize the infrared portion of the solar spectrum.  This energy could be harvested by thermophotovoltaic cells [Cou97, Dag98, Cou98, Cou99].  Ultimately however heat engines using Rankine, Stirling, Brayton, or Kalina cycles [EREN01] are likely to be chosen because their efficiencies can be much higher.  Assuming nanotechnology allows the production of strong materials that can operate extended periods at high temperatures, e.g. TiC (M.P. 4153K), theoretical thermodynamic efficiencies as high as 85-87% could be obtained (assuming an engine operating temperature at 60-70% of the M.P.)2  We will assume moderately conservative values of ~200 W/m2 and a 25% conversion efficiency, providing 50 W/m2 of electrical energy (~25 W/m2 after allowing for day/nite cycles) for the following discussions.3  In regions with greater than average sun exposure or with more efficient conversion technologies, the power available may be from 2-5 times greater.

Designs

Where do the designs come from?  As pointed out below, the consequences of the molecular manufacturing revolution will mean that people will not have to work to survive.  This suggests that many people will devote their time to designing molecular machinery and release the designs into the public domain for the fame and recognition this will provide.  It is also likely that open source designs will be viewed by the public as potentially safer.  This is because as Eric Raymond points out, "Given enough eyeballs, all bugs are shallow'' [Ray97].

Initiatives for open source design in molecular nanotechnology have been proposed [Bra00, Bru00].  Non-profit foundations will realize the advantages of open source designs for molecular nanotechnology and jump start the process by offering prizes as incentives for people to develop such designs.  Additionally wealthy individuals may directly fund some people to produce designs that they feel will add to the public benefit.  Even patented commercial designs need not represent significant barriers because a good design might be used by everyone on the planet.  For example a single patented simple design (provided it is widely used by billions of people) would allow very low royalties (say $0.001/person) that would still make inventors multi-millionaires.  Markets where open source designs compete with commercial designs will limit the amounts that commercial firms can charge for their products.

Limitations on Molecular Nanotechnology

One significant limit on the use of molecular nanotechnology for terrestrial applications turns out to be the global hipsithermal limit (the heat capacity of the planet).  This is generally taken to be in the vicinity of ~1015 watts [Fre99, Chapter 6: Power, Section 6.5.7, pg 175].  If world population stabilizes at ~1010 people, then heat capacity budget available for nanoconstruction is ~105 W/person.  Assuming nanorobots require ~10 pW each, this would allow ~1016 continuously operating nanorobots (~10 kg) per person [Fre99].  Based on our previous energy harvesting assumptions, we can conclude that the area requires to provide solar power for this quantity of nanorobots is ~4000 m2, or a plot of land ~64×64 m (~208×208 ft).  This is almost exactly 1 acre of land.  The total non-antarctic land area on the Earth is 34 billion acres.  After allowing for mountains and deserts, the "habitable" land per person would appear to be in the range of 4-5 acres [ORL00].  For a nanotechnology based society that may develop autonomous robots perfectly able to harvest energy (even functioning more efficently in environments such as deserts) then 6-7 acres/person could be available.  Thus we can project that unless human population increases significantly in excess of (a) our ability to construct cooling towers to radiate heat into space; or (b) our ability to migrate significant fractions of humanity to offworld locations -- the footprint of a nanotechnology enabled human society should be between 10 and 25% of the total land area.

The Impact of Open Source Molecular Nanotechnology

A wise person who recognizes the capabilities that molecular nanotechnology will provide should follow the following course of action.  First, you spend $2,200 and go buy yourself an acre of land in Arizona. For those textropian readers (extropians in Texas), 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).

Then you get your open-source nanoseed to assemble solar collectors over most of the property.  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. For this you will need ~10 kg of nanoassemblers, since they have a mass doubling time of ~1 hr [Dre92, pg 1 & 441]. 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).

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) [Hal98]. 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). { Average home now requires 16,000 board feet [NAHB2000] } 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. 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.

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. So the yacht and mansion are probably going to have to be built out of sapphire instead of diamond.  Sapphire (Al2O3) is a combination of aluminium and oxygen.  The oxygen you can get out of the atmosphere but the aluminium you have to get out of the soil or rock (7% of the crust is Al). That means that while building your mansion, its a requirement to build a very big swimming pool as well . I suppose if you really want, you build the mansion first because then you can build the yacht in the pool. Since you've got about 4× as much Si as Al in the crust, its likely that buried in your basement is a 1.3 Mkg supercomputer. 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.

Now, given all of that, can you reasonably expect any government to be able to hold that back once it becomes clear to people? The nice thing about it is that, even in this country, if I don't work (and can grow everything I need), I don't pay taxes (except the real estate taxes). But if I don't like those I can always live on the yacht.

Robert Freitas has estimated that Windsor Castle weighs 1.4 million kg.  { Warning: this calculation seems in conflict with the above figures for 2600 ft and 40,000 ft houses. It needs to be checked. } Of course building a castle of similar size would require more land area -- 1.2 million square feet (~20 acres) if you include the inner courtyards.

John Grigg, commented (here):

"I think in a society with a mature nanotech it is ethically the right thing to make sure all of its citizens have an adequate level of free medical, education, housing and food. I feel this is the humane thing to do yet I feel it should just be at a level to meet basic needs and not to elevate the lazy to a grand lifestyle. So for those who want the "good things of life" such as a mansion, education at Stanford, gourmet meals, and exotic cosmetic surgery will have to work for it."
I think the solution will be a trickle down effect.  As more and more "approved" designs are placed into the public domain the easier it will be for people to live a "grand lifestyle" and do very little to sustain themselves.  But that gets pretty boring after a while.  I think many people will seek to find something that distinguishes them from everyone else.

Conclusion

You have to get that with mature nanotech there is definitely no problem with "adequate" housing, food and almost all transportation. [e.g. anything short of relocating your Castle to Mars is cheap]. If the governments and/or non-profits and/or open source designers and prizes work correctly, you will likely have free medical (technology) as well.

People won't have a "far better standard of living", except in that they can purchase more fancy entertainment or could have more fame and recognition. Fame & recognition will tend to replace material success presumably, in a nanotech world. Fame will probably not be that interesting because I suspect most people like the idea of being "famous" because of the perks that go along (nice houses, cars, etc.). If you can have all of those things why would you want the headaches of the fans & paparazzi? So that leaves only "recognition". Presumably you get recognized for doing cool designs and donating them to the public.

As an addendum, depending on the costs of extracting carbon from the air, my energy estimates may be conservative by up to 2 orders of magnitude, so things could go much faster than I indicated (or you could buy a smaller plot of land). We have something like ~2 billion acres of land in the U.S. so there is almost an order of magnitude excess per person over the requirements for a cushy living. Those guys & gals living down under, now they are the really lucky ones, their land/person is 2 orders of magnitude over the requirements [Bra01]. And they have a heck of a lot more coastline along which to park all the yachts.

Notes

Footnotes

  1. See for example Table 6 from [Bra97] showing that nanoparts are primarily composed of C, Si, N, O, S and P.  Some use is made of F which is rarer.  See also Nanosystems [Dre92], Section 3.3.1b, pg 43 and Section 14.5.6b, pg 433.  Complex biological systems often use metals as catalysts but their fractional abundance is quite low.
  2. Current technologies based on gas turbines with operating temperature ~860º C (1133º K), have efficiencies of 40-56%.  In contrast future combined fuel-cell gas turbine technologies will be from 58-67% efficient [Lee96].
  3. This is significantly less than the 3600 to 6500 kWh/m2/day (300 to 561 W/m2 based on 12 hour days) [NCSC99].

References

Solar Cells, Photovoltaic, Energy Conversion

Created: Original Version: August 1999
Last Modified: June 6, 2006