In fact, we can be mathematically precise about this. Consider the equation for heat conduction (Q watts) through a spherical shell, where T and t are the outside and inside temperatures, R is the outer radius, r is the inner radius:

Q = 4 x k x pi x R x r x (T-t)/(R-r)

For R > 2r, this equation says that the power getting from the outside to the inside scales only linearly in the overall size of the system (and further increases in R/r make no more difference). But the volume of cryogen stored in the inside sphere scales as the size cubed. This means that the boiloff time scales inverse-quadratically in system size, which in turn means that you could construct a sufficiently large system that it wouldn't need topping up for a century or so (sufficiently large being a mere r=15m or 3000 tons of liquid nitrogen, and a cost of $50M or so). Such a system would virtually eliminate the risk that the patient is killed because the cryo company goes bust, because it would have zero maintenance cost, and would be like a "cryonics grave".

Cryonics Wants To Be Big

Cryonics scales very well. People who argue from the perspective that cryonics is costly are probably not aware of this fact. Even assuming you needed to come up with the lump sum all at once rather than steadily pay into life insurance, the fact is that most people would be able to afford it if most people wanted it. There are some basic physical reasons why this is the case.

So long as you keep the shape constant, for any given container the surface area is based on a square law while the volume is calculated as a cube law. For example with a simple cube shaped object, one side squared times 6 is the surface area; one side cubed is the volume. Spheres, domes, and cylinders are just more efficient variants on this theme. For any constant shape, if volume is multiplied by 1000, surface area only goes up by 100 times.

Surface area is where heat gains entry. Thus if you have a huge container holding cryogenic goods (humans in this case) it costs less per unit volume (human) than is the case with a smaller container that is equally well insulated. A way to understand why this works is to realize that you only have to insulate and cool the outside edge -- the inside does not collect any new heat. In short, by multiplying by a thousand patients, you can have a tenth of the thermal transfer to overcome per patient with no change in r-value.

But you aren't limited to using equal thickness of insulation. You can use thicker insulation, but get a much smaller proportional effect on total surface area when you use bigger container volumes. Imagine the difference between a marble sized freezer and a house-sized freezer. What happens when you add an extra foot of insulation to the surface of each? Surface area is impacted much as diameter is -- i.e. more significantly in the case of the smaller freezer than the larger one. The outer edge of the insulation is where it begins collecting heat. With a truly gigantic freezer, you could add an entire meter (or more) of insulation without it having a significant proportional impact on surface area, compared to how much surface area it already has. (This is one reason cheaper materials can be used to construct large tanks -- they can be applied in thicker layers.)

Another factor to take into account is that liquid nitrogen, the super-cheap coolant used by cryonics facilities around the world, is vastly cheaper (more than a factor of 10) when purchased in huge quantities of several tons. The scaling factors for storage tanks and high-capacity tanker trucks are a big part of the reason for this. CI has used bulk purchasing as a mechanism for getting their prices down to $100 per patient per year for their newer tanks. They are actually storing 3,000 gallons of the stuff and using it slowly over time, which implies there is a boiloff rate associated with the 3,000 gallon tank in addition to the tanks.

The conclusion I get from this is that there is a very strong self-interested case (as well as the altruistic case) to be made for the promotion of megascale cryonics towards the mainstream, as opposed to small independently run units for a few of us die-hard futurists. People who say they won't sign up for cost reasons may actually (if they are sincere) be reachable at a later date. To deal with such people's objections and make sure they remain reachable, it might be smart to get them to agree with some particular hypothetical price point at which they would feel it is justified. In large enough quantities, it is conceivable that indefinite storage costs would be as low as $50 per person, or 50 cents per year.

That is much cheaper than saving a life any other way. Of course there's still the risk that it might not work. However, given a sufficient chance of it working it could still be morally superior to other life saving strategies that cost more money. It also has inherent ecological advantages over other forms of life-saving in that it temporarily reduces the active population, giving the environment a chance to recover and green tech more time to take hold so that they can be supported sustainably and comfortably. And we might consider the advent of life-health extension in the future to be a reason to think  it a qualitatively better form of life-saving.

Note: This article only looks directly at cooling energy costs; construction and ongoing maintenance do not necessarily scale as dramatically. The same goes for stabilization (which I view as a separate though indispensable enterprise). Both of these do have obvious scaling factors however. Other issues to consider are defense and reliability. Given the large storage mass involved, preventing temperature fluctuations without being at the exact boiling temperature of LN2 is feasible; it could be both highly failsafe and use the ideal cryonics temperature of -135C rather than the -196C that LN2 boiloff as a temperature regulation mechanism requires. Feel free to raise further issues in the comments.

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The most important reason that cryonics wants to be big is because if people thought that they were going to be alive in the future, then they would work hard to prevent the future from going wrong. They would also work hard to prevent cryonics from going wrong, and it would be made illegal for cryopatients to be thawed, eliminating a huge risk in the success of cryonics.

Developed societies in the 21st Century have started to break down in certain ways because we live in "the long run" discounted by people who made bad decisions for us when they ran things decades ago. I've seen this happen in cryonics organizations, even though, as Roko speculates, you'd expect that the members who have a stake in cryonics' success would insist on better performance.

Absolutely true. The cryonics meme spread widely is more sustainable -- and thus more useful -- than if only a few people have it.

Not to mention the fact that it could raise the sanity waterline quite a ways. That is a benefit that would be of lasting value (and perhaps steer us clear of a few existential risks) regardless of whether cryonics works.

Obviously if we knew cryonics wouldn't work it would not raise the sanity waterline to pretend otherwise -- but the fact is that we don't know any such thing. It is a quite valid assumption that it will work, as far as we can tell. And the cheaper cryonics is, the less sane the refusal to consider it becomes.

For me, the deciding factor is cost. I would be willing to sign up for cryonics at 1/3 the current cost. However, this is unlikely, since I had to negotiate to get the smaller amount of life insurance I actually needed -- my cost would currently be about $15/month life insurance and $10/month CI fee. No matter how much we cut the cost of cryonics, my life insurance refuses to charge less. One solution is a cryonics group willing to take care of the life insurance themselves -- go under $100,000 -- then this would help cut the bottleneck cost.

Oh, also I'll commit to signing up for cryonics when it drops below $10/month. And perhaps before, since there's a good chance cryonics prices slowly drop or a singularity occurs before I'm 40.

Interesting that you think cryo is worth £6 a month but not £15 a month. What calculation did you do to get this figure?

In fact, we can be mathematically precise about this. Consider the equation for heat conduction (Q watts) through a spherical shell, where T and t are the outside and inside temperatures, R is the outer radius, r is the inner radius:

Q = 4 x k x pi x R x r x (T-t)/(R-r)

For R > 2r, this equation says that the power getting from the outside to the inside scales only linearly in the overall size of the system (and further increases in R/r make no more difference). But the volume of cryogen stored in the inside sphere scales as the size cubed. This means that the boiloff time scales inverse-quadratically in system size, which in turn means that you could construct a sufficiently large system that it wouldn't need topping up for a century or so (sufficiently large being a mere r=15m or 3000 tons of liquid nitrogen, and a cost of $50M or so). Such a system would virtually eliminate the risk that the patient is killed because the cryo company goes bust, because it would have zero maintenance cost, and would be like a "cryonics grave".

Given the large storage mass involved, preventing temperature fluctuations without being at the exact boiling temperature of LN2 is feasible; it could be both highly failsafe and use the ideal cryonics temperature of -135C rather than the -196C that LN2 boiloff as a temperature regulation mechanism requires. Feel free to raise further issues in the comments.

Wow, that's incredibly attractive - it would completely eliminate cracking as we pass through the glass transition temperature. I take it that would also reduce LN2 costs by a further 30% or so?

Does anyone have some actual numbers on what fraction of the expenses of existing cryonics companies are spent on cooling? That should give an indication on how much can be saved by scaling up.

Here is a table with Alcor costs. Surprisingly, for a Bigfoot dewar the LN2 is less than half the total cost. The other big ones are janitorial work for the space around it and alarm systems.