Comment on 'The aestivation hypothesis for resolving Fermi's paradox'
aa r X i v : . [ phy s i c s . pop - ph ] F e b Comment on ‘The aestivation hypothesis forresolving Fermi’s paradox’
Charles H. Bennett , Robin Hanson ∗ , and C. Jess Riedel † IBM Watson Research Center, Yorktown Heights, NY, USA Department of Economics, George Mason University, Fairfax, VA, USA Perimeter Institute for Theoretical Physics, Waterloo, Ontario, Canada
February 19, 2019
Abstract
In their article, ‘That is not dead which can eternal lie: the aestivationhypothesis for resolving Fermi’s paradox’, Sandberg et al. try to explainthe Fermi paradox (we see no aliens) by claiming that Landauer’s prin-ciple implies that a civilization can in principle perform far more ( ∼ times more) irreversible logical operations (e.g., error-correcting bit era-sures) if it conserves its resources until the distant future when the cos-mic background temperature is very low. So perhaps aliens are out there,but quietly waiting. Sandberg et al. implicitly assume, however, thatcomputer-generated entropy can only be disposed of by transferring it tothe cosmological background. In fact, while this assumption may apply inthe distant future, our universe today contains vast reservoirs and otherphysical systems in non-maximal entropy states, and computer-generatedentropy can be transferred to them at the adiabatic conversion rate of onebit of negentropy to erase one bit of error. This can be done at any time,and is not improved by waiting for a low cosmic background temperature.Thus aliens need not wait to be active. As Sandberg et al. do not providea concrete model of the effect they assert, we construct one and showwhere their informal argument goes wrong. In this note we critique the thermodynamic claims made by Sandberg et al. intheir article ‘That is not dead which can eternal lie: the aestivation hypothesisfor resolving Fermi’s paradox’ [1]. Our main point is related to these quotes: ∗ Email: [email protected] † Email: [email protected] he argument is that the thermodynamics of computation make thecost of a certain amount of computation proportional to the tem-perature...As the universe cools down, one Joule of energy is worthproportionally more. This can be a substantial ( ) gain...at least E ≥ kT ln(2) J need to be dissipated for an irreversible change ofone bit of information...It should be noted that the thermodynamiccost can be paid by using other things than energy. An orderedreservoir of spin or indeed any other conserved quantity can func-tion as payment...However, making such a negentropy reservoir pre-sumably requires physical work unless it can be found naturally un-tapped...irreversible operations must occur when new memory is cre-ated and in order to do error correction...A comparison of currentcomputational resources to late era computational resources hencesuggest a potential multiplier of !...For the purposes of this paperwe will separate the resources into energy resources that can powercomputations and matter resources that can be used to store infor-mation, process it... We adopt their terminology, using “civilization” to refer to an arbitrarily tech-nologically powerful agent in the universe, “reservoir” to refer to a boundedthermodynamic system (e.g., a battery) that can be manipulated by a civi-lization, and “bath” to refer to an effectively infinite thermalized system whosetemperature is exogenously determined (e.g., the cosmic microwave background)[2]. We understand their argument to be as follows [our words]:The fundamental thermodynamic resource of computation is negen-tropy, but for practical purposes this can be measured in energy(because accessible ordered reservoirs of conserved quantities besidesenergy appear to be a small fraction of all naturally occurring negen-tropy). A future civilization seeking to perform very extensive com-putations within thermodynamic constraints may utilize reversiblecomputing to minimize the amount of thermodynamic expenditureper unit of computation, but it is unavoidable that they must correcta residual rate of physical error. Correcting these errors ultimatelyrequires bit erasures, whereby the entropy is ejected into an externalsystem with an energy cost given by Landauer’s principle. Efficiencyis maximized when the system is at the temperature of the coldestavailable natural bath, which in the future will be that of the cos-mological background. Although civilizations may collect energy atearly times, they reap a much larger computational harvest if theystore that energy and spend it at later times when the cosmic back-ground is much lower.We are grateful to A. Sandberg for confirming that this is a fair summary of theargument [5].This informal argument conflicts with the intuitive notion that the funda-mental spendable resource for irreversible operations like bit erasure is negen-tropy and the conversion rate is very simple: one bit of negentropy erases one2it of error, regardless of the temperature of external baths [3]. As we willexplain, it appears Sandberg et al. err by implicitly assuming that the entropygenerated by bit erasure cannot be transfered into any bounded reservoir andinstead must be ejected into a particular unbounded bath, in this case the cos-mic microwave background (CMB). It is possible to build a toy model thatembodies this assumption, leading to thermodynamic incentives for agents towait (“aestivate” [8]) until a future colder period to perform irreversible opera-tions like bit erasure, but that model does not approximate our universe. Morespecifically there is no incentive to delay irreversible operations until1. the civilization has taken control of all accessible matter in the universe inthe sense that it can inhibit all non-adiabatic physical interactions fromoccurring, both within the matter and between the matter and the CMB;and2. that accessible matter has been fully exploited in the sense that it hasinternally thermalized, i.e., non-gravitational heat death, perhaps aftereons of computations.Furthermore, the aestivation incentive in such an expanding quasi-thermalizeduniverse is not at all specific to computation, but rather applies to any activitythat requires negentropy.In Appendix A we make some other, less important comments about discus-sion in Ref. [1].
To see how the informal reasoning of Sandberg et al. breaks down, we needa concrete model of their purported effect. Unfortunately, Ref. [1] does notprovide enough detail to unambiguously specify a model, so we do our best totranslate their informal description into the non-cosmological model below. (Weare grateful to the authors in assisting us through email correspondence, butthe following exposition should not be interpreted as being endorsed by them.)We take the universe to consist of these thermodynamic components:1. A memory tape of N bits. These bits are initially all zero, but they aresequentially randomized as the civilization performs computations (out-side the model) that generate occasional errors, which are swapped ontothe memory tape. Once the memory tape is full of randomized bits, theymust be erased to allow additional computations.2. An unusual reservoir that has the capacity to provide a large finite amountof energy in the form of useful work but that cannot absorb appreciable en-tropy . This could be a system with a tiny number of states with extremelylarge energy differences that is internally thermalized to a temperaturemuch higher than the temperatures of all other systems.3. A thermal bath of effectively infinite size, following an exogenously settemperature schedule T ( t ), with which the civilization can exchange anarbitrary amount of heat.4. A bit-erasing machine that also has a negligible number of internal states.If work is supplied to the bit eraser, it pumps entropy from the memorytape to the bath. This can be formalized in at least two ways:(a) taking the bit eraser to be a Szilard engine augmented so that it canperform a reversible swap operation between a memory bit and thebinary location (left or right) of the gas particle in the engine [3]; or(b) assuming the different memory configurations actually have very smallenergy differences, and taking the bit erasers to be a reversible Carnotengine that “cools” the memory tape to a sufficiently cold tempera-ture that all bits are zero with high probability.In particular, this is a non-relativistic model that can be analyzed with the stan-dard techniques of classical thermodynamics, the setting in which Landauer’sprinciple is traditionally derived. Following Sandberg et al., we have assumedthe key thermodynamic features of an expanding spacetime are fully capturedby the thermal-bath temperature schedule T ( t ) as a model for the CMB, andso are ignoring potentially important features like the increasing volume, de-creasing pressure, and decreasing particle density of the real CMB as it evolvesinto the future. In particular, we emphasize the possibility that a finite effectivebath size (e.g., from the finite number of CMB photon modes accessible from afinite volume) may invalidate conclusions drawn from this crude model, mootingboth the arguments of Sandberg et al. and our rebuttal.The unusual reservoir ( N of bits of the memory tape are random andneed to be erased, requiring the removal of an amount of entropy ∆ S = N ln 2.Then, by the second law, the entropy of the bath must increase by at least thisamount because, by assumption, neither the reservoir nor the bit eraser have anappreciable number of internal states. Since the bath is at maximum entropygiven its internal energy, an amount of heat energy ∆ Q = T ∆ S must be addedto the bath – by the definition of temperature – in order for its entropy toincrease by the necessary amount. And by conservation of energy this must besupplied as work W = ∆ Q = T N ln 2 from the reservoir.The conclusions of Sandberg et al. then follow: if T ( t ) is decreasing withtime, the civilization performs more total bit erasures before the work reservoir Note that if the photon mass is non-zero, this will become relevant at the extremelycold temperatures, k B · (10 − K) ∼ − eV / c , necessary to obtain the computationalenhancements Sandberg et al. assert. The experimental upper bound on the photon mass is10 − eV / c [7].
4s exhausted (and so, by assumption, more total computations) if it waits untila later time when T is lower. The key feature necessary for the above conclusions is that the reservoir can-not accept an appreciable amount of entropy despite being able to do prodigiousamounts of work. This appears in Ref. [1] as an assumption that all of the reser-voir’s internal energy is available to do useful work, a conflation of the energywith the free energy. As we will now show, the incentive to aestivate disappearswhen we drop the unreasonable assumption that exclusively reservoirs of thissort are accessible to the civilization.The real universe is full of subsystems, besides the CMB, that are out ofequilibrium with each other and therefore can accept additional entropy. Themost general possible reservoir has an entropy S and an internal energy U that isassociated with some maximum entropy S max ( U ) determined by physical prop-erties of the reservoir. These physical properties include things like the speciesof particles it is constructed from, the charges of any conserved quantities, andthe maximum volume the reservoir can occupy while maintaining its physicalintegrity. If S = S max then the reservoir has thermalized. Otherwise, if S is lessthan S max , then there generally exists a reversible transformation that movesthe entropy in the memory to the reservoir. Since all memory states have thesame energy, or nearly so, the total energy of the reservoir does not change.To illustrate this, assume for simplicity that the reservoir is composed ofmultiple discrete parts that each have a well-defined temperature. Consider firstjust two parts at different temperatures T and T . The parts can be connectedby a Carnot engine that generates work powered by allowing heat to flow fromthe hotter part to the colder one. So long as T = T , the Carnot enginecan power the bit eraser, reducing the temperature differential, to reversiblypump entropy from the memory tape into the colder reservoir part. (Ejectingthe entropy into a locally thermalized part of the reservoir in accordance withLandauer’s principle is no different than ejecting it into the CMB bath.) Thisprocess can continue until either the memory tape is blank or the temperaturedifference is exhausted ( T = T ), so that no further work can be extracted bythe Carnot engine. The maximum number of bits erased is set by the differencebetween the total initial entropy of the two parts and their total final entropywhen they have thermalized at the joint temperature set by conservation ofenergy. Since this is a reversible process, this bit-erasing capacity is ideal. It’s possible to construct counterexample for which S + N ln 2 < S max but there do notexist reversible physical transformations, formalized as Hamiltonian flow in the joint memory-reservoir phase space, that move all entropy from the memory to the reservoir. However,this can only be done by appealing to constraints that do not follow from the first or secondlaws of thermodynamics. This is not relevant in the present context because we are rebuttingthe thermodynamic arguments of Sandberg et al., and because matter content of the actualuniverse clearly has the ability to absorb huge amounts of entropy without ejecting it into theCMB.
5s more random bits – generated by external computations – are swappedinto the memory, one can keep erasing bits in the memory until all parts ofthe reservoir have equilibrated to the same temperature, i.e., the reservoir is atmaximal entropy for its energy. The maximum number of erasures that we canmake is given by ∆ S/ ln 2 = ( S max − S ) / ln 2, i.e., the initial negentropy of thereservoir measured in bits.Importantly, the erasures are reversible and we have not made use of any in-teraction with the CMB bath, so the erasures can be made at any time withoutregard for the changing bath temperature. It is only if the civilization irre-versibly pushes entropy into the uncontrolled CMB bath at an inopportunelyhigh temperature that it “eats the seed corn”, sacrificing a possible aestivationbonus in accordance with the previous section.Thus we come to our first conclusion: a civilization can freely erase bitswithout forgoing larger future rewards up until the point when all accessiblebounded resources are jointly thermalized. At that time, the contents of theuniverse would appear to be in equilibrium (heat death), much like the earlyuniverse before structure formation. This is very different from the presentuniverse, so there is currently no incentive for aliens to aestivate. In fact, asshow in the next section, quite the opposite. Now let us assume that the reservoir has been exhausted (internally thermalized)as described in the previous section. (This situation differs from our initial toymodel in that the reservoir, on its own, can do no useful work.) We supposecivilization desires to power further bit erasures by exploiting the temperature difference between the bath and the reservoir that is induced by the changingbath temperature T ( t ), i.e., powering the bit eraser with heat flow between thereservoir and the bath. Within this model, it is necessary for the civilization towait for the bath temperature to fall as far below the reservoir temperature aspossible to maximize the number of erasures performed.To see this explicitly, let us assume that the finite reservoir has a constantheat capacity C and initial temperature T R . The infinite CMB bath temperature T ( t ) falls from initial temperature T i to final temperature T f ≪ T i at a rate thatis slow compared to the speed at which the bit eraser can exhaust the reservoir.We show in Appendix B that, for quasi-static bath temperature T and reservoirtemperature T R > T , a maximum of N ( T, T R ) = Ck ln 2 (cid:18) T R T − − ln T R T (cid:19) (1)bits can be erased before the reservoir equilibrates to the bath. Now consider twostrategies as the bath temperature falls from T i to T f : the “greedy” strategycontinuously exploits any temperature differential between the bath and thereservoir to perform erasures, while the “patient” strategy aestivates until T = T f , running the bit eraser only once. 6n the first round of the greedy strategy, the civilization immediately per-forms N ( T i , T R ) erasures, thereby lowering the reservoir to the same temper-ature T i as the bath. Then after a while the bath temperature falls a smallamount, T = T i − ∆ T , and the civilization performs a round of erasures which,for small ∆ T , yields N ( T − ∆ T, T ) ≈ Ck ln 2 (cid:20)
12 ∆ T T + O (cid:18) ∆ T T (cid:19)(cid:21) ∝ (cid:18) ∆ TT (cid:19) ≤ (cid:18) ∆ TT f (cid:19) (2)bits erased. The civilization continues to perform subsequent rounds of erasureseach time the temperature falls ∆ T . The number of rounds that are performedbefore T = T f increases linearly with the inverse step size ∆ T − , but the numberof erasures per round is proportional to ∆ T , so the total number of erasuresperformed in these rounds vanishes in the continuous (maximally greedy) limit∆ T →
0. Therefore, the greedy strategy yields only the N ( T i , T R ) erasures fromthe initial round.On the other hand, for the patient strategy, only a single round of era-sures are performed after the bath has reached it’s final temperature, yielding N ( T f , T R ) erasures total, an improvement on the greedy strategy. Assuming avery cold bath, T = T f ≪ T R , the number of erasures scales proportional to theinverse final temperature of the bath: N ( T f , T R ) T/T R → ≈ C T R k T f ln 2 ∝ T f . (3)In agreement with the claims of Sandberg et al., we see that – once the reservoirhas been fully thermalized and only the reservoir-bath differential remains tobe exploited – the civilization is incentivized to perform all computations anderasures in the distant future when the bath temperature T has stabilized to itsminimum temperature T f (assuming the reservoir is sufficiently insulated).But here again is where the implicit assumptions by Sandberg et al. (at leastas we have interpreted them) can be disputed. The basic idea is that the civi-lization could power additional erasures – without the need for aestivation – bysimply corralling part of the infinite bath and treating it as an additional finitereservoir. Assuming only access to a small amount of inert insulating matter(which would have no thermodynamic value in a non-expanding universe) thecivilization can build a large container that is empty except for the blackbodyradiation it contains (which is initially equivalent to CMB radiation by virtueof the temperature of the walls). Now the civilization has two reservoirs, eachinternally thermalized at different temperatures. A reversible Carnot engine ex-ploiting their temperature difference can power the bit eraser, pumping entropyfrom the memory into the cooler reservoir, until the two reservoirs are at thesame temperature, as described in the previous section. This process – con-verting some of the bath into a new reservoir and then mining the temperaturedifference between reservoirs until they equilibrate – can be repeated for as longas there is any matter in the universe accessible to the civilization. Just as Note that the proton lifetime is constrained to be greater than ∼ years[7], much must push bit-erasure entropy into theuncontrolled bath.Thus, even beyond the normal incentive to acquire sources of negentropy(out-of-equilibrium reservoirs), the falling temperature schedule of the CMB isan additional incentive for the civilization to take control of as much of theuniverse as possible – even the parts that are thermalized and inert! We have concluded that a civilizations capable of reversible computing has noincentive to aestivate until after it has taken control of, and fully exploited, allaccessible matter in the universe.None of this is specific to computation. The incentive to wait, or lack thereof,applies just as well to a civilization whose terminal desires involve expend-ing work to move matter into particular configurations (e.g., galactic-scale artprojects) whose limiting cost is residual frictions, analogous to residual compu-tational faults necessitating error correction.We have not addressed many other potential issues that would arise in wait-ing until the far future of the actual universe, such as the decreasing speed withwhich thermalization with the CMB bath can happen as the photon densitygets lower, the ultimate limits of insulation, and complications from the finitesize of atoms. It’s unclear whether the aestivation incentive will persist, evenin the specific scenario discussed in the previous section, given a more realisticcosmological model.It has not escaped our notice that dark matter, though its nature remains amystery to us, may have a purpose for a powerful civilization able to produce it:to temporarily sequester most of the universe’s mass in a form whose dynamicsconserves not only energy and angular momentum, but to a good approximationentropy, thereby saving it until it can be most expeditiously converted back toordinary matter to power computation or other projects. Of course, one mighthope that such a civilization would preserve a few of the stars, supernovae, etc.as a grand public art project, beautiful and/or controversial, but consumingonly a small fraction of all resources. larger than the ∼ -year timescale on which the effective temperature of the CMB bathreaches its fixed point on account of CMB photons redshifting below the de-Sitter temperature T f ≡ T dS ≈ . · − K [6]. Other criticism
Here we make additional and less important comments. They are independentand so are not necessary to understand our main criticism above.
A.1 Thermodynamic costs of computation beyond erasure
Consider these quotes:
If advanced civilizations do all their computations as reversible com-putations, then it would seem unnecessary to gather energy resources(material resources may still be needed to process and store the in-formation). However, irreversible operations must occur when newmemory is created and in order to do error correction...the actualcorrection is an irreversible operation...Error rates are suppressedby lower temperature and larger/heavier storage. Errors in bit stor-age occur due to classical thermal noise and quantum tunneling.
Our most physically realistic models of computation, Brownian computers, haveanother big entropy cost of computation: “friction” due to driving motion “for-ward” at a finite rate [3, 4]. This entropy cost per gate operation goes inverselyas the time taken per gate operation. If errors happen at a constant physi-cal rate, then trading these costs sets an entropy-cost minimizing time periodper gate operation. If stored negentropy were the limiting resource, and notfor example computer hardware, then this would set an optimal rate for usingnegentropy.Sandberg et al. instead treat error correction as the only entropy cost, andthus say that the min entropy compute strategy is to wait until the universalbackground temperature reaches a low level.
A.2 Reversibility of cooling
This sentence in Ref. [1] is incorrect, possibly for similar reasons as we discussabove:
While it is possible for a civilization to cool down parts of itself toany low temperature, the act of cooling is itself dissipative since itrequires doing work against a hot environment.
Cooling does not need to be dissipative. That is, cooling a system requiresnegentropy but it does not necessarily destroy it; the negentropy used can berecovered if the system is allowed to warm up again. For instance, given acharged battery and two thermal reservoirs at the same temperature, negentropycan be extracted from the battery (in the form of an applied electromotive force,discharging the battery) and transfered to the reservoirs using a reversed Carnotcycle that pumps heat from the one to the other (resulting in a net temperaturedifference between them). This process is adiabatic and hence reversible.9hus the fact that error rates can rise with temperature is a reason to runa computer at a low temperature, but not necessarily a reason to wait for lowuniversal background temperatures.Likewise:
The most efficient cooling merely consists of linking the computationto the coldest heat-bath naturally available.
Allowing heat to directly flow from something warm (the computational ma-chinery) freely to something cool (the bath) unnecessarily increases entropy,and so is not the most efficient method.
B Total work extractable from a reservoir-bathdifferential
Here we calculate how much total useful work can be extracted from a reversibleengine (e.g., Carnot) operating between an infinite thermal bath at temperature T and a finite thermalized reservoir at initial temperature T > T if the reservoiris assumed to have constant heat capacity C . It is known that the infinitesimalwork dW generated by a Carnot engine is related to the heat leaving a reservoir dQ R and the heat entering the bath dQ B by the relations dQ R = dQ B + dW (conservation of energy) (4) dQ R dQ B = T R T (reversible heat engine) (5) C = dQ R dT R (constant heat capacity) (6)where T R is the instantaneous temperature of the reservoir. The total work isobtained by integrating dW from the initial condition T R = T to the asymptoticfinal state T R = T : W = Z dW = Z ( dQ R − dQ B ) = Z dQ R (1 − T /T R )= C Z T T dT R (1 − T /T R ) = CT ( β − − ln β ) (7)where β ≡ T /T . This work can be used to power the bit eraser at the Landauerlimit, yielding N = Wk T ln 2 = Ck ln 2 ( β − − ln β ) (8)erasures. 10 eferences [1] A. Sandberg, S. Armstrong, and M. Cirkovic, “That is not dead whichcan eternal lie: the aestivation hypothesis for resolving Fermi’s para-dox”, Journal of the British Interplanetary Society, , 406–415 (2016)[arXiv:1705.03394].[2] Some authors use “reservoir” to refer to effectively infinite system with ex-ogenously controlled parameters, and call everything finite simply a “sys-tem”.[3] C.H. Bennett, “The Thermodynamics of Computation — A Review.” Inter-national Journal of Theoretical Physics, 21, 905-940 (1982).[4] C.H. Bennett, “Logical Reversibility of Computation.” IBM Journal of Re-search and Development, 17, 525-532. (1973).[5] A. Sandberg, private communication.[6] J.P. Zibin, A. Moss, and D. Scott, “Evolution of the cosmic microwave back-ground,” Physical Review D, 76, 123010 (2007).[7] M. Tanabashi et al. (Particle Data Group), “Review of Particle Physics”,Physical Review D98