Energy, Complexity, and the Singularity

Chapter 8
Energy, Complexity, and the Singularity
Kent A. Peacock
The technology hype cycle for a paradigm shift —railroads, AI, Internet, telecommunica-
tions, possibly now nanotechnology —typically starts with a period of unrealistic expec-
tations based on a lack of understanding of all the enabling factors required.
—Ray Kurzweil, The Singularity Is Near , p. 263
8.1 A Contradiction
There is a striking dissonance between the futuristic optimism of the singularity
hypothesizers such as Kurzweil ( 2005 ), and the views of a host of other recent
authors who warn of the ecological challenges which presently cast a long shadowover the prospects for the human species. Thomas Homer-Dixon, for instance, has
stated that “We are on the cusp of a planetary-scale emergency ”(2007 , p. 308) due
to factors that include global warming, resource exhaustion, peak oil, and speciesextinctions. One cannot help but wonder whether these two disparate groups ofthinkers are even talking about the same planet —but, perforce, they are.
This paper will explore the relevance of ecological limitations to the possibility
of any sort of information-processing “singularity ”or technologically-mediated
“intelligence explosion ”in humanity ’s near future. The subtitle of Kurzweil ’s book
(2005 ) speaks of humans “transcending biology. ”If we are going to talk about
transcending our biological limitations we had better understand them ﬁrst. We
need a clear-eyed awareness of the biophysical imperatives that we will alwayshave to contend with so long as we wish to continue living on this planet, no matter
K.A. Peacock ( ✉)
Department of Philosophy, University of Lethbridge, Lethbridge, Canada
e-mail: kent.peacock@uleth.ca
© Springer-Verlag GmbH Germany 2017
V. Callaghan et al. (eds.), The Technological Singularity ,
The Frontiers Collection, DOI 10.1007/978-3-662-54033-6\_8153
how advanced our technology may become. And we need to grasp the ecological
challenges that our species faces today, which are mostly (and ironically) due to ourown evolutionary success. At that point we might be able to say whether Kurzweil ’s
information-processing “explosion ”can offer us any hope in meeting those urgent
challenges.
The seductive attraction of the singularity hypothesis is sugg e s t e db yt h em o v i e
Limitless (Dixon et al. 2011). A mysterious pharmaceutical has the power to vastly
increase its user ’s creativity, memory, a nd pattern-reco gnition ability. The protagonist
ﬁnds that he can think his way through all problems that come his way so long as he titers
his dosage correctly, and by the end of the movie he is fabulously wealthy and well on hisway to becoming President of the United States. This is merely a science ﬁction story, but
it seems easy to imagine that as in this movi e, if only we or something were dramatically
smarter than we are now, all other problems could be solved almost incidentally.
This is essentially the premise of the singularity hypothesis: take care of
information processing, and it will take care of everything else. That is why, inKurzweil ’s glowing picture of the future, the existential threats presently faced by
humanity, such as global warming, ice sheet collapse, resource exhaustion, speciesextinctions, and nuclear warfare, get only passing mention or are ignored entirely.As an anonymous referee for this paper put it, according to the hypothesis, “in the
next century we are going to develop an arti ﬁcial super-intelligence that will master
nanotechnology …If the super-intelligence is friendly it will be able to trivially
solve our environmental problems …”. My aim is to ask if it is reasonable to bet the
farm on the premise that we don ’t really have to worry about those environmental
problems because in only a few decades computer-assisted humanity will simplythink its way out of them. And my answer will be —almost certainly not.
8.2 Challenges
I’ll begin by reviewing some of the ecological reasons why many scientists believe
that humanity is now facing what is likely the biggest cluster of survival challengesin its evolutionary history.
8.2.1 Climate Change
At the top of the list is climate change due to anthropogenic global carbonization.Apart from warming of the troposphere and oceans, the risks attendant upon globalcarbonization include extreme weather (droughts, storms, wobbles in the polarvortex, ﬂooding, forest ﬁres, and killer heat waves), oceanic acidi ﬁcation, and
catastrophic sea level rise (Hansen et al. 2013b ; IPCC 2014 ). It is fondly hoped that
keeping the increase in global surface temperature under 2 °C above pre-industrial
levels will be suf ﬁcient to prevent “tipping points ”—that is, critical points at which154 K.A. Peacock
positive feedbacks cause some deleterious consequence of global carbonization
(such as ice sheet collapse or methane release) to accelerate exponentially. How-ever, even if we can hold global temperature increases below the 2 °C “guardrail ”
(which some scientists fear may be already impossible; Anderson and Bowes
2011 ), it is by no means clear that dangerous tipping points would not be reached
anyway. Sea level rise promises to be the most visible effect of global carbonizationin the years to come. There may already be enough heat in the seas to cause the vastbut highly vulnerable marine ice domes in the central basin of West Antarctica tocrumble (entailing an almost immediate jump of over 3 m in sea level; Pollard et al.2015 ; Alley et al. 2015 ).
What is the worst case scenario? Hansen et al. ( 2013a ) show that burning all the
fossil fuel there is to burn would eventually lead to a global “moist greenhouse ”
condition in which icecaps would disappear, sea level would be at least 60 m
higher, and the equatorial regions of the planet would be uninhabitable by largemammals (including humans). Other research shows that portions of the seas wouldeventually go anoxic or possibly even euxinic (a condition in which a body of waterbecomes dominated by anaerobic bacteria producing toxic hydrogen sul ﬁde; Ward,
2007 ). I prefer to believe that humanity could not be so foolish as to permit such an
extreme outcome, but policy cannot be based on wishful thinking. At present we arenot making anything remotely close to a suf ﬁcient effort to prevent such scenarios.
In the face of the present crisis, Kurzweil ’s glib remark (p. 249) that we should be
careful to not pull too much CO
2out of the atmosphere is, put charitably, not very
helpful.
8.2.2 Biodiversity and Ecosystem Services
For at least thirty years, biologists have been warning that humanity is in theprocess of engineering one of the major mass extinctions in the history of life onearth (Kaufman 1986 ; Wilson 1992 ; Brown 2011 ; Kolbert 2014 ). The problem is
not only the loss of irreplaceable species and all the hard-won genetic informationthey contain. Since 1970 the number of non-human animals has been reduced by
roughly one half —a process now called defaunation —while in the same period the
human population has doubled (Dirzo et al. 2014 ).
These grim facts pose an obvious moral challenge. But the biodiversity crisis is
of urgent practical concern as well. The plants and animals of the world provide
“ecosystem services ”(Costanza et al. 1997 ) through their production of oxygen,
maintenance of soil fertility, puri ﬁcation of water, and contributions to the stabi-
lization of climate —not to mention their provision of the vast biomass that humans
consume as food or materials. Unless we want to transition to some sort of totallyartiﬁcial habitat (which we might have to do on other planets) we have to grasp that
many of the features that make this planet pleasant and habitable for us are eithertotally a bioproduct (such as free oxygen), or partially or indirectly bioproducts
(such as fertile soils and many aspects of climate). The programmer in his cubicle8 Energy, Complexity, and the Singularity 155
gleefully coding next generation AI software breathes oxygen generated by the
forests and phytoplankton. If he hopes to keep coding he, or someone, is going tohave to respect the fact that whatever technological marvels we create, the photo-synthesizers must be taken care of. This is something that must be attended to on an
on-going basis; we cannot wait for the hypothetical super-intelligence of the future
to take care of it for us. It would be suicidal for humanity to assume that thewell-being of the myriad organisms we depend upon is “transparent to the user. ”
8.2.3 Energy —or, Where ’s My Jetsons Car?
Popular culture of the 1950s and 1960s exhibited a combination of technological
optimism and naïveté that now seems quaint. Recall George Jetson ’sﬂying car,
which burbled cheerfully as it delivered George and his family to their destinationsand then neatly folded up into a briefcase. It was con ﬁdently assumed that in the
not-too-distant future science would open the door to unlimited supplies of energythat would be “too cheap to meter ”. At the same time, few thinkers in an era when
the transistor had just been invented envisioned how quickly computing woulddevelop. In fact, things have turned out almost exactly the opposite: information
technology has exploded while energy technology (apart from some progress in
renewables) is stalled.
Compare the automobiles of today with those from the 1960s. Modern autos
have enormously more capable electronics, but the engines and transmissions workessentially the same way that they did ﬁfty years ago. At last, all-electric vehicles
are beginning to be genuinely competitive with internal combustion cars, enabledby long-awaited advances in battery technology. But for the most part they are stillcharged by electrical grids energized by the combustion of coal and natural gas —
methods that were old in the 1960s. With the recent and very hopeful growth of
renewable technologies this may change soon, but as of this writing we are still along way from weaning ourselves from the old dirty ways; indeed, humanity stillderives about 85% of its energy from fossil fuels.
No culture that hopes to maintain anything like our present level of population
and social complexity, let alone undertake dramatic leaps in technologicalsophistication, has a future if it must derive the larger part of its energy from thecombustion of a rapidly-dwindling, one-time-only stock of toxic sludge accumu-
lated in ancient anaerobic basins (Deffeyes 2005 ). Hydrofracturing ( “fracking ”)
only slightly extends the lifetime of this resource, at signi ﬁcant environmental cost;
fracking is the equivalent of sucking out the last dregs of a milkshake with a straw,and cannot be expected to provide energy security for more than a very few decades(Hughes 2014 ; Inman 2014 ). And let ’s not forget about climate change. Quanti-
tative studies (e.g., McGlade and Ekins 2015 ) show that we cannot burn the larger
part of the remaining fossil fuels if we want to have the slightest hope of preventing156 K.A. Peacock
the disastrous effects of global carbonization. Our technological society (with its
present level of complexity and population) has no long-term future if it mustdepend upon fossil carbon.
Despite this, it remains importantly unclear whether renewables (solar, biomass,
wind, and geothermal energy), or nuclear energy as it is presently implemented, can
provide enough net energy, quickly enough, to maintain our global civilization at itspresent level of complexity. Kurzweil himself believes that this challenge will beobviated as we move to renewables. He points out, correctly, that Earth is bathedwith thousands of times more solar energy than we need to power our culture.However, it still remains a matter of debate whether solar-powered technology hasto potential to replace oil. Ecologist Charles Hall is blunt:
I do not see …anything that implies a ‘business as usual ’(i.e., growth) as the most likely
scenario …Even our most promising new technologies appear to represent at best minor,
even trivial, replacements for our main fossil fuels at least within anything like the present
investment and technological environment …depletion seems to be effectively trumping
technological progress again and again. (Hall 2011 , p. 2497).
On the other hand, Mark Jacobson and co-authors have carried out a painstaking
analysis of possible alternative energies, and they argue, in contrast to Hall, thatwind, water, and solar power are in principle capable of supplying all of the world ’s
current energy needs; barriers to this result, they claim, “are primarily social and
political, not technical or economic ”(Jacobson and Delucchi 2011 ).
Fully replacing fossil fuels with renewable technology will require a huge
investment in new infrastructure, and a great deal of fossil fuel is going to have to
be burned in order to get that infrastructure up and running. Renewables also faceintense opposition from entrenched interests who wish to continue to pro ﬁt from the
present ways of generating and distributing energy. Despite these dif ﬁculties, recent
advances in solar and wind energy tend to support Jacobson ’s optimism, and I agree
with Kurzweil that renewables show great promise. But as with many of histechnological speculations, Kurzweil is too willing to treat an unsecured promissorynote as money in the bank. ( “[N]anotechology …in the 2020s will be capable of
creating almost any physical product from inexpensive raw materials and infor-
mation ”; p. 13.) We are emphatically not yet out of the woods. Solving the chal-
lenge indicated by Hall —ﬁnding ecologically sustainable ways of producing and
using energy that can do at least as much work for humanity as fossil fuels —is a
necessary condition for the possibility of a “singularity ”or indeed any further
dramatic and lasting development in the technological sophistication of humanculture.
8.2.4 The Troubles with Science
Kurzweil says that “we`re doubling the rate of progress every decade ”(p. 11) and it
is clear from the context of this quote that he is not talking only about information8 Energy, Complexity, and the Singularity 157
technology. However, in many respects that are highly relevant to human ﬂour-
ishing, it is simply not the case that the rate of advancement is even linear.
One important department of knowledge that is not growing exponentially is our
fundamental understanding of physics. In his controversial Trouble With Physics
(2006; see also Woit 2006 ), the distinguished theorist Lee Smolin suggests that the
story of modern physics since about 1975 could be called a “tragedy ”:
For more than two centuries, until the present period, our understanding of the laws of
nature expanded rapidly. But today, despite our best efforts, what we know for certain about
these laws is no more than what we knew back in the 1970s (Smolin 2006 , p. viii).
But what about lasers? Magnetic resonance imaging? The increase in the speed
and miniaturization of microelectronics (one of the few positive trends that hasbeen
quasi-exponential)? The Internet? Flat-screen TVs? GPS positioning? Thenear-total obsolescence of chemical photography due to CCDs? Smart phones andtablets? Photovoltaics? LEDs? Quantum computing (still largely theoretical butquite promising)?
All of these marvels are based on applications of physical principles, mostly in
the province of quantum mechanics, which were discovered before 1930 (Peacock
2008 ). The one really new thing that has appeared in physical science in the past
thirty years is dark energy (Kirshner 2002 ) and this was not so much an increase in
understanding as a stark reminder of how limited our understanding of the physicaluniverse still is. Most important, argues Smolin, we are presently stuck not merelybecause the problems faced in current theoretical physics are so technically dif ﬁcult,
but because of a complex of cultural, philosophical, and socio-economic blindersthat actively discourage the intellectual risk-taking that is essential for innovation.
One could make similar harsh observations about medicine: we still do not have
a cure for the common cold let alone most types of cancer, and the development ofnew antibiotics and vaccines has slowed to a crawl because there presently is nomodel for funding the necessary research and development. Stem cell technologyholds the promise of transforming the central focus of medicine fromrepair-and-support to regeneration, but (like quantum computing) it is in its earlyexploratory phase. Obviously, there have been signi ﬁcant improvements in medical
treatment in the past thirty to forty years, but like most other recent technological
advances they are for the most part incremental, re ﬁnements of principles that were
understood decades ago.
A Ptolemaic astronomer circa 1500 CE could have exclaimed, “Look, our
models are getting better and better at explaining the increasingly ﬁne observations
that our naked-eye astronomers are making! The number of epicycles is increasingexponentially! ”What he would have been missing was the fact that the proliferation
of ad hoc epicycles was a sign that the vein of geocentric astronomy was playedout. At critical times new, disruptive insights are needed. Just as a declining society
can only be saved by what Tainter ( 1988 , p. 215) calls a new “subsidy ”of energy,
at a certain point a stagnant knowledge paradigm can only be revived by a newsubsidy of creative insight (Kuhn 1970 ).158 K.A. Peacock
The lack of progress in fundamental physics is probably one of the main reasons
for our lack of progress in energy. At the end of this paper I will have more to sayabout why our ability to generate new insights is failing us precisely at the timewhen we need it the most.
8.3 Energy and Complexity
It is crucial to realize how important the energy question is for any discussion ofpossible technological advances. The need for energy is a matter of simple(non-equilibrium) physics. Any complex society is a physical system (technically, a
dissipative structure; Schneider and Sagan 2005 ) that can maintain its coherence
and complexity only if it is provided with a generous ﬂow of usable energy. The
greater the complexity to be maintained, the greater the energy ﬂow required. If the
energy ﬂow falters, the society must simplify itself proportionally or suffer collapse
(Tainter 1988 ). A generous energy ﬂow is a necessary condition for our present
global society to keep functioning at anything close to its present level of com-plexity. The energy a society needs in order to maintain its complexity comes in oneway or another from its “EROI ”, its“energy return on energy invested in producing
energy ”(Murphy and Hall 2010 ). No improvements in the ef ﬁciency with which
net energy is used can by themselves save a society whose EROI is continuallydiminishing, as is the world EROI today (Inman 2013 ). Efﬁciency can buy time, but
beyond a point ef ﬁciency measures can themselves be a drain since they also
demand resource-consuming complexity. In principle we could recycle every bentpaperclip, but at what cost?
Kurzweil states that he is a “patternist, someone who views patterns of infor-
mation as the fundamental reality ”(p. 5). This suggests a deep misunderstanding of
physics. Recall Rolf Landauer ’s famous dictum ( 1991 ) that “information is phys-
ical.”While the same bits of information can be encoded in many different physical
substrates, they must always be encoded on some physical substrate; there is no
such thing as pure information except as a mathematical abstraction. Landauer ’s
rule therefore demands that we consider the physical requisites for an advanced
society to develop and maintain a high level of informational complexity. Perhaps itis Kurzweil ’s fanciful metaphysics that has led him to underestimate the biophysical
requirements for his “information explosion. ”
Given the ecological trends cited above, it is very unclear that the complexity of
modern society can be sustained for much longer at its present level, let aloneexpanded enough to allow for a dramatic increase in information-processingcapacity. This is certainly the case even given the great increases in ef ﬁciencies due
to the hypothetical advances in nanotechnology and miniaturization that Kurzweilcites in his discussion of energy needs ( 2005 ). Kurzweil is right that in principle
much of our technology could be miniaturized, thereby (again, in principle)8 Energy, Complexity, and the Singularity 159
enabling higher complexity for a given energy ﬂow. However, miniaturization
needs a lot of supporting infrastructure. Giga ﬂop computer chips presently require
multi-billion dollar factories for their production; materials must be mined, shipped,and fabricated, and the energy and material requirements for these activities are
huge. When we estimate the ecological limits to complexity we must consider not
only the requirements of our end-product technology but also the requirements ofthe complex infrastructure required to produce and support those marvellousend-result devices. Some of those requirements (such as mining, agriculture, andforestry) cannot be miniaturized, because they involve the interaction of humantechnology with parts of the global ecosystem (such as its geology or forests) thatcannot be miniaturized. We can ’t nano-size the ecological impact of cutting down a
tree. Like humanity itself, the technological ecology we create cannot exist inde-
pendently of the biophysical ecology of the planetary system, and ultimately it must
scale with itand interface with itonitsterms.
A defender of the singularity hypothesis might say that I have simply failed to
grasp the magical power of exponential expansion. I address this point below.
8.4 Exponentials and Feedbacks
Kurzweil ’sSingularity is Near is a paean to the power of the exponential function.
For example, never mind that solar power presently provides only a tiny fraction ofour energy; it is expanding exponentially and therefore will soon take over theworld ’s energy production. We need a more balanced picture of how exponential
expansions work and then cease to work.
An exponentially growing quantity if unchecked will grow from background
noise to an impressive signal rather quickly; this is elementary. However, the mere
fact that some process is growing exponentially does not by itself guarantee that it
will keep growing; there will, with certainty, be feedbacks and tipping points thatwill slow or halt the growth.
A simple example of an exponentially growing system that hits a limiting
threshold is a population of yeast in a carboy of grape juice and sugar. In this idealenvironment the yeast organisms multiply exponentially. But their metabolism hasa waste product, ethanol, which is toxic to the yeast at a certain concentration(although desirable to the person who makes the wine). When that concentration is
reached the population of yeast sterilizes itself out of existence almost instanta-
neously. One can think of many similar examples. No exponential expansion can goon forever; something always has to give.
Exponential growth can be illustrated by a pond with water plants on its surface
which double their coverage every day. We are supposed to be amazed by the factthat if the surface of the pond is half covered on a certain day, it will be totally160 K.A. Peacock
covered the next day. The interesting question is what happens the day after. In
some cases symbiotic negative feedbacks will kick in and the growth rate will slowdown to a steady state; in other cases a predator will feast on the bloom, keeping itin check; and sometimes the plant growth will choke the pond by using up too
much oxygen or a vital nutrient.
Realistic systems in nature, such as ecosystems containing predators and prey,
undergo complex cycles due to their mutual interactions and the phase relationsbetween them; even economic systems can be modelled in such terms (Motesharreiet al. 2014 ). Negative feedbacks always damp out exponential growth sooner or
later, and these feedbacks may act gradually or drastically.
Kurzweil understands that no exponential process can go on forever, but he
dismisses the problems I describe here ( “The Criticism from Malthus, ”pp. 433 –
434) because, he argues, the energy requirements of advanced computers will be so
minimal that they will achieve the singularity before limiting factors can catch up
with their exponential growth in computing capacity, like a driver gunning his carto beat a yellow light. Again, Kurzweil fails to grasp the dependency of computingtechnology on the continued healthy functioning of its supporting ecological con-text. We can ’t wait for however many decades it takes for the super-intelligence to
appear, and then hope to go back and repair what is left of the planet.
For all his talk of the power of exponentials, Kurzweil is a remarkably linear
thinker. (After all, an exponential growth function is linear when expressed loga-
rithmically.) He sees one trend and extrapolates it, while failing to grasp that thereare other powerful trends and countervailing forces (many themselves growingnonlinearly) which must be expected to interact in complex and unpredictableways. The growth of information processing technology, while certainly important,is hardly the only major trend in our time, and supposing that it will allow us to“transcend biology ”is not even good science ﬁction. The continued existence of the
complex technological infrastructure that allows us to build our computers and
networks is utterly dependent upon the continuing health of a global ecosystem (the
“earth system ”) whose complex, interdependent operations we are now in the
process of thoughtlessly dismantling.
8.5 Ingenuity, not Data Processing
Kurzweil speaks of his “veneration for human creativity ”(p. 2), but at times he
exhibits a certain frustration with human limitations:
While human intelligence is sometimes capable of soaring in its creativity and expres-
siveness, much human thought is derivative, petty, and circumscribed (p. 9).
So painfully true. However, we should do a better job of understanding the
potentials of the human brain before declaring it obsolete.8 Energy, Complexity, and the Singularity 161
The most important capacity of the human mind does not lie in its abilities to
remember or calculate; these are modest compared to digital computers. The greatsurvival trick that the human animal has evolved and brought to a level unprece-dented in evolutionary history is ingenuity, the capacity for creative problem
solving. A nice demonstration of ingenuity is the sewing needle, which is not found
in the fossil record before about 30,000 years ago. As Fagan ( 2012 ) observes, the
unspectacular sewing needle allowed early humans in sub-arctic conditions to crafttailored clothing, and thus was likely one of many innovations that got our
ancestors through that harsh period. The possibility of the sewing needle is implicitin the physics of materials and therefore it could have been deduced by brute forceby some suf ﬁciently powerful digital computer, like a winning chess strategy. But
that is not how it actually came about.
Ingenuity is a poorly understood neurological capacity by which human beings
can occasionally introduce something new that expands the sheaf of survivaloptions. It is not a freakish phenomenon exhibited only by a few rare geniuses, but anatural human capacity like athletic or musical ability. Like such abilities, it ispresent in unequal amounts in different people and it may be suppressed by avariety of social, political, economic, and cultural factors; however, it can bepromoted by other factors (including education and opportunity).
Finding a creative innovation is like winning more “lives”in a video game.
Historically, human ingenuity in this sense is a proven commodity, but we also
know that it can be prevented from acting by powerful social forces such as dog-matic religion, ideology, vested interests ( ﬁnancial, political, intellectual, or cor-
porate), or the sheer lack of room to operate due to poverty or scarcity of resources.These anti-creative forces can be dominant in times of ecological stress (Peacock1999 ). Authoritarianism of all stripes (whether acting from naked self-interest or
misguided social concern) tends to see innovation as threatening (Whatmough1996 ). Arguably, many episodes of societal collapse in the past occurred because
human ingenuity either failed or was not permitted to operate. There is a real danger
now that as scarcity and other ecological challenges increase in our time, those whobeneﬁt from our present unsustainable system may well “double down ”and block
the innovations that are needed.
The need to protect and foster our capacity for ingenuity is, I submit, the greatest
challenge facing humanity right now, rising seas notwithstanding. Certainly it is ofinterest (although obviously also risky) to try to construct computers that might becapable of creativity. However, when we are faced with urgent, time-constraining
challenges such as global carbonization we should invest far more resources than
we are now into the one factor —human ingenuity —that has a proven track record
in solving apparently intractable problems. That is what is going to get us throughour present ecological bottleneck if anything can. There is no question that infor-mation technology can assist and supplement human ingenuity; this is alreadywell-demonstrated. One may also speculate that computers will someday exceed thecreative problem-solving ability of humans but that day has not yet come, and wecannot bank on it any more than I can do my household budget on the assumption
that I will win a major lottery.162 K.A. Peacock
8.6 In Summary
Kurzweil seems to be virtually oblivious to the magnitude and urgency of current
ecological challenges such as global carbonization. Humanity ’s immediate eco-
logical problem is this: the methods by which we presently garner the resources of
energy and materials that we need cannot go on because they are biophysicallyunsustainable. We are running a complex, globalized, industrialized society almostentirely on a source of energy (fossil fuels) that can be extracted in economicallysigniﬁcant quantities for only a few more decades (one to two) at most. Pollution
from the exploitation of this resource is well on its way to dangerously destabilizingthe planet ’s climate (through global warming) and the viability of the ocean ’s food
chain (through acidi ﬁcation). Other deleterious human impacts on the earth system
—through such factors as habitat encroachment and fragmentation, soil erosion,
deforestation, and over- ﬁshing —are by now on a geological scale.
The notion that a highly speculative increase in computing power could enable
us to leapfrog all of these ecological dif ﬁculties is at best a long shot. The way past
our ecological bottleneck is not to bet that we can transcend biology but to integrateour technology and its supporting infrastructure symbiotically with the Earth system(Peacock 2011 ). Regardless of what marvels of ef ﬁciency may eventually be
realized in microelectronics and nanotechnology, our elaborate technological
ecosystems of the future will be as dependent upon a ﬂourishing planetary biota as
we are now. And a key component of moving to that quasi-symbiotic state will beto engender the ﬂourishing of those human capacities that are most likely to con-
tribute to the innovations that are required. The ability of the human mind togenerate novelty, such as the not-so-humble sewing needle and of course computersthemselves, is well demonstrated; the possibility that machine intelligence could dothe same thing remains, at this writing, purely speculative. As discussed elsewherein this volume, machine intelligence also carries unknown risks (see also Barrat
2013 ; Gaudin 2014 ): even if the singularity does occur before the servers are
swamped by rising seas, how can we be sure that we would not simply have createda vast computer virus run amok? AI researchers may have to take precautionssimilar to those taken by medical researchers who study Ebola.
I hope it is clear that I do not claim that there is a dichotomous choice between
environmental remediation and AI research. The development of info- andnano-tech can and should continue, with suitable precautions. What I claim is thatwe can neither relyon nor wait for miraculous hypothetical developments in AI to
get us out of our present ecological jam.
In summary: necessary conditions for any dramatic technological advance (such
as the “singularity ”) include the following: the continued healthy functioning of the
earth system, and abundant and sustainable sources of non-fossil energy. And ourbest chance of satisfying these necessary conditions is not gambling on a techno-logical long-shot but doing everything we can to foster human ingenuity, the onefactor that has a proven capacity to generate game-changing innovation.8 Energy, Complexity, and the Singularity 163
Acknowledgements I thank Maxime Chambers-Dumont for assistance and anonymous referees
for helpful and stimulating comments. I am grateful to the University of Lethbridge for supportingmy work in many ways. Any errors, omissions, or misinterpretations remaining in this paper are
entirely my responsibility.
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Chapter 9
Computer Simulations as a Technological
Singularity in the Empirical Sciences
Juan M. Durán
9.1 Introduction
To talk of a ‘singularity’ evokes the idea of a natural occurrence beyond which the
course of humanity has changed in signiﬁcant ways. The Big Bang is one good exam-ple of such a singularity that aﬀects our future on physical and existential levels.
Now, to talk of a ‘technological singularity’ seems to evoke something else, some-
thing related to an occurrence that is the byproduct of human activity. Philosophers
have not yet come to an agreement on the notion of a technological singularity.
What seems to be common ground, however, is the idea that in order to speak ofa technological singularity, humans must somehow be displaced from the center of
the production of knowledge. Much of current literature asserts that the origin of
such a displacement is related to the introduction of computers and their pervasiveuse in our modern life. Either by means of the emergence and evolution of super-
intelligent machines (Good 1965 ;V i n g e 1993 ), or by means of powerful computers
that enhance human cognitive capacities (Kurzweil 2012 ), computers are changing
the way we gather and organize information about our world. Thus understood, the
notion of technological singularity is intended to underscore the existence of an epis-
temological barrier beyond which humans cannot trespass, and where computersbecome the center of the epistemological endeavor.
1
The specialized literature has mainly focused on problems of singularity stem-
ming from the philosophy of mind (Turing 1950 ), philosophy of economics (James
Miller 2012 ), and ethics (Hans Jonas 2011 ), just to mention a few. This paper, instead,
centers on the junction between the philosophy of science and the still young but vig-
orous philosophy of computer simulations. Concretely, I am interested in focusing
1Since the context is clear, from now on I will use the terms ‘technological singularity’ and
‘singularity’ interchangeably.
J.M. Durán ( ✉)
HLRS - University of Stuttgart, Stuttgart, Germanye-mail: duran@hlrs.de
© Springer-Verlag GmbH Germany 2017
V. Callaghan et al. (eds.), The Technological Singularity ,
The Frontiers Collection, DOI 10.1007/978-3-662-54033-6\_9167
168 J.M. Durán
the problem of technological singularity from the viewpoint of computer simula-
tions and their pervasive use in the empirical sciences. The general question that is
being posed here: under what conditions can computer simulations be considered atechnological singularity in the empirical sciences?
In this context, we should ﬁrst note that I am assuming that at least some computer
simulations do qualify as a technological singularity. This fact is, to my mind, uncon-troversial. It should not take much eﬀort to ﬁnd a case in current scientiﬁc practice
where a computer simulation advanced the general scientiﬁc knowledge of a target
system. However, to assume that some computer simulations qualify as a techno-logical singularity presupposes an understanding of what a technological singularity
entails. Allow me, then, to begin by drawing a minimal working characterization of
what makes a computer simulation qualify as a technological singularity.
A computer simulation is a technological singularity if humans have been displaced from
the center of production of knowledge, and if such knowledge is reliable to the extent of
being usable without further sanctioning.
Although this characterization needs clariﬁcation, it provides the ﬁrst basic intu-
itions on the issue. To begin with, displacing humans from the production of knowl-
edge is necessary, although not suﬃcient, for considering computer simulations asingularity, as is demonstrated by the use of computer simulations for ‘face recogni-
tion.’ Although such a simulation displaces humans in some clear respects, such as in
simulating how the human brain would analyze the large amount of data required for
face recognition, it does not render better information (e.g., the computer simulation
could not recognize a human face as fast and as accurate as a human could). Con-versely, a computer simulation could provide knowledge of an empirical target sys-
tem without necessitating the displacement of humans from the center of production
of knowledge. A simple example of this is a simulation of an orbiting satellite usingNewtonian mechanics. Humans have been calculating these orbits for many years
and there are no good reasons for thinking that a simulation necessarily displaces
humans from such simple calculations. As for demanding a reliable production ofknowledge, it is straightforward that such a claim is needed for entrenching the idea
of singularity. Although still in rough form, these intuitions concede the existence of
conditions under which computer simulations qualify as a technological singularity.Could we evaluate more precisely what these conditions are?
In 2009 Paul Humphreys wrote a cogent paper defending the novelty of com-
puter simulations in the philosophical arena. In that work, he introduced the notionof ‘anthropocentric predicament’ as the question about “how we, as humans, can
understand and evaluate computationally based scientiﬁc methods that transcend our
own abilities” (Humphreys 2009 , 617). At ﬁrst glance, the anthropocentric predica-
ment aims at fathoming the methods used by scientists for the evaluation of computer
simulations. Under this interpretation, the anthropocentric predicament is tailored tohuman cognitive capacities, and therefore to an anthropocentric epistemology. But
Humphreys’ intentions are precisely the opposite. To his mind, computer simula-
tions come to take the place of humans in the production of knowledge and, as such,
9 Computer Simulations as a Technological Singularity in the Empirical Sciences 169
“an exclusively anthropocentric epistemology is no longer appropriate because there
now exist superior, non-human, epistemic authorities” (Humphreys 2009 , 617).
Understood in this second sense, the anthropocentric predicament is the route
to considerations about computer simulations as a technological singularity in the
empirical sciences. However, as presented, it is silent on the conditions under which
a simulation produces knowledge of an empirical target system that is as reliable as ahuman. This paper, then, draws from the anthropocentric predicament and addresses
what I believe are the basic conditions for considering computer simulations as a
technological singularity. I begin by showing how, under the correct epistemologi-cal and methodological conditions, computer simulations are reliable producers of
simulation results about the empirical world. For this, I propose to revisit the anthro-
pocentric predicament as elaborated by Humphreys and argue, following the author,that an exclusively anthropocentric epistemology is no longer appropriate in a con-
text where reliable knowledge is also delivered by computer simulations. This ﬁrst
part of the paper shows in what sense the anthropocentric predicament is key forunderstanding computer simulations as a technological singularity. A second and
more extended part assimilates the previous outcomes and deals with the problem
of reliability at face value. For this, I rely on Alvin Goldman’s work on process
reliabilism . The core idea is that under the right epistemological and methodologi-
cal conditions, computer simulations are reliable processes that produce knowledgeabout the empirical target system. The challenge in this second part is to show what
those conditions are and why we are justiﬁed in believing in the reliability of com-
puter simulations. I then propose to approach this issue by ﬁrstly adopting a rep-resentationalist viewpoint, where a computer simulation is a reliable process if it
correctly represents the target system (and, as I will also argue, correctly computes
the simulation model). Thus understood, this approach greatly reduces the numberof computer simulations capable of qualifying as a technological singularity. This
outcome, although correct, seems to be at odds with some uses of computer simula-
tions in daily scientiﬁc practice. In eﬀect, there are concrete cases where computersimulations do provide reliable knowledge, even when the implemented simulation
model does not fully represent the empirical target system. The conceptual shift,
then, is to consider the many ‘epistemic functions’ that computer simulations per-form and allow them to qualify as a technological singularity. Good examples of such
epistemic functions are prediction and exploratory strategies. Due to lack of space,
however, I will leave unanswered the question of whether a non-representationalistcomputer simulation qualiﬁes (and, if so, under what conditions) as a technological
singularity in the empirical sciences.
9.2 The Anthropocentric Predicament
In 2009, Roman Frigg and Julian Reiss warned us of the growth of overemphasized
and generally unwarranted claims about the philosophical importance of computer
simulations. This growth was reﬂected in the increasing number of philosophers con-
170 J.M. Durán
vinced that the philosophy of science, nourished by computer simulations, required
an entirely new epistemology, a revised ontology, and novel semantics. Although
the authors admit the importance that computer simulations have in contemporarytheoretical and practical science, they believe that computer simulations hardly call
into question the basic philosophical principles of understanding science and con-
ceptualizing reality (Frigg and Reiss 2009 , 594–595). I share with Frigg and Reiss
the puzzlement on this issue. It is hard to sustain that a new scientiﬁc method (instru-
ment, mechanism, etc.), however powerful and novel it might be, could all by itself
imperil the current state of philosophy of science. It is still an open question, how-ever, whether or not Frigg and Reiss have correctly interpreted the underlying claims
of the authors they criticize.
An important consequence of the article was the reactions that arose within the
philosophical community. Paul Humphreys, for instance, directly engaged Frigg and
Reiss with an answer. He claimed that Frigg and Reiss’ assertions obscured the chal-
lenges that computer simulations pose for the philosophy of science. The core ofHumphreys’ reply was to recognize that the question about the novelty of computer
simulations has two sides: one side which focuses on how traditional philosophy
illuminates the philosophical study of computer simulations (e.g., through a phi-
losophy of models and a philosophy of experiment, as Frigg and Reiss claim); and
another side which exclusively focuses on aspects of computer simulations in and ofthemselves, that is, philosophical questions stemming from the very object of study
regardless of any clariﬁcation from a more familiar philosophy. It is this second way
of looking at the issue that gives philosophical importance to computer simulations.
Humphreys, then, elaborates on a set of novelties ascribed to computer simula-
tions that constitute distinctively new methods in the scientiﬁc and philosophical
arena. This set includes, among others, the ‘epistemic opacity’ of computer sim-ulations relative to a cognitive agent, that is, the impossibility of knowing all the
epistemically relevant constituents acting during a simulation. In short, being epis-
temically opaque means that, due to the complexity and speed of the computationalprocess, no cognitive agent could follow the entire simulation. A second novelty
that chimes with epistemic opacity is the ‘temporal dynamics’ of computer simula-
tions. This concept has two possible interpretations. Either it refers to the necessarycomputer-time to solve the simulation model, or it stands for the temporal develop-
ment of the target system as represented in the simulation model. A good example
of both interpretations of temporal dynamics is a simulation implementing a modelof the dynamics of the atmosphere that takes, say, 100days to compute.
These two novelties nicely illustrate what is typical of computer simulations,
namely, their inherent complexity, as the case of epistemic opacity and the ﬁrst inter-
pretation of temporal dynamics reveals; and the inherent complexity of the target
systems, as the case of the second interpretation of temporal dynamics shows. Now,what is common between these two novelties is, in turn, that they both entrench com-
puters as the main epistemic authority by displacing humans from the center of the
production of knowledge. Indeed, either because the process of computing is toocomplex for us to follow or because the target system is too complex for us to com-
9 Computer Simulations as a Technological Singularity in the Empirical Sciences 171
prehend, computers become the exclusive source for gathering information about the
world.
Humphreys called this feature the anthropocentric predicament ,w h i c hr e f e r st o
the idea of understanding the world from a non-human perspective by represen-
tational intermediaries tailored to human cognitive capacities (Humphreys 2009 ,
617). The anthropocentric predicament, then, gets its support from the view thatscientiﬁc practice only progresses because new methods are available for handling
large amounts of information. In former times, the amount of information collected
by a given discipline was, to a certain extent, manageable for the scientists. Theastronomers could keep their books and stellar maps, and even perform many diﬀer-
ent kinds of calculations by controlling every step of the process. Today’s scientiﬁc
practice, however, handles enormous amount of information that are virtually impos-sible to manage without the aid of technology. A good example of this is the Diﬀuse
Infrared Background Experiment on the NASA Cosmic Background Explorer satel-
lite which produces 160 million measurements per twenty-six week period (Wright1992 , 231). The new technology which Humphreys has in mind is, surely, the dig-
ital computer. An equally important aspect of the anthropocentric predicament is
that it requires computer simulations to represent an empirical target system. Such a
requirement seems to be a natural consequence of the issue at stake, for displacing
humans from the center of production of knowledge requires that knowledge to begrounded in the structure of the target system.
Thus understood, the anthropocentric predicament is the route to entrenching
computer simulations as a technological singularity in the empirical sciences. Nev-ertheless, in order to be a singularity, it is not enough for computer simulations to
simply set humans apart from the epistemic enterprise, it also requires the simula-
tion results to be epistemically on ap a r with the data that could have been produced
by a human agent. Indeed, a computer simulation that represents a sophisticated
Ptolemaic model could displace humans from the center of knowledge insofar as it
produces accurate results that, other things being equal, humans could not produceby themselves. However, such a computer simulation could not be counted as a reli-
able source of information about the planetary movement, and therefore it could not
seriously be considered as a reliable producer of knowledge. Computer simulationsare not epistemic leverage that turns any implemented model into insight about the
empirical world, nor can they simply displace human agents from the center of pro-
duction of knowledge by representing inherently complex target systems and readilyproducing results of intricate models. In order to be a singularity, computer simula-
tions must produce results that eﬀectively lead to knowledge about their empirical
target systems. To this end, computer simulations must be conceptualized as reli-
able processes in a speciﬁc sense yet to be determined. It is in this precise sense that
the anthropocentric predicament fails to ground computer simulations as a singu-larity, remaining silent on the conditions under which they are reliable producers of
knowledge about the empirical world.
The following section addresses the conditions for a reliable computer simulation.
To my mind, a reliable computer simulation is one that renders, most of the time,
valid simulation results about the empirical target system. A reliable computer simu-
172 J.M. Durán
lation, then, provides the justiﬁcation that our beliefs about the simulation results are,
most of the time, true rather than false of that empirical system, leading to knowl-
edge about such a target system. The question about singularity, then, is subsumedinto the question of what it means to have a reliable computer simulation.
Let it be noted that singularity entails reliability, although the converse is not
necessarily true. Many computer simulations are reliable in the sense just given,although they do not qualify as a singularity. The reason for this is fairly simple. A
computer simulation can be reliable even when it is sanctioned after the computation
of the simulation results. For instance, (Jenkins et al. 2014 ) present a simulation of
self-assembling DNA-coated spheres. The unusual feature of this simulation is that it
has thousands of conﬁgurations that are as energetically favorable as the real experi-
ment. Only expert knowledge can determine which simulation is more accurate thanothers. It follows that the simulation results are sanctioned after the computation of
the simulation, and therefore the simulation cannot be considered a singularity. In
the face of this, let me call the juncture of all methods that collectively grant reli-ability to the simulation before its execution on the computer, and therefore before
obtaining the simulation results, the pre-computed reliability stage .T h e r ei sa l s oa
post-computed reliability stage , which refers to methods for sanctioning the simula-
tion results after they have been obtained and, therefore, requiring the intervention of
an agent. Since singularity is only concerned with the pre-computed reliability stageof a computer simulation, there is no need to address issues related to post-computed
reliable stages. Allow me now to discuss in more detail what entails a pre-computed
reliability stage.
9.3 The Reliability of Computer Simulations
Epistemologists have taught us that questions about knowledge have their roots inthe notion of truth and epistemic justiﬁcation. While it is widely agreed that what is
false cannot be known, there is less consent on what it means to say that we know
something and why we are justiﬁed in believing so. In this paper I am only interestedin analyzing the justiﬁcation of believing that the simulation results are valid of a
t a r g e ts y s t e m .T ob ea valid simulation result is to match, with more or less accuracy,
the (theoretically) measured and observed values of the empirical target system.
With these ideas in mind, allow me to address the philosophical importance of
epistemic justiﬁcation for the singularity hypothesis. Let me begin by asking in what
speciﬁc sense are we justiﬁed in believing that a computer simulation renders knowl-
edge about the empirical world? A suitable answer is to consider the computer sim-
ulation as a belief-forming process, that is, as a process capable of producing resultsthat are, most of the time, valid of the empirical target system. If such results can be
produced, then we can say that we are justiﬁed in believing the simulation results
and, as such, in claiming for knowledge of the empirical target system. In plainwords, if the simulation results are acceptably close or similar to real-world mea-
9 Computer Simulations as a Technological Singularity in the Empirical Sciences 173
surements, observations, or even pen-and-paper calculations, then we are entitled to
claim empirical knowledge of that target system.
In epistemology, such an account is known as process reliabilism , where one of
the major contributors and theorist has been Alvin Goldman. In its simplest form,
reliabilism says that a belief is justiﬁed in the case that it is produced by a reli-
able process, where ‘reliable’ here means a process that produces, most of the time,truths (Goldman 1979 ). For instance, we know that ‘ 2+2=4 ’ because the rea-
soning process involved in addition is, under normal circumstances and within a
limited set of operations, a reliable process. According to Goldman, then, there isnothing accidental in knowledge that is produced by a reliable process. Reinterpret-
ing process reliabilism for computer simulations, we can say that a simulation is a
reliable process if it produces results that are, most of the time, valid of the target sys-tem. Following Goldman, there is nothing accidental about believing that a computer
simulation produces valid results of a target system (provided that certain conditions
are fulﬁlled) and, consequently, about the claim that we obtain knowledge of thattarget system. Thus understood, process reliability is resolved as the belief-forming
process that renders simulation results as valid for the intended empirical target sys-
tem. This point can be easily illustrated by considering CS
Ras the simulation results
andRWDas the data of its target system. According to reliabilism, then, we are justi-
ﬁed in believing the results of the computer simulation if ||CSR−RWR||≅0, that is,
if the simulation results approximate the real data measured, observed, or computed.
To put the same ideas in a rather diﬀerent form, the reliability of computer simula-
tions is built on the quantitatively assessed accuracy of its results. Such accuracy isobtained by two sources, namely, the representational capacity of the simulation and
a relatively error-free computation. The question about the reliability of computer
simulations and, therefore, of knowledge is now shifted to understanding these twosources.
Let me motivate this issue by brieﬂy enumerating which computer simulations
could not be regarded as reliable.
1. Cases of misrepresentations:
a. Any computer simulation that implements a known false model (e.g., the
Ptolemaic model of the solar system) could not be expected to render knowl-
edge of planetary movement.
b. Any computer simulation that has no representational underpinning of the tar-
get system, such as heuristic simulations. (e.g. the Oregonator is a simulation
for exploring the limits of the Belousov chemical reaction. Such a simulation
implements a model whose system of equations is stiﬀand therefore it might
lead to qualitatively erroneous results (Field and Noyes 1974 , 1880)). A par-
ticular case of this is:
i. Any computer simulation that renders unrealistic simulated results , that is,
results that cannot represent an empirical target system (e.g., a computer
simulation implementing a Newtonian model setting the gravitational force
174 J.M. Durán
toG=1m3kg−1s−2).2Such simulations violate the laws of nature and can-
not be considered empirically accurate.
2. Cases of miscalculations:
a. A computer simulation that miscalculates due to large round-oﬀ errors, large
truncation errors, and other kinds of artifacts in the calculation, such as ill-programmed algebraic modules and libraries. Such software errors cannot
stand for valid simulation results of the target system.
b. A computer that miscalculates due to physical errors, such as an ill-
programmed computer module or a malfunctioning hardware component.
Similar to (2.a) above, these types of errors warrant invalid simulation results
and, as such, do not render knowledge of the target system.
A generally valid principle in computer simulations is that there are no limits to
the imagination of the scientists. This is precisely the reason why simulations are, onemight argue, facilitating the shift from a traditional empirically-based scientiﬁc prac-
tice into a more rationally-based one. However, neither of the examples described
above ﬁt the conditions for a pre-computed reliable simulation. While simulationsbelonging to case (1.a) are insuﬃcient for an accurate representation the empirical
target system, those belonging to case (1.b) are highly contentious. The latter case,
as is illustrated by the Oregonator example, is trusted only insofar as the results aresubject to the subsequent acceptance by experts. Whenever this is the case, the sim-
ulation automatically fails to classify as pre-computed reliable and, therefore, vio-
lates the basic assumption of the singularity hypothesis. Although much of currentscientiﬁc practice depends on these kinds of simulations, they do not comply with
the minimal conditions for being a singularity, and therefore they inevitably fail to
qualify as one.
In the same manner, heuristic simulations must not necessarily render invalid
results. For this reason, they are useful simulations for exploring the mathemati-
cal limits of the simulation model, as well as the consequences of an unrealistically
constructed law of nature, among other uses. Such simulations facilitate the represen-
tation of counterfactual worlds, thought experiments, or simply fulﬁll propaedeuticpurposes, but given our current conception of technological singularity, they do not
qualify as such.
Besides their representational features, computer simulations are also part of the
laboratory instrumentarium , and as such are inevitably exposed to miscalculations
of diﬀerent sorts. A ﬁrst classiﬁcation of errors divides them into random errors ,
such as a voltage dip during computation, or a careless laboratory member trippingover the power cord, and systematic errors , that is, errors that are inherently part of
the simulation. Random errors have little philosophical value. Their low probability
2Unrealistic results are not equivalent to erroneous results. In this case, the results are correct of the
simulation model although they do not represent any known empirical system.
9 Computer Simulations as a Technological Singularity in the Empirical Sciences 175
of occurrence, however, do make a small contribution (although negligible) to the
frequency of a process of producing beliefs that are false rather than true. Systematic
errors, on the other hand, can be subdivided into logical errors (i.e., errors in the
programming of software, such as the errors illustrated in (2.a) above), and hardware
errors (i.e., errors related to the malfunctioning of the physical component of the
computer, exempliﬁed in (2.b) above).
This paper concedes that miscalculations do occur in the practice of computer
simulations, but assumes that they are rare and rather negligible for the overall eval-
uation of the reliability of computer simulations. The reason is that over the yearsof technological advancement, computers have become less prone to suﬀer from
failure. A host of recovering procedures such as duplication and redundancy mech-
anisms for critical components, functions, and data grant this dependability. Also,new techniques in the design and practice of programming, as well as the plethora of
programming languages and expert knowledge at the programmers’ disposal facil-
itate the assertion that computers are relatively error-free and fail-safe instruments.As a working assumption, then, I take that computer simulations are stable instru-
ments that, most of the time, do not incur in calculation errors that might alter its
results (or, if they do, such errors are entirely negligible).
9.3.1 Veriﬁcation and Validation Methods
The bluntly false and highly speculative examples used above constitute only a small
portion of computer simulations used in scientiﬁc practice. For the most part, sci-
entists interpret, design, and program the simulation of an intended target systemswith remarkable representational accuracy and on stable instruments. This paper
concedes this much. We must carefully distinguish, however, simulation results that
require further epistemic sanctioning from results whose validity has been grantedduring a pre-computed reliability stage. An argument is advanced to the eﬀect of
addressing veriﬁcation andvalidation methods applied during the pre-computed reli-
ability stage that grant validity to simulation results.
Veriﬁcation and validation methods are at the basis of claims about the reliability
of computer simulations. They build on the conﬁdence and credibility of simulation
results, and in this respect, understanding their uses and limits is central for claimsabout singularity. While veriﬁcation methods substantiate the scientist’s belief that
the mathematical model is correctly implemented and solved by the simulation, vali-
dation methods provide evidence that the simulation results match, with more or less
accuracy, empirical data. Let us take a closer look at what comprises each method.
The American Society of Mechanical Engineers (ASME), along with other insti-
tutions, adopted the following deﬁnition of veriﬁcation: “[t]he process of determin-
ing that a computational model accurately represents the underlying mathematical
model and its solution” (ASME 2006 , 7). Thus understood, veriﬁcation could be
obtained in two ways: by ﬁnding evidence that the algorithms are working correctly,
and by measuring that the discrete solution of the mathematical model is accurate.
176 J.M. Durán
The former method is called code veriﬁcation , while the latter is known as calcula-
tion veriﬁcation . The purpose of making these distinctions is to categorize the set of
methods for the assessment of correctness of the computational model with respect tothe mathematical model, as opposed to assessing the adequacy of the mathematical
model with respect to the empirical system of interest. Code veriﬁcation, then, seeks
to remove programming and logic errors in the computer program and, as such, itbelongs to the design stages of the computational model. Calculation veriﬁcation, on
the other hand, seeks to determine the numerical errors due to discretization approx-
imations, round-oﬀ errors, discontinuities, and the like. Both code veriﬁcation andcalculation veriﬁcation, are guided by formal and deductive principles, as well as by
empirical methods and intuitive practice (or by a combination of both).
Validation, on the other hand, has been deﬁned as “[t]he process of determining
the degree to which a model is an accurate representation of the real world from the
perspective of the intended uses of the model” (ASME 2006 , 7). Validation, then,
is somehow closer to the empirical system since it is concerned with the accuracyin the representation of such a model. Validation methods also make use of bench-
marks or reference values that help establish the accuracy of the simulation results.
Benchmarking is a technique used by computer scientists for measuring the perfor-
mance of a computer system based on comparisons between simulation results and
experimental data. The simplest way to obtain such data comes from performingtraditional empirical experiments. Now, since the true value of the empirical target
system cannot always be absolutely determined, it is an accepted practice to use a
reference value obtained by traditional measurements and observational procedures.A diﬀerent situation is when the value of the target system can be theoretically deter-
mined, as is the case in quantum mechanics where the value of the position of atoms
are obtained by theoretical methods. In such cases, the simulation results can bevalidated with high accuracy. In the same vein, results from diﬀerent but related
simulations could also be used for validation purposes, as these results can be eas-
ily compared to the simulation results of interest. Validation, then, aims at providingproof of the accuracy of simulation results with respect to the empirical target system
of interest. Thus understood, the appeal to validation methods as grounds for reli-
able processes brings out questions that lurk behind inductive processes. The generalconcern is that such methods only allow validation up to a certain number of results,
that is, up to those of which we have previous data. Due to their comparative nature,
these methods do not provide mechanisms for validating new, unknown results. Itfollows that validation is a method for assisting in the detection of errors, but not
designed for detecting misrepresentations of the target system.
It should not be expected, however, that during an actual veriﬁcation or valida-
tion process scientists decouple these methods. The multiple problems related to
mathematical representation, mathematical correctness, algorithm correctness, andsoftware implementation make the entire enterprise of veriﬁcation and validation
highly interwoven processes. Moreover, code veriﬁcation by formal means is virtu-
ally impossible in complex and elaborated simulations. Let it also be noted that not allveriﬁcation and validation methods are performed at the same stages of design and
output of a simulation. Some veriﬁcations are only carried out during design stages,
9 Computer Simulations as a Technological Singularity in the Empirical Sciences 177
while others, such as manufactured solutions , depend on the intervention of an agent.
Manufactured solutions are custom-designed veriﬁcation methods for highly accu-
rate numerical solutions to partial diﬀerential equations (PDEs). It consists in testingnumerical algorithms and computer codes by ﬁnding solution functions that have
altered the implemented PDEs, but which also satisfy such equations. As William
Oberkampf and Timothy Trucano indicate, “[a manufactured solution] veriﬁes manynumerical aspects in the code, such as the mathematical correctness of the numerical
algorithms, the spatial-transformation for the grid generation, the grid-spacing tech-
nique, and the absence of coding errors in the software implementation” (Oberkampfand Trucano 2008 , 723).
In a similar fashion, validation methods might focus on the design stages as well
as on the output of a simulation. It is easier to devise validation methods requiringthe intervention of an agent, for the construction and subsequent use of benchmarks
requires such involvement. Examples of this abound in the literature and there is
no need to discuss this point any further. One could always consult Oberkampf andTrucano’s list for the documentation of benchmarks, all of which must be in place for
successfully warranting accuracy of the computed results (Oberkampf and Trucano
2008 , 728).
9.4 Final Words
In this paper I defended the idea that, under the right conditions, computer simula-
tions are reliable processes that produce, most of the time, valid simulation results.
Valid simulation results are taken as knowledge of the target system, facilitating theclaim that computer simulations are a technological singularity. Now, in order to
fully qualify as a technological singularity, such results must not be sanctioned by a
human agent. On the face of it, the number of simulations that qualify as a techno-logical singularity has been reduced to a few well established cases with representa-
tional underpinning and error-free computations. Such representation and error-free
computations are grounded on veriﬁcation and validations methods, as elaboratedabove.
One immediate consequence is that the universe of computer simulations has
been signiﬁcantly reduced. At ﬁrst, this outcome might strike one as an undesir-able and anti-intuitive consequence. One might think that many computer simula-
tions are being used today as reliable processes producing valid results of a given
empirical system, and that there is no special problem in doing so. The general
trend nowadays is to overthrow humans as the ultimate epistemic authority, replacing
them with computer simulations (Sotala and Yampolskiy 2015 ). A good example of
this is the simulation of the spread of inﬂuenza, as expounded by Ajelli and Merler
(2008 ), where two diﬀerent kinds of computer simulations provide knowledge of a
hypothetical scenario. In some situations, in eﬀect, no further sanctioning is neededand the information provided by these simulations is used as obtained. However,
178 J.M. Durán
contrary to appearances, the vast majority of cases get their results sanctioned after
they have been produced, undermining the possibilities of becoming a technological
singularity. One might safely conclude that the number of computer simulations thatqualify as a singularity are, indeed, limited.
Admittedly, much more needs to be said in both directions, namely, what grounds
computer simulations as a technological singularity (especially regarding veriﬁca-tion and validation methods) as well as how current scientiﬁc practice accommodates
this philosophical view. Equally important is to elaborate on cases such as Ajelli et
al., where the simulation seems to be a singularity if used in certain situations andfails to be one in some others.
Acknowledgements This article was possible thanks to a grant from CONICET (Argentina). Spe-
cial thanks also go to Pío García, Marisa Velasco, Julián Reynoso, Xavier Huvelle, and Andrés Ilcic(Universidad Nacional de Córdoba - Argentina) for their time and comments.
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