Can we know if our universe is a simulation?

The ques­tion of wheth­er we might be liv­ing inside a com­puter sim­u­la­tion has inspired many a work of sci­ence fic­tion. But is it pos­sible to cal­cu­late the odds that we are the vir­tu­al cre­ations of a super­i­or intel­li­gence? A new study¹ aims to put to rest cer­tain mis­com­pre­hen­sions in the pop­u­lar culture.

Long before The Mat­rix² and the nov­el Simu­lac­ron³, which greatly con­trib­uted to open­ing up the concept of sim­u­lated real­it­ies in the col­lect­ive con­science, Pla­to, with his “allegory of the cave”, likened human beings to chained pris­on­ers unable to see real­ity. There is no doubt that the idea we live in a sim­u­la­tion is enti­cing. More recently, the 2020 Gon­court Prize win­ner The Anom­aly⁴ ques­tions how we, as a soci­ety, would deal with learn­ing that we might be liv­ing in such a reality.

In 2003, Nick Bostrom, a philo­soph­er at the Uni­ver­sity of Oxford, pub­lished an art­icle in which he ima­gined a tech­no­lo­gic­ally advanced civil­isa­tion who pos­sess the immense com­put­ing power required to sim­u­late new real­it­ies with con­scious beings in them⁵. His hypo­thes­is implies that if we lived in a sim­u­la­tion, it would be because there is a life form more intel­li­gent than us, cap­able of cre­at­ing such a uni­verse. Is this pos­sible? And how would we know that our daily lives – and more broadly the uni­verse – were not the avatars of some gigant­ic com­puter programme?

The argu­ment can be likened to pre­dict­ing wheth­er or not life exists else­where in the uni­verse. Until we find such extra-ter­restri­al life, how­ever, the only inform­a­tion we have is that it was able to start here, on Earth. Such argu­ments are par­tic­u­larly amen­able to Bayesian infer­ence – a type of ana­lys­is that cal­cu­lates the degree of con­fid­ence giv­en to a hypo­thet­ic­al cause. This algorithmic tech­nique uses Bayes’ the­or­em, which cal­cu­lates the prob­ab­il­ity of an event occur­ring by first con­sid­er­ing the prob­ab­il­ity that anoth­er sim­il­ar event that has already occurred. In Bayesian stat­ist­ics, you can lay out everything you know and everything you don’t know.

Set­ting up the sim­u­la­tion argu­ment in a Bayesian frame­work reveals that many of today’s hypo­theses – be they in favour of or against the exist­ence of a sim­u­lated real­ity – often have too many assump­tions built into them. For example, if the uni­verse is a sim­u­la­tion, one might assume that it is a “giant com­puter”. And even if it were, this is not evid­ence in itself that the uni­verse was cre­ated by a high­er intelligence.

Nor can it be said that the pres­ence of “flaws” (like the black cat that walks past twice in The Mat­rix) is evid­ence of a sim­u­lated world⁶. This hypo­thes­is is par­tic­u­larly incon­clus­ive because even if someone did notice such glitches, the “cre­at­or” could always rewind the sim­u­la­tion and delete the evid­ence (wip­ing the memory). Since there are also fun­da­ment­al com­pu­ta­tion­al lim­its that inev­it­ably make the sim­u­la­tion “grainy”, the cre­at­or might choose not to make a detailed phys­ic­al sim­u­la­tion of the entire uni­verse, but only our per­cep­tion of it.

Human­ity as we know it may one day dis­ap­pear or be sup­planted by one (or more) post-human spe­cies that might want to cre­ate sim­u­la­tions of their ancestors.

Human­ity as we know it may one day dis­ap­pear or be sup­planted by one (or more) post-human spe­cies that might want to cre­ate sim­u­la­tions of their ancest­ors – that is to say human beings with con­scious­ness, like us. But how do we know wheth­er we are the ori­gin­al human beings or already the sim­u­la­tions of a future society’s ancest­ors? Bostrom pro­posed a con­cep­tu­al frame­work in which to address this ques­tion and his sim­u­la­tion argu­ment con­tains three pro­pos­i­tions, one of which he reasoned must be true. Either:

1. human soci­et­ies invari­ably go extinct before reach­ing a stage where they are able to sim­u­late new realities;
2. even if they do reach this stage, they are unlikely to be inter­ested in sim­u­lat­ing a real­ity much sim­pler than their own;
3. the prob­ab­il­ity that we are liv­ing in a sim­u­la­tion is close to one.

Since the final out­come of Bostrom’s first two pro­pos­i­tions is that sim­u­la­tions do not exist, they can be col­lapsed into a single pro­pos­i­tion [1]. The tri­lemma thus becomes a dilemma in which there are now two possibilities:

1. a nat­ur­al non-sim­u­lated uni­verse (ours);
2. an “ori­gin­al” nat­ur­al uni­verse that spawns one or more sim­u­la­tions that may them­selves spawn fur­ther sim­u­la­tions, one of which would con­tain our universe.

In the absence of any oth­er inform­a­tion, both scen­ari­os should be con­sidered on an equal foot­ing accord­ing to a basic ten­et in stat­ist­ics – Laplace’s “Prin­ciple of Indif­fer­ence”, which states that in the absence of evid­ence, all hypo­theses should be con­sidered equally likely. But, the fact that the sim­u­lated hypo­thes­is neces­sar­ily con­tains one nat­ur­al uni­verse amongst the many sim­u­lated uni­verses means that there would be a slightly less than 50% chance that we live in a com­puter sim­u­la­tion. The reas­on for the slightly less than 50% chance is that it is impossible to prove wheth­er or not we are liv­ing in a sim­u­la­tion. Even if we were vir­tu­al beings, there would be no real evid­ence to prove it.

Anoth­er import­ant pre­cept of Bayesian stat­ist­ics, Occam’s razor (which states that the simplest explan­a­tion, all things being equal, is usu­ally the right one) is also dif­fi­cult to form­ally build into the sim­u­la­tion hypo­thes­is. This is because we don’t know how many sim­u­la­tions are plaus­ible and because we don’t really know how to math­em­at­ic­ally describe the com­plex­ity asso­ci­ated with each real­ity. So, while there is a less than 50% chance that we live in a sim­u­la­tion, this fig­ure should be treated as an abso­lute upper lim­it. Indeed, even when we gen­er­ously ignore the inher­ently overly-com­plex nature of the sim­u­la­tion hypo­thes­is, there is no way make the sim­u­la­tion odds bet­ter than 50%.

The main chal­lenge in such stud­ies is, simply, the lack of inform­a­tion. The only real fact we have to go on is that we exist. Even adding the extra con­di­tion that we ourselves haven’t launched a sim­u­la­tion barely affects the final outcome.

Say we did start sim­u­lat­ing real­it­ies, how­ever, and there were con­scious entit­ies in them that were unaware that they were liv­ing inside those sim­u­la­tions, then that would flip all the odds. This is because we would be chan­ging the ini­tial con­di­tion from a (nul­li­par­ous) real­ity that can­not give birth to new real­ties to a (parous) real­ity than can gen­er­ate oth­er real­it­ies. It would then become highly prob­able that we live in a sim­u­lated universe.

Nev­er­the­less, accord­ing to Bayesian stat­ist­ics, the most likely out­come of this scen­ario is that we live in a uni­verse where it’s not pos­sible to stim­u­late new realities.

This appar­ent para­dox is well described by the Amer­ic­an the­or­et­ic­al phys­i­cist Sean Car­roll⁷. He argues that if you have a hier­archy of (Incep­tion-like) real­it­ies in which each sim­u­la­tion launches its own sim­u­la­tion, then there would be a reduc­tion in com­pu­ta­tion­al abil­ity at each sub­sequent level. This means that each sim­u­lated uni­verse would be sim­pler than the uni­verse in which it was created.

So, while you would still be able to pro­duce sim­u­la­tions, and pre­sum­ably even very impress­ive sim­u­la­tions, the low­est levels in these wouldn’t have the soph­ist­ic­a­tion to host truly con­scious entit­ies. There is the pos­sib­il­ity, non­ethe­less, accord­ing to Car­roll, that we live in one of these “low levels of reality”.

Work­ing on such ideas is import­ant, espe­cially when we hear about the incred­ibly high “bil­lion-to-one odds” that we live in a non-sim­u­lated uni­verse often cited in the pop­u­lar cul­ture⁸. This fig­ure implies an incred­ible cer­tainty and was obtained by extra­pol­at­ing cur­rent com­puter trends and cap­ab­il­it­ies. This premise, how­ever, con­tains an inher­ent uncer­tainty if treated in a Bayesian frame­work: we can­not simply exclude the pos­sib­il­ity of a nat­ur­al uni­verse outright.

Per­haps we need to go from think­ing that liv­ing in a sim­u­la­tion is an inev­it­ab­il­ity to think­ing that it is a some­what unlikely situ­ation?⁹

Interview by Isabelle Dumé