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