# We live in an unbreakable simulation: a mathematical proof.

Ac­tu­ally, the ti­tle is a sen­sa­tion­al­ist lie de­signed to at­tract at­ten­tion. I have no proof. Ob­vi­ously. I’m not a math­e­mat­i­cian. But if I did, it would go some­thing like the fol­low­ing.

Step 1: As­sume that there are ul­ti­mate laws of physics gov­ern­ing ev­ery­thing in the world. Say, the wave func­tion of the Uni­verse, whose knowl­edge al­lows one to know the Mul­ti­verse, as it was, is or will be. Or some other set of laws.

Step 2: Write these laws as a math­e­mat­i­cally con­sis­tent for­mal sys­tem rep­re­sent­ing some­thing akin to the Teg­mark Level IV Ul­ti­mate en­sem­ble.

Step 3: By Godel’s in­com­plete­ness, there are some the­o­rems in this for­mal sys­tem that can­not be proven.

Step 4: By con­struc­tion, these the­o­rems cor­re­spond to phys­i­cal laws whose ori­gins must for­ever re­main a mys­tery to those in­side the Mul­ti­verse, be­cause they are a part of it.

Step 5: The con­sis­tency of our Mul­ti­verse can be proven in a for­mal sys­tem which de­scribes phys­i­cal laws of a larger world, in which our Mul­ti­verse is a small part of, es­sen­tially a simu­la­tion.

Step 6: Since we can­not de­ter­mine the ori­gins of our own physics, we can­not figure out a way to break out of our simu­la­tion.

On the bright side, there is a Corol­lary: Every level above us is also a simu­la­tion, so we are not alone!

• I’m down­vot­ing pri­mar­ily to dis­cour­age de­liber­ately sen­sa­tion­al­ist ti­tles. I don’t want to start see­ing “What this AI Gate­keeper did will shock you!” and “Five rea­sons why MWI will show you how ev­ery­thing you thought you knew about quan­tum me­chan­ics is a lie!” and “Th­ese ten effec­tive al­tru­ists will re­store your faith in hu­man­ity!”

• By all means, though I would to­tally read “What this AI Gate­keeper did will shock you!”

• Got the AI to let him out of the box.

• What a let­down.

• I’m sens­ing some kind of corol­lary of the law that “any head­line that ends with a ques­tion mark can be an­swered with “no”″ (para­phrased from mem­ory).

• Aside from the sen­sa­tion­al­ism, I re­mark that you’re (re)defin­ing “simu­la­tion” to mean “world whose be­havi­our is equiv­a­lent to that of a simu­la­tion” and that the ax­iom you adopt in step 1 already trans­par­ently im­plies that our world is such a world. So you kinda do have a proof—but it’s of the form “Sup­pose p. Then it fol­lows that p.”.

• Step 3: By Godel’s in­com­plete­ness, there are some the­o­rems in this for­mal sys­tem that can­not be proven.

No. That is not what Godel’s in­com­plete­ness the­o­rem says.

• Step 5: The con­sis­tency of our Mul­ti­verse can be proven in a for­mal sys­tem which de­scribes phys­i­cal laws of a larger world, in which our Mul­ti­verse is a small part of, es­sen­tially a simu­la­tion.

Are you as­sum­ing that ev­ery pos­si­ble mul­ti­verse ex­ists? If so, it seems pretty ob­vi­ous that there’s a uni­verse that con­tains ours. If not, you still have to prove that the mul­ti­verse given here ex­ists.

• None of the replies to this post ac­tu­ally ad­dress the cru­cial part of the ar­gu­ment: the step from the ex­is­tence of math­e­mat­i­cal truths be­yond the reach of a spe­cific for­mal­iza­tion of math­e­mat­i­cal rea­son­ing, to the ex­is­tence of a re­al­ity be­yond or out­side a spe­cific phys­i­cal the­ory of ev­ery­thing, on the grounds that a math­e­mat­i­cal the­ory of physics must be sub­ject to Goedelian in­com­plete­ness.

• Given the ex­tremely nega­tive re­ac­tion, I will delete this post to­mor­row, un­less some­one offers a good rea­son not to.

• It may serve as a helpful ex­am­ple to other users of what sorts of posts re­ceive nega­tive feed­back.

• I sus­pect based on how my com­ment is voted up that much of the down­vot­ing isn’t the con­tent so much as the de­liv­ery.

• I also think that is the cause of al­most all the down­votes, the num­bers match well. The ideas pre­sented are about in­ter­est­ing and rele­vant top­ics so po­ten­tially worth­while even if the spe­cific proof does not hold up. If not for the ap­pear­ance of cer­tainty (esp. “math­e­mat­i­cal proof”) where you should have been offer­ing it up as some­thing you’d like thoughts on (esp. if you had spe­cific ques­tions, pointed out parts you were less sure about, etc) I would likely have up­voted, as is I only didn’t down­vote be­cause it seems you’ve lost more than enough karma for this already and it would feel like kick­ing a dead horse. I’m sure by now any­one who sees this will re­al­ize click­bait ti­tles are not a great way to get points on less­wrong.

• I ex­pected at least one re­ply of the form “your ar­gu­ment sucks, but let me try to steel­man this one part of it...” but alas.

• Be­cause it is already down­voted to in­vis for any­one who cares, and some of us found it mildly amus­ing.

• Quick search of “define simu­la­tion” yields this:

Si­mu­la­tion is the imi­ta­tion of the op­er­a­tion of a real-world pro­cess or sys­tem over time.

You say ( I para­phrase): We live in an un­break­able simu­la­tion and can’t break out, but so does ev­ery level above us. And pre­sum­ably ev­ery level be­low us as well.

So I might ask, a simu­la­tion of what? A simu­la­tion of some re­al­ity that is not a simu­la­tion? But I thought you just said ev­ery level is an un­break­able simu­la­tion.

So I might ask, what is a simu­la­tion, or what do you mean by a simu­la­tion? Be­cause in my think­ing, if you’re simu­la­tion is not a simu­la­tion of some­thing else, then it is re­al­ity. So we live in a uni­verse that has phys­i­cal laws, which means it goes clunk­ing along ac­cord­ing to rules we did not write and can­not change. To you that sounds like a simu­la­tion, but to me, in the ab­sence of it be­ing a simu­la­tion of some­thing else, it sounds like re­al­ity.

• Right, a good ques­tion. I did not mean a simu­la­tion of some­thing, rather “let’s set up some rules and see what hap­pens”. In the same sense that the Con­way’s Game of Life is a simu­la­tion of life. And yes, to those in­side it is re­al­ity. And to those out­side it is a small sub­set of re­al­ity. And my origi­nal point was that those in­side can po­ten­tially in­fer that there must be some­thing out­side by hit­ting the limit of what they can ex­plain. But they have no hope of break­ing out. This last ar­gu­ment, of course, re­lies on the ten­u­ous as­sump­tion of the phys­i­cal laws be­ing math­e­mat­i­cal struc­tures and ev­ery event in the world be­ing, in essence, a the­o­rem.

• Cool enough.

Am I cor­rect that you sug­gest an in­finite regress, or rather progress? That ev­ery higher level is also a rule-fol­low­ing game set up as a sub­set of a (pre­sum­ably) yet more com­plex level above it? And that there is no end to this pro­gres­sion, no top level?

• I did not mean to sug­gest it when I started writ­ing the origi­nal post, but the logic, flawed as it is, seems to be point­ing that way.

• You can nei­ther prove nor dis­prove that we are in a simu­la­tion, just as you can nei­ther prove nor dis­prove the ex­is­tence of God. In both cases, you can­not come up with a mea­surable ex­per­i­ment, your claim is not falsifi­able, so you can­not use the sci­en­tific method to prove or dis­prove it, and the dis­cus­sion will in­evitably lead to an ar­gu­ment about se­man­tics: “how do you define simu­la­tion”, “how do you define god”, “how do you define define”, etc.

Al­most all similar ar­gu­ments I wit­nessed ended in an ar­gu­ment about se­man­tics, where one came up with his own defi­ni­tion of a term and tried to prove or dis­prove it, in­stead of fo­cus­ing on a com­monly ac­cepted defi­ni­tions agreed by both par­ties.

• Pre­sent an ar­gu­ment as a proof, or an out­line as a proof, and math­e­mat­i­ci­ans will take that as an in­vi­ta­tion to tear it to shreds.

I hear them growl­ing now.