# [Question] What shape has mindspace?

Episte­molog­i­cal sta­tus: Bab­bling.

Let map each mind in mindspace to how al­igned it is. We are try­ing to op­ti­mize . To that end, lem­mata are helpful which talk about the shape of mindspace. That’s why we try to call it a space even be­fore defin­ing what cat­e­gory it lives in.

To op­ti­mize a func­tion, start with a di­verse enu­mer­a­tion of its do­main. The de­on­tolog­i­cal enu­mer­a­tion cov­ers all oth­ers with con­stant-fac­tor over­head, but the con­se­quen­tial­ist enu­mer­a­tion gives us more prop­er­ties to work with.

Every mind has an im­plicit util­ity func­tion . fac­tors through as a func­tion, but not as a con­tin­u­ous func­tion, let alone a -mor­phism. That’s why we’ve re­cently moved away from ex­plicit util­ity max­i­miz­ers.

Use math­e­mat­i­cal lan­guage to tell our story! Then we might guess where it’s go­ing.

• I did some work in this di­rec­tion when I wrote about phe­nomenolog­i­cal com­plex­ity classes. I don’t lay it out in much de­tail in that post, but I be­lieve we can build on the work I do there to con­struct a topol­ogy of mindspace based on the as­sump­tion of a higher-or­der the­ory of con­scious­ness and a for­mal model of the struc­ture of con­scious­ness grounded in in­ten­tion­al­ity by (and here’s where I’m not sure what model will re­ally work) pos­si­bly treat­ing minds as sets within a topolog­i­cal space or as points on man­i­folds and then be­ing able to say some­thing about the minds we do and don’t find in topolog­i­cal spaces with par­tic­u­lar prop­er­ties.

Alas this is all cur­rently spec­u­la­tion and I haven’t needed to go fur­ther than point­ing in this gen­eral di­rec­tion to do any of the work I care about, but it is at least one start­ing point to­wards work in this di­rec­tion.

• I’m scep­ti­cal that whether a mind is al­igned has any­thing to do with whether it is con­scious.

• Sure, but that is­sue is ir­rele­vant to the ques­tion you’re ask­ing. You can dis­agree with how I choose to con­vert “con­scious” into a tech­ni­cal term from a folk term and even if you agree with my con­ver­sion per­haps dis­agree with whether or not some­thing must be con­scious in that sense to be al­igned, but you asked about mindspace and those doc­u­ments, al­though driv­ing at other pur­poses, lay out some back­ground that could be used to ap­proach the ques­tion.

• From what I see, the phe­nomenolog­i­cal com­plex­ity classes sep­a­rate minds based on what they are think­ing about, while al­ign­ment de­pends on what they are try­ing to do.

treat­ing minds as sets within a topolog­i­cal space

If a mind is a topolog­i­cal space equipped with a sub­set, what sort of mind would the set be­ing full im­ply?

• If a mind is a topolog­i­cal space equipped with a sub­set, what sort of mind would the set be­ing full im­ply?

That I’m not sure, as I haven’t worked this out in much de­tail. I just sort of have a vague math­e­mat­i­cal in­tu­ition that it might be the right sort of way to model it (n.b. I dropped out of a math phd af­ter 6 years to do a startup, if that’s some rough guide to how much to trust my math­e­mat­i­cal in­tu­ition).

For what it’s worth, here’s some notes I found that I wrote about this a while ago. I make no promises that any of this makes any sense or that I would still agree with any of it, but it is what I wrote about it a while ago:

### Math­e­mat­i­cal Foun­da­tion of Phenomenology

So that phe­nomenolog­i­cal com­plex­ity classes are ap­pli­ca­ble to as many uni­verses as pos­si­ble, in­clud­ing our own, it has a rigor­ous math­e­mat­i­cal foun­da­tion that makes as few as­sump­tions as pos­si­ble and eas­ily trans­lates into the stan­dard lan­guage of phe­nomenol­ogy. That said, it is not a the­ory of ev­ery­thing, and so sup­poses that

• the uni­verse is made of stuff in con­figu­ra­tions called states that are re­lated to each other by cau­sa­tion,

• math­e­mat­ics can be ap­plied to stuff, states, and cau­sa­tion,

• and states can be par­tially or­dered by cau­sa­tion.

Let pro­cess de­note a set of states par­tially or­dered by cau­sa­tion. Pro­cesses in­clude sim­ple phys­i­cal pro­cesses mod­eled by atoms and quarks, stochas­tic pro­cesses like Brow­n­ian mo­tion and waves, mechanis­tic pro­cesses like lev­ers and clocks, phe­nomenolog­i­cal pro­cesses like cats and hu­mans, so­cial pro­cesses like or­ga­ni­za­tions and friend­ships, and a uni­ver­sal pro­cess that in­cludes all states and which we re­fer to as the uni­verse, re­al­ity, or the world. Every pro­cess is a sub­set of the uni­verse, in­clud­ing the empty pro­cess that con­tains no state.

We can then con­struct a topolog­i­cal space, called pro­cess space, on the sub­set pro­cesses of the uni­verse where

• ev­ery pro­cess, in­clud­ing the uni­ver­sal pro­cess and the empty pro­cess, is a mem­ber of the topol­ogy,

• the union of pro­cesses is it­self a pro­cess,

• and the finite in­ter­sec­tion of pro­cesses is it­self a pro­cess.

Pro­cess space, be­ing a topol­ogy, au­to­mat­i­cally gives us a lot of con­structs to work with. Each pro­cess has an in­te­rior defined as the pro­cess con­tain­ing it­self and all the pro­cesses within it. We can fur­ther define filters in pro­cess space as the par­tial or­der­ing of pro­cesses by sub­set, and then the clo­sure of a pro­cess will be all the pro­cesses within the limit of the filters with the pro­cess’s in­te­rior as their base. Th­ese defi­ni­tions are re­spec­tively analo­gous to sub­ject, ex­pe­rience, and con­text in the stan­dard ter­minol­ogy of phe­nomenol­ogy, but are strictly on­tolog­i­cal and lack con­found­ing tele­olog­i­cal mean­ings. We’ll use these on­tolog­i­cal terms in the re­main­der of the in­tro­duc­tion for pre­ci­sion but switch the more com­mon ter­minol­ogy in the di­alec­tic for read­abil­ity.

Pro­cesses may con­tain within them par­tial in­for­ma­tion about their filters in their par­tially or­der set of states. This is pos­si­ble be­cause par­tial or­der­ing on filters

Phenomenol­ogy is the study of pro­cess filters, and the filters on a pro­cess are closed un­der finite in­ter­sec­tion, which is to say that the com­mon­al­ities of any two ex­pe­riences is it­self an ex­pe­rience, and up­wards closed un­der sub­set, which means any part of an ex­pe­rience is it­self an ex­pe­rience. Then we can un­der­stand the largest filter on a pro­cess’s in­te­rior, which is to say the filter that can­not be made any larger and still have the pro­cess’s in­te­rior as its base, as the prin­ci­pal ul­tra­filter on the pro­cess’s in­te­rior or sim­ply the pro­cess’s ul­tra­filter. It triv­ially fol­lows that a pro­cess’s ul­tra­filter con­tains ev­ery filter on the pro­cess as a sub­set, thus a pro­cess’s ul­tra­filter can be un­der­stood as the to­tal­ity of a sub­ject’s ex­pe­rience.

Thus far our the­ory is , and so when we talk about a pro­cess’s ul­tra­filter we are talk­ing about all the ex­pe­riences a sub­ject might or will have, de­pend­ing on the na­ture of causal­ity. Yet each filter that is not it­self the ul­tra­filter has su­per­sets, which we might call “fu­ture” ex­pe­riences. Since we are our­selves pro­cesses em­bed­ded in the topolog­i­cal space, at any “mo­ment” of ex­pe­rience we have “fu­ture” ex­pe­riences, and so when we talk about a pro­cess’s ul­tra­filter it’s use­ful to have a no­tion of the ul­tra­filter in time for uni­verses like our own where the state of stuff is grouped in par­tially or­dered sub­sets of the power set of state sets that ad­mit a no­tion of “be­fore” via sub­set, “af­ter” via su­per­set, and “now” by choos­ing an ar­bi­trary set as refer­ence point.

• Isn’t pro­cess space just dis­crete, be­cause ev­ery sub­set of a pro­cess, a set par­tially or­dered by cau­sa­tion, is par­tially or­dered by cau­sa­tion, so a pro­cess? Topol­ogy doesn’t give you much if you don’t re­strict which sets are open.

Each pro­cess has an in­te­rior defined as the pro­cess con­tain­ing it­self and …

Isn’t this a type er­ror? Pro­cesses con­tain states, not pro­cesses.