AlexMennen(Alex Mennen)

Karma: 3,389
• I guess what I was try­ing to say is (al­though I think I’ve par­tially figured out what you meant; see next para­graph), cul­tural evolu­tion is a pro­cess that ac­quires adap­ta­tions slowly-ish and trans­mits pre­vi­ously-ac­quired adap­ta­tions to new or­ganisms quickly, while biolog­i­cal evolu­tion is a pro­cess that ac­quires adap­ta­tions very slowly and trans­mits pre­vi­ously-ac­quired adap­ta­tions to new or­ganisms quickly. You seem to be com­par­ing the rate at which cul­tural evolu­tion ac­quires adap­ta­tions to the rate at which biolog­i­cal evolu­tion trans­mits pre­vi­ously-ac­quired adap­ta­tions to new or­ganisms, and con­clud­ing that cul­tural evolu­tion is slower.

Re-read­ing the part of your post where you talked about AI take­off speeds, you ar­gue (which I hadn’t un­der­stood be­fore) that the rise of hu­mans was fast on an evolu­tion­ary timescale, and slow on a cul­tural timescale, so that if it was due to an evolu­tion­ary change, it must in­volve a small change that had a large effect on ca­pa­bil­ities, so that a large change will oc­cur very sud­denly if we mimic evolu­tion quickly, while if it was due to a cul­tural change, it was prob­a­bly a large change, so mimick­ing cul­ture quickly won’t pro­duce a large effect on ca­pa­bil­ities un­less it is ex­tremely quick.

This clar­ifies things, but I don’t agree with the claim. I think slow changes in the in­tel­li­gence of a species is com­pat­i­ble with fast changes in its ca­pa­bil­ities even if the changes are mainly in raw in­no­va­tive abil­ity rather than cul­tural learn­ing. In­no­va­tions can in­crease abil­ity to in­no­vate, caus­ing a pos­i­tive feed­back loop. A species could have high enough cul­tural learn­ing abil­ity for in­no­va­tions to be trans­mit­ted over many gen­er­a­tions with­out hav­ing the in­no­va­tive abil­ity to ever get the in­no­va­tions that will kick off this loop. Then, when they start slow­ing gain­ing in­no­va­tive abil­ity, the in­no­va­tions ac­cu­mu­lated into cul­tural knowl­edge grad­u­ally in­crease, un­til they reach the feed­back loop and the rate of in­no­va­tion be­comes more de­ter­mined by changes in pre-ex­ist­ing in­no­va­tions than by changes in raw in­no­va­tive abil­ity. There doesn’t even have to be any evolu­tion­ary changes in the pe­riod in which in­no­va­tion rate starts to get dra­matic.

If you don’t buy this story, then it’s not clear why the changes be­ing in cul­tural learn­ing abil­ity rather than in raw in­no­va­tive abil­ity would re­move the need for a dis­con­ti­nu­ity. After all, our cul­tural learn­ing abil­ity went from not giv­ing us much ad­van­tage over other an­i­mals to “ac­cu­mu­lat­ing de­ci­sive tech­nolog­i­cal dom­i­nance in an evolu­tion­ary eye­blink” in an evolu­tion­ary eye­blink (quo­ta­tion marks added for ease of pars­ing). Does this mean our abil­ity to learn from cul­ture must have greatly in­creased from a small change? You ar­gue in the post that there’s no clear can­di­date for what such a dis­con­ti­nu­ity in cul­tural learn­ing abil­ity could look like, but this seems just as true to me for raw in­no­va­tive abil­ity.

Per­haps you could ar­gue that it doesn’t mat­ter if there’s a sharp dis­con­ti­nu­ity in cul­tural learn­ing abil­ity be­cause you can’t learn from a cul­ture faster than the cul­ture learns things to teach you. In this case, yes, per­haps I would say that AI-driven cul­ture could make ad­vance­ments that look dis­con­tin­u­ous on a hu­man scale. Though I’m not en­tirely sure what that would look like, and I ad­mit it does sound kind of soft-take­offy.

• There’s more than one thing that you could mean by raw in­no­va­tive ca­pac­ity sep­a­rate from cul­tural pro­cess­ing abil­ity. First, you could mean some­one’s abil­ity to in­no­vate on their own with­out any di­rect help from oth­ers on the task at hand, but where they’re al­lowed to use skills that they pre­vi­ously ac­quired from their cul­ture. Se­cond, you could mean some­one’s coun­ter­fac­tual abil­ity to in­no­vate on their own if they hadn’t learned from cul­ture. You seem to be con­flat­ing these some­what, though mostly fo­cus­ing on the sec­ond?

The sec­ond is un­der­speci­fied, as you’d need to de­cide what coun­ter­fac­tual up­bring­ing you’re as­sum­ing. If you com­pare the cog­ni­tive perfor­mance of a hu­man raised by bears to the cog­ni­tive perfor­mance of a bear in the same cir­cum­stances, this is un­fair to the hu­man, since the bear is raised in cir­cum­stances that it is adapted for and the hu­man is not, just like com­par­ing the cog­ni­tive perfor­mance of a bear raised by hu­mans to that of a hu­man in the same cir­cum­stances would be un­fair to the bear. Though a hu­man raised by non-hu­mans would still make a more in­ter­est­ing com­par­i­son to non-hu­man an­i­mals than Ge­nie would, since Ge­nie’s en­vi­ron­ment is even less con­ducive to hu­man de­vel­op­ment (I bet most an­i­mals wouldn’t cog­ni­tively de­velop very well if they were kept im­mo­bi­lized in a locked room un­til ma­tu­rity ei­ther).

I think this makes the sec­ond no­tion less in­ter­est­ing than the first, as there’s a some­what ar­bi­trary de­pen­dence on the coun­ter­fac­tual en­vi­ron­ment. I guess the first no­tion is more rele­vant when try­ing to rea­son speci­fi­cally on ge­net­ics as op­posed to other fac­tors that in­fluence traits, but the sec­ond seems more rele­vant in other con­texts, since it usu­ally doesn’t mat­ter to what ex­tent some­one’s abil­ities were de­ter­mined by ge­net­ics or en­vi­ron­men­tal fac­tors.

I didn’t re­ally fol­low your ar­gu­ment for the rele­vance of this ques­tion to AI de­vel­op­ment. Why should raw in­no­va­tion abil­ity be more sus­cep­ti­ble to dis­con­tin­u­ous jumps than cul­tural pro­cess­ing abil­ity? Un­til I un­der­stand the sup­posed rele­vance to AI bet­ter, it’s hard for me to say which of the two no­tions is more rele­vant for this pur­pose.

I’d be very sur­prised if any ex­ist­ing non-hu­man an­i­mals are ahead of hu­mans by the first no­tion, and there’s a clear rea­son in this case why perfor­mance would cor­re­late strongly with so­cial learn­ing abil­ity: so­cial learn­ing will have helped peo­ple in the past de­velop skills that they keep in the pre­sent. Even for the sec­ond no­tion, though it’s a bit hard to say with­out pin­ning down the coun­ter­fac­tual more closely, I’d still ex­pect hu­mans to out­perform all other an­i­mals in some rea­son­able com­pro­mise en­vi­ron­ment that helps both de­velop but doesn’t in­volve them be­ing taught things that the non-hu­mans can’t fol­low. I think there are still rea­sons to ex­pect so­cial learn­ing abil­ity and raw in­no­va­tive ca­pa­bil­ity to be cor­re­lated even in this sense, be­cause higher gen­eral in­tel­li­gence will help for both; origi­nal dis­cov­ery and un­der­stand­ing things that are taught to you by oth­ers both re­quire some of the same cog­ni­tive tools.

• The­o­rem: Fuzzy be­liefs (as in https://​​www.al­ign­ment­fo­rum.org/​​posts/​​Ajcq9xWi2fmgn8RBJ/​​the-credit-as­sign­ment-prob­lem#X6fFvAHkxCPmQYB6v ) form a con­tin­u­ous DCPO. (At least I’m pretty sure this is true. I’ve only given proof sketches so far)

The rele­vant defi­ni­tions:

A fuzzy be­lief over a set is a con­cave func­tion such that (where is the space of prob­a­bil­ity dis­tri­bu­tions on ). Fuzzy be­liefs are par­tially or­dered by . The in­equal­ities re­verse be­cause we want to think of “more spe­cific”/​”less fuzzy” be­liefs as “greater”, and these are the func­tions with lower val­ues; the most spe­cific/​least fuzzy be­liefs are or­di­nary prob­a­bil­ity dis­tri­bu­tions, which are rep­re­sented as the con­cave hull of the func­tion as­sign­ing 1 to that prob­a­bil­ity dis­tri­bu­tion and 0 to all oth­ers; these should be the max­i­mal fuzzy be­liefs. Note that, be­cause of the or­der-re­ver­sal, the supre­mum of a set of func­tions refers to their poin­t­wise in­fi­mum.

A DCPO (di­rected-com­plete par­tial or­der) is a par­tial or­der in which ev­ery di­rected sub­set has a supre­mum.

In a DCPO, define to mean that for ev­ery di­rected set with , such that . A DCPO is con­tin­u­ous if for ev­ery , .

Lemma: Fuzzy be­liefs are a DCPO.

Proof sketch: Given a di­rected set , is con­vex, and . Each of the sets in that in­ter­sec­tion are non-empty, hence so are finite in­ter­sec­tions of them since is di­rected, and hence so is the whole in­ter­sec­tion since is com­pact.

Lemma: iff is con­tained in the in­te­rior of and for ev­ery such that , .

Proof sketch: If , then , so by com­pact­ness of and di­rect­ed­ness of , there should be such that . Similarly, for each such that , there should be such that . By com­pact­ness, there should be some finite sub­set of such that any up­per bound for all of them is at least .

Lemma: .

Proof: clear?

AlexMen­nen’s Shortform

8 Dec 2019 4:51 UTC
7 points
• The part about deriva­tives might have seemed a lit­tle odd. After all, you might think, is a dis­crete set, so what does it mean to take deriva­tives of func­tions on it. One an­swer to this is to just differ­en­ti­ate sym­bol­i­cally us­ing polyno­mial differ­en­ti­a­tion rules. But I think a bet­ter an­swer is to re­mem­ber that we’re us­ing a differ­ent met­ric than usual, and isn’t dis­crete at all! In­deed, for any num­ber , , so no points are iso­lated, and we can define differ­en­ti­a­tion of func­tions on in ex­actly the usual way with limits.

• The the­o­rem: where is rel­a­tively prime to an odd prime and , is a square mod iff is a square mod and is even.

The real meat of the the­o­rem is the case (i.e. a square mod that isn’t a mul­ti­ple of is also a square mod . Deriv­ing the gen­eral case from there should be fairly straight­for­ward, so let’s fo­cus on this spe­cial case.

Why is it true? This ques­tion has a sur­pris­ing an­swer: New­ton’s method for find­ing roots of func­tions. Speci­fi­cally, we want to find a root of , ex­cept in in­stead of .

To adapt New­ton’s method to work in this situ­a­tion, we’ll need the p-adic ab­solute value on : for rel­a­tively prime to . This has lots of prop­er­ties that you should ex­pect of an “ab­solute value”: it’s pos­i­tive ( with only when ), mul­ti­plica­tive (), sym­met­ric (), and satis­fies a tri­an­gle in­equal­ity (; in fact, we get more in this case: ). Be­cause of pos­i­tivity, sym­me­try, and the tri­an­gle in­equal­ity, the p-adic ab­solute value in­duces a met­ric (in fact, ul­tra­met­ric, be­cause of the strong ver­sion of the tri­an­gle in­equal­ity) . To vi­su­al­ize this dis­tance func­tion, draw gi­ant cir­cles, and sort in­te­gers into cir­cles based on their value mod . Then draw smaller cir­cles in­side each of those gi­ant cir­cles, and sort the in­te­gers in the big cir­cle into the smaller cir­cles based on their value mod . Then draw even smaller cir­cles in­side each of those, and sort based on value mod , and so on. The dis­tance be­tween two num­bers cor­re­sponds to the size of the small­est cir­cle en­com­pass­ing both of them. Note that, in this met­ric, con­verges to .

Now on to New­ton’s method: if is a square mod , let be one of its square roots mod . ; that is, is some­what close to be­ing a root of with re­spect to the p-adic ab­solute value. , so ; that is, is steep near . This is good, be­cause start­ing close to a root and the slope of the func­tion be­ing steep enough are things that helps New­ton’s method con­verge; in gen­eral, it might bounce around chaot­i­cally in­stead. Speci­fi­cally, It turns out that, in this case, is ex­actly the right sense of be­ing close enough to a root with steep enough slope for New­ton’s method to work.

Now, New­ton’s method says that, from , you should go to . is in­vert­ible mod , so we can do this. Now here’s the kicker: , so . That is, is closer to be­ing a root of than is. Now we can just iter­ate this pro­cess un­til we reach with , and we’ve found our square root of mod .

Ex­er­cise: Do the same thing with cube roots. Then with roots of ar­bi­trary polyno­mi­als.

• The im­pres­sive part is get­ting re­in­force­ment learn­ing to work at all in such a vast state space

It seems to me that that is AGI progress? The real world has an even vaster state space, af­ter all. Get­ting things to work in vast state spaces is a nec­es­sary pre-con­di­tion to AGI.

• Ok, I see what you mean about in­de­pen­dence of ir­rele­vant al­ter­na­tives only be­ing a real co­her­ence con­di­tion when the prob­a­bil­ities are ob­jec­tive (or oth­er­wise known to be equal be­cause they come from the same source, even if there isn’t an ob­jec­tive way of say­ing what their com­mon prob­a­bil­ity is).

But I dis­agree that this makes VNM only ap­pli­ca­ble to set­tings in which all sources of un­cer­tainty have ob­jec­tively cor­rect prob­a­bil­ities. As I said in my pre­vi­ous com­ment, you only need there to ex­ist some source of ob­jec­tive prob­a­bil­ities, and you can then use prefer­ences over lot­ter­ies in­volv­ing ob­jec­tive prob­a­bil­ities and prefer­ences over re­lated lot­ter­ies in­volv­ing other sources of un­cer­tainty to de­ter­mine what prob­a­bil­ity the agent must as­sign for those other sources of un­cer­tainty.

Re: the differ­ence be­tween VNM and Bayesian ex­pected util­ity max­i­miza­tion, I take it from the word “Bayesian” that the way you’re sup­posed to choose be­tween ac­tions does in­volve first com­ing up with prob­a­bil­ities of each out­come re­sult­ing from each ac­tion, and from “ex­pected util­ity max­i­miza­tion”, that these prob­a­bil­ities are to be used in ex­actly the way the VNM the­o­rem says they should be. Since the VNM the­o­rem does not make any as­sump­tions about where the prob­a­bil­ities came from, these still sound es­sen­tially the same, ex­cept with Bayesian ex­pected util­ity max­i­miza­tion be­ing framed to em­pha­size that you have to get the prob­a­bil­ities some­how first.

• I think you’re un­der­es­ti­mat­ing VNM here.

only two of those four are rele­vant to co­her­ence. The main prob­lem is that the ax­ioms rele­vant to co­her­ence (acyclic­ity and com­plete­ness) do not say any­thing at all about probability

It seems to me that the in­de­pen­dence ax­iom is a co­her­ence con­di­tion, un­less I mi­s­un­der­stand what you mean by co­her­ence?

cor­rectly point out prob­lems with VNM

I’m cu­ri­ous what prob­lems you have in mind, since I don’t think VNM has prob­lems that don’t ap­ply to similar co­her­ence the­o­rems.

VNM util­ity stipu­lates that agents have prefer­ences over “lot­ter­ies” with known, ob­jec­tive prob­a­bil­ities of each out­come. The prob­a­bil­ities are as­sumed to be ob­jec­tively known from the start. The Bayesian co­her­ence the­o­rems do not as­sume prob­a­bil­ities from the start; they de­rive prob­a­bil­ities from the co­her­ence crite­ria, and those prob­a­bil­ities are spe­cific to the agent.

One can con­struct lot­ter­ies with prob­a­bil­ities that are pretty well un­der­stood (e.g. flip­ping coins that we have ac­cu­mu­lated a lot of ev­i­dence are fair), and you can re­strict at­ten­tion to lot­ter­ies only in­volv­ing un­cer­tainty com­ing from such sources. One may then get prob­a­bil­ities for other, less well-un­der­stood sources of un­cer­tainty by com­par­ing prefer­ences in­volv­ing such un­cer­tainty to prefer­ences in­volv­ing easy-to-quan­tify un­cer­tainty (e.g. if A is preferred to B, and you’re in­differ­ent be­tween 60%A+40%B and “A if X, B if not-X”, then you as­sign prob­a­bil­ity 60% to X. Per­haps not quite as philo­soph­i­cally satis­fy­ing as de­riv­ing prob­a­bil­ities from scratch, but this doesn’t seem like a fatal flaw in VNM to me.

I do not ex­pect agent-like sys­tems in the wild to be pushed to­ward VNM ex­pected util­ity max­i­miza­tion. I ex­pect them to be pushed to­ward Bayesian ex­pected util­ity max­i­miza­tion.

I un­der­stood those as be­ing syn­onyms. What’s the differ­ence?

• I do, how­ever, be­lieve that the sin­gle step co­op­er­ate-defect game which they use to come up with their fac­tors seems like a very sim­ple model for what will be a very com­plex sys­tem of in­ter­ac­tions. For ex­am­ple, AI de­vel­op­ment will take place over time, and it is likely that the same com­pa­nies will con­tinue to in­ter­act with one an­other. Iter­ated games have very differ­ent dy­nam­ics, and I hope that fu­ture work will ex­plore how this would af­fect their cur­rent recom­men­da­tions, and whether it would yield new ap­proaches to in­cen­tiviz­ing co­op­er­a­tion.

It may be difficult for com­pa­nies to get ac­cu­rate in­for­ma­tion about how care­ful their com­peti­tors are be­ing about AI safety. An iter­ated game in which play­ers never learn what the other play­ers did on pre­vi­ous rounds is the same as a one-shot game. This points to a sixth fac­tor that in­creases chance of co­op­er­a­tion on safety: high trans­parency, so that com­pa­nies may ver­ify their com­peti­tors’ co­op­er­a­tion on safety. This is closely re­lated to high trust.

• I ob­ject to the fram­ing of the bomb sce­nario on the grounds that low prob­a­bil­ities of high stakes are a source of cog­ni­tive bias that trip peo­ple up for rea­sons hav­ing noth­ing to do with FDT. Con­sider the fol­low­ing de­ci­sion prob­lem: “There is a but­ton. If you press the but­ton, you will be given $100. Also, press­ing the but­ton has a very small (one in a trillion trillion) chance of caus­ing you to burn to death.” Most peo­ple would not touch that but­ton. Us­ing the same pay­offs and prob­a­bil­ies in a sce­nario to challenge FDT thus ex­ploits cog­ni­tive bias to make FDT look bad. A bet­ter sce­nario would be to re­place the bomb with some­thing that will fine you$1000 (and, if you want, also in­crease the chance of of er­ror).

But then, it seems to me, that FDT has lost much of its ini­tial mo­ti­va­tion: the case for one-box­ing in New­comb’s prob­lem didn’t seem to stem from whether the Pre­dic­tor was run­ning a simu­la­tion of me, or just us­ing some other way to pre­dict what I’d do.

I think the cru­cial differ­ence here is how eas­ily you can cause the pre­dic­tor to be wrong. In the case where the pre­dic­tor simu­lates you, if you two-box, then the pre­dic­tor ex­pects you to two-box. In the case where the pre­dic­tor uses your na­tion­al­ity to pre­dict your be­hav­ior, Scots usu­ally one-box, and you’re Scot­tish, if you two-box, then the pre­dic­tor will still ex­pect you to one-box be­cause you’re Scot­tish.

But now sup­pose that the path­way by which S causes there to be money in the opaque box or not is that an­other agent looks at S...

I didn’t think that was sup­posed to mat­ter at all? I haven’t ac­tu­ally read the FDT pa­per, and have mostly just been op­er­at­ing un­der the as­sump­tion that FDT is ba­si­cally the same as UDT, but UDT didn’t build in any de­pen­dency on ex­ter­nal agents, and I hadn’t heard about any such de­pen­dency be­ing in­tro­duced in FDT; it would sur­prise me if it did.

• 16 Sep 2019 2:15 UTC
LW: 4 AF: 2
AF
I don’t know if I’m a simu­la­tion or a real per­son.

A pos­si­ble re­sponse to this ar­gu­ment is that the pre­dic­tor may be able to ac­cu­rately pre­dict the agent with­out ex­plic­itly simu­lat­ing them. A pos­si­ble counter-re­sponse to this is to posit that any suffi­ciently ac­cu­rate model of a con­scious agent is nec­es­sar­ily con­scious it­self, whether the model takes the form of an ex­plicit simu­la­tion or not.

• I think the coun­ter­fac­tu­als used by the agent are the cor­rect coun­ter­fac­tu­als for some­one else to use while rea­son­ing about the agent from the out­side, but not the cor­rect coun­ter­fac­tu­als for the agent to use while de­cid­ing what to do. After all, know­ing the agent’s source code, if you see it start to cross the bridge, it is cor­rect to in­fer that it’s rea­son­ing is in­con­sis­tent, and you should ex­pect to see the troll blow up the bridge. But while de­cid­ing what to do, the agent should be able to rea­son about purely causal effects of its coun­ter­fac­tual be­hav­ior, screen­ing out other log­i­cal im­pli­ca­tions.

Also, coun­ter­fac­tu­als which pre­dict that the bridge blows up seem to be say­ing that the agent can con­trol whether PA is con­sis­tent or in­con­sis­tent.

Disagree that that’s what’s hap­pen­ing. The link be­tween the con­sis­tency of the rea­son­ing sys­tem and the be­hav­ior of the agent is be­cause the con­sis­tency of the rea­son­ing sys­tem con­trols the agent’s be­hav­ior, rather than the other way around. Since the agent is se­lect­ing out­comes based on their con­se­quences, it does make sense to speak of the agent choos­ing ac­tions to some ex­tent, but I think speak­ing of log­i­cal im­pli­ca­tions of the agent’s ac­tions on the con­sis­tency of for­mal sys­tems as “con­trol­ling” the con­sis­tency of the for­mal sys­tem seems like an in­ap­pro­pri­ate at­tri­bu­tion of agency to me.

• I sup­pose why that’s not why we’re min­i­miz­ing de­ter­mi­nant, but rather frobe­nius norm.

Yes, al­though an­other rea­son is that the de­ter­mi­nant is only defined if the in­put and out­put spaces have the same di­men­sion, which they typ­i­cally don’t.

• First, a vec­tor can be seen as a list of num­bers, and a ma­trix can be seen as an or­dered list of vec­tors. An or­dered list of ma­tri­ces is… a ten­sor of or­der 3. Well not ex­actly. Ap­par­ently some peo­ple are ac­tu­ally dis­ap­pointed with the term ten­sor be­cause a ten­sor means some­thing very spe­cific in math­e­mat­ics already and isn’t just an or­dered list of ma­tri­ces. But what­ever, that’s the term we’re us­ing for this blog post at least.

It’s true that ten­sors are some­thing more spe­cific than mul­ti­di­men­sional ar­rays of num­bers, but Ja­co­bi­ans of func­tions be­tween ten­sor spaces (that be­ing what you’re us­ing the mul­ti­di­men­sional ar­rays for here) are, in fact, ten­sors.

• What this means is for the Ja­co­bian is that the de­ter­mi­nant tells us how much space is be­ing squished or ex­panded in the neigh­bor­hood around a point. If the out­put space is be­ing ex­panded a lot at some in­put point, then this means that the neu­ral net­work is a bit un­sta­ble at that re­gion, since minor al­ter­a­tions in the in­put could cause huge dis­tor­tions in the out­put. By con­trast, if the de­ter­mi­nant is small, then some small change to the in­put will hardly make a differ­ence to the out­put.

This isn’t quite true; the de­ter­mi­nant be­ing small is con­sis­tent with small changes in in­put mak­ing ar­bi­trar­ily large changes in out­put, just so long as small changes in in­put in a differ­ent di­rec­tion make suffi­ciently small changes in out­put.

The frobe­nius norm is noth­ing com­pli­cated, and is re­ally just a way of de­scribing that we square all of the el­e­ments in the ma­trix, take the sum, and then take the square root of this sum.

An al­ter­na­tive defi­ni­tion of the frobe­nius norm bet­ter high­lights its con­nec­tion to the mo­ti­va­tion of reg­u­lariz­ing the Ja­co­bian frobe­nius in terms of limit­ing the ex­tent to which small changes in in­put can cause large changes in out­put: The frobe­nius norm of a ma­trix J is the root-mean-square of |J(x)| over all unit vec­tors x.

• “Con­trol­ling which Everett branch you end up in” is the wrong way to think about de­ci­sions, even if many-wor­lds is true. Brains don’t ap­pear to rely much on quan­tum ran­dom­ness, so if you make a cer­tain de­ci­sion, that prob­a­bly means that the over­whelming ma­jor­ity of iden­ti­cal copies of you make the same de­ci­sion. You aren’t con­trol­ling which copy you are; you’re con­trol­ling what all of the copies do. And even if quan­tum ran­dom­ness does end of mat­ter­ing in de­ci­sions, so that a non-triv­ial pro­por­tion of copies of you make differ­ent de­ci­sions from each other, then you would still pre­sum­ably want a high pro­por­tion of them to make good de­ci­sions; you can do your part to bring that about by mak­ing good de­ci­sions your­self.

• Con­sider read­ing a real physi­cist’s take on the is­sue

This seems phrased to sug­gest that her view is “the real physi­cist view” on the mul­ti­verse. You could also read what Max Teg­mark or David Deutsch, for in­stance, have to say about mul­ti­verse hy­pothe­ses and get a “real physi­cist’s” view from them.

Also, she doesn’t ac­tu­ally say much in that blog post. She points out that when she says that mul­ti­verse hy­pothe­ses are un­scien­tific, she doesn’t mean that they’re false, so this doesn’t seem es­pe­cially use­ful to some­one who wants to know whether there ac­tu­ally is a mul­ti­verse, or is in­ter­ested in the con­se­quences thereof. She says “there is no rea­son to think we live in such mul­ti­verses to be­gin with”, but pro­po­nents of mul­ti­verse hy­pothe­ses have given rea­sons to sup­port their views, which she doesn’t ad­dress.

• #1 (at the end) sounds like com­plex­ity the­ory.

Some of what von Neu­mann says makes it sound like he’s in­ter­ested in a math­e­mat­i­cal foun­da­tion for ana­log com­put­ing, which I think has been done by now.