riceissa

• riceissa 28 Oct 2014 7:52 UTC

  31 points

  on: 2014 Less Wrong Cen­sus/​Survey

  I took the sur­vey.

• riceissa 19 Nov 2018 2:33 UTC

  14 points

  AF

  on: Topolog­i­cal Fixed Point Exercises

  My solu­tion for #3:

  Define $g:[0,1]\to R$ by $g\left(x\right)=f\left(x\right)-x$. We know that $g$ is con­tin­u­ous be­cause $f$ and the iden­tity map both are, and by the limit laws. Ap­ply­ing the in­ter­me­di­ate value the­o­rem (prob­lem #2) we see that there ex­ists $x\in [0,1]$ such that $g\left(x\right)=0$. But this means $f\left(x\right)=x$, so we are done.

  Coun­terex­am­ple for the open in­ter­val: con­sider $f:(0,1)\to (0,1)$ defined by $f\left(x\right)=x/2$. First, we can ver­ify that if $0<x<1$ then $0<x/2<1/2<1$, so $f$ in­deed maps to $(0,1)$. To see that there is no fixed point, note that the only solu­tion to $x/2=x$ in $R$ is $0$, which is not in $(0,1)$. (We can also view this graph­i­cally by plot­ting both $y=x$ and $y=x/2$ and check­ing that they do not in­ter­sect in $(0,1)$.)

• riceissa 3 Jan 2019 7:13 UTC

  12 points

  on: What ex­er­cises go best with 3 blue 1 brown’s Lin­ear Alge­bra videos?

  Some other sources of ex­er­cises you might want to check out (that have solu­tions and that I have used at least partly):

  • Mul­ti­ple choice quizzes (the ones re­lated to lin­ear alge­bra are de­ter­mi­nants, el­e­men­tary ma­tri­ces, in­ner product spaces, lin­ear alge­bra, lin­ear sys­tems, lin­ear trans­for­ma­tions, ma­tri­ces, and vec­tor spaces)

  • Vipul Naik’s quizzes (dis­clo­sure: I am friends with Vipul and also do con­tract work for him)

  Re­gard­ing Axler’s book (since it has been men­tioned in this thread): there are sev­eral “lev­els” of lin­ear alge­bra, and Axler’s book is at a higher level (em­pha­sis on ab­stract vec­tor spaces and co­or­di­nate-free ways of do­ing things) than the 3Blue1Brown videos (more con­crete, work­ing in $R^n$). Axler’s book also as­sumes that the reader has had ex­po­sure to the lower level ma­te­rial (e.g. he does not talk about row re­duc­tion and el­e­men­tary ma­tri­ces). So I’m not sure I would recom­mend it to some­one start­ing out try­ing to learn the ba­sics of lin­ear alge­bra.

  Gra­tu­itous re­marks:

  • I think differ­ent re­sources cov­er­ing ma­te­rial in a differ­ent or­der and us­ing differ­ent ter­minol­ogy is in some sense a fea­ture, not a bug, be­cause it al­lows one to look at the sub­ject from differ­ent per­spec­tives. For in­stance, the “done right” in Axler’s book comes from one such change in per­spec­tive.

  • I find that learn­ing math­e­mat­ics well takes an un­in­tu­itively long time; it might be un­re­al­is­tic to ex­pect to learn the ma­te­rial well un­less one puts in a lot of effort.

  • I think there is a case to be made for the im­por­tance of strug­gling in learn­ing (dis­clo­sure: I am the au­thor of the page).

• riceissa 19 Nov 2018 1:54 UTC

  12 points

  AF

  in reply to: Davidmanheim's comment on: Topolog­i­cal Fixed Point Exercises

  Here is my at­tempt, based on Hoagy’s proof.

  Let $n\ge 1$ be an in­te­ger. We are given that $f\left(0/n\right)=f\left(0\right)\le 0$ and $f\left(n/n\right)=f\left(1\right)\ge 0$. Now con­sider the points $0/n,1/n,\dots ,(n-1)/n,n/n$ in the in­ter­val $[0,1]$. By 1-D Sperner’s lemma, there are an odd num­ber of $j\in \{0,\dots ,n\}$ such that $f\left(j/n\right)\ge 0$ and $f\left(\right(j-1\left)/n\right)\le 0$ (i.e. an odd num­ber of “seg­ments” that be­gin be­low zero and end up above zero). In par­tic­u­lar, $0$ is an even num­ber, so there must be at least one such num­ber $j$. Choose the small­est and call this num­ber $j_n$.

  Now con­sider the se­quence $(j_n/n{)}_{n=1}^{\infty }$. Since this se­quence takes val­ues in $[0,1]$, it is bounded, and by the Bolzano–Weier­strass the­o­rem there must be some sub­se­quence $(k_n/n{)}_{n=1}^{\infty }$ that con­verges to some num­ber $x\in [0,1]$.

  Con­sider the se­quences $\left(f\right((k_n-1)/n){)}_{n=1}^{\infty }$ and $\left(f\right(k_n/n){)}_{n=1}^{\infty }$. We have $f\left(\right(k_n-1\left)/n\right)\le 0\le f\left(k_n/n\right)$ for each $n\ge 1$. By the limit laws, $(k_n-1)/n\to x$ as $n\to \infty$. Since $f$ is con­tin­u­ous, we have $f\left(\right(k_n-1\left)/n\right)\to f\left(x\right)$ and $f\left(k_n/n\right)\to f\left(x\right)$ as $n\to \infty$. Thus $f\left(x\right)\le 0$ and $f\left(x\right)\ge 0$, show­ing that $f\left(x\right)=0$, as de­sired.

• riceissa 19 Nov 2018 1:29 UTC

  11 points

  AF

  in reply to: Hoagy's comment on: Topolog­i­cal Fixed Point Exercises

  I’m hav­ing trou­ble un­der­stand­ing why we can’t just fix $n=2$ in your proof. Then at each iter­a­tion we bi­sect the in­ter­val, so we wouldn’t be us­ing the “full power” of the 1-D Sperner’s lemma (we would just be us­ing some­thing close to the base case).

  Also if we are only given that $f$ is con­tin­u­ous, does it make sense to talk about the gra­di­ent?

• riceissa 29 Nov 2018 7:44 UTC

  9 points

  on: Turn­ing Up the Heat: In­sights from Tao’s ‘Anal­y­sis II’

  Can you say more about why ex­er­cise 17.6.3 is wrong?

  If we define $f:[0,1]\to R$ by $f\left(x\right):=x/(1+x)$ then for dis­tinct $x,y\in [0,1]$ we have $$|f\left(x\right)-f\left(y\right)|=|\frac{x}{1+x}-\frac{y}{1+y}|=\left|\frac{x-y}{(1+x)(1+y)}\right|<|x-y|$$

  We also have $f^{\prime }\left(0\right)=1$ since $$\underset{x\to 0;x\in (0,1]}{lim}\frac{f\left(x\right)-f\left(0\right)}{x-0}=\underset{x\to 0;x\in (0,1]}{lim}\frac{x}{(x+1)x}=1$$

  In gen­eral, the deriva­tive is $f^{\prime }\left(x\right)=1/(1+x{)}^2$, which is con­tin­u­ous on $[0,1]$.

• riceissa 25 Jul 2018 22:09 UTC

  8 points

  in reply to: avturchin's comment on: Prob­a­bil­ity is Real, and Value is Complex

  I was con­fused about this too, but now I think I have some idea of what’s go­ing on.

  Nor­mally prob­a­bil­ity is defined for events, but ex­pected value is defined for ran­dom vari­ables, not events. What is hap­pen­ing in this post is that we are tak­ing the ex­pected value of events, by way of the con­di­tional ex­pected value of the ran­dom vari­able (con­di­tion­ing on the event). In sym­bols, if $A\subset \Omega$ is some event in our sam­ple space, we are say­ing $E\left(A\right)=E(X\mid A)$, where $X:\Omega \to R$ is some ran­dom vari­able (this ran­dom vari­able is sup­posed to be clear from the con­text, so it doesn’t ap­pear on the left hand side of the equa­tion).

  Go­ing back to cousin_it’s lot­tery ex­am­ple, we can for­mal­ize this as fol­lows. The sam­ple space can be $\Omega =\{\text{win},\text{lose}\}$ and the prob­a­bil­ity mea­sure is defined as $P\left(\right\{\text{win}\left\}\right)=1/{10}^6$ and $P\left(\right\{\text{lose}\left\}\right)=1-1/{10}^6$. The ran­dom vari­able $L:\Omega \to R$ rep­re­sents the lot­tery, and it is defined by $L\left(\text{win}\right)={10}^6$ and $L\left(\text{lose}\right)=0$.

  Now we can calcu­late. The ex­pected value of the lot­tery is:

  $$E\left(L\right)=L\left(\text{win}\right)P\left(\right\{\text{win}\left\}\right)+L\left(\text{lose}\right)P\left(\right\{\text{lose}\left\}\right)={10}^6/{10}^6+0\cdot (1-{10}^6)=1$$

  The ex­pected value of win­ning is:

  $$\begin{array}{cc}E\left(\right\{\text{win}\left\}\right)& =E(L\mid \{\text{win}\left\}\right)\\ & =L\left(\text{win}\right)P(\text{win}\mid \{\text{win}\left\}\right)+L\left(\text{lose}\right)P(\text{lose}\mid \{\text{win}\left\}\right)\\ & ={10}^6\cdot 1+0\cdot 0\\ & ={10}^6\end{array}$$

  The “probu­til­ity” of win­ning is:

  $$Q\left(\right\{\text{win}\left\}\right)=P\left(\right\{\text{win}\left\}\right)E\left(\right\{\text{win}\left\}\right)=\frac{1}{{10}^6}\cdot {10}^6=1$$

  So in this case, the “probu­til­ity” of win­ning is the same as the ex­pected value of the lot­tery. How­ever, this is only the case be­cause the situ­a­tion is so sim­ple. In par­tic­u­lar, if $L\left(\text{lose}\right)$ was not equal to zero (while win­ning and los­ing re­mained ex­clu­sive events), then the two would have been differ­ent (the ex­pected value of the lot­tery would have changed while the “probu­til­ity” would have re­mained the same).

• riceissa 14 Mar 2019 23:13 UTC

  5 points

  on: Open Prob­lems Re­gard­ing Coun­ter­fac­tu­als: An In­tro­duc­tion For Beginners

  The link no longer works (I get “This pro­ject has not yet been moved into the new ver­sion of Over­leaf. You will need to log in and move it in or­der to con­tinue work­ing on it.“) Would you be will­ing to re-post it or move it so that it is visi­ble?

• riceissa 8 Dec 2018 5:32 UTC

  4 points

  on: LW Up­date 2018-12-06 – Table of Con­tents and Q&A

  Is there (or will there be) a way to see a list of the lat­est posts, re­stricted to posts that are ques­tions? (I am won­der­ing about this both in the GraphQL API and in the site UI.)

• riceissa 29 Nov 2018 20:40 UTC

  3 points

  in reply to: TurnTrout's comment on: Turn­ing Up the Heat: In­sights from Tao’s ‘Anal­y­sis II’

  I think we are work­ing off differ­ent edi­tions. Ac­cord­ing to the er­rata, the con­di­tion for strict con­trac­tion was changed to $|f\left(x\right)-f\left(y\right)|<|x-y|$ for all dis­tinct $x,y\in [a,b]$.

• riceissa 27 Aug 2018 4:56 UTC

  2 points

  in reply to: Qiaochu_Yuan's comment on: “Flinch­ing away from truth” is of­ten about *pro­tect­ing* the epistemology

  I had a similar thought while read­ing this post, but I’m not sure in­vok­ing causal­ity is nec­es­sary (hav­ing a di­rec­tion still seems nec­es­sary). Just in terms of propo­si­tional logic, I would ex­plain this post as fol­lows:

  1. Ini­tially, one has the im­pli­ca­tion $X⟹Y$ stored in one’s mind.

  2. Some­one as­serts $X$.

  3. Now one’s mind (per­haps sub­con­sciously) does a modus po­nens, and ob­tains $Y$.

  4. How­ever, $Y$ is an un­de­sir­able be­lief, so one wants to deny it.

  5. In­stead of re­ject­ing the im­pli­ca­tion $X⟹Y$, one adamantly de­nies $X$.

  The “buck­ets er­ror” is the im­pli­ca­tion $X⟹Y$, and “flinch­ing away” is the de­nial of $X$. Flinch­ing away is about pro­tect­ing one’s episte­mol­ogy be­cause deny­ing $X$ is still bet­ter than ac­cept­ing $Y$. Of course, it would be best to re­ject the im­pli­ca­tion $X⟹Y$, but since one can’t do this (by as­sump­tion, one makes the buck­ets er­ror), it is prefer­able to “flinch away” from $X$.

  ETA (2019-02-01): It oc­curred to me that this is ba­si­cally the same thing as “one man’s modus po­nens is an­other man’s modus tol­lens” (see e.g. this post) but with some ex­tra emo­tional con­no­ta­tions.

• riceissa 4 Apr 2018 23:17 UTC

  2 points

  on: Op­por­tu­ni­ties for in­di­vi­d­ual donors in AI safety

  I don’t see refer­ence num­ber 17 (“Per­sonal cor­re­spon­dence with Carl Shul­man”) used in the body of the post. What in­for­ma­tion from that refer­ence is used in the post?

• riceissa 5 Jul 2017 19:19 UTC

  2 points

  on: Timeline of Carl Shul­man publications

  I re­cently wrote an up­dated timeline. It in­cludes not just for­mal pub­li­ca­tions, but also blog posts and con­ver­sa­tions. To see just the for­mal pub­li­ca­tions, it is pos­si­ble to sort by the “For­mat” column in the full timeline and look at the rows with “Paper”.

• riceissa 28 Sep 2016 23:03 UTC

  2 points

  in reply to: VipulNaik's comment on: Linkposts now live!

  I con­firm that I also ex­pe­rience this prob­lem, but I don’t have ad­di­tional in­sight on the cause.

• riceissa 22 Sep 2014 9:21 UTC

  2 points

  in reply to: Metus's comment on: Open thread, Septem­ber 15-21, 2014

  I usu­ally ask these as ques­tions on Quora. Quora is in­cred­ibly tol­er­ant of even inane ques­tions, and has the benefit of al­low­ing oth­ers to provide feed­back (in the form of an­swers and com­ments to the ques­tion). If a ques­tion has already been asked, then you will also be able to read what oth­ers have writ­ten in re­sponse and/​or fol­low that ques­tion for fu­ture an­swers. Quora also has the op­tion of anonymiz­ing ques­tions. I’ve found that always con­vert­ing my thoughts into ques­tions has made me very con­scious of what sort of ques­tions are in­ter­est­ing to ask (not that there’s any­thing right with that).

  Another idea is to prac­tice this with writ­ing down dreams. After wak­ing up, I of­ten think “It’s not re­ally worth writ­ing that dream down any­way”, whereas in re­al­ity I would find it quite in­ter­est­ing if I came back to it later. Forc­ing one­self to write thoughts down even when one is not in­clined to may lead to more se­d­u­lous record-keep­ing. (But this is just spec­u­la­tion.)

• riceissa 24 Nov 2018 7:43 UTC

  1 point

  on: LessWrong an­a­lyt­ics (Fe­bru­ary 2009 to Jan­uary 2017)

  There are some more data (post count, com­ment count, vote count, etc., but not pageviews) at “His­tory of LessWrong: Some Data Graph­ics”.

• riceissa 2 Feb 2018 8:41 UTC

  1 point

  in reply to: LessWrong's comment on: Open thread, Jan­uary 29 - ∞

  do we have any statis­tics about it?

  For ses­sions and pageviews from Google An­a­lyt­ics, I wrote a post about it in April 2017. Since you men­tion scrap­ing, per­haps you mean some­thing like post and com­ment counts; if so, I’m not aware of any statis­tics about that.

  Wei Dai has a web ser­vice to re­trieve all posts and com­ments of par­tic­u­lar users that I find use­ful (not sure if you will find it use­ful for gath­er­ing statis­tics, but I thought I would men­tion it just in case).

• riceissa 14 Sep 2017 18:43 UTC

  1 point

  in reply to: Wei_Dai's comment on: AALWA: Ask any LessWronger anything

  In some re­cent com­ments over at the Effec­tive Altru­ism Fo­rum you talk about anti-re­al­ism about con­scious­ness, say­ing in par­tic­u­lar “the case for ac­cept­ing anti-re­al­ism as the an­swer to the prob­lem of con­scious­ness seems pretty weak, at least as ex­plained by Brian”. I am won­der­ing if you could elab­o­rate more on this. Does the case for anti-re­al­ism about con­scious­ness seem weak be­cause of your gen­eral un­cer­tainty on ques­tions like this? Or is it more that you find the case for anti-re­al­ism speci­fi­cally weak, and you hold some con­trary po­si­tion?

  I am es­pe­cially cu­ri­ous since I was un­der the im­pres­sion that many peo­ple on LessWrong hold es­sen­tially similar views.

• riceissa 28 Sep 2014 8:51 UTC

  1 point

  in reply to: mushroom's comment on: Open thread, Septem­ber 22-28, 2014

  Gw­ern still links to some of mu­flax’s writ­ings, us­ing his own back­ups. Googling some­thing like “site:gw­ern.net mu­flax” turns up some re­sults (though not many).

• riceissa 11 Sep 2014 3:05 UTC

  1 point

  in reply to: Emile's comment on: Open Thread: how do you look for in­for­ma­tion?

  It’s worth not­ing that there is also Duck­DuckGo (a search en­g­ine), which has bang ex­pres­sions for out­sourc­ing re­sults. Just to give some of the equiv­a­lents for those listed above: “!gi” for Google Images, “!yt” for YouTube, “!w” for Wikipe­dia, etc. To be sure, one has to rely on Duck­DuckGo for adding the ex­pres­sions (al­though I’ve had suc­cess sug­gest­ing a new ex­pres­sion be­fore).