riceissa

Degree of duplication and coordination in projects that examine computing prices, AI progress, and related topics?

2019-04-23T12:27:18.314Z · score: 25 (7 votes)

Comment by riceissa on Diagonalization Fixed Point Exercises · 2019-04-14T19:57:38.709Z · score: 11 (3 votes) · LW · GW

Thoughts on #10:

I am confused about this exercise. The standard/modern proof of Gödel's second incompleteness theorem uses the Hilbert–Bernays–Löb derivability conditions, which are stated as (a), (b), (c) in exercise #11. If the exercises are meant to be solved in sequence, this seems to imply that #10 is solvable without using the derivability conditions. I tried doing this for a while without getting anywhere.

Maybe another way to state my confusion is that I'm pretty sure that up to exercise #10, nothing that distinguishes Peano arithmetic from Robinson arithmetic has been introduced (it is only with the introduction of the derivability conditions in #11 that this difference becomes apparent). It looks like there is a version of the second incompleteness theorem for Robinson arithmetic, but the paper says "The proof is by the construction of a nonstandard model in which this formula [i.e. formula expressing consistency] is false", so I'm guessing this proof won't work for Peano arithmetic.

Comment by riceissa on Diagonalization Fixed Point Exercises · 2019-04-14T19:41:46.836Z · score: 11 (3 votes) · LW · GW

My solution for #12:

Suppose for the sake of contradiction that such a formula $ϕ$ exists. By the diagonal lemma applied to $\neg ϕ$ , there is some sentence $ψ$ such that, provably, $\neg ϕ (┌ ψ ┐) \leftrightarrow ψ$ . By the soundness of our theory, in fact $\neg ϕ (┌ ψ ┐) \leftrightarrow ψ$ . But by the property for $ϕ$ we also have $ϕ (┌ ψ ┐) \leftrightarrow ψ$ , which means $\neg ϕ (┌ ψ ┐) \leftrightarrow ϕ (┌ ψ ┐)$ , a contradiction.

This seems to be the "semantic" version of the theorem, where the property for $ϕ$ is stated outside the system. There is also a "syntactic" version where the property for $ϕ$ is stated within the system.

Comment by riceissa on Diagonalization Fixed Point Exercises · 2019-04-01T18:56:07.202Z · score: 9 (2 votes) · LW · GW

Attempted solution and some thoughts on #9:

Define a formula $ξ (v)$ taking one free variable to be $f (┌ ϕ ┐, ┌ f (v, v) ┐)$ .

Now define $ψ$ to be $f (┌ ξ ┐, ┌ ξ ┐)$ . By the definition of $f$ we have $ψ \leftrightarrow ξ (┌ ξ ┐)$ .

We have $ϕ (┌ ψ ┐) \leftrightarrow f (┌ ϕ ┐, ┌ ψ ┐) \leftrightarrow f (┌ ϕ ┐, ┌ f (┌ ξ ┐, ┌ ξ ┐) ┐) \leftrightarrow ξ (┌ ξ ┐) \leftrightarrow ψ$

The first step follows by the definition of $f$ , the second by the definition of $ψ$ , the third by the definition of $ξ$ , and the fourth by the property of $ψ$ mentioned above. Since $ψ \in S_{0}$ by the type signature of $f$ , this completes the proof.

Things I'm not sure about:

It's a little unclear to me what the $S y n (A, B)$ notation means. In particular, I've assumed that $f$ takes as inputs Gödel numbers of formulas rather than the formulas themselves. If $f$ takes as inputs the formulas themselves, then I don't think we can assume that the formula $ξ$ exists without doing more arithmetization work (i.e. the equivalent of $ξ$ would need to know how to convert from the Gödel number of a formula to the formula itself).

If the biconditional " $\leftrightarrow$ " is a connective in the logic itself, then I think the same proof works but we would need to assume more about $f$ than is given in the problem statement, namely that the theory we have can prove the substitution property of $f$ .

The assumption about the quantifier complexity of $S_{0}$ and $S_{1}$ was barely used. It was just given to us in the type signature for $f$ , and the same proof would have worked without this assumption, so I am confused about why the problem includes this assumption.

Comment by riceissa on Open Problems Regarding Counterfactuals: An Introduction For Beginners · 2019-03-26T04:22:52.885Z · score: 1 (1 votes) · LW · GW

That link works, thanks!

Comparison of decision theories (with a focus on logical-counterfactual decision theories)

2019-03-16T21:15:28.768Z · score: 57 (17 votes)

Comment by riceissa on Open Problems Regarding Counterfactuals: An Introduction For Beginners · 2019-03-14T23:13:52.958Z · score: 5 (3 votes) · LW · GW

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?

Comment by riceissa on What exercises go best with 3 blue 1 brown's Linear Algebra videos? · 2019-01-03T07:13:11.920Z · score: 12 (6 votes) · LW · GW

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).

GraphQL tutorial for LessWrong and Effective Altruism Forum

2018-12-08T19:51:59.514Z · score: 52 (11 votes)

Comment by riceissa on LW Update 2018-12-06 – Table of Contents and Q&A · 2018-12-08T05:32:18.233Z · score: 4 (3 votes) · LW · GW

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.)

Comment by riceissa on Turning Up the Heat: Insights from Tao's 'Analysis II' · 2018-11-29T20:40:19.507Z · score: 3 (2 votes) · LW · GW

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

Comment by riceissa on Turning Up the Heat: Insights from Tao's 'Analysis II' · 2018-11-29T07:44:32.574Z · score: 9 (2 votes) · LW · GW

Can you say more about why exercise 17.6.3 is wrong?

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

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

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

Comment by riceissa on LessWrong analytics (February 2009 to January 2017) · 2018-11-24T07:43:02.644Z · score: 1 (1 votes) · LW · GW

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

Comment by riceissa on Topological Fixed Point Exercises · 2018-11-19T02:33:57.115Z · score: 14 (5 votes) · LW · GW

My solution for #3:

Define $g : [0, 1] \to R$ by $g (x) = f (x) - x$ . 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 $g (x) = 0$ . But this means $f (x) = x$ , so we are done.

Counterexample for the open interval: consider $f : (0, 1) \to (0, 1)$ defined by $f (x) = x / 2$ . 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 $(0, 1)$ .)

Comment by riceissa on Topological Fixed Point Exercises · 2018-11-19T01:54:05.398Z · score: 12 (4 votes) · LW · GW

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

Let $n \geq 1$ be an integer. We are given that $f (0 / n) = f (0) \leq 0$ and $f (n / n) = f (1) \geq 0$ . 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 $f (j / n) \geq 0$ and $f ((j - 1) / n) \leq 0$ (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 $(f ((k_{n} - 1) / n))_{n = 1}^{\infty}$ and $(f (k_{n} / n))_{n = 1}^{\infty}$ . We have $f ((k_{n} - 1) / n) \leq 0 \leq f (k_{n} / n)$ for each $n \geq 1$ . By the limit laws, $(k_{n} - 1) / n \to x$ as $n \to \infty$ . Since $f$ is continuous, we have $f ((k_{n} - 1) / n) \to f (x)$ and $f (k_{n} / n) \to f (x)$ as $n \to \infty$ . Thus $f (x) \leq 0$ and $f (x) \geq 0$ , showing that $f (x) = 0$ , as desired.

Comment by riceissa on Topological Fixed Point Exercises · 2018-11-19T01:29:27.876Z · score: 11 (3 votes) · LW · GW

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?

Comment by riceissa on "Flinching away from truth” is often about *protecting* the epistemology · 2018-08-27T04:56:37.943Z · score: 2 (2 votes) · LW · GW

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.

Comment by riceissa on Probability is Real, and Value is Complex · 2018-07-25T22:09:12.180Z · score: 8 (3 votes) · LW · GW

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 $A \subset Ω$ is some event in our sample space, we are saying $E (A) = E (X ∣ A)$ , where $X : Ω \to R$ 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 $Ω = {win, lose}$ and the probability measure is defined as $P ({win}) = 1 / 10^{6}$ and $P ({lose}) = 1 - 1 / 10^{6}$ . The random variable $L : Ω \to R$ represents the lottery, and it is defined by $L (win) = 10^{6}$ and $L (lose) = 0$ .

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

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

The expected value of winning is:

\begin{matrix} E ({win}) & = E (L ∣ {win}) = L (win) P (win ∣ {win}) + L (lose) P (lose ∣ {win}) = 10^{6} \cdot 1 + 0 \cdot 0 = 10^{6} \end{matrix}

The "probutility" of winning is:

Q ({win}) = P ({win}) E ({win}) = \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 $L (lose)$ 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).

Comment by riceissa on Opportunities for individual donors in AI safety · 2018-04-04T23:17:16.221Z · score: 2 (1 votes) · LW · GW

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?

Timeline of Future of Humanity Institute

2018-03-18T18:45:58.743Z · score: 17 (8 votes)

Comment by riceissa on Open thread, January 29 - ∞ · 2018-02-02T08:41:16.996Z · score: 1 (1 votes) · LW · GW

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).

Comment by riceissa on Could you be Prof Nick Bostrom's sidekick? · 2017-12-06T01:46:25.212Z · score: 0 (0 votes) · LW · GW

Based on descriptions on the FHI website, it looks like Kyle Scott filled this role, from July 2015 to September 2017.

From the earliest snapshot of his FHI bio page:

Kyle brings over 5 years of operations experience to the Future of Humanity Instutute. He keeps daily operations running smoothly, and manages incoming and outgoing requests for Prof. Nick Bostrom.

Strategically, he works to improve the processes and capacity of the office and free up the attention and time of Prof. Nick Bostrom.

Kyle came to the Future of Humanity Institute from the Effective Altruism movement, determining that this job position would be his most effective contribution to society. Learn more about Effective Altruism here.

The page is still up but it doesn't look like he holds the position anymore.

He seems to be a project manager at BERI now:

Kyle manages various projects supporting BERI's partner institutions. He graduated Whitman College with a B.A. in Philosophy. He spent two years working in career services and subsequently moved to Oxford where he worked for 80,000 Hours, the Centre for Effective Altruism and most recently at the Future of Humanity Institute as Nick Bostrom's Executive Assistant.

On November 13, 2017 FHI opened the position for applications.

ETA: Louis Francini comes to the same conclusion on Quora. (Context: I asked the question on Quora, figured out the answer, posted this comment, then Louis answered my question.)

Comment by riceissa on AALWA: Ask any LessWronger anything · 2017-09-14T18:43:40.475Z · score: 1 (1 votes) · LW · GW

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.

Timeline of Machine Intelligence Research Institute

2017-07-15T16:57:16.096Z · score: 5 (5 votes)

Comment by riceissa on Timeline of Carl Shulman publications · 2017-07-05T19:53:41.356Z · score: 0 (0 votes) · LW · GW

Thanks for the feedback. I could add wordcount. Not sure what you mean by quality rating; LW, OB, and EA Forum have their own voting/rating mechanisms but are not compatible (so putting them in a column might be confusing, although grouping by venue and looking at ratings within each venue might be interesting). Summary would be the most time-consuming to produce, and many of Carl's posts have summaries at the top.

Comment by riceissa on Timeline of Carl Shulman publications · 2017-07-05T19:19:21.017Z · score: 2 (2 votes) · LW · GW

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".

LessWrong analytics (February 2009 to January 2017)

2017-04-16T22:45:35.807Z · score: 22 (22 votes)

Comment by riceissa on Linkposts now live! · 2016-09-28T23:03:50.150Z · score: 2 (2 votes) · LW · GW

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

Comment by riceissa on A critique of effective altruism · 2016-07-25T19:38:39.183Z · score: 0 (0 votes) · LW · GW

Hi Evan, did you ever write this post?

Wikipedia usage survey results

2016-07-15T00:49:34.596Z · score: 7 (8 votes)

Comment by riceissa on Gauging interest for a Tokyo area meetup group · 2014-12-02T00:47:16.528Z · score: 0 (0 votes) · LW · GW

Okay I've created a Facebook group here: https://www.facebook.com/groups/LessWrongTokyo/

(To be sure, I don't currently live in Tokyo, but I visit there every summer and would be very interested in attending during that time.)

Comment by riceissa on 2014 Less Wrong Census/Survey · 2014-10-28T07:52:57.928Z · score: 31 (31 votes) · LW · GW

I took the survey.

Comment by riceissa on Open thread, September 22-28, 2014 · 2014-09-28T08:51:23.614Z · score: 1 (1 votes) · LW · GW

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).

Comment by riceissa on Open thread, September 15-21, 2014 · 2014-09-22T09:21:34.567Z · score: 2 (2 votes) · LW · GW

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.)

Comment by riceissa on Open Thread: how do you look for information? · 2014-09-11T03:05:37.911Z · score: 1 (1 votes) · LW · GW

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).

Comment by riceissa on Sequence translations: Seeking feedback/collaboration · 2012-07-10T23:26:58.823Z · score: 1 (1 votes) · LW · GW

I am also interested in doing Japanese translations.

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