[math-fun] Turing test in 10 years?
I'm much less optimistic than Dan Asimov re machine intelligence. The difference with computer chess is, chess ratings allowed us to estimate progress and extrapolate it 10 (or whatever) years ahead. With the Turing test, I see no analogous thing and no way to extrapolate future progress. I actually invented a vastly superior measure of "intelligence" to the Turing test, which by the way also was invented (essentially the same idea) by Marcus Hutter: http://rangevoting.org/WarrenSmithPages/homepage/works.html paper #93 it to some extent would allow extrapolation of future progress, though it certainly is not as easily employed as chess ratings.
http://lesswrong.com/lw/42t/aixistyle_iq_tests/ discusses some research that attempts to turn Hutter's AIXI into an IQ test that could be uniformly applied to humans, AI programs, cats and dogs, etc. One issue with this line of attack is that simple Q-learning algorithms already outperform humans (see for example http://users.dsic.upv.es/proy/anynt/paper1-comparing.pdf). Many, but perhaps not all, would prefer a measure of intelligence for which current AIs are below the human level. -Thomas C On Tue, Jun 10, 2014 at 4:45 PM, Warren D Smith <warren.wds@gmail.com> wrote:
I'm much less optimistic than Dan Asimov re machine intelligence.
The difference with computer chess is, chess ratings allowed us to estimate progress and extrapolate it 10 (or whatever) years ahead. With the Turing test, I see no analogous thing and no way to extrapolate future progress.
I actually invented a vastly superior measure of "intelligence" to the Turing test, which by the way also was invented (essentially the same idea) by Marcus Hutter:
http://rangevoting.org/WarrenSmithPages/homepage/works.html paper #93
it to some extent would allow extrapolation of future progress, though it certainly is not as easily employed as chess ratings.
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Thomas Colthurst, it is always good to see you here. On Tue, Jun 10, 2014 at 6:41 PM, Thomas Colthurst <thomaswc@gmail.com> wrote:
http://lesswrong.com/lw/42t/aixistyle_iq_tests/ discusses some research that attempts to turn Hutter's AIXI into an IQ test that could be uniformly applied to humans, AI programs, cats and dogs, etc.
One issue with this line of attack is that simple Q-learning algorithms already outperform humans (see for example http://users.dsic.upv.es/proy/anynt/paper1-comparing.pdf). Many, but perhaps not all, would prefer a measure of intelligence for which current AIs are below the human level.
-Thomas C
On Tue, Jun 10, 2014 at 4:45 PM, Warren D Smith <warren.wds@gmail.com> wrote:
I'm much less optimistic than Dan Asimov re machine intelligence.
The difference with computer chess is, chess ratings allowed us to estimate progress and extrapolate it 10 (or whatever) years ahead. With the Turing test, I see no analogous thing and no way to extrapolate future progress.
I actually invented a vastly superior measure of "intelligence" to the Turing test, which by the way also was invented (essentially the same idea) by Marcus Hutter:
http://rangevoting.org/WarrenSmithPages/homepage/works.html paper #93
it to some extent would allow extrapolation of future progress, though it certainly is not as easily employed as chess ratings.
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Two random math typography questions: 1. Any opinions on the best symbol for "such that"? I've seen colon, vertical-bar, and flipped-epsilon/member-of. 2. A colleague asks how to LaTex a symbol for "loves" (hey, it's about social discovery graphs) consisting of a heart overlaid with an arrow (left-to-right, or bidirectional when requited). Any recipes? Thanks! If you prefer, feel free to just reply to me directly: mlb@well.com
2. A colleague asks how to LaTex a symbol for "loves" (hey, it's about social discovery graphs) consisting of a heart overlaid with an arrow (left-to-right, or bidirectional when requited). Any recipes?
Do you want other ideas or advice on constructing that symbol. I believe a heart is the first or second example in the Metafont manual. Whit
On 2014-06-11 09:19, Whitfield Diffie wrote:
2. A colleague asks how to LaTex a symbol for "loves" (hey, it's about social discovery graphs) consisting of a heart overlaid with an arrow (left-to-right, or bidirectional when requited). Any recipes?
Do you want other ideas or advice on constructing that symbol. I believe a heart is the first or second example in the Metafont manual.
latex provides \heartsuit (as well as \clubsuit, \spadesuit ... etc.), if that helps.
Whit
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="Michael Greenwald" <mbgreen@seas.upenn.edu> On 2014-06-11 09:19, Whitfield Diffie wrote:
2. A colleague asks how to LaTex a symbol for "loves" (hey, it's about social discovery graphs) consisting of a heart overlaid with an arrow (left-to-right, or bidirectional when requited). Any recipes?
Do you want other ideas or advice on constructing that symbol. I believe a heart is the first or second example in the Metafont manual.
latex provides \heartsuit (as well as \clubsuit, \spadesuit ... etc.), if that helps.
Thanks for the suggestions! I found \heartsuit and \Heart using the neat http://detexify.kirelabs.org/classify.html Now we simply want to overlay it with \longrightarrow How hard could it be? Surely hacking MetaFont is doubtless The Right Thing, but we were hoping for something quick and dirty, more like an update some old-school mechanical typewritten <heart><backspace><arrow> ...what one might've resorted to for, say, APL, INTERCAL (or, heh, Knuth's pre-Tex MS for volume 4!). While brute over-striking is less tasteful, it seems like the ability to create compound symbols this way sure would be handy. However, from what I've found on the web, I'm discouraged there's any easy win for even this. "As it should pierce a hundred thousand hearts. But I might see young Cupid¹s fiery shaft"
I'd suggest TikZ as the Right Thing these days. On Wed, Jun 11, 2014 at 11:48 AM, Marc LeBrun <mlb@well.com> wrote:
="Michael Greenwald" <mbgreen@seas.upenn.edu> On 2014-06-11 09:19, Whitfield Diffie wrote:
2. A colleague asks how to LaTex a symbol for "loves" (hey, it's about social discovery graphs) consisting of a heart overlaid with an arrow (left-to-right, or bidirectional when requited). Any recipes?
Do you want other ideas or advice on constructing that symbol. I believe a heart is the first or second example in the Metafont manual.
latex provides \heartsuit (as well as \clubsuit, \spadesuit ... etc.), if that helps.
Thanks for the suggestions! I found \heartsuit and \Heart using the neat http://detexify.kirelabs.org/classify.html Now we simply want to overlay it with \longrightarrow How hard could it be?
Surely hacking MetaFont is doubtless The Right Thing, but we were hoping for something quick and dirty, more like an update some old-school mechanical typewritten <heart><backspace><arrow> ...what one might've resorted to for, say, APL, INTERCAL (or, heh, Knuth's pre-Tex MS for volume 4!).
While brute over-striking is less tasteful, it seems like the ability to create compound symbols this way sure would be handy. However, from what I've found on the web, I'm discouraged there's any easy win for even this.
"As it should pierce a hundred thousand hearts. But I might see young Cupid¹s fiery shaft"
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
On Wed, Jun 11, 2014 at 11:48 AM, Marc LeBrun <mlb@well.com> wrote:
Surely hacking MetaFont is doubtless The Right Thing, but we were hoping for something quick and dirty, more like an update some old-school mechanical typewritten <heart><backspace><arrow> ...what one might've resorted to for, say, APL, INTERCAL (or, heh, Knuth's pre-Tex MS for volume 4!).
Here's a stackoverflow question about horizontal space in latex: http://tex.stackexchange.com/questions/74353/what-commands-are-there-for-hor... -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
On 2014-06-11 19:29, Mike Stay wrote:
On Wed, Jun 11, 2014 at 11:48 AM, Marc LeBrun <mlb@well.com> wrote:
Surely hacking MetaFont is doubtless The Right Thing, but we were hoping for something quick and dirty, more like an update some old-school mechanical typewritten <heart><backspace><arrow> ...what one might've resorted to for, say, APL, INTERCAL (or, heh, Knuth's pre-Tex MS for volume 4!).
Here's a stackoverflow question about horizontal space in latex: http://tex.stackexchange.com/questions/74353/what-commands-are-there-for-hor...
... and I think http://tex.stackexchange.com/questions/67912/large-negative-spaces?lq=1 gives exactly what you need in its definition of \negphantom{}. You can do \heartsuit \negphantom{\heartsuit} \leftarrow, for example.
For #1, I've also seen leftarrow; this is the notation used, for instance, in the programming language scala: The set comprehension {f(x) | x ∈ X and P(x) is true} becomes the "for" comprehension for (x <- X if P(x)) yield f(x). Web programming languages with comprehensions tend to use "in" or "of": JavaScript (ES6): [for (x of X) if P(x) f(x)] Haxe3: [for (x in X) if P(x) f(x)] CoffeeScript, Python: [f(x) for (x in X) if P(x)] Here's a wiki page on how it's done in lots of languages: http://en.wikipedia.org/wiki/List_comprehension On Wed, Jun 11, 2014 at 9:59 AM, Marc LeBrun <mlb@well.com> wrote:
Two random math typography questions:
1. Any opinions on the best symbol for "such that"? I've seen colon, vertical-bar, and flipped-epsilon/member-of.
2. A colleague asks how to LaTex a symbol for "loves" (hey, it's about social discovery graphs) consisting of a heart overlaid with an arrow (left-to-right, or bidirectional when requited). Any recipes?
Thanks! If you prefer, feel free to just reply to me directly: mlb@well.com
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
="Mike Stay" <metaweta@gmail.com> For #1, I've also seen leftarrow; this is the notation used, for instance, in the programming language scala:
The set comprehension {f(x) | x ∈ X and
P(x) is true}
Thanks for the links! The specific idiom we were trying to symbolize succinctly was "For all X there exists a Y such that..." Regarding funny symbols, although right now I'm hoping for an easy win, for the future I'll keep TikZ in mind (I've also long wanted an "elongated P" sign for "product integral") Thanks! --MLB
On Wed, Jun 11, 2014 at 2:23 PM, Marc LeBrun <mlb@well.com> wrote:
The specific idiom we were trying to symbolize succinctly was "For all X there exists a Y such that..."
Ah! For quantifiers, a period/full stop is often used: ∀x. ∃y. P(x, y) similar to the way lambda is used in lambda calculus: λx. λy. λz. xz(yz) because all three are binding occurrences of the variable. The period is not pronounced after a "for all" and is pronounced "such that" after a "there exists". -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
I believe that quite commonly in mathematical logic, exactly what Mike said is typically used without the periods: ∀x ∃y P(x, y) or ∀x ∃y ∋ P(x,y) to mean "For all x there exists a y such that P(x,y)" --Dan On Jun 11, 2014, at 1:42 PM, Mike Stay <metaweta@gmail.com> wrote:
On Wed, Jun 11, 2014 at 2:23 PM, Marc LeBrun <mlb@well.com> wrote:
The specific idiom we were trying to symbolize succinctly was "For all X there exists a Y such that..."
Ah! For quantifiers, a period/full stop is often used: ∀x. ∃y. P(x, y) similar to the way lambda is used in lambda calculus: λx. λy. λz. xz(yz) because all three are binding occurrences of the variable. The period is not pronounced after a "for all" and is pronounced "such that" after a "there exists".
="Dan Asimov" <dasimov@earthlink.net> I believe that quite commonly in mathematical logic, exactly what Mike said is typically used without the periods:
∀x ∃y P(x, y) or ∀x ∃y ∋
P(x,y)
to mean "For all x there exists a y such that P(x,y)" --Dan OK so in the first example here the "such that" is simply implicit and in the second it is explicitly written as "backwards member-of". I personally like either of those for this purpose. But from this discussion I'm getting uncomfortable with vertical bar; this isn't a set comprehension so much as a logical statement. And while the colon is ASCII friendly, I'd rather not overload ordinary text punctuation marks with technical interpretations if possible. Does anyone think that either nothing or "nolispe" would be an awful choice?
If you find somewhere a usage of some obscure character that you want, copy and paste it into your text. Another trick is to code the character in HTML, e.g. "&foobar;". Save the HTML as a .html file, open the file with a browser, and then copy and paste. -- Gene
________________________________ From: Marc LeBrun <mlb@well.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Wednesday, June 11, 2014 1:23 PM Subject: Re: [math-fun] Such that & cupid
="Mike Stay" <metaweta@gmail.com> For #1, I've also seen leftarrow; this is the notation used, for instance, in the programming language scala:
The set comprehension {f(x) | x ∈ X and
P(x) is true}
Thanks for the links!
The specific idiom we were trying to symbolize succinctly was "For all X there exists a Y such that..."
Regarding funny symbols, although right now I'm hoping for an easy win, for the future I'll keep TikZ in mind (I've also long wanted an "elongated P" sign for "product integral")
Thanks! --MLB
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On this page, draw whatever funky TeX symbol you desire with your cursor. This thing will give you a best guess what the symbol is. http://detexify.kirelabs.org/classify.html On Wed, Jun 11, 2014 at 3:22 PM, Eugene Salamin via math-fun < math-fun@mailman.xmission.com> wrote:
If you find somewhere a usage of some obscure character that you want, copy and paste it into your text. Another trick is to code the character in HTML, e.g. "&foobar;". Save the HTML as a .html file, open the file with a browser, and then copy and paste.
-- Gene
________________________________ From: Marc LeBrun <mlb@well.com> To: math-fun <math-fun@mailman.xmission.com> Sent: Wednesday, June 11, 2014 1:23 PM Subject: Re: [math-fun] Such that & cupid
="Mike Stay" <metaweta@gmail.com> For #1, I've also seen leftarrow; this is the notation used, for instance, in the programming language scala:
The set comprehension {f(x) | x ∈ X and
P(x) is true}
Thanks for the links!
The specific idiom we were trying to symbolize succinctly was "For all X there exists a Y such that..."
Regarding funny symbols, although right now I'm hoping for an easy win, for the future I'll keep TikZ in mind (I've also long wanted an "elongated P" sign for "product integral")
Thanks! --MLB
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-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
I was brought up with the long vertical bar used in *set-builder* notation: when you define a set as all members of an existing set, *such that* some conditions hold. It seems more common these days for people to use the colon, but as an old stick-in-the-mud I prefer the vertical bar -- it's more dramatic. For other uses, I was brought up on the "flipped epsilon", a backwards epsilon (written as a backwards c with a middle bar, not as two mini-c's) with its middle bar extended to the left about two character-lengths. A number of people also use "s.t." to abbreviate "such that", but I prefer the symbol -- it's more distinctive and language-independent. (Almost every class where I've used the symbol, I've had to explain it to the class, which had never seen it before.) --Dan On Jun 11, 2014, at 8:59 AM, Marc LeBrun <mlb@well.com> wrote:
1. Any opinions on the best symbol for "such that"? I've seen colon, vertical-bar, and flipped-epsilon/member-of.
On the contrary, I've usually seen (and written) this symbol as
a backwards epsilon (written as a backwards c with a middle bar, not as two mini-c's) with its middle bar extended to the right (not left) about two character-lengths:
* * * ***************** * * * --Dan On Jun 11, 2014, at 11:22 AM, Dan Asimov <dasimov@earthlink.net> wrote:
For other uses, I was brought up on the "flipped epsilon", a backwards epsilon (written as a backwards c with a middle bar, not as two mini-c's) with its middle bar extended to the left about two character-lengths.
Magma has constructors which I find very useful, employing "|" for "such that"; [I haven't come across a "cupid" operator yet, but the manual is 5000 pages long, so I might have missed it ...] There doesn't seem to be any equivalent in Maple, which is a moderate nuisance. I'm constantly having to dream up contortions along the lines of max(seq( max(0, min(1, k - A[i]))*A[i], i = 1..nops(A))); say, to find the maximum element less than k of an array A of numbers. Then running it two or three times to debug it. The inconvenience is compounded by the remarkable "feature" that conditional expressions will compile, but only as the result of a function --- a syntactic blunder that leaves me lost for words. And by the way, there is no straightforward way to build the sequence element-by-element within a loop --- at least, there is, but it's horribly slow --- A := [op(A), x]; Instead the user is supposed to create a structure called a "table" to fill, maintaining a separate counter to index it, then convert it afterwards. Sigh! But perhaps I'm overlooking something. Has anybody out there found a good workaround? Fred Lunnon On 6/11/14, Marc LeBrun <mlb@well.com> wrote:
Two random math typography questions:
1. Any opinions on the best symbol for "such that"? I've seen colon, vertical-bar, and flipped-epsilon/member-of.
2. A colleague asks how to LaTex a symbol for "loves" (hey, it's about social discovery graphs) consisting of a heart overlaid with an arrow (left-to-right, or bidirectional when requited). Any recipes?
Thanks! If you prefer, feel free to just reply to me directly: mlb@well.com
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participants (11)
-
Dan Asimov -
Eugene Salamin -
Fred Lunnon -
Marc LeBrun -
Michael Greenwald -
Mike Stay -
Rowan Hamilton -
Thane Plambeck -
Thomas Colthurst -
Warren D Smith -
Whitfield Diffie