[math-fun] Fixed points of Google translate ?
A offline comment by Bill G. prompted me to think about the following problem: Let gt(x) be "Google translate" of some corpus x from some language D into some language R. Let gt^-1(y) be the "Google translate" of y in the language R back to the language D. Let rt(x) by the "round trip" translate of x in D to R and back to D. What are the fixed points of rt(x) ? They obviously imply fixed points of gt(rt(x)). It would be interesting to build a simple process to grab some random text from the web & see if rt^n(x) converges to a fixed point for some n. What types of phrases might cause rt^n(x) to "explode" without bound? Are there any "implosions", where rt^n(x) becomes empty? Are there cycles, such that rt^n(x) never converges, but rt^(n+m)(x)=rt^n(x) for some m and for all n>some p ? For a given language, and a word w within that language, there must exist at least one comprehensible sentence containing that word w. Determine the fixed points for each of these sentences.
I conjecture that the fixed point is independent of the input, and constitutes the Question of Life, the Universe and Everything. [The answer was earlier conjectured by Adams to be 42, until I pointed out in a post prompted by Conway that it is actually 24.] WFL On 3/2/13, Henry Baker <hbaker1@pipeline.com> wrote:
A offline comment by Bill G. prompted me to think about the following problem:
Let gt(x) be "Google translate" of some corpus x from some language D into some language R.
Let gt^-1(y) be the "Google translate" of y in the language R back to the language D.
Let rt(x) by the "round trip" translate of x in D to R and back to D.
What are the fixed points of rt(x) ?
They obviously imply fixed points of gt(rt(x)).
It would be interesting to build a simple process to grab some random text from the web & see if rt^n(x) converges to a fixed point for some n.
What types of phrases might cause rt^n(x) to "explode" without bound?
Are there any "implosions", where rt^n(x) becomes empty?
Are there cycles, such that rt^n(x) never converges, but rt^(n+m)(x)=rt^n(x) for some m and for all n>some p ?
For a given language, and a word w within that language, there must exist at least one comprehensible sentence containing that word w. Determine the fixed points for each of these sentences.
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Here is a site that does English <-> Japanese until a fixed point is found. http://www.translationparty.com/ When we found the site a few years ago, my friend discovered that "Naruto" expanded forever. The step from English to Japanese would give the word both in English and Japanese, so the total length doubled each round trip. The translator isn't fooled by that any more. It looks like it's very nearly fooled by "Naruto Naruto", after a few doublings it is ended by the strange appearance of some other word. On 3 March 2013 00:29, Henry Baker <hbaker1@pipeline.com> wrote:
A offline comment by Bill G. prompted me to think about the following problem:
Let gt(x) be "Google translate" of some corpus x from some language D into some language R.
Let gt^-1(y) be the "Google translate" of y in the language R back to the language D.
Let rt(x) by the "round trip" translate of x in D to R and back to D.
What are the fixed points of rt(x) ?
They obviously imply fixed points of gt(rt(x)).
It would be interesting to build a simple process to grab some random text from the web & see if rt^n(x) converges to a fixed point for some n.
What types of phrases might cause rt^n(x) to "explode" without bound?
Are there any "implosions", where rt^n(x) becomes empty?
Are there cycles, such that rt^n(x) never converges, but rt^(n+m)(x)=rt^n(x) for some m and for all n>some p ?
For a given language, and a word w within that language, there must exist at least one comprehensible sentence containing that word w. Determine the fixed points for each of these sentences.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
"Peter Piper picked a peck of pickled peppers" after about 11 round trips converges to "1 Pickle, goose" On Sat, Mar 2, 2013 at 11:19 AM, Mitchell <mitchell.v.riley@gmail.com>wrote:
Here is a site that does English <-> Japanese until a fixed point is found.
http://www.translationparty.com/
When we found the site a few years ago, my friend discovered that "Naruto" expanded forever. The step from English to Japanese would give the word both in English and Japanese, so the total length doubled each round trip. The translator isn't fooled by that any more.
It looks like it's very nearly fooled by "Naruto Naruto", after a few doublings it is ended by the strange appearance of some other word.
On 3 March 2013 00:29, Henry Baker <hbaker1@pipeline.com> wrote:
A offline comment by Bill G. prompted me to think about the following problem:
Let gt(x) be "Google translate" of some corpus x from some language D into some language R.
Let gt^-1(y) be the "Google translate" of y in the language R back to the language D.
Let rt(x) by the "round trip" translate of x in D to R and back to D.
What are the fixed points of rt(x) ?
They obviously imply fixed points of gt(rt(x)).
It would be interesting to build a simple process to grab some random text from the web & see if rt^n(x) converges to a fixed point for some n.
What types of phrases might cause rt^n(x) to "explode" without bound?
Are there any "implosions", where rt^n(x) becomes empty?
Are there cycles, such that rt^n(x) never converges, but rt^(n+m)(x)=rt^n(x) for some m and for all n>some p ?
For a given language, and a word w within that language, there must exist at least one comprehensible sentence containing that word w. Determine the fixed points for each of these sentences.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
"Find prime numbers for which the square of the prime plus one is twice the square of another prime." converges to "Times Square Plaza, Prime Minister Prime Minister 2." after 11 roundtrips. Can anyone find a mathematical phrase (beyond, say, arithmetic) which retains its mathematical meaning in fixpoint? No fair using symbols! Charles Greathouse Analyst/Programmer Case Western Reserve University On Sat, Mar 2, 2013 at 2:11 PM, W. Edwin Clark <wclark@mail.usf.edu> wrote:
"Peter Piper picked a peck of pickled peppers" after about 11 round trips converges to "1 Pickle, goose"
On Sat, Mar 2, 2013 at 11:19 AM, Mitchell <mitchell.v.riley@gmail.com
wrote:
Here is a site that does English <-> Japanese until a fixed point is found.
http://www.translationparty.com/
When we found the site a few years ago, my friend discovered that "Naruto" expanded forever. The step from English to Japanese would give the word both in English and Japanese, so the total length doubled each round trip. The translator isn't fooled by that any more.
It looks like it's very nearly fooled by "Naruto Naruto", after a few doublings it is ended by the strange appearance of some other word.
On 3 March 2013 00:29, Henry Baker <hbaker1@pipeline.com> wrote:
A offline comment by Bill G. prompted me to think about the following problem:
Let gt(x) be "Google translate" of some corpus x from some language D into some language R.
Let gt^-1(y) be the "Google translate" of y in the language R back to the language D.
Let rt(x) by the "round trip" translate of x in D to R and back to D.
What are the fixed points of rt(x) ?
They obviously imply fixed points of gt(rt(x)).
It would be interesting to build a simple process to grab some random text from the web & see if rt^n(x) converges to a fixed point for some n.
What types of phrases might cause rt^n(x) to "explode" without bound?
Are there any "implosions", where rt^n(x) becomes empty?
Are there cycles, such that rt^n(x) never converges, but rt^(n+m)(x)=rt^n(x) for some m and for all n>some p ?
For a given language, and a word w within that language, there must exist at least one comprehensible sentence containing that word w. Determine the fixed points for each of these sentences.
On 3/2/13, Charles Greathouse <charles.greathouse@case.edu> wrote:
"Find prime numbers for which the square of the prime plus one is twice the square of another prime." converges to "Times Square Plaza, Prime Minister Prime Minister 2." after 11 roundtrips.
Uh-huh. Well, anyone can make a mistake ... WFL
On Sat, Mar 2, 2013 at 4:18 PM, Charles Greathouse < charles.greathouse@case.edu> wrote:
"Find prime numbers for which the square of the prime plus one is twice the square of another prime." converges to "Times Square Plaza, Prime Minister Prime Minister 2." after 11 roundtrips.
Can anyone find a mathematical phrase (beyond, say, arithmetic) which retains its mathematical meaning in fixpoint? No fair using symbols!
I found one on the first try: "addition is commutative." http://www.translationparty.com/#10772163 -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
Although my first answer "addition is commutative" is not a statement *of* arithmetic, it is *about* arithmetic. So here is another that does not concern arithmetic: "This is a cosine calculation." quickly terminates at "This is the cosine calculation." which I think is close enough to count. http://www.translationparty.com/#10772198 On Sat, Mar 2, 2013 at 6:00 PM, Robert Munafo <mrob27@gmail.com> wrote:
On Sat, Mar 2, 2013 at 4:18 PM, Charles Greathouse < charles.greathouse@case.edu> wrote:
"Find prime numbers for which the square of the prime plus one is twice the square of another prime." converges to "Times Square Plaza, Prime Minister Prime Minister 2." after 11 roundtrips.
Can anyone find a mathematical phrase (beyond, say, arithmetic) which retains its mathematical meaning in fixpoint? No fair using symbols!
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
On Sat, Mar 2, 2013 at 11:19 AM, Mitchell <mitchell.v.riley@gmail.com>wrote:
The step from English to Japanese would give the word both in English and Japanese, so the total length doubled each round trip. The [[Bing translate]] isn't fooled by that any more.
I often have to translate to and from Japanese myself. The large-number name "Nayuta" (那由他 or 那由多, "10^60" originally from Sanskrit meaning "impossibly large number") was imported from Chinese by Buddhist priests and was never native even in China. On translationparty.com it quickly expands into the somewhat humorous "All Satan and Devil Devil Devil-multiple solutions with multiple solutions". A feature (or common idiomatic construct) in Japanese that contributes to word-doubling is that a word appearing once is a modifier, but used twice it can mean an absolute thing. For example, "almond" is アーモンド in Japanese, which is simply a phonetic transliteration ("Ahh-mondo."). When I asked for "almonds" in a gift shop I was directed to candy bars containing almonds. I repeated my request, "いいえ アーモンド。アーモンドアーモンド。" (which I'm sure was complete nonsense, but crudely translated I said: "NO almond. Almond Almond!".) I was then directed to the almonds.
On 3 March 2013 00:29, Henry Baker <hbaker1@pipeline.com> wrote:
Let gt(x) be "Google translate" of some corpus x from some language D into some language R.
Let gt^-1(y) be the "Google translate" of y in the language R back to the language D.
Let rt(x) by the "round trip" translate of x in D to R and back to D.
What are the fixed points of rt(x) ?
Naturally we'd like to ask this question about arbitrary language-pairs, thus the gt() function should have a subscript indicating the "from" and "to" languages. My examples above involve gt_en_ja(x) and gt_ja_en(x). For any i != j, the gt' function is just the gt function with the subscripts reversed: gt'_j_i() = gt_i_j(), and rt(x) is gt_j_i(gt_i_j(x))
They obviously imply fixed points of gt(rt(x)).
There are many trivial fixed points in Google translate, which leaves unrecognized words alone. Slightly less trivially, western proper nouns are transliterated into Katakana, and commercial names (companies, brands) often use the Latin alphabet because it is appealing. "Robert's almonds" finds a fixed point very quickly because of Katakana transliteration.
[...]
Are there any "implosions", where rt^n(x) becomes empty?
Google never seems to return a blank string -- at the very least it will just give you the same thing you put in, untranslated.
Are there cycles, such that rt^n(x) never converges, but rt^(n+m)(x)=rt^n(x) for some m and for all n>some p ?
It would naturally be fun to consider three-language cycles, such as gt_en_fr(gt_de_en(gt_fr_de(x))) which I'm sure would have been of interest to Hofstadter when he was working on Lewis Carroll's Jabberwocky.
For a given language, and a word w within that language, there must exist at least one comprehensible sentence containing that word w. Determine the fixed points for each of these sentences.
Not for any word w, because there are instances of two words in language A getting translated into the same word in language B. Perhaps I misunderstand your assertion. -- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
At http://www.translationparty.com/#10771789, starting with: Take the cube root of your number, submit it to RIES, then express your original number as "5 to the power of 3". It eventually leads to this 4-cycle: 4N: Take the route number of Hokkaido University 5 cube strength three stars. 4N+1: ルート番号北海道大学 5 キューブ強度の 3 つ星を取る。 4N+2: Take route number Hokkaido University 5 cube strength three stars. 4N+3: ルート番号北海道大学 5 キューブ強度 3 つの星を取る。 The site claims, "Yes, I know it repeated a set of 4. That's not equilibrium." but I suspect it would satisfy Henry Baker's "rt^(n+m)(x)" question. Of slightly less mathematical interest is "can you start with X and converge on the negation or converse of X?". Here is an example, and probably a victim of the Yoda-like grammar of Japanese [1]: www.translationparty.com/#9111 let's go! The spirit is willing but the flesh is weak. into Japanese: 精神が喜んでですが、肉は弱いです。 back into English: Is that the spirit is willing flesh is weak. ... back into English: Weak of mind and body willing. back into Japanese: 心と体を喜んでの弱い。 back into English: Weak of mind and body willing. Equilibrium found! - Robert [1] http://www.textfugu.com/season-1/japanese-grammar-with-yoda/ (It's worth seeing for the picture alone) On Sat, Mar 2, 2013 at 11:19 AM, Mitchell <mitchell.v.riley@gmail.com>wrote:
Here is a site that does English <-> Japanese until a fixed point is found.
http://www.translationparty.com/ On 3 March 2013 00:29, Henry Baker <hbaker1@pipeline.com> wrote:
[...] Are there cycles, such that rt^n(x) never converges, but rt^(n+m)(x)=rt^n(x) for some m and for all n>some p ? [...]
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
Just by putting in random numbers after the # in the link [1] I found a simple "explode without bound" with linear growth: Starting with "Yuki", for n>=7, rt^{2n}("Yuki") = "... 4 4 4 4 4 4 4 4 4 4 4 Quaternary Yuki a. older kids." with n-1 repetitions of the initial "4 ". http://www.translationparty.com/#10271381 [1] Note: There are many profanities in translationparty.com's past history. You have been warned. On Sat, Mar 2, 2013 at 9:29 AM, Henry Baker <hbaker1@pipeline.com> wrote:
[...]
What types of phrases might cause rt^n(x) to "explode" without bound?
[...]
-- Robert Munafo -- mrob.com Follow me at: gplus.to/mrob - fb.com/mrob27 - twitter.com/mrob_27 - mrob27.wordpress.com - youtube.com/user/mrob143 - rilybot.blogspot.com
participants (6)
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Charles Greathouse -
Fred lunnon -
Henry Baker -
Mitchell -
Robert Munafo -
W. Edwin Clark