"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.