The Icelandic Publishers of Sabine Hossenfelder's first book, Lost in Math asked me if I would write a foreword for the book, which will appear later this year. Here it is, in English. :)
It is so easy to get lost in math. Some years ago a group of American mathematicians discovered an interesting "fact" about 3. Take any real valued valued function f. If there is are 3 real numbers such that f(a) = b and f(b) = c and f(c) = a, that cycles back to itself in 3 iterations then for every positive integer there is a real number that cycles around and comes back to itself exactly that integer times. The Russian mathematician, Sharkovsky, independently discovered that fact and a lot more. He reordered the positive integers and showed any integer had the same property as "3" for integers further along in his new ordering. Really bizarre.
Nicely written, but after the long discussion of the hierarchy problem I was expecting another mention of Sabine's work to close the piece. But may be I am just suffering from Eucliean (Greek!) thinking 😄
Much of this goes right past me because I have limited knowledge of physics. Regardless, its refreshing to see adults disagree, perhaps strongly disagree, and yet remain cordial and civil with one another. The struggle between truth and beauty- whether in science or art- remains an interesting conversation. I lean more toward classicism but of course I grew up in Anglo Canada when the world map was mostly red :) Thanks for this interesting article.
It is so easy to get lost in math. Some years ago a group of American mathematicians discovered an interesting "fact" about 3. Take any real valued valued function f. If there is are 3 real numbers such that f(a) = b and f(b) = c and f(c) = a, that cycles back to itself in 3 iterations then for every positive integer there is a real number that cycles around and comes back to itself exactly that integer times. The Russian mathematician, Sharkovsky, independently discovered that fact and a lot more. He reordered the positive integers and showed any integer had the same property as "3" for integers further along in his new ordering. Really bizarre.
where can I read more about this? Any examples?
about what?
Nicely written, but after the long discussion of the hierarchy problem I was expecting another mention of Sabine's work to close the piece. But may be I am just suffering from Eucliean (Greek!) thinking 😄
Great stuff! Happy to see the collab 👊🏼
Much of this goes right past me because I have limited knowledge of physics. Regardless, its refreshing to see adults disagree, perhaps strongly disagree, and yet remain cordial and civil with one another. The struggle between truth and beauty- whether in science or art- remains an interesting conversation. I lean more toward classicism but of course I grew up in Anglo Canada when the world map was mostly red :) Thanks for this interesting article.
thanks
Sharkovsky, but I found it in wikipedia
ok...