No, Tukey did not "invent" the FFT. He rediscovered it, as did a number of others over the years since -- who else? -- Gauss first created it.
http://en.wikipedia.org/wiki/Fast_Fourier_transform
A quote: "This method (and the general idea of an FFT) was popularized by a publication of J. W. Cooley and J. W. Tukey in 1965,[2] but it was later discovered (Heideman & Burrus, 1984) that those two authors had independently re-invented an algorithm known to Carl Friedrich Gauss around 1805 (and subsequently rediscovered several times in limited forms)."
But either way wouldn't the importance for the field of computing in this case be more on the application of the algorithm and not who published first? I.e. if no one knows about a computable algorithm used sparingly 150 years earlier then I don't think it's completely unfair to give some credit to one who later rediscovers and popularizes that algorithm.
According to the Wikipedia article the Cooley-Tukey algorithm was an independent re-discovery so it's not as if Tukey had read Gauss and then tried to steal the credit (it wasn't even noted until almost 20 years later that Cooley-Tukey was a rediscovery of a Gaussian algorithm).
It's almost unfair though... I think if we really deeply dove into what mathematicians like Gauss, Euler, Cauchy, etc. came up with that there may be other "CS" algorithms that were innovated hundreds of years before computers were available to really popularize them. Every time I read about Euler and Gauss especially I end up even more impressed.
Separate issue. My objection was solely to correct the incorrect claim that Tukey invented the FFT. And this is in no way meant to disparage what Tukey did accomplish, only so that the history reads correctly.
> I don't think it's completely unfair to give some credit to one who later rediscovers and popularizes that algorithm.
Yes, but describing him as the inventor goes too far.
How are the actions of "invention" and "rediscovery" different? Is it less impressive that someone came up with a great idea simply because someone else did it first in a different context? Obviously Gauss should be celebrated too (and obviously is), but I don't see anything wrong with applauding Tukey either...
Simply put, the use of "invention" for a rediscovery deprives the idea's originator of any credit.
> I don't see anything wrong with applauding Tukey either...
My objection was only for misidentifying him as the inventor of the idea. Surely you are aware that in current practice only the originator of an idea gets credit for "inventing".
http://www.cis.rit.edu/class/simg716/Gauss_History_FFT.pdf
Besides Gauss, many others including Runge (yes, that Runge) and Burkhardt (yes, the one on Einstein's committee) independently discovered the FFT well before the 1950s. Like so much of Gauss's work, his work on the FFT was unpublished during his lifetime.
Probably it was the conjunction of the algorithm and the emerging power of the digital computer that caused the Cooley-Tukey paper to take off at that historical moment.
foo <-read.csv("foo.csv")
Getting summary descriptive statistics, item counts, scatter plots and histograms is often as easy as
summary(foo)
table(foo$col)
plot(foo$xcol, foo$ycol)
hist(foo$col).
I think that is lot simpler than a 4 or 5 command pipeline that can be mistake-prone to edit when you want to change column names or things like that. I still do these kinds of things in the shell sometimes, and I don't know if I can put my finger on when exactly I would drop into R vs write out a pipeline, but there IS a line somewhere...
R also supports the use of atomic operations on vectors (it automatically maps the operation over the vector), and other idioms that would be liabilities in other programming languages, but hugely beneficial in this one area.
I still haven't found a language that treats reading (and then processing) a CSV file more easily than R.
Conveniently, R should be really easy to pick up for someone familiar with working with a POSIX shell or Bash. For example, to see all variables defined in the current namespace, just type ls().
R is basically the POSIX mentality applied specifically to data processing, instead of general-purpose work.
Which isn't to say that it's not a phenomenally powerful and capable tool. I'm just referring to its accessibility.
(head -5; tail -5) <data
but that's a bit misleading. These don't work. seq 20 | (head -5; tail -5)
(head -5; tail -5) < <(seq 20)
Both giving just the first five lines.If you use "seq 10000 | (head -5; tail -5)" you'll get the first and last lines as expected since head hasn't consumed too much of the file.
I don't think this invalidates his example, but it could mention this subtle caveat. :-)
seq 1 20 >file.txt
(head -5; tail -5) <file.txtPipe sends stdout to stdin of the next process. cat sends stdin back to stdout. Piping to cat is rarely eventful (unless you use a flag like cat -n).
http://svnweb.freebsd.org/base/release/9.1.0/usr.bin/rs/
Not finding 'describe' at present (I shall persist). There seem to be few dependencies in these source files...