[seqfan] Re: Quasilog

David Wilson davidwwilson at comcast.net
Mon Oct 17 14:34:38 CEST 2011

Mathematicians are all the time coining new terms and repurposing old ones,
not because they want to clutter the lexicon, but because it is easier 
to wield
the name than the idea it stands for. If others find the qlog term 
I am not wedded to it, I merely coined the term to show the similarity with
the log scale, and to avoid continual repetition of the formula 
arsinh(x/2)/(log 10).

Yes, qlog is a stretch and a squish away from arsinh, but as arsinh is not
thoroughly covered in the high school curriculum, I am sure that all readers
would immediately appreciate its properties as a plotting scale. If we 
adopt the
scale in the OEIS, I think it is a good idea if we have a page 
explaining its properties
and why we used it.

Indeed, an editor (other than myself) has already composed an OEIS page 
the scale that incorporates the terms quasilogarithm and qlog. I think 
it would
be possible to explain the scale in terms of arsinh without introducing 
the new term,
however, I think the new term has some value in that we can talk about a 
"qlog scale
which immediately conjures up the similarity to the log scale, and we 
can talk about
qlog10(x) = arsinh(x/2)/(log 10) analogously to log10(x) = log(x)/(log 10).

Depending on not or whether we adopt the term (or indeed the scale) we could
label the graphs as follows

     Scatterplot of arsinh(A000045(n)/2)/log(10)


     Scatterplot of qlog10(A000045(n))

On 10/16/2011 11:20 PM, Maximilian Hasler wrote:
> To be honest, I find it a bit exaggerated to give a new name to a
> function which is up to a constant factor identical to the perfectly
> well established and well known function Arsinh.
> (while I don't mean at all to question the usefulness of this function
> or any of its variations for the given purpose of plotting signed
> integer values on a (quasi)logarithmic scale.)
> Maximilian

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