[seqfan] Re: Chewing an old bone
David Wilson
davidwwilson at comcast.net
Wed Oct 26 01:05:14 CEST 2011
Reasons can be put forth in favor of any plotting scale. Suppose we
devise a scale
that plots 777 at 100 and all other values at 0. The unique virtue of
this scale is that
you can look at the plot and immediately know if 777 is in the plot
range. This is a
feature that neither qlog(n) nor the log(|n|+1) plot can boast, so
perhaps we should
add this plot as well? I'm guessing most of you would disagree.
Similarly, the purported virtue of the log(|a(n)|+1) plot is that it
allows you to visually
compare magnitudes of positive and negative values. But wait...how do
you know
which of the values are positive and which negative? That information is
not in the plot.
I think you really have to go on a serious fishing expedition to find a
very few sequences
where a log(|a(n)|+1) plot might arguably supplement a qlog(n) plot.
These sequences
certainly don't include increasing, decreasing or nonnegative sequences,
where the
qlog(n) plot beats the log(|a(n)|+1) plot hands down.
So I stick with my opinion that if the qlog(n) plot is adopted, it
should replace the
qlog(|n|+1) plot as it was designed to do.
On 10/25/2011 4:52 AM, Benoît Jubin wrote:
> David W, I agree that qlog is an injective function, whereas absolute
> value is not (say, on Z), so you are right for the information
> content. But I think that qlog is not always better than log(|.|+1)
> when it comes to visualization... and visualization is actually the
> purpose of plots.
>
> Charles's example above is the basic example, and conversely imagine
> also this one: let a(n) be the sequence defined by:
> a(n) = exp(3*n) if n even
> a(n) = -exp(pi*n) if n odd
> Then from a qlog plot one might conjecture that a(n) ~ (-1)^n*exp(c.n)
> for some c, but on the log(|.|+1) plot one will see the small
> discrepancy between even and odd arguments. There are probably some
> "real life" examples of such sequences already in the OEIS.
>
> I think that these are the simplest examples, and that there are many
> others where, roughly speaking, the log(|.|+1) plot makes it easier to
> see some patterns or discrepancies in the scattering of dots than the
> qlog plot, in particular regarding asymptotic behavior. Actually, the
> logarithmic scale is not the issue, here: sometimes, it's just more
> useful to plot |a(n)| than a(n) -- but I am not suggesting to add this
> one: I'm happy with the current graphs.
>
> Finally, I still agree that the qlog plot is a very nice addition --
> and I said: "addition"!
>
> Benoit
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