­xkcd thread

Not so fast, at least if we’re in the complex domain. For example, the arithmetic mean of [2, i 2] is 1+i which has a smaller magnitude than either inputs.

I suspect there’s still convergence, but we have to be careful.

The ExplainXKCD page for this comic already has a Python implementation, along with an exhaustive analysis.

I won’t vouch for any of that, but it’s there.

Heh, I wonder how hypercomplex numbers behave.

Yeah, I figured I’d have to be a lot faster than I am if I were to get there first. I kind of want to do a visual thing showing of the a-mean, g-mean, median and the xkcd-function behaves for different distributions, but not enough to do the work. :smiley:

Maybe someone should forward this one to Matt Parker of Standup Maths. He likes to do unnecessary work.

Not exhaustive, the analysis is restricted to non-negative reals.

I feel this is a case where some people will chuckle because they get the joke and know other people will not, even though the joke itself is not the funny.

And the arithmetic mean of -1 and 1 is 0, which is also smaller in magnitude than either of the inputs. Which is why I specified “At least, if you’re starting with positive values.”.

That’s the point made in the mouseover text: Toss together any set of “averaging” functions you want, and as long as the median is one of them, the others won’t matter much. You could even do something crazy like the weighted arithmetic mean of the largest and smallest, which is most definitely not a good averaging function for almost any inputs, and it’ll still converge.

Of course, the lesson from this is that, in any data set where you’re sufficiently ignorant of the meaning to consider using the Gmdn, you should probably just use the median and be done with it.

Said another way, any averaging function throws away a lot of information. When averaging, it’s way too easy to throw out 100% of the baby along with most of the bathwater. Only if you understand your data can you reliably hold onto the kid when you give the bassinet the old heave ho! :wink:

He missed an intermediate circle between “Mastercard” and “Audi” for Disney.

But homemade placebos are the best!

Not “exhausive”, then. “Exhausting.”

Turn in your math nerd card.
:stuck_out_tongue:

Huh? Disney’s logo does not include any intersecting circles.

It’s unfortunate he couldn’t have had one for Venn Diagram, but there are no three mutually intersecting circles that are a subset of the others.

Disney sometimes uses a stylized version of the outline of Mickey Mouse’s head which is just three circles.

But that doesn’t really fit the pattern. They aren’t of equal size, and they’re silhouettes, not empty circles.

As is the MasterCard logo:

Sort of. They’re colored, but clearly overlapping circles with clearly differentiated outlines. I can’t get a good image to display on this board (Discourse doesn’t seem to be able to parse the links), but if you click on the embedded link in my post, you’ll see that they are pure black silhouettes, with no outlines, which doesn’t fit Randall’s pattern.

I’m not sure if this one is supposed to be somehow a joke about the coronavirus, or a joke about Munroe’s anemic social life in general.