Periodic spiral graph interpretation

[DaveC426913]

TL;DR

Is this graph spiral or merely polar?

Could someone explain the geometry of this graph?

• Why does the radial distance vary non-uniformly? To-wit: Distance from origin to Nov 2020 is much larger than Nov 2020 to Nov 2021
• Why are there two areas - one above and one below - the centre line?

https://www.nytimes.com/2022/01/06/opinion/omicron-covid-us.html

 

[Mark44]

Summary:: Is this graph spiral or merely polar?

Could someone explain the geometry of this graph?

• Why does the radial distance vary non-uniformly? To-wit: Distance from origin to Nov 2020 is much larger than Nov 2020 to Nov 2021

It's spiral, and the only reason for doing it this way is to convey the information in less space than a linear graph would take. The radial distance varies, I believe, to leave room for the bulging sections.

Why are there two areas - one above and one below - the centre line?

To display the data for 1) Apr to Oct of 2020, and 2) for Apr to Oct of 2021.

Don't overthink this...

 

[DaveC426913]

To display the data for 1) Apr to Oct of 2020, and 2) for Apr to Oct of 2021.

Don't overthink this...

No, I mean why is it symmetrical about the centerline? This is common in graphs that differentiate gender - having male on one side and female on the other, but I doubt that the case here.

 

[DaveC426913]

The radial distance varies, I believe, to leave room for the bulging sections.

Except it doesn't do that.

 

[FactChecker]

No, I mean why is it symmetrical about the centerline?

I think that is just a decision that the graph-maker made. It may have no significance at all, except that someone thought the graph looked better that way (and I tend to agree).

 

[Mark44]

No, I mean why is it symmetrical about the centerline?

Because that's how the person who made the graph wanted it.

Except it doesn't do that.

Sure it does -- look how fat the sections for January are.

Again, don't overthink this.

 

[DaveC426913]

Sure it does -- look how fat the sections for January are.

Yet the biggest gap between 2020 and 2021 is in October.Anyway, I grant your point. So much visualization opportunity lost. I will just have to out this rendering down as an affront to the god of graphs.

 

[mfb]

It's weird. The width of the path is the daily cases, the angle is the time in the year, the distance to the origin seems to have no significance.

 

[berkeman]

IMO, it looks like some intern at the NYT had way too much time on their hands, and basically hand-drew a graph to try to visualize the data. There are clear non-symmetries that suggest the hand-drawn aspect. Whatever.

 

[DaveC426913]

There are clear non-symmetries that suggest the hand-drawn aspect.

Are you sure that's an asymmetry? The curve on the bottom will have will appear to have an amplified amplitude, because its ... er ... x-axis is compressed.

 

[berkeman]

Are you sure that's an asymmetry? The curve on the bottom will have will appear to have an amplified amplitude, because its ... er ... x-axis is compressed.

Whelp, if I were an intern trying out different graphing schemes and saw that apparent misinformation in my graph, I'd change to a single-sided representation... Interns, kids, what'cha going to do...

 

[DaveC426913]

I added an analysis, above.

 

[berkeman]

Wait, so YOU are the intern?

 

[DaveC426913]

Wait, so YOU are the intern?

What? No.
I just Photoshopped the diagram.

When you see the lines that are perpendicular to the curve, the asymmetry disappears.

These circles are centred on the central black line. Their radii touch both red curves. So upper and lower red curves are symmetrical about the black central line.

 

[OmCheeto]

It's weird. The width of the path is the daily cases, the angle is the time in the year, the distance to the origin seems to have no significance.

Comparing their graph to an Archimedean spiral(r = aθ + b), I found that if I shift their graph to the right by ≈58 pixels, it comes out pretty close.

 

[DaveC426913]

Comparing their graph to an Archimedean spiral(r = aθ + b), I found that if I shift their graph to the right by ≈58 pixels, it comes out pretty close.

Huh. I guess the asymmetry of the spiral is also an optical delusion.

 

[OmCheeto]

Huh. I guess the asymmetry of the spiral is also an optical delusion.

Possibly. I notice that if I fiddle with the constants for the Archimedean spiral, I get an even closer fit, and an apparent stretching in the quadrant 1 and 3 directions displays itself.

I'm not sure I've ever smooshed something diagonally, mathematically.
I might be able to get a perfect fit, if I can figure that out.
Off the top of my head, it looks like a pain in the butt.
I could rotate everything 45° counter clockwise and then smoosh it in the y direction.
Perhaps I'll try googling this for a better method. My brain is just too old.

 

[DaveC426913]

Sunuvagun. I would not have believed it if I hadn't seen it.

I think two things threw me.
1. There's a missing quadrant:

2.
The slope varies wildly along the slope.