# 2884: Log Alignment

 Log Alignment Title text: A video can have a log scale that's misaligned with both the time AND space axes.

## Explanation

In the comic, we see a background distribution of straight and parallel (but notably off-orthogonal) lines, such as might normally define the log-magnitude on a log-log or semi-log graph. But there are no perpendicular gradations and the bar graph drawn upon it appears to have no relation with the background, drawn distorted in an almost Dalíesque manner, as if it were a projection of one twisted in 3d space. Both its bars and the base/vertical axes seem to have no relation to the supposed underlying log-scale.

With the slight exception of the bar tops crossing the log lines at an angle, and the curved vertical axis having graduation ticks that bear no linear or log relation with the intersecting background, the distorted bars only travel unidirectionally across the underlying parallels and could feasibly be read as indicating a definitive magnitude (or range) of some kind. Or at least could with number-labels to give an idea of what values to associate with each log-line. That two bars appear from outside the frame of the comic (the base axis having fallen out of the bottom of the frame) might not even matter, so long as we can work out what quality or sample each of the bars represents (being similarly unlabeled).

The humour in the comic is that a more practical log-chart can be seen as the result of logarithmically compressing a normal chart in one or both axes. Normal parallel and perpendicular axes remain straight lines when doing this; lines that aren't parallel or perpendicular to the squishing process get turned into curves of the exact kind depicted. A plot can be made according to measures not consistent with the graph axes, especially where other factors dictate the plotting, but then it is more common to make use of variant grid systems.

Skewed log charts are real and occur in fields of science with useful applications. For example, a "Skew-T log-P diagram" depicts the relationship between temperature and pressure of a parcel of air in the atmosphere. On this chart, the x-axis is skewed with relation to the rest of the graph, and its isotherms, or lines of equal temperature, slant diagonally upwards and to the right of the diagram. The y-axis is normal and represents pressure on a log scale. A more detailed explanation can be found here, and there are several related pressure/temperature charts which optimise the dimensional comparisons and skewings to allow for the results of somewhat codependent variables (such as normal changes along a slice of altitudes) to produce lines that are more recognisably consistent, or revealing of actual signature changes that provide more key information to those who study such diagrams.

The title text further reinforces the concept of misalignment by stating that the time axis represented by the progressive changing of a moving image can be misaligned against (by the other elements of the data within the video itself, including any log scale element), adding at least one further dimension through which to twist and skew axial and non-axial components of such a dynamic graph. It's possible this may be a reference to cutting between scenes in TV shows.

## Transcript

[Distorted bar graph on top of gray log scale lines in the background that are slightly tilted, with the lower ends on the left]
[Caption below the panel:]
There's actually no rule in math that says your log scales have to be aligned with your graph axes.

# Discussion

so does anybody know how a video with a misaligned log scale even looks? like what does a log scale even mean for a video? 172.71.99.18 19:30, 22 January 2024 (UTC)mstrofcmdy209

I think he's suggesting that the video shows the changes in a graph over time, and the misalignment could also change during the video. Barmar (talk) 20:47, 22 January 2024 (UTC)
Imagine that a plot is just a 2D picture, or even more fundamentally as a function taking two variables and returning a pixel color. Changing an axis of the plot to be logarithmic is equivalent to applying a non-uniform scaling to one of the input variables to that function. In this comic that non-uniform scaling has instead been applied along an axis that does not correspond to either the X or Y axes but instead some combination of the two. A video can similarly be thought of as a function of 3 variables (X, Y, T) and so the non-uniform log scaling could be applied along an axis that is some combination of the X, T, and T axes. 172.71.154.252 23:37, 22 January 2024 (UTC)
it's time, probably -jade 172.69.64.198 20:28, 22 January 2024 (UTC)
LOG is also a video format, though I don't understand this well enough to discern whether this might be part of the joke or an unintentional coincidence.172.70.86.80 09:59, 23 January 2024 (UTC)
It's not rendered in capitals, it's just "log." In log video formats, the logarithm of the pixel values is recorded, rather than the actual value. This results in a better match between the dynamic range of the camera and what is being recorded, so you get better precision in the values where it counts, and less precision where it doesn't. E.g. in an 8-bit linear scale, you have to round values between 3 and 4, because you can only record integers from 0 to 256. But in a made-up hypothetical 8-bit log scale where you take the base 10 log and multiply by some k (here let's say k=106.3, which is 256/log(256)), you could record your 3 as 51 (log(3)*k), 4 as 64, and you'd have everything from 51 to 63 to represent the values between 3 and 4 (e.g. 52 would be 3.08, 53 would be 3.15, 54 would be 3.22, etc.). The downside is that in exchange for that expansion at the low end, you'd to record both 224 and 225 as 250 (because they are 249.8 and 250.0), so you get dynamic range compression at the other end. It doesn't have much to do with this comic directly, because the the pixel values in this graph are either on (here grey rather than black) or off, no intermediate values. JohnHawkinson (talk) 14:46, 24 January 2024 (UTC)
it's pretty common for videos to have flashbacks and scene changes. Graphing the electron beam for crt video would be pretty pretty straightforward, just wavy line(s) with pulses that mean go down one line and back the far "left."108.162.216.19 17:14, 23 January 2024 (UTC)

There seems to be a subtle relativity joke in the title text, with misalignments in both time and space being a reference to spacetime. 172.71.154.42 (talk) 00:05, 23 January 2024 (please sign your comments with ~~~~)

Shall we try to straighten out the plot with regards to the axes, leaving the log stripes all wavy? For kicks? -- Enfield (talk) 02:14, 23 January 2024 (please sign your comments with ~~~~)

https://xkcd.com/356/ Bischoff (talk) 08:33, 23 January 2024 (UTC)
Before I tapped that, I KNEW what it would be, LOL! I refer to that comic all the time, whenever I do it to myself. :) NiceGuy1 (talk) 00:56, 31 January 2024 (UTC)

I feel like this comic, along with others like 2023: Y-Axis and 2311: Confidence Interval should go in a category for misleading charts. -- 172.69.33.111 (talk) 02:23, 23 January 2024 (please sign your comments with ~~~~)

Can you create a chart to illustrate the use of chart comics?172.71.242.13 09:37, 24 January 2024 (UTC)

It may be interesting to refer to a tephigram instead of, or as well as, a SkewT-LogP as a tephigram has no normal axis. In my opinion, this makes the point even stronger. A tephigram shows the same lines as a SkewT-LogP but pressure is drawn as a curve, which straightens out the entropy lines. Temperature (te) and entropy (phi) lines are straight and normal to each other, but at around 45° to the page. 172.71.178.176 14:14, 23 January 2024 (UTC)

Hi, I'm new here! I created an "undistorted" version of the comic, and I would like to add it to the explanation, but the site is telling me I don't have permission to create new pages (in order to upload the file). How can I add it? Rayna (talk) 08:50, 24 January 2024 (UTC)

There's some degree of activity necessary, as an anti-griefer measure. Not sure how much age/editing it might currently be set as (and it wouldn't be wise to have details stated outright, or dedicated wannabe griefers could do just enough standard and benign participation to then do what they really want).
In the interim, you could still upload it to some external generic image-sharing site (that you're comfortable with) and give the link here with explicit permission for someone who is an established uploader to copy it into the wiki proper. A bit of fuss, but it's worked for me in the past (never having bothered to get an account, and mostly no desire to do so). 172.70.85.153 13:08, 24 January 2024 (UTC)
Here it is! Could someone upload it, and is it possible to somehow be attributed to me? https://imgur.com/a/vEcHKez Rayna (talk) 05:37, 29 January 2024 (UTC)
Well, an Imgur link is good enough for the Comments, anyway. :) NiceGuy1 (talk) 00:56, 31 January 2024 (UTC)

I still think this explanation is janky, and buries the lede about how the comic accurately depicts exactly what it's describing (a perfectly normal bar graph, squished logarithmically in a way which does not line up with its axes). But I don't know how to fix this. 108.162.245.30 20:46, 10 February 2024 (UTC)

oh god is that an illusion or what o-o 172.68.34.17 17:00, 28 March 2024 (UTC)