Editing 2884: Log Alignment

{{comic
| number    = 2884
| date      = January 22, 2024
| title     = Log Alignment
| image     = log_alignment_2x.png
| imagesize = 351x312px
| noexpand  = true
| titletext = 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 {{w|Salvador Dalí|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 {{w|graduation (scale)|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 [https://www.researchgate.net/figure/Curvature-introduced-by-pen-type-recording-system-Comparison-of-a-raw-seismogram-showing_fig5_364100386 other factors dictate the plotting], but then it is more common to make use of {{w|Graph paper#Examples|variant grid systems}}.

Skewed log charts are real and occur in fields of science with useful applications. For example, a "{{w|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 [https://www.noaa.gov/jetstream/upperair/skew-t-log-p-diagrams 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.

==Transcript==
{{incomplete transcript|Do NOT delete this tag too soon.}}

:[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.

{{comic discussion}}

[[Category:Math]]
[[Category:Bar charts]]