On occasion, I use formulations like “all other things equal, more X is better” or “all other factors equal, more X is better”. (I will stick to the former below.)
While such formulations are convenient, they are also potentially dangerous, as they almost always involve unstated assumptions about what is or is not “equal”, in what sense they are “equal”, and/or what still needs to be changed in what manner.
To get a first idea of the issues, consider an old Soviet-era joke (paraphrased from memory):
Says the American to the Russian: In the U.S., we have freedom of speech. If I wanted to, I could stand in front of the White House and shout “Down with Reagan!” and nothing bad would happen to me.
Says the Russian to the American: So what? I can stand in front of the Kremlin and shout “Down with Reagan!” and nothing bad would happen to me either.
In the comparison of the two situations, something that should have been changed for a fair comparison has not been changed—the point was not to get away with shouting “Down with Reagan!” but “Down with [whoever is the local bigwig]!”.
Sadly, the reason that an updated version of this joke does not work in 2024 is that the wrong thing has changed in real life: Ideally, someone shouting “Down with Putin!” in front of the Kremlin should have no reason to fear political persecution, which would remove the point of the Russian’s (deliberate?) misconstruction. Reality is different. Instead, we now have the problem that someone shouting “Down with Biden!” in front of the U.S. White House has great reason to fear such persecution, which invalidates the American’s claim. (He might still get away with a “Down with Reagan!”, however. To investigate an update of the joke to 2024 on an “all other things equal” basis is left to the reader.)
I use “Russian” over “Soviet” mostly because this has been the phrasing on all my encounters, but sticking with “Russian” has the advantage of making the joke usable in a post-Soviet context. This gives yet another example of how changing or not changing something can be beneficial or detrimental, if from a different angle.
Similar issues often come into play with “all other things equal”, because keeping all other things equal is usually inappropriate or outright impossible. Often some discretion is needed as to what is or is not to be kept equal; often a choice has to be made whether thing A is kept constant at the cost of a change to thing B or vice versa. Consider a claim like “All other things equal, someone lighter [in weight] will be skinnier.”. If the intent is on height, body type, state of training, etc., the claim holds. (And this is indeed the likeliest interpretation.) However, consider BMI: If we compare two persons of the same height that differ in weight, their BMIs will differ. Clearly, then, not all things are equal.
If we take a less likely interpretation of the original claim and keep BMI fixed (together with body type, etc.), and leave height variable, the claim is actually reversed—the heavier person will be skinnier. (There is a flaw in the conception of BMI, the use of height squared instead of cubed, which gives taller persons higher BMI values relative shorter persons than they “should” have.)
Then we have issues like why someone is lighter: If the one has a lesser mass than the other, we have one situation; if the two have the same mass while being in environments with different gravitational pulls, another.
The preceding paragraph is a good example of how tricky things can be: I originally used the formulation “All other things equal, someone lighter will be skinnier.”. On proof-reading, I added a “[in weight]” to avoid confusion with other senses, e.g. that someone might be lighter in skin tone. In a next step, I found myself confronted with the difference between mass and weight, which I had not considered when writing the first version, and added the above paragraph.
To make matters even more complicated. the original formulation might have been taken to relate to mass, rather than weight, by most readers (and the author) and many readers will not be aware of the difference between mass and weight in the first place. We might then need to change different things and/or be explicit about different changes with different persons involved.
Likewise, if we say that body proportions are fixed, then a value like shoulder width divided by (overall) height will remain constant, but the absolute value of the shoulder width will vary if the height does. With a varying height, we cannot have proportions and absolute measures equal.
In many ways, it is like pretending to have a see-saw, where the position of one end of the plank determines the position of the other end, while we actually have a water balloon, where pushing some point inwards causes many other points to move outwards. We might fix some points on the balloon, e.g. by putting a finger on them, but we cannot fix them all, because water compresses poorly and the result would be that we could not push that original point inwards. Again, then, what points are left movable and what are fixed?
Assuming superhuman strength or some machine, such a push might be successful, as long as the balloon does not break. With regular human strength, the compression would be too small to bother with.
Use of an “air” balloon would make things easier, as air compresses much more readily than water; however, even here, the limit might come disappointingly early.
Both see-saws and balloons should be seen as metaphors: We can certainly find objections even to a see-saw in an “all other things equal” scenario. For instance, a claim “All other things equal, having one end of the plank lower will keep the other end higher.” might work if factors like the length of the plank are kept constant and the angles relative some reference plane are allowed to vary—but if both the length and the angles are kept constant, problems ensue. (One reconciliation would be to keep the length constant but to shift the plank so that it no longer pivots around the mid-point. If so, having the one end lower would also imply having the other end lower.)
A mirror to “all other things equal” is the Latin “mutatis mutandis”, which I often use in the abbreviated form “m.m.”. This amounts to roughly “having changed what should be changed” and gives a greater emphasis on the need to change, as opposed to the need to keep equal, which can give a better perspective.
A claim like “The Americans can shout ‘Down with Reagan!’ in front of the White House. The same, m.m., does not apply to Russians.” would then likely be understood to replace Reagan and the White House with their closest Soviet equivalents. (No, not “Russian equivalents”, as there is no guarantee that the counterpart to Reagan would actually be Russian. Changes are tricky.)
Unfortunately, ambiguity about what should or should not be changed often remains, and the phrases are not always trivially exchangeable. (The original joke could be viewed as having correctly changed the location, while failing to change the person.)
Those reading older English texts, texts written by Classicists, or similar, might also encounter “ceteris paribus”, which is the Latin equivalent of “all other things equal”. I am often tempted to use it myself, but fear the reduction in understandability. The phrase “mutatis mutandis” is similarly obscure but differs in (a) having a convenient and reasonably accepted-in-English abbreviation, (b) not having an established English equivalent. Other cases of such abbreviations include “e.g.” and “i.e.”, both of which are perfectly acceptable in English, but where “for instance”/“for example” respectively “that is” should be preferred when not abbreviating. (Note how the full phrases have English equivalents but the abbreviations do not.)
Such examples give another angle to the main topic, namely that superficially similar cases need not be so when we look more in detail. Again, we need to pay attention to what does or does not change, should or should not change, is or is not fungible, etc.
It might even be argued that “mutatis mutandis” would be a better starting point for this text. (A mental rewrite is left to the reader.)
The main reason for going with “all other things equal” was an original wish for a disclaimer on my use of the phrase, but the topic turned out to have much more potential during a brief brainstorming. (I changed my goal. While such changes have a different character and are off-topic, they are interesting in their own right.) A secondary reason was, however, exactly obscurity and fungibility: the one phrase is much more widely understood than the other. (I did not change my entry point.)
The following is an automatically generated list of other pages linking to this one. These may or may not contain further content relevant to this topic.