…one must not think ill of the paradox, for the paradox is the passion of thought… — Kierkegaard
I am thinking, and firstly learning about, ‘mutual exclusivity’. It’s interesting to me. Here is some of my thinking that this learning process activated. Please note, there is some winking in my wondering (hence, the title as it is).
I understand that ‘mutual exclusivity’ is a concept from mathematics, from statistics and more specifically from the study of probability. I presently understand it as a mechanism where events that are mutual exclusive, are events that cannot happen at the same time.
Would I then be mistaken to continue thinking that these events are not possible to be combined and that therefor these events can not occupy the same space and time?
Yes, in my ignorance, questions pop up. I’m still learning about ‘mutual exclusivity’’s deeper meaning and about how to perform computations associated with it. So, my mind begins to wonder.
What if the fact that events cannot happen at the same time, are not happening at the same time, because of the manner with which we look at the events to begin with, rather than because of some intrinsic attribute of the events that are believed not to be possible (or that are considered to be irrational) to occur at the same time? OK, that’s a mouth full. What I think I am asking is:
- if there is a cup of coffee (‘A’) and there is a cup of tea (‘B’);
- if there is a group of humans that is asked by an other individual (yet not asked in person but rather by means of a questionnaire): “which do you prefer, ‘A’ or ‘B’?“
- if this questionnaire allows for only 3 answers: ‘coffee’, or ‘tea’ or ‘no preference’…
…is then a ‘mutual exclusivity’ not simply imposed, by the design of the questionnaire and this by ignoring dynamic attributes?
Concretely this seems, for the moment, to mean to me that the asked human(s) must express one and only one preference, or must express not to have any preference. I guess that some (to me) unknown amount of individuals might be clear on how to answer this. Though, would all and every individual have such a fixed clarity?
The answer of “no preference” could in turn be interpreted by the person indirectly asking about the preference (and who is only looking at the answers in a data set organized in a table, combined with the output from other individuals who were asked the same question) as: “…so, x, y and z individuals can be offered a random choice of these two offered drinks;” or as: “I would offer nothing at all to this individual, or that individual, claiming to have no preference possibly because they like neither coffee nor tea“.
Now, what if the individual presented with the obligation of choice is polyamorous about her or his relationship with both coffee and tea; then surely, “no preference” would be a betrayal as much as only choosing “tea” over “coffee” or vice versa; no?
So, it feels to me that the resulting data set seems to create ambiguity in the reader of the data set (I being one such yet-unclear reader). What could be the usefulness of such data set, I wonder. I truly wonder and do not yet judge. I also laugh, indeed, equally so, what is the use of all this writing here? The answer to that could be someone else’s blog post…
In support of such blog-post: someone, whom I care about (measurably more than tea or coffee), recently claimed that those who speak too much (this can be substituted with “write”) probably like espresso rather than an average cup of coffee.
Indeed, this unveils yet another issue with the questionnaire: what kind of coffee (or tea)? This is then compounded by a dilemma when the individual begins realizing how one could be judged by others if choosing one kind over another. Therefor, instead, the individual might be tempted choosing, perhaps falsely, one of the many types of tea categorized under the choice “tea” (…not to mention, the problem with “tea” and all those non-tea-based “teas” which, might be generally better labelled as infuses…). This, I sense, could thus lead to biased data and a false sense of mutual exclusivity.
Is then this ‘mutual exclusivity’ possibly a construct (sure, I assume not at all times), out of some (lazy) convenience? Does it serve a model rather than serve the complexity of (human) experience / of the realities of complex dynamic systems?
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Perhaps, less social or psychologically-motivated: does such exclusivity ignore going beyond some possibilities outside of Newtonian physics or outside of binary logic?
…Or is the “construct” not that of ‘mutual exclusivity’ alone but also, or rather, that of an educator aiming to simplify the introductory teaching of ‘mutual exclusivity’? Do we, as learners, first have to unquestioningly submit and accept such over-simplifications to become enabled to understand the basics? Surely, I agree, I do need it… While the risk does exist that over time, and across learning as a habituation process, someone could forget one’s love for the other choice.
Nevertheless, it would be nice to be hinted, that exciting complexities need to be considered towards future learning, which could be leading to possible paradoxes, dissonances or fuzzinesses. It’s OK, the evaluator of the data will survive; it’s only coffee or is it tea?
This forecasting of future learning would map out a learning path to me which I could look forward to while at the presently bland stage of looking at a simple (and perhaps somewhat acceptably flawed) data set towards learning about ‘mutual exclusivity’. Easily solved: I’m now hinting this to myself.
I imagine such intuitively felt potential complexity is implied in questions that bubble up in my thinking and this as a side-effect of my process of learning. To continue, for the brave reader, here is another one:
What if the preference (i.e. ‘coffee’, tea’, ‘no preference’) is defined or influenced by an external factor (or a set of factors)?
For instance, one could assume the existence of a third influencing item, catalyzing or weighing the choice into a certain direction. Note, ironically, this assumption of there only being a third and not a fourth, etc., feels as a reduction as well to me, and one that could almost equally influence the questioned output (i.e. a data set of three possible answers collected from a set of individuals and organized in a table).
Anyway, such external influence does not yet feel too far-fetched to be a possibility. I feel it is more realistic than a choice created as being a static attribute (i.e. a clearly definable choice, at all times, in all environments, with or without any additional actors; e.g. “I am a coffee drinker; period.“). I think such external influencing attributes seem to feel to be more common than a clear inherent preference to the individual being asked as implied in the basic introduction of ‘mutual exclusivity’?
For instance, coffee is preferred over tea depending on the time of day. Tea is preferred depending on other people with whom the individual, who is asked about the preference, is meeting with.
Imagine then, in addition, if those people would be met at the time of day that would make the individual prefer coffee, this imaginary individual here would still choose tea since the individual, at that time and in that space, who would otherwise decide for a preference of coffee versus tea, has now decided this as being less weighted than her/his social interaction and experience of bonding as symbolized by the ritual of the tea drinking with others, who prefer tea (or so the individual assumes).
So, under these external attributes, the individual chooses to drink tea whereas otherwise, when no one else is there at that time, the individual would choose coffee. Unless, there is an article in her/his favorite newspaper questioning the health benefits of the one over the other.
At that same moment, yet on another day, the individual, as a biological system, simply is not thirsty. Then “preference” of any kind becomes temporarily irrelevant. If at that moment the individual were to answer to the inquiry, she/he would (have to) then dismiss this possibility of their reality as non-existent in the model.
Or, surely, such situation does not have to result in a one-time outlier on a scatter diagram. Contrary, as in a diplomatic ping-pong match of thinking where no one thought has to win, it might equally result in an outlier on such scatter diagram; if the individual were a consistent creature of unwavering habit and ritual. Mmmmmm, come to think of it, could one actually plot this triangulation of choice onto a scatter diagram? I need to check this.
“Not thirsty” as a preference option is non existent in the given questionnaire. By the way, as suggested previously, this is different from not having a preference, from liking either equally as much, and different from not liking coffee nor tea. Though, the individual does not realize that with sufficient explicit and subliminal messaging he or she will believe to be thirsty after all for that or the other beverage.
No, such playful consideration of complexity is not nihilism nor defeatism. I will return in vigor to my learning of these basics and that during and following this writing.
Options, options, options of recombinable outcomes that are being less-then-mutually exclusive, if seen over time and space and thus in changing contexts. Perhaps, I am trying too much to make a model as a 1:1 representation of the complexities of reality?
At least, I suppose that in some of the above scenarios, the data collected is hence dramatically influenced not by the preference of the individual as if a static fact (i.e. “it’s just a preference“). Rather, it is defined by other attributes that temporarily weigh in more. This statement too seems to be an abstraction of sorts and therefor could lead to a (useful) reductionist model. Nevertheless, it feels as less dismissive of experiential complexities and it feels as more sensible towards deviations, away from the idea of fixed preferences (over time and space), as the one I was presented with at first.
If my thinking is flawed, where is it flawed? (besides an obvious and dismissive and debasing: “you’re making it all too complex; who gives a ****, dude!“)
Gosh, indeed, suddenly ‘mutual exclusivity’ becomes excitingly complex and granted, who cares? Well, …I do :-p
How would one go about calculating such externally influencing factors? How do statistics that do not consider such externals actually provide sufficiently accurate information for interpretation? So much still to learn…
With this writing, I have just further carved out my passion and vigor to continue learning about this ‘mutual exclusivity’. It’s rejuvenating to realize I know so little and could still explore so much.
I mean, I’m really just starting and the application of the “general multiplication rule” versus the “addition rule” alone is already intriguingly startling. That’s perhaps for another post.
For the moment I will continue my very basic study, accepting the choices between “cat or dog” and “coffee versus tea”.