Two times two is four

Here is another comment response the system threw out for being too long, and that I thought was worth bringing up to a blog post. This is thanks to Stephen Shimshock, who commented on the Of hypotheses and tools, models and frameworks post. Stephen mentioned how my diagrams (in the Better confluence diagrams post) that placed patterns like beaver dams, bees nests, dictators and discussion groups into locations could be confusing because they seem to claim that the placements are definitive. I hadn't meant to claim that, and in fact went back and added a note about it in the post itself.

I often come up against this issue when talking to people about sensemaking models and frameworks. They say, that's nice if you are talking about things like tastes and opinions, but there are large areas where everyone agrees on things, and what is the point of pretending to consider differences there?

I have two responses to this argument. The first is that there is little utility in making definitive placements of anything in a sensemaking space, since exploring similarities and differences in placement is the whole point of the thing. If something is so very well known that every possible person in every possible context is sure to agree, it is probably not connected to the reason you are doing the sensemaking anyway. If it's worth thinking together about, it is unlikely to be as common as you think. And if some things that never differ do slip in and everybody agrees on them, what is the harm in letting them stay? It reminds me of what we used to say when we found a little bug in our food: it won't eat much.

Second, be careful about what you think everyone knows, because it is not always what you think it is. Even the same person at different times in their life or in different contexts (where different identities come to the fore, for example) might place things in different spots. Even "things we can all agree on" sometimes hold hidden diversity.

Now here is my all-time favorite example of a perfectly known, universal, extreme-hierarchy item that isn't. Years ago I was reading Bertrand Russell's "A History of Western Philosophy" and came across this quote:

"... individuality -- what distinguishes one man from another -- is connected with the body and the irrational soul, while the rational soul or mind is divine and impersonal. One man likes oysters, and another likes pineapples; this distinguishes between them. But when they think about the multiplication table, provided they think correctly, there is no difference between them."

When I read this, I burst out laughing, jumped out of the bathtub and ran to read it to my husband. Why? Because I am blessed with the neurological quirk of synesthesia, and specifically the type called ordinal linguistic personification. That's a fancy term that means, to me, numbers and letters (and some other abstract symbols) are not shapes or mental constructs but living beings. Some are my friends and some ... are not my friends. Supposedly this is "cross-talk" between brain regions, the dealing-with-beings circuits mixing with the dealing-with-symbols circuits. As a result I am far from having no "individual" or "irrational" reaction to the multiplication table, a construct which Russell used many times to symbolize that which is unequivocally known (yes, right there in the bottom right hand corner).

To me, the very idea of multiplying and adding numbers is grotesque, like blending cats. I often confuse adding with multiplying, because it is all artificial and nonsensical. It is like a second language into which I must translate with difficulty, partly because doing arithmetic produces emotions that make it difficult to do quickly. Sometimes encountering the beauty of an arithmetic statement is akin to suddenly seeing a wonderful picture -- I simply have to stop and enjoy the view. Other arithmetic operations are dark alleys with frightening aspects, and coming upon them suddenly makes me shudder and back away. Imagine adding up your checkbook and suddenly finding you are holding a dead mouse.

In third grade the teacher often had us play a game where she would read out arithmetic operations one after another in rapid-fire speech, and we were to keep a running answer. For example, she would say "five plus three", then "times four", then "divided by two", then "plus nine", and so on. I always got stuck on the first operation. I sat there thinking "what is five plus three?" with five-beings and three-beings swimming around me. By the time I worked my way to five plus three being eight (that being a preposterous answer but correct, like a toad and a magpie making a moose), the rest of the class was way ahead. I usually sat drawing doodles or staring out the window until the game was over. Even today when I wrote the title of this post (2x2=4) I had a few moments of panic while I tried to guess whether it was true or not. I think it is. (The quirk has its up sides: apparently better-than-average reading and writing speed, visual memory and pattern recognition (2D only!), spelling accuracy, and maybe some degree of richness of experience (at least I can't imagine the poverty of such a depopulated universe), so turn your pitying eyes away, all ye who judge, but at any rate that is not the point of this post. The point is how the things we consider most universal may not always be. Not only that, but among synesthetes, each has their own universe of individual, irrational meaning: my five may be as nasty as your two, while your five may eat out of your hand.)

Do I "think correctly" about this? Obviously not, according to Bertrand Russell (who in his defense probably never heard of synesthesia). But considering that the incidence of synesthesia continues to go up and up (it was once estimated at 1 in 20,000 and is now up to 1 in 20), it's certainly something to think about. The most amazing part of the story is that the study of synesthesia lay dormant for several decades of the past century (it fell out of style with the advent of behaviorism) and millions of people were dismissed as strange, or more likely, like myself, learned to hide their way of seeing things. It makes me wonder how many other cognitive and perceptual diversities we overlook as we talk about what "we" know and how "we" think. I've heard that some people might have four or more types of cone cells for seeing colors, and that some people experience greater ranges of taste. Perhaps there are many more such differences. One reason we might not see them, even in plain view, is that being different is scary. I've graduated from telling only my closest friends about this quirk to being able to admit it to the world, but it took decades to accomplish the task, and I would never have made the leap if I could not link such an essay as this to authorized (hierarchical) defenses that make it clear I am not insane or delusional (or just credulous).

I also found this gem of a connection in Dostoyevsky's wonderful Notes from the Underground years after that. I'll shorten the passage as much as I can (but here are links to the longer version; part is in Chapter III and part in Chapter IV of Part I):

[When some are] confronted with the impossible they subside at once. The impossible means the stone wall! What stone wall? Why, of course, the laws of nature, the deductions of natural science, mathematics.... [Y]ou have just to accept it, there is no help for it, for twice two is a law of mathematics. Just try refuting it.... Merciful Heavens! but what do I care for the laws of nature and arithmetic, when, for some reason I dislike those laws and the fact that twice two makes four? ... Oh, absurdity of absurdities! How much better it is to understand it all, to recognise it all, all the impossibilities and the stone wall...

 ...man is a frivolous and incongruous creature, and perhaps, like a chess player, loves the process of the game, not the end of it. And who knows (there is no saying with certainty), perhaps the only goal on earth to which mankind is striving lies in this incessant process of attaining, in other words, in life itself, and not in the thing to be attained, which must always be expressed as a formula, as positive as twice two makes four, and such positiveness is not life, gentlemen, but is the beginning of death. Anyway, man has always been afraid of this mathematical certainty, and I am afraid of it now. Granted that man does nothing but seek that mathematical certainty, he traverses oceans, sacrifices his life in the quest, but to succeed, really to find it, dreads, I assure you. He feels that when he has found it there will be nothing for him to look for. When workmen have finished their work they do at least receive their pay, they go to the tavern, then they are taken to the police-station--and there is occupation for a week. But where can man go? Anyway, one can observe a certain awkwardness about him when he has attained such objects. He loves the process of attaining, but does not quite like to have attained, and that, of course, is very absurd. In fact, man is a comical creature; there seems to be a kind of jest in it all. But yet mathematical certainty is after all, something insufferable. Twice two makes four seems to me simply a piece of insolence. Twice two makes four is a pert coxcomb who stands with arms akimbo barring your path and spitting. I admit that twice two makes four is an excellent thing, but if we are to give everything its due, twice two makes five is sometimes a very charming thing too.

Twice two makes four, the "stone wall" of fact, is definition. It is What-Is. Understanding it all, recognizing it all, all the impossibilities and the stone wall, is sensemaking. It is What-Appears. It is the process of the game, not the end of it. If we care about nothing but pushing on towards certainty, what we find is not life but the beginning of death. And there will be nothing left to look for.

Having said all that, I'm the first to admit that certainty is as attractive as it is pert and insufferable. You see how easy it is to slip into assertion, as shown by my here-is-a-beaver-dam diagrams. You'd think I would know better, but we are all vulnerable to, as the anthropologist Diana Forsythe termed it, "'I am the world' thinking." While definition has its purposes, it is useless for sensemaking. I'd even go so far as to say that definition is the opposite of sensemaking. Every time a person says "this is how things are" the only reasonable response is to take sides. It is only when we remember to say "this is one view of how things are, and here is another, and ..." that we start getting somewhere.

I guess what I'm saying is, well, Stephen said it so well in his comment that I'll let him say it again here:

I see the entire framework as negotiated space. Even when you look at the "simple" or "pure hierarchy" area, what is known to one may not be known to another. Each of us have our own framework, and any group framework is a negotiation of meaning for that specific context. This is exciting because it offers (depending on how sense making is set up) the opportunity for many voices (from all levels of power) to get incorporated into a general understanding. And, if the process is done ongoing that understanding can change and grow with the community context.

Precisely. And that "general understanding" can be and should be as diverse as the community itself.