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January 18th, 2022

The transitive law of equality states that if A = B, and B = C, then A is equal to C. This is pretty simple and self-apparent. But in many cases, a lazy string of thoughts perverts the pattern of this transitive law. The key to the transitive law of equality is the concept of an equal sign. It indicates that two things are exactly alike in the way in question - with math it’s just about always a quantity of some kind. 4 is equal to 4, always.


The ideal of strict equality is impractical outside of the world of mathematics, and yet people still import the transitive law of equality to make sense of the world. But without the dependable symmetries and equalities of numbers, the equal sign in the transitive law blurs, leaving the door of thinking ajar to pollution.


Instead of equality, the next best thing is used, and this is literally the next best thing. To couch it -ridiculously- in the land of numbers, we might ask: which is more closely equal to the number four? 738 or 5?


Well the real answer to this question is neither. Neither 738 nor 5 are equal to the number 4. But this isn’t how the modern person will answer the question. The words ‘more closely’ in the original question make it seem like there’s a lot of wiggle room, and that we need only determine which number is more like 4. But equal as a quality is unique. It’s a bit like a specific time and date. We might have a January 18th each year, but January 18th of this year is certainly no where near a perfect replication of January 18th of last year. There is merely an association vaguely related to the angle of the sun’s rays as they hit the planet, and the position of the planet in its journey around the sun. But it’s absurd to think that the two separate days are equal in any way.


Yet this is exactly what occurs in much of human thought. A is kind of like B, and B is kind of like C, so A and C must be pretty much the same exact thing. This isn’t logic at all. It’s mere association. This logic by association is the logic of tribal thinking. It’s form of heuristic where long history has somehow ingrained it in our thinking that it’s safe to assume that if a person is associated with one thing in particular, that they are likely inline with all other associations that fall in line without the one particular thing.


Heuristics, like stereotypes, exist for a reason: more often than not, the assumption that flows from the heuristic or stereotype is actually correct. The number of times when the assumption does not flow in the correct direction is small enough relative to being correct that this sort of thinking has survived evolutionary pressures.  And since it works more often than not, and it saves time, there’s little reason to delve in deeper beyond what simple associative conclusions arise.


As our species devises and partakes in increasingly complex ways of cooperating and conglomerating, the success of such heuristics may decay more and more, but the important thing to note regardless of how our collaborations evolve is that a reliance on such logic by association is always fraught with a very real possibility of being totally and completely incorrect.


It’s this heuristic that allows us to ‘jump to conclusions’ so to speak. But jumping to a conclusion is also the fastest way to being incorrect.


As the world speeds up, and time whizzes past faster with age, the need to slow our knee-jerk reaction to grab at the quickest conclusion becomes all the more pertinent. As time increases, the likelihood we encounter a situation where our heuristics fail increases, making our default thinking less and less reliable with time.



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