Mathnificent Word of the Week

Originally posted on
November 26, 2024

scheme

Photo by Mo Tawil on Pexels

scheme

/’skēm/

noun

The functions that must satisfy the conditions and the compatibility demanded within a topological space.

“The scheme was a success because the responsibilities were properly distributed and well-rehearsed.”

Photo by Mo Tawil on Pexels

Be certain without ever even thinking about crossing your fingers.

Yes, many mathematicians and other folks who are drawn to the sciences tend to be intense planners. Sometimes a little overwrought in that planning, yet there are times that that level of thoroughness is paramount to reaching success due to the impact of what a failure in execution could bring to not only those intimately involved in the production, but also the many who’d be impacted by its long-term ongoing ripple effects. 

Can we ever reach 100% certainty of success before embarking on a mission? It seems far-fetched to insist upon that mindset yet — what about space exploration? Or, as seen in the image above, deep-sea exploration. Seems like all variables must be considered, examined, and rehearsed ad nauseum to even be able to understand where the weak points exist. The risks are the most risky of all the risks to exist.

After this month’s federal election here in the states, I got to thinking about mathematical schemes* – a concept that exists in algebraic geometry. The guy that will be President of my country in just a few short weeks (I avoid saying his name for fear that that acknowledgement might give him even an ounce more of power) is going to do harm to many people, an amount of which is so large a number that it’s easier to list those he will not unduly harm (that would be the people who identify themselves to have the same traits [personality and otherwise] as himself).

When the word scheme is commonly used, you think of a plan that – though clever – may also be sneaky, secret, or even dishonest. Not so in mathematics. There is no trickery at play. In fact, it’s practically the opposite – where transparency and every detail is openly discussed and and examined in the vibe of no-stone-let-unturned. All input from all experts involved is welcome – and needed. In a recent Math WoW for the word function, the key component of that word is not about the power of, say, the “function of a tool” but the function of the relationship between the tool and the human using it as well as the relationship between each human using their own tools in harmony, in a group, together.

So. Producing a successful (mathematical) scheme takes time. Much trial and error – but in spaces with less reverberation. There’s no short-cut, no “this person is an expert in this thing, and so is that person in that other thing, let’s go execute on this scheme.” Nope — all players must rehearse together, using their functions, as a team so that any incompatibility is exposed in order for it to then be rectified – before the time comes to do that deep-sea exploration.

I am hoping that there are political (mathematical) schemes in the early stages of development, now, and that the team members can, and will, rehearse over and over. Then, when it’s time to hit the GO button, just as if we’re all going up into space or down into the ocean, all systems will have already been put through their motions multiple times – and then we can grab at that opportunity to shift the power.

* a scheme is hella difficult to explain and I, admittedly, slightly simplified the definition for this Math WoW. If you’d like to dig in further I found this paper by contemporary mathematician Peter Nelson to be helpful.


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