Mathnificent Word of the Week
Originally posted on
January 10, 2023
Photo by Ryutaro Tsukata via Pexels
neighborhood
/ˈnā-bər-hood/
noun
The set of all points with distance from a given point strictly less than a specified value.
“As she drew on the graph, Ms. Stoltz explained how to define the neighborhood within a triangle or a rectangle.”
Photo by Ryutaro Tsukata via Pexels
One of the most important things in mathematics are relationships.
The other day I was thinking about manifolds because, c’mon, look at this wacky shape, isn’t it cool? And while I was reading about them, I was reminded that just like most things in the study of topology (which lives within the massive discipline of geometry), defining what the neighborhood is within a manifold is integral to the very definition of the manifold itself.
manifold - top view
Now, I realize what I’m about to posit sounds like a Carrie Bradshaw question, but: Is defining what my neighborhood is an integral part of defining who I am?
For my computer science friends and any other readers who have dabbled in the world of information technology, I’d bet you’re quite familiar with neighborhoods in regards to data networks. These tech networks also have trees (that have branches!) and paths (of information going from Point A to Point B and on and on to other Points). It’s all further evidence that people have been humanizing math forever-eva. All of this was born from stuff like graph theory, and combinatorics, in addition to the aforementioned topology and geometry.
So, in my process of defining my neighborhood using the mathematical definition, I label myself as the ‘given point’. Then I need to specify the value of the distance from myself to all those points in my set (AKA in my neighborhood). Do I take on a value that is large, as in: Is my neighborhood global? Or do I define the measurement of my neighborhood to actually be local, so maybe it’s synonymous with the borders of my state, or my town, or the company I work for.
Looking at the word value and considering how important that word is to me IRL, I realize that since we’re now talking about human relationships, I need to recognize one of the other meanings of the word value: worth. Not the worth of others in the neighborhood nor the worth of myself, but the worth of the relationship itself; the worth of generating it and maintaining it, for everyone that is a part of it.
And that’s what convinced me that defining my neighborhood does indeed contribute to defining who I am; it’s kind of the mathy version of Show me who your friends are and I’ll tell you who you are, except instead of focusing on the reflective part of that saying, the focus is on – as with any good mathematical concept – the relation of all the elements that are present, and what they can produce together, being the parts of a whole (neighborhood).
In 2023 and beyond, my neighborhood includes all y’all. The value (measurement) I specified is my potential reach to readers like you as well as the value (worth) of the relationship we have with each other.
How do you define your neighborhood, especially as you start putting action to your 2023 plans?
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