I just gave you the definition of a vector. And let me tell you, vectors are an incredibly concise way to provide a whole lot of information.

If you haven’t noticed, I like the way concepts are contained in the principles of physics and mathematics. Most people never get past the requirements to learn and become frustrated¹I honestly think frustration is part of the process of learning by trying to replicate how someone²and lots of someones decided to write down how they observed the world and used those observations to make predictions.

From one perspective, all of the science and mathematics we learn is just the way someone once asserted that if we write the formula this way, if we assign the variables in this manner, if we use an equation, an outcome would be known. And that outcome could help them make a choice. And that choice would benefit them³So, and this is key, the truth is whoever’s system we learn and follow could be entirely wrong..

So choosing to believe that knowing a magnitude and direction is the right way to describe a force in the world is just that – a choice. Remember that.

Just like Venn diagrams, I find vectors helpful in grasping how to interact, and succeed, in the world.

When I encounter new people and new situations that I know are going to have power over my little universe⁴And how I hate to admit anyone has power over me!, I generally try to figure out HOW MUCH⁵magnitude power they have and WHAT⁶direction their motivations are. Basically, I try to figure out their vector as it relates to me.

Direction, most people think, is where you are going. Is it? Is it where you are going? Or does it also tell you where you come from?

My boss recently retired, and I admit, I have been analyzing him and all the people I work with as vectors. Where did they come from? Where are they trying to go? How are they influencing me as they transverse this universe I also inhabit? 

If you are going to be part of a team⁷Not that I suggest doing this, it is a good idea to understand where the team members come from. Each of us has our own universe. I try to understand mine, but I also want to understand the universe you are in. After all, more data leads to better predictions. 

Magnitude is tricky. One of my favorite concepts from linear algebra⁸I love linear algebra. But that is another letter. is transformations. I see a vector in a space, but I want to look at it a different way. Matrix mathematics, should I fully understand the relationships between two universes, allows me to take the definition of a vector from one universe and represent it in a new universe. The trick⁹should I chose to make the transformations reversible, as I recall, is to make sure you can reverse the transformation and not lose any information¹⁰I am pretty sure that type of transformation is a translation..

With magnitude and direction, with the information of the original universe and the new universe, and with a translation set up, so much information is available to me.

But. There is a catch. I can’t forget an important reality. It is unlikely I really understand the relationship between the two universes, and thus it is unlikely my transformations are really translations. It is unlikely I can base all my decisions on this perspective. I can’t forget that I don’t only know what I observe. I also know my observations are certainly not complete. Or, as one of my favorite bosses once told me, “Remember you don’t know what you don’t know.”

Another great thing about vector math is projections. Even if you cannot transform a vector from one universe to the other, you can see the projection of a vector in another universe onto your own.

Last week, I had a coworker tell me they weren’t going to read my emails. For a millisecond, I saw red. I mean, how could it not be offensive to tell someone the emails I wrote were not a priority¹¹In my universe, I hear, “What you have to say is not important.? And, to be honest, that may be how they feel about me and my emails. I don’t know. The vector of not reading my emails is coming from their universe. I only know how it appears in mine — a projection from their environment into my environment almost always loses some of the information¹²Aren’t vectors fun? So much more can be said about them!.

I spend a lot of time predicting things about my life and the people in my life¹³Call me Cassandra. For example, my commute. I want it to be deterministic. I want to know when I leave the office at X time, I will be home¹⁴and sipping a cider by Y o’clock. Unfortunately, since I commute in the DC Metro Area, this is not possible¹⁵Washington, DC is not deterministic in many ways. But that is also another Letter.. So the vector I observe of my bus driver, my bus route, the traffic around me, and the possibility of the Presidential motorcade planning to transverse the national mall makes it almost impossible to determine when I will be reunited with a Strongbow¹⁶Yes, a plebeian cider. But an most excellent one!.

I am sometimes led astray when I don’t recognize all the things I don’t know. So, this is not a perfect model. It is a start. Remembering it is just a start brings us back to the choice to follow the model and see where it leads, which is part of what makes the journey interesting.