Life and dx

Life and Calc

As I was sweeping the basement of an unfinished house my thoughts drifted into a flurry. All kinds of emotions from love, hate, pride and uncertainty. It was precisely at this moment when I realized that I was listening to my mind on autopilot. These were all ideas that I’ve thought about just with different endings and openings. The point is I wasn’t in control. The entity in control was a collection of past selves, their collective feelings, some of which I don’t need to revisit, many of which that’s already been processed. As soon as I realized this I set my mind straight, focus on things that important things. How can I increase shareholder value? Just kidding, not really, but what problems can I solve in construction. Imagine if every construction worker was 10% more efficient, we would save money on building houses. The labour shortage would be tamed, most importantly I’d make money doing something that matters.

Connection to Calculus

\(\int f(x) dx \rightarrow \ \sum_{i=1}^{100} f(x_i) \Delta x\)

\( f(\Delta x) = \Delta y \rightarrow \sum_{i=1}^{100} \Delta y \Delta x\)

This makes a little rectangle. Let’s say with these little rectangles you can make any shape(dog)

|          _ _
   |         |   |_ _
  _|         |       |
 | |_______|         |
 |         |    _    |
 |   _ _   |   | |   |
 |  |   |  |   | |   |
_|__|___|__|___|_|___|____

---

Now let’s imagine these little rectangles shrink so small into parts called infinitesimal units.

\(\Delta x \rightarrow dx\)

\(\Delta y \rightarrow dy\)

\(\sum_{i=1}^{100} \Delta x \Delta y \rightarrow \int_{1}^{100} f(x) dx\)

Now since we have really really small pieces we can make a better dog

|         
   |          _..__
   |        .'     `-.
   |       /  (o) (o) \
  ((_     |            |
   \  `'-.|      __    |
    )      `-._______.-'
   /                  \
  /   _.._      _.._   \
 |   /    \    /    \   |
_|__(_\____)__(_\____)__|___

Now, thank you for reading this far my point is our life is made up of these infinitesimal parts. Parts that seem like they don’t matter but they do. Over time as .

\(100 \rightarrow \infty \text{ and } x \rightarrow \infty\)

All we can really control are the tiny little moments, even as small as the thought you are having at this every instance.

The reason I wanted to write this is because the dx better illustrates why you should care about all the small moments in life, specifically our thoughts, because thoughts →actions→habits→life. I would always tell myself ‘‘just this once”, or “I’ll start tomorrow”, or a “small little bit can’t hurt”. These statements are true, it doesn’t really matter if I start now, and that little piece of fast food isn’t going to cause cancer, but its much deeper than just a moment. Infact, that might be the last time you thought about it, because pretty soon the next time someone brings up fast food you are probably going to eat it without thinking about it. I can admit this has happened to me so many times, where I’ll say I’m going to listen to podcasts and take my laptop to bed, and just watch videos all night long, ruining the next day.