It’s no secret that I have had and am having great personal struggles in many areas of my life. As I fight to make sense of my life and where I am, I have many conversations seeking the wisdom of those I trust. Last week, in one of these conversations, I was reminded once again of a principle I learned a while ago from a different wise friend. I believe I need to write it down and attempt to explain this principle so it sticks this time. I know that truth, the kind of truth that has power to change life, can come from many sources and in unexpected ways.
To explain it, I ask you to hearken back to college or high school calculus, or at least algebra and I’ll attempt to explain enough for the principle to come across. It shouldn’t be much of a surprise that I would get understanding by using calculus as a metaphor for personal growth principles — a few months ago I used some concepts from physics to explain why certain things stick with me.
The Graph of Personal Growth
Let’s imagine you have a graph of some curve. (I apologize I don’t currently have any diagrams to help you visualize this, it was a lot easier to just get the concepts out than figure out how to get adequate images to describe it.) The X axis represents time: the further to the right you get, the later it is. The Y axis can represent anything we are measuring, something we want to improve. To make it something everyone can relate to, let’s picture the Y axis as being the amount of money we have saved. The higher up on the Y axis, the more money we have saved. But, this can be applied to most anything that we measure, just search for “quantified self” for examples of what many people are using to measure growth in their life.
So, if you are like me and many others in this difficult economy, I can imagine that looking at this graph would be somewhat discouraging. The point at the current point in time isn’t as high on the Y axis as you would like. Looking at this graph with that perspective would very easily make you want to give up on your goals of saving. So, let’s bring the principle that was brought back to my attention last week into the picture to help shift this perspective. It wasn’t explained exactly in these terms this time, but the idea very easily concisely mapped to calculus.
Simply stated, this shift in perspective should be this: the most important thing in personal development and growth is actually the sign of the derivative of the magnitude of some measurement versus time. Restated in the context of our example: the most important thing in reaching our savings goals is the sign of the derivative of amount of money over time. Let me explain this fundamental building block of calculus so this makes sense. Those that understand and remember calculus can skip this next section.
What is a derivative?
As we study graphs and curves in algebra, an important part of describing them is the slope of the line. Slope has always been described to me as the rise over run. Compare two points on the graph that have a straight line between them. The rise is the vertical distance between the points. The run is the horizontal distance. All in all, slope is an easy concept, as we can map it to things we are familiar with, like a ramp or the slant of a roof.
Unfortunately, most graphs are not like those clean straight lines we studied in algebra. But, the same principles apply. Pick two points and the slope between them is also the rise over run. The difference is this won’t exactly match the curve like in our simpler examples. It will essentially be the average of the curve. With another example that we all understand, think of a plot of position over time. What is the slope of that line? Essentially, it’s the speed you are traveling. That slope is the average speed you were driving between those two positions. But what if you wanted to know how fast you are going at a precise moment in time? This is where the derivative is useful. (It is interesting to note that Newton came up with the concepts of calculus to describe the laws of motion, so this example is very apropos.)
To get an accurate speed at a point in time, you want the slope line to pass through that exact point. To estimate this, just pick two points on the curve on each side of that point. To get a more accurate estimation for that point, you would move those points closer to the point of measurement. Imagine if you brought those points in so close the slope line only passed through that exact point of measurement. In mathematical jargon, this is the limit as the length of the slope line between those two points approaches zero.
Why the sign of the derivative?
Notice when I introduced the concept, I said the important part was the sign of the derivative. Why is this the important part of the perspective shift? Going back to the example of saving money, the derivative is the rate at which you are saving; “I’m saving $100 per week”. If you are adding money to your account, the slope line is angled upward. If you are withdrawing from the savings, the line is angled downward.
If you were talking to me about your savings, what if I asked you merely, “Are you progressing toward your savings goal?” I didn’t ask how much you are saving every month, just “are you getting closer to your goal”. To give me the answer, you would just need to know if the derivative of your savings balance at a given time is positive or negative. If positive, yes, you are improving! Yes, you are progressing toward the goal.
The Power of Now
I’ve recently been begun re-reading “The Power of Now” on suggestion of another wise person in my life. To summarize the ideas of this book and other similar things I’ve read, the key to happiness and peace in life is being in the present moment. The past is gone. The future hasn’t yet happened. All you have is this exact moment. So which direction are you pointed in, at this exact moment? Again, isn’t this the sign of the derivative of the curve, by the limit definition? If the past is gone and the future is not yet, and they are not to be considered for your happiness, a measurement that is a numeric magnitude doesn’t make sense. You can only assign a magnitude in comparison to something else. So, for your happiness, you only need the sign of this derivative.
The other nice thing about this perspective is that you can then also ignore how high on the Y axis you are at this given moment. You may be at the lowest point you have been in a long while. Or, you may be higher than you’ve ever been. But, if you only care about the sign of the derivative, it doesn’t matter*. It only matters if you are headed upwards or downwards.
A very personal example and application of this principle is found in the heuristics my nephrologist and I use to determine how I am doing. I have chronic kidney disease and renal failure, and had a kidney transplant two and a half years ago. To monitor how well my kidneys are doing, I have regular blood tests, one of which measures the amount of creatinine in my blood. It is a by-product of the muscles and primarily filtered by the kidneys, and the larger amount you have in your blood indicates the less effectively your kidneys are working.
Now, if we merely went by the magnitude of the creatinine levels as an indicator of my health, it would be discouraging and would probably precipitate treatments I don’t necessarily yet need. Additionally, we’re not even sure if we can use the normal guidelines used for adults, as creatinine is relative to muscle mass and mine is definitely different in proportion and amount due to my dwarfism. So how do we interpret my health? Put in these mathematical terms: what is the sign of derivative of my creatinine levels over time? (Okay, this is slightly confusing, as a higher creatinine level means lower kidney function. Pretend that the curve is just inverted so the positive/negative will work.) If that derivative is positive or 0, I’m getting better or holding steady. IF it is negative, my kidney function is deteriorating.
Though I’m at times discouraged by my current levels as they are a reflection of my health, I consistently have to remind myself that what we seek is this derivative to be positive or 0. Holding steady or improving? Good.
What’s the sign of your derivative of personal growth? Or, how do I make sure it is positive?
This, of course, is a whole other blog entry in itself. But as I bring all things back to the spiritual in my life, as my understanding becomes the synthesis of the truth found in all pursuits, in math and science, in philosophy and religion of all persuasions, and even in the arts, I have leave with some quotes that come to mind. One, from among the most significant music of my life. And the other from stories and words of the sacred books of my faith:
“Life can hold you down,
When you’re not looking up”
- Creed, “Inside Us All”
When Moses and the Israelites were in the wilderness, they face a plague of fiery serpents. God gives Moses instructions on how those that were bit would find relief:
And the Lord said unto Moses, Make thee a fiery serpent, and set it upon a pole: and it shall come to pass, that every one that is bitten, when he looketh upon it, shall live.
And Moses made a serpent of brass, and put it upon a pole, and it came to pass, that if a serpent had bitten any man, when he beheld the serpent of brass, he lived.
The Israelites had to merely lift their gaze to the serpent on the pole, and they were healed.
To tie it all together, then, to what do I strive to look to, so that my personal growth derivative is positive?
Look unto me in every thought; doubt not, fear not.
Behold the wounds which pierced my side, and also the prints of the nails in my hands and feet; be faithful, keep my commandments, and ye shall inherit the kingdom of heaven. Amen.
I hope you can find the source to which you look up in your own life, whatever it may be for you, so that your personal growth derivative may be positive. I hope you can make this shift in perspective in your life, as I am striving to do so in mine.