Humans like to measure things, have objective definitions of what “is” - proof of concept of understanding; a standard of reference. Creating organization in an entropic world makes us feel like we are in control. This has partially risen from our fear of the unknown from an evolutionary standpoint (darkness in a cave means potential predators; we wish to light up this cave so we are aware of the dangers that reside within; we cast light and make decisions based on what we observe). The same metaphors can be translated from a physical to nonphysical standpoint based on the social structures that currently exist: casting light on the unknown, general satiation of curiosity, and knowledge acquisition for social survival.
But what about the seemingly immeasurable? How do you quantify self?
You can measure the external self through examining the hardware that makes up our skin, blood, bones. That’s easy enough. We can attribute numbers to them: 206 bones in the body, 32 teeth, 20 extremities in form of digits, 4 vascular chambers in the heart, 26 feet of intestines wrapped tightly around our abdomen, an even greater length of DNA (6 feet in each cell x 10 trillion cells) compressed by histones into spirals. We have 86 billion neurons, and they spark connections with each other, within and outside of our brain. The body is a beautiful, supremely efficient machine, optimized through generations of adaptivity. With utmost coordination, we create beautiful things that inspire emotion in other humans around us, in form of artistic, musical, edible, engineered artifacts. As a species, we imagine, communicate those imaginations through a vehicle of language, navigate complex social structures to turn those mental images into reality. On becoming, a vision changes as it continuously manifests.
But back to the question: how would you quantify self? This challenge is especially hard because even while we can measure the external self in some capacity, the internal self is constantly changing. In the same way that an artifact "becomes", our identity emerges and changes - there is an original thesis based off metrics in certain definitions of success and fulfillment, we acquire continuously diverse meanings of transcendence as we go through our own deeply personal journey, and we adapt our actions along the way. But predicting our final identity from the get go is as futile of a process in perfection in the same way an original blueprint of a building is different from what is the built outcome, whether adapting to practical boundaries (like the laws of physics, monetary scarcity, availability of construction workers, political zoning limitations) or changes around intentionality (architectural trends, flux of enthusiasm and energy around the project (read: boredom), general human fickleness).
To further complicate things, an identity changes even more so when you try to introspect on it. Similar to the electron, we are unable to immediately observe it: when we cast light on it, photons change its course of the observed electron. In other words, when we try to define our identity, it fractures and its properties change.
Heisenberg's uncertainty principle states that we can only observe position or velocity of an particle. If you try to understand your own identity in the same framework, which would you choose to have complete clarity on?
From a positional standpoint, it is helpful to understand where you are - it provides context. But it’s unreasonable to define someone based on where they currently are, versus their derivative: which takes into account desire to change and ability to enact change. While position is a more rationalistic approach to evaluate current conditions, at the end of the day, I personally think understanding the derivative is a more optimistic outlook and is more indicative of one’s fullest potential self.
Numerically, in the same ways that you would run a discounted cash flow model on a company (discounting all future cash flows to a present value), the weight that you could place on a derivative (determining % value of future identity in present terms) depends primarily on 3 things: 1) growth rate, 2) amount of time forecasted into the future, and 3) discount rate - translating to our current example, opportunity cost of complacency (in other words, certainty of change).
In other words, a greater emphasis should be placed on derivative as it is correlated to motivation: if change is consistently above 0, is sticky (lasts through time), and is highly motivated. For the last point, change is usually catalyzed by survival instincts, like adapting to pain or a tragedy (stress), but sometimes out of love (perhaps eustress) - to become better for something greater than yourself.
Out of those two, the latter, though more infrequent, is the more sustainable choice. Love compounds over a longitudinal period of time - though likely day to day, the change that is motivated from pain is appears greater, there is a longer benefit to maintaining a steady compounding increase. To put in numbers: a 1% daily increase over a course of year results in a (1.01)^365 = 38x change, whereas a 10% daily increase over a course of a month results in about a (1.10)^30 = 17x (less than half).
TLDR; in summary, it is difficult if not impossible to quantify or measure identity on the intangible level, but perhaps a conclusion we can come to mathematically speaking is to more strongly take into account the derivative of change than current position when valuing the self. And that in terms of maximizing this derivative, requires sustainable growth over a longer term period of time (likely to come from a place of love versus fear / pain).