Discrete versus Continuous

I have a degree in mathematics and I’m a self-admitted geek. This will be important to know as I’m going to introduce the concepts of a discrete function versus a continuous function, in this devotion.

I’ll be gentle.

A discrete function is a process that ends in one of a finite number of possible outcomes. For example, when you throw a dice, you know that it is going to land with one of six faces on top showing 1,2,3,4,5 or 6 dots. Another discrete function is a coin toss. You toss a fair coin and you know it’s either going to show heads or tails.

A continuous function, on the other hand, has a infinite or very large number of outcomes. For example, every light bulb will eventually fail and have to be replaced. The question is how long from it being first installed will it be before it fails. Some light bulbs fail quickly (maybe some problem when it was made in the factory) but most of them last the twenty or so years advertised and then fail, some sooner, some later. Another continuous function is our own death. At birth, the average person can be expected to live for about 75 years but we all know people who have died much younger and much older than that average.

A meme I saw on social media showed steps next to a ramp. The steps represent a discrete function (you are either on one step or another) while the ramp represents a continuous function (there is an infinite number of spots between the bottom and the top of the ramp). Ironically, people tend to think in a discrete manner even when the process and outcomes are much more complex. 

Have you ever watched a baseball game where the batter, who has a .500 average, is batting for the second time (after striking out in his first at bat), and thought it was his turn to whack that ball?

A situation I dealt with, a lot, was other executives who would look at something like a flu shot (approximately $20) and compare that to a hospital stay for pneumonia complication from the flu (approximately $50,000), and jump to the conclusion that investing in flu shots for our members would save money and allow us to lower the premium rate. (spoiler alert - it does not mainly because you have to pay for the flu shots for everyone and the chance of developing pneumonia complication from the flu is low).

The point is that when you compare two things, you need to take both severity (how much something costs) and incidence (the chance of something happening) into consideration.  In life, most things are continuous in nature and we find a means to look at them in a discrete manner to understand or get insights into them.

“But if you call yourself a Jew and rely on the law and boast in God and know his will and approve what is excellent, because you are instructed from the law; and if you are sure that you yourself are a guide to the blind, a light to those who are in darkness, an instructor of the foolish, a teacher of children, having in the law the embodiment of knowledge and truth— you then who teach others, do you not teach yourself? While you preach against stealing, do you steal? You who say that one must not commit adultery, do you commit adultery? You who abhor idols, do you rob temples? You who boast in the law dishonor God by breaking the law. For, as it is written, “The name of God is blasphemed among the Gentiles because of you.” For circumcision indeed is of value if you obey the law, but if you break the law, your circumcision becomes uncircumcision. So, if a man who is uncircumcised keeps the precepts of the law, will not his uncircumcision be regarded as circumcision? Then he who is physically uncircumcised but keeps the law will condemn you who have the written code and circumcision but break the law. For no one is a Jew who is merely one outwardly, nor is circumcision outward and physical. But a Jew is one inwardly, and circumcision is a matter of the heart, by the Spirit, not by the letter. His praise is not from man but from God.” - Romans 2:17-29 ESV

Salvation is a free gift from God by repenting and believing in Jesus Christ as your savior. But that is just the first step on our faith walk. Expanding our mind to focus on God and not ourselves is a lot of the journey.

Life is a continuous function.