Many elements of our universe function in algorithmic patterns, such as philosophy — The Turing Test; mathematics — The Sieve of Eratosthenes; pastimes — Chess (MTD-f, specifically, in reference to computer programs); economics — Algorithmic trading; psychology — The Thurstone Scale. These are only a few examples. What if, say, each individual’s degree of generosity could be characterized based on a formula, or a graph?

Bacteria multiply by binary fission after reaching a certain size. Their maximum growth rate in a given medium at a certain temperature is consistent from trial to trial. In other words, if you put the same bacteria into the same conditions, they will always take the same amount of time to double in number. A growth curve can be constructed to denote the “doubling time” or “generation time.”

Typically, three stages are observed. “Lag” phase, the first, represents a period of adjustment for the bacteria after they are introduced into the new medium. It takes them some time to “gear up” their own enzyme levels, metabolic precursors, etc. to make full use of the newly available nutrients. The growth is low but increases steadily. When the growth rate hits its maximum, the bacteria are said to be in “log” or “exponential” phase. Bacteria will stay in log phase until nutrients begin to run out and, thus, enter “stationary” phase, a time of declining growth rate. Sometimes a fourth stage is observed, “death” phase, where the number of bacteria decreases dramatically as cells begin to die off due to crowding, lack of resources, etc.

Because the growth of the bacterial culture is exponential in nature, semi-log paper is utilized in order to represent this trend.

Note: Different species of bacteria have different doubling times; however, the general trend of “lag,” “log,” “stationary,” and “death” phases are similar for all.

Growth Curve

As observed in the graph above, there are two curves present — The absorbance curve corresponds to the amount of turbidity present in the samples of bacteria taken at each consecutive time interval whilst the cell number, i.e. titer, illustrates the actual number of living bacterial cells present at each consecutive time interval. The concept is that as growth progresses, the sample would become more turbid due to the opacity of cells, as would the cell number; thus, the absorbance and titer curves are parallel to each other under normal circumstances. Additionally, the actual number of cells can never surpass the amount of turbidity.

This general “growth curve” idea can, thus, be adopted to depict human opportunity and willingness for generosity.

Each individual’s degree of generosity varies depending on their personality and the presence of extraneous variables much like a bacterium’s doubling time is dependent on its species and other factors, which will be discussed shortly. Using bacterial growth curve as reference, the absorbance curve symbolizes one’s opportunity for altruism whilst the titer exemplifies one’s willingness for altruism. One’s willingness will never surpass one’s opportunity to contribute. You may argue that in a circumstance where a certain person is someway impaired, hindering his/her opportunity to succor, but wills to help, that person’s willingness surpasses his/her opportunity. That, however, is not the case. If said person were truly willing to contribute, he/she would devise a way to overcome the obstacle(s), even if s/he would be helping indirectly. Willingness, which indicates desire and completion of task, would equal opportunity in such a situation.

Let’s now adjust the graph to fit the new conditions, shall we?


Lag Phase: Recognition*

During the lag phase, the individual becomes aware of his/her new environment and will slowly adjust to his/her surroundings. The term “environment” may denote any atmosphere — A small group gathering, a city, a library, etc. Once the entity becomes comfortable, s/he will begin to acknowledge his/her potential to assist those whom occupy the same environment. The duration of the lag phase is dependent on which individual is being observed, but the same individual will always take the same amount of time to adapt to each new environment, extrinsic factors aside.

Log Phase: Progression*

Increasing opportunities for charity will be thrust upon the individual as time progresses. Initially, the individual may feel reluctant to succor but a gradual escalation in willingness will be observed as more resources and contingencies for selectivity are offered. This phenomenon resembles a ball cycling downhill — Once it [the rolling] starts, conscious effort must be exerted in order to stop it.

Stationary Phase: Deliberation*

There comes a point when one realizes how much effort has already been invested into a subject(s) and begins to evaluate whether future sacrifice ought to be proffered. During this time, one may feel compelled to finish his/her current beneficences but remains ambivalent towards further benefactions.

Death Phase: Declension**

If the individual decides to remain philanthropic, then a downward curve representing that environment [the environment the individual is currently occupying] will not be observed. However, if the alternative decision is made, the death phase will be observed on the graph.

* Under the null hypothesis that no extraneous variables are present.
** Not always observed. Presence of death phase is dependent on outcome of stationary phase and extraneous variables.

The scenario below summarizes the aforementioned stages of generosity in a more comprehensible manner. (Please excuse the names — The author was having a little fun.)

Mary Anne Lou attends a party in celebration for Bobby Joe’s twenty-first birthday. Unaccustomed to the drinking atmosphere, she feels remotely aloof at first but soon finds the company enjoyable. Billy Bob, Jr. (one of the guests) manages to consume so much alcohol he is physically and mentally incapable of driving his tractor home. Mary Anne Lou, the only sober invitee, volunteers to drive Billy Bob.

Upon returning to the party, Mary Anne Lou is bombarded with a myriad of requests for transportation back to their [the intoxicated guests] homes as well. Realizing that the party has, thus, ended and that these dipsomaniacs are a hazard to themselves, others on the road, and the unsuspecting cows, she escorts each of them to their home. Much to Mary Anne Lou’s dismay, the last passenger has an esophagogastric dysfunction, leading to all sorts of different aromatic souvenirs in her truck. Guess who gets to clean up the mess?

The subsequent morning, the exhausted Mary Anne Lou receives a call from Betty Sue and Earlene — They had left their purses at Bobby Joe’s house and request she fetch and deliver the purses to them. What will Mary Anne Lou do?

Up till now, we’ve only delved into the variable-independent aspects of human generosity. However, the outcome of everyday occurrences is, indubitably, governed by a myriad of extrinsic factors. Hence, let’s now examine bacterial growth taking these extrinsic factors into account.

Many people have heard of ampicillin, chlorine dioxide (bleach), and/or chloramphenicol, but few understand their significance other than “they’re antibiotics/disinfectants that… help people stay healthy?”

Bacteriostatic agents stop the growth of bacteria but do not kill them, e.g. chloramphenicol. In the event a bacteriostatic antibiotic is added to microorganism sensitive to it, both turbidity and titer would level off and stay constant. For bactericidal non-bacteriolytic agents, e.g. bleach, which simply kill the bacteria, a drastic decrease in cell number would result whilst the turbidity would level off and stay constant. Finally, bactericidal bacteriolytic agents such as ampicillin kill bacteria by lysing their cell envelope; thus, both turbidity and titer would drop drastically.

The amount of turbidity and the number of cells observed within an allotted time is dependent on (1) the type of antibiotic and (2) when the antibiotic was administered. A variety of different growth curves can, thus, be obtained through altered combinations of agents implemented at different time intervals.

Extrinsic variables that act on our original model of generosity work in a similar manner. Take the Mary Anne Lou scenario once again for example, but this time noting extraneous factors.

Case #1:

Mary Anne Lou attends a party in celebration for Bobby Joe’s twenty-first birthday. Unaccustomed to the drinking atmosphere and lacking good company, she wishes Bobby Joe the best, bequeaths to him his presents, and leaves before she has to endure another conversation with a foul-breathed drunkard.

Extrinsic factor: Undesirable atmosphere/company
When factor took effect: Onset of lag phase
Conclusion: Because Mary Anne Lou did not successfully overcome the lag phase, no Progression resulted. Both opportunity and willingness curves flatlined at their initial stage.
Case description: Benefactostatic


Case #2:

Mary Anne Lou attends a party in celebration for Bobby Joe’s twenty-first birthday. Unaccustomed to the drinking atmosphere, she feels remotely aloof at first but soon finds the company enjoyable. Billy Bob, Jr. (one of the guests) manages to consume so much alcohol he is physically and mentally incapable of driving his tractor home. Mary Anne Lou, the only sober invitee, volunteers to drive Billy Bob.

Because of the time, Mary Anne Lou decides not to return to the party, instead, selects to drive back home. Half-way home, however, she receives a phone call from Bobby Joe who implores that she takes his plastered friends home for safety purposes. Feeling too exhausted at this point to take care of others, Mary Anne Lou declines the request and suggests they spend the night at Bobby Joe’s house instead.

Extrinsic factor: Time, personal exhaustion
When factor took effect: Log phase
Conclusion: Though Mary Anne Lou surpassed the lag phase, extrinsic factors contributed to her subsequent decline in willingness to continue sacrificing herself for others. The opportunity to assist was still provided to her; hence, incline and later stagnancy are observed for that curve. Note, however, that the curve is not as steep as that of the original. This is due to the fact that the extrinsic variable was dealt before completion of the log phase.
Case description: Benefactocidal non benefactolytic


Once again, a variety of outcomes may ensue — These are only a few simple examples. Typically, though, a depressed willingness curve is observed. This can be explained with one of two opposing, yet strikingly similar, perspectives.

As has been implied throughout this entry, humans are inherently good. It is due to the numerous extraneous factors that one becomes selfish and hostile. Those who are obstinately able to overlook these negative, extraneous factors are, then, capable of assisting others ad infinitum. Such individuals, unfortunately, are on the brink of extinction.

The alternative school of thought, which proposes that humans are inherently evil, is likewise justifiable. The aforementioned extraneous factors are good in this case. Those who are persistently able to recognize these seemingly subtle but more often than not blatantly obvious extraneous factors and respond accordingly are, then, capable of assisting others ad infinitum. These individuals are also on the brink of extinction.

Whether you hold the former perspective or the latter, the general idea remains the same — We reside in a macrocosm where the majority of people give little to no thought for others, and even if they do, it would only be a short-term affair. Once they tire of their dependability, previous acts of compassion can no longer provide “warm-and-fuzzy” feelings, or these feelings are no longer worth the effort. Furthermore, few of these short-term affairs are altruistic in nature; most are conceived from ulterior motives.

So, before you go off on a rant about how dismal the world is, how unlucky you are, and/or how rapacious the current society is, ask yourself — What can I change about myself first to make the world a better place before criticizing everyone else? It’s impossible to make others perceive the condition of world in the same manner as you see fit.

You can’t make others see, especially when doing so is against their will.

And on that note, I shall depart for bed. Au revoir until next time, my little munchkins.