a trinity of infinities

Explanations of the Triune God often resort to analogies. These analogies tend to suggest that each of the three parts must be less than the whole. And a triangular division into three also tends to suggest that the whole must be finite: else how could something be a third of infinity?

Yet a mathematical analogy for infinity is available. Suppose that someone counts, and never stops counting. The resulting collection of numbers is "all the multiples of 1". These are usually called the natural or whole numbers. The entire collection is limitless, which is provable by a straightforward test. Any time you think you've reached the largest number, count one more time. The next number is greater than any of the prior numbers, so it's a new number (i.e. not equal to any of the others). Therefore the set is produced by a well-understood procedure, and nevertheless infinite or unbound.

Now consider some different procedures that result in different sets. The numbers 3, 4, and 5 have no factors in common; none is a multiple of the other two. 3, 4, and 5 are quite distinct. Now, for each number in the set from before, i.e. all the multiples of one, multiply that number by 3. If it helps, think of two tedious people standing side by side. After the first person counts, the second person immediately multiplies the new number by three. This set is "all the multiples of 3". Like all the multiples of 1, it's produced by a well-understood procedure, and nevertheless infinite or unbound.

We can do the same for 4 and 5. Finally, there's four infinite sets: the multiples of 1, 3, 4, 5. Since the procedure to construct the set of multiples of 3 consisted of multiplying each multiple of 1 by 3, all the multiples of 3 are also multiples of 1. The same applies to all the multiples of 4 or 5. These sets are provably infinite and still included in the "whole" original set, the multiples of 1. We have a trinity of infinities that are still contained in a infinite whole.

Although the member-numbers of the three infinite sets all belong to the set of natural numbers, the three sets aren't completely distinct. Presently, there are numbers that are multiples of both 3 and 4 (the multiples of 12), or 3 and 5 (the multiples of 15), or 4 and 5 (the multiples of 20). If it's more satisfying to consider three distinct infinite sets, then alternative procedures could accomplish that goal. However, the cost is greater complication and the exclusion of many former multiples. For the "3" set, instead of multiplying each natural number just by 3, 1) multiply by 3 then 2) multiply by 4. The result is a multiple of both 3 and 4, simply because it's equal to 3 multiplied by "other stuff" (i.e. the original natural number) and equal to 4 multiplied by "other stuff" (i.e. the original number multiplied by 3 a moment ago). Similarly, 3) multiply that by 5 to achieve the end goal of a number that's a multiple of 3 or 4 or 5. Now take that number and 4) add 3. This final number is a multiple of 3, because it's 3 added to a multiple of 3. On the other hand, it isn't a multiple of 4, because it's 3 added to a multiple of 4, which is 1 too few to "reach" the next multiple of 4. Neither is it a multiple of 5, because 3 is 2 too few to "reach" the next multiple of 5. Presto! The procedure can start with any (all) natural number and construct a number that's a multiple of 3 but not 4 or 5. Procedures that are broadly similar can produce an infinite set of numbers that are multiples of 4 but not 3 or 5, and an infinite set of numbers that are multiples of 5 but not 3 or 4. Due to the logical fact that a particular number can't both be a multiple and not be a multiple, it's a logical impossibility for a number that belongs to one of these sets to belong to either of the others. The first few members of the "3" set are 63, 123, 183, 243. The "4" set, 64, 124, 184, 244. The "5" set, 65, 125, 185, 245. (Naturally, the predictable gaps of 60 between adjacent numbers are due to 3 times 4 times 5. If you graphed these procedures as mathematical functions, with the result as the vertical axis and the starting number as the horizontal axis, you would see a set of closely space parallel lines.)

All different, all infinite, all drawing from the same source.

wrong question

Presently in the USA, I've observed more speculation than usual about the question of whether God favors particular outcomes in professional sporting events. Let me repeat the same opinion I always have for this category of questions. If your desire is to decode a supernatural Hand from out of the prosaic ups and downs that fill daily reality, then you're asking the wrong question entirely.

It's the wrong question for two simple reasons. God is too big, and the stakes too small. There are innumerable circumstances that are better opportunities for undeniable and necessary divine intervention. A sporting event is over in less than a day. Its consequences last for no longer than months and amount to not much more than lots of exchanges of money and perhaps some awards and/or injuries. Winning is of course a formidable obstacle to the players, but for God it's no trouble at all. It's not anywhere close to miraculous.

If you crave a real test, then consider a situation in which lives are in danger and in which no mere person could do enough. Like sporting events, obviously these situations also happen every day. People wage seemingly hopeless battles for the prizes of survival, dignity, relationships, and many others. Is God at work in those many battles? Like in the song "Take Me Out to the Ballgame", does He "root! root! root!" for good to win every time? 

I suppose that the eternal mystery of the unfathomable thoughts of the Infinite One prevent anyone from saying for sure that He contemplates professional sporting events. Nor can anyone say for sure that God contemplates anything else. But we do know that He cares about people.

advice to counteract consumerism

Last time, I opined that consumerism wasn't invented by Americans. Nevertheless, the USA economy is largely based on the consumption of its ordinary people. The pressure to consume can flow through obvious routes, like billboards and TV commercials and ads in printed or digital publications. It also can flow through subtle routes, like peer pressure and status-seeking and desires concealed by self-deception. Fortunately, Christians aren't helpless against the empty values of consumerism, and I have some advice to counteract it.

First, be on guard for consumerism's influence. Signals abound: excessive usage of credit, "fits" of shopping that consist of a string of unplanned purchases in a short time period. However, quantity isn't the only factor. Consider a vivid obsession of just one specific product, entangled with hopes and longings. Beware the thought, "If I had this, I would be so happy."

The dividing line is illustrated by the biblical story of Abraham's willingness to sacrifice Isaac, which ranks among the most disturbing sections. That extreme is in contrast with a petty soul who refuses to sacrifice mere stuff for God's sake. In my opinion, Christian devotees aren't required to live according to vows of poverty, but they're required to be "ready" to take such a vow. Anything is up for "grabs" by the Lord of all. This is a useful test. Nonessential things are to be held loosely. And most things that average Americans possess are nonessential.

In addition to conscious detachment from material goods, regular giving is a potent vaccine. Givers tend to not overspend their income. When they give, they reiterate that selfish hoarding is incompatible with Christian attitudes. Resources that are given away can't act as temptations to find fulfillment outside of God's kingdom.

While Christians certainly don't need to give everything they own or earn, they may wish to forgo their usual items from time to time. Withdrawal of these familiar items forces fewer distractions and dependencies. God remains. He's always present, but people often look elsewhere when they have the opportunity. Consumerism is the substitution of a never ending stream of trinkets.

I don't believe that objects are evil. I believe that inappropriate attention to objects can obscure God. Objects appear to be solid saviors for one purpose or another, and by comparison God appears to be shadowy and untouchable. Christian devotees should invert that perspective. God should be the solid savior who surpasses  every weaker competitor, and by comparison objects should appear to be flimsy pretenders that break and rot.

consumerism is not an American invention

People work frenziedly, then spend frenziedly, in order to accumulate frenziedly. Sellers and producers advertise frenziedly. Credit is lent frenziedly (i.e. "revolving" credit). To complain about "consumerism" is generally to complain about these economic frenzies. Christianity emphasizes morals, people, and relationships, which puts it into conflict with consumerism's values of greed, inanimate objects, and exclusive ownership.

Maybe consumerism was "perfected" in the USA. The joint causes could be abundant resources and population, technological and financial ingenuity, relatively unhampered markets, and sufficiently competent oversight. Large roles are played by the most successful retailers, product-making corporations, mass media, investment funds. Undoubtedly the economy, consumerism, and culture have reshaped one another. For now, the strongest bastion of consumerism is right here.

It's too simplistic, however, to equate consumerism and American culture. People are born with grasping urges for novelty. They reach for anything that promises to please. No teaching or training is necessary. Consumerism has extended deep roots in some nations, yet it spreads and grows to others without much resistance. Culture always matters, but culture itself changes over time.

"Rich" observers marvel at the simple contentment of people who live in nations that have minimal economies and technology. But this appearance is misleading. All people can adapt to their economic surroundings. One constant across all times and places is that people notice and compare their wealth and/or status. Some learn to be happy despite the differences, but some don't. Beyond a minimum standard of food and clothing and shelter, people can be quite happy as long as they don't consider themselves poor...

The gap is one of scope and opportunity. When societies produce very few goods for the domestic market, and mechanization and communication are primitive, the economic stratification in the society seems to be smaller. Americans have the option to consume in countless ways, and they're encouraged to exercise that option. Once presented with similar levels of encouragements and options, why wouldn't the same hold true for those of any culture? Immigrants to the USA who achieve acceptable income tend to start consuming at comparable rates, although their consumption patterns vary. "Consumerism" is what a typical person naturally does with their discretionary income, i.e. the remainder after taxes and bills and necessities. Lesser amounts of discretionary income are the likelier explanation for less consumerism. The cause isn't American culture, it's human nature.

impossibility or incorrigibility?

I'm somewhat amused when I read the perspective, "Merely eating less and exercising more is an approach to weight loss whose effectiveness has been disproved innumerable times throughout recorded history." While I agree that it's ridiculous to think that a person of any shape can target any weight they wish, surely it's beyond doubt that weight is affected by habits of eating and physical activity? Practically speaking, people come naturally in all sizes, but each person has the final decision on how to adjust those two "levers". Someone with the same inborn body range as me could be heavier or lighter than me, via the multitude of choices.

Some cultures put excessive emphasis on weight. Like the stars on the Dr. Seuss "sneetches", it's an easily identifiable distinction for sorting individuals by superiority. Cultural taboos and attitudes are quite variable. People who would be acceptable in one society could be scorned in a second. No sensible or universal rationale is necessary for the shaky "morals" of appearance and behavior that are invented by capricious earthly judges.

As Christians who follow God's laws, we think differently. In this case, we recognize the plain sin of gluttony, but we also acknowledge that conspicuous sins are often less deadly to the spiritual life than unseen or subtle sins. A greedy dependence on food may attract more stigma than a greedy dependence on money. Regardless, Christians shall forbid either in order to be free from enslavement to any created thing.

And when we repent of gluttony or the worship of Mammon, we live in faith of the possibility of change. We don't scoff at the idea of self-discipline. Instead we comply with the metaphorical crucifixion of our sinful leanings. Rather than contemplating and wrestling with temptation, we do something simpler: we deny it less than a toehold in our thoughts. The path to committing a sin of action or omission starts by committing the sin mentally within one's fantasies or mental plans.

Cynics are accurate in their observations of the failures of the unspiritual person to achieve personal transformation through weak natural willpower. Flesh demands fleshly actions. In contrast, Christians exercise their godly focus in practice. They release their hungers to Him, and they're revitalized to reject sin in general, including the unspiritual person's fixation on gluttony.

the poor don't choose to be poor

Some Christians profess a curious viewpoint on poverty. They say that within an economy of uncontrolled markets, voluntary decisions of many people are the only factors that explain economic results. Therefore, everyone has nobody to blame but themselves. In the competition of buyers and sellers, including when the negotiated items are jobs (i.e. labor, "human resources"), anyone can succeed if only they try.

Ridiculous. Economically speaking, people aren't indistinguishable "commodities" and markets aren't perfectly meritorious or open. That ideal is theoretical, like calculating physics without including friction. People differ in their inborn talents, education, upbringing, and so forth. In any case, markets don't always reward or even consider the most valuable/productive people.

I find it easier to appreciate this point by envisioning an instant switch between the circumstances of my life thus far and the life of someone else. I've received love and encouragement from my social networks (no, I'm certainly not referring to Facebook). I've received a good education. I've received relatively good care of my nutrition and health. I've received ethical and religious instruction.

These are advantages that I could easily assume everyone else also has. However, after swapping my life's advantages for another life's downfalls, can I realistically suppose that I'd achieve the same level of economic "success"?  Don't misunderstand or misconstrue my meaning; I agree that personal initiative and strength of character are hugely important ways to compensate for many formidable obstacles. But can we honestly suppose that every person in the middle class would have still ended in the middle class, had they hypothetically started in a lower class? Do we naively presume that every imagined transplant would grow to a beautiful rose, blossoming regardless to a predetermined height from out of the least nurturing soils? Without the basic skills and interpersonal connections that markets require, someone with the best intentions or a revolutionary idea could still be one of the poor. For that matter, a long string of bad luck can transform the fortunate to the unfortunate.

Of course, this complex reality of a "poverty trap" doesn't lead to the conclusion that the poor can only be economic dependents forever. Rather, when people are caught in traps, the more charitable action is to help them climb out of the trap. And provide sustenance until the assistance allows them to start participating sufficiently in markets in a more independent mode. The aforementioned ideal, income level being a personal decision, is really a goal. Just as Christians cannot force other Christians to seek God (although they can and should encourage/spur/exhort/cajole/discipline/etc), people cannot be forced to put in the necessary effort to earn the economic outcomes which they claim to want. However, charitable Christians will offer every opportunity and support to those people who do. They'll sacrifice their temporal excess resources in order to bless fellow sinners who lack.

Christians administer mercy economically, as they keep in mind the divine mercy they continue to receive. Christians aren't meant to have the mindset, "I've earned every cent I have and you've earned every cent you have. Since we're individuals in a dog-eat-dog and king-of-the-hill world, I and my finances have no relationship whatsoever to you and your finances. Don't complain to me about the markets' rejection of your utter lack of starting capital. You really should have thought of that before you became peasants."

coercive public school prayer is no panacea

As easy as it was to forward email about any angry topic whatsoever, Facebook may have succeeded in simplifying such communication still further. Based on my experience, "Status" sometimes is about sounding off on the fervent yearning to "bring prayer back to public schools". Unfortunately, were this accomplished, it would be a symbolic gesture at best.

Nondisruptive voluntary prayer remains a cherished human right, in school or elsewhere. Admittedly, the parameters and limitations of "nondisruptive" and "voluntary" are rather sharply drawn, but the set rules are firmly in place. At times the restriction or the praying can be overzealous, and either one needs to be corrected. As long as nobody oversteps their bounds, prayer per se is certainly not "forbidden" in public schools.

Moving along, the next question is the details of the proposal. What do the words "bring prayer back to public schools" really mean? Naturally, this assumes that the person's "status" is a truly desired change that flesh-and-blood teachers and students will do, not a wishful-thinking slogan or outburst. Does it mean nothing more than a three-minute moment of silence, in which active young children are expected to be quiet and sedate if they aren't opting to pray?

To the contrary, my presumption is that what the status-writer would like is a short recitation of a canned prayer, taught and led by the teacher. After all, allowing the teacher to make whatever extemporaneous prayer he or she likes is probably not what the status-writer intends! Since there can be no religious test for public school teachers, that would be an "anything goes" proposition, perhaps including teachers who are - gasp! - atheistic.

Then the next practical question is who will write The Prayer that's taught in public schools, and who will approve it. Is there to be a tyranny of the majority, in which the religion with the least number of naysayers has the privilege of educating the rest to rigid conformity? If not, and The Prayer must meet at least a minimal standard of acceptability by a wide range of religious believers, then my suspicion is that in the end it will be "cleansed" of most doctrines that the status-writer holds dear. Claims that Jesus resurrected, or that the Bible (KJV? NIV? Septuagint?) is truth, won't last long. Does this form of completely inoffensive prayer have much to do with Christianity?

Imagine that The Prayer is eventually written and duly recited in classrooms. What is the expected outcome? Will students who are coerced into memorizing and mumbling mush act more holy? Will teachers who hurry through in order to get to the day's lesson have epiphanies? When casual attendance of weekly church services isn't enough to turn people into disciples, what effect could The Prayer have? Needless to say, those who disagree with the statements won't be any closer to salvation by mouthing the words.

Religious instruction or Bible classes are much more likely to raise children who have the right knowledge. Yet those are highly inappropriate in a school targeted at the general public. Parents may not agree with all or any of the content in those classes, and they'd be rightly irritated by the school's attempts to introduce contradictions. Far better would be if parents could select separate schools that target their particular beliefs. Everyone surely realizes that this solution has been in place in the USA for many, many years?...

I'll grant that the removal of coercive public school prayer is a symbol of the reduced influence of Christianity in the USA's culture. And its symbolic importance incites visceral feelings among some Christians. But it seems to me that a symbol is all it can be. Reversing it won't reset the past decades.