The Philosopher, the Cave, and the Mathematician

I have a funny story from when I was younger, and reflecting on it just now, I realized that it is helpful for understanding one aspect of Plato’s story about the cave. Well, it’s a funny story insofar as a story about a math problem can be funny I guess.

I have a friend who’s very good at math. He has a bachelor’s degree in the subject. One day, he and I heard an intriguing word problem. I can’t exactly remember the details anymore — something about twenty people at a table who can give invitations to one another, but only to the person across the table or to the east of them, and what’s the greatest number of invitations that can be passed, except that I feel like it was somehow even more complicated than that.

Anyhow, he and I both set our minds to working on the problem. I wasn’t able to find an answer, but he was. The answer he gave, though, seemed, based on the thinking I had done, like it must be wrong. The number was too small.

I told him so, and he explained how he got to the answer. It was pretty simple actually, he said, once he realized that such-and-such a well known formula was all that needed to be applied to the initial figures. I was personally unfamiliar with that formula, but it seemed to me that it couldn’t be the right one to use, and I tried to express why, in my fumbling and less sophisticated way.

He wouldn’t be convinced. The next day he told me he had called up a friend with a degree in mathematics, explained the problem, set out his solution, and the friend had agreed with him entirely. But I was still uncertain. We kept discussing it until I found the simplest way to explain my objection.

“But the two people across the table from each other can each give an invitation to the other. Isn’t your formula assuming that an invitation only crosses the table once, in one direction? And isn’t that going to mess up the final number in a pretty big way?” It was something like that.

His eyes rolled back in his head a little bit, and his brow furrowed, and he began speaking to himself in little whispers. Finally he nodded. “Yes, you’re right. My answer can’t be correct. But what you need to know, John, is that I studied pure mathematics, and this is applied math, which is not the same thing. That’s why I missed a step.”

We never bothered finding the actual answer to the problem. I look back on that conversation with some pride, still.

But there was one particular moment in the conversation that is frozen vividly in my mind, that I will never forget. My friend had a frown. The pads of the fingers of both open hands were covering his eyes and gently massaging, trying to keep his frustration at bay. “I just don’t know how to explain this to you, John. I don’t know how to be any more clear than I’m already being. I’m not sure what it will take to show you that you’re wrong.”

He assumed that our disagreement was a consequence of his wisdom and my error. And it very well could have been! But that’s a dangerous assumption to begin with. Perhaps the most fatal assumption of all.

It’s the assumption that the philosopher first had to give up in order to become a philosopher. It’s the assumption the philosopher will encounter again and again, endlessly, upon returning to the cave.

I wasn’t the philosopher in the conversation with my friend. I just had the good luck to be less wrong than my better educated friend. But that experience gave me an insight into the life of the philosopher in the cave.

We in the cave are so certain that we know what we’re talking about, and that anyone who disagrees or doubts just knows less than we do. We have reasons, and we have confidence, but that doesn’t mean we know what we’re talking about. And insisting that it does mean that, can only leave us looking foolish when we’re eventually shown to be utterly wrong.

Language-learning update late 2022

How goes the language learning these days?

Slowly! That’s how.

I gave a list of my top nine languages previously in a different post; they were German, French, Greek, Latin, Hebrew, Italian, Arabic, Russian, and Mandarin. And they still are — that remains my list. I spend a bit of time on each of these on a regular basis, though I focus the great majority of my effort on German, Greek, and Latin.

I think that a major part of why my progress seems to have slowed is because I’ve been having so much success with Zettelkasten. My Zettelkasten (which I’ve discussed in the past; google the word if it’s unfamiliar) has been growing at a remarkable rate. I’ve been so excited about it, and as fast as it’s going, I find myself wishing it could progress even faster.

That project has taken a lot of time and energy out of my average day. As a result, my language learning efforts survive, but they are hanging on by a thread, it sometimes feels. Some of my other habits have dropped away entirely to make room for the Zettelkasten.

Still, I read some Greek every day, study German every day, and learn a bit of Latin every second day. My other languages make an appearance about once a week. I’ve been on my current schedule for a little over a year. My best guess is that at my current pace, it will probably be at least a couple years more before I even begin to develop anything resembling fluency. And as you can tell by my hedging, even two years is likely over-optimistic.

Still. It takes very little time or effort every day, and if I could begin to grow more fluent, then in a few years I’ll be very grateful that I stuck with it.

My language journey is certainly nothing impressive. If all goes as planned, though, it will eventually be a testament to the power of a little dogged patience.

It’s not brain drain, it’s vice drain

I’m certainly not in favour of all things that could fit under the banner of socialism or communism. Some stupid and evil things have been done within the realm of those labels. Still, I do believe that it is allowable and desirable to have a government that fights wealth inequality, especially by helping the poor, but also by counteracting to some degree and in some way the efforts of the wealthy to enrich themselves. An excessive concentration of wealth in few hands is bad for the political community, and also unhealthy for those who are rich.

Plato in the Laws, and in a different way Thomas More in Utopia, considered it a valuable thing to place constraints and obstacles against people growing too wealthy.

But people get fearful when they hear this sort of talk. If we don’t give smart people the chance to get really wealthy in our political community, then they’ll leave us for someplace where they can get really wealthy! Then we’ll have no smart people left. That’s brain drain. So the thinking goes.

As a matter of fact, that’s not quite correct though. It’s not smart people who will leave. Smart people like to live in places that are welcoming to, respectful of, and facilitative for intellectual activity and intellectual achievement. If we want to keep smart people around, we should focus our efforts on those things.

Who then will take off in a huff when denied the chance to become obscenely wealthy? Only the avaricious. And we are almost certainly better off without them.

I know that that’s not the approved thinking in the world of capitalism. The greed of the greedy is the real fuel that powers our economy, alongside the desperation of the needy. If we frustrated the lusts of the greedy, and addressed the fears of the impoverished, how could the economy hope to carry on?

This is where I suspect that Belloc’s distributism holds great opportunities for us today, if we can search them out.

We desire the philosopher king

If you knew someone who was much wiser than you, and who also knew you well and had your best interests at heart, then would you, even as an independent adult, accept their guidance?

Well, before we go further, let’s clarify some things. How do we know, in the first place, that this person is so wise? Let’s say they’ve written books and articles, and delivered speeches and lectures, they’ve given interviews and engaged in debates, and you’ve read or heard enough of these compositions to be absolutely convinced that this is a person who isn’t faking it. This person is leagues smarter than you and I are, and this person doesn’t focus on trivial stuff; political matters, moral, social, psychological, economic, historical, religious, financial, developmental, health, and other contemporary debates — this is a well-rounded, wise person.

Let’s say furthermore that everyone you know, especially the smartest people you know, will agree that this is a brilliant person, even if some do so only grudgingly, whether because of ideological differences or differences of approach or sheer envy. Likewise, no one can deny the moral reliability and the astonishing compassion of the person. This is someone recognized for wisdom, and long recognized, not a passing fad.

I think that probably most of us would follow that person’s guidance.

In the modern world, we tend to think that there are really only two conceivable reasons why we might want to obey someone: either representation, or compensation. The person who legitimately commands us is either a representative leader who was elected as part of the processes of the state (or a person who acts on behalf of such elected representatives, eg a police officer enforcing laws), or else is a business owner or manager whose satisfaction with us will determine our present and future economic prospects. In those two cases, we will readily do as we’re told. Otherwise, we resist.

What this seems to mean is that we put the needs of the body over all else. We obey the state even when we don’t like it, ultimately, because we don’t want to be thrown behind bars. We obey our bosses at work because we don’t want to end up penniless on the street. But what about the soul? What about the mind? What about human dignity, or the desire for glory?

We forget that wisdom is the most important qualification for leadership. It is absolutely a necessity for responsible leadership, and it is also sufficient in itself. Better to follow the person of great wisdom than the one adorned with fancy titles.

Seek out wise people, and follow their lead. Even more urgently: seek to become that wise person, no matter how long it takes.

Reading a history book backwards

There’s something I’ve been trying this past year, and it’s been going really well. I’m excited to share it. It stems from my desire to be more knowledgeable about history.

When I was in college, I was most excited about taking classes in philosophy, literature, theology, those sorts of things. I took lots of classes of that sort, and learned plenty and overall enjoyed myself greatly.

And then I graduated, and I realized that I could study those things on my own time, at my own pace, in the order I want, often with much more profit than when I was studying the same texts for a class. How disappointing. Much of my college education began to feel a bit redundant.

I took some language classes as well in college, and some few history classes, and I left college resolving to study more languages and more history on my own time, to catch up on what I had missed. I believed they were important things to grasp.

Imagine my dismay, then, when I realized that unlike philosophy, history and languages are dreadful to study on your own. The structure of a class, the guidance of a professor, the company of fellow-sufferers, makes such a great difference. I failed abysmally in my early attempts to study these things after college. I took to telling people that if I could do my college education again, I would probably have focused much more on history and languages.

Recently, I’ve been trying to find ways to get better at teaching myself languages and history. The biggest lesson I’ve learned so far is that consistent, small habits are even more important for studying independently than they are for learning in a class. But I’ve also discovered another valuable tip this past year.

I bought a book of Canadian history, because I am shamefully ignorant about the history of the country in which I have been a citizen all my life. I started reading it from the beginning, multiple times, and hardly made any headway.

And then, on a whim, I tried reading it in reverse. I read the last chapter. After all, that’s closest to me, most relevant to me. But there were aspects of that chapter that referred back to earlier chapters. So I read the second-last chapter, and then read the last chapter again. And then I read the third-last chapter, and the second-last, and the last. I’ve been continuing on in that same pattern ever since.

It’s a great way to read history. It keeps it interesting, and it helps everything make sense and fit into place.

This isn’t an approach you’d want to use in studying for a class in school, probably, because it’s incredibly slow. It requires the investment of much time and patience.

For self-study, though, if you’re not in a hurry, I currently feel like this is the best way to learn about history. Give it a try!

Interior mortifications

In the Catholic tradition of spiritual growth, “mortifications” refers to (unenjoyable) practices by which we can unite ourselves to the sufferings of Christ. Fasting from food or from certain kinds of food would be examples of this, or kneeling for extended periods in prayer.

Hunger for exterior mortifications can be a good thing, and the absence of such hunger is probably a sign of a problem in a Christian’s spiritual life. Even if we aren’t always engaged in those practices, it is no doubt healthy to be inspired to engage in them.

When inspired to do so, I would say, do practice exterior mortifications, but cautiously. Be careful about doing too much, which can be spiritually harmful (and in some cases may even do damage to health or relationships or to others). It’s better to start by erring on the side of doing too little at first, and then to add more later when ready.

We very often forget this, but it is valuable to try to make exterior mortifications secret, not even letting one hand know what the other is doing, so to speak. Keep it between oneself and God. If the mortifications are much harder to sustain when they’re secret, that tells us something about our motives. If they aren’t hard to sustain, then we should all the more continue to keep them hidden, a secret for oneself and God.

Some mortifications are difficult to do secretly with others around, but it is valuable to find a way to mortify ourselves even then, because that is when we are most tempted to pride or malice. The mortifications best suited for the company of others, indeed which draw their terrible power precisely from the presence of others, are interior mortifications. Rather than accepting bodily pain, interior mortifications accept mental or emotional pain. When someone speaks unkindly, accept it without complaint. When someone accuses falsely, accept it without protest.

It seems that it is hard to overdo interior mortifications. There is endless opportunity to practice them, and somehow failure to do well doesn’t bring a sense of shame and discouragement in the same way that failure in exterior mortifications can.

The person who continually seeks to practice interior mortifications is a meek and humble person (which is not to say a weak person). These people have unseen depths beneath the surface. Their silences have more power than most people’s words. They are in truth unbreakable, immovable, unconquerable, no matter how they might first appear from the outside.

The Smartest Person I Know

One day, I hope, I will be the smartest person I know. If I can (I’m sure I can’t) I will be the smartest person in the world. Arrogant? Hubristic? No, I don’t believe so, though certainly it is at best aspirational, and unlikely nearly to the point of impossibility.

That’s my goal, and I think it’s a good goal to have. It’s a high bar, obviously. I’ve met some smart people in my life, and in reality I have no desire to upstage them or outshine them. I love that they are smarter than I am, and I bear them no ill-will for their brilliance.

Still, I think it is no insult to them, is maybe indeed a compliment to them, for me to set my mind to competing with them.

In a way, it is my way of recognizing my debt to them, communicating my admiration for them, my sympathy with their goals.

Socrates in a few places encourages his listeners to adopt this attitude of intellectual competitiveness. I think it is the best sort of competition there can be.

I want to be better at Greek than any of my amazingly talented friends and professors, though I know I am currently a long way from that. I want to have a mastery of modern logic or economics that would impress authorities in those fields (I’m even further from attaining those goals!). I want to grasp the facts and patterns of history and be able to call them to mind readily when I need them.

I don’t think it’s likely that I’ll succeed in any of these goals, especially while pursuing them all simultaneously. I also don’t think any of them are completely impossible or out of reach, however unlikely. But most importantly, I have no doubt that in aiming for goals like these ones, I will make progress on a scale that I could never have imagined without such goals.

Strauss’s Phases of Human Thought

I realized that Leo Strauss seems to distinguish five phases of development within human thought. These can map to historical eras, and Strauss often does attempt to illustrate them in this way, but they are more sort of existential modes than historical periods. They won’t correspond exactly to historical periods, and they won’t always move predictably in the sequence outlined. Still, they are useful for understanding how and why different groups will thing or speak in particular ways.

The Cave. This is humanity’s original and default way of thinking. It is something like superstition. It wishes to explain the whole world in ways that bring order and comfort and meaning, and through social cooperation and competition a given group will come to inhabit a shared cave, a shared horizon.

The Cave and the Philosopher. Out of a given cave, certain people or small groups will find their way out into the light, into philosophy, into a sense of the meaning and importance of nature as nature. The philosophers who emerge in this way will look back to the cave and its inhabitants, and will understand the cave and the caves more completely than any of those inhabitants is able to.

Political Philosophy. The phase of political philosophy follows on the inevitable tensions and clashes between the philosophers on the one hand and the inhabitants of the cave (often referred to in the singular simply as “the city”) on the other. In this stage, the philosophers have come to grasp their responsibility to the city and their dependence on it, and have worked out ways to draw out potential new philosophers from the cave while causing minimal harm either to the city or to the philosophic community.

The Cave Beneath the Cave. A new sort of cave forms in the attempt at enlightenment, at bringing those in the cave into a greater awareness of and acceptance for philosophy. The city cannot understand philosophy as it is, and so must attach itself to a shadowy misunderstanding of philosophy. In this way they leave their original cave only to enter a new cave, and this time, their cave is a deeper one, further from the light of genuine philosophy. Convincing themselves that they have already exited the cave of superstition and have attained the full benefits of philosophy (or that apparently more successful portion of philosophy which is natural science), they are stuck behind new and stronger barriers which separate them from philosophy itself.

The Reading of Old Books. To exit from the deeper cave calls especially for a study of old books, the study of accounts of philosophy that predate the attempts at enlightenment. It is only in scrutinizing the original conflicts and negotiations between the philosophers and the caves that we are enabled to recognize the inadequacy of our deeper cave, and to find the genuine alternatives that are available to us and obscured from us. If “Straussianism” can be said to mean anything, perhaps it refers to this.

Having kids makes the future closer and more substantial

“Ten years from now” used to feel like a long, long, really long way away. Won’t I pretty much be an old man by then? Will I even still be alive when I reach that age? It was difficult to imagine, and there was no need to try.

It’s having kids that has upended my sense of perspective. Ten years from now my children will still be pretty young. And so will I! Right? I’ll be healthy and strong and with a whole life ahead of me!

Being able to think in terms of years and decades in that new way has had some big implications for how I think about my time and my habits in the short term.

Studying a language on Duolingo for two or three years years used to sound like a terribly long, tedious, painful, boring prospect. But if it’s easy to imagine a moment ten years from now, then that two-year stint ahead of me now is hardly a bump on the road.

If I have a reading project that will take years before it gives me any sort of impressive payoff for my studiousness, then looking at it from the standpoint of the present makes it feel futile and overwhelming. Looking at it from a perspective that’s rooted five years in the future, or ten, or fifteen, makes it something exhilarating. Just think how much I will know when this project is in the rearview mirror!

I’ve heard that it’s hard to sustain excitement over a long time. I find that that’s not necessarily true. If I can keep the longer perspective in view, and see who I will become, and how easy the process of getting there is as long as I’m patient, I find I’m invariably able to feel great anticipation.

And sustaining excitement like that is exactly what it takes to stick with a project and make it a reality, which makes subsequent projects all the more plausible and exciting. It’s a virtuous circle. One of many gifts I did not expect to receive from my children.