Author Archives: Aron Wall

About Aron Wall

I am a physics professor at Syracuse University, as of 2026. Before that, I read Great Books at St. John's College (Santa Fe), got my physics Ph.D. from U Maryland, and did my postdocs at UC Santa Barbara, the Institute for Advanced Study in Princeton, and Stanford. My first faculty position was at the University of Cambridge. The views expressed on this blog are my own, and should not be attributed to any of these fine institutions.

A Path to Practical Wisdom

Here is one way to become wise:

1. Start by getting really good at one or more skills.  It isn’t important how useful the skill is for “real life”; it only requires that it be something difficult which requires you to improve.  It could be gardening, video games, cooking, sports, or whatever.  This requires:

a. large amounts of practice
b. feedback from reality — notice what works and what doesn’t.
c. take the feedback into account and change what you do so that it works better
d. but it is okay to deliberately experiment with making “mistakes” as long as they contribute to learning.

2. Now formulate the lessons you learned from #1 as maxims:

a. try to put it into words (though some people do it more intuitively).  Keep it simple enough to remember, and abstract enough that it has a chance of applying to OTHER situations as well.
b. notice when it actually does so
c. take this wisdom into account when dealing with the other subject matter.
d. but every rule has exceptions!  You can’t list all the exceptions, so only obey the maxim when it actually makes sense to do so, or when you are deliberately trying it out as an experiment to see what happens.

3. Other people are probably better than you at discovering maxims:

a. learn from people who are doing this
b. but recognize that the maxims (2) are based on an invisible pyramid of observations (1) and can’t be appreciated without you doing some amount of 1 and 2 yourself
c. so you still have to check what actually makes sense and works!  Just because it sounds good doesn’t mean it is useful to YOU (or anyone).
d. even wise people can still be idiots, especially when they trust too much in their own wisdom.  (But sometimes it is good to experiment with trusting too much to see what happens as a result, etc.)

In all of the above, there are two completely different kinds of risk, one good and one bad:

DANGEROUS RISK that will possibly seriously hurt you, or things/people you care about.  The wise person almost always steers widely clear of this.  The only exception is a risk for great gain, and even then it is usually better to formulate an alternative safer plan.  (But if your heart tells you to put yourself in danger, sometimes you need to put yourself in danger.)

SAFE RISK where failure is primarily a learning experience with no permanent harm.  The wise person seeks out this kind of risk on a regular basis, because learning is extremely important, especially if you want to avoid dangerous risks!

Some amount of moderation is needed to ensure you can emotionally recover.  If failure hurts enough to make you reject future learning, then that was actually a dangerous risk!  But usually the difference between these kinds of risk is assessed objectively, not based on your feelings.

All of this is more oriented around how to excel at whatever you put your mind to, rather than what your goals should be in the first place.  There is also a spiritual wisdom that enables us to have the correct goals (hint: worship God and serve him alone) but this post isn’t really about that more important subject.  It’s more about how to get better at practical applications of life skills.

Perhaps there is some even higher perspective from which practical wisdom and spiritual wisdom eventually converge and become the same thing.  This blog post isn’t exactly about that either.  That is, I won’t tell you how the convergence happens, but it is possible that if you pursue wisdom heartily enough, you will find this out on your own (possibly by straying from the techniques mentioned above, if you learn that something else works better).

A Dream

It was the year 2010 (or possibly 2011).  I was sleeping on a sofa bed in my (then-) fiancee Nicole’s living room, and I had the following strange dream.

I dreamed I was standing in a spacious stone church, the kind with stained glass windows and a few tourists mulling about quietly somewhere.  In the church was a table.  On the table was a book.  The book had been written by a saint (but the dream did not specify the name).  And I knew that the book had the following words written in it:

“The Lord does not easily let us cease praying to him, but so great is the compassion that wells up in the heart of the Holy Trinity for us, that he is loath to lose anything so precious to him.”

I awoke, and while these words were still fresh in my mind, I wrote them down and also committed them to memory.

Notes on specific words:

1. Compassion: this word had a strong flavor of the Latin word “misericordia”.  (Although the words I received were in English, I did not get the sense that this was the original language of the text.)

2. Loath: this might also have been “reluctant”, I was not entirely sure upon consideration.

Apart from such tiny uncertainties, I can vouch that this was the sentence, almost word-for-word.  (And yes, this was an exceedingly unusual degree of precision, compared to normal dreaming; in fact I cannot recall any other time when I remembered, after waking, a dream sentence containing so many subordinate clauses!)

I am personally inclined to think that this dream was a true revelation about God and prayer, given by the Spirit.  But whether any actual historical saint wrote these words, who can say?  It would be amazing to stumble across these words later in some library.  But it also seems unlikely, as there is no need for the books that have survived, to be revealed in dreams.

Mathematical Physics Maxims

Most of this will be completely incomprehensible if you aren’t mathematically trained.  I’m putting it out there anyway.


Thou shalt not confuse a vector space with its dual.  Thou shalt not add unnecessary structure without good cause.  Be careful not to identify objects related by noncanonical isomorphisms.  When composing isomorphisms, bear in mind the possibility of a “twist” when thou comest back to the same object again.

Do not favor subspaces over quotient spaces, nor quotient spaces over subspaces, but give equal justice to all methods of reduction.

Never be unjust to a mathematical entity, lest it rise up against you.  When something is taken away from a system, it is often needful to add something as well, to compensate it and to preserve its integrity.

Study a nonlinear thing by passing to a bigger linear algebra.


0 is a natural number.  Always include the identity, or the empty object, when you allow more than one of a thing.  Almost everything there can be two of, there can also be zero of.  But, if thou allowst only 1 of a thing, do not consider 0 to be a special case!  This rule of “0” holds in additive contexts; in multiplicative contexts “1” is nothing.

Know the properties of nothing.  Not by memorization, but in your soul.


“I came to wonder how much understanding anything (a term, a system, etc.) meant merely being used to it.  (Similarly I have observed with anything new in art, that when people say either that they cannot understand it or that they have come to understand it, that seems to mean largely either that they are not habituated to it or that they are).”  — St. T.S. Eliot.

You feel like you understand a thing, when you can represent it to your mind in multiple ways, and can also convert between them in your mind as needed.

Try to reverse premises and conclusions.  See if it still works.

You do not know a thing, until you know how it behaves in a greater and smaller number of dimensions.

real : complex : quaternionic :: orthogonal : linear : symplectic.

Temptation

[rough notes pulled from an old note in my email]

I now see why, as a person progresses in virtue, they become subject to increasingly subtle temptations.

Actually it isn’t about virtue per se, but about achieving any great task.  There is a series of increasingly convincing counterfeits to the goal, and accepting any of them, or giving up, leads to losing the goal…

Why does Aristole think virtue is a noble and rare thing?  Almost anyone, who isn’t unlucky in their temperament, can achieve the “mean” along some trait, if this simply means being nearish the center of a normal distribution.

The difficulty arises when you need to get through a very tiny, and hard to find, door.  The only way, other than astonishing luck, is feedback from reality.  Something must tell you when you are getting “warmer” or “colder”.  Virtue is paying attention to this feedback, and adjusting your search accordingly.  (Actually the process can tolerate quite a bit of error as long as you keep checking which direction you need to go from here!)

Inventing a lightbulb.  First you have to want something weird that doesn’t yet exist.  Then you have to try a bunch of things that don’t work.  Because they don’t work, you have to eventually give up on ALL of these attempts, until you find the thing that does work.  But you can’t give up too early, or too late.

Failures (fatal errors):

– giving up on the task entirely
– never attempting a concretely testable idea
– NOT eventually giving up on any specific implementation that can’t work.

Failures (recoverable):

– spending too much time on a bad idea, or too little time on a good one.
– walking past the right idea without noticing it, as long as you don’t reject it forever.

This also operates on the meta level.  Feedback loops surrounding and regulating feedback loops.  You have to detect if you are trying an infinite series of ideas that can’t work, to break out of the cycle.  (But not too soon!)  You have to detect if your way of doing feedback is itself subtly wrong.

In general the opposite vices are: clinging to unreal greatness, vs settling for mediocrity.

Presumption vs Despair.

Need to have obstinacy with respect to the goal, but not with respect to the specific means to the goal.

Not everybody can invent a lightbulb.  Most people should give up!  (But not on whatever task they eventually find to do instead.)

Physics.  Crackpots cling to a “revolutionary” idea that doesn’t work.  Incremental researchers never try to do the great thing.  Genius will try out a sequence of increasingly promising ideas, right on the edge of being “crackpot”, but without clinging to any of them, and continually testing and refining their intuition about what works.  Until finally they get “lucky”.  It really happens because they tried a thousand things.  But the luck never finds those without skill in defeating temptation.  Again, natural talent is also required.

Those who never stop being students (in bad ways).

Those who never stop being students (in good ways).

Once an obviously great thing is discovered, things open up a bit.  Feedback from reality is still needed, but becomes much easier when the overall contours of what is correct have become clear.  Eventually the great inventor leaves the task to others and looks for a new project…

Does this also apply to other, more obvious temptations?  Avarice collects, but fails to appreciate the increasing pile of dead desires.  In contrast, a no longer desired lust raises questions about its purpose much more quickly…  phantasy vs biology.  We want different things in different ways.  Complete mental unity is not possible, only a dynamic search.  If your ideal of being virtuous is inherently impossible, don’t be surprised if you find yourself choosing vice instead.

Necessarily, religion is subject to similar temptations, as there are an enormous number of superstitious counterfeits to an authentic faith in God.

The agnostic who gives up on the search, but also the hypocrite who wants their concept of God to flatter their own ego.  The anxious fundamentalist who just wants a list of rules and safe beliefs, not seeing that God wants a change of heart that could never be accomplished by those means.  The sellout to worldly ambition, with a charade once a week, to appease the religious instinct.

In fact we are told salvation would be impossible, but for the fact that it is actually God who is seeking us.

To enter into any spiritual ministry is to increase the number of temptations.  This happens, not just because of opposition, but because of the nature of the task itself.  It simply is not enough to have an overall intention to seek the will of God, as if putting yourself on the right “team” suffices.  It is also needed for both character and methods to reflect the gospel of Christ.  In this case, loyalty requires obstinacy with respect to Christ’s chosen means as well as Christ’s ends.  (But, in a way that is still modulated to some degree by feedback.)

Those who confuse lust for the supernatural as love for God.  The fanatic with a persecution complex, who interprets himself being found annoying, as positive feedback that he is doing God’s will.  But also, the worldling who can’t bear to be unpopular.  The visionary, with a “message” from God, that might well be coming from their own brain noise.  The caring pastor, who comes to conflate success in ministry, with the will of God.  The pastor who thinks of “faith” as making reckless decisions about the congregation’s money and buildings, in light of a future “revival” that will justify his ministry (to the glory of God of course).

The pastor who only tells people what they want to hear.  The pastor who only tells people what they don’t want to hear.  The pastor who speaks the word when he should be listening for it.  The pastor who assumes everyone experiences temptation in the exact same way he does.

The three temptations of Christ.  (Or, the temptation of not trying to be like Christ at all.)  Mixing any political agenda whatsoever with the Gospel (except in rare cases, with fear and trembling).

To reject a path that includes temptation—thinking that this danger is the most important feature of the path—can itself be a serious temptation.  Because the goal of seeking the path is not to avoid temptation altogether.  The goal isn’t even to never succumb to temptation—as long as we are able to recover from it.  (Remember: feedback.)  The goal is to reach the goal.

Idol Hours

Idol Hours

When you see the abomination
Standing where it should not be
The phone in your hand
Where prayer should be
Come out of her, my people
Put your phone down and talk to me
Be separate, be clean
And you will be sons and daughters to me
Not at the table, dears,
Not at the dinner table.