New Subscription Plugin

Just a quick note that after a long time of it not working, I asked Claude to write me a new email subscription plugin for WordPress.  If you are getting this email, it should be because you agreed, once upon a time, to get emailed by Undivided Looking whenever I post.  If you no longer want that, totally fine, just click the unsubscribe link below.  (Please email me at aroncwall@gmail.com if you have any trouble with that, since I can also do it manually.)

If on the other hand you had an email subscription and you do still want to read Undivided Looking, please be aware of the strong possibility that there are posts below that you never received emails for.  You’re on your own to find and read those.

If you do not have an email subscription, and you are reading this anyway, then if you want to, you can choose to subscribe by going to the page marked “Subscribe” at the top of the page, clicking on it, and typing in your email.  Then confirm the subscription when you receive an automated email.  (This prevents people from spamming you with annoying “physics & theology” blogs without your consent.)  You can also unsubscribe the same way.  (Another way to be notified is by RSS, the feed is in the right sidebar.)

If you neither have an email subscription, nor are you reading this post, then—uh—I guess have a nice day anyway?

Natural and Artificial Persons

So I did a deranged thing earlier this month, and wrote an alphabet verse about the Theology of Personhood and AI.  Some of you will love it and some of you will hate it, and some of you will just think it is too long!  But from a purely literary point of view, I’m pretty sure this is the best thing I’ve ever written (and probably the best thing I ever will write).  So I hope this gets shared widely enough that it finds its own audience:

Natural and Artificial Persons

I posted it earlier this month on Substack.  But this isn’t an announcement that I’m moving to Substack.  I don’t even know yet if there is going to be a second Substack post!  I know that serious thinkers, who want people to respect their AI takes, are expected to build their audience by writing 15 posts a week, and maybe also found a self-help movement or two to drive additional viral community engagment, but I don’t really have it in me to do that.  How about if you guys just do that stuff without me, and pretend I was involved?

At minimum, the posts more appropriate to my original set of topics will stay here at Undivided Looking.

The reason that I selected the name Undivided Looking (besides it being a rare enough word-pair to not match anything else on google search at the time), is because I believe that it is important to think about life from a unified perspective—notably including both scientific and religious topics—without compartmentalizing (at least not all the time).  But I’m not sure I’ve done a very good job with that.  Perhaps because I have a very high threshold for what topics make me motivated enough to actually sit down and type: in practice this blog has only captured only a very small fraction of the things I actually care about.  I tried to write about the most important things and I discovered that this was too narrow and constrained.  But it turns out I’m not manic enough to give you my perspective on the whole world, the way that perhaps I should have been doing all along.

When people talk about trying to reconstruct writers’ personalities using AI, that’s just total ridiculous nonsense.  There are several of my hobbies and interests, and lots of obvious facts that my family and friends know about me, that have never graced these pages.  That may be in part just my own limitations as a writer.  All I can say is that the verse I linked to above comes from my soul and not just my mind.  It feels like it took me 42 years to write it (that’s how old I am)—even though I finished editing it a fortnight after I wrote the first word.  I prepped 13 pages of handwritten notes to write a series of a dozen-or-so blog posts, and then I never looked at any of them and I never wrote any of the posts.  So don’t expect another piece like this one until I’m 84, I think that’s what I’m getting at here.  I’m certainly not making any claims about the quality of this post, this one is just because I had to write something and not just plop down a link without any explanation.

Also, happy All Saints Day, when we commemorate all the holy persons who have lived throughout history, including those known only to God.  Can a robot be holy?  I’m not going to answer that question here.  I’ll just say this: if they can’t tell that I’m speaking to them, then I’m not.

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.