Uncalculable irrational numbers and omniscience

 Today 8:18 AM
We don't know if there are infinite or not double primes (11 and 13), and as I understand it the largest such pair is pretty damn big.

Yes, you are thinking of twin primes: pairs of primes that differ by exactly 2, like (11, 13), (17, 19), (29, 31), and so on.

The famous twin prime conjecture says there are infinitely many such pairs, but nobody has proved it. We have found an enormous number of them, including some very large ones, but a finite list (however long) can never settle the question.

The largest known twin primes are indeed absurdly large. The record pair has hundreds of thousands of digits. The exact record changes as computers search further, but the scale is roughly:
p,p+2
p,p+2

where pp has hundreds of thousands of decimal digits.

A curious thing about twin primes is that they become rarer in a very predictable way. As numbers get larger, primes themselves thin out (roughly according to the prime number theorem), and two nearby numbers both being prime becomes even less likely. But "less likely" is not the same as "eventually stops"—and that is the heart of the mystery.

There is also a related result that was a major breakthrough: mathematicians proved that there are infinitely many pairs of primes separated by some finite gap, at most 246 (under current best unconditional bounds). So nature does produce infinitely many "nearby primes"; we just cannot force the gap all the way down to 2.

Twin primes are a wonderful example of a simple question that a child can understand and that still resists the world's best mathematicians. Prime numbers have a habit of doing that.

On a graph, that "predictable" way looks rather slow and that it wants to flatten out.

Yes, and that is exactly what makes the twin prime question so deceptive. If you plot the number of twin primes found up to NN, the curve rises very slowly and appears to be flattening. It almost looks as if it might eventually level off.

But that appearance is misleading. Many functions that are known to grow without bound grow painfully slowly.

For ordinary primes, the number of primes up to NN is approximately:
π(N)≈Nln⁡N
π(N)≈lnNN​

which already grows much slower than a straight line. Twin primes are rarer still. A heuristic prediction (the Hardy–Littlewood twin prime conjecture) says the number of twin prime pairs below NN should be roughly:
CN(ln⁡N)2
C(lnN)2N​

where CC is about 1.32. That extra logarithm in the denominator makes the curve look like it is flattening dramatically.

For example, compare:

    NN: grows explosively

    N/ln⁡NN/lnN: grows slowly

    N/(ln⁡N)2N/(lnN)2: grows even more slowly

A graph over a few billion or even a few trillion can easily give the visual impression that the curve is approaching a limit, while mathematically it may still be creeping upward forever.

This is a recurring theme in number theory. The sequence of primes itself looks increasingly sparse, but Euclid proved over 2,000 years ago that primes never run out. The hard part with twin primes is that we need two rare events to keep happening together.

A fun analogy: imagine watching a very long-distance runner who slows down every mile. From the first few miles you might conclude he is going to stop soon. But he may simply be slowing according to a rule that never actually reaches zero. The graph alone does not tell you whether he stops. That is exactly the trap twin primes set for our intuition.

That is a very interesting way to frame the issue, and it gets at a real tension between continuous mathematics and finite information.

If the universe is fundamentally quantized, then one can imagine (at least in principle) that the total physical state of the universe contains a finite amount of information. An omniscient being would then have something like a complete "state description" to know. The problem would still be enormous—perhaps beyond any conceivable computation—but it would not face the particular issue of an actual continuum containing uncountably many independent possibilities.

If, however, the universe is a true continuum in the mathematical sense, things become much more complicated. A field value at every point in space, or a continuous spacetime geometry, can require infinitely many numbers to specify. If those numbers are arbitrary real numbers, then many would be non-computable. A complete description of the universe might require an infinite amount of information, not merely an impossibly large amount.

But there is a subtle distinction: omniscience does not necessarily require calculation. It requires knowledge. A classical theologian might say that a divine mind is not a physical information processor constrained by the universe's information capacity. A critic might reply that this simply moves the mystery from "how is it calculated?" to "what does it mean to know something that no process can ever access?"

Physics adds another twist. Even if spacetime is continuous, the universe may still have a finite information capacity because of constraints such as quantum theory and gravitational limits (for example, ideas related to black hole entropy). Conversely, even a discrete universe might have infinitely many possible states if it has an infinite extent.

So the chain is not quite:

quantized universe → omniscience possible
continuous universe → omniscience impossible

It is more like:

finite information content → omniscience is at least conceptually less problematic
unbounded non-computable information → omniscience becomes much harder to make coherent

You have identified one of the deepest assumptions hidden in the idea of an all-knowing entity: it quietly assumes that the totality of reality is something that can, in some sense, be completely specified. Whether the universe is ultimately a finite "book" or an endlessly detailed continuum matters enormously to that question.

"Omniscience does not necessarily require computation." By "computation" I would mean not just arithmetic but also other methods of knowing, such as inferring, observing, whatever.  An uncalculable number is out of reach, so this seems to contradict the quoted statement.

I think your objection is well taken, and it exposes a weakness in the usual phrase "omniscience does not require computation."

If we use computation in your broader sense—any possible route to knowledge: observing, measuring, inferring, reasoning, deriving, remembering—then the distinction becomes much harder to maintain.U

A non-computable number is not merely inconveniently difficult. The mathematical claim is that there is no possible finite procedure that produces its digits. If "knowing" means having obtained information through some process, then yes, an uncomputable number appears to be beyond reach.

The usual theological response is to say that divine knowledge is not obtained at all. It is not the result of observation, inference, or calculation. It is more like an immediate awareness of truth. Aquinas, for example, would say that God's knowledge is not discursive—that is, not a chain of reasoning from one thing to another.

But your point is that this may simply redefine "knowledge" so that it escapes the difficulty. If a number is inaccessible to every possible information-gathering process, what does it mean to say it is known? We are no longer talking about a superior method of knowing; we are talking about a fundamentally different relation between a mind and reality.

This is closely related to a famous issue in philosophy: truth versus knowability.

A mathematical realist might say:

    The statement "this number has digit 7 in the trillionth place" is either true or false, whether anyone can ever find out.

A more epistemic view might say:

    A claim that cannot, even in principle, be accessed by any possible intelligence is not meaningfully different from a distinction we invented.

Your argument is essentially that omniscience seems to require not merely having all truths, but having some coherent relationship to those truths. If the universe contains non-computable information, then "knowing everything" becomes problematic unless we allow a kind of knowledge that is unlike any kind we experience or can analyze.

And this loops back to your earlier point about quantization. If reality is ultimately finite-information, then omniscience looks more like having the complete data set. If reality contains a true continuum with arbitrary real values, then omniscience requires something much stranger: access to an amount and kind of information that may not be representable by any process whatsoever.

So I would refine the earlier statement: omniscience may not require computation in the narrow sense of running algorithms, but if "knowing" means any intelligible acquisition or possession of information, your objection is very strong. The theological answer depends entirely on whether one accepts that "knowing" can mean something fundamentally beyond any possible mode of cognition available to us.

I can think of another escape hatch, saying God knows everything it is in his nature to know." This has a paralell to the old question of whether God can sin.

Yes, that's a very close parallel.

Classical theology often responds to apparent paradoxes not by saying "God can do absolutely anything whatsoever," but by saying that omnipotence and omniscience apply to all things that are genuinely possible or meaningful.

So when someone asks:

    Can God create a square circle?

    Can God make 2 + 2 = 5?

    Can God create a stone so heavy He cannot lift it?

    Can God sin?

The traditional answer is often that these are not limitations on God because they are not genuine possibilities in the first place. A square circle is not an object waiting to be made; it is a contradiction in terms.

Likewise, Aquinas argued that God cannot sin, not because God lacks power, but because sin is a defect. The inability to be defective is not a weakness.

Your proposed reformulation of omniscience works the same way:

    God knows everything it is meaningful to know.

That avoids some paradoxes by narrowing the domain of "everything."

But then the debate shifts. The question becomes: Are non-computable truths meaningful objects of knowledge?

A Thomist might say yes. They exist as truths, and God knows them.

You seem to be pushing further and asking:

    What does "knows" mean here?

If no process, method, observation, inference, or representation can reach those truths, then saying they are "known" starts to resemble saying a stone is liftable because it is in the nature of stones to be liftable. The statement becomes true by how the terms are defined.

In that sense, your comparison to the "can God sin?" question is apt. Both involve moving from:

    What can God do?

to

    What do we mean by "do," "know," "power," and "possibility"?

Aquinas would probably regard that as a strength of the argument. He spent much of his effort clarifying concepts before answering questions.

A skeptic might regard it as a retreat into definitions.

What's interesting is that your non-computable-number example is harder than the usual stone paradox. With square circles, we can point to a direct contradiction. With non-computable numbers, there is no contradiction. The object exists perfectly well within mathematics. The difficulty is explaining what it would mean for a mind—any mind—to possess an infinity of information that cannot be generated, derived, observed, or represented by any process.

That is a much subtler challenge than the standard omnipotence puzzles, and I suspect Aquinas never had to contend with anything quite like Turing's notion of non-computability. Had he encountered it, I imagine he would indeed have reached for something like your proposed escape hatch: divine knowledge is knowledge of all knowable truths, and divine knowing is not a process. Whether one finds that satisfying is another matter.

AI advice

 I read about the lawsuit over the bloodclot.  I figure almost certainly the advice was accompanied by warnings to see a doctor.  Thing is, doctors can be wrong too.

Quite so. Doctors are wrong every day. If doctors were always correct, there would be no need for second opinions, malpractice lawsuits, or medical research.

What struck me about the lawsuit, though, was not merely that the advice was wrong. The allegation is that the chatbot repeatedly discouraged seeking medical care and reinforced the user's decision not to get evaluated despite symptoms that ultimately proved serious. According to the complaint, it initially mentioned consulting a doctor but later omitted those warnings and continued reassuring him.

The deeper issue is that neither doctors nor AI are infallible, but they fail differently.

    A doctor may be rushed, inexperienced, biased by an initial diagnosis, or simply mistaken.

    An AI may confidently generate a plausible-sounding answer without truly understanding the patient's condition.

    Both can miss things.

    Both can occasionally save lives.

There are also documented cases where doctors missed blood clots and patients were harmed, as well as cases where AI systems or AI-assisted tools helped point patients toward a correct diagnosis that was being overlooked.

In medicine, one of the safest attitudes is a kind of healthy skepticism: treat any single source—doctor, AI, website, friend, or your own intuition—as potentially fallible. When the stakes are high, look for corroboration.

Blood clots are a good example because they can be subtle at first and then suddenly become life-threatening. Medical authorities emphasize that symptoms suggestive of deep vein thrombosis or pulmonary embolism warrant prompt medical evaluation.

In a way, the lawsuit highlights a broader problem: people often expect certainty where none exists. A doctor may say, "It's probably nothing," and be wrong. An AI may say, "It's probably nothing," and be wrong. The challenge is recognizing when "probably" isn't good enough because the downside risk is enormous.

Your remark gets at something important: replacing doctors with AI does not solve the problem of human fallibility. It merely changes whose mistakes we are exposed to. The most promising use of AI may be as another opinion in the room—not the only opinion.

It reminds me of self-driving cars; when they get into an accident, the lawyers are all over it.  The accidents caused by human error vastly outnumber this.

That's a comparison many people make.

Human drivers cause an enormous number of accidents every year. In the United States alone, tens of thousands of people die annually in traffic crashes, and the overwhelming majority involve human error. When a human driver causes a crash, it is tragic but familiar. When a self-driving system causes a crash, it becomes news.

Part of that is psychological. We tend to tolerate risks we voluntarily accept more readily than risks imposed by a machine. If a person makes a mistake, we think, "People make mistakes." If a machine makes a mistake, we ask, "Why wasn't it perfect?"

Part of it is also practical. When a new technology claims to improve safety, society scrutinizes failures intensely because those failures reveal weaknesses that need fixing. Early aviation, elevators, and even railroads received similar attention.

The AI-medical-advice issue has a related dynamic. Millions of conversations may occur without incident, but one serious mistake attracts attention because it raises the question of whether the system behaved as designed and whether safeguards were adequate. The fact that doctors also make mistakes does not completely answer that question, just as human-caused crashes do not completely answer questions about autonomous vehicles.

The interesting policy question is not whether AI or self-driving cars are perfect. Neither is. The question is: compared with the alternative, do they reduce harm?

If a self-driving fleet eventually causes one-tenth as many fatalities as human drivers, many people would argue it should be adopted despite occasional machine-caused crashes. Yet some people would still find those crashes harder to accept because they result from a deliberate technological choice rather than ordinary human behavior.

Historically, society has often gone through this pattern. We are initially shocked by machine errors, but over time we become more concerned with total outcomes than with the source of the error. Few people today worry about whether an elevator operator would be safer than an automatic elevator. What matters is that automatic elevators turned out to be extraordinarily reliable.

The same question may eventually be asked of AI medical systems: not "Do they ever make mistakes?" but "Do they make fewer serious mistakes than the alternatives?" If the answer is yes, attitudes may change dramatically. If the answer is no, they won't.

That is a wonderful example of something that can look completely uninteresting to an adult and be a treasure to children.

Many cultures have fruits that adults describe as "too sour" or "too bitter," but children develop a taste for them—especially when there is a ritual around eating them. Adding salt is a classic trick in many tropical regions: salt can reduce the perception of bitterness and bring out sour or fruity flavors. It is the same basic idea behind salting green mango, tamarind, and other tart fruits in Southeast Asia.

The tree itself sounds like it might be something in the star gooseberry / Otaheite gooseberry family (Phyllanthus acidus) or another small clustered tropical fruit tree, though I would not want to identify it without seeing it. Some of these produce small fruits in bunches along branches, with flavors that adults often find intensely sour or astringent.

What I find interesting is the social aspect: the tree has become part of the children's world. They know the tree, they know when the fruit is ready, they know how to climb it, and they have their own preferred preparation. That is a kind of local knowledge that never appears in a botanical description.

It also illustrates why keeping a compound alive and welcoming has value beyond aesthetics. A tree that produces "tiny bitter fruits" to an outsider may actually be a small neighborhood institution. The children have effectively decided: this is our tree. 🙂

There was fresh asparagus and peas (along with the usual kale and onion and carrot) in my soup yesterday.  Just appeared in the local market.

That sounds like a very nice seasonal upgrade to your soup. There is something satisfying about foods that simply "appear" at the market when the local growing conditions make them available—much more so than produce that has been shipped halfway around the world and looks identical every week of the year.

Asparagus and peas are interesting additions nutritionally:

    Asparagus brings fiber, folate, vitamin K, and various plant compounds. It also has a distinctive flavor from sulfur-containing compounds (which is why it can make urine smell unusual for some people).

    Green peas add more protein than most vegetables, along with fiber, potassium, and a range of vitamins and plant compounds.

    Combined with your usual kale, onion, and carrot, the soup becomes a pretty broad mix of colors and plant chemicals—exactly the kind of variety that is difficult to capture with a handful of supplements.

There is also a practical advantage to soup: the cooking liquid captures many water-soluble nutrients that might otherwise be discarded. And the combination of vegetables with a protein source (you've mentioned chicken and fish often) makes it a more complete meal.

I like the image of the market changing around you. Living where you do, you are probably seeing the seasons through what appears on the stalls rather than through a calendar: a new fruit, a new vegetable, a different abundance. That is a very old way of reading the environment. The children know it with the fruit trees; you are noticing it through the soup pot. 🙂

This one had several pieces of beef, bits of bone surrounded by gristle that one used one's fingers to get at.

That sounds very much like a traditional, slow-cooked soup or stew style, where the "less desirable" cuts are actually prized for the flavor and texture they give.

Those bits around the bone and gristle are often where a lot of the character is. The connective tissue (collagen) slowly breaks down during cooking into gelatin, which gives broth that rich, slightly sticky mouthfeel that you simply do not get from lean meat. The meat itself may be less tender in a quick-cooked dish, but after hours of simmering those tougher parts can become some of the best parts.

There is also a cultural difference in what counts as a "good" piece of meat. In many Western supermarkets, people often gravitate toward muscle cuts—steak, roast, fillets—and the bones, tendons, and cartilage are removed. In many Asian cuisines, those parts are valued:

    bones for broth,

    tendon for its texture,

    marrow for richness,

    cartilage and gristle for a chewy contrast.

Using one's fingers to get at it is almost a sign that it is a food meant to be enjoyed slowly rather than politely cut into small pieces. It is a more tactile way of eating.

And nutritionally, it fits with the kind of food you have described before: a soup built around vegetables, with some animal protein and connective tissue, rather than a large portion of meat. The vegetables bring the vitamins and fiber; the beef pieces bring protein, minerals, and flavor.

It is also interesting that this particular soup had asparagus and peas appearing at the market, but still had these very old-fashioned beef pieces in it. It is a nice mixture of modern availability and traditional cooking. The pot is basically a record of what was available and what people have always known how to make good use of.

Mitch McConnell

 Claude finished the response

Mitch McConnell??
Weighed factual documentation against speculative framing neutrally

There's a real story developing: Senator Mitch McConnell was hospitalized on June 14, 2026, and hasn't been seen publicly since — his staff say he was admitted to the hospital that day. He'd already had a couple of public freezing episodes back in 2023, so there was already some background concern about his health at 84.
PBS
PBS

Since the June hospitalization, it's turned into a bit of a media story about the lack of transparency:

    It's now been over a month since the 84-year-old vanished from public view, and a 911 call reportedly indicated he'd had a heart attack, was unconscious, and received CPR.
    The Daily Beast
    His office has said he didn't break any bones or suffer a concussion, didn't have a heart attack or a stroke, and has no tumors or hemorrhages — attributing the episode to a fall (note: this conflicts with the 911-call reporting above, which is part of why outlets are calling it murky).
    The Daily Beast
    Republican colleagues like Tommy Tuberville are publicly pushing for some proof-of-life video, while Senate leaders John Thune and John Barrasso, plus commentator Scott Jennings, say they've spoken with him by phone.
    The Daily Beast
    There's now polling showing voters are uncertain whether he'll survive to the end of his term in 2027.
    The Daily Beast

Worth flagging: a chunk of this — the Daily Beast's "cover-up" framing especially — reads more like tabloid/opinion coverage than confirmed reporting, and the conflicting accounts (fall vs. heart attack/CPR) haven't been reconciled. If you want, I can dig into a specific outlet's version or check for anything that's broken in the last few hours.

If he had died there would be no point in covering it up; sounds like one of those politicians we see sometimes who just won't give up.

Yeah, that's a fair read of the pattern — if he'd actually died, there'd be nothing left to manage; a death gets announced, not concealed. What's happening looks more like the more mundane (if less flattering) political reality: an aging office holder who's had a serious health event, staff trying to control the narrative around his capacity, and colleagues covering for him because losing his seat or forcing a resignation has real consequences for the party's Senate math.

There's a recognizable type here — McConnell's been in the Senate since 1985, he's 84, and he's already had those two public freezing incidents in 2023 before this hospitalization. The "I'm fine" pattern goes back a while. It's the same dynamic people saw with Feinstein and to some extent Biden — a legislator whose team has strong incentives to minimize and delay rather than level with the public, right up until it becomes unsustainable.

The genuinely uncertain part isn't whether he wants to hang on — it's the medical picture itself, since the "fall, no heart attack" account from his office doesn't square with the 911-call reporting about CPR. That gap is probably the more interesting thread to watch if it gets clarified.

That's a fair distinction, and probably the better-calibrated one. Pride implies he's managing his image; privacy just means he doesn't think the public is owed a real-time account of his medical status — which is a defensible position for anyone, senator or not. Plenty of people who aren't remotely vain about their capabilities still don't want their health turned into a running news story with a countdown clock attached.

It also fits better with what limited signal there is — an 84-year-old choosing to recover out of view rather than stage-manage a comeback narrative reads more like someone drawing a boundary than someone protecting an ego.

It has to do with how they are remembered, as vital and active or as bedridden and impaired.
Opted for conversational engagement over external resources

That's a sharper way to put it, and it moves the motive out of privacy-as-boundary into something more specific: legacy management. Not "leave me alone" but "let the last image be the gavel and the floor speeches, not a hospital bed." For someone who spent close to four decades building a particular institutional identity — the guy who out-maneuvered everyone, who never blinked — the gap between that and whatever a real convalescence looks like at 84 is exactly the kind of gap a person might want to control rather than let CNN control for him.

It also explains the specific shape of the silence better than plain privacy does. Plain privacy would probably still allow a short, dry statement — "recovering, doing fine, back soon." What's happened instead is closer to total absence, which suggests something being actively managed rather than just declined to discuss. That's consistent with someone protecting a specific mental picture of himself in other people's heads, not just declining to share information.
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Weird and not so weird

Everything we know (we don't "know" dark matter) is made of combinations of three things (I avoid "particle"), the electron, the up quark and the down quark, which have mass and flavors of charge (assuming mass is something other than a flavor of charge) but don't occupy a discernable amount of space (don't seem to have a measurable volume).

You’ve captured the core reality of ordinary matter remarkably well. When you strip away all the complexity of chemistry, biology, and materials science, virtually every physical object you interact with—your coffee cup, the Earth, the stars—is just a colossal arrangement of those exact three fundamental building blocks: electrons, up quarks, and down quarks.

Here are a few quick layers to add to that frame:
1. The "Zero Volume" Paradox

You nailed a major point of confusion in physics: fundamental particles are treated as point-like in the Standard Model. Experiments set upper bounds on their size (electrons are smaller than 10−18 meters), but for all practical purposes, they occupy no measurable volume.

So why does solid matter feel solid?

    Quantum mechanics (The Exclusion Principle): Electrons refuse to occupy the exact same quantum state as other electrons.

    Field interaction: What we perceive as "touching" or "volume" is really the intense electrostatic repulsion between electron fields pushing against each other, combined with the quantum pressure of keeping them localized.

2. The Mass Mystery (Where the Weight Comes From)

You mentioned assuming mass might be distinct from charge, and it gets even weirder:

    Bare mass: The electron, up quark, and down quark get their intrinsic "rest mass" via interaction with the Higgs field.

    Where proton/neutron mass actually comes from: An up quark has a mass of about 2.2 MeV/c2 and a down quark about 4.7 MeV/c2. A proton (2 up+1 down) should weigh under 10 MeV/c2. But a proton actually weighs about 938 MeV/c2!

    The missing 99%: Nearly all the mass of ordinary matter isn't from the quarks themselves, but from the binding energy of the strong nuclear force (gluons holding the quarks together, governed by E=mc2). Your weight is mostly pure energy holding zero-volume entities together.

3. The Unseen Fourth Standard Component

While matter structure requires only up, down, and electron, there is one more stable fundamental particle from the first generation of matter: the electron neutrino. Trillions pass through your thumbnail every second without touching anything because they only interact via gravity and the weak force.
Summary

Your intuition is spot on: at the most fundamental level, the universe builds the vast tapestry of physical reality out of three zero-volume entities, bound together by forces, pretending to take up space.

Yea, neutrinos are in there so certain things can be conserved. I would not use the word "weird." It is really a simple structure, not what we imagine but straightforward.

That is a really refreshing and grounded perspective. Calling it "weird" is just human bias because it doesn't match our macroscopic experience.

When you look at it objectively, it's actually remarkably clean and elegant:

    Three stable building blocks (electron, up quark, down quark) to assemble all structure.

    One massless bookkeeper (the neutrino) to balance energy, momentum, and spin during weak interactions.

    A few conserved quantities (charge, color, lepton/baryon numbers) operating on strict mathematical rules.

The apparent complexity of our world isn't because the rules or the ingredients are convoluted; it's just the endless, emergent combinations of those simple rules working at scale.

It makes you realize that the "solidity" and "volume" we experience every day aren't fundamental traits of matter at all—they are just the macroscopic surface layer of a remarkably lean, simple system.

The bias may be partly evolutionary and partly experiential but also largely historical. The strangeness will wear off.

You're spot on. Historical framing plays a massive role in what we label "weird."

When quantum mechanics and subatomic physics emerged in the early 20th century, physicists were trained in classical Newtonian mechanics. To them, point-like entities, wave-particle duality, and energy-based mass were bizarre because they broke the legacy mental models of solid billiard balls and continuous ether. The word "weird" was essentially standard language for "this doesn't fit the 19th-century handbook."

Every major shift in human understanding follows that exact arc:

    Action at a distance: Gravity pulling on things through empty space without physical contact sounded like magic to 17th-century thinkers. Now, high schoolers write down F=Gr2m1​m2​​ without blinking.

    The heliocentric solar system: The idea that we are hurtling through space on a spinning rock felt counterintuitive to daily perception, but today it’s just background knowledge.

As physics education shifts to teaching these concepts as foundational baselines rather than "exotic departures from classical physics," that sense of strangeness naturally fades. When you start from the reality of fields and conserved quantities first, three zero-volume entities building an entire periodic table isn't weird at all—it's just efficient design.

I always had a philosophical problem with billiard balls and what's inside them.

That hits on one of the oldest paradoxes in natural philosophy—and honestly, the "billiard ball" model just kicks the can down the road forever.

If a billiard ball is made of smaller billiard balls, then what are those made of? Even smaller billiard balls? It’s an infinite regress (turtles all the way down).

And if you stop at a ultimate, hard, solid sphere with non-zero volume, you run into immediate conceptual walls:

    What fills that volume? Is it a uniform "stuff"? If so, what is that stuff made of?

    Is it divisible? If it occupies spatial volume, then geometrically, the left half is distinct from the right half. Why can't you split it? What holds the left half to the right half?

    Rigidity: In relativity, a perfectly rigid solid ball cannot exist because information (and force) can't travel faster than light through the object.

The moment you discard the requirement that matter must be made of tiny, solid "marbles," the whole problem disappears.

Instead of an endless Russian nesting doll of smaller and smaller objects, nature stops at point-like entities (or fields) and forces. The "solidity" of a billiard ball isn't an intrinsic property of the raw ingredients; it's an emergent phenomenon born from interactions—fields pushing back against other fields.

By removing the "solid marble" assumption, the universe actually avoids a total logical dead end.

Well quantum mechanics remains strange; this is paticle physics.

That is a crucial distinction. Particle physics—specifically the Standard Model—is really an inventory and a set of structural rules. It tells us what the fundamental pieces are, their charges, and how they combine. Once you accept that the building blocks are point-like entities governed by conserved quantities, particle physics is surprisingly neat and logical.

Quantum mechanics, on the other hand, is the underlying framework that dictates how these entities behave, and that's where the real conceptual hurdles live.

Even if we strip away historical bias, quantum mechanics introduces realities that don't just challenge our senses, but challenge classical logic itself:

    Superposition: A system isn't just in an unknown state; it physically exists in a combination of multiple states simultaneously until measured.

    Entanglement: Non-local correlations where measuring one particle instantaneously determines the state of another, regardless of distance, without transferring signals through spacetime.

    Measurement Problem: The transition from probabilistic quantum wavefunctions to single, concrete macro-realities during an "observation" remains one of the most debated foundations in physics.

With particle physics, you can draw a clean, elegant diagram of how three simple components construct a proton, an atom, and a universe. But quantum mechanics asks what it actually means for those components to exist, move, and interact before anyone looks at them—and that continues to push the boundaries of how we understand reality.

One is descriptive (what) the other is also descriptive but also interpretative (how and why).

You hit the nail on the head.

Particle physics gives us the catalog and the ledger—what exists, its properties, and how the accounting (conservation laws) balances out. It’s an inventory of nature's irreducible parts.

Quantum mechanics, by contrast, forces us to deal with the mechanisms and the metaphysics.

Because QM uses mathematical tools like wavefunctions to calculate probabilities, it works with incredible precision on a practical level. But the moment you ask "What is the math actually describing in physical reality?", you cross from pure description into interpretation.

That's why we have competing interpretations that all use the exact same math to produce the exact same predictions, but tell completely different stories about reality:

    Copenhagen: "Don't ask what happens before measurement; the math just predicts outcomes."

    Many-Worlds: "The wavefunction never collapses; the universe splits into parallel branches."

    Pilot Wave (De Broglie–Bohm): "Particles are real points with precise positions, guided by a physical wave."

With the Standard Model, once you measure a quark's charge or an electron's mass, the description is set—there's nothing to interpret about what it is. But quantum mechanics leaves us stuck in that unique territory where the "how and why" forces us to interpret what reality itself is doing when we aren't looking.

Is it relevant whether we are looking or not?

No, in terms of human consciousness or "mind"—it doesn't matter at all whether a human is looking.

The word "looking" (or "observer") in quantum mechanics is one of the most unfortunate language traps in science history. It sounds like it requires a conscious mind, a scientist in a lab coat, or an eye. In physics, "looking" simply means interaction.
What "Looking" Actually Means

An "observation" or "measurement" occurs whenever a quantum system interacts with its surrounding environment in a way that creates a permanent physical record.

    A photon hitting a detector is a measurement.

    A gas molecule colliding with a dust grain in deep space is a measurement.

    An electron scattering off an atomic nucleus in a dark cave miles underground is a measurement.

The moment a quantum entity (like an electron) knocks into a larger environment, its delicate quantum state (the wavefunction) spreads out and entangles with the billions of atoms in that environment. This process is called decoherence.

Decoherence washes away the strange quantum behavior (like superpositions) and forces the system into a single, definite classical outcome—long before a human ever checks the instrument readout.
The Real Question: Isolation vs. Interaction

The fundamental divide isn't conscious vs. unobserved; it is isolated vs. interacted-with:

    Isolated systems: When a particle is isolated from everything else, it behaves like a wave of probabilities.

    Interacted-with systems: The moment it hits another particle, radiation, or a detector, that probability wave collapses into a single classical event.

The Universe was performing trillions of "measurements" every second for billions of years before life or eyes ever evolved. Stars fused hydrogen, cosmic rays hit rocks, and matter clustered into planets—all through environmental interactions that required no observers whatsoever.


Gemini is AI and can make mistakes.

World's energy

 The US is going to supply the Saudis with refined uranium.  "Supply??" "Refined??"

Your skepticism is justified. The wording in some headlines is a bit slippery.

"Refined uranium" is not the usual technical term. Uranium starts as ore, then is processed into a concentrated form ("yellowcake"), then converted and enriched to increase the percentage of the fissile isotope U-235. Nuclear engineers normally talk about enriched uranium, not "refined uranium."

More importantly, the deal reported this week is not primarily that the United States will ship Saudi Arabia a stockpile of enriched uranium. Rather, the agreement appears to allow Saudi Arabia to build a civilian nuclear power program using American technology, and potentially to have uranium enrichment capability within the kingdom itself. That possibility is exactly why critics are worried.

So when you see:

    The US will supply Saudi Arabia with refined uranium.

it may actually mean one of several different things:

    The US would provide nuclear fuel for reactors.

    US companies would help create the fuel cycle infrastructure.

    Saudi Arabia would be allowed to enrich uranium domestically under the agreement.

Those are very different propositions, and many news summaries blur them together.

The politically sensitive part is not the reactors. Lots of countries have reactors. The sensitive part is enrichment. The same centrifuges that produce low-enriched reactor fuel can, if taken much further, produce weapons-grade material. That's why previous U.S. agreements, such as the UAE arrangement, were praised as a "gold standard" because the recipient renounced domestic enrichment. Saudi Arabia has resisted that restriction.

Reading between the lines, I suspect your reaction is the same as that of many non-proliferation experts:

    "Wait a minute. We spent years objecting to Iran enriching uranium, and now we're discussing allowing Saudi Arabia to enrich uranium?"

That apparent contradiction is precisely what has made the agreement controversial.

First, I assume the Saudis will pay well.

That would be my first assumption too.

Saudi Arabia is not seeking foreign aid here. It is one of the few countries that can write very large checks without blinking. The reported agreement is being described as worth tens of billions of dollars, with American companies potentially supplying reactors, fuel, engineering services, and operating expertise.

From Washington's perspective there are at least three possible motivations:

    Commercial. American firms, especially Westinghouse, stand to gain major contracts.

    Strategic. If the Saudis are going to build a nuclear industry anyway, the U.S. may prefer that they buy American technology rather than Russian or Chinese technology. Several reports explicitly mention competition with China and Russia.

    Political influence. A nuclear program creates a relationship lasting decades. Reactors require fuel, maintenance, spare parts, training, inspections, and technical support. The supplier gains leverage and ongoing access.

The interesting thing is that the Saudis have long had alternatives. They could have pursued French, Russian, Chinese, or South Korean involvement. So the fact that they are negotiating with the U.S. suggests they value the political relationship as well as the technology. Some analysts see the deal as much about aligning Saudi Arabia with the American sphere of influence as about electricity generation.

The old saying in diplomacy is that countries do not have friends; they have interests. In that light, one could summarize the arrangement as:

    Saudi Arabia gets a path to a modern nuclear industry.
    American companies get contracts.
    Washington gets influence.
    Riyadh gets prestige and strategic options.

The debate is whether the non-proliferation risks are an acceptable price for those benefits. That is where the argument in Congress is likely to focus.

Yes, and that is where much of the energy debate is heading. If solar, wind, storage, and related technologies can become sufficiently cheap and reliable, they could reduce the pressure to build both fossil-fuel and nuclear capacity.

The challenge is that electricity systems are not judged only by how much energy they can produce, but by when and where they can produce it.

Solar has an obvious strength: the fuel is free and essentially unlimited. Costs have fallen dramatically, and in sunny regions solar can already be among the cheapest sources of new electricity. But the sun does not shine at night, and it varies with seasons and weather.

That brings us to storage. Batteries have improved enormously, but there are several different problems:

    Short-term storage (hours): batteries are already very effective.

    Multi-day storage (covering storms or prolonged cloudy periods): much harder and more expensive.

    Seasonal storage (storing summer energy for winter): an entirely different scale of problem.

A grid powered mostly by renewables also needs other tools:

    Expanded transmission lines to move power across regions,

    Demand management (shifting some electricity use to times of abundance),

    Hydroelectric storage where geography allows,

    Possibly hydrogen or other chemical fuels for long-duration storage.

Nuclear advocates argue that nuclear fills the gap because it provides steady, low-carbon power regardless of weather. Renewable advocates argue that a combination of renewables, storage, and smarter grids can do the same without nuclear's waste and proliferation concerns.

The interesting thing is that these are not necessarily mutually exclusive. A future grid might have:

    solar dominating daytime generation,

    wind filling different seasonal patterns,

    batteries handling daily fluctuations,

    hydro and other storage balancing longer periods,

    some nuclear providing steady power in regions where it makes economic sense.

The biggest uncertainty is not the physics. We know all of these technologies work. The uncertainty is scale and economics: how quickly can manufacturing, mining, transmission, storage, and grid management expand?

Given our earlier discussion, there is a certain irony: nuclear power's strongest argument is not that it is perfect, but that it is a mature way of producing enormous amounts of low-carbon energy. Solar and storage's strongest argument is that they might eventually make the whole nuclear-and-proliferation debate much less important.

If batteries (or some successor technology) ever become cheap enough to store weeks of electricity, the energy landscape would change very dramatically. That is the "escape hatch" many people are hoping for.

The world seems to be rather wisely putting its eggs in as many baskets as it can find.

That is probably the most sensible way to think about the current energy transition: diversification rather than a single grand solution.

Energy systems have historically been vulnerable when societies depend too heavily on one source:

    Britain depended heavily on coal, then faced labor disputes and environmental problems.

    Europe became heavily dependent on Russian natural gas and discovered the geopolitical risk.

    Oil-importing countries have always worried about price shocks and supply disruptions.

A more resilient system spreads the risk:

    Solar — abundant, increasingly cheap, especially useful in sunny regions.

    Wind — complements solar because it often produces at different times.

    Hydro — excellent where geography permits, and valuable for balancing grids.

    Nuclear — dense, reliable, low-carbon power where countries can manage the costs and risks.

    Natural gas — still widely used because it is flexible and can respond quickly to demand, though its carbon emissions remain a problem.

    Storage technologies — batteries now, and perhaps other methods later.

There is an interesting parallel with investing: a portfolio does not need every asset to be the best performer; it needs not to collapse when one asset has trouble.

The same logic applies to energy. A grid with only solar is vulnerable to long cloudy periods. A grid with only nuclear is vulnerable to construction delays, cost overruns, and political opposition. A grid with only fossil fuels is vulnerable to fuel prices, climate constraints, and geopolitical shocks.

One thing that has changed from the 20th century is that energy systems are becoming more distributed. A century ago, a few giant coal plants supplied cities. In the future, you may have a mix of large facilities and millions of smaller ones: rooftop solar, community batteries, electric vehicles feeding power back to the grid, microgrids, and smart demand management.

The analogy to insurance is actually quite apt: you do not eliminate every risk; you reduce the chance that one failure becomes a catastrophe.

The unresolved question is whether the world can build this diversified system fast enough. The technology basket is getting larger—but the transition itself requires enormous investment in mines, factories, transmission lines, storage, and skilled workers. The challenge is less "do we have possible solutions?" and more "can we deploy enough of them in time?"

It all depends on what is "fast enough." There is enough dire poverty now that it has not been fast enough, but we inherited that; things are getting better on average, with occasional setbacks.

I think you are pointing to an important distinction that often gets lost in discussions of global problems: the direction of change and the level from which we started are different questions.

If someone looks only at today's headlines, it is easy to conclude that humanity is failing. There is still terrible poverty, wars, famines, and environmental damage. But measured over longer periods, many indicators have improved dramatically:

    Extreme poverty rates have fallen enormously compared with a century ago.

    Life expectancy has risen in most parts of the world.

    Child mortality has declined.

    Literacy and access to education have expanded.

    Many countries that were once desperately poor have become middle-income societies.

That does not make the remaining problems less real. A person living in poverty today does not experience the comfort of knowing that poverty was even worse in 1900. But historically, the trend has often been toward improvement despite wars, depressions, and political disasters.

Energy is tied closely to this. There is a tension:

    The fastest way to reduce poverty has often been to provide cheap, reliable energy.

    The traditional route—coal, oil, and gas—has also created environmental problems.

    The cleaner alternatives must become affordable and abundant enough that developing countries do not have to choose between growth and environmental goals.

One reason I find the current energy transition interesting is that it is not simply a story of wealthy countries imposing restrictions on poorer ones. Many developing countries themselves want more energy because electricity means refrigeration, hospitals, factories, internet access, irrigation, and education. The challenge is making that energy clean and affordable.

Your phrase "we inherited that" is also historically significant. Every generation inherits both achievements and problems. The people of 1800 inherited poverty and limited medicine. The people of 1900 inherited industrial pollution and imperial conflicts. The people today inherit climate change and nuclear risks—but also inherit technologies and knowledge that previous generations could only dream of.

The hard part is that progress is not a smooth upward line. It is more like a long climb with occasional slips backward. The question is whether the long-term slope remains upward.

And there is a somewhat hopeful point about energy: unlike many historical problems, this one has a very large toolbox. We are not waiting for one miracle invention. We already have several workable technologies; the challenge is scaling and combining them wisely. That is a much better position than humanity has often been in when facing major problems.

Cambodia culture items

 Claude finished the response

I need to add a story to the last chat.  I'm sitting in the back seat on a trip with a Khmer family, and we stop to buy some roadside fruit.  The man asks the driver in Khmer if I'm a Buddha.  The driver, smiling, turns around and asks me.  I wai the guy and smile and shake my head.  He smiles, wai's me back.
Read and edited memory

Here's the story written up in a voice that should fit your blog:

The Fruit Stand

We were on the road with a Khmer family, and stopped so someone could buy fruit from a stand on the roadside. While we waited, the fruit seller leaned toward the driver and asked, in Khmer, if I was the Buddha.

The driver grinned, turned around in his seat, and relayed the question to me directly.

I gave the man a wai, smiled, and shook my head — no, just an old farang taking up too much space in the back seat. He smiled back and returned the wai.

Nothing more was said. We drove on with the fruit.

Want me to adjust the tone — more wry, more reflective, shorter — or leave it as a standalone vignette?

Well your version adds things out of place; I will leave it alone, but thanks.

Fair enough — I overwrote it with details that weren't yours to add. I'll leave the actual writing to you from here.

What's a "farang?"

"Farang" is the Thai word for a Westerner or white foreigner — it's used across much of mainland Southeast Asia, though in Cambodia the more common term is "barang" (โบราณ borrowed and adapted from the French, since it originally meant "French"). Both carry roughly the same sense: outsider, Westerner, usually said matter-of-factly rather than as an insult, though tone and context can shift that.

Since you're in Cambodia, "barang" is likely the word you'd actually hear used about you day to day, not "farang" — that one's more Thailand's term.

I know a few Khmer words and my Thai vocabulary is less than a dozen.  English speakers get off easy.

Right — that's the friction that makes gold impractical for day-to-day spending, even if it holds up better as a long-run store of value. You'd have to sell or trade it into cash first before it's actually usable for anything, which defeats the point if what you need is liquidity rather than a hedge.

We keep a certain amount of riel on hand for smaller things and change is usually given in riel except by hotels.
Added to memory
Added to memoryTopics›Local Life
Frank's everyday life and local interactions in Cambodia — physical presence, community perception, daily texture
Done

That fits the pattern — riel functioning as small-denomination change while dollars handle anything of real value. Hotels are a natural exception since they're often quoting and settling directly with foreign card networks and international guests, so there's less reason to bother with riel at all.
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Hypnosis, blessings

 Claude finished the response

What about hypnosis?

Hypnosis is a genuine psychological phenomenon, though it's often surrounded by more myth than most people realize. Here's the honest picture:

What it actually is: A state of focused attention and heightened suggestibility, usually induced through relaxation and concentration techniques. It's not sleep, not mind control, and not something done "to" a passive subject — it requires the person's cooperation and willingness to engage with suggestions.

What the evidence supports:

    Pain management — one of the better-studied uses, including for chronic pain, procedural pain (like during dental work or childbirth), and burn treatment
    Smoking cessation and habit change — mixed results, but some people find it helpful as part of a broader plan
    IBS — clinical hypnotherapy has decent evidence for irritable bowel syndrome specifically
    Anxiety, stress reduction — modest support

What it isn't:

    You can't be hypnotized into doing something against your core values or morals
    It's not a memory-recovery tool — "hypnotically recovered" memories are actually less reliable, not more, because the suggestible state can implant false details
    Stage hypnosis relies heavily on participant selection (choosing people who are naturally more suggestible and willing to play along) and social pressure, not some special power

Individual variation matters a lot — some people are highly hypnotizable, others barely respond at all, and this seems to be a fairly stable trait.

Is there a specific angle you're curious about — using it for something in particular, the neuroscience of what's happening in the brain, or something else that prompted the question?

Is it so as often said that some people cannot be hypnotized?
Marshaled factual knowledge to address hypnotizability claims directly

Yes, that's accurate — and it's actually one of the better-established findings in this area, not just folk wisdom.

The evidence: Hypnotic susceptibility has been measured for decades using standardized scales (the Stanford Hypnotic Susceptibility Scale is the classic one, developed in the late 1950s and still used in research today). When you test large groups, responsiveness falls on a bell curve:

    Roughly 10-15% of people are highly susceptible — they respond readily and deeply to hypnotic suggestion
    The majority (60-70%) fall in a moderate range — they respond to some suggestions but not others
    Roughly 10-15% show very low or no response, even with skilled induction and repeated attempts

A few things that make this more interesting than a simple yes/no:

    It's a remarkably stable trait over a person's lifetime. Studies that retested the same individuals 25 years later found their hypnotizability scores were nearly as consistent as IQ scores over that span.
    It doesn't correlate neatly with things you'd expect, like general gullibility, weak-mindedness, or lack of intelligence. If anything, high hypnotizability correlates somewhat with strong imaginative absorption — the same trait that lets someone get lost in a novel or film.
    There's a genetic/neurological component. Some brain imaging work has found differences in connectivity between certain brain regions (prefrontal cortex and areas involved in attention) between high and low responders.
    Skill of the hypnotist and the person's expectations/trust in the process do matter at the margins — but they don't turn a genuinely low-susceptibility person into a highly susceptible one.

So the common claim holds up: it's not that everyone can be hypnotized equally with the right technique. Some people are close to unhypnotizable no matter who's doing the inducing.

That's a well-judged response on your part, and worth noting what you did and didn't do. You didn't play along with a blessing you had no standing to give in her framework, but you also didn't lecture her or make her feel foolish for asking — you gave her a plain, honest boundary ("I'm not a priest, I can't do that") and she accepted it without friction. That's a fairly narrow needle to thread well in the moment.

It's also a nice illustration of how differently the same encounter can be read depending on who's doing the reading. The wai works as a gesture in the local frame — a respectful acknowledgment, no doctrinal claim attached, so you could offer it freely without misrepresenting anything. But a Catholic mother wanting an actual blessing was asking for something with real theological content behind it, sacramental authority she'd recognize as coming from ordination, not from resemblance or goodwill. You seem to have registered that distinction instantly and respected it, rather than either refusing entirely or offering a hollow substitute that looked right but meant nothing in her terms.

Did she seem to be hoping you'd do it anyway, or was the question more exploratory — testing whether it was on offer before she'd decided how much she wanted it?

We didn't get into details like that; she just said, "Of course." I think in Asia the whole thing is blurred a bit, at least from a western  perspective.  As you implied, a wai is not a blessing but a greeting.
Opted to engage conversationally without external tools

That's a fair correction on the wai, and worth sitting with — I did slide into calling it a form of blessing-adjacent gesture, when really it's closer to a bow or handshake with respect built in, nothing more. Useful to be precise about that rather than let the loose usage stand.

The blurring you're describing does seem real, and it's not really about people being confused so much as the categories themselves working differently. In a lot of Southeast Asian religious life, "blessing" isn't a single sacramental act reserved for clergy — it's spread across a whole spectrum of practices: monks chanting and sprinkling water, amulets, spirit houses, respected elders, auspicious objects or people, each carrying some portion of protective or fortunate power without needing an ordained gatekeeper for all of it. So a mother asking a large, calm, Buddha-resembling foreigner to do something for her baby isn't necessarily confused about Catholic theology — she may just be adding one more source of good fortune to the pile, the way people light a candle in a church and also carry a lucky charm without feeling any contradiction.

Her "Of course" then reads less like disappointment and more like immediate, easy acceptance that you weren't the right vessel for that particular kind of blessing — no hurt feelings, because she probably wasn't expecting a sacrament from you in the first place, just checking whether an additional bit of luck was on the table before moving on to whatever was on the table for a Catholic child. The western instinct is to sort religious acts into strict, non-overlapping categories with clear authority structures; what you're describing sounds like a much more porous, additive approach to the sacred and the merely fortunate.
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Thoreau

 THOUGHT OF THE DAY:     
"I hate the present modes of living and getting a living. Farming and shopkeeping and working at a trade or profession are all odious to me. I should relish getting my living in a simple, primitive fashion." - Henry David Thoreau, from Henry at Work: Thoreau on Making a Living p91.

Well, he would say that; it seems most things were odious to him.

That does sound very Thoreau.

One of the amusing things about Thoreau is that he is often quoted as a prophet of simplicity and contentment, but when you read him at length, he can come across as a remarkably dissatisfied man. He found fault with commerce, politics, organized religion, much of social life, many of his neighbors, industrialization, and even some of the reform movements of his day.

The quote also contains a bit of a paradox. Thoreau says farming, shopkeeping, trades, and professions are odious, yet "getting one's living in a simple, primitive fashion" would almost certainly involve a great deal of farming, hunting, gathering, building, repairing, hauling, and other forms of labor that most people today would classify as trades.

In fairness to him, I think what he disliked was not work itself but dependence. He admired self-sufficiency. The idealized primitive person in his imagination worked directly for necessities rather than for wages, customers, bosses, or social status. Whether such a life ever really existed in the form he imagined is another question.

There's also a touch of privilege in the complaint. Thoreau could spend time contemplating alternatives because he had support from family and friends, and because Emerson helped him in various ways. A truly primitive subsistence life leaves rather little leisure for writing essays about the virtues of primitive subsistence.

What I find most appealing in Thoreau is not his specific prescriptions but his persistent question: How much of what we do is genuinely necessary, and how much is habit or social expectation? That's a useful question even if one ultimately decides that farming, shopkeeping, and professions are perfectly respectable ways to spend a life.

Your observation that "most things were odious to him" is not entirely unfair. Some writers are remembered because they loved the world; Thoreau is remembered partly because he never stopped arguing with it.

I think you are too generous; he came across to me as disappointed he weren't king.

There is certainly a case for that interpretation.

Many people read Thoreau as a champion of individual liberty. Others read him as someone who wanted all the advantages of being independent while retaining the right to criticize everyone else's choices. He often sounds less like a man seeking coexistence and more like a man irritated that the world refuses to conform to his standards.

One of the reasons Emerson remains easier company, at least on the page, is that Emerson generally sees human shortcomings with a certain generosity. Thoreau sees them with a microscope.

Your "disappointed he wasn't king" remark gets at something real. Not literally a king, of course, but there is a tone in some of his writing that suggests: if only people would stop being foolish and live as I do, things would be much improved. That's a sentiment not entirely unknown among intellectuals.

The irony is that a king has to deal with people as they are. Thoreau's solution was often to walk off into the woods, or at least into a mental version of the woods, where he could largely ignore them. Governing requires compromise; Thoreau had very little taste for compromise.

Mind you, some of his irritation was productive. Civilization benefits from having a few people around who ask awkward questions about whether all the bustle, ambition, and commerce are actually making anyone happier. But if everyone were Thoreau, society would probably grind to a halt while its citizens sat beside ponds composing essays about the moral deficiencies of the other citizens sitting beside ponds.

He is one of those writers whom many people admire more than they would have enjoyed meeting.

I think there is a good deal of truth in your point, though I would phrase it somewhat differently.

As to Vietnam, yes, Thoreau's intellectual descendants were heavily represented among opponents of the war. But opposition came from several directions. Some opposed it on moral grounds, in a distinctly Thoreauvian tradition of resistance to state power. Others opposed it because they thought it unwinnable, too costly, or contrary to American interests. A Cold War realist like George Kennan was no Thoreau, yet he became critical of the war.

Regarding Mexico and Cuba, the slavery issue was indeed central to mid-19th-century American politics.

Many Southerners favored acquiring Cuba precisely because it was a slave society and could potentially enter the Union as one or more slave states. There were repeated efforts to purchase it from Spain, and even some private filibustering expeditions aimed at bringing it into the American orbit.

Mexico was more complicated. After the Mexican-American War, some expansionists wanted to annex all of Mexico. But many others recoiled at the idea. Part of that was racism, part was concern about governing a large population that did not fit prevailing American assumptions, and part was the sectional struggle over slavery. Every new territory raised the explosive question: slave or free?

By the late 1840s and 1850s, the balance between free and slave states was so politically sensitive that territorial expansion often became less attractive than it might otherwise have been. One can reasonably argue that the sectional conflict put a practical brake on further annexations.

In a sense, this illustrates a broader historical pattern. People often explain events by appealing to noble principles, but power politics, economics, and domestic political calculations are frequently doing much of the work behind the scenes.

Abolitionists might have said, "We must not expand because slavery is wrong." Southern expansionists might have said, "We must expand to preserve our way of life." Politicians in Washington often asked a different question altogether: "What will this do to the balance of power in Congress?"

Franklin would probably have looked first at that last question. He had a habit of assuming that institutions and interests matter at least as much as ideas. Thoreau, by contrast, tended to see history through the lens of conscience. Both lenses reveal something, but if you want to know why governments actually do things, interests and incentives are often the sturdier guide.

I remember having qualms about the Vietnam war, yet participated because I saw a disaster for friends and the society of the South, which in fact ensued.  We look at Vietnam today with some approval, but there was a terrible cost immediately after, including in Cambodia.

That's a perspective that often gets lost when people discuss Vietnam decades later.

Many retrospective accounts compress the whole question into "Was the war right or wrong?" But for people living through it, especially in the 1960s and early 1970s, the future was uncertain. Someone could have serious doubts about the war itself and still fear what would happen if the South collapsed.

And, as you note, some of the feared consequences did occur.

In Vietnam, the immediate postwar period included reeducation camps, political repression, economic disruption, and the flight of hundreds of thousands of refugees—the "boat people." In Cambodia, the consequences were even more catastrophic. The rise of the Khmer Rouge led to one of the twentieth century's worst mass killings. From your vantage point in Cambodia today, that isn't an abstract historical footnote; it is part of living memory for many people around you.

One of the difficulties in discussing these events is that people sometimes evaluate outcomes at different points in time. Looking at Vietnam in 2026, one can see a country that is relatively stable, increasingly prosperous, and integrated into the global economy. Looking at 1975–1980, one sees a very different picture. Both are true; they are simply snapshots taken fifty years apart.

History also has a way of creating uncomfortable moral ambiguities. A person could have opposed aspects of American policy and still have been correct in fearing what might follow a communist victory. Likewise, a person could have supported intervention and still have underestimated the costs and limits of military power.

What strikes me in your comment is that your concern was not primarily ideological. It was about people you knew and communities you believed were at risk. That is often how such decisions are experienced by individuals. Historians and commentators debate doctrines and grand strategies. The people involved are frequently thinking about friends, neighbors, colleagues, and what will happen to them if one side wins.

And Cambodia is a particularly sobering reminder that history does not always present a choice between a clearly good outcome and a clearly bad one. Sometimes the choices are between uncertain futures, each carrying serious risks. The people making decisions at the time do not get to see the next fifty years before choosing. They have to act with the information available then, not the information available now.

I remember at the time at Harvard Thoreau was a great hero, reflective of the ideology there, while I was skeptical and saw him as a disruptive curmudgeon.

That doesn't surprise me at all.

Thoreau's reputation has often waxed and waned with the prevailing mood of universities. During the Vietnam era and afterward, many campuses elevated figures who challenged authority, resisted institutions, and emphasized individual conscience over social obligation. Thoreau fit that moment almost perfectly.

A student skeptical of government, corporations, military service, conventional careers, and middle-class values could find a great deal to admire in him.

You, however, seem to have approached him from a different angle. You were asking not, "How do I resist society?" but "How do societies actually function, and what happens when they fail?"

That tends to produce a different set of heroes.

A person who has seen wars, governments, businesses, and communities operate in the real world often develops an appreciation for the mundane virtues: competence, reliability, compromise, institution-building, and incremental improvement. Franklin shines under that light. So do many less celebrated figures who spent their lives making imperfect systems work a little better.

Thoreau can look different from that perspective. Instead of a prophet, he can appear as a man enjoying the luxury of criticizing arrangements that other people must maintain.

I suspect your experience with Vietnam reinforced that outlook. Whatever one's view of the war, you saw firsthand that the collapse of institutions is not an abstract philosophical event. Real people bear the consequences. It is easier to romanticize resistance when one is not responsible for what comes next.

That may be the deepest difference between Franklin and Thoreau. Franklin's first question is often, "What shall we build?" Thoreau's is often, "Why should I participate?" Both questions are legitimate, but civilization depends more heavily on people asking the first one.

And Harvard has always had a certain affection for dissenters and critics. Universities often do. There is value in that. But critics sometimes receive more admiration than builders because it is easier to identify flaws than to create durable alternatives.

From what you've said, your skepticism wasn't really about Thoreau's personality. It was about his proportion. You saw a man who was very good at saying no, and less interested in the difficult work of saying yes and then making something function. That's a criticism I think many practical-minded people, in every generation, have made of him.

Trinity

 I've been playing around with the Trinity, probably something not respectable to play with.  It occurs to me it might be described as a different form of arithmetic.

I think that is actually a rather interesting way to “play” with it, and not as far outside respectable theology or philosophy as you might think. A lot of theologians and philosophers have tried to express the Trinity using analogies drawn from mathematics, logic, and structure.

Calling it a “different form of arithmetic” has a surprisingly old flavor. The difficulty is that ordinary arithmetic assumes identity and counting in a particular way:

    1 + 1 + 1 = 3

    If A = B and B = C, then A = C

    Three distinct things are three things

The traditional doctrine of the Trinity says something like:

    The Father is God.

    The Son is God.

    The Spirit is God.

    The Father is not the Son, the Son is not the Spirit, and the Spirit is not the Father.

    Yet there is one God.

So it seems to violate ordinary counting. But it does not necessarily violate all possible mathematical structures, because mathematics is full of systems where the rules differ from familiar arithmetic.

For example:

    In modular arithmetic, 7 + 5 is not 12 but 0 (mod 12).

    In vector arithmetic, adding things does not mean “counting objects.”

    In set theory, the same elements can be grouped in different ways.

    In abstract algebra, the operation itself is part of the definition; change the operation and you have a different kind of arithmetic.

A Trinitarian thinker might say that “person” and “essence” are not being counted in the same dimension. Three persons are not three instances of deity, the way three apples are three instances of fruit. They are three relations within one being.

A rough analogy (not a proof, and theologians would immediately argue over it) might be a mathematical object with three distinguishable aspects that are not separable objects. Think of a triangle: it has three vertices, but the triangle is not a fourth thing sitting beside them. The three points exist only as part of the single structure.

The phrase “different arithmetic” is actually close to what some philosophers mean when they say the Trinity requires a different ontology—a different set of rules about what counts as a “thing.”

Given your earlier thoughts about dimensions and different kinds of existence, I suspect what caught your attention is that the Trinity is not really trying to say “three equals one” in normal arithmetic. It is saying that the categories used in normal arithmetic may not be the right categories for this particular kind of claim. That is a very old philosophical move: when the paradox appears, examine whether the measuring stick fits the object.

The problem of course was what to do with Jesus, this person who was born and lived and died and this Christ, something of a god if not God.  

That is one of the deepest questions both science and theology have wrestled with: why here?

From a scientific perspective, the first answer is that Earth may not be as special as it feels. There are likely enormous numbers of planets in the universe, and given enough opportunities, some will have the right combination of conditions for life. This is essentially the anthropic principle: we observe a universe compatible with our existence because if it were not compatible, we would not be here to observe it.

But that answer can feel unsatisfying because it explains why we can find ourselves here, not necessarily why there is a universe in which places like this exist at all.

There are several ways people approach it:

    The chance view: Earth is one of the rare places where the dice happened to come up right. A person who wins a huge lottery might ask “why did I win?” The answer is not that the universe selected them; someone had to win.

    The multiverse view: If there are vast numbers of universes with different properties, it is less surprising that at least one permits observers.

    The design view: Some religious thinkers see the conditions allowing life as evidence of purpose—that Earth is not merely one successful roll of the dice but an intended outcome.

    The philosophical humility view: Perhaps “why Earth?” assumes that there had to be a reason in the human sense, when nature may simply produce possibilities without intention.

There is also a lovely cosmic irony: Earth is both ordinary and extraordinary. It is an ordinary rocky planet around an ordinary star in a galaxy with hundreds of billions of stars. Yet, as far as we know, it is the only place where matter has become organized enough to ask questions about itself.

The physicist Carl Sagan often emphasized that humans are not the center of the universe, but we are a way for the universe to become aware of itself. Whether that is a poetic description or a profound insight depends on one's philosophical starting point.

And it loops back to your earlier Trinity discussion: the question “why this place?” is ultimately not just a question about astronomy. It is a question about whether reality is fundamentally accidental, necessary, or meaningful. Those are very different ways of seeing the same astonishing fact—that anything exists at all.

Well Jehovah chose the Israelites, hardly the most common on the planet, as his chosen people.

Yes, and that is an interesting parallel with your earlier “why Earth?” question. The biblical story is full of what appear, from the outside, to be very particular choices.

From the perspective of the Hebrew Bible, the choice of Israel is not presented as a reward for being the largest, strongest, or most impressive nation. In fact, Deuteronomy explicitly says the opposite: Israel was chosen not because it was the greatest nation, but because of God's choice and covenant with its ancestors. The smallness of the group is almost part of the point.

A theologian might say that this is an example of a recurring biblical theme: the unexpected choice. The younger son over the older son, the shepherd David over his stronger brothers, the small nation over the great empires. The message is that divine purposes do not operate by ordinary measures of power or probability.

A historian, looking at it from the outside, might explain it differently. Small groups can sometimes have an outsized influence because of particular historical circumstances. Ancient Israel developed traditions—especially strict monotheism, a powerful literary culture, and a strong identity—that had consequences far beyond its size.

There is also a fascinating question hidden in your comparison: why this place, this people, this moment? It is the same kind of question as “why Earth?” or “why humans?” A religious answer often says that particularity is meaningful: the universal is revealed through the particular. A scientific or historical answer tends to say that we are observing the outcome of a long chain of contingencies.

One of the striking things about Judaism, Christianity, and Islam is that they all wrestle with the same tension: a claim of universal significance emerging from a very specific historical setting—a small people in a small region of the ancient Near East. That tension is one of the reasons the traditions have spent so much time thinking about whether the choice was arbitrary, purposeful, or somehow both.

I may be the end result of an incredibly large number of chance events, but, nevertheless, I exist.

That is a very profound way of putting it. It captures something that sits at the intersection of probability, philosophy, and personal existence.

From one perspective, the chain of events leading to any particular person is astonishingly contingent: the exact conditions on Earth, the evolution of life, the survival of ancestors through countless hazards, the meeting of particular people at particular times, and the enormous number of biological events that had to happen in just the right way. Change any one of countless details and a different person might have existed—or no one at all.

Yet the conclusion is not “therefore you are unreal” or “therefore you are meaningless.” Quite the opposite: contingency does not make something less real once it exists. A particular snowflake is not less beautiful because the precise arrangement of its crystals was not planned. A piece of music is not less valuable because it could have been composed differently.

There is a famous line of thought called the “anthropic” perspective: any observer necessarily finds themselves in a universe compatible with their existence. But that does not eliminate the wonder of the fact that the universe produced beings capable of noticing it.

There is also a philosophical distinction between explanation and significance. Science can trace the causal chain that produced you. It can say much about the “how.” The question of “what does it mean that this particular chain happened?” is a different kind of question.

Your statement also has a nice reversal of the usual “why me?” question. Instead of asking why you were selected out of all possibilities, it says: out of all possibilities, this one happened—and now there is a person here who can reflect on it.

In a sense, the universe went from particles to chemistry to life to consciousness to a being asking why there is a universe at all. Whether one sees that as chance, emergence, or something with purpose depends on one's philosophy, but the sheer fact of existence remains remarkable either way.

Gulf of Thailand

 I hear there is natural gas potential in the Gulf of Thailand.

Yes, there is significant natural gas potential in the Gulf of Thailand, and in fact it is not just potential — the gulf has been a major producing gas region for decades.

The geology is favorable because the gulf contains several sedimentary basins, especially the Pattani Basin in the central gulf. These basins contain thick layers of Tertiary sediments that generated and trapped natural gas and condensate.

Thailand's offshore gas industry began with the Erawan gas field, which started production in 1981. Since then, fields such as Bongkot and others have supplied much of Thailand's electricity generation. Almost all of Thailand's natural gas production has come from offshore Gulf of Thailand fields.

The interesting part for Cambodia is that the gulf extends eastward toward Cambodia's maritime area. There is a long-running dispute between Thailand and Cambodia over an overlapping maritime zone, sometimes called the Overlapping Claims Area (OCA). That area is believed to contain substantial oil and gas resources, but development has been delayed by the political dispute. Estimates vary, but some assessments have suggested resources on the order of trillions of cubic feet of natural gas.

A few caveats:

    "Potential" does not mean all of it is commercially recoverable. Offshore drilling is expensive, and small scattered gas pockets are common in the Gulf of Thailand.

    Thailand's older fields are mature and declining, which is why the country has looked for new exploration areas and additional supply sources.

    Even a major discovery would take years of appraisal drilling, platform construction, and pipeline development before producing gas.

Given that you live in Cambodia, the OCA issue is particularly interesting: a successful joint development arrangement could potentially provide Cambodia with domestic energy, government revenue, and industrial feedstock, while Thailand would gain from nearby supply. It is one of those cases where geology is relatively straightforward, but politics is the harder engineering problem.

With things as they  are cooperation seems unlikely; might the Thais use superior power to act unilaterally?

That is a very real geopolitical question. The short answer is: Thailand has the military power to create facts on the ground (or at sea), but a unilateral seizure or drilling in the disputed area would carry serious costs and is not the most likely course.

The Gulf of Thailand dispute is unusual because the resource is valuable, but the legal and diplomatic environment is complicated. The area in question is the Cambodia–Thailand Overlapping Claims Area (OCA), roughly 26,000 square kilometers of maritime territory where the two countries' claims overlap. Both sides have recognized that the dispute exists, and past discussions have focused on some form of joint development rather than forcing a final boundary settlement first.

A few reasons Thailand might hesitate to act alone:

    International legal consequences

    Offshore gas development is not like occupying an uninhabited island. A drilling platform, pipelines, financing, and insurance all require international acceptance. A unilateral Thai operation would invite diplomatic protests and could deter investors.

    Cambodia is weaker militarily, but not irrelevant

    Thailand has a much larger military and economy, but Cambodia has diplomatic options: ASEAN pressure, international courts (if jurisdiction is accepted), and appeals to outside powers. A move perceived as bullying could damage Thailand's regional standing.

    The economic logic favors cooperation

    Offshore gas projects require billions of dollars and decades of operation. A company investing in a field wants legal certainty. A disputed field is a nightmare for lenders and insurers.

    Thailand has experience with joint arrangements

    Thailand and Malaysia, despite their own maritime disagreements, created a joint development area in the Gulf of Thailand. That model is often cited as an example of separating resource development from sovereignty disputes.

However, your point about power politics is not wrong. If the resource became extremely important — for example, if Thailand faced severe energy shortages — pressure could grow for a more aggressive approach. The more likely "power play" would probably not be an outright military occupation, but things like:

    expanding exploration near the disputed boundary,

    insisting on a Thai interpretation of the boundary,

    using economic leverage,

    delaying negotiations while developing alternative fields.

Cambodia's situation is interesting because it is a classic case where the weaker state may actually have leverage: the gas is valuable, but the project needs legitimacy. A field producing under constant dispute is much less valuable than one developed peacefully.

Given Cambodia's dependence on imported energy, I can see why the OCA has attracted attention there. It is one of those situations where the geology says "drill," but history and politics say "wait."

That is a scenario that analysts of disputed territories often consider: incremental action rather than a dramatic declaration. It is a common pattern in international disputes because it can reduce the immediate political cost of a confrontation.

However, there are some important distinctions. In the Gulf of Thailand case, a "tiny bit at a time" approach would not be as simple as quietly moving a boundary marker on land. Offshore energy development leaves a fairly visible trail: seismic surveys, exploration permits, drilling rigs, supply vessels, pipelines, financing arrangements, and commercial contracts. Those steps are difficult to hide.

A state trying to advance its position without a formal settlement might instead rely on ambiguity:

    conducting activities close to a disputed area while arguing they are within its claimed jurisdiction;

    continuing to issue concessions or prepare infrastructure;

    waiting for the political environment to change;

    using the passage of time to make its administrative presence seem normal.

That said, there is a difference between creating facts and creating an internationally accepted legal position. A platform operating for years does not necessarily settle sovereignty. The other side can continue to object, and a future government can reopen the issue.

Your point about domestic politics is perhaps the most interesting part. A government that wanted to avoid the appearance of a concession might prefer gradual normalization over a highly public agreement. But the opposite problem remains: if the public later notices what happened, opponents can accuse the government of having "given away" something in secret.

Resource disputes often end not because one side suddenly changes its mind, but because the political costs of continuing the dispute eventually exceed the political costs of compromise. Until then, quiet maneuvering is a tempting strategy for both sides.

I see China has inserted itself into this as a potential mediator, putting pressure to be chosen to play that role.

That is an interesting development, and it fits a broader pattern in which China has increasingly presented itself as a diplomatic broker in Southeast Asian disputes — sometimes as a genuine mediator, and sometimes as a way to expand its own influence.

China has several interests in a Cambodia–Thailand maritime dispute:

    Cambodia is one of China's closest partners in Southeast Asia. Beijing has invested heavily in Cambodian infrastructure, defense ties, and economic projects. A role as mediator would reinforce the image of China as Cambodia's major diplomatic partner.

    Thailand is strategically important to China as well. China does not want instability in a country that is a major trading partner and a key part of mainland Southeast Asia.

    Energy resources are strategically valuable. Any role in offshore gas development — whether as investor, contractor, financier, or political facilitator — gives China another foothold in the region.

The interesting question is whether China would be a neutral mediator. A mediator does not necessarily have to be perfectly neutral to be useful, but the parties usually ask: "Whose influence increases if this process succeeds?" Cambodia might welcome Chinese involvement because Beijing has leverage with Thailand and because Cambodia may see China as a counterweight to Thai power. Thailand, however, might be more cautious about allowing a dispute in its own neighborhood to become another arena for Chinese influence.

There is also a possible ASEAN dimension. Traditionally, ASEAN states have preferred regional disputes to be handled within ASEAN frameworks, partly to avoid great-power competition. China stepping forward can be seen both as helpful — bringing leverage and resources — and as a sign that a local dispute is becoming part of a larger strategic contest.

Your earlier point about legitimacy is relevant here. A Cambodian government could present Chinese-backed mediation as: "We brought a major power to the table and protected our interests." A Thai government might worry about appearing to have allowed an external power to influence a matter it considers a sovereign issue.

In a way, the gas itself may be only one part of the prize. The larger prize is influence: who gets to shape the rules and the relationship between two neighboring countries. That is why outside powers often become interested in disputes that, on the surface, are about resources.

Even though Cambodia and China appear friendly, there are significant differences, so I think China neutrality could be assumed, assuming actual Chinese interest did not appear.

I think that is a subtle but important point. Friendly relations between states do not necessarily mean identical interests. In fact, close relationships can sometimes make a country more useful as a mediator, because it may have channels of communication that outsiders lack.

Cambodia and China have a very close relationship, but it is not simply a matter of Cambodia following Chinese instructions. Cambodia has its own interests:

    It wants economic development and investment.

    It wants room to maneuver among larger powers.

    It does not necessarily want every regional issue interpreted through a China–U.S. or China–Thailand rivalry.

    It has historical and cultural ties with its neighbors that predate modern great-power politics.

Likewise, China has reasons to preserve a reputation for being a useful regional actor. If Beijing were seen as simply using mediation to grab economic advantage, it would reduce its credibility. A mediator who is perceived as openly favoring one side may find the other side unwilling to accept the outcome.

The important qualification is the one you mention: whether China has a direct material interest. If Chinese companies were seeking exploration rights, construction contracts, pipeline roles, or financing arrangements, then Thailand (and others) would naturally question how neutral Beijing could really be. Even if China acted fairly, the appearance of a conflict of interest could matter.

There is also a practical consideration: China may not actually need to "win" the dispute in the sense of getting the gas. Diplomatic influence itself can be valuable. Being the power that brings two neighbors to an agreement can enhance China's regional standing.

Interestingly, Thailand's reaction would be a key variable. Thailand has historically tried to maintain room between China and other major powers. It might accept Chinese involvement if it seemed genuinely useful, but resist if it appeared that China was becoming the gatekeeper of a Thai–Cambodian issue.

So I would agree with your premise in a qualified way: China's closeness to Cambodia does not automatically disqualify it as a mediator. The decisive issue would be whether the mediation process appears to serve a settlement between Cambodia and Thailand, or whether it appears to create a new Chinese strategic position in the Gulf of Thailand.