On Being Human

(And still mostly wrong)

“… And sin, young man, is when you treat people like things. Including yourself. That's what sin is.”

“It's a lot more complicated than that—”

“No. It ain't. When people say things are a lot more complicated than that, they means they're getting worried that they won't like the truth. People as things, that's where it starts.”

“Oh, I'm sure there are worse crimes—”

“But they starts with thinking about people as things…”

In my recent digression on Deming I promised to write about simplicity. But this essay has overtaken the author and acquired a life of its own. The story has diverged in the telling. I hope you still enjoy the journey.

The above quote is now my all-time favourite. I must confess that I did not fully enjoy Terry Pratchett’s Carpe Jugulum the first time I read it. But this discussion between the uber-powerful witch Granny Weatherwax, and the earnest pastor Oats in particular drew me back, as did his innovative solution to the peril they were in. And ultimately, her solution, which reads like a good detective novel. Where did Granny Weatherwax hide the body? Her body, that is.

Half-a-dozen reads later, I enjoy each repeat a bit more. Every time, without fail. The mark of a good book is that it draws you in again and again, and every time you don’t just find something new, but also find the old more satisfying. Like a really good cup of tea.¹

This post is not primarily about sin. And yet it may turn out to be. Shall we see where it leads?

Lies to Children

I started a post about simplification. It then captured my imagination and mutated. Simplicity can give rise to enormous complexity. Hidden deep within this text you will find out why cars start due to relativity.² You will also acquire a deep and abiding dislike of your high school chemistry teacher (and possibly even of me).

My original title was “Lies to Children”, which is still a good title, even if it’s now just a sub-heading. It evokes an emotional response. “Lie-to-children” even has its own Wikipedia entry now. Jack Cohen (a scientist) and Ian Stewart (a mathematician) first thought it up in 1994, but it only really gained traction when they wrote a book about The Science of Discworld, together with—of course—Terry Pratchett. About 200,000 people whipped it off the bookseller’s shelf in the first year. Some even paid for it.

In three words Cohen and Stewart have pretty much adequately summarised the entire literature of popular science. This observation will naturally piss off many contributors to the genre, and almost all of its readers. That doesn’t make it any less true, but there is a catch.

The basic idea behind “lies to children” is that pretty much any popular description of how something works necessarily entails gross over-simplification. In fact, almost anything we can grasp as humans involves a cartoon-like quality. This is why you still—to this day—encounter people who have a vision of a hydrogen atom that involves a tiny nucleus and an orbiting electron; or people who think of DNA as a stylised spiral staircase; or (worst of all) views of natural selection as ‘survival of the fittest’.

In fact, if you Google “model hydrogen atom”, most of the top hits you’ll get will point you to Bohr’s 1913 model. Which is significantly more sophisticated than that orbiting planet model I’ve just been rude about. And is still often used to introduce students to atoms (and confuse them) only to be cast aside for better quantum mechanical representations, which will confuse even more by describing electrons as standing waves that can be represented by a probability distribution that the electron will be somewhere in the region around the nucleus. With areas that are verboten. And a generous helping of mathematics—the time-independent Schrödinger equation.

But way back when, scientists worked out that there were still some issues. Schrödinger indeed provides probability distributions, and predicts energy levels and the shapes of orbitals. But we need so much more.

In 1928, Paul Dirac introduced relativity to the mix—the relativistic wave equation. This accounts³ for things like the fine structure of the spectral lines you get from hydrogen …

(Hydrogen spectral lines eye candy is from the Wikipedia page).

… which is pretty important if, for example you’re an astronomer. Look at all those damn lines. Who would have thought that something as ‘simple’ as the hydrogen atom can produce such complex, observable behaviour? And even this relativistic correction is insufficient on its own to do something seemingly simple—predict the colour of gold!

Yep. To compute the optical absorption spectrum of the metal Au with its 79 electrons, we need even more theory. Dirac is necessary (Schrödinger predicts that gold, is well, silvery), but not sufficient.⁴ I’m told the solution demands multi-electron quantum mechanics, many-body physics, and indeed relativistic density functional theory. It gets worse, too (The New Zealand connection). Which is about where I call “Uncle”—or any damn relative you want. Just let me out of here.

The Catch

Here’s an observation. Consider it carefully. Is it true? Is it true for you?

Most readers of Pop Sci get stuck. As I just did.

I think it is true. I’m no slouch when it comes to internalising and testing new models of how the world works, but again and again I find myself reading further—and then bumping into topics that are only taught at a postgraduate level in say maths or physics or proteomics, or whatever. Do you encounter the same problem?

There’s a sort of band gap between the popular text with its hand-wavey but digestible metaphors, and ‘really’ understanding good models of the world. Often this apparently tiny gap involves a PhD, ten years of heavy research, and repeated failures. A better metaphor might be that Pop Sci is in limbo around Dante’s nine circles of hell—and there are huge intellectual gaps between each of the circles. You need a sufficient quantum of intellectual energy to leap across the gap. Or Virgil as guide and mentor. Once you get really deep into Hell, the fun begins.

So there are two distinct flavours of “lies to children”. The first is where we placidly accept the lie, and end up believing it’s true. This is Pop Sci as entertainment. The second is where we accept the lie but also try to move on, however much it hurts. We internalise the lie, digest it, and then we reject it as we move on to a more profound lie. And so on… Pop Sci as a starting point. This is much more difficult, as bridging literature is sparse or nonexistent. It’s my kind of Pop Sci.

To bed this all down, I’m now going to explore an area a bit more comfortable for me than relativistic DFT—but be warned! If you think you understand pH, chances are you’re about to confront some serious dysphoria. I’ll get a bit technical too, so if you find it all a bit too much (or angry-making) then just skip down a few sections to the one titled “A matter of faith”. I’m sure nobody will think less of you if you do this. And if you’re sure I’ve made a mistake, point it out. I likely have.

“A simple example”

What is pH?

If you look in very simple texts, this will be represented as “the log of the reciprocal of the hydrogen ion concentration”. This is, of course, wrong. A very crappy lie to children. More sophisticated texts will explain pH as the “log of the reciprocal of the hydrogen ion activity,” introducing you to the common ion effect.

For which I have a convenient metaphor, aka lie. It’s a lovely lie, so I’m going to relish it. Imagine you’re at a party. If it’s the sort of party I was invited to as a child, then there are not too many people in the room, so it’s easy to spot a friend and move unimpeded across the room to chat to them, inevitably about nerdy things like pH.

If you were a popular kid who went to popular parties, however, the room would be packed with screaming hyperactivity, and your progress would be hindered at every step by people bumping into you, laughing, dancing, telling jokes, and spilling drink down your front, drink that smells almost but not quite exactly unlike orange juice, with a strong suspicion that vodka may have been added. This is the common ion effect. Other ions get in the way, so you need some sort of factor (gamma) that represents this hindrance in moving around at the party.

\(\mathrm{pH}=\log\frac{1}{\gamma\left[H^{+}\right]}\)

Which too is—quite naturally—a lie-to-children. In fact, this sort of representation of pH is utter thermodynamic nonsense! At this point, if you calm your rage—either at me, or your high school chemistry teacher—then you will immediately see that you can’t even begin to talk about a significant quantity of H⁺ ions without considering the other negatively charged ion that must be there. We don’t walk around with glasses full of water and hydrogen ions and nothing else, as the charge needs to balance.

So we make assumptions. In fact, as recently as 2002, there were eight subtly different definitions of pH. Nobody wants 8 standards. So in that year, RP Buck and colleagues got together at the International Union of Pure and Applied Chemistry (IUPAC) and constructed a unifying definition. The authors explain:

The concept of pH is unique among the commonly encountered physicochemical quantities listed in the IUPAC Green Book [3] in that, in terms of its definition [4], pH = −lg aH it involves a single ion quantity, the activity of the hydrogen ion, which is immeasurable by any thermodynamically valid method and requires a convention for its evaluation.

So we make that assumption (The Bates-Guggenheim convention), and all is hunky dory, right? Almost. There’s fine print. You need something called a Harned cell. Here’s the next practical set of lies to children:

The Harned Cell needs platinum, hydrogen (H₂), a standard buffer containing chloride ions, and a silver-silver chloride electrode. All carefully put together in the right order.

Skipping over the Nernst equation (easily looked up) and Debye-Hückel theory (ditto), all you also now need is an unbroken chain of calibration, with measurement of the uncertainties along the way—a topic that should be intensely familiar to you if you read my previous “flat plane” post: What is Your Flat Plane?

And one more thing.

One More Thing

In my very first post, which explained how science reasonably can work, we found that all theories are false, but some are useful. Our approach is to attack each theory as vigorously as we can; even those few that withstand our sharpest arrows are only ever considered ‘true’ for now. There are no ground truths—but this doesn’t paralyse us, because we can still make assumptions and then test them.

So you already know that all of the above pH theory has yet more hidden assumptions we likely need to actively seek out. Practically, the killer here for me is this:

The activity coefficient of chloride (like the activity coefficient of the hydrogen ion) is an immeasurable quantity. However, in solutions of low ionic strength (I < 0.1 mol kg –1), it is possible to calculate the activity coefficient of chloride ion using the Debye–Hückel theory. This is done by adopting the Bates–Guggenheim convention, which assumes the trace activity coefficient of the chloride ion γ °Cl is given by the expression…

Nope, I’m not going to explore this in any more depth. You can look up the Bates-Guggenheim convention in the IUPAC document, which I’ve referenced above. Did you spot the kicker? Yes. It’s this:

However, in solutions of low ionic strength (I < 0.1 mol kg^–1)

Now I’m a clinician. I deal with things like pH and ionic strengths daily, every time I look at a blood gas analysis or a lab report on “Creatinine and electrolytes”. I deal with human plasma, where the ionic strength is about 300 mmol/L, or about 0.3 mol kg^–1.

Oops! So the pH and ion effects I deal with every day are way above that IUPAC upper limit. Three times greater! Effectively, we’re dealing with yet more lies-to-children! Fortunately we have workarounds. The obvious one is that reference laboratories dilute human plasma specimens when they examine concentrations of ions, to meet the magic I < 0.1 mol kg^–1 criterion. Let’s not even talk about the implications for the condition of pseudohyponatraemia, however.⁵

Aww, heck, pseudohyponatraemia

I’m sorry. I just can’t help myself at this point. Forgive me—or just skip this section.

Doctors obfuscate. We take simple terms like “low serum sodium concentration” and baffle you with medicalese—here ‘hyponatraemia’. This is mostly not our fault. We were taught it in medical school, as were our teachers; at one stage, you struggled to even get into medical school if you hadn’t done Latin. I did Latin.

Actually, most of the 3 million terms that infest Medicine are Latin, Greek, or an incoherent mixture of the two. So ‘hyponatraemia’ is pretty mild. Try pityriasis lichenoides et varioliformis acuta, or tuberculosis cutis miliaris acuta disseminata for size. And then, because even we become tired of this stuff, we invent acronyms and initialisms. PLEVA. VEXAS. And so on.

And quite often, something only resembles a condition. So we get pseudohypoparathyroidism, and—wait for it—its own close resemblance, pseudopseudohypoparathyroidism. And, inevitably, apparently low serum sodium, that isn’t. Pseudohyponatraemia.

There is, of course, a story here. In days of yore, we used to measure the amount of sodium in a blood sample using a flame photometer. Just as hydrogen has a pretty emission spectrum, so does sodium—with a prominent yellow line. If you use a photoelectric cell for measurement, you can measure the intensity of the sodium line in a known volume of plasma, and work out the sodium concentration. We don’t do this any more.

But when we did, there was a problem. Pseudohyponatraemia. If a substantial part of the volume of the sample was taken up by another substance—protein, or glucose, or fat—then the measured amount of sodium would be less. The thing that counts is, of course, the activity of the sodium ion, as we’ve just painstakingly discovered. The party analogy, and all that.

So modern instruments measure that activity. But there are several catches. One is that the numbers then need to be transformed into ones that doctors understand. We were trained at medical school by people who were trained by people who understood values derived from flame photometry. So the familiar normal ranges are still those. This is not a problem, because the lab kindly, automatically and even secretively makes the conversion.

And, in fact, many of the devices we use at the front end of the hospital have reliable, accurate, built in ion-sensitive electrodes that do all of this. Automagically. Today, a “blood gas analysis” in ED delivers so much more—including a ‘concentration’ of sodium, potassium, calcium and so on. It just works.

You would think, therefore, that the problem of pseudohyponatraemia would be utterly and totally a thing of the past. Not quite. You see, if I send off that same sample to the lab, quite because of our desire for accuracy, the specimen will first be diluted, and then exposed to the ion-sensitive electrode.

Can you work out what happens? Yes. When the lab works back to “full strength”, then those interfering substances which took up part of the volume will put their finger on the balance once more, producing pseudohyponatraemia. This is not quite relativistic density functional theory, but it does require a bit of thought. Okay, I’ve indulged my compulsion to explain. We can resume.

Pitzer

Ironically (or perhaps, ionically), there is a different way of doing all of the above that works for brines of up to molar concentrations. It’s called the Pitzer ‘virial’ approach and has been around since 1973, although it’s taken decades to check, and interest has only spiked in recent years.

But here’s my problem. It’s the one I’ve already described—we either need deep expertise in this specific topic, or a Virgil to guide us. Otherwise we run the risk of dangerous misunderstanding. So at the end of the day, I resort to acknowledging that when, faced with a serum sodium of, say, 143 mmol/L, I know that (a) it’s the activity that counts; (b) the activity is somewhere down there at 115; (c) the machine or lab is likely measuring actual activity and then translating this up to the number I now read; and (d) it doesn’t matter that much in most cases (apart from pseudohyponatraemia) because I generally know how to deal with the numbers I am given.

And there’s another issue with Pitzer. Recall how IUPAC goes to great lengths to point out that the concept of the activity of a single ion in solution is thermodynamically meaningless? Well, with Pitzer we’re pretty much empirically doing just that! It just works better in extreme circumstances. We’ve come full circle.

A matter of faith

Can you see how we started with lies-to-children about pH and ion strength, and we worked through progressively more complex lies-to-children—and then we realised that dealing with something as ‘simple’ as the pH or sodium concentration in plasma involves not just huge complexity, but a certain amount of trust in the process?

It turns out that everything we do involves similar trust. If you’re wearing your MAGA cap rather than your thinking cap, then this can rapidly lead to dismay, and even deep mistrust. We’ve seen a lot of this recently, with COVID-19, and many medical therapies (including vaccines) and the rise of crazy talk now that RFK Jr is polluting everything he touches with a strong dose of loony.

So how do we regain a sense of balance? Whom do we trust? The paradox here is that we were often better off simply trusting the science—as conveyed by people who have studied this science for decades, and upheld the tradition of ongoing, good research. Doing your own research is often a source of terminal confusion.

Surely, a few percent of papers that are published are bullshit. In future posts—once we’ve built our basic toolbox—we will dissect many of these. They are usually easily identifiable as BS.

The vast majority of scientific papers are currently indistinguishable from well-reasoned, capable, competent science—at least, using our current tools, applied in the hands of competent people. They are not only “as true as they can be given our current knowledge”, but also usually far better than the vapid ‘insights’ of people who only claim to know better, without sufficient proof of work.

After some investment, you will also find it easier to identify these people and understand their motivation. But in our search for simplicity, I think there’s something more basic we can extract.

A basic misunderstanding

There’s no doubt we’re seeing the rise of fascism around the world. It’s not just Trump. Lots of little mini-me Trump clones are springing up all over the place, like poisonous mushrooms in a field fertilised by bullshit. There’s Orban in Hungary, and Erdogan in Turkey, and Meloni in Italy and Le Pen in France, and so on and so on. Many have been festering underground for years, and have only recently popped their tiny mushroom heads through the cowpats.

They share many things in common—populism; distortion of the media and suppression of criticism; rewriting of history; machismo, “strong leadership” and belittling ‘the weak’ (who are paradoxically still somehow a ‘threat’); and a deep and resonant rejection of science as I’ve defined it. And they surely treat people as things.

But there’s something even simpler and more fundamental they’ve missed. Consider the following two scenarios. They relate to Rousseau’s picture right at the start, The Hungry Lion throws itself on the Antelope.

Two Scenarios

In both scenarios, it is 50,000 years ago, and you unexpectedly find yourself on an island, populated by large ferocious beasts. In the picture, Rousseau got many things wrong, but he does a lot that’s right too. One is a sense of dread. The worry is not the lion. It may be the leopard, lurking in the foliage above. And what is that Dark Thing on the left?

Back to our scenarios. They differ, as follows. In Scenario A, you are on your own. In Scenario B, you have someone else with you. What’s the difference?

Can you see that in Scenario A, you are almost certainly going to die; while in Scenario B, you own the island! The difference is that in Scenario B, you each cover the other person’s back. The thing that makes us human is that we are not just transactional beings, but that we have an inner model of other people that allows us to unite for our common good. We cannot solve or even comprehend all of the risks on our own. So we work together. We establish networks of trust, with win-win outcomes.

There is a tiny proportion of people who lack this sort of internal model, and we call them psychopaths. In modern communities, they often rise to positions of power through deceit—but ultimately they subvert and destroy all they touch. This is the key observation: treating people as things is what will destroy us. It is the antithesis of being human.

Most people are not psychopaths. But they may nevertheless be easily led. The malaise I’ve described is a transmissible disease. Everyone needs to ask the simple question “Am I treating other people as things?” Which brings us back to Deming.

As I see it, however, there’s something even simpler at work here. We answer the question “How do I see the world?” in one of just two ways.

It is simple!

We have a stark choice:

• Start from a position of similarity; or

• Start from a position of difference.

Again, this comes back to good science. In doing good science, we assume similarity between our model and reality, and then move on to test this assumption.

In contrast, if we start by assuming that two people are basically different, then the only way we can refute this perceived difference is by “showing they’re the same”. But this is impossible! Some later test may and likely will show ‘differences’. The negative consequences are profound.

Deceit is intrinsic to this model. ‘Others’ are somehow, inherently strange and different. Each individual is just that—an individual. Any negotiation is fraught, and wherever we look, we will see differences. Even if we perceive similarities, we can argue that “internally, your perception of red is not the same as my perception of red”. Philosophers have written crazy books on just this sort of nonsense.

If however we start by assuming that others are similar to us, co-operation makes more sense. Communication is easier too. We can discuss our shared perception of not just ‘red’, but very abstract concepts like ‘fairness’, and ‘justice’ and ‘sin’. We can certainly find differences—and determine whom we can trust—but we’re working from an assumed common model that we can test and refine. Other people are not things. They are us. This is what powers society—and rejection of this insight is what destroys us. Isn’t that simple?

In my next post, I’ll look at trust.

My 2c, Dr Jo.

1. Admittedly, lapsang souchong can be an acquired taste, too.

2. At least, cars based on the internal combustion engine, with a lead-acid battery.

3. Dirac almost accounts for the fine structure of the hydrogen spectral lines. There is the matter of the Lamb shift. If you click on that link, read the Wikipedia article with extreme skepticism, as it embodies (reifies) yet more lies to children, treating ‘virtual photons’ and ‘vacuum energy fluctuations’ as if they are ‘real things’ rather than computational conveniences.

4. And to really do your head in, yes, 82% of the voltage in a lead-acid battery is due to relativistic effects.

5. If you read the 2002 IUPAC pH document, there is a whole bunch of extra assumptions—many of them reasonable; there are also a number of areas of uncertainty.