Seven Years

Potions for Muggles is seven years old! Amazingly, I’m still writing. In the early years, I felt that my writing was improving, but more recently I feel I’ve reached stasis. Perhaps I haven’t stretched myself by trying to learn some new things about the art and craft of writing. This is something I need to ponder.

 

I haven’t spent much time writing about magic and science lately. Although I tried to revive this by reading Terry Pratchett’s original Discworld series parlayed into the Science of Discworld, I ultimately did not find it as interesting. So, I’m on the lookout for some potentially new and interesting fiction that will spark creative themes. I haven’t yet searched in earnest.

 

Quite a number of posts were related to new teaching protocols related to the Covid-19 global pandemic. I did learn some new tricks, but I’ve mostly reverted to the old storehouse of pedagogy I’ve built up over the years. Teaching remotely or masked was not as bad I as anticipated, but I still prefer face-to-face and personally meeting and chatting with my students with as few barriers as possible (masks and Zoom boxes, primarily).

 

There were more posts than usual about my research-related thoughts on non-equilibrium thermodynamics, kinetics, and living systems. Much of this stemmed from reading challenging scientific papers and books that are more obscure, but I think there are some very interesting nuggets that have helped me progress in thinking about the age-old question: “What is life?”

 

And yes, a large portion of my posts are still about books and articles that I’ve read. Going out less because of the pandemic means staying at home and reading more. Not a bad thing, necessarily.

 

As with every new year, I don’t make resolutions or predictions. Maybe I’ve grown old, a little jaded, a little less expectant, but perhaps I’m also more comfortable in my routine and where I am in life. Supposedly I’m a little past the lowest dip in the happiness curve, but I frankly can’t tell.

 

It’s nice to take a moment to reflect when reaching a milestone of sorts. I don’t have anything Halloween-themed to say, but since I just finished Lewis Structures in my G-Chem classes this past week, here’s my Quest for a Stable BOO!

Extra Life

I enjoy Steven Johnson’s books – a blend of history, science, and creativity, that strikes just the right balance for my reading interests. His latest book, Extra Life, is subtitled: “A short history of living longer”. Average global life expectancy has only recently risen significantly over the past century thereabouts, especially as infant/child mortality has reduced, among many other improvements in medicine, public health, and work safety. 

 

There is a chapter that recaps the masterful story Johnson tells in the book that made him famous, The Ghost Map – whereby several unsung heroes traced the outbreak of cholera in the East End of London to a contaminated water source. But there are several other interesting stories. I was familiar with the role of Mary Montagu and variolation – which then led to vaccination, one of the most important advances in public health. I’d heard of W.E.B. DuBois’s work in Philadelphia, although Johnson provided a number of details I wasn’t aware of. I did not know about the work of Nancy Howell among the !Kung tribe in the Kalahari – a very fascinating read.

 

Johnson takes great pains to repeat one of his main points – that such “discoveries” or “improvements” came about through the concerted effort of many people, not just a lone genius. This is apparent in his story about pasteurization. We’ve heard of Louis Pasteur, but perhaps not about the many other folks who were key to its widespread use. We’ve heard of Alexander Fleming and penicillin, but if not for many others, not much would have come out of his serendipitous discovery. It’s the network of people that push for change that ultimately led to large segments of humankind being able to enjoy longer, perhaps, healthier lives. Johnson also shines a light on the role of data and statistics in all of this – I liked how his examples highlighted this aspect.

 

What I was really interested in was what Johnson had to say about transhumanism and the quest to extend life significantly further than what seem to be the present limits. Our bodies are programmed to die after some time – it’s built into our biology or at least we and many other organisms have evolved to reproduce offspring and then die ourselves in the hope that the children are able to repeat the feat in the next generation. Johnson touches on the topic in the last bit of his epilogue. There isn’t much groundbreaking on the scientific front, I’m sorry to say, which is why the popularity of sci-fi and fantasy in plumbing this topic will continue – Voldemort notwithstanding. Maybe there will be some sort of strange merging of mind and machine, and transhumans live in virtual reality. Then the bonus of classic video games will finally become reality: Extra Life!

 

P.S. Two of Johnson’s other books, I’ve recently blogged about: Wonderland and How We Got to Now.

Learning Machines

Over the years I’ve read secondary sources referring to Alan Turing’s famous 1950 paper (“Computing Machinery and Intelligence”, Mind, 1950, 59, 433-460) but only last week did I finally read the original paper. It opens with the question: “Can machines think?” and sets out the principles from what is now well-known as “The Imitation Game” (also a title on a recent movie biopic on Turing). After describing his thoughts on why the answer would be a carefully-qualified “yes, in the not-so-distant future”, Turing also takes time to answer possible objections to his position.

 

Today’s post is not about Turing machines or whether machine intelligence can sufficiently mimic human intelligence, but focuses on the last section of the article, “Learning Machines”, in line with my interests in teaching and learning. It begins with an objection to his thinking machine: a “machine can only do what we tell it to do”. Turing responds by proposing the setup for a nuclear reaction: If the setup of an “atomic pile” is sub-critical, firing a neutron at the pile causes some change but does not lead to a sustained chain reaction. But if it has reached “critical mass” (of fissile material), bombarding neutrons will trigger the chain reaction. Turing wonders whether this is an analogy for how the human mind learns.

 

I find this analogy interesting. Suppose there are some students who have learned some chemistry or did the reading beforehand, and a combination of some knowledge and its rudimentary organization prepares the mind to learn something new in a sustained way. Suppose there are other students who aren’t sufficiently prepared (they’re still in the “subcritical” domain). Then when encountering the lesson in class, things click for some students such that they really “get it” while for others, the lesson seems to make sense but is not enduring and they can look back at their notes with little or no understanding. I’ve certainly encountered both groups in my classes, and likely a continuum of “partial-understanding” cases in between.

 

The situation is more pronounced when the subject material is conceptually difficult, unfamiliar, abstract, mathematical, or all of the above. Chemistry spans all these categories. Since introductory chemistry and physical chemistry are classes I’ve taught almost every year for twenty years, I can attest that incoming students who had a strong secondary school chemistry preparation do well and struggle less in the introductory classes. No surprises there. They’ve seen some of the material before and therefore have “critical” background and content knowledge, although in many cases not well organized (i.e., they know a bunch of useful yet isolated facts). In physical chemistry, the students are on the same footing conceptually, but those who are much more comfortable with mathematical language and equations, are significantly more successful. For those who are not, the math bogs them down from grasping the abstract conceptual material in a sustained way.

 

Can we imagine a machine with enough “background” knowledge learn something in a new way going beyond the rules of its programming? Can it make new rules? Does the concept of “critical” content apply and if so, how? I’m not sure, although I can imagine it following the tropes of sci-fi sentient machines. But is there a more fundamental limitation in machines that humans can transcend?

 

Turing provides an intriguing analogy. In a parenthetical statement, he writes: “Mechanism and writing are… almost synonymous”. The context is imagining a machine that is child-like, in the sense of its capacity to learn. One can imagine an educational “program” being fed to the machine that moves it from child-brain to adult-brain, assuming that the brain is like blank sheets of paper that can be filled with writing. Since machines are by nature mechanistic, introducing a program by writing data into memory is certainly what computers do. But this doesn’t get around the seeming divide between syntax and semantics. If you don’t comprehend a language, it’s all syntax to you. But to those who understand it, the language acquires meaning – it signifies something, i.e., the symbols truly symbolize!

 

All this makes me think of assessment. How do we assess if a student has learned something? On an exam, I (the examiner) ask questions, and the student provides answers. Assuming a written exam, I read the syntax of the students and decide if the semantics of that syntax corresponds to understanding. This is trickier than it looks. First, consider the two extremes. A student who leaves it blank or writes irrelevant nonsense clearly has not demonstrated knowledge. A student who nails the answer carefully and critically, in my interpretation, has demonstrated learning. But for the majority of students, I get something in between – a partial, somewhat garbled understanding. Perhaps some learning has taken place, but perhaps it’s a data dump, such that you might expect from a machine search.

 

What gets the student from partial understanding to more complete understanding? There must be a refinement process that goes on. Exactly how that happens in the human mind is less than clear. One can imagine machines going through refinement algorithms of some sort as part of machine learning. But by using the word “algorithm” have I unwittingly restricted the process to be mechanistic in a way dissimilar to how humans learn? I’m not sure. If complexity, by definition, cannot be simulated by an algorithm, then perhaps there are some types of learning that a machine cannot attain. Machines can learn simple things, complicated things, but not complex things. If chemistry isn’t merely complicated but complex, a machine can’t learn chemistry in the same way a human can.

 

A final tidbit from Turing’s paper is his suggestion that randomness be included in the algorithm for learning to take place. This is a messy and far-ranging topic, but my brief thought on the matter is that it allows us to simulate an anticipatory system that can adapt to changing environmental conditions. Biology features control systems via feedback and feedforward loops, and one can imagine a machine doing something similar. Perhaps that’s where the critical line lies. But it’s possible that the gulf between semantics and syntax cannot be bridged even if the imitation might fool us more than once.

Exceptions: Who Cares?

I got annoyed at myself while teaching my General Chemistry classes this past week. I had a meta-moment or an epiphany while I was going through the motions of explaining some observed chemistry-related factoids. I’m good at explaining this stuff because I’ve spent a lot of time thinking about it, not just at the superficial level but a little more deeply. But even as I was talking in class, a part of my mind was questioning why I was doing so. Is this factoid or its explanation even important? At the General Chemistry level? At some point, I transitioned into saying that the rest of the explanation was beyond the purposes of the class, but I would be happy to discuss the subject at length in office hours. I don’t think the students noticed my frustration with myself; but then again no one has come by my office to query me about the finer points yet.

 

Today’s rant is about exceptions-to-the-rule that showed up this past week in my General Chemistry classes. With some examples, I will briefly state the general rule, why the general rule is important, the exceptions, and then rhetorically pose the question “Who Cares?” Finally, I will muse about some situations where one might care about the answer.

 

To write the ground state electronic configuration of an atom, one can mechanically use two rules: place electrons in the lowest energy orbitals first, and each orbital can only accommodate two electrons. (They’re called the “aufbau” and “Pauli” principles respectively.) Why is this important? Chemistry is all about what electrons are doing in an atom. Knowing something about their arrangement allows us to describe chemical structure and reactivity. Why the ground state? Under standard conditions, electrons arrange themselves to be in the most stable state which has the lowest energy – what we call the ground state. But there are exceptions. For example, chromium’s valence electron configuration is 4s¹3d⁵ in its ground state rather than the expected 4s²3d⁴ if you followed the two rules. There are less-than-satisfactory “explanations” for these provided in the typical G-Chem textbook, but I say: Who Cares?

 

There’s a third rule mentioned when it comes to writing ground state electron configurations known as Hund’s Rule: When you place more than one electron in orbitals of the same energy, put the electrons in separate orbitals and keep them spin-aligned where possible. Why is this important? Having electrons in separate orbitals is useful when we discuss covalent chemical bonds as the overlap of singly-occupied orbitals from when two atoms approach each other. Thus, knowing this helps us understand chemical structure and reactivity. There’s also an explanation why the electrons should be spin-aligned But: Who cares?

 

After students learn to write ground state electron configurations of neutral atoms, we move on to ions. Once again, learning this is useful to subsequently describe chemical structure and reactivity of ions. Generally, ions follow the same rules as neutral atoms except when you get to the transition metals. An example exception to the rule: For d-block atoms, when removing electrons, remove the valence s electrons before the seemingly “higher energy” d electrons. Once again, there is an explanation. And once again: Who cares?

 

Once we can write electron configurations for atoms and ions, we can discuss several useful trends across the periodic table. For example, the first ionization energy of an atom decreases down a column and increases across a row. Why is this useful? Knowing the trends tells you that the bottom left corner of the periodic table (Francium) has the lowest ionization energy, and the top right corner (Helium) has the highest ionization energy. This allows you to classify elements into two broad categories: metals and non-metals. Those two categories can then broadly be used to classify three types of chemical bonds (metallic, ionic, covalent) and relate these to the macroscopic properties of compounds. It’s one of the most useful classifications in chemistry. But there are exceptions to the ionization energy trend. Going across a row, there are two kinks. I wrote a previous post examining this (which I assign as optional reading for the curious student). With regard to this exception: Who Cares?

 

What made me annoyed about these exceptions is that their inclusion in the textbook and on typical standardized exams results primarily in a mechanism to identify students who know the exceptions and can (somewhat vaguely) articulate them. The explanations in G-Chem textbooks for these cases are incomplete at best and downright misleading at worse. If that’s all we use them for – as a way to separate the A from the B students – then I for one would prefer to jettison them. Who Cares?

 

Who might actually care? The inorganic chemist might. When you’re delving into the details of transition metals, detailed knowledge of electron configurations and spin states are important. The curious student might. What makes chemistry interesting is that while the general rules are a powerful way of organizing knowledge, there are all sorts of intriguing exceptions that give chemistry its unique unruly flavor. The messy details become very interesting if you’re really into chemistry! In my classes, I regularly include little tidbits outside of the standard syllabus in the hope I will intrigue students into wanting to explore the subject more. I want students to be surprised by chemistry!

 

The Pauli Exclusion Principle is one such under-utilized concept. It’s not just an esoteric rule about quantum numbers – it gets at the heart of what keeps fundamental particles distinct, and yet indistinguishable when they “switch” places and you can’t tell the difference. It’s why humans can’t walk through brick walls even though atoms are mostly empty space – a demonstration I do every year after which I throw in a tidbit about quantum tunneling. It explains the shape of molecules through VSEPR theory. It’s both strange and surprising. I try to tell students this every year. Not sure if they believe me.

 

I haven’t decided what to do about the exceptions I’ve mentioned when I teach first-semester G-Chem again (next Fall semester). I’ve made my peace with including orbitals in G-Chem, since they are quite interesting and useful in discussing some of the nuances of electronic structure. But I’m no longer as interested in, for example, students memorizing exactly how to draw the five d-orbitals transformed in Cartesian space. I wonder what else I will get annoyed by as we progress through the semester. Last Fall, I was just trying to not screw up and do the best I can for my students while teaching remotely. But now I have more bandwidth to think a little more carefully about what’s important and why we should care about some particular concept as a foundation for learning chemistry.

Prelude to Dune

In preparation for the upcoming Dune movie, I’ve decided to remind myself of the Duniverse. Two months ago, I read The Science of Dune, a collection of essays by Duniverse fans, many of whom are also scientists, about the finer points of spice, stillsuits, shields, suspensors, and more. I decided not to re-read Frank Herbert’s classic novel this time around, although I did so six years ago when I watched the documentary Jodorowsky’s Dune. I’ve decided not to re-watch Lynch’s version from a quarter-century ago; I remember it being rather uneven. I also have no interest in the sequels to Dune by Herbert. I think the original novel stands alone well. It’s a decision I made a long time ago pre-internet. Web-browsing provided further confirmation that I wouldn’t find them interesting.

 

However, I also learned about the prequels to Dune co-written by Herbert’s son (Brian) and another sci-fi author Kevin Anderson; I’ve never read anything from either of them. One caught my eye – The Butlerian Jihad, set ten thousand years before the events of Dune. It purports to tell the story of why and how thinking machines of the general artificial intelligence variety were destroyed by mankind, and how those early events shaped the politics and economics of the Duniverse. Since I’m interested in the conflicting ideas surrounding A.I., and have written several posts based on non-fiction reading, I decided to give the prequel a try.

 

There is an appeal for origins stories. Back in my younger days, I loved The Silmarillion, having read and re-read The Lord of the Rings many times over. High elves, of greater power and stature, in the First Age when the world was young take on a dark lord much more powerful than Sauron; Morgoth is in fact Sauron’s old boss. In the movie world, I very much enjoyed X-Men: First Class and the first Iron Man movie. You can do a lot with origin stories, well-told. (The Star Wars prequel trilogy on the other hand isn’t as great; although there are some excellent moments – when Darth Maul shows up for example.)

 

So, how is The Butlerian Jihad as a novel? It’s faster paced than Dune, consisting of short chapters that move the action along briskly. The back story about humans ceding their autonomy to A.I. and then becoming enslaved by it is not a new idea. In fact, there are two takeovers. The first is when a small group of ambitious and clever humans conduct a swift coup, wresting power from an old staid Galactic empire. One of the conspirators is a gifted programmer who injects advanced A.I. into the machines to aid in the coup. Safeguard are included in the code, but over time a member of the oligarchy gets lazy and the machines takeover. The old oligarchy tries to bide its time while serving their new machine masters; they are now cyborgs with interchangeable machine bodies connected to a brain in a jar.

 

The machine’s new empire is still opposed by human-controlled planets – a loose alliance of rebels withstanding the takeover advances of the machines. On these human planets, the dangers of A.I. takeover has resulted in a ban on “thinking machines”. Thus, much depends on slave labor – a problem in itself. Accompanying the main story thread is a side-story on what is happening on the planet Arrakis, the desert planet of the titular Dune. The reader is introduced to the local inhabitants, both humans and sandworms. The beginnings of the spice trade begin to unfold, although some of the powerful effects of the spice are not yet apparent, but rather hinted at – as if the authors were giving you a wink of what’s to come. If you’ve already read Dune, this makes sense of what would otherwise be confusing.

 

Unlike the original Dune or Tolkien’s books, I didn’t get the feeling that I would re-read The Butlerian Jihad. While it tries to take on weighty ideas, it feels light – an enjoyable read, but nothing special and I’m not sure it would add to the pleasure of re-reading Dune. In contrast, my reading of The Silmarillion enhanced my reading of Lord of the Rings, and I expect to semi-regularly revisit these books regularly which I’ve read multiple times already!

 

I did enjoy several of the pithy sayings that began each short chapter in The Butlerian Jihad, as voiced by an appropriate character in the novel. One of the original conspirators that overthrew the Old Empire has this to say:

 

Humans tried to develop intelligent machines as secondary reflex systems, turning over primary decisions to mechanical servants. Gradually, though, the creators did not leave enough to do for themselves; they began to feel alienated, dehumanized, and even manipulated. Eventually humans became little more than decisionless robots themselves, left without an understanding of their natural existence.

 

It’s a good summary of the A.I. part of the story, which otherwise does not loom that largely in the narrative. There is an interesting robot with a mind of its own who is trying to learn the ins and outs of human behavior and has this to say:

 

Intuition is a function by which humans see around corners. It is useful for persons who live exposed to dangerous natural conditions.

 

I’d say it is useful for all humans, not just those in a dangerous situation. Although perhaps lazy humans failed to practice their intuition as part of letting themselves be dehumanized. Intuitions can lead one astray, but they may also provide insight in a way that a mechanical algorithmic approach cannot. For better or worse.

 

Finally, my favorite quote is voiced by Holtzman, the flamboyant inventor-scientist in the story:

 

“Systematic” is a dangerous word, a dangerous concept. Systems originate with their human creators. Systems take over.

 

In our day and age, with its infatuation of setting up systems and machine learning, this prelude serves as a warning. Perhaps a little anarchy is a good thing.

Framing Energy

Most of my students can trot out the standard definition of energy: “the ability to do work”. If asked to categorize ‘types’ of energy, they will default to the two broad categories of potential energy and kinetic energy. This says something about the effectiveness of the education system in secondary school science in conveying these notions. It may also reveal the analogies that have been found useful to describe energy phenomena to schoolkids. But it may also be a hint of how a reductionist Newtonian mechanics has permeated our view of nature.

 

I wonder how energy was described before this renaissance of physics and its accompanying mathematical tools. When putting on our ‘science hats’, we might scorn the ancient ideas that seem tinged with magic and mysticism, and yet embrace them when packaged as Force-wielding Jedi masters in the Star Wars saga. The scientific view we have imbibed implies detachment. We observe. We experiment. We are separated from the object of our study.

 

Our categorization of the two broad categories of potential and kinetic energy may be a consequence of this detached worldview. Let’s take the easier one first. If asked what kinetic energy is, my students will undoubtedly say “energy due to motion” and can even trot out a formula (E = ½ mv²) to calculate it. There are two internal labels attached to the object: it has a mass (assumed as a constant for now) and it has a velocity at a particular instant of time. With some prompting, my chemistry students would likely classify thermal energy (the various motion of molecules) and photon energy (the vibration of waves) as types of kinetic energy, in addition to their classical mind’s-eye picture of atoms moving in space. Electrons within an atom are in constant motion – so they should also possess some kinetic energy. In any case, all these are conceived as being solely “internal” to the moving object.

 

Potential energy, on the other hand, is more nebulous to students. Most of them would be able to recite the vague mantra that it is “energy due to position or state”. Exactly what that means is illustrated by specific examples, of which there are many. Gravitational and electrostatic potential energy are two that are well-known to students, as is the idea of energy “stored” in (Hooke’s Law) springs. There’s more vagueness when it comes to thinking about chemical energy (“stored in chemical bonds”) or nuclear energy (“stored in nuclei?”); and soon potential energy is a catch-all for anything that can “store” energy before being turned into motion. It’s potential. Not actual. Yet. Sounds oddly Aristotelian. In any case, there’s something “systemic” about potential energy – you have to consider the object, not in isolation, but where it is placed within a larger system. This may give rise to forces that act on the system that “tell” it what happens in the next instance or time-step.

 

Students will trot out multiple formulas for different situations to calculate potential energy. On occasion, a curious student will wonder why there are so many different ones, and we can proceed into a discussion of systems and reference states. This introduces a certain arbitrariness – after all we, the observers, have chosen to define the reference states thereby allowing us to come up with a formula or equation. The student experiences a little discomfort but then doesn’t worry too much, and the nagging thought of arbitrariness disappears. While I’ve referred to “students” liberally in the last several paragraphs, I should make clear that I too am a student who sometimes behaves in similar ways to my students. I’m briefly puzzled, and then something else that I have to do invades my mind, and the ephemeral strange feeling evaporates away.

 

Even as I’m teaching quantum chemistry, that sense of division between the potential energy and the kinetic energy remain – at least in the way we frame how to solve the Schrodinger equation for the models that we’ve introduced (particles-in-boxes, oscillators, rotors, atoms with nuclei and electrons). Odd ideas of wave-particle duality show up. We substitute Newtonian determinism for Born probabilities, but haven’t really changed the underlying paradigm. Although there are glimpses that potential energy and kinetic energy are coupled – the electron doesn’t fall into the nucleus of a hydrogen atom with Heisenberg’s Uncertainty Principle kicking in.

 

I was a little disheartened after grading my most recent G-Chem exams. A number of students seemed rather confused about how to solve a photoelectric effect problem. Instead of thinking conceptually about the different entities and their associated energies, it looks like they just tried to plug numbers into equations they could think of, even though I had explicitly stressed in class the importance of utilizing the conceptual picture and not to play the equation hunting-game which easily leads one astray. Maybe it was the pressure of being in an exam that caused their minds to fog. I was also less than impressed by the vagueness of explaining why atomic emission lines are observed. Granted, it can be a tricky concept. An electron is losing potential energy as it “drops” from a higher energy state to a lower one, and that energy is converted to a photon emitted from the atom. Some students conflated parts of their explanation with the photoelectric effect, suggesting to me that they didn’t quite understand the distinction between the two.

 

What would a pre-renaissance observer make of rainbows? A sign from God? Or a sign of gold? Leprechaun magic has some appeal, I suppose. In any case, there is an appeal to an external cause that increases the “size” of possibly existing entities. This is opposite to the scientific reductionist’s answer to why rainbows are observed. My reflex is to discuss the physical nature of light rather than leprechauns, but I wonder if my reflexive thoughts are honed by too narrowly framing the possibilities. Maybe this works for “simple” things such as rainbows, but fails when it comes to “complex” entities such as organisms. But rainbows and organisms are still part of a larger ecosystem to which they owe their existence. The way we frame our discussion of energy, the representative models we use, and why it can all be so confusing, perhaps hints at something more profound. If only I could grasp it.

Free Will

Can science explain everything?

 

If by everything, one means the natural physical material world, then perhaps eventually yes, although mysteries might remain. But what about metaphysical entities? Positing that everything only consists of the physical is a philosophical, not a scientific, argument. But science is greedy and constantly attempts to colonize the metaphysical realm. One recent area in which this might be happening is the concept of free will.

 

In Bjorn Brembs’ article (Proc. R. Soc. B, 2011, 278, 930-939), the author begins with several provocative questions.

 

What could possibly get a neurobiologist with no formal training in philosophy beyond a few introductory lectures, to publicly voice his opinion on free will? Even worse, why use empirical, neurobiological evidence mainly from invertebrates to make the case? Surely, the lowly worm, snail or fly cannot be close to something as philosophical today as free will?

 

Brembs weaves an interesting story about adaptive behavior using a range of invertebrates as examples. How do you stay alive and not be eaten by predators? How do you find food when there’s a famine in your vicinity? Turns out that you want to incorporate some degree of randomness into your actions, making it more difficult to predict what you’ll do, and that the actions (or reactions) can be honed by responding to changes in your environment – assuming you’re still alive. There’s an interesting interplay between learning from external stimuli and learning from internal ‘self’ mechanisms. There’s even a part of an insect brain (“mushroom bodies”) that helps control the balance between these two sources.

 

In animals and humans, the situation is both murkier and more complex. We can and do self-initiate actions, our behavior is also dependent on our experiences up to the present moment and on the present, possibly novel, external prompt that might motivate an action. This sense of agency, sidestepping the complicated question of defining consciousness, is what we humans might call free will. Brembs argues against strict determinism or dualism, and instead suggests that we consider free will not (strictly) as a metaphysical identity, but rather as a “quantitative, biological trait, a natural product of physical laws and biological evolution.”

 

Picking up on these ideas, the psychologist Thomas Hills argues for a concept he calls “neurocognitive free will” (Proc. R. Soc. B, 2019, 286, 20190510). To set the stage, Hills defines what he means by conscious control.

 

Conscious control processes are effortful, they focus attention in the face of interference, they experience information in a serial format (one thing at a time), they can generate solutions that are not hard-wired, and they operate over a constrained cognitive workspace – working memory – to which ‘we’ have access and can later report on as a component of conscious awareness. When additional tasks are added to consciously effortful tasks performance suffers. Effortful processes sit in contrast to automatic processes, which are fast and parallel, and do not require conscious awareness. Effortful tasks can be made automatic through repetition (like reading and driving) …

 

Hills assumes that alternative possibilities must be present and able to be acted on for an organism to be ‘free’. Like Brembs, Hills identifies two broad situations where an organism needs to generate such alternatives: exploration and outwitting adversaries. Why and where does this behavioral variability arise? Hill writes:

 

There is a finite precision on cognitive abilities, which is a result of a trade-off between computational accuracy and the metabolic cost of information processing. This can lead to sensory noise, … channel noise, … synaptic noise … Neural systems are commonly characterized as having a sensitive dependence on initial conditions of arbitrarily small size… What matters more for free will is where the decision to modulate variability comes from. If conscious control in any way influences unpredictability, then consciousness is in the loop that governs future behaviour.

 

Some animal experiments are cited, where neural activity involving past experiences is observed even when the external stimuli are no longer present. Apparently this ‘replay’ also happens in dreams. Hills argues that when encountering a ‘choice’, this replay kicks into action by sort-of running a quick (simplified) simulation that takes into account past experience (both good and bad) and exploring different routes. Some of this may be automated or partially automated (I’m assuming), but conscious control is also present and actively involved. In a sense, one predicts what happens to future self in these scenarios. The process may not use all the information streaming in. In fact, conscious control inhibits acting immediately while all this deliberation is taking place. As to the feeling that we have some control in the act of choosing, Hills argues that our ignorance of the future represents the other side of the same coin.

 

… it is exactly the finding out – the initiation of the search and the choice among alternatives – that is the basis of the self’s emergent will and its genuine freedom. The bringing of forth of a self-identity is the evaluation of alternatives through self-simulation. If a historical self emerges through conscious deliberation, and that deliberation involves simulation of alternative futures over which the self chooses, then a historical identity and the capacity for free choice arise in tandem.

 

Could machines have free will? Or at least the ability to “creatively” choose among multiple alternatives? In tandem with Brembs and Hills, the physicist Hans Briegel has an interesting theory which he calls “projective simulation” (Sci. Rep. 2012, 2, 522). First, he tackles the question of why we are reluctant to say machines have free will even though we might ascribe to them some form of intelligence (“the capability of the agent to perceive and act on its environment in a way that maximizes its chances of success”). It’s because the underlying stratum is an algorithm – which is therefore predictable regardless of whether it is deterministic or probabilistic.

 

Briegel has three pillars for his projective simulation. The first is memory – you have to be able to store knowledge of past action. But if memory is all-controlling, there’s no room for variation and adaptation. That’s where randomness comes into play, when it introduces variation at the very point when an organism interacts with its environment. It’s crucial that this randomness be tied to functional ability. Finally, the simulation (with many similarities to what Hill describes) does a random walk through “clips” of episodic memory – a stripped-down version of a detailed simulation. These clips have linkages of different strengths which modulate the probability that the random walker traverses them. But new clips can be created that are not memories but inventions and fabrications, maybe through a mash-up. We can imagine unicorns even if we’ve never seen one. According to Briegel:

 

The fundamental problem is… how freedom can emerge from lawful processes. Both the freedom of self-generated action and the freedom of conscious choice require, at a certain level, some notion of room to manoeuvre, which is consistent with physical law… Room and ultimately freedom arises in two ways, first by the existence of a simulation platform, which enables the agent to detach itself from an immediate (stimulus-reflex type) embedding into its environment and, second, by the constitutive processes of the simulation, which generate a space of possibilities for responding to environmental stimuli. The mechanisms that allow the agent to explore this space of possibilities are based on (irreducible) random processes.

 

All this makes me thinks of games – there are underlying rules, yet the outcome cannot necessarily be pre-determined until the game is actually played. While there are “no-luck” games such as Tic-Tac-Toe where the range of possibilities can be enumerated easily, with more complex and interesting strategy games, the possibilities cannot be computed especially once you throw in dice rolls and/or drawing from a card deck. When I’m playing a game, I try to anticipate what the other players might do. I also have strategies in mind based on previous games I’ve played – those that worked and those that didn’t work. I also have to account for how the current situation on the board may differ from the previous games I’ve played. I’m not sure how exactly I compute all these possibilities, but eventually it’s my turn and I make my move. I don’t suffer from “analysis-paralysis” when playing a game, but maybe it’s because I’m not sufficiently patient, or alternatively maybe because I’m generally decisive.

 

If I had a computer app associated with a game I’m playing, would I use it as an aid? I don’t know since I’ve never tried it personally. I don’t play games on the computer since I already stare at the screen for many hours when I’m at work. But I could imagine that if you’re playing a computer game, you could have an app that does some predictive simulation based on what has unfolded so far in the present game, while also feeding in information from previous games – basically an algorithm that chunks through data. But while that might make you better informed, the result of the game is still open and you’ll have to play to the finish. Perhaps that’s akin to the “freedom” alluded to by the authors I mentioned in today’s post. I certainly feel that I have free will when making at least some of my choices. But I don’t doubt that unconscious factors come into play in every choice that I make.

Element of Surprise

I’ve finally started on The Science of Discworld, co-authored by Terry Pratchett, Ian Stewart, and Jack Cohen. It’s an offshoot from the fifth Rinceworld novel that I found tedious, except for the interesting science bits related to Ponder Stibbons and Hex, the computing machine. In The Science of Discworld, Hex is put to work to create a new universe that results in round worlds, i.e., spheres rather than discs. The wizards then try to understand aspects of this new universe. Each short fictional chapter involving the protagonists of Discworld is paired with a non-fiction chapter describing the relevant science (up to the year 1999 when the book was first published).

 

Chapter 8 (“We are Stardust”) gets us to the first bits of chemistry. The authors briefly discuss the elements of the Greek philosophers culminating in Empedocles’ theory of Earth, Air, Water, and Fire. I do the same on the first day of any introductory chemistry class I teach (for both science majors and non-majors). While I use the Aristotelian principles, I liked how the authors describe why the Four Elements theory seemed to make sense:

 

The one good idea that emerged from all this was that ‘elementary’ constituents of matter should be characterized by simple, reliable properties. Earth was dirty, air was invisible, fire burned, and water was wet.

 

They continue with a description of the work of the alchemists, who over time found these four elements too limiting. New phenomena did not fit. Hence, the alchemists introduced new elemental principles such as Sulphur and Salt. I used to talk about these in class, but I now skip them. I go straight to Lavoisier and the importance of performing separations and getting accurate measurements of weights. Lavoisier came up with 33 elements including a few errors, and we’ve been able to extend this to 118 elements today.

 

The fictional Discworld has other elements not found in our physical universe. Key among them is narrativium. As the authors write, it’s what “makes stories hang together. The human mind loves a good dose of narrativium.” I’d agree. While this certainly applies to good fiction, it equally applies to non-fiction. The best explanations tell a story that allows us to grasp what it means conceptually. But in our shaping of the narrative, we inevitably highlight some aspects while obscuring others. It’s the nature of the story-telling of science. Throughout the course of the semester, I frequently circle back to an earlier concept in chemistry and elaborate on it, making it a little more complex, and a little less simplistic from when I first discussed it with the students. I once overheard a P-Chem student tell another student, that everything they learned in G-Chem was a lie. I wouldn’t go so far; I’d say it was a simplification for good reasons.

 

The best part of stories, though, is the element of surprise! It’s what makes you sit up and pay attention! I try to regularly employ it throughout my classes. I liked that the authors of The Science of Discworld categorize their fifth element – quintessence – as Surprise! There are many surprises in science – it is indeed stranger than fiction. Fundamental physics is a great place to tell these surprising stories. We think we know what the rules are, but then… surprise! Something doesn’t quite fit and the evolving story turns toward the unexpected.

 

Chapter 12 (“Where do Rules Come From?”) is especially excellent. Having just read Fundamentals by a Nobel-prize winning physicist who goes over similar ground, I’m enjoying the juxtaposition and variety of examples generated from these two very different books. Pratchett, Stewart, and Cohen, pose the very interesting question:

 

Could the entire universe sometimes build its own rules as it proceeds?... It’s hard to see how rules for matter could meaningfully ‘exist’ when there is no matter, only radiation – as there was at an early stage of the Big Bang. Fundamentalists [i.e., strict reductionists] would maintain that the rules for matter were always implicit in the Theory of Everything, and became explicit when matter appeared. We wonder whether the same ‘phase transition’ that created matter might also have created its rules. Physics might not be like that, but biology surely is. Before organisms appeared, there couldn’t have been any rules for evolution.

 

I’ve discussed this in several blog posts, including one on biological relativity. I do think however that chemical evolution forms a continuum with biological evolution; there’s no easy clear-cut way to say where one ends and the other begins. Boundaries are fuzzy. You might be able to articulate simple rules, but it’s not so easy to determine the outcome when complexity mysteriously arises. The authors use Langton’s Ant as an example to illustrate emergence, the opposite of reductionism although possibly not its exact polar opposite. Running backwards and forwards may not yield the same results. Here’s what the authors have to say:

 

Emergent phenomena, which you can’t predict ahead of time, are just as causal as the non-emergent ones: they are logical consequences of the rules. And you have no idea what they are going to be. A computer will not help – all it will do is run the Ant very fast.

 

This last point, however, is more interesting than the authors realize. If you had a model running on an algorithm that accurately simulates the rules, and you could run the model faster than the ‘real’ system (by coarse-graining), you can now make predictions and react to them. This is the heart of anticipatory systems that make biology what it is. But where the model deviates from the real system, inconsistencies begin to appear, then build up, until at some point the model fails and the predictions become way off. How do we prevent this? By introducing another system to keep track of it – thus the different ‘levels’ in biology that act and interact with or sometimes counteract each other. Such ‘control’ systems attempt to limit the element of surprise, but cannot fully eliminate it. That’s what makes life interesting and why I think life continues to evolve. It’s built into the rules somehow, although I can’t quite articulate what those are exactly. That’s what makes a system truly complex – it cannot be subdivided into algorithms and simulated exactly. You have to live life in reality, surprises and all. Hopefully one’s life has a good dose of narrativium!