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.
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