Turing Conjugation - by Kevin Lacker - Morning Light
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Turing Conjugation<br>Kevin Lacker<br>Jun 11, 2026
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There’s this concept of “Russell conjugation”. You can have two phrases that in a technical sense, mean the same thing. But you imply a different emotion with each one. What’s the difference between being stubborn, and being persistent?
Of course, there are many words that mean approximately the same thing, just with a different connotation. (Did Bertrand Russell invent Russell conjugation, or did he discover it?) This is a “conjugation” because there’s a specific, parallel transformation you can do with the different words. You take the positive emotion and turn it into the negative emotion. “Confident”, swapping good for bad, becomes “arrogant”.<br>Thanks for reading Morning Light! Subscribe for free to receive new posts and support my work.
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I guess I should back up and talk about “conjugation” itself. In the most common meaning of the word, conjugation is about verbs. Like singular or plural. I jump, he jumps. I think, he thinks. For mathematicians, though, there are also a lot of concepts in math which are called “conjugates”. The one you’ve most likely heard of is with complex numbers.<br>2 - i<br>2 + i
If you swap i with -i, you get the “complex conjugate”. This one is particularly interesting because the complex conjugate behaves in exactly the same way as the original number. There’s no difference between i and -i. If you redo the whole world of mathematics but replace i with -i, it’s all the same. This is as opposed to, for example, 2 and -2, which you can tell are different because one satisfies x * x = x + x and the other doesn’t.
Like the right-hand rules in physics. If you consistently use the “left-hand rule”, ie the opposite of whatever the right-hand rule tells you, then your answer to all physics questions will still be correct, because left and right are symmetric in physics. (Reverse definitions where appropriate. And weirdly enough, this is only approximately true, until you get to the weak nuclear force interacting with fermions.)<br>This mathematical conjugation is really a lot more similar to Russell conjugation than grammatical conjugation, isn’t it? I feel like it’s no coincidence that Russell was a mathematician who studied the philosophical foundation of mathematics, where questions like the philosophical difference between i and -i come up.<br>The Original Turing Test
An unusual, often overlooked aspect of Turing’s classic paper where he invented the Turing test is that he first describes a slightly different game. There’s three people: a man, a woman, and an interrogator of either gender. The interrogator can only communicate through written messages, the man pretends to be a woman in the messages, and the point of the game is that the interrogator has to figure out which person is the real woman, just from their written communication.<br>Only after introducing the gender game does he go on to describe what we now call the “Turing test”. Instead of asking philosophically, “is the computer intelligent”, we should ask, “does it act in a way that is equivalent to being intelligent”.<br>Implicit in this framing, I think, is that Turing is saying, if it acts like it’s intelligent, then essentially, it is intelligent. And if people object philosophically, you can use this fallback mechanism. It’s like a debate trick to defeat opponents who want to declare themselves the victor by definition. You can say, yes, yes, technically according to your definition it isn’t intelligent. But in all externally observable ways it’s intelligent, so let’s just treat it like it’s intelligent.<br>(And you have to wonder, why did Turing include the original gender-based imitation game at all? It isn’t really necessary to clarify the concept. But if you accept his definition of AI, as so many people have, then by analogy, perhaps you should also accept the principle for the original game, that if someone behaves indistinguishably from a woman then they essentially are a woman. Maybe Turing really wanted to make that point, but the only way to communicate this concept in 1950 was to write the foundational paper for a big new intellectual field, and sneak this argument in on the side.)<br>Turing Conjugation
So extract just the philosophical trick that Turing is doing here. We have a debate which is fundamentally tied to a fuzzy definition. Are the computers intelligent? And we can clarify that debate by replacing the “is” with “acts indistinguishably from”. This turns a philosophical question into an engineering question.<br>Are the philosophical questions and the engineering questions the same? Well, not exactly, but I feel like in the long run, it’s going to win out. As you live your life, if two things seem identical, it’s human nature to treat them as identical. But even if you don’t agree, it’s worth conjugating these questions about whether an AI is intelligent, to whether...