Do Wizards Believe in Magic?

A more-than-somewhat oblique look at the issues of trying to define machine ‘intelligence’

Two hobbits are sat in a tavern in a quiet backwater of The Shire. After a prolonged silence devoted to the appreciation of their mugs of Bucktooth’s Old Tawny, one turns lazily to the other and mumbles …

“I see the Rollyberry Magic Man’s been caught out once and for all!”
“How’s that?” asks the other.
“Those acorns he was making appear out of thin air … Turned out he had them stuffed up his sleeves all along.”
“So, he’s a fake then?”
“S’pose so. Doesn’t surprise me though. I always had my suspicions about that bloke. Old Bill Gamwise reckons, when he made that fire appear from nowhere, he had a contraption made out of flints in his pocket.”
“Hmm, so probably all the magic he’s done has been phoney then?”
“Yep, reckon so … “

A further period of ‘reflection’ follows … Eventually …

“So, do you think there really IS any magic then?”

“S’pose so; somewhere. Don’t you?”
“I’m not sure. What exactly IS magic?

Another pause …

“Well, it’s something that can’t be explained, isn’t it?”
“Explained by who?”
“What do you mean?”
“Well, WHO has to be able to explain it for it not to be magic?”
“Well, us, I s’pose.”
“What do mean, ‘us’? Me or you?”
“Does it matter?”
“Well, yes, it does really. With all due respect, Pippy, you’re not exactly the brightest tankard on the shelf. You still think I’ve pulled your nose off when I show you my thumb between my fingers. You still don’t know how the coin gets behind your ear. I guess lots of things might seem like magic to you that don’t to me. You might not be the best judge”
“Cheeky bugger! OK, OK, BOTH of us then. No, wait, EITHER of us. Whoever’s there to decide, I suppose. ALL of them. No, hang on; maybe I mean ANY of them!”
“So it’s not magic if SOMEONE can see how it’s done?”
“Right.”
“So, The Rollyberry Man was magic until someone found the acorns and flints but he’s not now?”
“Er, well, no; I s’pose he never was magic really because HE could always explain it, even if we couldn’t.”
“So a magician can’t ever believe in magic? Because he’d always know how it was done?”
“Well, he wouldn’t believe his own magic, no, but he might believe in REAL magic.”
“So what’s REAL magic then?”
“Well, it’s something that can’t be explained, isn’t it?”
“That’s what you just said about ordinary magic!”
“Bugger. Oh, alright then; it’s something that can’t be explained by ANYONE; not just a few people or SOME people but ANYONE!”

A further pause … and more ‘reflection’ …

“So, do wizards believe in magic?”
“WHAT?”
“Well, wizards do things that can’t be explained, don’t they? And none of us know how it’s done; so that’s magic, right?”
“Er, yes.”
“So don’t THEY know how they do it?”
“OF COURSE THEY KNOW HOW THEY DO IT!!”
“So, it’s not magic then! If they know how it’s done then it’s not magic. It might seem like magic to everyone else but not to them because they know how it’s done. It must seem perfectly normal to them. Wizards can’t believe in magic!”
“Oh, shut up and drink your beer …”
“It’s funny though. I’m sure I’ve heard Gandalf talk about ‘magic’. Why would he say that? If he knows how he does it then it’s not magic. So, why would he say ‘magic’? Is he just saying ‘magic’ because it’s real magic, not fake magic? But how would he know if the person he was talking to could tell the difference between real magic and fake magic? And that would depend on the person themselves, wouldn’t it? So how would he know what real and fake magic were anyway? Maybe he …”
“I’m going home …”

We move now in time and space to find two computer scientists sitting in a coffee shop. One of them takes a sip from her skinny, decaf latte with sugar-free vanilla and just a light dusting of nutmeg but no whipped cream (otherwise known as a ‘chinless wonder’) and begins …

“I see they’re saying that program didn’t really pass the Turing Test, after all.”
“What program?”
“That program that pretended it was a ten-year-old autistic Venezuelan girl with ADHD. Apparently, they’re not convinced anymore.”
“Not convinced about what? Not convinced that it passed the test; or not convinced that they did the test properly; or not convinced that the test makes sense in the first place? Personally, I’d go for the last one!”
“Eh?”
“Well, what is the Turing Test? What does it test?”
“Err, the Turing Test says that if a human can’t tell the difference between a machine and another human then the machine must be intelligent; that’s Turing’s ‘Imitation Game’.”
“What sort of human?”
“What?”
“A clever human or a thick human?”
“Does it matter?”
“Of course it matters. My Gran thinks the TV is alive; she thinks it’s intelligent when it reminds her to change channels to watch Eastenders! Anything would pass the Turing Test if she was the judge. A pocket-calculator, the toaster …”
“OK, OK, so not your Gran, then!”
“So, who? You or me? Computer scientists? Programmers?”
“Er, no; someone NORMAL!”
“Define NORMAL?”
“Well, AVERAGE, then!”
“Who’s average? The person the machine’s being compared to or the person doing the testing?”
“Er, I guess they’re both average.”
“And, if they’re not? Then I suppose the test won’t work? To implement the Turing Test, we have to find someone who’s completely average? No, wait, TWO people who are completely average? How many of them are there around – and how would we tell?
“Well, to be fair, the Turing Test is a bit more complicated than that. It actually says an intelligent program will fool 30% of people for five minutes. So, I guess that means a cross-section of people?”
“Actually, no, it doesn’t say that. The original paper simply says ‘I believe that in about fifty years’ time it will be possible to program computers … to make them play the imitation game so well that an average interrogator will not have more than 70% chance of making the right identification after five minutes of questioning’.”
“Same thing, surely?”
“No. not the same thing at all. Actually, Turing is indeed describing an AVERAGE interrogator – not averaging out the test over a range of people. But the really important point is that it’s not a TEST at all!”
“Eh?”
“It’s not a test; it’s simply a PREDICTION. Turing describes the game to be played by a machine IMITATING intelligence. Then he makes a guess as to how far we may have come by 2000. That’s not a DEFINITION of intelligence. How could that possibly work with ONE person for FIVE minutes?”
“So what was the point then?”
“Well, the original 1950 paper has a much wider discussion of what intelligence might be – particularly MACHINE intelligence; what it might mean for a machine to APPEAR to THINK, rather than ACTUALLY think; how that might show itself, etc. A large part of the paper is actually devoted to countering various arguments why machines might not be able to do that. Unfortunately, most people only know the one paragraph with the 50 years, five minutes and 70% bit; and they think THAT’S the Turing Test!”

They both pause for a moment to sip hot froth.  Then …

“So how DO we test for intelligence then?”
“Well, I guess we could make the test longer … and bigger?”
“Meaning?”
“Well, more people doing Turing’s ‘interrogation’ and giving them longer to do it?”
“That’s getting more complicated. How many and how long?”
“Well, I don’t know, really. I’m just making a point. Ultimately, I suppose EVERYONE there was … and as long as it took … maybe FOR EVER?
“That’s not going to work, is it?”
“No, not really. Well then, I suppose we need to find something more reliable; more accurate; more consistent.”
“Er, right … How?”
“I don’t know. How could we administer a single effective interrogation that consistently reflected a typical human and get the job done quickly?”
“Search me!”
“How about programming a machine to do it?”
“WHAT?”
“How about programming a machine to be an average human and let that machine decide whether or not is was talking to a machine or a human?”
“Let me get this right … YOU WANT TO USE A MACHINE TO TEST FOR INTELLIGENCE IN ANOTHER MACHINE?”
“Yeah, why not?”
“Would that work?”
“Search me!”
“And, the machine doing the testing; would that make it intelligent? Or would it depend on whether the machine it was testing was intelligent? Or whether it could tell the difference?”
“I don’t know! Would an intelligent machine KNOW it was an intelligent machine?”
“I’m going home … “

“Would an intelligent macine know it was an intelligent machine?”  That remains a very good question … Turing himself side-stepped this precise issue by always very distinctly discussing artificial intelligence rather than whatever real intelligence might be.  Certainly, no question of self-awareness ever raised its head as such (although occasionally hinted at when countering arguments against machine intelligence).  “The original question, ‘Can machines think?’ I believe to be too meaningless to deserve discussion.” he wrote.  Instead, he asked, “Are there imaginable computers which would do well in the imitation game?”.  Quite simply, in principle, and putting precise numbers aside, we’ve known the answer to this question to be ‘Yes’ for some time.  It’s really just a question of how good we want them to be.  (There’s no logical significance in levels of convincing 10%, 50%, 90% of people 30%, 50%, 70% of the time; only the figures of 0%, 100% or ‘somewhere in-between’ are distinct to an argument about what may or not be possible.)  However, the cyclic question of whether a machine would know whether it was intelligent itself – more formally worded as could a machine test itself for intelligence – has interesting parallels in Gödel’s Incompleteness Theorem, Turing’s earlier work with the Halting Problem and is essentially similar to the question of whether wizards think they’re doing magic.

Although there’s no intention to make direct comparisons between the two dialogues above, there are connections.  Actually, it’s not axiomatic that wizards know how they perform magic.  Gandalf appears to know what he’s doing, for example, but it’s pretty obvious that Harry Potter and his chums – at least while still learning – don’t; but they still manage to do it after a fashion.  In the real world, it’s possible to teach a child to perform a ‘magic’ trick – based on some interesting physical principle, which neither they nor the person they demonstrate it to actually understand.  (Putting a piece of card over a glass of water for then inverting it, for example, can be both demonstrated and observed without awareness of how exactly the water stays in place.)  Similarly, it’s debatable whether you have to understand intelligence to have intelligence.  By most standard dictionary definitions of intelligence, you probably don’t.  Using a machine to test another machine for intelligence is an extreme example but extending Turing’s question literally: Is it possible for a machine to exhibit signs of intelligence? … the answer is clearly Yes they’ve been doing that for some time now and they’re getting better – although some people are more easily convinced than others.  The original programmer, for example, would be a tough nut to crack in this respect and would probably have to see evidence that the machine had extended itself beyond its initial coding.  This is very much where we are with this argument at present although there’s a fair consensus that, given time, it will all happen.

To finish, there’s a final comparison of interest between magic and machine intelligence, in terms of general belief.  In bygone days, there would have been general acceptance of magic on some level because so much of life wasn’t understood well enough to explain it.  On the other hand, the notion of something artificial exhibiting intelligence would have been ridiculed.  Today, those positions are reversed.  Taking ‘magic’ broadly to mean ‘outside of science’, most supporting ideologies are essentially religious in nature; belief in magic performed by ordinary people is very limited.  However, in contrast, acceptance of the concept of machine intelligence has become mainstream.  It’s always worth bearing in mind that, over short and long periods of time, these perceptions are more cyclic than we often realise.