I love Flowers for Algernon, but Understand is my favorite short story of all time.
'Flowers' gets around it by starting with a mentally retarded protagonist and specifically trying to avoid any consequences of superintelligence beyond the emotional & social journey, so most of the story is accomplished 'on the runway', as it were, and is about everything but what he learns & does with his intelligence which is pushed into the background. You can see how it starts getting handwavy as soon as the protagonist takes off to smarter than Keys himself, and he starts having to show the progress by him simply doing ordinary-human things but much faster than a dimmer human, like rearranging the bakery for more efficiency or learning Sanskrit in a week. While it's nice to be able to read German or Sanskrit, it's not particularly useful, especially if you are interested in neuroscience; a real protagonist would be doing things Keys can't even imagine, which sound like gibberish like 'ordinary differential equations' or 'symplectic manifold'. Any societal implications are simply ignored.
With 'Understand', Chiang starts with an intelligent protagonist, in a strictly realistic universe other than the superintelligence, where he's well aware there would be major societal consequences and military implications and the protagonist can't simply sit around and play with his lab mouse. So his back is against the narrative wall from the start. He cannot do his usual world-building tricks because he's both ruled out the world mechanics he is usually in a privileged position to understand impossibly well because he made them up in the first place, and because he's not smart enough to write the superintelligent character he's assigned himself. It's an interesting story, but I agree that it can't be considered his best. Because he can't write that story as well as he wants to, and no one can.
This is kind of how "Excession" by Iain M Banks is. Much of the dialogue in the book is supposed to be between the hyperintelligent AI "Minds" that are the ships in his Culture universe. It's supposed to be in a form similar to how they talk to each other. It's quite hard to read. I can never decide which of the two (gibberish or dumbed down) it is. Probably both.
Ditto this, but for any domain specialization.
A lot of fiction gives me a bad case of something which I don't have a term for but it seems like it might be the inverse of the Gell-Mann Amnesia Effect:
Basically, I was fine with the story until it got technical in a way that I know well, and the technical aspects of the story were so egregiously sloppy, I could no longer suspend my disbelief. And then even the nontechnical aspects just annoyed me because I figured, if the author was such an idiot they couldn't bother to look up how lasers work or whatever, they probably got everything else wrong too. Even the parts I'm not a specialist in, which I had previously just been taking on faith, I am now forced to assume that a specialist in those things would also find them laughably bad. And the whole work is ruined for me.
(To be clear: If the author would just say, "these are magic lasers" or some other form of "a wizard did it", okay that's fine, it's fiction, I'll accept that, let's see how the story develops from there. It's when they try to claim they're real-world lasers but then merrily ascribe them impossible traits, that I get brain-jammed.)
Of course Stephenson figured out how much battery a useful EV would need, before concocting a throwaway line about it. In 1992.
I'm not entirely sure if that's true. It might be, I honestly don't know, but my personal suspicion is that there's such a thing as what I'll just go ahead and call a threshold intelligence level. In other words, a level of cognitive capacity beyond which a creature that attains said level can functionally conceptualize things far above its actual ability to understand them in detail. This allows discussion and exploration of certain extremely advanced concepts well enough to form a narrative without falling into complete incomprehension.
Chimpanzees might be far enough below this threshold level that even a basic story would cause them difficulty no matter how learned they are educated or bred to be, and a complex story about, say space ships or high performance aircraft would be completely outside their conception. Humans on the other hand might be able to stretch their imagination much further towards the extremes of conceptualization. However, I also think it might have its limits, namely that there are things which if explained to us would leave even the brightest humans as befuddled as a dog being lectured on internal combustion mechanics.
perhaps even smarter than a post singularity intelligence, for instance,
we are "computationally" equivalent to a turing machine: a tape with symbols on it and a head that reads and writes symbols to the tape according to rules.
the natural generalization of a turing machine to infinity would be a hyper turing machine: an infinitely wide tape and infinitely many heads.
if one were to employ some kind of godel numbering esque scheme, most (the overwhelming majority) of the symbols the hyper turing machine used in it's operation/had in it's rule lookup table would correspond to transcendental numbers, e.g. pi or e (cuz their cardinality is larger than natural numbers).
The alphabet our math uses is pretty much all finite. What percent of the axioms and theorems that you know are infinitely long? Shouldn't the overwhelming majority of axioms and theorems be infinitely long (and in particular map onto an uncountable set? (e.g. transcendental numbers).
So a hyper turing machine would be a supra-mathematical entity. But you can pretty much use math to deduce that.
Why do you think that?
We know of modes of computation different from Turing machines, quantum computers. There's nothing saying there might not be yet other kinds of computers currently undiscovered.
That's wrong. Quantum computers are Turing complete just like any other form of computation we've found / invented. You can't do something on a quantum computer that you can't do on any computer, albeit in some cases you can get a speed-up by using a quantum computer.
but essentially turing machine/quantum turing machine have the same kinds of inpus/outputs or domain/range, whereas a hyper turing machine has a bigger domain/range.
The only way I see to reach this conclusion is to assume Turing machines are all that exist, and the conclusion follows.
Basically, either humans operate like Turing machines, or we're magic.
That description of a "hyper Turing machine" is pretty boring and ridiculous, such a machine trivially solves any computational problem we have because you can embed the problem into the transition function. Here is a sketch of how to do it: Let's call the heads on each tape 0, 1, ...; and let the input be on tape 0. Then the following is a machine that _decides_ a given language:
1. read the input and place the first symbol to tape 1, the second table to tape 2, ... . This takes a single step!
2. Read the whole input by reading a single symbol from each tape, and accept it if it is in the language. This can be done because the transition function can map each string to accept or reject state directly now.
Now, here is the kicker: there are uncountably many "hyper" Turing machines but only countably many strings, so almost all of these machines cannot be described, and there cannot be a universal "hyper" Turing machine. So, I don't think they are that interesting.
Note that the alphabet here is still finite, the infinity is handled by having infinitely many tapes (this is equivalent to going through the trouble of building up something like Goedel encoding). Moreover, I didn't specify the number of tapes here, but countably infinitely many tapes are enough, so you don't need to build an "uncountably-wide" tape. The point I'm trying to make is that if you let a Turing machine-like thing to have countably infinite descriptions, then the description may as well be "look up the solution" so it gets boring from that point on. We need only countably infinite descriptions because a language is countably infinite (because it is a subset of the set of all strings). If one tries to do some shenanigans like making the languages also have higher cardinalities, well just pump up the cardinality of the "hyper" Turing machine to match and you'd end up with the same proofs with slight changes.
> The alphabet our math uses is pretty much all finite. What percent of the axioms and theorems that you know are infinitely long? Shouldn't the overwhelming majority of axioms and theorems be infinitely long (and in particular map onto an uncountable set? (e.g. transcendental numbers).
As for this, we _want_ all of that (and proofs) to be finite. That gives a lot of nice structure we can work with when dealing with first-order logic and proving stuff like compactness and (in)completeness. All of our axioms and theorems are finite (assuming using FOL), we just have countably infinitely many of them (building countably infinitely many theorems is trivial, as for axioms: axiom schemas are just a countably infinite collection of axioms).
This was all to set the record straight when it comes to computability theory. If you want tamer examples of hypercomputation, there is a lot of work on oracle machines and Turing machines that can take infinitely many steps. I think those would be better examples for the "we can reason about 'supra-mathematical' entities using plain old math." claim you are making. Although, I am not buying into this because these are all mathematical entities. We do mathematics because it is an interesting endeavor, and computability is important only in that it helps us understand the math we are doing (can we prove all "true" statements? can we devise an algorithm to solve X?), anything beyond that is still math, and a lot of the notions here (Turing machine as a proxy for algorithm, using first order logic, picking a particular set of axioms) are arbitrary choices that work well so that we can do math with a foundation that won't make us lose much sleep.
let me try and rephrase some of what you are saying to check my understanding
set of strings is countably infinite
so my "supra mathematical entity" is boring because for any given problem we could pose it can just function as a lookup table
even if you made an alphabet (strings whose characters had decimal places or something) that was bigger, then it would still be kinda boring cuz the hyper hyper turing machine would still be a lookup table (though maybe even the machine in my example could still just be a lookup table for an uncountably large language on account of having uncountably many tapes/heads).
i'm not sure if it was intended by you but my (somewhat crackpot) takeaway from your response is,
at the limit, computation and memory become the same thing (i was physics undergrad so this still feels profound to me lol (no postgrad yet maybe one day when i am richer) (and maybe also timely w/ gpt3 XD))
also i think i am still digesting notion that there is no general version of hyper turing machine
That's pretty much what I wanted to mean. Although I called it "boring", it was not to take a jab but more so because there is not much effort to spend to understand the limitations of such a machine once you can encode the whole language into the machine's look-up table. Also, such an extension makes us lose the ability to simulate other extended machines in general. Extensions to Turing machines are interesting because of how they may alter the limits of computability (in a completely hypothetical setup) and complexity, and I had some fun when writing the response although I called that specific machine model boring because it ended up being too powerful to be interesting (from a computability theory perspective).
the set of all strings is countably infinite like the natural numbers
however human language when actually spoken can contain recursive implicit meanings and subtext, so maybe even though it's just strings, if you made the implicit context explicit it would be uncountably infinite, much like the real numbers, even though in practice the meaning a human can grok from any given sentence is bounded like a ieee floating point number.
but i find it somewhat interesting that whereas all ieee floats have a certain amount of meaning they can carry around/a set amount of decimal places, the way we encode implicit meanings and tones into language is uneven, it's not character by character (but it can be if you add an accent or tone to a character even in non tonal languages),
like, what if you could design a number system more like human language where the decimal places somehow only showed up under certain conditions (maybe you could argue complex numbers are kinda like that, since the imaginary or real parts will appear and re apper under certain operations)
could you design a number system or an algebra in such a way that it was up for interpretation lol (or if not why not)
one thing is that you can interpret numbers in terms of geometry, but the interpretation is one to one, and thus boring compared to the interpretability of strings.
also maybe lambda calculus is somewhat interpretable in this way, and it can encode numbers and algebraic rules
maybe logical conclusion of this train of thought is the IO monad XD
tl;dw: There's different axes of intelligence, and you can setup the situation perfectly to fake the character's intelligence. You can also fake wisdom/intelligence by taking as much time as you need to come up with the smartest/best response to a situation.
Doesn't apply exactly here (He has written Gods, but they are still "mostly" human except for knowing a lot more about their world), but it's good advice.
Mimsy Were the Borogoves by Lewis Padgett explores this to an extent.
[1] - https://en.wikipedia.org/wiki/Lewis_Padgett
[2] - https://www.amazon.com/Last-Mimzy-Stories-Henry-Kuttner/dp/0...
But I make one exception - Brain Wave by Poul Anderson. In it, ordinary people become much more intelligent. Their speech patterns change into very few words, because a more intelligent listener would be better at inferring meaning from the context.
I found it to be one of the most thoughtful explorations of super-intelligence and how it becomes qualitatively different than conventional intelligence.
I came away from it thinking, "This is Limitless if it were written by a grownup"
I understand the commenter's sentiment though--it's difficult to read an earnest story about a super intelligent trans-human because the archetype of "cool and collected super genius" has been done to death and has become cringeworthy.
At a certain scale I believe one exerts a "gravitational" influence, and this book explored that neatly
Just kidding
Briefly, there is an energy damping field that projects in a beam from something near the center of our galaxy. One of the effects of this field is to slow down the speed of neural activity. The Sun's orbit around the galaxy takes it through this field periodically.
When it enters the field the effect is to make everything with a brain about 1/5th as smart as it was, which usually results in a mass extinction of any species that depended on its brain to survive. That's what did in the dinosaurs for instance which had been near human intelligence before that (the book is from 1954 which is before we figured out what really did them in).
Humans evolved while the Earth was in the field, evolving neurons and brain structures that can get to normal human intelligence even with the degrading effects of the field.
The start of the novel is set when Earth moves out of the field and so over the next few weeks everything with a brain gets about 5 times smarter than it was before.
That has lots of consequences. For example a lot of how we handle animals is based on the animals not being smart. It gets a lot harder to be a pig farmer, say, when your pigs get human genius level intelligence. Of course the farmer is a lot smarter too, but still it will take some time to upgrade the farm to deal with super-genius pigs and the pigs aren't going to just idly wait for that.
The novel looks at that and a ton of other changes as Earth adapts and develops to deal with this.
[0] at parties, it sounds better than SF