Church-Turing Thesis Cannot Possibly Be True [video]
microsoft.com
microsoft.com
It's one of those talks that seems to talk about things I know but then immediately jumps to theories and definitions I have never heard of. "Sequential algorithms were axiomatized in 2000" - This "axiomization" was apparently performed by the author of the talk, my Googling says. All links about things talked in this talk just seem to lead to other texts and such by this author. Might not be a good sign but maybe it's just a very hard to grasp realm.
Anyway, broadly, the Church-Turing thesis is not a theorem and cannot be proven true or false (so said my professors and Wikidepia). Effectively, it is a definition of computation that has so far been accepted because nothing fundamentally different and more powerful than a Turing machine has been exhibited (there is a theorem that Turing machines, partial recursive functions and the lambda calculus are equivalent - and then there's the jump to "these are really general and I think that about covers it" but still, not a theorem, not provable).
My hunch is the author is mixing in "higher-order" logic "version of Church-Turing" into their argument. Which is basically "cheating", switching to an effectively different question without making things clear. However, I simply don't know. This is basically opaque to my mere MA-level maths.
This is not quite correct: It cannot be proven true. But it could be proven false with a counterexample. The speaker would simply have to point to a concrete algorithm that can be performed by a person with pencil and paper but not by a Turing machine (or vice versa).
I haven't had the time to watch the video, but from the comments here it appears that the speaker did not provide such an example.
One is the real-number GCD algorithm; basically the same as Euclid's standard GCD algorithm, but with real numbers. He seems to be arguing that since Turing machines cannot represent real numbers, they cannot compute this algorithm. On the other hand, it can be easily computed with pen and paper, and he gives an example of a ruler-and-compass algorithm for evaluating it.
To me this seems a little wishy-washy; a Turing machine can approximate the problem to an arbitrary degree of precisions, just as a pen-and-paper approach is only capable to executing to a finite degree of approximation. Still, an "idealized" ruler and compass does provide a framework for describing an algorithm which is not directly Turing computable.
In fact Algebra has very deep connections to pen and paper geometry.
Apart from that... Due to the increased use of statistics, the postulates of CS might shift. One example being CAP theorem.
Every number that has periodicity in its decimals is rational... √2 doesn't have periodic decimals.
Transcendental numbers are non algebraic numbers, ie. they are not the root of any non zero polynomial with rational coefficient. √2 is algebraic
> Still, an "idealized" ruler and compass does provide a framework for describing an algorithm which is not directly Turing computable.
You could describe such an algorithm, but you could not do it in this universe. This is called hypercomputation.
"If non-computable inputs are permitted then non computable outputs are attainable"
What you're describing is the reverse direction, simulating a TM with pencil and paper, and this is doable so long as you are allowed two stacks of paper to work with, and an unlimited supply of pencil/paper. The question of simulating TMs in the real world really doesn't have anything to do with the Church-Turing thesis, though.
>Despite the generality of what I wrote above, the only feasible counterexample would be one that people can do on paper but a Turing machine somehow can't.
If some dimensionless measurable physical constant were a non-computable number, then the Church-Turing thesis would be false. In fact, if we think that certain quantities are in some sense random or arbitrary, rather than something that could be written as an equation, we should expect the Church-Turing thesis to be false with probability 1.
That's what I'm describing, but what is it the reverse of?
You wrote: "If theoretical physics can find a complete model of all particles and spacetime, and we can show that a Turing Machine can emulate it", to which I added "then a person with pencil and paper can simulate its execution", so putting these together a person with pencil and paper can simulate your complete physics model. How does that suffice as a counterexample to the Church-Turing thesis?
Also once we're talking real world, entropy is finite and there's only so many computations you can do before you run out
Church-Turing is an approach, a labeling, a thesis, not a theorem. Not being a theorem, it is not subject to proof.
One could exhibit a plausible argument that Church-Turing is wrong but that argument would not be a proof. It would not involve a sequence of mathematical argumentation that is standard for those artifacts which we call proofs. Just no.
Pointing to a concrete algorithm would not be a "proof". Maybe it would be very persuasive and the world would be persuaded to abandon Church-Turing. Still it would not be a proof.
Edit: I will admit my claim here involves a "mathematicians' thesis" that proofs are mathematical objects rather than just extra-strong arguments. So be it. I believe the whole reason Church-Turing is labeled a "thesis" rather than a theorem was because it's framers were using this distinction. And the distinction appears in the foundation of mathematics. Philosophers still argue for and against the continuum hypothesis even it's well not to be provable or disprovable - the argument is whether assuming it's true or falsehood produces good or bad mathematics. etc.
No, this is a circular definition. We define an "algorithm" as something that can be performed by a Turing machine. So the Church-Turing thesis is a trivial tautology. (Though of course a useless one.)
No, that's a terrible definition, and it isn't what computer scientists typically use, though it might be what one says if they're not careful. If someone says that "algorithm" means "what a Turing machine can compute", it's because they believe the Church-Turing thesis, which says that they're the same. If they're the same, then you can talk about them interchangeably, and "Turing machine computations" have a cleaner definition than "pen and paper algorithms", so it's convenient to talk about "Turing machine computations" as if that's the ground truth.
But if the Church-Turing thesis is false, then they're not the same, and you should be very careful not to mix them up. And we need a word for "the sorts of things you can compute by hand by a set of well-defined steps", and that's what "algorithm" has always meant.
EDIT: Note that I'm making a prediction. If a person told you that "algorithm" means "what a Turing machine can compute", ask them what "algorithm" means if the Church-Turing thesis is false. My prediction is that they'll use a different defintion, based on what you can effectively compute by hand, like the "Effective Method" wikipedia article that my sibling posted.
https://en.wikipedia.org/wiki/Effective_method
"- It consists of a finite number of exact, finite instructions.
- When it is applied to a problem from its class:
- It always finishes (terminates) after a finite number of steps.
- It always produces a correct answer.
- Its instructions need only to be followed rigorously to succeed. In other words, it requires no ingenuity to succeed."
"Several independent efforts to give a formal characterization of effective calculability led to a variety of proposed definitions (general recursion, Turing machines, λ-calculus) that later were shown to be equivalent."
Concretely, that problem might look something like:
"Given N non-communicating humans, each of whom see the same 1000x1000 b/w grid. Emit the same answer as 99% of the humans to the question of whether the grid contains a Q."
That would be a problem where, if you could prove that humans can do it, but TMs can't, you've refuted the CTT.
Do I have that right?
Humans do all sorts of things that Turing machines don't (e.g. a Turing machine can't hold a pencil), so the question there is what constitutes an "algorithm" which comes right back to the definition of computation. Even an example that was obviously "computation" in the intuitive sense wouldn't make the Church-Turing definition "false", it would just mean that it defines something different from what we thought it defines.
So if you toss out the idea of computation involving digital computers, you can exhibit something not (exactly) Turing computable. If you have a chaotically behaving dynamic system and call it a computer, then you have something where computation becomes something in the eye of the beholder.
I'm not sure what questions this answers but there you are.
[1] https://www.researchgate.net/publication/221512843_What_Is_a...
In general, a chaotic system can only be said to "solve" a problem if it can be configured to reliably arrive at (an encoding of) the solution for a given instance, despite any chaotic behaviour exhibited by the system. It wouldn't be reasonable to, for example, claim that a Turing machine cannot solve the problem of predicting the behaviour of a chaotic system with some particular initial conditions, if you couldn't reasonably conifgure the chaotic system itself to do that either.
What a standard Turing machine cannot do is entangle and superpose states. (It can only simulate it at high and variable cost.)
Remember that a Turing machine is an abstract thing. Building an ideal one is not possible. You can try though.
One might say that a "classical analogue" computer that "outputs" line segments could output the square root of two but an digital computer could merely "represent" it.
That could be pure sophistry, especially since such classical analogue never have real infinite precision. But it seems like that's the sort of thing being claimed here.
- You can't output a voltage of sqrt(2) because you output a finite amount of electrons in each timeframe, so your resolution is limited.
- We don't know if you can output a signal of length of sqrt(2) because we aren't sure yet whether time is infinitely divisible [1]
- You might be able to position gears or other physical objects with infinite precision, but reading the value with a higher precision than one plank length seems impossible [2]
Computers can also work symbolically rather than based on some direct binary representation. I think equality and especially comparison become more difficult to determine, but it remains possible.
Here is a fully expanded representation: 1.
Of course my choice of base is a bit exotic, but the point is that no matter what, we're working on symbols. We're just used to seeing some as more direct analogues of numbers than others.
For a proof, consider the fact that every representable number, by definition (I know I haven't given a formal definition), is represented by some finite string. But the number of finite strings is countable. So it must be a measure zero subset of [0, 1], so a random sample is representable with probability zero.
How long is that piece of string?
a) Here, have a look at it. It's exactly that long.
b) 4.51 inches
both answers are correct. "a" is correct by definition. "b" may be totally correct if we add a precision to the answer, like +- 0.01 or whatever we find true.
With how much precision can you measure it?
With how much precision can you describe it?
The answers are pretty similar for humans or turing machines IMO.
There is a debate about that in the philosophy of physics and mathematics. AFAIK, according to the current state of physics real numbers cannot be realized within a finite amount of space, at least Gisin [1] recently argued that way and I've seen other arguments for this view before [2,3,4,5:167-170]. I also remember some argument based on thermodynamics but cannot find the reference.
[1] https://arxiv.org/pdf/1803.06824.pdf [2] https://arxiv.org/abs/math/0411418 [3] https://news.ycombinator.com/item?id=14080024 [4] https://ptolemy.berkeley.edu/~eal/pnerd/blog/are-real-number... [5] https://www.sciencedirect.com/science/article/pii/S030439750...
Ruler and compass are made of atoms though. Or, if not atoms, planck units or something.
What, that's cheating you say? You wanted an exact decimal expansion? Well, you're right, a Turing machine can't produce that. But neither can a ruler and compass.
Same goes for printing 0 to an infinite number of decimal places.
I suspect that the proof is that geometry is uncomputable.
You can "compute" sqrt(2) by the geometric construction of a unit square and "drawing" the diagonal.
You cannot do it physically, because marks on paper are not geometric primitives: points are not 0-dimensional; when drawn with a pencil, they have a physical size. A line on paper is not 1-dimensional, etc. But on the other hand, all physical computers are actually equivalent to finite state machines: they don't have infinite (or, unbounded) storage.
I'm halfway through the video, and they are discussing this: the fundamental limit of Turing machines, etc., is that they cannot do an infinite (or unbounded) amount of work in a finite number of steps. As a result, geometric constructions a la Euclid are not computable.
In practice, anything you do with a ruler and compass has an equivalent representation in polynomials that is exactly computable.
¹ http://mathworld.wolfram.com/ConstructibleNumber.html ² http://mathworld.wolfram.com/AlgebraicNumber.html ³ http://mathworld.wolfram.com/ComputableNumber.html ⁴ http://mathworld.wolfram.com/MeasureZero.html
If the problem is "compute and output the decimal representation of the square root of two", then neither the human nor the Turing machine can do it in finite time, because that decimal representation is infinite. In fact, as far as I know this falls out of the scope of the Church-Turing thesis because most definitions of algorithms include that they must run in a finite number of steps, so there is no algorithm to do that.
If the problem is "compute and output a symbolic representation of the square root of two" (in some symbol system where it is finite), then the human and the machine can both do it.
If the problem is "compute and output a segment whose length is sqrt(2) times the length of this segment"... I don't think that's what computation is about. You might as well claim the Church-Turing thesis is false because a Turing machine cannot wave its hand.
I think that qualitatively we can agree that the ruler-and-compass construction of the square root of two is an algorithm. It's a repeatable procedure that can be described in a finite set of steps, and will always yield a provably correct answer. Whereas "waving a hand" is not an algorithm, but the same qualitative definition.
The speaker wrote a paper that proved the Church-Turing thesis for sequential algorithms, primarily by defining in strict terms what a sequential algorithm is. Ruler-and-compass constructions are not sequential algorithms by this definition, and the difficulty in specifying the parameters for a generalized "algorithm" is apparently what leads him to the conclusion that the Church-Turing thesis cannot be true in general.
newtype Real = Real { isGreaterThan :: Rational -> Bool }
sqrt2 :: Real sqrt2 = Real (\r -> r * r < 2)
Doing arithmetic on these numbers is a more complicated matter. But this representation is exact.
newtype Real = Supremum {
isGreaterThan :: Rational -> Bool
}
sqrt2 :: Real
sqrt2 = Supremum (\r -> r * r < 2)My representation is based on dedekind cuts, implemented in Haskell, which is based on the lambda calculus. There are countably many lamdda terms. Thus, I can only represent countably many real numbers. My representation can store all the computable numbers, but there are computable numbers that are not algebraic.
For example, e is not algebraic, but it is computable. Here is a representation of e
factorials :: Rational
factorials = 1:zipWith (*) [1..] factorials
eApproxes :: [Rational]
eApproxes = scanl (+) 0 (map recip factorials)
e :: Rational
e = Rational (\r -> any (r <) eApproxes)Note that there is a commonly accepted extension that is more powerful than a Turing machine: Probabilistic Turing machines. I'm guessing the proof of equivalence generalizes to partial recursive functions and the lambda calculus if you add a 'random oracle'.
An interesting counter-argument is that real random oracles don't exist, and that in reality, we can simulate probabilistic computation using Pseudo Random Number Generators. So:
* True probabilistic computation isn't possible * And anyway, deterministic computation gets close enough to probabilistic computation through PRNGs
Alternatively, one might argue one could build a 'real' random oracle by reading from a 'true' random source. E.g. Cosmic microwave background, atmospheric noise, quantum fluctuations or a video of lava lamps. There is a difference between a random source and a random oracle, but with sufficient storage, that can be patched.
————
The thesis asserts this: If an algorithm A computes a partial function f from natural numbers to natural numbers then f is partially recursive, i.e., the graph of f is recursively enumerable.
The thesis has been formulated in 1930s. The only algorithms at the time were sequential algorithms. Sequential algorithms were axiomatized in 2000. This axiomatization was used in 2008 to prove the thesis for sequential algorithms, i.e., for the case where A ranges over sequential algorithms.
These days, in addition to sequential algorithms, there are parallel algorithms, distributed algorithms, probabilistic algorithms, quantum algorithms, learning algorithms, etc.
The question whether the thesis is true in full generality is actively discussed from 1960s. We argue that, in full generality, the thesis cannot possibly be true.
These can all be converted into sequential algorithms with some overhead. Is there an actual proof in the video or just an argument that something that can't be made sequential must exist?
The problem is that, as far as I know, sequential algorithms form a uniform class, because e.g. equivalence between different sequential models like Turing machines and the untyped lambda calculus can be proved. AFAIK, this is not possible for parallel models of computation, there are different models of them with different expressivity. (I'm not an expert on that, so take this with a grain of salt and please correct me if I'm wrong!)
Or essentially, you can always simulate parallel algorithms on sequential hardware.
Of course you are correct if the sequential OR is executed naively :-)
...or if you force side-effect free short-circuiting within the sequential OR execution. But then it wouldn't really the same OR (as in the parallel case), now would it?
For all the parallel modes of computation I've seen, you can pretty easily simulate them on a single machine by just keeping the full state of each machine and simulating each time unit 1 machine at a time. It's slow, but equivalence isn't about speed.
ie IF (A OR B) THEN ...
Now this casual remark during my work time is starting to bother me a lot, and I really hope some distinguished expert could jump into the discussion. We know that the pi calculus can embed the lambda calculus (and similar for other parallel models of computation), and I've always assumed that the opposite is not generally true - that you cannot express all parallel computations on Turing machines or in lambda calculus such that the same input yields the same output, at least not if you allow some of the computations not to terminate.
Now I'm no longer sure about that and cannot find any foundational theorem that would prove this.
Am I the victim of a prejudice? :o Where are the computer scientists when you need them?
Don't get me wrong, I do believe you, but am looking for the relevant theoretical results about this.
One simple model of a parallel Turing machine is one with multiple tapes, each with its own read-write head. They all operate simultaneously based on the global state. This is a very general form of parallelism.
Wikipedia has an article [1] about them with some references for proofs that they're equivalent to single-tape Turing machines, but I encourage you to try to prove it yourself. It's fairly simple to prove, I'm pretty sure I've seen it as an undergraduate-level homework problem.
If you want a hint, try increasing the number of tape symbols so that you can encode the entire global state on one cell of the single-tape machine. It's a bit more work, but you can also show that two symbols are enough to simulate a Turing machine with any number of symbols.
Try coming up for a proof for the case where each head moves in the same direction so they're always all on the same position of their tapes first. This can be extended to the general case by some annoying bookkeeping.
Second, the result is unrelated to the Church-Turing thesis in the first place, since it's only about relative efficiency, whereas the Church-Turing thesis is about computability.
Every quantum algorithm can be simulated by a classical computer, so quantum computing cannot possibly disprove the Church-Turing thesis. However, there's a stronger variant of the Church-Turing thesis which also takes performance into account, and it's plausible that quantum computers can contradict this stronger version (although we're very far away from actually proving that).
Basically the distinction can be best illustrated with bozo/bogo sort. The definition many people use is:
1. Randomly shuffle the input
2. See if it is sorted, if not go to 1.
The problem, as explained to me by an algorithms lecturer a long time ago, is that the algorithm is not guaranteed to finish, and more over the same input may or may not result in it finishing on different runs.
Per that lecturer a “correct” bozo sort is
1. Generate a list of every permutation of the input
2. Iterate the list until you find a sorted entry and return that.
It has computable best case, worst case, and average case (all terrible). It is guaranteed that the same input will always produce the same output (terminate vs not terminate).
Obviously you could optimize this if you had an algorithm that could shuffle an input such that you were guaranteed that if you shuffled it’s own output you were guaranteed to produce every ordering of the original input. Then you would get closer to: shuffle; check; repeat. But still note that there is no random involved :)
To answer your original question, indeed probabilistic algorithms are an extension of normal algorithms. One way to make the extension (and retain the property that algorithms give the same output on the same input) is to add a 'random oracle'.
[1] https://en.wikipedia.org/wiki/BPP_(complexity) [2] https://en.wikipedia.org/wiki/Church%E2%80%93Turing_thesis#V...
The output is a random variable.
Randomized algorithms are often used to avoid falling into worst-case scenarios and improve run-time, like with quicksort, or to avoid settling in local minima like with simulated annealing.
"Starting from an initial state and initial input (perhaps empty),[4] the instructions describe a computation that, when executed, proceeds through a finite[5] number of well-defined successive states, eventually producing "output"[6] and terminating at a final ending state"
The "finite" bit I guess is the key thing, that I think was what my lecturer would have been getting at - the canonical bozo sort is not - you could just run for ever, as you might not /ever/ produce a correctly sorted version of the input. That article also points to "randomized algorithms", taking some random input (you could image random input being an RNG seed I guess?).
That article does include monte carlo algorithms, which technically could not terminate (Montecarlo simulation of a bouncing photon could technically go for ever) so I am left confused.
The lecturer was Prof. Tadao Takaoka, who was great, and apparently (per google) was on the editorial board of the journal Algorithms (http://www.mdpi.org/algorithms/editors.htm)
I think for something like this, you could do asymptotic analysis of the expected run-time. Assuming all elements are distinct, there are n! permutations, so each would have a 1/n! chance of being selected each iteration. (But it's rather late, and this is a poor medium for discussing math, and someone has probably already done this, so I'm not going to go any further.)
Perhaps-Algorithm A:
step 1: x := sample a value from a roll of a fair D6
step 2: print x
Can we argue that we're in a well defined state after step 1 has executed? We have some variable x bound to one value from {1, ..., 6}, with a known probability distribution, although we don't know which integer we've got.
edit: on the other hand perhaps we're just haggling over definitions here. it is definitely the case that non-terminating algorithms exist and can be useful, and non-deterministic algorithms exist and can be useful. it might be the case that some powerful theory and analysis restricts attention to terminating, deterministic algorithms, it doesnt meant that that's all there is.
We have? I believe the probability is ~34%. http://mathworld.wolfram.com/PolyasRandomWalkConstants.html
If you could post a text summary of this part, we'd be very grateful.
https://gist.github.com/RoyTinker/1a7e27cb4dbd468b45586a380f...
You can compute as many digits as you want, but when trying to measure it, at some point Heisenberg (or Planck to be more precise) will stop you.
But Shor complains their axiomatisation does not include probabilistic algoriths, quantum algorithms.
In this talk Gurevich argues that in full generality of the term "algorithm" the thesis can not be true.
1 - https://cstheory.stackexchange.com/questions/88/what-would-i...
All that being said, I don't buy what Yuri is selling. Even quantum computing can be simulated with a classical computer (with exponential slowdown), so I'm not seeing what's going to turn out to be more fundamental at least in a theoretical sense. Practically people might not care (yes technically you can simulate that graphics card in lambda calculus, but practically you would never do that and the guys building these things probably don't care about the church turing thesis), but the effective computability definition feels pretty effective. Either way, I'm not going to loose too much sleep over it. At the end of the day I'm more interested in looking for ways to be more effective and I'm not really interested in whether or not what I'm doing fits into the current definition of effective computability.
ANNOUNCER: So it's my distinct pleasure, and privilege, to host Yuri for a talk on a topic I have discussed with him since I was even a student: models of computation. And through the years, we have interacted in various ways, on both fundamentals of models of computation and then abstract state machine applications, and at this point, it's also probably the last talk that Yuri will give at this institution, as he is moving to Michigan next week. But I have no doubts that there will be many opportunities to interact with Yuri in the future. I hear that there's a birthday party coming up in a couple of years, and it was always a pleasure to participate in these events. So, without more adieu, please go ahead.
YURI: Thank you very much. It's a pleasure for return for a day.
[First slide appears]
>My scholarly friend Nachum Dershowitz and I published a long paper
>"A natural axiomatization of computability and proof of Church's thesis", Bulletin of Symbolic Logic, 2008
>where we proved Church's thesis for classical algorithms.
>Here classical is not the counterpart to quantum as is common in quantum literature. By classical algorithms we mean traditional algorithms from antiquity to Turing's time, also known as sequential algorithms.
>The claim that the Church-Turing thesis cannot be true in general is implicit in:
>"What is an Algorithm?" SOFSEM 2012, Springer LNCS 7147 (2012)
>The main goal of this talk is to clarify things and argue for the claim.
YURI: In 2008 Nachum Dershowitz, my very learned scholarly friend and myself, we wrote this paper, we proved Church's thesis, and Turing's thesis, but on very technical-- they are slight differences, it's a technicality -- for classical algorithms. Now what do we mean by classical algorithms? Now quantum people hijack the word "classical" -- it became to mean non-quantum, but our meaning was classical in the sense: algorithms from time immemorial, certainly, until 1950s, 1960s. So, this is the algorithm that Church and Turing had in mind when they put forward their theses. So, another name for these classical algorithms was traditional algorithms, or sequential. I will call them mostly sequential, because the first sort of non-classical, non-traditional algorithms were parallel, and so there was this -- there was traditional or non-sequential. You can generalize, and generalize, then it's not completely obvious why it should be even true.
YURI: I had this argument implicitly published years ago, but as you see:
[Second slide appears]
>There is a a problem with long scholarly papers: it takes time to read them, and there is a tendency to skim.
>Peter Shor: The Dershowitz-Gurevich paper says nothing about probabilistic or quantum computation. It does write down a set of axioms about computation, and prove the Church-Turing thesis assuming those axioms. However, we're left with justifying the axioms. Neither probabilistic nor quantum computation is covered by these axioms (they admit this for probabilistic computation, and do not mention quantum computation at all), so it's quite clear to me these axioms are false in the real world, even though the Church-Turing thesis is probably true.
>Nov, 22, 2010. https://cstheory.stackexchange.com/questions/what-would-it-m...
>The great hero of quantum computing has not read the paper.
===========================================================
I hope this will help you decide whether or not to make time to watch the video, although I agree it would be helpful to have a complete transcription available.
I shall repeat my complaint about AV only material on HN: not everyone (wants to/can/has time to) watch and listen to 10 minutes of reading spread out to 50 minutes.
It continues to frustrate me.
(tbc not faulting the speaker here).
I’m convinced this would help conference videos that frequently do just have points where just the slide is shown (WWDC videos have this a lot - where frequently the speaker isn’t being shown). There should clearly be a standardized video codec for exactly this ;)
They’d rather make a video than write an architecture document. And what happens when someone has a question or complaint about the middle of the video? How do you come back in a week to review the second to last part?
Learn to take screenshots and do some light typesetting. Spell it out for people (in my case, they are literally getting paid to do the work).
Doesn’t work for people who can’t see.
Doesn’t work for people in environments where the above two are essentially true.
25 minutes is still longer than 10 minutes (transcript, slides would be even shorter although less informative), and I was being conservative about reading speed.
This is not (as) available for a video if at least some component of the lecture requires being able to see
I'm trying 1.5x, but then when he is speaking it is too fast
>skip ahead
I skipped the introduction, but the standstill periods are too short, and you have no way of knowing when something interesting will happen, so skipping ahead entails missing things. This is where a copy of the slides is particularly useful: you can identify those slides you don't comprehend, or of particular interest, and sit through the speaking just for these portions.
It is absolutely incredible how fast some of them have the audio going at. (It also makes any pausing or lag in your application excrutiating. It turns out 10ms being “noticeable” is more a factor of how you interact with an application.
I would expect that the skill does translate to them being able to understand arbitrary speakers sped up more than a regular person could manage. I’d be curious if any HN readers using screen readers could confirm/tell me I’m talking nonsense :)
I use a text to speech program at ~850wpm and I also watch lectures sped up to x4 regular speed. So yes, it does generalize.
Just transcribe it and include the slides! If you can afford the speaker you can afford to make it accessible.
This work from Alonzo Church gave us https://en.m.wikipedia.org/wiki/Lambda_calculus which in turn provides recursive function abstraction and thus lexical scope. While this model of computation is older than OOP it currently seems to be having a modern renaissance in its influence of language design.