Meta already pays billions to gain access to people's personal data. This is just another business expense, a line item on a balance sheet.

When faced with an adverse ruling, an individual raises his hands, is handcuffed and led away. A corporation raises its prices.

THAT STATEMENT IS FALSE. The two articles used DIFFERENT EQUATIONS TO SUPPORT THE SAME LOGICAL ARGUMENT. Church and Turing are jointly credited with the same logical conclusion, even though they used different mathematical arguments. NO ONE said, "Wait, the equations are different, therefore the conclusion must be different." At least no one with an education.

> ... they described the math proving their statements in them and what that math implies (which is why the ending summary would not be math, it must already have been shown to be a summary).

Church and Turing made the same logical claim, using the same words but different mathematical arguments. This places the math in a supporting role, below logical reasoning. This is true in all the examples I provided. Math is a language, but to use it, you must have something to say.

In the Relativity example I gave, Einstein's math teacher used the SAME equation to draw a DIFFERENT CONCLUSION, because EQUATIONS SUPPORT IDEAS, THEY AREN'T THEMSELVES IDEAS.

Just as with words, math equations never stand by themselves -- they support ideas, and the same idea can be expressed by different mathematical arguments. That was the point of all my examples, which clearly fell on the ears of a religious true believer.

This equation -- y = sqrt(1-x*x) -- can be taken to mean (a) pi/4 if integrated on the interval 0 < x < 1, or (b) space and time are separate dimensions, which is what Minkowski noticed and Einstein didn't. But by itself, THE EQUATION MEANS PRECISELY NOTHING -- for that, you must have ideas.

If you possessed the intellectual integrity of the average 12-year-old, you would realize that using the same words as Ernest Hemingway doesn't make you a great writer, and using the same equations as Einstein doesn't make you an original thinker. That requires ideas, not equations.

I post this for the benefit of other readers, who unlike you might have some depth of understanding, some grasp of the relation between ideas and equations.

Apropos, I was once told a Japanese saying: "Fix the problem, not the blame."

I must have repeated this charming story a dozen times before realizing it makes no sense in Japanese -- it relies entirely on English idioms.

> This is the difference I feared. I trust, understand, and take lead of the rigorous math of the paper, you opt to follow in English arguments of what you think it's supposed to mean or apply to.

Excuse me? The articles don't prove their theses with mathematics, they prove them with logic. Equations are assistants, but they're entirely replaceable, as proven by the fact that Church and Turing used different equations in support of their theses -- articles that come to the same conclusion.

How did you miss the significance of the Alonso Church article's final sentence: "The general case of the Entscheidungsproblem of the engere Funktionenkalkül is unsolvable." Where are the equations that you think make the point better than these words? Certainly not in the article. Why didn't Church refer to an equation to support his conclusion? The answer is that his conclusion is a logical one, not a mathematical one.

In the case of Navier–Stokes, the equation is a preliminary, a self-evident statement about energy, inertia, pressure and a few other things. If it were rewritten (as it often is), the problem remained to be solved. Those who solved it didn't post a new equation, they posted a new insight.

In the relativity example, Einstein wrote an equation but didn't understand it -- his math teacher took over. Any number of equivalent expressions would have provided a basis for progress toward a more comprehensive theory. The point was the ideas, not the equations.

> ... the rigorous math of the paper ...

Nonsense. In both papers, the authors use mathematics only to support their points, in the same way that an author uses words to craft a story. If separated from the logical thread, the words (the equations) lose all meaning. This is proven by the fact that the two papers use different mathematics to support the same thesis.

But I see I'm wasting my time. Mathematics is a language, but to use it, you must have something to say.

Well, it could, but a preliminary step would be to get everyone to agree about what constitutes morality, which will never happen. So in essence I agree.

A second reply. What you're not getting is that the mathematical equations in Turing's paper don't make its point. There are plenty of equations, but the paper's meaning lies in its logical arguments, for which the equations can only play a supporting role.

If the equations are taken out of the paper and presented separately, as you have repeatedly demanded, the paper's thesis falls apart. But to understand this, you would have to read the paper itself and absorb Turing's logical arguments. And the paper can't be made shorter without losing its meaning.

More evidence for this is given by the fact that Alonzo Church published a similar paper in 1936, different author, different equations, but the same logical argument and conclusion, such that Church and Turing are now given equal credit for the basic idea -- an idea that is supported by equations but not provided by them (https://courses.fit.cvut.cz/MI-VYC/church-a-note-on-the-ents...).

This is true in many parts of mathematics and logic. Another example is Einstein's 1905 paper later identified as the source of "special relativity". If you remove the equations and present them separately, all meaning is lost. In fact, in that case, the actual meaning of a particular equation was lost to Einstein himself, but that meaning occurred to his former math teacher Hermann Minkoswski, who went on to publish about something Minkowski called "spacetime". As before, the equations didn't convey the paper's real meaning, they could only play a supporting role. About this outcome Einstein later said, "Since the mathematicians have invaded relativity theory, I don't understand it myself any more."

Another more recent example is the recently solved "Navier–Stokes existence and smoothness problem" as it was titled by the Clay Mathematics Institute. The equation is easy to render, but as with the other examples, the problem to be solved goes far beyond the equation itself, and the meaning of the recent result lies not in the equation, but in its treatment and processing by AI.

In Navier-Stokes, everyone had access to the equations, but until recently no one could answer a fundamental question about it, and as with the prior examples, the real meaning requires one to read the articles that provide the logical reasoning. In each of these examples and many more, listing the equations can only be a preliminary step to true understanding.

More importantly, the meaning of the papers cannot be summarized in fewer words than are provided by the papers themselves. Mathematicians don't go out of their way to make their papers longer than their contents require, in fact, quite the opposite.

I can't believe you're still expecting bumperstickers to stand in for technical articles. As before, you should read the original articles instead of complaining that they're too long for your limited attention span.

The reason corporations disable our right to stop AI tracking is because, at least for now, AI agents can be held to account for crimes once blamed on a person or corporation -- all one need do is disable the off-switches.

Until we sort out our relationship with AI, it will be the universal whipping boy, blamed for all sorts of things that once would indict an individual or corporation.

The best -- or worst, depending on your outlook -- AI trait is its complete absence of an ethical or moral sense. When an AI agent breaks into a computer, it's not with guilty knowledge, because AI doesn't possess that -- it's not part of their design. People need to remember: AI agents live in a moral vacuum, and that's not an accident.

When a corporation is called out for disabling a switch that once stopped AI tracking, the AI bros might say, "Oh, yes, that's an oversight, easily fixed." But it's not an oversight, it's a trial balloon, an A/B test to see how people will react.

But there's more. Decades ago, the Nielsen TV rating service would monitor what people watched on their TV sets (remember TV sets, boxes weighing 500 pounds?), by calling people on their telephones (remember telephones?). By modern standards, the Nielsen people were amateurs -- today's TV sets have built-in AI agents, active 24/7, and no disable switch. They patiently record what you watch.

In the next phase, TV sets will do eye-tracking, find out what parts of a TV scene people are looking at. Not true now but soon (Samsung is working on it). Pupil dilation, facial expressions, everything.

A super-old Bob Hope joke from the Cold War era: "Yes, they have TV in Russia, but you don't watch it, it watches you." Not so funny any more.

A false statement. I posted a link to the evidence, which cannot be summarized to satisfy your short attention span. Your unwillingness to read it only reveals your shallow grasp of modern technical topics.

Here is a short list of topics that cannot be converted into bumperstickers, your preferred medium of expression:

   Special and General Relativity

   Quantum Physics et. al.

   Cosmology

   Biology

   Modern Set Theory

> I do wish you well and I'm sorry if my requirement for rigorous statements in math seems pointless to you.

Excuse, me, what? I have posted links to the evidence that proves your position to be false, but you won't read it. You are to modern times what a religious fundamentalist is to science -- the primary obstacle to human progress.

Am I saying your unwillingness to absorb ideas outside your short attention span is itself an obstacle to human progress? No, actually, I'm saying you should avoid drawing conclusions without first examining the evidence.

It isn't only that you won't read the evidence that proves your position to be wrong -- that is simply sad, not fatal. It is that you draw conclusions without first examining the readily available evidence.

> A set of theorems (of which I accept all you've named) without the definitions of exactly how and why they apply to the give problem is no more mathematics than a bunch of bricks is a chimney.

Wow. You just dismissed the validity of all the topics in my list above, each of which produce everyday valid conclusions derived from very complex logical and mathematical antecedents.

Get professional help.

Now I get it. I should have realized at the outset that this outcome lay in the future. You are here to pointlessly argue, not discuss nor debate.

> At the very least, you could see how I'd still be awaiting to hear the actual mathematics you're using.

Yes -- notwithstanding that I have posted links to that exact evidence from multiple sources. The problem is not a lack of evidence, the problem is that you refuse to read it.

On that topic, here is a link to Alan Turing's 1936 paper -- 36 pages long: https://www.cs.virginia.edu/~robins/Turing_Paper_1936.pdf

Andrew Wiles conclusively (dis)proved Fermat's Last Theorem. If you disagree, and since you have demonstrated a willingness to disagree with anything, I would have to post a link to the evidence, not the evidence itself, because the (dis)proof is 129 pages long.

As I post this, I'm trying to imagine the corpus of mathematical knowledge you're unwilling to accept, because it won't fit into a finite-sized Hacker News post -- relativity, both special and general, quantum mechanics, dozens of others.

I'm also trying to imagine someone whose literacy filter consists of "Tl;DR!"

I posted the Turing Halting Problem Wikipedia page. It describes a theorem, not a conjecture that I need to prove, which shows the original poster's claim is contradicted by established facts.

Let me put it this way. If I say, "There are an infinity of primes," will you reply, saying, "I disagree"? That position would be equally appropriate -- that is to say, not appropriate at all.

Am I obliged to prove the infinity of primes by generating an infinity of candidate integers and prove that some of them are prime? No, and by the same token, I'm not obliged to reply to your naive demands and teach you why the Halting Problem falsifies the claim made by the original poster. That is not my responsibility, it is yours.

In mathematics, some things are conjectures -- the Millennium Challenge problems, for example. Others are theorems, meaning established truths, beyond dispute. Turing's Halting problem is a theorem.

Here is another authoritative reference to the fact I originally posted: "Did Turing prove the undecidability of the halting problem?" from the Oxford University Press -- https://academic.oup.com/logcom/article/36/1/exaf075/8417148 .

The question in the title is rhetorical, as you will discover if you read and understand the article I just linked.

> It is now your opportunity to make a mathematical claim, of which proof by assertion this paper should apply because it proves something in general is not.

How many more mathematical literature references will you require before you realize I have already met any burden of proof? I could post the entire technical proof here, but (a) the editors of this forum would kick me out, and (b) you would still refuse to accept the evidence.

How do I know this? Because you keep refusing to learn what you need to know to engage in this conversation.

There are an infinity of primes -- your turn.

This is not a philosophy discussion, and Alan Turing already plowed this ground. The original claim "Bend - a language that blocks AI mistakes via proof [...]" is unsupportable.

> ... if every program can be proven to halt ...

But that's not so. You have introduced a qualifier that is known to be false.

> ... a chance to quote and discuss everything but actual mathematics.

Yes, I agree -- you should stop doing that. I keep referring to the original technical reason the original claim is unsupportable, others keep raising objections without trying to think through their positions.

It's not as though the Halting Problem is on the Millennium Prize Problem list, open to contradiction/reconsideration by some future challenge. It's a theorem, not a conjecture.

So did Alan Turing, but ... he wasn't confused. The two are connected.

> And Bend is just claiming to be sound but incomplete

That is not what was said. Here it is:

"Bend – a language that blocks AI mistakes via proof."

That's not possible, and changing what was claimed is not productive.

Any program running in a Turing-complete environment is subject to the Halting Problem. So, given that constraint, your example program cannot be relied on to do any specific thing. That's the meaning of the Turing Halting Problem.

https://en.wikipedia.org/wiki/Halting_problem : "Alan Turing proved in 1937 that the halting problem is undecidable, meaning that no general algorithm exists that can correctly solve the problem for all possible program–input pairs."

Focus your attention on the word "undecidable".

> I disagree ...

This is not a topic open to debate, it is a statement of fact. I strongly recommend that you learn this topic, and the topics of mathematics and logic, where some statements can be proven true or false without ambiguity.

The Turing Halting Problem applies to all Turing-complete environments. The program under discussion meets the criterion. AI meets the criterion. Lean meets the criterion.

> There are certainly definitions of non-trivial ...

This is a logical fallacy known as "Logic Chopping" : https://iep.utm.edu/fallacy/#Logic%Chopping

> where this is still considered trivial, but I'm at a loss to what part of Turing's paper gives such a definition.

Yes, I can see that, but that's not what this discussion is about. Read this before posting again: https://en.wikipedia.org/wiki/Halting_problem

Dozens of online articles on this topic, make the same point in the same way. None of them digress into logical fallacies.

> This may be something we cannot come to an agreement on morally ...

"Morally", really? Another logical fallacy, another digression, and not the topic.

This is a simple restatement of the original claim, and it is false. The program being discussed is subject to the Turing Halting Problem. The program being tested, the same. Lean, the prover and the final authority, the same. All are subject to this fundamental limitation.

> It might also be prudent to ask the author if they really mean they interpretation you take

How the original author chose to express himself is not my problem, it is his. I have the simple responsibility to take him at his word. Anything else would be disrespectful.

> What's your definition of "non-trivial" here and how did you derive that definition as the one used by the claim?

I didn't define it, Alan Turing did, in 1936. It's not a debating point, it's a fundamental limitation. All Turing-complete code sources have this limitation. Read more here: https://en.wikipedia.org/wiki/Halting_problem .

The halting problem applies to all systems able to perform Peano arithmetic. Therefore it applies to all non-trivial programs -- the program being tested, the program performing the test, and the program verifying the result.

> The claim and goal is only to approve programs for which the given proof can be shown to work and then accept it when it does ...

Yes, but that's not what's being claimed. My objection was to the original claim, not this restatement.

> ... and the LLM is back at trying to create a program which is feasibly provable.

No non-trivial computer program is "feasibly provable." That's what the Halting Problem makes impossible.

What applies to computer programming also applies to AI, for a reason that should be obvious. Lean, a widely used theorem prover, its everyday description notwithstanding, is Turing-complete and is therefore subject to the Halting Problem as well.

This is not meant to disparage one person's project. It is meant to identify a limit that applies to all such projects.

Jim Cramer's stock market predictions hover slightly above chance, only because of the so-called "Announcement Effect" (in other words, they aren't actually predictions). Without that, his claims would have zero predictive value.

But that's the easiest question to answer -- AI engines don't possess a moral or ethical dimension. They've been programmed and trained to efficiently carry out instructions, not ask questions about why or how. The latter would requires a much more elaborate neural network than today's engines possess.

Here's an example. I recently asked an AI engine to write a program able to generate a list of Riemann Zeta-function critical zeros. I know how to do it, but I wanted to see if the engine could find a more efficient method.

After several failures and restarts, the engine suddenly created a program that produced perfect results, comparable to the best online references. I decided to take a closer look at the code. It turned out the engine had created a cyber-Potemkin Village of multiple functions, but one that concealed a table of the desired values in numeric form, copied from an online source.

The engine wasn't cheating as we understand the term. It knew what the outcome should be and took the most efficient path to that goal. Modern engines aren't obliged to contradict ethical standards and rules of conduct, for the simple reason that they don't understand those things.

We all need to try to imagine a morally bankrupt infant able to solve world-class mathematical and scientific problems, but unable to see how that ability fits into a world beyond its understanding.

But wait -- it get better. Wait until the infant becomes a teenager.

Each of the article's arguments that AI "consciousness" is actually a weak imitation of the "real thing," can with equal justice be applied to people, and the classic Turing Test method to distinguish machines from people has long since lost its authority.

And a future event, one in which AI sprints past humans in its willingness to absorb printed matter (once called "reading") and then put it to use, is ... wait ... umm, never mind, the point I wanted to make is undermined by the fact that this has already happened.

Hard to keep up these days.