I agree with Sergiu's perspective. AI is a powerful tool that can speed up discovery. It will replace humans at many routine mechanical tasks, but will not be able to discover new paradigms.
"Should measures of intelligence consider other factors than speed, specifically human factors such as the ability to understand the algorithmic, step-by-step, structure of a given task and design a machine that can implement it?"
I've been working intensely with AI to write a program to model a chemical reaction system I am studying. It does very well at writing or modifying the code for specific narrow portions. But it does not have a grasp of the big picture, so many if its modifications are not very efficient and get off track of the larger goal. It still works like a brilliant but dense assistant. But maybe that will change with better models.
Ultimately, since it is modeled on the same hierarchy as the human brain, there is no reason to think it won't ever get to the 'AHA' moments by examining enough variants. The question in my mind is whether it will recognize them.
The trouble I see is that a spiffy Mechanical Turk performing a specific trick causes many people to turn off their critical faculties, and start extrapolating unrealistically.
Some of those are hype/marketing types who sniff their own farts all day and think they don’t stink, but hugely problematic are the consumers of such hype (especially corporate ones), who have bought into the unevidenced idea that the A”I” we have available today is inevitably transformative, and that first movers will fare better than deliberate movers.
And so AI is supporting incredible shoddy decision-making that — shockingly, I know — further entrenches the need to use AI. All the while calling it “progress” and “shareholder value”.
There are several problems, and the most important one is that it conflates three distinct ideas: an event horizon, tidal destruction, and a spacetime singularity. Penrose’s theorem does not say what the passage suggests.
1. Crossing an event horizon does not mean being torn apart
For a sufficiently massive black hole, nothing locally dramatic happens at the event horizon. An infalling observer can cross it without noticing anything special at that moment.
The event horizon is a causal boundary: once inside, no future-directed causal trajectory can reach the exterior universe. That’s the part that makes Vinge’s analogy reasonable: crossing represents a point beyond which return—or communication back—is impossible.
But it is not where gravitational forces become infinite.
In fact, the tidal force at the horizon of a Schwarzschild black hole scales roughly as
\frac{GM}{r_s^3}\propto \frac{1}{M^2},
so larger black holes have weaker tidal forces at their horizons. For a supermassive black hole, you could cross the horizon while experiencing quite modest tidal forces.
2. The singularity is not defined by infinite tidal forces
The sentence
“eventually, but inevitably, be torn apart by infinite tidal, gravitational forces—whence ‘singularity’”
is misleading.
In the classical Schwarzschild solution, tidal curvature does indeed diverge as r\to0. An extended object approaching that region would undergo increasingly extreme tidal deformation—“spaghettification.”
But that’s not fundamentally what physicists mean by a spacetime singularity.
Modern general relativity normally characterizes a singular spacetime by geodesic incompleteness: roughly, there exist freely falling trajectories that simply cannot be continued beyond a finite value of their proper time or affine parameter.
This distinction is important because curvature does not necessarily have to become infinite for a spacetime to be singular in the technical sense.
3. That is not what the Penrose singularity theorem proves
This is the biggest technical error.
The 1965 Penrose singularity theorem does not prove that:
someone crossing a black-hole event horizon will eventually encounter infinite tidal forces.
Very roughly, Penrose proved that if a spacetime satisfying appropriate conditions contains a closed trapped surface, then under suitable causal and energy assumptions, the spacetime must be null-geodesically incomplete.
Symbolically, the conclusion is something like
\text{trapped surface + causal/energy conditions}
\quad\Longrightarrow\quad
\text{geodesic incompleteness}.
It does not establish that curvature becomes infinite. It does not describe an observer being torn apart. And it does not establish the familiar r=0 Schwarzschild singularity specifically.
That generality is precisely part of what made Penrose’s result so profound. Before Penrose, one might suspect that singularities were artifacts of the extreme symmetry of idealized solutions such as Schwarzschild. Penrose showed that gravitational collapse produces singular behavior under remarkably general conditions without assuming spherical symmetry.
4. “Whence singularity” gets the conceptual relationship backwards
The passage seems to suggest:
infinite gravitational/tidal force → singularity → therefore the name “singularity.”
That’s not really right.
A mathematical singularity is, broadly speaking, where the mathematical description ceases to be regular or extendible in the relevant sense. In GR, Penrose’s formulation avoids trying to treat the singularity as an ordinary point of spacetime at which one simply evaluates the gravitational field and gets “infinity.”
Indeed, saying “at the singularity the tidal force is infinite” needs care, because the singularity isn’t generally a point belonging to the spacetime manifold at all. The classical spacetime ends.
5. The observer’s fate is also more nuanced
For the simplest nonrotating Schwarzschild black hole, once someone crosses the horizon, reaching the future singularity in finite proper time is unavoidable.
But saying this universally about “a black hole” is too broad. Rotating Kerr black holes have a much more complicated idealized causal structure, including inner horizons, and realistic interiors involve difficult questions of instability and mass inflation. Penrose’s theorem itself does not tell us the detailed fate of a particular observer after horizon crossing.
6. The Nobel statement is slightly misleading too
Penrose did receive half of the 2020 Nobel Prize in Physics, but the Nobel citation was:
“for the discovery that black hole formation is a robust prediction of the general theory of relativity.”
That recognition centered on his 1965 singularity-theorem work, so connecting the Nobel to the theorem is reasonable. But saying he received the Nobel simply “for the Penrose singularity theorem” isn’t quite the official characterization.
⸻
So I would rewrite the underlying physics something like this:
Vinge’s analogy invokes the event horizon of a black hole: a causal boundary beyond which an observer cannot return or communicate with the exterior universe. Crossing the horizon itself need not involve extreme gravitational forces, particularly for a supermassive black hole. In classical general relativity, gravitational collapse can nevertheless lead to a spacetime singularity. Penrose’s 1965 singularity theorem established, under remarkably general conditions, that the formation of a trapped surface implies geodesic incompleteness—a breakdown of the classical spacetime description—without requiring the special symmetries of earlier black-hole solutions.
And there’s an interesting irony here: Vinge’s metaphor works better if you don’t describe the event horizon as the place where you get destroyed. His point was epistemic/causal: from outside the technological singularity, you cannot reliably extrapolate what lies beyond it. That’s actually rather close to the genuine significance of an event horizon—a boundary on what can causally reach an observer—rather than a boundary at which physics suddenly becomes infinitely violent.
Like Digital Canary, my fear isn't that AI will somehow forcefully replace humans but that humans will too readily cede to AI. To quote the article, "Elsewhere [Poincaré] described having mathematical insights that came suddenly to him, after months of unsuccessful reflections, while he was absorbed in unrelated activities. I don’t think there is a serious working scientist who has not had similar experiences." This is correct. These kinds of flashes of insight cannot be calculated or even predicted. They just happen (and for me, at least, are what I, as a scientist live for--such a rush!). The article comments on a need to redefine intelligence; I think what will be redefined is creativity. People mistake AI's ability to compose a sonnet "in the style of Mozart" as equalling Mozart's brilliance and creativity, but it's not. My fear is that people will become lazy, will cede creativity to AI because it can do these kinds of parlor tricks. But AI will never develop to the point of having those flashes of creativity. Creativity isn't just "creation". It is creation of something so new, so different, that it cannot possibly be arrived at by accident or calculation. I already see a degradation of normal human creativity as children are offered "toys" that are ever more realistic, allowing no room for imagination. Just as sinister, the bean-counting that has overtaken assessment of research productivity. Now, committees count the numbers of papers, not their quality and impact. The busyness required to produce large numbers of papers suppresses the time needed to exercise the kind of creativity Poincaré alluded to: It takes TIME for knowledge to percolate and the brain to wrestle with a problem before the solution presents itself in that precious "aha" moment.
An interviewer once asked Lou Reed where Walk On The Wild Side came from. His response was something like: If I knew, don't you think I'd write one every week?
What I found interesting about this article was that some of the original efforts to measure human intelligence, before the so-called "IQ test", were to record human reaction times.
Obviously machines have a massive advantage over humans in this respect. And they have had this advantage for a very long time at this point.
But anyone who is doing creative work in STEM will quickly realize that as valuable as these devices are as computational aides and managing information, there is something still lacking in what they are able to do. Will we be able to improve this situation in the future?
I agree with Sergiu's perspective. AI is a powerful tool that can speed up discovery. It will replace humans at many routine mechanical tasks, but will not be able to discover new paradigms.
"Should measures of intelligence consider other factors than speed, specifically human factors such as the ability to understand the algorithmic, step-by-step, structure of a given task and design a machine that can implement it?"
I've been working intensely with AI to write a program to model a chemical reaction system I am studying. It does very well at writing or modifying the code for specific narrow portions. But it does not have a grasp of the big picture, so many if its modifications are not very efficient and get off track of the larger goal. It still works like a brilliant but dense assistant. But maybe that will change with better models.
Ultimately, since it is modeled on the same hierarchy as the human brain, there is no reason to think it won't ever get to the 'AHA' moments by examining enough variants. The question in my mind is whether it will recognize them.
The trouble I see is that a spiffy Mechanical Turk performing a specific trick causes many people to turn off their critical faculties, and start extrapolating unrealistically.
Some of those are hype/marketing types who sniff their own farts all day and think they don’t stink, but hugely problematic are the consumers of such hype (especially corporate ones), who have bought into the unevidenced idea that the A”I” we have available today is inevitably transformative, and that first movers will fare better than deliberate movers.
And so AI is supporting incredible shoddy decision-making that — shockingly, I know — further entrenches the need to use AI. All the while calling it “progress” and “shareholder value”.
Yes.
Our amazing, vast, wonderful universe is either the creation of design or of random chance. It can't be the latter. There has to be the Creator.
There are several problems, and the most important one is that it conflates three distinct ideas: an event horizon, tidal destruction, and a spacetime singularity. Penrose’s theorem does not say what the passage suggests.
1. Crossing an event horizon does not mean being torn apart
For a sufficiently massive black hole, nothing locally dramatic happens at the event horizon. An infalling observer can cross it without noticing anything special at that moment.
The event horizon is a causal boundary: once inside, no future-directed causal trajectory can reach the exterior universe. That’s the part that makes Vinge’s analogy reasonable: crossing represents a point beyond which return—or communication back—is impossible.
But it is not where gravitational forces become infinite.
In fact, the tidal force at the horizon of a Schwarzschild black hole scales roughly as
\frac{GM}{r_s^3}\propto \frac{1}{M^2},
so larger black holes have weaker tidal forces at their horizons. For a supermassive black hole, you could cross the horizon while experiencing quite modest tidal forces.
2. The singularity is not defined by infinite tidal forces
The sentence
“eventually, but inevitably, be torn apart by infinite tidal, gravitational forces—whence ‘singularity’”
is misleading.
In the classical Schwarzschild solution, tidal curvature does indeed diverge as r\to0. An extended object approaching that region would undergo increasingly extreme tidal deformation—“spaghettification.”
But that’s not fundamentally what physicists mean by a spacetime singularity.
Modern general relativity normally characterizes a singular spacetime by geodesic incompleteness: roughly, there exist freely falling trajectories that simply cannot be continued beyond a finite value of their proper time or affine parameter.
This distinction is important because curvature does not necessarily have to become infinite for a spacetime to be singular in the technical sense.
3. That is not what the Penrose singularity theorem proves
This is the biggest technical error.
The 1965 Penrose singularity theorem does not prove that:
someone crossing a black-hole event horizon will eventually encounter infinite tidal forces.
Very roughly, Penrose proved that if a spacetime satisfying appropriate conditions contains a closed trapped surface, then under suitable causal and energy assumptions, the spacetime must be null-geodesically incomplete.
Symbolically, the conclusion is something like
\text{trapped surface + causal/energy conditions}
\quad\Longrightarrow\quad
\text{geodesic incompleteness}.
It does not establish that curvature becomes infinite. It does not describe an observer being torn apart. And it does not establish the familiar r=0 Schwarzschild singularity specifically.
That generality is precisely part of what made Penrose’s result so profound. Before Penrose, one might suspect that singularities were artifacts of the extreme symmetry of idealized solutions such as Schwarzschild. Penrose showed that gravitational collapse produces singular behavior under remarkably general conditions without assuming spherical symmetry.
4. “Whence singularity” gets the conceptual relationship backwards
The passage seems to suggest:
infinite gravitational/tidal force → singularity → therefore the name “singularity.”
That’s not really right.
A mathematical singularity is, broadly speaking, where the mathematical description ceases to be regular or extendible in the relevant sense. In GR, Penrose’s formulation avoids trying to treat the singularity as an ordinary point of spacetime at which one simply evaluates the gravitational field and gets “infinity.”
Indeed, saying “at the singularity the tidal force is infinite” needs care, because the singularity isn’t generally a point belonging to the spacetime manifold at all. The classical spacetime ends.
5. The observer’s fate is also more nuanced
For the simplest nonrotating Schwarzschild black hole, once someone crosses the horizon, reaching the future singularity in finite proper time is unavoidable.
But saying this universally about “a black hole” is too broad. Rotating Kerr black holes have a much more complicated idealized causal structure, including inner horizons, and realistic interiors involve difficult questions of instability and mass inflation. Penrose’s theorem itself does not tell us the detailed fate of a particular observer after horizon crossing.
6. The Nobel statement is slightly misleading too
Penrose did receive half of the 2020 Nobel Prize in Physics, but the Nobel citation was:
“for the discovery that black hole formation is a robust prediction of the general theory of relativity.”
That recognition centered on his 1965 singularity-theorem work, so connecting the Nobel to the theorem is reasonable. But saying he received the Nobel simply “for the Penrose singularity theorem” isn’t quite the official characterization.
⸻
So I would rewrite the underlying physics something like this:
Vinge’s analogy invokes the event horizon of a black hole: a causal boundary beyond which an observer cannot return or communicate with the exterior universe. Crossing the horizon itself need not involve extreme gravitational forces, particularly for a supermassive black hole. In classical general relativity, gravitational collapse can nevertheless lead to a spacetime singularity. Penrose’s 1965 singularity theorem established, under remarkably general conditions, that the formation of a trapped surface implies geodesic incompleteness—a breakdown of the classical spacetime description—without requiring the special symmetries of earlier black-hole solutions.
And there’s an interesting irony here: Vinge’s metaphor works better if you don’t describe the event horizon as the place where you get destroyed. His point was epistemic/causal: from outside the technological singularity, you cannot reliably extrapolate what lies beyond it. That’s actually rather close to the genuine significance of an event horizon—a boundary on what can causally reach an observer—rather than a boundary at which physics suddenly becomes infinitely violent.
Like Digital Canary, my fear isn't that AI will somehow forcefully replace humans but that humans will too readily cede to AI. To quote the article, "Elsewhere [Poincaré] described having mathematical insights that came suddenly to him, after months of unsuccessful reflections, while he was absorbed in unrelated activities. I don’t think there is a serious working scientist who has not had similar experiences." This is correct. These kinds of flashes of insight cannot be calculated or even predicted. They just happen (and for me, at least, are what I, as a scientist live for--such a rush!). The article comments on a need to redefine intelligence; I think what will be redefined is creativity. People mistake AI's ability to compose a sonnet "in the style of Mozart" as equalling Mozart's brilliance and creativity, but it's not. My fear is that people will become lazy, will cede creativity to AI because it can do these kinds of parlor tricks. But AI will never develop to the point of having those flashes of creativity. Creativity isn't just "creation". It is creation of something so new, so different, that it cannot possibly be arrived at by accident or calculation. I already see a degradation of normal human creativity as children are offered "toys" that are ever more realistic, allowing no room for imagination. Just as sinister, the bean-counting that has overtaken assessment of research productivity. Now, committees count the numbers of papers, not their quality and impact. The busyness required to produce large numbers of papers suppresses the time needed to exercise the kind of creativity Poincaré alluded to: It takes TIME for knowledge to percolate and the brain to wrestle with a problem before the solution presents itself in that precious "aha" moment.
Creativity.
An interviewer once asked Lou Reed where Walk On The Wild Side came from. His response was something like: If I knew, don't you think I'd write one every week?
Carlos Santana said similar.
What I found interesting about this article was that some of the original efforts to measure human intelligence, before the so-called "IQ test", were to record human reaction times.
Obviously machines have a massive advantage over humans in this respect. And they have had this advantage for a very long time at this point.
But anyone who is doing creative work in STEM will quickly realize that as valuable as these devices are as computational aides and managing information, there is something still lacking in what they are able to do. Will we be able to improve this situation in the future?
Time will tell.
Delighted to see this superb article finally on substack - thank you Sergiu
"Science fails to recognize the single most
Potent element of human existence
Letting the reins go to the unfolding
Is faith, faith, faith, faith" -Serj Tankian, System of a Down