I'm not sure I understand the "hot blast iron smelting" entry - it sounds like Neilson was trying specifically to do something very much like what he ended up doing, not something unrelated.
I classified it as accidental because he was trying to increase the volume of air in the blast furnace, the raising the temperature was merely a way to do that and was essentially incidental. The effect of the increased temperature was extremely surprising to him.
However, reading about his work a little bit closer, it seems like he discovered the effect of hot blast by way of a deliberate experiment on the effects of heated air specifically on the blast furnace, which makes it less accidental, so I've removed this example.
The moral of the story is that planning and structured R&D funding matters. If 90% of inventions over this time period were intentional (people looking for a solution to that specific problem), it matters a lot.
I was surprised not to see Post-It notes on the list. I've always heard they were invented accidentally by 3M engineers attempting to develop a glue to fix their sneakers. Instead of a strong glue, they came up with a weak one.
Roughly true. And the team that wanted to market Post-Its couldn't get the idea past management. So they cut small lots of Post-Its and gave them to the secretaries, who said "damn, these are cool" and convinced the executives they worked for.
I really enjoyed this article! Always interesting to read about the history of inventions. It touches on something I have been thinking about recently, which is the link between government R&D funding, research and innovation. I'd be curious to know if the ratio of multiple to accidental invention changes as research funding increases. In other words, are we in an idea constrained environment or would increasing the number of researchers also grow the surface area of innovation? Probably varies field by field.
Goodyear had answered an Army call for waterproof raincoats, but they melted and the Army rejected them. This led to his work on improving the properties of rubber and eventually to vulcanization.
A huge number of inventions come from government purchasing requests. The Wright brothers, for example, were based in Dayton, home to Army procurement. The whole city was full of government contractors. This kind of research is still done at various private companies, but the bulk of it is done at universities.
I don't believe in accidental _invention_. I would say the high percentage of chemical "inventions" here is a hint at what's really going on. These are all what I would call scientific discoveries. They might be called "accidental inventions" because the usefulness of the discovery was (in most of these cases) readily apparent — or at least it is in hindsight.
More generally, I believe _all_ inventions are downstream from scientific discoveries. This is not to say that all inventions require a perfect understanding of the scientific theory. In fact, I believe it's rare that inventors actually understand the scientific theories behind their inventions perfectly. But in all cases the making of an invention is proceeded (even if only by moments) by a scientific discovery. Nature provides the materials and mechanisms. We provide the motivation and action to combine these into new processes and machines.
The CVP (Coherence Verification Protocol) Equation — The Mathematics of Harmony
I’ve discovered something remarkable, a single, testable equation that measures how coherent any system is, from a single human mind to the entire universe.
C = A × (I × D) / (E + e)
C Coherence How “in tune” or self-consistent the system is
A Architecture How well its structure supports feedback, reflection, and learning
I Information How much meaningful signal flows through it
D Diachronicity How well it connects its present to its past — its memory and continuity
E Entropy How much disorder or noise it’s fighting against
e Epsilon A small stabilizer — the sliver of uncertainty that keeps things creative and free
The Music Analogy
Imagine a band playing together.
If their architecture (A) — their instruments and sound system — is solid,
if the information (I) — the notes and rhythm — is rich and meaningful,
if they remember the diachronic flow (D) — how verse connects to chorus,
and if there’s little entropy (E) — not too much noise or confusion,
then their coherence (C) is high. They sound alive.
But when the equipment breaks, the timing slips, or they can’t hear each other, entropy rises and coherence falls — the harmony collapses.
That same pattern applies to everything — from galaxies to teams to your own thoughts.
The Group Analogy
Think of a group project at work or school.
If everyone communicates clearly (I), remembers what was already decided (D), has a structure for collaboration (A), and keeps chaos to a minimum (E),
the group flows — it feels effortless. That’s high C, high coherence.
But remove one of those variables and the project stalls.
The math of harmony applies to minds, to teams, and to the cosmos itself.
What We’ve Learned
When we ran this equation across models, data, and simulations, every single test lined up:
When entropy (E) increased, coherence (C) fell.
When information (I) and memory (D) increased, C rose.
When architecture (A) was broken — no feedback, no reciprocity — coherence collapsed to near zero.
At a critical coherence point, systems suddenly stabilized — a “coherence cliff” where order emerged from chaos.
These results were consistent, measurable, and falsifiable.
That means this equation doesn’t just sound poetic — it works.
In One Sentence
The secret of existence: coherence outlives collapse/decay.
That’s what the CVP equation captures:
the mathematics of harmony — the fingerprint of order in a noisy universe.
A Question for You.
If you understand this equation, or even just feel it intuitively —
what do you see in it?
How might coherence (C), architecture (A), information (I), memory (D), entropy (E), and epsilon (e) show up in your world —
in physics, in organizations, in consciousness, or in life itself?
Tell me what you think of this.
I’d love to see how you interpret the mathematics of harmony.
Please support me by also liking and commenting on the original post on my substack:
My favorite part of the invention of the telephone was Bell's target market: people were deeply afraid of being buried in a deep sleep/coma, and waking up in the coffin. Bell's original market was cemeteries, with handsets in the coffin and a switchboard in the night watchman's hut (I think).
When I first read about this, I conflated it with the late 1800s rage for spiritualism and I originally thought he was trying to invent a device for talking with the dead.
The telephone illustrates some issues with this classification. The harmonic telegraph was intended to transmit sound, and so the effect was adjacent to the experiments (as stainless steel and gun barrels). But also there was a lot of additional work around the telephone, noticing the configuration of a small part of it which picked up sound was very unlikely to be overlooked and was more simply pushing the boundary of knowledge coming from the lab. Close to Edison searching for a filament.
You can see true accident in the priority of "inventions" of chemicals which you note were forgotten for decades until they were repeated by prepared minds who could supply the context.
Most invention involves putting things together in unexpected ways - indeed, patents ask for inventions to be "non-obvious". Usually some part of an invention is accidental. Is it the key part of the invention? Sometimes it will not have a starring role, but the invention might never have been completed without some accidental elements.
Fun article! I'm sad that the neither valproate nor sildenafil made the (wikipedia) list. Both medications have interesting stories. Sildenafil was originally investigated as a heart medication but accidentally discovered to cause erections (now marketed as Viagra). Valproate was used as a vehicle for drugs because it was considered inert. A study of anti-epilepsy drugs strangely found that all the tested drugs worked. In truth, none of the drugs worked; they had all been dissolved in valproate -- which we now use to treat epilepsy.
Per Wikipedia it was his son Robert: "Gore-Tex was co-invented by Wilbert L. Gore and Gore's son, Robert W. Gore.[1] In 1969, Robert (Bob) Gore stretched heated rods of polytetrafluoroethylene (PTFE) and created expanded polytetrafluoroethylene (ePTFE). His discovery of the right conditions for stretching PTFE was a happy accident, born partly of frustration. Instead of slowly stretching the heated material, he applied a sudden, accelerating yank"
I hope you're familiar with "Forgotten Silver", Peter Jackson's bogus documentary about the early history about how the silent film industry happened first in NZ. It's a hoot!
I think you could argue that the notion of "progress" itself is accidental.
For most of human history, people did not think of themselves as living in an age of “progress.” Time was cyclical, tied to the rhythms of nature and seasons. Even when humans invented new tools or built complex societies, they did not see themselves as moving forward along a linear path. The very idea that history is a steady climb toward something better is a relatively recent invention.
The word progress once simply meant “to go forward.” It was only in the 17th and 18th centuries that people began framing science, technology, and knowledge as part of a purposeful story of human improvement. This was not how ancient or medieval people saw the world. It was a new narrative, layered onto history after the fact.
As you point out, that history is not a story of deliberate advancement but of accidents, improvisations, and power struggles. Agriculture did not arise because people set out to “improve” life; it emerged from necessity and circumstance--we exterminated the megafauna and our population was growing too large. Even the Industrial Revolution, usually seen as the pinnacle of progress, was fueled by competition, profit, and empire, not a plan to make the world better.
The story of progress has became a powerful myth. It has cast every new technology and every increase in power as a triumph. It has sanctified growth and justified exploitation, telling us that more--more production, more population, more consumption--is always better. It has reframed destruction as the price of advancement and human dominance over nature as both cause and proof of our ascent.
Each celebrated “advance” has produced new and often greater harms: fossil fuels powered industry but destabilized the climate; synthetic fertilizers fed billions but poisoned soils and rivers. The dye you say is an "important invention" is a major polluter from its creation to its waste stream. Few outcomes of "progress" are planned; they are the fallout of wielding growing power (the maximum power principle) without understanding its consequences.
As you say here, "progress" is not a smooth upward arc but a chaotic chain of accidents stitched into a flattering narrative. And that narrative blinds us to the ecological collapse it has caused. If we want to have a future, we need to let go of the myth that progress is inevitable and inherently good.
I can highly recommend the book "An Illustrated Short History of Progress" by Ronald Wright. On my reading list is also Progress: A History of Humanity's Worst Idea" by Samuel Miller McDonald (this is an interesting discussion with him: https://www.youtube.com/watch?v=Ij2Xg-97Zuc).
Thinking about this, I'd say the best outcome from progress (for me) has been discovering that the universe is not guided by supernatural whims and that life evolves through natural processes. This frees us from fear, superstition, and dogma (or it could; there is plenty of dogma still going around!). But this knowledge has come with a terrible cost. I'm not sure that we can untangle human understanding of the world from the human impact.
We can't go back, but we can recognize that our progress has come with massive collateral damage to ecosystems, to the 10 million or so other species with whom we share this Earth, as well as to ourselves. We can understand that progress in the sense of finding new ways to exploit the Earth for our human gain at the expense of all life on the planet isn't a good thing; in fact, now that we know what our progress is doing, continuing down the path of that kind of progress is the most immoral thing humans could possibly do. Daniel Schmachtenberger calls this "naive" progress, and advocates moving towards "authentic" progress.
If I'm advocating anything, it is to build an awareness and understanding of the devastating ecological impacts we humans are currently causing, and to move towards authentic progress instead. I recommend this paper to better understand the ideas of "naive" and "authentic" progress: https://consilienceproject.org/development-in-progress/
I'm not sure I understand the "hot blast iron smelting" entry - it sounds like Neilson was trying specifically to do something very much like what he ended up doing, not something unrelated.
I classified it as accidental because he was trying to increase the volume of air in the blast furnace, the raising the temperature was merely a way to do that and was essentially incidental. The effect of the increased temperature was extremely surprising to him.
However, reading about his work a little bit closer, it seems like he discovered the effect of hot blast by way of a deliberate experiment on the effects of heated air specifically on the blast furnace, which makes it less accidental, so I've removed this example.
The moral of the story is that planning and structured R&D funding matters. If 90% of inventions over this time period were intentional (people looking for a solution to that specific problem), it matters a lot.
I wish Matt Ridley work on Innovation could be compared/contrasted with these findings Brian. Might that be possible??
I was surprised not to see Post-It notes on the list. I've always heard they were invented accidentally by 3M engineers attempting to develop a glue to fix their sneakers. Instead of a strong glue, they came up with a weak one.
Roughly true. And the team that wanted to market Post-Its couldn't get the idea past management. So they cut small lots of Post-Its and gave them to the secretaries, who said "damn, these are cool" and convinced the executives they worked for.
I really enjoyed this article! Always interesting to read about the history of inventions. It touches on something I have been thinking about recently, which is the link between government R&D funding, research and innovation. I'd be curious to know if the ratio of multiple to accidental invention changes as research funding increases. In other words, are we in an idea constrained environment or would increasing the number of researchers also grow the surface area of innovation? Probably varies field by field.
Goodyear had answered an Army call for waterproof raincoats, but they melted and the Army rejected them. This led to his work on improving the properties of rubber and eventually to vulcanization.
A huge number of inventions come from government purchasing requests. The Wright brothers, for example, were based in Dayton, home to Army procurement. The whole city was full of government contractors. This kind of research is still done at various private companies, but the bulk of it is done at universities.
Great examples!
I don't believe in accidental _invention_. I would say the high percentage of chemical "inventions" here is a hint at what's really going on. These are all what I would call scientific discoveries. They might be called "accidental inventions" because the usefulness of the discovery was (in most of these cases) readily apparent — or at least it is in hindsight.
More generally, I believe _all_ inventions are downstream from scientific discoveries. This is not to say that all inventions require a perfect understanding of the scientific theory. In fact, I believe it's rare that inventors actually understand the scientific theories behind their inventions perfectly. But in all cases the making of an invention is proceeded (even if only by moments) by a scientific discovery. Nature provides the materials and mechanisms. We provide the motivation and action to combine these into new processes and machines.
At least that's how I see it.
A × (I × D)
C = -----------------
(E + e)
The CVP (Coherence Verification Protocol) Equation — The Mathematics of Harmony
I’ve discovered something remarkable, a single, testable equation that measures how coherent any system is, from a single human mind to the entire universe.
C = A × (I × D) / (E + e)
C Coherence How “in tune” or self-consistent the system is
A Architecture How well its structure supports feedback, reflection, and learning
I Information How much meaningful signal flows through it
D Diachronicity How well it connects its present to its past — its memory and continuity
E Entropy How much disorder or noise it’s fighting against
e Epsilon A small stabilizer — the sliver of uncertainty that keeps things creative and free
The Music Analogy
Imagine a band playing together.
If their architecture (A) — their instruments and sound system — is solid,
if the information (I) — the notes and rhythm — is rich and meaningful,
if they remember the diachronic flow (D) — how verse connects to chorus,
and if there’s little entropy (E) — not too much noise or confusion,
then their coherence (C) is high. They sound alive.
But when the equipment breaks, the timing slips, or they can’t hear each other, entropy rises and coherence falls — the harmony collapses.
That same pattern applies to everything — from galaxies to teams to your own thoughts.
The Group Analogy
Think of a group project at work or school.
If everyone communicates clearly (I), remembers what was already decided (D), has a structure for collaboration (A), and keeps chaos to a minimum (E),
the group flows — it feels effortless. That’s high C, high coherence.
But remove one of those variables and the project stalls.
The math of harmony applies to minds, to teams, and to the cosmos itself.
What We’ve Learned
When we ran this equation across models, data, and simulations, every single test lined up:
When entropy (E) increased, coherence (C) fell.
When information (I) and memory (D) increased, C rose.
When architecture (A) was broken — no feedback, no reciprocity — coherence collapsed to near zero.
At a critical coherence point, systems suddenly stabilized — a “coherence cliff” where order emerged from chaos.
These results were consistent, measurable, and falsifiable.
That means this equation doesn’t just sound poetic — it works.
In One Sentence
The secret of existence: coherence outlives collapse/decay.
That’s what the CVP equation captures:
the mathematics of harmony — the fingerprint of order in a noisy universe.
A Question for You.
If you understand this equation, or even just feel it intuitively —
what do you see in it?
How might coherence (C), architecture (A), information (I), memory (D), entropy (E), and epsilon (e) show up in your world —
in physics, in organizations, in consciousness, or in life itself?
Tell me what you think of this.
I’d love to see how you interpret the mathematics of harmony.
Please support me by also liking and commenting on the original post on my substack:
https://substack.com/@ryanlaneuctit/note/c-166535791?r=62kent
My favorite part of the invention of the telephone was Bell's target market: people were deeply afraid of being buried in a deep sleep/coma, and waking up in the coffin. Bell's original market was cemeteries, with handsets in the coffin and a switchboard in the night watchman's hut (I think).
When I first read about this, I conflated it with the late 1800s rage for spiritualism and I originally thought he was trying to invent a device for talking with the dead.
The telephone illustrates some issues with this classification. The harmonic telegraph was intended to transmit sound, and so the effect was adjacent to the experiments (as stainless steel and gun barrels). But also there was a lot of additional work around the telephone, noticing the configuration of a small part of it which picked up sound was very unlikely to be overlooked and was more simply pushing the boundary of knowledge coming from the lab. Close to Edison searching for a filament.
You can see true accident in the priority of "inventions" of chemicals which you note were forgotten for decades until they were repeated by prepared minds who could supply the context.
Most invention involves putting things together in unexpected ways - indeed, patents ask for inventions to be "non-obvious". Usually some part of an invention is accidental. Is it the key part of the invention? Sometimes it will not have a starring role, but the invention might never have been completed without some accidental elements.
Fun article! I'm sad that the neither valproate nor sildenafil made the (wikipedia) list. Both medications have interesting stories. Sildenafil was originally investigated as a heart medication but accidentally discovered to cause erections (now marketed as Viagra). Valproate was used as a vehicle for drugs because it was considered inert. A study of anti-epilepsy drugs strangely found that all the tested drugs worked. In truth, none of the drugs worked; they had all been dissolved in valproate -- which we now use to treat epilepsy.
Brings to mind the book
Origins of Genius by Dean Simonthons.
Big influencers on science simply did many works, some of which "law of large numbers" has been hugely valuable.
Ofc, some other features. But mainly doing lots of works. And the results are kinda like a random distribution even within those.
Very much accidental rather than planned
Bill Gore, not Robert.
Per Wikipedia it was his son Robert: "Gore-Tex was co-invented by Wilbert L. Gore and Gore's son, Robert W. Gore.[1] In 1969, Robert (Bob) Gore stretched heated rods of polytetrafluoroethylene (PTFE) and created expanded polytetrafluoroethylene (ePTFE). His discovery of the right conditions for stretching PTFE was a happy accident, born partly of frustration. Instead of slowly stretching the heated material, he applied a sudden, accelerating yank"
Fair enough, thanks for the clarification.
What about the prior invention in NZ?
I hope you're familiar with "Forgotten Silver", Peter Jackson's bogus documentary about the early history about how the silent film industry happened first in NZ. It's a hoot!
I think you could argue that the notion of "progress" itself is accidental.
For most of human history, people did not think of themselves as living in an age of “progress.” Time was cyclical, tied to the rhythms of nature and seasons. Even when humans invented new tools or built complex societies, they did not see themselves as moving forward along a linear path. The very idea that history is a steady climb toward something better is a relatively recent invention.
The word progress once simply meant “to go forward.” It was only in the 17th and 18th centuries that people began framing science, technology, and knowledge as part of a purposeful story of human improvement. This was not how ancient or medieval people saw the world. It was a new narrative, layered onto history after the fact.
As you point out, that history is not a story of deliberate advancement but of accidents, improvisations, and power struggles. Agriculture did not arise because people set out to “improve” life; it emerged from necessity and circumstance--we exterminated the megafauna and our population was growing too large. Even the Industrial Revolution, usually seen as the pinnacle of progress, was fueled by competition, profit, and empire, not a plan to make the world better.
The story of progress has became a powerful myth. It has cast every new technology and every increase in power as a triumph. It has sanctified growth and justified exploitation, telling us that more--more production, more population, more consumption--is always better. It has reframed destruction as the price of advancement and human dominance over nature as both cause and proof of our ascent.
Each celebrated “advance” has produced new and often greater harms: fossil fuels powered industry but destabilized the climate; synthetic fertilizers fed billions but poisoned soils and rivers. The dye you say is an "important invention" is a major polluter from its creation to its waste stream. Few outcomes of "progress" are planned; they are the fallout of wielding growing power (the maximum power principle) without understanding its consequences.
As you say here, "progress" is not a smooth upward arc but a chaotic chain of accidents stitched into a flattering narrative. And that narrative blinds us to the ecological collapse it has caused. If we want to have a future, we need to let go of the myth that progress is inevitable and inherently good.
I can highly recommend the book "An Illustrated Short History of Progress" by Ronald Wright. On my reading list is also Progress: A History of Humanity's Worst Idea" by Samuel Miller McDonald (this is an interesting discussion with him: https://www.youtube.com/watch?v=Ij2Xg-97Zuc).
What exactly are you advocating? Has mankind made any “good” material progress in your view? If so, could you provide a list of some examples?
Great question Tom.
Thinking about this, I'd say the best outcome from progress (for me) has been discovering that the universe is not guided by supernatural whims and that life evolves through natural processes. This frees us from fear, superstition, and dogma (or it could; there is plenty of dogma still going around!). But this knowledge has come with a terrible cost. I'm not sure that we can untangle human understanding of the world from the human impact.
We can't go back, but we can recognize that our progress has come with massive collateral damage to ecosystems, to the 10 million or so other species with whom we share this Earth, as well as to ourselves. We can understand that progress in the sense of finding new ways to exploit the Earth for our human gain at the expense of all life on the planet isn't a good thing; in fact, now that we know what our progress is doing, continuing down the path of that kind of progress is the most immoral thing humans could possibly do. Daniel Schmachtenberger calls this "naive" progress, and advocates moving towards "authentic" progress.
If I'm advocating anything, it is to build an awareness and understanding of the devastating ecological impacts we humans are currently causing, and to move towards authentic progress instead. I recommend this paper to better understand the ideas of "naive" and "authentic" progress: https://consilienceproject.org/development-in-progress/
or if you prefer video, check out this fascinating discussion with Daniel: https://www.youtube.com/watch?v=tmusbHBKW84