Great show if you can find it. Another show, Connections, is much more popular, and traces the family tree of various inventions. Again, highly recommended!
I miss all those relatively unflashy science programmes. They all have to be a bit over the top and made into rather showy but shallow “event” TV, probably featuring Brian Cox on a mountain or in a desert for some reason.
I'd bet economics. There are magic $/experiment thresholds where it becomes possible for scientists to try something, and one the threshold is crossed a bunch of people explore the same area at the same time.
Take neural nets. FLOPS/$ crosses some magic number so that universities can afford the hardware, and bam; AI everywhere. No obvious theoretical breakthroughs since the 70s, but suddenly the field gets intense due to economics.
The discovery of blackholes was not done by any kind of experiment. Leibniz and Newton's invention of calculus was likewise not a matter of experiment.
Evolution is more debatable, it seems that Darwin's voyages of discovery were certainly an important part of his thinking. Still, it happened ~200 years after European ocean expeditions really started taking off, so doesn't seem like it was cutting edge experimentation.
The evolution of ideas seems like a much more plausible explanation.
I visited the Whipple Museum of the History of Science in Cambridge last month; from their display, I think Darwin and Wallace were limited by the instruments rather than their transportation. Microscopes were very expensive back then, and Darwin at least felt he had to prove his worth as a scientist using his microscope before being taken seriously about anything else.
It wasn’t microscopes so much as detailed and thoughtful observation of macro phenomena—fossil and living specimens from around the world—that sparked the theory of speciation from natural selection. That is, it was noting the morphological, as opposed to cellular, differences and similarities among closely related species—and realizing that environmental factors drove them—that led to understanding.
Microscopes were invented in the 1600s and cell biology as a discipline began soon after. But the dynamics of speciation were perhaps too grand to have been noted in the minutiae of slides.
And it would not be for almost another century after Darwin till we understood that the mechanics of evolution were driven by random mutations of DNA.
Newton's discovery clearly was a matter of experiment. We don't call them "Newton's Laws" because the person who discovered them liked Newton. The man was a physicist. He was interested in problems like mapping the motion of things like planets. That sort of hobby requires a certain amount of data to be gathered.
Leibniz I'm not sure about, but given the timing? There was definitely a lot of interest in basic physics at the time and I bet that was related to his interests, somehow. It isn't a hard set of coincidences to imagine. That was all being fueled by improvements in measuring technology.
Evolution of ideas is plausible, but it suggests a remarkably homogeneous intellectual environment in a time where communication was expensive. Economic forces are a lot more likely to me, they scale. What we see in maths is usually one genius can discover a huge amount of stuff very quickly, they don't need to wait for other people to have ideas for them. They just need a little push in what to direct their attention to.
Lots of physics experiments are actually thought experiments, they don't require money. The motions of the planets and stars had been largely mapped for more than 50 years or more by the time Newton came up with his novel mathematical description of them.
> Evolution of ideas is plausible, but it suggests a remarkably homogeneous intellectual environment in a time where communication was expensive.
Science doesn't often advance alone, it requires communication between scientists. And that same communication spreads ideas among those scientists, until they build a common understanding.
> Lots of physics experiments are actually thought experiments
It is impossible to do physics by thought experiments. There are an infinite number of logically consistent mathematical models of universes out there, only a small subset of them match up reasonably well to the one we exist in. Science requires experiment. It doesn't have to be the same person doing the experimenter and interpreting the results, true enough, but the interpreter is still bottlenecked by data collection.
> Science doesn't often advance alone, it requires communication between scientists
No it doesn't. The whole point of this thread is that science often advances in parallel with no communication between scientists. Once the raw data has been collected - which is an economic issue - or conditions arise where a new problem needs to be solved - also economics - then it is a relatively short matter of time until someone comes up with a compelling theory. One very bright scientist can often exhaust a big chunk of what can be deduced from the currently collected data. And the implication of this is every time there is an economic advance in the cost of data collection there will be a big boom in scientific understanding.
People rediscover calculus to this day, every so often we all get a laugh because some very bright doctor figures out he can sum rectangles under a curve. The only limiting factor is whether people realise that they need to describe curves, areas and tangents precisely.
> The whole point of this thread is that science often advances in parallel with no communication between scientists.
I can only suppose that you are taking 'communication' to mean only direct communication via face-to face conversation or the exchange of letters, but communication is a transitive operation, and, in fact, your thesis is tacitly predicated on this leading to the dissemination of knowledge. The more I learn about the actual history of science (as opposed to 'scientific genius' hagiography) the clearer this becomes.
If you are looking for an economic perspective on this, the emergence of the infrastructure of academic publication would be a good place to start.
> It is impossible to do physics by thought experiments.
Thought experiments are an important tool used by many brilliant physicists when it is not possible to carry an actual experiment yet. Their usefulness is in the opposite of what you say: sure, they can't prove a teory correct, but they can point out potential problems by finding contradictions. As an example, here you can find a famous and very important thought experiment in the field of thermodynamics: https://en.m.wikipedia.org/wiki/Maxwell%27s_demon
>It is impossible to do physics by thought experiments. There are an infinite number of logically consistent mathematical models of universes out there, only a small subset of them match up reasonably well to the one we exist in.
Strongly disagree. The mathematical universes are heavily ordered by their simplicity and logical consistency and you can sort through them with thought alone.
Also, anyway, the act of 'doing physics' includes a lot more than the somewhat small category of 'testing hypotheses with experiment'. It's like 95% model building and 5% experiment.
Sure, but for the vast majority of physical theories before electrodynamics, our senses plus a few ancient instruments (meter sticks, hourglass, scales) were plenty enough. Galileo's relativity principle and his observation that all objects fall at the same rate in a vacuum were based on thought experiments and physical intuition, not actual experiment (apparently, he did try later to actually perform the experiment, but I think it didn't really work).
> The whole point of this thread is that science often advances in parallel with no communication between scientists. Once the raw data has been collected - which is an economic issue - or conditions arise where a new problem needs to be solved - also economics - then it is a relatively short matter of time until someone comes up with a compelling theory.
Sure, people can discover things in isolation. But science only advances when others learn of those things and can build upon them. Neither Newton nor Galileo nor the person in the article invented all of their theories from first principles - they were building on lots of thought and ideas that they had learned from other scientists.
> People rediscover calculus to this day, every so often we all get a laugh because some very bright doctor figures out he can sum rectangles under a curve.
Actually, calculating surface areas in this way is very very old - according to this Science article [0], it was already in use around 50 BCE. So it's not actually surprising that it has been rediscovered independently. I don't think much of Newton's work has been, apart from Leibniz (though that might also be because it's been so widely disseminated afterwards).
Johannes Kepler was effectively Newton’s experimentalist. His detailed observations of the planetary orbits led him to formulate equations of motion that Newton later explained as the dynamics of force, mass, acceleration, etc.
nonetheless, most major advances require the invention of a new measuring device _before_ the ideas become real, this has largely been based
on economic development.
You can pretend the world is filled with tiny creatures all day long, but until you can see them with a microscope, it’s just an imaginative idea, not science.
That is true today, but the majority of physical theories up to, say, Maxwell or so could have been discovered and verified with nothing more complex than your eyes, a well-measured distance and a decent hourglass. And they were discovered with that + the early telescopes, nothing more complex than that.
Do you have a citation for that? It is undergrad level maths and I struggle to believe the technique is news to the AI people. The mathematicians would have known about it in theory for centuries.
1) Schmidhuber does NOT claim to have invented it. He even provides lots of really old references. You know it's old when he didn't invent it, at least in his own mind.
2) even with his generous attributions, "the first application of backpropagation to neural networks" is from 1980.
3) "LeCun et al. (1989) applied backpropagation to Fukushima’s convolutional architecture (1979)".
In other words, the chain rule is really old but figuring out how to use that to adjust weights in neural nets was surprisingly unobvious. It was even more unobvious that that was a good way of adjusting weights.
I've glanced through that material, and I still think it is all obvious. It just wouldn't have worked any earlier than when the results started coming out. If they'd tried these techniques in the 50s it'd have been computationally impossible. If they try them in 2020 they're computationally trivial.
These results would have all started to happen at about the time the cost of computation was within reach of the researcher's budgets. The "theoretical" breakthroughs are of the form "we can implement this technique from the 60s and get good results". Which is impressive, but it does not represent breakthroughs of knowledge as much as incremental improvements in hardware crossing key thresholds. The breakthrough is detecting that hardware can make something work now.
It seems to me that we had to wait until decent memory sizes and decent fp performance was a lot cheaper and therefore much more accessible => much easier to do experiments without having to justify them to higher-ups => somebody figured out 1) how to do backpropagation on neural nets and 2) that it was useful.
In other words, it wasn't obvious at all. It required experimentation.
It would have been practically useful from the 60's (for small neural nets and high-value problems) and 70's (not so small neural nets or lower-value problems) if somebody had figured out how to do it and that it was a useful thing to do.
We might note that it wouldn't have been useful if it was discovered much earlier. There is a minimum amount of computation required to get good results out of neural nets that we've only been crossing relatively recently. From some perspectives the technique could be argued as the most computationally intensive approach to problem solving humans have employed to date.
Somewhat related: I just read a history of England where it was stated that country parsons had a very, very good living and not much work to do, up until 1850 or so, and many of them devoted their energies to all sorts of useful projects.
Also music. Antonio Vivaldi was a priest, but had a special dispensation that excused him from most of the required duties. Gave him a lot of time to compose music.
Very different as Vivaldi was an Italian (and presumably a Catholic priest) and he would have needed the special dispensation form his duties.
What was specific to the Anglican church in England at the time was that because of the control of the church by the state and the aristocracy it was possible for people with the right connections to be just handed the job with little requirement to do it. IIRC they could even pay curate to do the actual work.
Thank you, my comment was intended to apply specifically to the Church of England. Any community that wanted a church was required to set aside farmland whose produce would be used to fund it, and the people had to donate their labor to work the land.
So the English church had a rather unique arrangement where each parish had a source of funds independent of central government or church bureaucracy. That was the attraction of the job for intellectuals. As long as you kept your head down and didn't screw up big time, you were left alone.
Bill Bryson’s a short history of the world is very good on this.
Yes Parsons had a class-based sinecure and several of them made huge contributions to science and society. But the vast majority did or achieved nothing and were a drain on resources.
The first wave of globalisation- caused largely by the US ice trade - where taking ice from lakes meant refrigerated train carriages and ice warehouses in Chicago and new York, and refrigerated ships crossing the Atlantic. Suddenly small farms in England, France and Vermont were competing with Iowa corn fields.
There was a 1870s collapse in food prices and the subsequent collapse in social structures - we simply could not afford to keep indolent parsons, and now their “parsonages” are prized second homes
You make it sound as though the pastoral and spiritual care of their congregations was worthless. In a world where belief in God was widespread and living conditions tough, the value of a parson was not just in their scientific or artistic contributions.
But most barely did that. Of course there were good spiritual leaders, but imagine you went to every US Ivy League college, took all the trust fund students for the next decade and replaced all the priests in all American churches with those trust funded students.
Would they have a sense of mission - or would they feel entitled and frustrated at the same time? Some would do well of course. But without training, without a calling, it’s not great.
That’s the situation - the social elite of a nation simply sat as mid level church managers.
We assume Woodforde (the parson in mid 18 early 19 century England is fairly representative. Yes weddings christenings and burials but mostly … nothing much beyond weather and food.
Did he support a new school, improve the unionisation of the farm workers, yadadada
Society grows or stagnates. Having the elite supported by the majority of workers and then just sitting back and stagnating seems … worthless.
How many of us are pushing in the right direction - that history will look back in two centuries and say “good”
Of all the worthless things one can do, picking out one aspect of society 150 years ago and critiquing it by modern standards has to rank at the very top.
> Parsons had a class-based sinecure and several of them made huge contributions to science and society. But the vast majority did or achieved nothing and were a drain on resources
The people who would have been paying a tithe[1] to their local church presumably. In the UK there was this thing where the second son of some rich family would typically go into the church (because the first son was going to inherit and there were only so many occupations that were respectable for a rich person to do - any kind of actual work not really being among them).
[1] Percentage of earnings, canonically a tenth, but not sure whether/how much that was always the case.
That somehow or other is hiding huge and important details - an area of active historical research / speculation.
Personally I put the birth of the Industrial Revolution up
There in the top five moments of human history something like
Fire
Domestication of wheat
Wheel
Cortez meeting Montezuma
Industrial Revolution in Northern England of all
Places
Whatever it was it happened once. And we have copied it not replicated it (look at Meiji restoration with emperors wearing bowler hats “just in case it helps”.)
We cannot get off this train, so we really need to know how the train works
> Michell was also the first to apply the new mathematics of statistics to astronomy. By studying how the stars are distributed on the sky, he showed that many more stars appear as pairs or groups than could be accounted for by random alignments. He argued that these were real systems of double or multiple stars bound together by their mutual gravity. This was the first evidence for the existence of physical associations of stars.
What is our modern understanding of this? Are there kinds of local clusters you could detect with the naked eye?
This mindfuck struck me too. Could a physicist speak to this? Is a black-hole universe a theoretical possibility because it’s a valid solution, say, of the Einstein field equations? Or is it a possibility simply because it’s not falsifiable?
I believe Penrose and Hawking both like this idea, or rather the idea that black holes spawned "baby universes" [1].
Something is falsifiable if you can think up some empirical test that would refute it. That test doesn't need to be feasible. In the case of black hole universes, such a theory may be falsifiable, but we don't know enough about the composition of black holes to even formulate the tests. I'm not a physicist, but my impression is that falsifiability is less important to physics than the ability for a hypothesis to predict and explain observed phenomena.
I don’t think it’s possible to say. Our current definitions of spacetime is limited to what is in the observable universe. What’s on the other side could be a whole different universe with similar spacetime. Or it could be an infinite void. Or it could literally not exist. Or it could be a vast sea of cream cheese. We don’t know, and according to our current understanding of physics, it is impossible for us to ever know.
Edit: not a physicist by the way, would also love someone who actually knows what they’re talking about to butt in.
You're probably joking, but in case not, I would point out that black holes evaporate quickly at small scales, and cannot be smaller than the Planck length.
One of my pet peeves is this vague idea about the universe being an infinite fractal, universes inside atoms, etc. It's an appealing idea, but it's totally inconsistent with quantum mechanics and the difference between the strength of forces on different length scales.
This is one of those ideas that is so wrong that it is right:
> He reasoned that such particles, emerging from the surface of a star, would have their speed reduced by the star’s gravitational pull, just like projectiles fired upward from the Earth. By measuring the reduction in the speed of the light from a given star, he thought it might be possible to calculate the star’s mass.
>Michell asked himself how large this effect could be. He knew that any projectile must move faster than a certain critical speed to escape from a star’s gravitational embrace. This “escape velocity“ depends only on the size and mass of the star. What would happen if a star’s gravity were so strong that its escape velocity exceeded the speed of light? Michell realized that the light would have to fall back to the surface.
I wouldn't say that. Yes, it's not exactly our modern understanding, but the core idea is the exact same: stars can get big enough that even light, which is super fast, can't escape them, and that was an entirely novel idea in his time.
I think it's more that the effective idea is the same, while the core idea is what is so vastly different. He was arguing as if light was affected by gravity. This is totally missing the rather revolutionary idea of general relativity, best explained by John Wheeler: "Spacetime tells matter how to move; matter tells spacetime how to curve".
Can you say more about what's wrong about it? It seems plain right to me, in Newtonian physics, assuming only that light has a speed (which was not at all a crazy thing to think at that point), and historians of cosmology usually agree (source personal communication, so I could be wrong).
Once you know speed of light is the maximum possible speed, you can try to guess what happens when you have enough mass to make escape velocity higher than the speed of light (it is not possible, therefore you can't escape).
I've never liked the "escape velocity >= c" explanation of why you can't get out a black hole. The escape velocity for a body at a given point is the velocity needed to escape from that point ballistically.
If you don't limit yourself to entirely ballistic trajectories you can escape without ever reaching that point's escape velocity.
To explain why nothing, not even things on non-ballistic trajectories, cannot get out of black holes you've got to turn to weird headache inducing general relativity stuff.
You are correct. It's a fortunate coincidence and nothing more.
It's much easier to think of the gradual warping of spacetime around a black hole so that more and more directions are down. East? No, that's really east and down. Left? Nope, you thought you were going left but it is left and down. Less and less "up" is available to you until you are on a knife edge where you can make an orbit (assuming a non-rotating black hole, no angular momentum) around the event horizon with a photon. Beyond that, everything is some flavor of down.
Well, if you go with Newton's explanation for light, it's quite obvious that it can only follow ballistic trajectories.
One would certainly not expect elementary particles to function like rockets.
But yeah, nobody could come with a description of a black hole anything like the modern one before 1900. Anything older is certain to be very different.
That's right. The Earth's escape velocity is just over 11km/s or 4000km/h. If you have a rocket that only has enough force to propel you at say 100km/h away from the earth you can go anywhere you want in the universe - provided you keep applying that force through thrust. If you stop the rocket you will be subject to gravitational force to bring you back (or until the gravitational pull from other bodies of becomes dominant)
Yup. Those in the 1700s who wrote about stars with so much mass that light cannot escape would have known that their calculations only applied to ballistic trajectories. They would have believed that non-ballistic objects such as rockets would be able to escape because all they had was Newtonian physics.
That when mass becomes high enough that light can't escape nothing else can escape either doesn't pop out of the math until you have general relativity.
Newton introduced the corpuscular theory of light, in modern terms saying that light is made of tiny particles. Once you have that, it becomes natural to think that light is probably attracted by gravity just like everything else is.
The wave theory of light came quite a bit later, in Maxwell's time.
It's not a question of enough mass. It's a question of being compact enough. There is no minimum mass for a black hole, but the smaller the mass, the smaller the surface area of the horizon (the 2-sphere that the mass has to collapse inside to form the hole).
> Once you know speed of light is the maximum possible speed
But he didn't postulate this at all. He simply postulated (as per Newton) that light is made of particles with mass, which could thus be affected by gravity. Since they are moving at a finite speed, the light particles would be slowed down by gravity, and eventually completely stopped.
He further proposed, based on this model, that the mass of an object could potentially be determined by determining how much slower the particles were moving.
This doesn't work. Light doesn't really get slowed down by gravity, and you definitely don't have any slow light that was created from stars trillions of miles away.
It's a cool idea, but doesn't work with how light actually propagates.
> No portrait of Michell exists, but he was described as “a little short man, of black complexion, and fat.”
Why are Wikipedia contributors hallucinating the meaning of "black complexion"? Apparently since "black people" were not capable of intelligent thought, "black complexion" means "In this case it means he was sad and melancholy".
Do Wikipedia contributors then think that "fair or white complexion" must mean "happy and high-spirited"?
Or is it because all the black people around in the medieval era were uneducated slaves performing menial tasks? What terminology would be used describe the complexion of people of "black African appearance" if "black complexion" meant "sad and melancholy" people?
Charles II was described as "tall black man" when he was on the run during the civil war. I guess those on the look out for him were supposed to look for a tall, "sad and melancholy" looking man, as though that would be a help in picking him out, forgetting that in the middle of a bloody civil war there would be lot of sad people of all heights, shapes and widths out and about.
I didn't, because we were talking about how the word was used in the 18th century, and at that time the word meant "temperment." Words shift in meaning.
Are you saying that you think that description means the Michell was likely African-American? Or are you just saying that that description refers to a physical trait of being relatively dark-skinned for a Caucasian, instead of a behavioral trait?
I would have parsed that as meaning he behaved in a generally dour way.
Why would Michell have to be African-American? Didn't African-Africans exist in the medieval era?
Since when has the word "description" referred to a person's temperament?
The only time it seems that "complexion" refers to a person temperament is only when if taken literally it refers to a very dark-skinned person or what we call a "black man" in our era, like an African, a Melanesian or a South Asian.
For instance General Monck was described as a "black man" with a sanguine complexion, which should tell you that he was actually a "black man", because sanguine is the reddish-brown, or fawn color that Africans and South Asians exhibit.
Would that mean the "black" used to describe him meant he was sad and melancholy when on the other hand sanguine meant cheerful?
I think you should check the depiction of an English monarch on the frontispiece of Hobbes Leviathan, and also learn about Anton Wilhelm Amo, before concluding that a the term "black complexion" must refer to the temperament of an insightful natural philosopher.
It seems like he had a brain like Einstein but didn't have the means around him at the time to cultivate his ideas. Definitely in the majority I'm sure. Only some are in the right place at the right time.
This seems like a legitimate scientific question. What is the mass of the observable universe, and can light escape it? It's no more pointless than asking what the universe was like at the big bang or what it will be like 10^100 years from now.
George Green, who discovered Greens Theorem, was such a bumpkin. His father was a miller in the unfashionable countryside, and he had a modest education. A mystery of math history is how such a bumpkin was so poorly versed in advanced mathematics (inaccessible to someone far from a university, where such knowledge was confined at that time), discovered such remarkable mathematics that the average engineering undergrad knows his name.
Frankly history is replete with bumpkins making extraordinary discoveries. Being a bumpkin is associated with ignorance, not stupidity. Intelligence is pretty uniformly distributed, even among the black, short, fat, and bumpkins.
Interesting and original scifi plotline: humans encounter hayseed, never-been-to-the-city aliens. Perhaps they 'jacked their spaceship; or maybe they're a bit like The Dukes of Hazzard, using their ship to do handbrake turns, and yelling "yeehaw".
Great show if you can find it. Another show, Connections, is much more popular, and traces the family tree of various inventions. Again, highly recommended!