See Liba Taub’s study in Aetna and the Moon. The material for universal gravitation and inertial orbits is in Plutarch, On the Face that Appears in the Orb of the Moon 6–11 (= Moralia 922f-926b); on other solar systems, see Lucretius, De Rerum Natura 1.1052-1082 and 2.1048-1089.

We learned about the Pre-Socratics in school. Unfortunately I’ve forgotten almost everything. But who knows if what we learned is even true.
I hate that I’m ignorant about this subject. I found one of your YT videos on ancient science https://www.youtube.com/watch?v=Iq_E2R_hvTY&ab_channel=WonderfestScience. I’ll also get your book soon. Thanks!

Aristotle is perhaps the first full scientist; he founded the enterprise of system-wide formalization we now call “science.”

But there were proto-scientists before him, experts in various fields who began discussing methodology and using formal empirical methods to arrive at conclusions, in direct contravention of previous folk/myth methodologies. They were called the “Pre-Socratics,” possibly the first of which was Thales. I have an appendix on this group of “transitional fossils” as it were—half-scientists, half-speculators—in The Scientist in the Early Roman Empire. I otherwise start my history of ancient science with Aristotle and explain why there (Chapter 3).

When I asked if the Greeks were the first scientists, I meant as a formal, method-conscious enterprise (was Aristotle the first scientist?). From my point of view, that’s what makes science, science. It’s defined by its reliance on methodology and a set of principles, such as testability, reproducibility and falsifiability; otherwise the term “science” would be too loose a term and pretty much any enterprise would be considered science, which is counterintuitive.

But thank you for sharing information on this interesting subject with us. This is definitely something I plan to learn more about in the near future.

I was under the impression that back then people were a lot more religious than us. What if we compared today’s West with the ancient West? Would you still say that the percentage is roughly the same?

No. As I said, the percentages have shifted notably toward secularism. Not only among the elite, but especially among the commons. Religiosity in the U.S. is at around 85% (Europe 75%) compared to what would surely have been over 99% in antiquity; because ancient rationalists tended to be religious still, in the same way as our Founding Fathers were in 1776. So there has been change, but as I said, it seems oddly slow a change given that it’s been two thousand years.

Also, would you say that having access to more data makes you more rational?

No. Only access to more tools of rationality makes you more rational. Irrational people can spin whatever they want out of any quantity of data.

Rationality is also not intelligence. Very intelligent people can even be more skilled at being irrational (which is why many high IQ people have totally bonkers conspiracy-theory worldviews). The smarter you are, the better able you are to rationalize any insanity against any evidence.

Information is not knowledge; knowledge is comprehension of the significance of information. Knowledge is not intelligence; intelligence is skill at problem solving (the ability to turn information into knowledge and “use” that knowledge to achieve an objective, which objective need not be in any way rational). Intelligence is not rationality; rationality requires understanding how the brain’s innate reasoning capabilities are flawed and what must be done to correct for them (meaning our brain’s ability to draw inferences in closer alignment to reality; which is more than merely problem solving or information processing). And rationality is not wisdom; one must reliably and consistently apply one’s rationality to all domains of one’s understanding to achieve wisdom (whereas most people only compartmentalize what subjects they apply even their skills of rationality to).

Let’s say Socrates was asked the age of the Universe and he said that he didn’t know the answer, would he be less rational on this issue than a modern commoner who has looked at the evidence and accepted that the Universe is 13.8 billion years old? I think the two are not comparable. I believe Socrates would be rational or in the worst case non rational, but certainly not irrational compared to the modern commoner.

The example has nothing to do with measuring rationality. Admitting ignorance is only one component of a rational mindset, and is no more rational than concurring with the conclusions of sound evidential reasoning. Aristotle advanced reasons to believe the universe is infinitely old. His reasons were relatively sound, and in cosmological terms may be correct: most leading cosmological theories today entail past eternality prior to our local Big Bang event. But there is nothing irrational or nonrational in saying the evidence available to him suggests it is more likely than not the universe is past eternal. By contrast to a then-Jew or Christian insisting the earth is past finite and thus has a definite age “because the Bible says so.” They’d be potentially “correct” (insofar as we meant “universe” to mean only our local verse), but for no rational reason whatever; whereas Aristotle could be wrong, but for a perfectly rational reason.

Archimedes developed a proto-calculous and if it hadn’t been temporarily lost due to Christian negligence, it would have saved Newton time in his development of calculus.

Yes.

The questions of laws of motion and planetary theory are a wholly separate matter (that was also going on back then, also mostly lost, but had little to do with Archimedes; I tell that story more in Scientist).

What Archimedes did sounds so impressive. Would it be accurate to say that science began with the Greeks and Romans?

Science as a formal, method-conscious enterprise, yes. “Science” in the looser sense of “whatever people figured out whenever about whatever” is older than even the human race (e.g. we have evidence folk-nature and craft knowledge begins with Homo habilis if not earlier, probably including astronomical and medical knowledge). It’s important to keep these distinct, if you want to make sure what it is you are explaining or asking about. I discuss what the difference is and why it matters in Scientist.

I would like to learn more about ancient science. Thank you for the book recommendations. Apparently your book is out of stock.

It will always be in stock. Whatever vendor you checked may be out for a moment, but they restock within 24 hours (often in mere hours). Delays are more common now due to the pandemic, but otherwise never significant in duration. Just check back. (Meanwhile, kindle and audible editions are always available, and instantaneously.)

Michio Kaku said that an ancient group of philosophers (and musicians) called the Pythagoreans compared reality to a musical symphony and even suggested that there are other worlds out there. As you know this is how String Theory describes reality. So my question to you is, is there historical evidence that the Pythagoreans predicted the existence of the Multiverse? If the Pythagoreans did believe that there are other worlds out there, how would we know if they weren’t referring to galaxies?

No. Pythagoreans were largely irrationalists, and their only significant contribution to science was in launching harmonics as a formal science (but they made little progress in it; empiricists took up the mantle and advanced the science thereafter). Also much that is “claimed” about them is myth and legend, so I doubt it can be known what if anything they ever really said about “other” worlds.

We have a better read on what the atomists (who were very much anti-Pythagorean) said about this. And from very early on atomist cosmologies routinely argued that stars were distant suns with their own planets and civilizations and that there were probably infinitely many of these. They even proposed some of those worlds contain inhabitants—aliens—of advanced nature and that our impression of the gods arises from a kind of accidental “television” signal our brains pick up from those aliens and then mistake as depicting gods. This is closer to single-universe theory (one universe, with countless other worlds in the straigtforward sense). It has no similarity to string theory or multiverse theory.

I am not aware of any evidence of any ancient belief in multiverse theory. Ancient cosmologies are all universe theories, differing only on how big the universe is, what’s in it, and how it’s arranged. This includes even religious believers (the idea that heaven and hell exist in “other dimensions” and don’t have visible, reachable, physical locations in this universe did not exist in antiquity; that was invented far later).

After reading your reply it dawned on me that in the same comment that I was criticizing the irrationality of modern commoners, I made an irrational claim myself. How embarrassingly ironic. I was under the impression that back then people were a lot more religious than us. What if we compared today’s West with the ancient West? Would you still say that the percentage is roughly the same?

Also, would you say that having access to more data makes you more rational? I would argue that it doesn’t. Rationality means that you are basing your beliefs on evidence. If you don’t have access to the data that would support or refute a certain claim, and you don’t accept that the claim is true, then you are not being irrational. Right? Let’s say Socrates was asked the age of the Universe and he said that he didn’t know the answer, would he be less rational on this issue than a modern commoner who has looked at the evidence and accepted that the Universe is 13.8 billion years old? I think the two are not comparable. I believe Socrates would be rational or in the worst case non rational, but certainly not irrational compared to the modern commoner.

Regarding Archimedes, thank you for the information. You’re right, I meant to say Principia. So basically, Archimedes developed a proto-calculous and if it hadn’t been temporary lost due to Christian negligence, it would have saved Newton time in his development of calculous. What Archimedes did sounds so impressive. Would it be accurate to say that science began with the Greeks and Romans? I would like to learn more about ancient science. Thank you for the book recommendations. Apparently your book is out of stock.

I would like to ask one more question but if you are limited with time feel free to ignore it. In another documentary on the multiverse Michio Kaku said that an ancient group of philosophers (and musicians) called the Pythagoreans compared reality to a musical symphony and even suggested that there are other worlds out there. As you know this is how String Theory describes reality. So my question to you is, is there historical evidence that the Pythagoreans predicted the existence of the Multiverse? If the Pythagoreans did believe that there are other worlds out there, how would we know if they weren’t referring to galaxies?

Well, your first qualifier is apposite: the difference between then and now is the percentage of people who are rational and empirical and not particularly superstitious and religious. That percentage has gone up, enormously. So you can’t really compare ancient elites (in fact, even a subset thereof; plenty were not so rational) with modern commoners. That disguises what has actually changed: more commoners now have access to and achieve elite intellectual capability (by ancient standards).

Nevertheless, that that percentage gain, though considerable, is nevertheless still alarmingly low is due to the fact that humans are apes. Our brains are naturally superstitious and irrational. Rational empiricism and effective critical thinking are artificial software patches we invented in the cultural package we try to install in each generation to override and “fix” their otherwise hopelessly broken biological brains.

And all the gains that has achieved signal that access to education (and its quality and type, and related investment resources, e.g. nutrition, safe home and community environments, etc.) is the determining factor. We have done relatively poorly at that even the last hundred years, much less two thousand. We should be investing many times more of our GNP to education at all levels (and direct that money more wisely). Ironically it is biological irrationality that keeps us from doing that (the vicious circle of irrational people irrationally hoarding wealth rather than investing it in the society they must endure and depend on, thus preventing us from efficiently getting rid of by aging-out-of-service those very same irrational people).

As to your question, I don’t know what you mean by Newton’s “Pancyprian” (there is no treatise by Newton of that name). I assume you meant to type Principia? That would be his treatise advancing the laws of motion and posing their application to planetary theory. It is notable for its development of a system of calculus (i.e. a means of calculating infinite sums), mathematization of the principle of inertia, the proposal and measurement of universal gravitation and its relation to mass and distance, and deriving Kepler’s laws of planetary motion therefrom (which Kepler had deduced empirically, not derived from theory), among a lot else.

This is a bunch of different things. It sounds like you saw something about calculus. Which is just one of those things. Because the Archimedes Codex was indeed a hymnal that was written over a scraped-off collection of otherwise lost scientific and mathematical treatises by Archimedes (an example of the catastrophic disinterest medieval Christians had in science, caused by their inherent anti-empiricism the seeds of which were laid in the ancient period as I document in The Scientist in the Early Roman Empire). And one of those treatises we recovered developed a proto-calculus more or less similar to Newton’s.

It’s important to understand the context of that. Before Archimedes developed that proto-calculus (which was otherwise completely lost; thus Newton had to reinvent the wheel as it were), the only way to “sum” infinite sequences was by the “method of exhaustion” (whereby you keep adding successively small fractions until you have as precise a figure as you need), which was more of a hack than a solution (since you could never actually ascertain the sum, just get as close to it as you wanted and had time for).

Archimedes came up with a means of actually solving the problem (principally in his treatise Method of Mechanical Theorems) by, essentially, using analysis of geometric curves to determine the actual sum of an infinite series. Which is the first step to developing a formal calculus. Archimedes had only just published it, probably before his death. He didn’t get to apply the method in any of his other scientific work. We don’t know if anyone continued where he left off (most ancient mathematics was lost in the Middle Ages, even in extant mentions).

So what Archimedes did is remarkable, impressive, and important. But it wasn’t really a fully developed calculus (though Newton could have built a calculus out of it had he known of it). And this is just a mathematical technique. Archimedes did not “discover” any of the scientific stuff in Newton’s Principia. Ancient scientists did muse about a lot of it (e.g. inertia and universal gravitation were live concepts debated at the time) but we don’t know that anyone developed empirically confirmable scientific laws out of them. The closest we could say is regarding the laws of planetary motion, though that would be Ptolemy centuries later, not Archimedes:

Ptolemy developed a law of planetary motion called “equal angles in equal times” which was very successful in predicting planetary motion. After Kepler over a thousand years later decided to rethink the solar system on a heliocentric basis, he transformed Ptolemy’s “equal angles in equal times” law into an “equal areas in equal times” law based on parabolas (not an alien notion to Ptolemy, e.g. his model for lunar motion—which is, after all, in reality geocentric—used combined motions to trace a parabolic orbit), which drew on another ancient mathematician, Apollonius of Perga (a friend and correspondent of Archimedes), who developed techniques for analyzing and quantifying parabolic sections (which planetary orbits actually are).

But even that, again, is not “the same thing” (equal angles in equal times is not exactly the same as equal areas in equal times, though the one did inspire the other), and wasn’t Archimedes.

Anyway, I have a question for you Richard about a probably historical event. I watched a documentary a while ago that claimed that Archimedes produced a piece of work on the same subject and perhaps on a similar level as Newton’s Pancyprian (I find that hard to believe given that Archimedes lived in antiquity), but unfortunately a Christian scribe scribbled over it, thus ruining our ability to access his full work. Is there any truth to this?

It’s unclear. He doesn’t say he did this or saw anyone do this. He cites it the way any “common knowledge” is cited; and “common knowledge” is often enough hearsay or false.

Because he is responding to the literature, he may simply have gotten this idea from Hipparchus or Strato or others citing them. Since we can’t tell, we can’t claim to know, and consequently we can affirm nothing as to where or how Philopon got this idea.

By contrast, Aristotle describes learned facts that cannot have been known any other way than running the experiment. Unlike Philopon, Aristotle is not commenting on centuries of prior published empirical studies on falling objects. Even prior armchair theorists did not say the things Aristotle is, so he can’t have gotten it from them either. Again, unlike Philopon.