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When did science start?

Archimedes participated in many debates about his findings with contemporaries, indicating that much independent thought was going on at that time.
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While there was certainly a lot of inquiry and experimentation among the Greeks, there was very little systemized investigation as we would know it today. Much of what they did was trial and error, or direct imitation of natural forms and processes. Much of their work was based around pre-existing religious or philosophical principles; and results were often manipulated to fit their expectations, rather than the other way around. What few breakthroughs did exist, existed in isolation, lacking the theoretical foundation to expand on them; and were most often viewed as little more than toys (eg. Hero's steam engine). Some came very close, most notably Aristotle, but his rejection of inductive reasoning in favour of a purely deductive approach limited the ability of his followers to further develop a formalize scientific method.

Agreed but the point I was making that no-one took it any further. It seemed to be an end in itself.

If you define science as the application of the modern scientific method; then you can trace it back to the High Middle Ages. Most of the basic practices had existed earlier, but there was not really a widespread adoption of a formalized process of investigation consisting of deductive and inductive reasoning. Europeans of that period started to synthesize a systematic approach to investigation from the works of the Greek and Muslim scientists.

One of the most notable is the Franciscan friar Roger Bacon, who produced one of the earliest codifications of what we now call the Scientific Method, based on Aristotelian deductive reasoning, combined with the inductive methods, skepticism, and mathematics of Muslim researchers, exemplified by Ibn al-Haytham. Unlike many of his contemporaries, he did not reject inductive reasoning the way that Aristotle did. He also advocated less reliance on authority, and more direct observation and experimentation. He also called for a similar reform of theological study, emphasizing understanding of the ancient languages of scriptural writing and rejecting the influence of authorities and dogmas as corrupting of the faith; as well as recommending more extensive study of the sciences by theologians.

He was far from the only one engaged in experimental scientific learning; William of Ockham, and Albert Magnus being two other prominent names form his time; but pursued a much more varied and extensive range of study than most.
 
Here's an interesting perspective of ancient science:
The Forgotten Revolution
In The Forgotten Revolution: How Science Was Born in 300 BC and Why It Had to Be Reborn (Italian: La rivoluzione dimenticata), Russo stresses the well-established fact that Hellenistic science reached heights not achieved by the Classical age science, and proposes that it went further than ordinarily thought. These results were lost with the Roman conquest and during the Middle Ages, because the scholars of that period did not have the capability to understand them. The legacy of Hellenistic science was one of the bases of the scientific revolution of the 16th century, as ancient texts started once again to be available in Europe.

According to Russo, Hellenistic scientists were not simply forerunners, but actually achieved scientific results of high importance, in the fields of "mathematics, solid and fluid mechanics, optics, astronomy, anatomy, physiology, scientific medicine",[1] even psychological analysis. They may have gone so far to discover the inverse square law of gravitation (Russo's argument on this point hinges on well-established, but seldom discussed, evidence). Hellenistic scientists, among whom Euclid, Archimedes, Eratosthenes, developed an axiomatic and deductive way of argumentation. When this way of argumentation was dropped, the ability to understand the results went lost as well. Thus Russo conjectures that the definitions of elementary geometric objects were introduced in Euclid's Elements by Heron of Alexandria, 400 years after the work was completed.[1] More concretely, Russo shows how the theory of tides must have been well-developed in Antiquity, because several pre-Newtonian sources relay various complementary parts of the theory without grasping their import or justification (getting the empirical facts wrong but the theory right).
RUSSO
THE FORGOTTEN REVOLUTION
 
Here's an interesting perspective of ancient science:

RUSSO
THE FORGOTTEN REVOLUTION

It's interesting but reminds me of claims made about science in the bible, koran etc. All knowledge has already been discovered but strangely never anything passed our present understanding.

Another review is here

Here Russo discusses present education in physics.

In physics courses the student
(now unaware of the experimental basis
of heliocentrism or of atomic theory, ac-
cepted on the sole basis of the author-
ity principle) gets addicted to a complex and mysterious mythology, with or-
bitals undergoing hybridization, elusive
quarks, voracious and disquieting black
holes and a creating Big Bang: objects
introduced, all of them, in theories to-
tally unknown to him and having no un-
derstandable relation with any phe-
nomenon he may have access to

With this understanding of modern knowledge I would doubt the rest of his scholarship.
 
This is something for you philosophers of science out there.

Modern science is typically said to have started in the 16th and 17th centuries during the scientific revolution. However, there was clearly research earlier, in the Middle Ages (both in Europe and the Islamic world) as well as in the ancient world. Not just ancient Greece, but also in places like Babylonia and Egypt (though heavily mixed with superstition). Carl Sagan talked quite a bit about the experiments and theories of the pre-Socratic philosophers in Cosmos (easily found on Youtube). He also referred to Lucretius as the first popularizer of science.

Are these ancient thinkers properly referred to as scientists or not? If what they did was not science, what was it? Certainly many of the questions they tried to answer would be considered scientific today. That itself is not enough though, as many of the questions religions try to answer are scientific questions.

I think this is a fun question. Kind of like the ones that the two old ladies on Saturday Night Live used to ask. (e.g. - "The Holy Roman Empire was neither holy, nor Roman nor an empire, discuss amongst yourselves.")

But I'm going to go out on a limb and risk ridicule by arguing that modern science is only possible with (relatively) modern mathematics. For example, before calculus we lacked the tools to mathematically express changing systems (and make testable inferences about these systems). Before modern statistics we could not express the significance of data.

Certainly formal logic, which dates back much further than advanced mathematics, is also central to science. While we're at it, the printing press also helps, since without it we had a much harder time distributing the results of our research to other people who could independently verify results. But if I had to choose one thing that differentiates modern science from natural philosophy I am going to go with the contributions of late 17th century mathematicians.
 
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It's interesting but reminds me of claims made about science in the bible, koran etc. All knowledge has already been discovered but strangely never anything passed our present understanding.
The kind of claims you mention have no similarity to the research done by Russo. The evidence that more was going on than has been generally known during the Hellenistic period is substantial -- unlike the fanciful stuff one gets from biblical passages. Eratosthenes' measurement of the earth's circumference, Aristarchus' heliocentric system and recent findings like the Antikythera mechanism, the Archimedes palimpsest lend a great deal of credence to Russo's thesis. I suggest you read the book before being so dismissive.

Another review is here
Did you really read this review? It is sympathetic to Russo's views and is quite favorable.
For example:
"The novelty of these conclusions is such that one
might be tempted to react with plain disbelief, if
not with a shrug. The reader should, however,
avoid such a reaction, because the scholarly support
is unquestionably impressive. It includes a
methodological novelty, this time in the examination
of the original sources. Thanks to his dual competence
in science and philology, Russo does away
with a time-honored habit among scholars of antiquity—
namely, that humanists only deal with
“literary” sources and historians of science with the
“scientific” ones. The scarcity of the extant sources
on science in antiquity forces the modern scholar
to look for all second- or third-hand information
scattered and interspersed through the literary
ones. The examination of many more sources than
the traditional ones not only adds to the historical
perspective but yields new findings in the history
of science."


Here Russo discusses present education in physics.

...

With this understanding of modern knowledge I would doubt the rest of his scholarship.

I'm not sure what the above comment means. Russo is discussing the nature of physics education, not his "understanding of modern knowledge." Wikipedia describes him as:
Lucio Russo is an Italian physicist, mathematician and historian of science. Born in Venice, he teaches at the University of Rome Tor Vergata.
Did you read and try to understnad the above quote before you posted it?
 
The kind of claims you mention have no similarity to the research done by Russo. The evidence that more was going on than has been generally known during the Hellenistic period is substantial -- unlike the fanciful stuff one gets from biblical passages. Eratosthenes' measurement of the earth's circumference, Aristarchus' heliocentric system and recent findings like the Antikythera mechanism, the Archimedes palimpsest lend a great deal of credence to Russo's thesis. I suggest you read the book before being so dismissive.


Did you really read this review? It is sympathetic to Russo's views and is quite favorable.
For example:
"The novelty of these conclusions is such that one
might be tempted to react with plain disbelief, if
not with a shrug. The reader should, however,
avoid such a reaction, because the scholarly support
is unquestionably impressive. It includes a
methodological novelty, this time in the examination
of the original sources. Thanks to his dual competence
in science and philology, Russo does away
with a time-honored habit among scholars of antiquity—
namely, that humanists only deal with
“literary” sources and historians of science with the
“scientific” ones. The scarcity of the extant sources
on science in antiquity forces the modern scholar
to look for all second- or third-hand information
scattered and interspersed through the literary
ones. The examination of many more sources than
the traditional ones not only adds to the historical
perspective but yields new findings in the history
of science."




I'm not sure what the above comment means. Russo is discussing the nature of physics education, not his "understanding of modern knowledge." Wikipedia describes him as:
Lucio Russo is an Italian physicist, mathematician and historian of science. Born in Venice, he teaches at the University of Rome Tor Vergata.
Did you read and try to understnad the above quote before you posted it?

Oh, I knew the review was favourable, that wasn't the problem. Somebody who thinks that modern education in physics leads to an addiction of mysterious mythology isn't anybody I can take seriously.
 
Oh, I knew the review was favourable, that wasn't the problem. Somebody who thinks that modern education in physics leads to an addiction of mysterious mythology isn't anybody I can take seriously.

So, his research and scholarship concerning the Hellenistic period is questionable because of his opinion about the authoritative nature of the education of (presumably Italian) physics students.
Well, OK.
 

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