Tuesday, July 11, 2006


The Scientists Have New Clothes?

To begin, I hope with my last post you didn’t come away thinking that I am a religion basher. My sole intent was and is to set up the background and context in which this change occurred, where philosophy instead of asking both the “how” and the “why” questions, ended up only addressing the “why”. Now the next thing we might suppose is that it was with the advent of modern science that the riff occurred. It is contended by many, that science as we know it only originated in the last five or six hundred years. Many propose that the vocation itself can be traced back to Francis Bacon (1561–1626), with his method. I will later speak of Bacon, however for now we will look another way. You might say, what is modern science? I would respond that the essence of modern science is when you use the tools of logic in concert with empirical consideration to expand ones knowledge of the natural world. I’m sure Bacon, if around today, would take umbrage with my simple definition, for he took many pages in his work entitled Novum Organum (New Instrument) to describe it. However, in general I would wager that if you offered this definition up to the scientists of today, they would find it acceptable.

So, is it true that it has only been in the last few hundred years that such a methodology manifested to expose truth? Let’s once again look back to ancient Greece to see if this method was used in their times. To begin, I could mention many of their great mathematicians such as Pythagoras, but then I’m sure it would be argued that he was solely a mathematician and thus his work and intent had little to do with revealing truths of the natural world. So we won’t go there.

The person that I propose as being a true scientist by the modern standard is Archimedes (287BC - 212BC). Now Archimedes is proported to have been a mathematician, physicists, astronomer, philosopher and inventor. This certainly sounds more like a description of a man of the Renaissance rather then one of ancient times. First, his contributions to mathematics are staggering. They include methods and proofs for calculating areas and volumes in geometry and of course much more. The discovery which he felt to be his greatest was his proof that any sphere bounded by a corresponding cylinder was 2/3 of its area and volume. He is also known to have proved and formulated the attributes of leverage. This accounts for instruments and machines such as scales, jacks and the block & tackle, just to name a few. He calculated with fair accuracy the circumference of the earth, 1800 years before Columbus was supposed to have prove it round. As many may be aware he is credited to have developed the "Principle of Buoyancy", referred to as "Archimedes Principle", which is summed up in the modern era within a relationship called specific gravity. This of course is what he is most popularly known for. It is fabled he was inspired to the discovery while lowering himself into a bath and observed it overflowing. After which he leaped from the bath, o' naturale and ran into the street shouting "Eureka"(I‘ve found it)! It might be suggested that from this account ideas and expressions such as “absent minded professor” and “nutty professor” sprang, not to mention “the naked truth”. All kidding aside, the important point is that Archimedes used mathematics coupled with logic and reason supported by empirical evidence to arrive at many of these discoveries.

To further my claim, it was not until quite recently, that it was most fully realized just how similar his ideas and methods were to that of modern science. This came to light with discovery of what is known as Archimedes Palimpsest in the early 1900’s, which has only recently been made legible. It spells out among other things what is referred to as Archimedes “method“. This mathematical method contains the germ of the idea which became Calculus, which was later to be independantly developed by Newton and Leibniz in the late 1600’s. This germ of an idea was to incorporate the concept of infinity into the solving of mathematical problems. A quote that I find particularly interesting from this ancient manuscript is as follows:

... certain things first became clear to me by a mechanical method, although they had to be proved by geometry afterwards because their investigation by the said method did not furnish an actual proof. But it is of course easier, when we have previously acquired, by the method, some knowledge of the questions, to supply the proof than it is to find it without any previous knowledge.

This would appear to confirm that Archimedes certainly thought that the way to understanding involved both logical consideration along with empirical evaluation. So now then, is modern science all that modern or is it simply the rediscovery and implementation of ancient methods? If so, then why were these ancient methods only resurrected with the dawn of the modern era? Also, are modern ideas and methods of understanding completely consistent with them? Most importantly, what can be gained in examining our current position in this regard? As we continue I will raise more for you to consider and I hope also discover.

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I have been reading a lot about Leibniz lately. He's the most famous mathematician I knew the least about. And now he's not. Oh MAN did he ever take to Descartes. I have no comment on his Philosophy other than I found the exposition of it interesting.

Hey Phil, do you think Archimedes may have taken credit for stuff he learned from the Egyptians? What the heck, they were Greek by then, right? At least the Pharoahs.
Hi Steven,

So you have been reading about Leibniz, the other father of Calculus. Actually l myself don’t know much of the man beyond his mathematical contributions. However I do know enough that I find it odd that you came away with the thought that he considered himself a disciple of Descartes, as he actually had problems with his philosophy as it relates to the foundations of science, with being more in the Bacon camp where inductive reasoning is to be given greater importance, which Newton also having the same opinion. Leibniz would claim that good science was the synthesis of what he called the truth of reason and the truth of facts. He believed man required the benefit of the truth of facts as only God could command enough reason to have the universe understood in terms of reason alone. This opinion you can find in his metaphysical work called The Monadology . I don’t know what you might think of it, yet it left me to believe he should have stuck strictly to Mathematics and stayed away from physics and philosophy.

As for whether I feel Archimedes may have taken some of the credit due to more ancient Egyptian mathematicians, I don’t actually believe so as being in the opinion he is generally undervalued for his contributions with the emphasis being on his influence in creating what is recognized as modern science. Now if you asked me about Newton in this regard I would say it’s more possible that perhaps he might have had access to a copy of Archimedes Palimpsest which could have given him a starting point for his development of Calculus, along with of course the insights given in Analytic geometry which were established by Descartes, with its coordinate system named in his honour. Anyway I have written a piece dealing with both Descartes and Bacon respectively in this blog further on where I expand on my thoughts a little more.


I find it odd that you came away with the thought that he considered himself a disciple of Descartes

Oops, I see I wrote "took too", I meant: "took IT to" Descartes. Sorry, I meant he opposed him. Yes Phil, I read about the Monads, I agree Leibniz should have stuck with Science more. But those were Religious times, heavily so. Leibniz worked hard to re-unify the Catholic and the new Protestant churches as well.

I read the Encyclopedia Brittanica article. The Wiki article seems a bit soulless in comparison. Just the Science bits of Leibniz' life are amazing, though, he's also considered the father of Modern Geology!

Leibniz was sponsored by a family, the Dukes of Hanover in Germany. The last of the 3 dukes who sponsored him was the very young George Louis, whose interests tended not to the Philosophical but rather to Drinking and Womanizing. Leibniz despised him, he was nowhere the man his father and brother were, so Leibniz took every opportunity he could to travel and get away.

History remembers George Louis a bit differently ... he would succeed Queen Anne to become George I, King of England, the only one who couldn't speak English!

I'll concede to point on Archimedes, however I do know that Plato was influenced by his Egyptian friend, one Soter, especially in regards to his musings on Atlantis. The Ancient Egyptians were fantastic at Arithmetic but not Mathematics. In Arithmetic, they has something like 10 different systems of measurement, hence Plato's calculations of Atlantis' geography were quite a bit off, some feel by a factor of 10.
Hi Steven,

In respect to how religion formed or one could say distorted or obscured the insights of Leibniz, I would say you are correct. However Descartes was not to be so influenced, yet rather the opposite, as to have his understanding to place limits on religious truth ratheras to recognize what reason demands . I then find Leibniz to be simply a man as like most as one of his times, rather than one of the future which Descartes certainly was who’s thoughts would later inspire those like Darwin and Einstein. This was first made evident for me when Einstein discussed in the context oif his own theory(s) what IS required to understand and extend it with him saying:

” Thus Descartes was not so far from the truth when he believed he must exclude the existence of empty space. The notion indeed appears wbsurd, as long as physical reality is seen exclusively in ponderable bodies. It requires also the idea of the field as the representative of reality in combination with the general principles of releativity, to show the true kernel of Descartes’ idea; there exists no space “empty of field” .

-Albert Einstein- Relativity (The Special and General Theory)- page 177- [Crown Trade Paperback, second edition]

As for Plato being a benefactor of Egyptian wisdom I would agree, yet also point out as being equally influenced by thinking and philosophy originating to the east, This then has what we call western thought as a synthesis of both the ancients of two worlds and cultures, with the Egyptian scholars principally concerned with the how, while those of the east as to the why. This has always left me to wonder that despite the success of Liebniz/Newton’s calculus as to have us better to understand to be able to predict the actions of the world, that its granular nature has formed a barrier to thinking of what represents to be the holistic nature which equally begs description, for which it has little utility. That’s to remind as Plato said that the world is not to be found as to be understood by its becoming’s, yet rather why are to occur by the nature of what has it being.


Phil, I wish to share two passages with you on Leibniz and Descartes, bearing in mind Descartes was born 50 years before leibniz and Leibniz was four years old when Descartes passed away in 1650.

The first is from Wikipedia, but the second and most relevant in my mind I rewrote from my 1993 Volume 7 of the Micropedia of the Encyclopedia Britannica>

From Wiki's entry on Leibniz:

Leibniz contributed a fair amount to the statics and dynamics emerging about him, often disagreeing with Descartes and Newton. He devised a new theory of motion (dynamics) based on kinetic energy and potential energy, which posited space as relative, whereas Newton felt strongly space was absolute. An important example of Leibniz's mature physical thinking is his Specimen Dynamicum of 1695.[30]

Until the discovery of subatomic particles and the quantum mechanics governing them, many of Leibniz's speculative ideas about aspects of nature not reducible to statics and dynamics made little sense. For instance, he anticipated Albert Einstein by arguing, against Newton, that space, time and motion are relative, not absolute. Leibniz's rule is an important, if often overlooked, step in many proofs in diverse fields of physics. The principle of sufficient reason has been invoked in recent cosmology, and his identity of indiscernibles in quantum mechanics, a field some even credit him with having anticipated in some sense. Those who advocate digital philosophy, a recent direction in cosmology, claim Leibniz as a precursor.

From EB:

Contrary to Descartes, Leibniz held that it would not be contradictory to posit that this world is a well-related dream. If visible movement depends on the imaginary element found in the concept of extension, it can no longer be defined by simple local movement; it must be the result of a force. In criticizing the Cartesian formulation of the laws of motion, known as mechanics, Leibniz became, in 1676, the founder of a new formulation, known as dynamics, which substituted kinetic energy for the conservation of movement.
Hi Steven,

Actually I’ve become aware of Leibniz central role in the development of the dynamical approach to physics resultant of my reading of a Book by Prof. Harvey Brown called ‘Physical Relativity’. In this book Brown makes the argument for the dynamical approach, with pointing out that although SR departs from the notion of absolute time, it still clings to the concept of absolute space, with General Relativity an attempt to resolve this. However according to Brown Einstein was not entirely successful in this in the denial of the existence of a preferred (fixed) reference frame, which the insistence for is the central premise of his book. However he does point out Einstein’s thoughts in all this when he says in page 140 the following:

”It was a source of satisfaction for Einstein in developing the theory of General Relativity ( he was able to eradicate what he saw as an embarrassing defect of SR; violation of the action-reaction principle. Leibniz held that a defining attribute of substance as their both being acted and acted upon. It would appear Einstein shared this view (He wrote in 1924 that each physical object ‘influences and in general is influenced in turn by others. It is contrary to the mode of scientific thinking, he wrote in 1922, ‘to conceive of a thing ....which acts itself, but which cannot be acted upon’.). But according to Einstein the space-time continuum, in both Newtonian Mechanics and special relativity, is such a thing. In these theories space-time upholds only half of the bargain; it acts upon physical bodies and or fields, but is in no way influenced by them.”

So I find it curious for someone like you, that expounds on the importance of mathematical insight in physics to be so concerned with the metaphysical underpinnings as much as you are. Not that I find this in contradiction, yet rather impressed you recognize that it be important. I myself have spent much time on this problem, to find that the difficulty to be more related to how most all think resolution must be entirely one way or the other and have my own thoughts on all of this. I’m hoping some day these thoughts might be have proved justified in finding that someone else strikes upon them, who is actually a physicist of note, with ability and thus able to extend them to full explanation, part which of course would incorporate a vigorous mathematical treatment and description. In the meantime I’more then content to read, study and gather my thoughts and look forward to discovering how they might work in better completion.


Thanks Phil. When I started back on my boyhood love of Math/Physics approx 1 year ago, I swore to myself I would allow absolutely zero "Philosophy" at the time.

I was young in the field and therefore ignorant of course as those two things have a way of going together, and thanks to you and Plato I learned not to confuse "Philosophy": with "Pop Philosophy", which I abhor and continue to abhor.

What you taught me was to rather, focus on the 3 men, Socrates, Plato and Aristotle, on which our entire culture is built, and stray not a whit (or at least as little as possible), and I have you to thank for that.

I also appreciate the whole "Descartes v. Leibniz" debate thanks to your blog, and how under-appreciated Leibniz is in the pantheon of the greats. My mind in more open now because I am more knowledgeable.

OK then that's it for me on this mini-essay. This is the 8th I believe out of the 23 you have up on the subject, I have more reading to do. ;-)
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