Herakleitos preceded Leucippius and Democritus, evensong Panta rhei should precede atom,

The division of matter into particles was based on the alchemical knowledge of corpuscles. Corpuscles were undefined blobs seen in a primitive microscope, with the additional ability to transform as an entity, or as a mass group in some inaction or reaction. Thus a corpuscle was variously described as elastic or fluid or rigid.

Leibniz delivered a paper in which he proposed that corpuscles be considered as elastic rather than rigid like billiard balls in order to fully explain the observed behaviours and the conservation of mass produced with velocity as Descartes opined. Newton on the other hand demonstrated that such a quantity, a mathematical product could not be conserved because an object moving with 2 components of velocity was combinatorialy resolved by Pythagoras theorem. Huygens thus resolved the conservation law by relating it directly to Pythagoras, but further the Total mass producted with velocity of a collision system was conserved. It therefore seemed mathematically of little significance whether the corpuscles were" soft" or " hard"!

Newton reduced the mathematical framework to point masses in order to simplify and draw out the principles. For astrologers it made little difference, because the stars and planets could be regarded as points in the sky.

However, as Leibniz had pointed out, for everyday mechanical situations engineers had to consider the sizes and properties of materials, and a elastic ball/ corpuscle was a better description than a point mass.

The rise of a fluid mechanical description was a long and treacherous one, in the meantime engineers building bridges and structures had all they needed to build trustworthy edifices. Those who worked with aero hydrodynamic situations were not so fortunate. Bernoulli and Euler felt they had the measure of the fluid / water situation mathematically, but D'Alembert showed that mathematics could not be trusted in this regard!

The problem was wrestled with by Navier and Stokes, with an interest Shown by Maxwell. The result was masses of data but no real resolution. Maxwell was inspired to set out a mathematical model of the probable or statistical behaviour of a large number of particles in a volume. Thus he laid the ground for a statistical approach to fluid mechanics, introducing several key concepts, including perfectly elastic corpuscles, and the mean path length. Up until then fluids had to behave in streams.
Liquids and gases were now distinguished by stream or particle behaviour, and the Kineyic theory of gases and subsequently all matter was launched on its path to eventual dogma. In so doing particle theory received a much needed boost over the wave mechanical versions that were being developed with great difficulty because of the additional complexities of not modelling the path in a complex flow accurately, and because the differential equations were intractable to solution, and potentially an extremely large set.

Leibniz foresaw that computational machines would be necessary to solve any " real" or truly mechanical description of interactions of evn the mallets complexity. He set out several designs to build such machines to do the numerical data crunching. In addition he also highlighted that the mathematical terminology and praxis of his day was too cumbersome to deal with these spatial conceptions. He continually raised the problem, asking for a solution from the most gifted of his generation. He got very little response.
The issues were mainly geopolitical rather than academic. The European continent was in frequent turmoil, dividing along national or state lines. Despite the connections between the secret societies, the royal philosophical societies and royal family connections, there was no real interest in fostering international cooperation in the philosophical schools of thought. In fact, quite the reverse happened, where national interests brought to positions of authority extreme dogmatists who endeavoured to win the " war" on the propaganda front philosophically. So I guess it is not so strange that an obscure family, the Grassmann's should come up with the solution, especially as it required a pure focuss on the " elementary" aspects of every subject. Being heavily involved in Prussian primary education, and the Humboldt reforms, meant the family had to focus on these areas of every subject with fresh and revisionist eyes.

Justus Grasdmann started the family tradition, but it was Hermann that set out the fundamental revision of the system, philosophically, exemplifying his analysis with the single handed creation of a new " branch" or rather he hoped "root " of a mathematical Natural Philosophy based on the principles of Extensive Magnitudes, extensive Quantity measures, extension into all space, Der Raum, with an analytical and synthetic method to guide and equip the process.

Only a few, Peano being one, paid any attention to his philosophical treatise. It was modest in comparison say to the Principia of Newton, or the works of Leibniz, but it was seminal. The only comparable contemporary was Sir William Rowan Hamilton, who acknowledged its genius, and set off to catch up with Grassmann in his own work on Quaternions.. Later, Robert Grassmann got Hermann to redact and review his earlier, totally unsuccessful book along more populist lines, adding in the course of this a major part of his own philosophical work. In Fact Robert published further versions of the Ausdehnungslehre title under his own name, advancing his own theoretical and philosophical ideas. It is the 1844 version that is wholly and completely Hermanns., but it is the 1862 version which panders to mathematicians, rather thn to natural philosophers.

So the two important features of developing a proper mechanical description of fluidic corpuscular behaviour which Leibniz foresaw as a necessity were eventually delivered to a world no longer interested in these fundamental distinctions. Despite being heavily influential in Academia, Grassmann's work was made out to be Obscure! It is not. In addition. Academia did not want these new dangled computers to undermine their power base, so they fought tooth and nail to marginalise them, especially in mathematics. It has only really been in the aero hydrodynamic industries where academia had no power base, and in fact were hired and fired on business success criteria, that the pioneering work in fluid dynamics using computers and numerical modelling was established. Later, under business and academic cooperative agreements funded by governments these research facilities were moved back into closer connection with Academia.

The result has not been uniformly good. Industry thrives on innovation, academia thrives on stagnation. If it were not for government funding initiatives mant universities would have gone to the wall, with the more innovative researchers taking positions in industry. However, having a professor or two on the payroll does have a business advantage especially if trying to convince governments to fund innovation?

Where are we today? Making giant leaps in fluid dynamical modelling of " real" physical behaviours for the entertainments industry, through computer graphics research. This is the state of play. Academia does not have the power to control as it used to. Now business concerns control the development of this modelling of the interaction of fluid corpuscles. The very models of our reality are now set out as computer processing strategies of huge data sets of measurements in real time. We can model reality using fluid dynamics and fluid dynamic interactions, but we do not believe what we see because an academic whispers in our ear" it's not real!".

Today we tend to openly rely on such academics to shape our thinking, But we have always done that. What is real is that we can model real dynamics in real time using a fluid dynamic theory of matter, if we want to, right now! Leibniz, Benoulli, Euler, Stokes, Navier and Newton would be overjoyed.


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