Descartes (1596-1650), the Dualist. Part 1: Maths and Cosmology.

Part 2 of Descartes (next post), will discuss his philosophy which is his most important contribution (even if it is malignant). This post is Part Five of the series, 'Science and Philosophy'.

“Modern Science it can be said, began with Descartes. Like Francis Bacon he strove to create a new methodology, but his was based more on deduction than experience.” (Commins, Linscott, p. 159).

(Comment: Bacon [late 16th century] promoted ‘induction’ from experimentation, calling the method ‘new’. Descartes [middle third of the 17th c.] offered ‘deduction’ from general observations, suggesting it was ‘new’. Both claims are untrue. Deduction and induction long predate both men.)

Introduction

Modern science, cosmology, physics and our worldview are based entirely on philosophical assumptions which might be wrong.  We looked at Copernicus, whose system and theory was incorrect, premised on circular orbits and ‘crystalline spheres’.  Copernicanism as first proposed, was largely incoherent, and organised around the ancient Pythagorean-Platonic concepts of Sun Worship and Aristarchian heliocentricity.  Copernicus provided no observational proof whatsoever for his theory. 

Neither did Kepler, who used Tycho Brahe’s detailed observations and may have killed Brahe to access his journals.  Kepler’s complicated geometry seemed to offer some ‘proof’ of planetary elliptical orbits and movement around the Sun.  Much of what Kepler offered was however inaccurate or wrong.  His maths could just as easily have proven the Tychonic geo-helio-centric system or geo-centricity. 

As a Lutheran devotee and a member of the ‘new religion’ which opposed the Catholic Church, and as an acolyte of Plato and Pythagoras, Kepler made the philosophical decision to support heliocentricity.  It was philosophy and maths, not ‘science’ which informed that decision.  ‘Out with the old, in with the new’, was the zeitgeist of Kepler’s era.

Disputatious Descartes

Now we move on to Descartes.  In teaching Descartes to young minds, I would offer to look at Descartes from 2 angles.  First, we would explore what the Catholic Descartes had to say about the universe and cosmology, which usually surprised the audience.  Second, we would explore Descartes the fervid philosopher, who issued quite basic and incorrect philosophies that have long distorted Western civilisation. These are rarely taught.

In fact, it can be stated that the truncated misrepresentation of ‘Cartesian’ philosophy is a virulently destructive influence in Western history (Sorell, 1987, Wiker 2008).  First, his abstract deductive mathematics has corrupted the very concept of providing proofs. Second, the incorrect claim that Descartes only supported mechanical-materialism is a destructive chimera. We cover these in the next post.

But first his cosmology.

Grids and Coordinates

Descartes arrives one generation after Kepler.  The Keplerian system had isolated the Earth in a far corner of space.  This misanthropic philosophy troubled the Catholic René Descartes (d. 1650).  Descartes wanted to reestablish the importance of the Earth and humans through appeals to our cognition and by locating the Earth and emphasising its importance within its ‘small corner of the universe’. 

Descartes most important work was the 1637, ‘Discourse on the Method of reasoning well and Seeking Truth in the Sciences".  In this book there is an appendix called ‘La geometrie’.  This appendix outlines his geometrical contributions to mathematics and informs his cosmology. 

Descartes developed a model in which the universe could be mathematically mapped, using ‘Cartesian Coordinates’.  

In his ‘Discourse on the Method’, Descartes attempted to prove that:

·        We can resolve geometrical problems with equations,

·        We can resolve problems with equations that cannot be solved with geometry,

·        Mathematical equations should be used to discover and explain reality.

An example of standard geometrical methods includes multiplication, division, or square roots.  Descartes’ system extends this to more complex formulas and equations and bases them on a reference grid.  He then builds his formulas using the grid reference lines and ‘coordinates’, and graphs his equations.  Descartes was perhaps the first mathematician to graph geometrical calculations. 

Cosmology

Cartesian cosmology is also based on a reference grid.  Descartes rejected the Keplerian view that the universe was a sphere and proposed that it was really laid out along a mathematical grid.  He partitioned his grid into the Euclidean geometrical x, y, z coordinates.  This allowed Descartes to measure the length, width and height of the universe, much as Euclidean geometry is used to measure l, w, and h of a building or room.  Using this grid, he could map planetary locations and mathematically situate the Earth as a ‘room’ within the ‘house’ of the universe (Smith, 2003). 

‘Cartesian coordinates’ can be useful.  At least they attempt to align models to physical reality as humans view it.  The problem for Cartesian cosmology was the issue of an absolute reference.  Since he believed in Copernicanism, no reference point existed from which to establish his ‘coordinates’.  He could never explain on his grid where exactly the ‘Earth’s corner’ was, or how to locate it (Descartes, in ed. A. Buchenau, 1992).  His cosmological model therefore made little sense.

Space and materiality

Frustrated by this obvious problem, Descartes came to believe that empty space did not exist at all but was filled with material. This was not a new idea. In the Cartesian-view, space is made up of ‘bodies’ and their extensions.  It is akin to an aether, though with more materiality and mass. These ‘bodies’ are of all sizes and shapes.  They can be large or very small.  There is no place in the universe where a ‘body’ does not exist.  There is no place in the universe where these ‘bodies’ will not have an impact or attraction.

This is hinting at gravity which was adumbrated by the medieval Scholastics and picked up by Descartes as well as by Newton (Ariew, 1992). The 6th century Byzantine Christian philosopher John Philoponus had proposed postulates on inertial motion which were studied and changed by naturalists during the medieval period ending up influencing the physics of Pierre Gassendi in the 16th century. Gassendi pre-dates both Descartes and Galileo yet few know of Gassendi or those who preceded him.

For Descartes, when we measure ‘space’, we are really measuring the ‘bodies’ which are compacted together.  From this compaction the Cartesian coordinates possess their intrinsic dimensions.  Descartes believed that matter had no inherent qualities but was simply the ‘brute stuff’ (his own words), which occupied space.  Yet that ‘brute stuff’ was profoundly important and measureable (Rodis-Lewis, 1992).

Utility

Descartes was certainly an innovator with geometry and graphing equations.  He obviously had the time, the leisure and the money to engage in modelling abstractions.  Most of what he proposed has been amended. This however should not detract from this contributions even if his geometry has been superseded.

“In this case and throughout La Géométrie, Descartes uses oblique coordinates that are intrinsic to the problem. That is, the coordinates designate distances that are given naturally by the figures in the problem. In contemporary analytic geometry, we use typically use orthogonal axes (with x as the horizontal axis and y as the vertical axis) for our coordinate system, and these axes are, as it were, extrinsic to the problem.” (Standford Philosophy post)

Cartesian maths impacted both philosophy and physics.  His mathematical approach did stimulate others to research and experimentation, even if his observations or conclusions were incorrect (Sorell, 1987, Gaukroger, 1995):

1.      Colours were caused by the rotation of ‘spheres’ of light (incorrect),

2.      White light was the pristine form of energy (light and kinetic energy are different, though light can be viewed as a form of energy),

3.      Formulation of the law of light refraction (now called ‘Snell’s law’),

4.      Motion was derived as mass x velocity (Newton’s ‘momentum’ and opposed to Leibniz who stated more accurately that motion is mass x velocity squared, or what we call ‘kinetic energy’),

5.      Vortices and ‘vortical’ motions exist and operate without interventions (unproven but related to gravitational attraction),

6.      The human heart is a mechanical pump (Harvey and others had also proposed the same),

7.      The universe is a clockwork mechanism created by God (deistic view and discussed in the next post).

Confusion

In the 17^th and 18^th centuries there was an explosion of confusion in cosmological physics.  There was no consensus, nor even proof for many proposed theories.  We have ‘Cartesian coordinates’, Leibniz with his ‘defined space’, Berkeley and his ‘stars’, Euler and his ‘absolute space and time’, along with Newton and his ‘absolute space’.  None of them in the main, agreed with each other and none of them had mechanical proof.  

The 17^th and 18^th centuries were an era of scramble within physics and cosmology, as philosophers and physicists tried to provide the mechanical proofs for Copernican-Keplerian theory which had yet to be offered or discovered.  No single ‘rational path’ to greater ‘knowledge’ existed in reality, as offered in our standard textbooks. It was flux and discord. The underlying differences in philosophy between the main actors made the interpretation of any evidence problematic (Sorell, 1987).

Into this maelstrom of uncertainty Kant (1724-1804) arrived in the 18^th century with his ‘circular motion’ theory to try and fill the cosmological holes left by Copernicus, Kepler and Newton. Kant’s theory is somewhat supportive of Euler’s concepts but at odds with many of his contemporaries. 

In summary none of these models, including that of Kant, actually worked.  In fact, the turmoil produced by these philosophical and mechanical constructs ends up in the chaotic schizophrenia of Kantian philosophy itself.  Kant’s theology is one of the great influencers and distorters within the Western philosophical tradition, and it is based in large measure on Cartesian philosophy (Gaukroger, 1995hh).

Bottom Line - Philosophy

Saying Descartes invented ‘modern science’ by proposing ‘deductive reasoning’ is just an expression of ignorance, rubbishing 3 millennia of learning and experimentation. Almost everything Descartes created or modelled can be found within the works of medieval Scholastics, not to mention Euclid and his schoolmen (Ariew, 1992) amongst many other philosophers and natural scientists. His great invention was to graph geometric equations.

In relation to cosmology and mathematics, the Cartesian system of coordinates was an unproven and unworkable theory.  Without an absolute frame of reference, provided by Newton with ‘space’ as a fixed absolute, Descartes could never geometrically identify the Earth’s location or even movement within the universe. 

Descartes more important contribution is in philosophy.  In his Discours de la Méthode (1637), Descartes outlines his belief that a system of knowledge should start from first principles and proceed mathematically to a series of deductions, reducing the physical world and cosmology to maths.  This philosophy becames a foundation stone for ‘science’. Thus we end up with the mathematical fantasy worlds of Einstein (Einstotle) and the Relativists. We will discuss Cartesian philosophy in the next post.

===Sources, some reading

Descartes, René, Die Prinzipien der Philosophie, ed. A. Buchenau, Philosophische Bibliothek, Vol. 28 1992

Commins, S. Linscott R., Man and the Universe: The Philosophers of Science, 1947 pp 159-216.

Ariew, Roger, 1992, “Descartes and Scholasticism: the intellectual background to Descartes’ thought,” in The Cambridge Companion to Descartes, edited by John Cottingham, Cambridge: Cambridge University Press, pp. 58–90.

Gaukroger, Stephen, 1995, Descartes: An Intellectual Biography, Oxford: Clarendon Press.

Rodis-Lewis, Genevieve, 1992, “Descartes’ life and the development of his philosophy,” in The Cambridge Companion to Descartes, edited by John Cottingham, Cambridge: Cambridge University Press, pp. 21–57.

Smith, Kurt, 2003, “Was Descartes’s Physics Mathematical?” History of Philosophy Quarterly, 20 (3): 245–256.

Sorell, Tom, 1987, Descartes, Oxford: Oxford University Press.

Wiker, B. 2008, 10 Books that screwed up the World, Regnery Publishing.

==Series

Introduction: Science as an output of Philosophy

Part One: Science as Philosophy or Scientism

Part Two: Copernice the Confused (1473-1543). Copernicanism is Philosophy not ‘Science’.

Part Three: Kepler the Conniver (1571-1630). Philosophical choice over scientific veracity.

Part Four: Kepler the Conniver (part 2). Maths which could prove other models.