Momentum, Force, Inertia, Middle Ages, Buridan

WHAT’S MASS? It is not an easy question. An answer for inertial mass was given seven centuries ago. Astoundingly, it’s still the foundation of our most modern physics. Let me explain.

Momentum, force, and inertial mass were defined from trajectory deviation, first. This, I will show below, is incredibly modern (the idea is found in Riemann ~ 1860 CE next). This was all in Buridan’s work, in the Fourteenth Century (14C).  Jean Buridan postulated the notion of motive force, which he named impetus. Consider this, from Buridan’s Quaestiones super libros De generatione et corruptione Aristotelis:

“When a mover sets a body in motion he implants into it a certain impetus, that is, a certain force enabling a body to move in the direction in which the mover starts it, be it upwards, downwards, sidewards, or in a circle. The implanted impetus increases in the same ratio as the velocity. It is because of this impetus that a stone moves on after the thrower has ceased moving it. But because of the resistance of the air (and also because of the gravity of the stone) which strives to move it in the opposite direction to the motion caused by the impetus, the latter will weaken all the time. Therefore the motion of the stone will be gradually slower, and finally the impetus is so diminished or destroyed that the gravity of the stone prevails and moves the stone towards its natural place. In my opinion one can accept this explanation because the other explanations prove to be false whereas all phenomena agree with this one

 In 14 C, In The Late Middle Ages, Buridan Defined Momentum And Force By Considering Deviation Of Particle Trajectory

In 14 C, In The Late Middle Ages, Buridan Defined Momentum And Force By Considering Deviation Of Particle Trajectory

Just a word of the modernity of it all: the idea translates directly into defining force(s) with changes of distance between geodesics (in differential manifold theory).

Buridan states that impetus = weight x velocity (modern momentum). All the predecessors of Buridan thought one needed a force to keep on moving, but Buridan did not. Famous predecessors such as Hibat Allah Abu’l-Barakat al-Baghdaadi, who modified Avicenna’s theory, which followed John Philoponus believed in inertia NOT. They all followed Aristotle, who believed all and any motion died away, if no force was applied. (Not to say no Muslim ever invented anything scientific: the Uzbek ibn-Musa al-Khowarizmi crucially put the finishing touch on the zero, which he partly got from India, in the Ninth Century.)

Buridan’s pupil Dominicus de Clavasio in his 1357 De Caelo, pointed out that this extended to gravity:

“When something moves a stone by violence, in addition to imposing on it an actual force, it impresses in it a certain impetus. In the same way gravity not only gives motion itself to a moving body, but also gives it a motive power and an impetus, …”.

Buridan knew celestial bodies were moving from inertia: “God, when He created the world, moved each of the celestial orbs as He pleased, and in moving them he impressed in them impetuses which moved them without his having to move them any more…And those impetuses which he impressed in the celestial bodies were not decreased or corrupted afterwards, because there was no inclination of the celestial bodies for other movements. Nor was there resistance which would be corruptive or repressive of that impetus.”

By definition, inertial mass is what resists an applied force. The greater the resistance to a force, the greater the inertial mass of what it is applied to.


Buridan’s Revolution:

Buridan introduced p = mv, called it “impetus” and stated that it did not change if no force was applied. Thus Buridan buried the complete idiocy known as Aristotle’s physics. (That Aristotle could be a complete idiot at the mental retard level is philosophically, and historically capital, as Aristotle set in place the leadership system through celebrities, which we enjoy to this day).

Buridan’s Inertia Law is known as Newton’s First Law (because Buridan was from Paris, while Newton demonstrates the superiority of the English born three centuries later by attributing to him what Isaac did not discover).

More generally Newton asserted clearly his Second Law: dp/dt = F (where  F is the Force, by definition). It’s an axiom. (Weirdly the Second Law implies the First…)


Force = Deviation From Trajectory:

This is Buridan’s idea. It was taken over again by Bernhard Riemann, in the early 1860s (five centuries after Buridan’s death). In modern mathematical parlance, force is depicted by geodesic deviation. It’s this idea which is at the triple core of Einstein’s theory (with the idea that gravitation/spacetime is a field, and that it’s Newton’s theory, in first order).

So this is ultramodern: the idea got carried over in “Gauge Theories”, and, because there are several forces, there are many dimensions.


Thought Experiment Often Precedes Experiment: 

Yesterday I bought a (2015) book by a (British academic) historian of science. In it, the honorably paid professional asserted modern science started with Tycho in 1572. Tycho, a Count set his student Kepler onto the refined study of the orbit of Mars. Both Tycho and Kepler were 5 star scientists (differently from, say Copernicus or Einstein, both of whom too little inclined to quote their sources). So they were, because, differently from, say, Obama, they had strong personalities. Great ideas come from great emotions. Tycho believed the Ancients had lied. And he was right, they had lied about the orbits of the planets: observations with the same instruments gave different results from the ones the Ancients had claimed.

The preceding shows that this trite notion is profoundly false; the scientific revolution was launched by Buridan and his students (among them Oresme, Albert of Saxony), contemporaries and predecessors (including Gerard de Bruxelles and the Oxford Calculators). Some of their work on basic kinematics, the exponential and the mean theorem of calculus was erroneously attributed to Galileo or Newton, centuries later.

To believe everything got invented around the seventeenth century is not to understand how the human mind works. Experience has to be preceded by thought-experiment (even Einstein understood that). Buridan and his contemporaries did the preliminary thinking (while others were making clocks and hydraulic presses). All of this would become immensely easier after the invention of algebra and Descartes’ analytic geometry, true.

So let’s have a loving and admirative thought for Buridan, the main author of the scientific revolution, whose reputation was destroyed by the CATHOLIC STATE: Buridan’s astronomical reputation was destroyed by the Catho-fascists, more than a century after his death. That’s why the heliocentric system is attributed to an abbot from a rich family (Copernicus), instead of the master physicist said abbot was forced to read as a student.

Studying the history of science, and mathematics uncovers the fundamental axioms, in the natural order given by their obviousness.

Determining which ideas came first, and why is not about determining who is the brightest child, or most impressive bully in the courtyard. In 1907, Einstein made a big deal that he, Albert, was the discoverer of Energy = Mass (“E = mc2”). A careful inspection shows that this either reflects dishonesty, or misunderstanding on his part. Or both. I will address this soon, as I keep on studying mass and momentum.

Buridan put momentum at the core of physics, and thought-measured if dynamically. Momentum is still at the core: photons have momentum, but not mass.

It’s important to realize that many of the latest ideas in physics (all of “Gauge Theories”)  rest on an idea invented in Paris seven centuries ago. Not to slight it, or to heap contempt on all the noble Nobels. But, surely, the time has come for really new ideas!

Patrice Ayme’  


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22 Responses to “Momentum, Force, Inertia, Middle Ages, Buridan”

  1. brodix Says:

    One notion to add to the foolishness category is the idea that time is symmetric, because the laws of physics allow it to go either way and its apparent asymmetry is only emergent with entropy.

    This silly idea is based on the notion that the scalar measure of time, duration, is more fundamental than what is actually being measured, action, since it is assumed that time is some essential dimension, but that we can only measure events occurring within it.

    Yet what is being measured, action, is inertial(momentum) and that is what makes time asymmetric. As in the earth spinning one way and not the other.

    Now action only occurs within the present state, which would make time an effect of the change resulting from action.

    • Patrice Ayme Says:

      Good point. That the fundamental laws of physics are time symmetric is not even true, BTW: it’s PCT which is conserved, not T alone.
      I also believe that what I call the Quantum Interaction is not time symmetric. Quantum Mechanics actually uses time as a one parameter group of transformation.

      • brodix Says:

        Not that anyone(other than you) remotely associated with the field would even think the thought through, as it refutes spacetime as a physical explanation for GR.
        Though it has much deeper implications, given the sequencing of experience, aka time, is the basis of navigation, narrative, history, causal logic, etc.
        So explaining it as an emergent effect would have significant repercussions. The Catch 22 is that the more educated people are and thus qualified to comment, the more their sense of reality is based on an educated narrative paradigm, rather than a more experiential and emotive sense of presence.
        It is the sort of idea that would likely take generations for the larger conceptual issues to really sink in.

        • Patrice Ayme Says:

          Poincare’ and even Einstein, were not keen on the SPACETIME idea (it came from Minkowski, Einstein’s professor, who did not see to it that Einstein get a job, BTW… Although he certainly deserved one, for pre-1905 work…) Actually I may broach that subject next… The space versus time thing…

          The fact that Quantum does not treat space and time equally is clear for anyone, or should be clear for anyone taking a basic Quantum course.
          However notice it took 32 years to realize that the famous DE BROGLIE-“Schrodinger” equation had the POTENTIAL on the right hand side (Bohm-Aharanov effect, 1956…)

          • brodix Says:


            Yes, physics has mostly been spinning its wheels for the last thirty years and digging a deeper hole in the process, so an ideal like this could be the sort of blunt force trauma to the privates that might get its attention, but consider the broader sociological consequences;

            What if we lived in a world where feedback and reciprocity were understood as real, unavoidable consequences and the bottom line as little more than punctuation? Where means mattered more than ends? Why life really is a journey, not a destination? Where the present is the only reality, the past as residue and the future as probabilities?

            We are very linear, narrative, object focused people and this is not the sort of understanding that would come easily, but if the edifice of physics was to implode… It might just get enough attention to get the ball rolling.

  2. Gmax Says:

    So the angle that force is geodesic convergence is so old, it is not just Riemann, as you use to say, bUT those dudes from the Middle Ages? What the f? Really? Wow!

  3. Paul Handover Says:

    I have read this post and the following comments several times but still struggle to fully understand the core message. One has to be so careful to use terms and explanations that people like me can grasp!

    I am not a stupid man and have long been interested in the general ideas flowing from the quantum world. Such as the idea that defining reality is not easy. That the act of observation influences reality (I think). That the arrow of time is irreversible.

    So, please, in a few sentences that this aging Brit can follow 😉 what is the central message of your essay?

    • Gmax Says:

      I think Patrice said that several very modern ideas in physics originated in the Middle Ages. The idea is that momentum force, mass all come from change of trajectory.

    • Patrice Ayme Says:

      Dear Paul: I don’t know what you can follow, aging or not. What I do know is that some world class physicists and mathematicians may get angry from what I wrote (because they tend to be). I have had the angry confrontations in the past, on stuff that looked obvious to me, but was unconventional. The more correct, and the more unconventional, the greater the expression of sentiments below the belt.
      On Black Holes I was right, turned out… two or three decades later.
      OK, let’s do it this way: why don’t you ask ONE (or 2, or 3, or 4…) precise questions? An essay like that has probably 2, 3 dozens ideas running in parallel. It’s like one of these CPUs with three dozens cores, which are coming soon to a computer near you…

  4. Patrice Ayme Says:

    Brodix: What’s going to implode first is the ice sheets of Antarctica, and then the question will be asked; why did the scientists not see it come?

    • brodix Says:


      What is going to implode first is a rather ginormous financial bubble of notational assets far exceeding real value, on which many of our social expectations are premised. The current presidential campaign is one of the many symptoms of the tensions and strains building toward this coming earthquake.

      This may actually serve to sustain current physical theory for many more decades, much like the collapse of the Roman empire and the ensuing dark ages were a likely factor in the geocentric cosmology of epicycles lasting as long as it did.

  5. Paul Handover Says:

    My first question, and a query.

    My simple understanding of mass is that it is the measure of the resistance of a body to acceleration. Is that correct?

    And I don’t understand what you are saying when you write, “Just a word of the modernity of it all: the idea translates directly into defining force(s) with changes of distance between geodesics (in differential manifold theory).”

    • Patrice Ayme Says:

      1) F = ma (Newton). One should rather say that mass (INERTIAL mass) is a measure of the resistance to force (acceleration measures that resistance).
      My point, a subtle one, is that Buridan did NOT distinguish, at first, with his impetus between m and a. So he used, or, rather, observed the more general:
      F = d(mv)/dt.
      This implies Newton’s second law, but it’s more general (because m can vary!)

      That F = d(momentum)/dt was ultramodern: neither Relativity nor Quantum take the mass m very seriously. What’s serious is momentum. (E,P) is the 4 dimensional energy-momentum vector of Relativity. The Uncertainty Relationship involves MOMENTUM, not “mass”.

      2) Point about the definition of force is the core of Bernhard Riemann’s Habilitationschrift:

      A student having taken a course in advanced differential geometry would understand what I said (if she had taken a bit of physics too). This is the core idea of gravitation and Quantum Field Theory.
      We are doing into core here… Brace for tomorrow essay, which gives a simple direct derivation of relativistic mass. All what’s required is an intuitive understanding of Poincare’ and Lorentz’s Relativity.

  6. Patrice Ayme Says:

    [Sent to Linkedin, about: see far below…]

    Weinberg does not know as much as he (implicitly) claims he does (I bought his book). For example, he looks down quite a bit on Descartes, although Descartes invented the mathematics, in particular algebraic geometry, which all of physicists, mathematicians and engineers have used ever since. In particular Fermat, who then invented calculus, including its main theorem (that integration and differentiation are inverse to each other). Only then came Newton (although Newton did not discover much of what his name is now attached to!) Unfortunately, neglecting most of what happened turns history into nationalistism.

    In general, books recently written on the history of science all make the systematic mistake of overlooking the enormous progress made in mathematics and physics, starting with Fibonacci, Gerard de Bruxelles, the Oxford Calculators, and especially Buridan and his student Oresme, Albert of Saxony, and even Leonardo Da Vinci (who did a bit of serious physics).
    Patrice Ayme

    Injected in LinkedIn:
    Physicist’s story of science breaks historians’ rules | Science News

    Nobel laureate Steven Weinberg says evaluating science’s past requires knowledge of the present.

    Physicist’s story of science breaks historians’ rules preview image

    Physicist’s story of science breaks historians’ rules

    Nobel laureate Steven Weinberg says evaluating science’s past requires knowledge of the present.

  7. ianmillerblog Says:

    The time may have come for new theories, Patrice, but my guess is you won’t see them any time soon. You may or may not be surprised, but most would, at how reluctant most scientists are to actually think about a new idea, especially it it requires removing an old one.

    I know that in one way Newton’s first law is merely the second one with zero force, but I think it was important at the time to overturn Aristotle’s claim that force had to be applied to keep it going.

    • Patrice Ayme Says:

      It is Buridan, not Newton who contradicted Aristotle: this was one of the main point of my essay (and several before that). Newton parroted Buridan word for word, in the Second/First laws.

      There have been many theories, all in a crazy context of (poorly digested) Quantum Field Theory. I have my own theory, which implies Dark Matter (Dark Energy is something else… Not known in enough detail, BTW)

  8. Nature Of The Physical Law & Reaction Law | Patrice Ayme's Thoughts Says:

    […] an axiom the use of which bring the correct theorems. The same sort of reasonings established the First and Second Laws of motion, which were discovered by the stupendous genius Buridan, three centu… BEFORE Newton. […]

  9. Why This Site Shouldn’t Interest Most Americans | Patrice Ayme's Thoughts Says:

    […] Buridan also invented the hard part of Newton’s laws (three century before Newton). Actually Buridan anticipated not just Newton, but also Riemann’s force theory (used by Einstein and Al. in the Theory of Gravitation aka “General […]

  10. EugenR Says:

    Patrice, i fead this assay and all the comments, mainly from brodix and your responses. It is an important article with many ideas that needs to be developed more. Could you put all the relevant parts together?

    • Patrice Ayme Says:

      Thanks Eugen for the compliment. I wonder what you mean by “putting the relevant parts together”. But I will have a look, I can be pretty incoherent, at least in appearance. I often write loose essays, with many ideas inside to keep them interesting, and pursuing tendrils of unlikely (but influential) causal chains. Instead of being dry and concise. I had a look at Montaigne a year or two ago, and he was using, it seems the same general method, at least in his first essay.

      What I tried to say in the ‘Einstein didn’t think of gravitational waves first’ essay
      is that we have to be weary of Einstein. I love Einstein and read him approvingly for decades. Only later did I discover that Lorentz, Poincare’ and others discovered Relativity. Aside from writing a nice abstract in German (1905), and advertizing it don’t really know what Einstein did in Relativity (and I have struggle to understand Relativity for decades, now I think I get it, paradoxes included; it’s like a particular case of my subjacent theory).

      Einstein was especially a genius at picking up other people’s ideas. He did that for the Brownian motion, he did it with photoelectric effect, with Planck (Planck was furious). He did it with Relativity (nobody of note said anything). He did if with Bose-Einstein statistics, he did it with the nonlocal EPR.

      In the case of the EPR the input from Karl Popper may have been crucial, and one will think that the more, the more Popper one reads. There is actually a POPPER THOUGHT experiment, a variant of the EPR. Of course not as important than my variant of the two-slit.

      The crux is that I believe that Einstein made a big mistake in his Photoelectric paper of 1905, justly famous, and for which he got the Nobel (said Nobel.Org). He assumed the particle stayed a particle when in translation, and that led to 112 years of error by physicis viewed as a culture:

      A bit more of defiance vis a vis Einstein may lead to a revolution in Physics…

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