Related:

• The origin of force
• Physical quantity

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Scientific Revolutions

Name of school	Axiom	Algorithm	Revolution?
Ptolemy	Stationary Earth	Trigonometry	Yes
Euclid	Fifth postulate	Pythagoras theorem	Yes
Newton	Force laws	Kepler’s rule	No

This table shows that once the practitioners of a school realize that axioms are independent of algorithms a scientific revolution follows. A scientific revolution happened in astronomy when Copernicus realized that he could use the same trigonometric framework known as the Ptolemaic model to describe a system where the Earth was one of the planets. Before Copernicus, astronomers used the success of the algorithm to prove the absolute truth of the axiom.

In mathematics a scientific revolution occurred when Gauss and Lobachevsky realized that Euclid’s axioms were not absolute truths and the consistency of the Euclidean geometry did not prove the truth of its axioms. They realized that the fifth postulate was independent of the algorithmic geometry, e.g., Pythagoras theorem used to compute distances. This realization started a true revolution in mathematics.

In physics axioms are still called “laws.” Newton first defined his laws in the Definitions section of the Principia (or “anticipated” them as I.B. Cohen calls it) and then stated his definitions as “axioms, or laws of motion.” Gradually, Newton’s definitions gained more and more authority and evolved from definitions to axioms, to laws of motion and finally to absolute laws of nature.

The mechanics part of the Principia is very thin. In fact, there is no “Newtonian mechanics” in Newton’s Principia. This is true because Newton did not use units. Modern physics, on the other hand, is defined as a consistent system of units made of physical quantities. Newton’s astronomical computations in the Principia are independent of axioms and laws of book 1. They are simple applications of Kepler’s rule. Subsequent generations of Newtonians turned this tiny sample of proportional computations into a vast consistent system of units known today as Newtonian mechanics.

But Newton’s laws as the fundamental doctrine of the Newtonian school has survived without change. This doctrine is, as all doctrines must be, independent of computations. No computation contains doctrines. In other words, metaphysics is never a part of mechanics. Definitions, axioms, laws are metaphysics. Computation with physical quantities is mechanics. These are independent of each other.

Physicists, on the other hand, still believe that when they do computations with physical quantities they use Newton’s laws:

Newton’s laws == Newtonian mechanics

This is the pre-revolutionary view. For instance, astronomers using the Ptolemaic theory before the revolution argued that the trigonometric framework which made accurate predictions included the axiom that the Earth was stationary at the center of the universe. They defended the thesis that the trigonometric model was coupled to the axiom of stationary Earth and that the model would not work without the axiom, therefore, the axiom must be absolutely true. This is the same argument physicists still use to defend Newton’s laws: Newtonian mechanics works, therefore, Newton’s laws must be true.

Only after the scientific revolution people realize that axioms are independent of algorithms. Axioms are arbitrary. Axioms cannot be proved by algorithms or experiments.

The fundamental axiom of physics is the assumption of force as the universal cause of all phenomena. That’s why all derivations in physics either start with F=ma or assume it. But the unmeasurable force F can never be found in any formulas used in computations. This is why physicists call their derivations computation. In other words, physicists call symbolic manipulation of symbols associated with metaphysical laws of Newton computation. Instead of removing metaphysics from physics modern physicists call their metaphysics physics.

Physicists say that Newtonian mechanics works and it makes accurate predictions therefore Newton’s axiom of force as the universal cause must be true. When will physics abandon this pre-scientific belief and be ready for a scientific revolution? When will physicists realize that algorithm is independent of the axiom and that there is no Newton’s laws in Newtonian mechanics?

First step should be to establish awareness of the pre-scientific state of physics. Do you think in physics axioms are believed to be coupled to algorithms? And if so, would decoupling axioms and algorithms create a scientific revolution as it did in astronomy and mathematics?

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. . . that the simple rules of cellular automata can somehow generate fundamental laws of physics.

To me such a claim does not make sense. How can one derive laws from other laws? Laws are definitions. Newton’s laws are definitions Newton called “axioms or laws of motion.” All “laws of physics” are such definitions unless they are derived from experiments, then they are not laws but proportionalities.

Physics does not deal with laws, fundamental or otherwise. Physics deals with physical quantities. To overrule physical quantities by citing laws of physics is metaphysics. Can cellular automata solve physical problems that are usually solved by physical quantities? This seems like a better question.

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Kepler’s laws challenged Aristotelian and Ptolemaic astronomy and physics.

Maybe. But that’s not our problem anymore. Newton replaced Aristotle long time ago as the head of the scholastic corporation. Our challenge and duty as scientists is to question the doctrine of a forceful Newtonian nature to be the legal and true doctrine of nature.

Related posts:

• Aristotle/Newton
• Scholastic corporation

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This definition of physical quantity is free of metaphysics. If physics is defined as the science that studies physical quantities and physical quantity includes nothing but a number and a unit, then, we must conclude that anything which is not a physical quantity does not belong to scientific physics. We can easily define a scholastic type of physics or metaphysics by defining physical quantity as

This metaphysical physics would allow deep philosophical discussions of laws, principles and conjectures of all kinds but will be unable to make predictions because nature recognizes only true physical quantities and ignores the rest. Metaphysical physics is a lot of fun but it is no different than pre-Newtonian Peripatetic philosophy. As is well-known Peripatetic philosophers endlessly discussed laws and principles of their own definition and published long commentary on them. Galileo noticed the corruption of physics and eliminated the metaphysical part by making geometry the language of physics. In the 18th and 19th centuries great scientists developed the concept of physical quantity and made physics a rigorous science based on quantities tied to a consistent system of units. There is no room in the quantitative scientific physics for qualitative philosophy expressed as authoritative laws, principles, conjectures and branded equations. Therefore, a set of rules and definitions and principles called “Newton’s laws” is not a part of the science of physics. Newton’s laws can be a nice topic to discuss in a scholastic discussion group but not in physics.

Physicists may use such philosophical arguments as heuristics and pedagogy the way Einstein did but metaphysical elements will always exist independent of physical quantities. This means that the authority of physics comes solely from physical quantities and never from heuristics and metaphysics. No metaphysical law can be offered as an authority over a physical quantity. A scientific physicist works strictly with physical quantities.

So, to say that “Newton’s laws predict planetary orbits” as one hears all too often, is to assert Newton’s authority over physical quantities. “Newton’s laws” is not a physical quantity. Doing physics by invoking “Newton’s laws” reduces physics to metaphysics. No orbit ever heard of “Newton’s laws.” All that orbit knows is its radius and period. But if you say “Newton’s force describes orbits” that would be a scientific statement because Newton’s force F is a legal physical quantity. Do you see how the point of view changes from a scholastic discussion on Newton’s laws to a scientific discussion about a physical quantity? It is possible to discuss scientifically if force describes orbits but it’s not possible to discuss orbits with “Newton’s laws” because “Newton’s laws” is not a physical quantity.

This distinction is usually lost on students who are attracted to physics after reading science-fictional philosophy the media associates with physics. Beware that if it is not a physical quantity it is not physics. It is metaphysics. No exceptions.

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Newton then projects the properties of the sling rotation to planetary orbits. These properties are radial acceleration, the “endeavor” to fly off and the tension on the string dubbed “force.” According to Newton all orbits are rotational and have the same properties as the sling motion.

Newton’s claim that orbits are rotational is wrong. Either Newton goofed, or more likely, he was spin doctoring rotation in order to make his occult force the cause of planetary orbits. Rotation and revolution are ruled by different rules and orbital motion is free of the tension on the radius. The tension in the string exists because radius is constrained. In orbital motion such a radial constraint does not exist and therefore, Newtonian force does not exist.

Rules for rot and rev

Rotation	Revolution

Rotation is ruled by radian motion, Θ = S/R or S = R Θ. According to this rule, for a given radius R, increasing Θ by turning the sling faster, will increase S and consequently, the radius R will want to increase proportionately, but since R is constrained and kept constant by the string, that additional motion belonging to R will manifest itself as tension on the string. The increase in S will be a measure of this tension.

Newton, on the other hand, interprets the sling motion in terms of the force he just defined. As the sling rotates, the stone stretches the string and endeavors to fly off and the centripetal force draws the stone back toward the hand to make the orbit happen. Newton hereby defines force as the cause of the sling orbit. Then Newton claims that the same mechanism creates all orbits because “all bodies endeavor to recede from the centers of their orbits.” For example, the Moon is a body in orbit, and just like the sling, it must be hurled by something, and in this case, that something is “the hand of God” or gravity. And like the sling, the Moon, too, endeavors to fly off along the tangent but it is held in its orbit by the centripetal force acting instantaneously.

Newton’s attempt to describe planetary orbits as rotational motion fails. The Moon’s orbit is not described by the radian rule. Increasing R does not increase the orbital arc the Moon describes in unit time. On the contrary, the Moon obeys Kepler’s rule and moves according to the rule S :: R^-1.5. Unlike the sling motion, increasing R decreases S.

In orbital motion the integrity of the radius is not respected because there is no material radius connecting the mover and the moved. In fact, there is no mover. Newton ascribes material qualities to orbital radius which is nothing more than distance created by the orbit. The orbital radius is not constrained because it does not exist. Without the sling the string will continue to exist but without the orbit there will be no radius. Therefore, in orbital motion, there is no radial or “centripetal” acceleration and there is no “endeavor” to fly off. Orbits are inertial, i.e., geometric and Keplerian, and not dynamical and Newtonian. This is proved by the fact that all of the rotational elements Newton projected to orbital motion by turning them into occult qualities must be eliminated in order to describe orbits.

These Newtonian elements, force F, mass m, and acceleration a, are always eliminated from orbital computations.¹ This cannot be otherwise because orbits do not obey the radian rule, orbits obey Kepler’s rule. Newton defined his centripetal force to define orbital motion as rotational motion. But Newton’s force fails to describe orbits and consequently it is eliminated from computations of orbits. Yet, following Newton blindly, physics textbooks still enforce Newton’s absurd explanation of orbital motion.

1. Keplerian part of acceleration, that is, R/T^2 = radius/period^2, remains, what is eliminated is the Newtonian label acceleration. [↩]

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Maybe something that I wrote in an earlier post can be useful here. I propose to divide physics into two distinct academic divisions: physics and fine physics. In fine physics, as in fine art, there will not be a requirement to conform to a standard of evidence. Already string theorists use fine art concepts such as elegance and beauty as fundamental concepts of string theory.

Also, just like art, string theory can only be defined by way of its practitioners: String theory is what string theorists do. There is no independent definition of string theory and this is how string theorists like it.

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If a problem is independent of a term that problem is independent of that term.

Example: Given f(x0, x1), then, the problem modeled by f(x0,x1) is independent of any term xn > x1.

Question: This principle is generally accepted and used in physics. For instance orbital motion is described by f(R,T) where x0 = radius = R and x1 = period = T, and it is independent of a constant term x2 = mass = m. Physicists apply this principle and say that “orbital motion is independent of m.”

I am wondering, though, if this principle is a casuistic principle in physics or if it is a general principle which is valid unconditionally. In the example above, f(R,T) is also independent of x3 = force = F, but physicists do not use this principle in the case of force F and they don’t say “the orbit is independent of force F.” This suggest to me that in physics this is a casuistic principle.

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I understand this feeling. At times I felt the same way. But unlike the holographic principle, the surface of a building is not proportional to the happiness of the people living inside it. The residents of the building may be as happy as anyone else and pay no attention to the ugly side of the building.

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These paper figures that come out of paper but could never fully free themselves from the background inspire us to speculate on the most fundamental philosophical question: Is there a theater of operations where phenomena happen? Or asked in the language of physics, Is there a background? If so what type is it? Ether? Vortex? Vacuum? Density continuum? Is it neutral or dynamic and interactive? Linear or non-linear?

In the case of the paper artwork, the “phenomena” come out of the paper background, in other words, the flat background curls up into some shape that we perceive as familiar objects. When a figure is cut and it curls out of the background it leaves a hole in it. Apparently, conservation laws are not valid in this world, at least not at this scale.

1. from Mathematics under microscope. [↩]

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I assume that the spiral shape arises because the bottom of the vortex touches the sphere?

Here’s a simplified geometry of the same phenomenon:

This is figure 11.7: Shape of liquid surface in a rotating bucket, in Equilibrium statistical physics by Michael Plischke and Birger Bergersen. They reason that “in a normal fluid, rotating uniformly, the shape of the upper surface is determined by a balance between the centripetal and gravitational forces giving

But I believe that the shape can be investigated geometrically without considering gravity or pressure. I don’t know if this is true. I have a sketch here that was inspired by Doug’s comment at Mass.

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1. No unit

Initially a proportionality new to physics is stated without a unit. In the 18th century physics textbooks stated “Newton’s law” as 1/R2. Just like that, no unit, no constant and no M&ms attached to it yet.

2. Personal units

Any length can be chosen as a unit to make measurements and accordingly in this early stage every physicist defines his own unit and tries to enforce it as the absolute true unit. Chaos ensues. Concerns are voiced for unification of physics.

3. Standard unit

At this stage a senior physicist defines a new unit by using a gadget he calls an experiment and enforces it as the true unit by his authority. His definition becomes the standard used by every practitioner and enters the textbooks under his name.

4. Constant of nature

The next generation learns about the standard unit in textbooks and believes it to be a constant of nature and eventually a physicist formally elevates the unit into the status of an absolute property of nature discovered by physicists.

5. Variable constant of nature

When a physical quantity is finally coupled to a constant of nature and becomes textbook material, active research ceases on it. But there will always be some enterprising physicists who will refuse to let such a valuable professional commodity as a constant of nature die a peaceful death in textbooks and they will re-open research on it by defining it as a variable constant. This is, of course, no different than re-opening research on the meter, the unit of length, by defining it as a variable constant of nature. Physicists who speculate about G, the unit of force, as a variable constant of nature look as foolish.

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Let’s look at an example from Wikipedia. Power is a physical quantity:

• P is the physical quantity of power
• 42.3 * 10³ is the numerical value of {P}
• W is the symbol for the unit of power [P], the Watt.

A physical quantity is defined as a number multiplied by a unit. This definition says nothing about the physicallness of the physical quantity. It only says that if you define a unit and multiply it by a number then the resulting quantity is a physical quantity. Let’s define the physical quantity of power in terms of the unit of authority, W = the Wig. We’ll obtain the same result for power P

• P is the physical quantity of power
• 42.3 * 10³ is the numerical value of {P}
• W is the symbol for the unit of power [P], the Wig.

Indeed, a person with more authority is more powerful than another person with less authority.

The definition of “physical quantity” makes sense because we are living in a definitional world, not in an absolute world with discontinuities. This also supports the density continuum view, e.g., software and steel are equally “matter,” they happen to have different densities. This result follows directly from the denial of the Newtonian atomic materialism.

Physics itself, in theory, is sensibly based on a definition that allows a natural description of nature by definitions:

What makes physics a scholastic and authoritarian profession and therefore the anti-science is the fact that physicists defined physical to be only what is included in their professional code called physics. So, in practice, physicists really use another definition of physical quantity:

According to this definition only quantities expressed by an official and legal physics unit is considered a physical quantity.¹ This is how physicists assert the ownership of scientific concepts that for generations lived independent of physics and its doctrines.

If we uphold the original definition of physical quantity we must conclude that there is no physical/non-physical duality. There is only legal/non-legal duality enforced by physics professionals who defined non-legal to be unphysical.²

If physicists’ definition of the physical quantity is true, then we must believe in a definitional nature: The standard is the unit. Or the standard is the thing. If it has a unit it exists. No one owns nature. It’s yours and mine. Nature doesn’t belong to a professional class.

1. This makes sense because the scholastic corporation defines standards and sells them to engineers, governments and the media. [↩]
2. All professionals find in themselves the right to enforce their definition of legal as the only truth to protect their monopoly. Physics is no different. [↩]

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Here’s the derivation: F is the Newtonian force. By definition the Newtonian force acts instantaneously from a distance. Therefore, for the Newtonian force all distances are zero. As far as F is concerned radius R of any orbit is zero because F traverses any distance in zero time. Therefore, for F, time terms in an equation are always zero. Time does not exist for F. Consequently, the period of any orbit, as seen by F, is always zero.

So we can write F=ma as

Therefore the fundamental equation of the precise science of physics is:

But any science which is based on an equation of type

will have in its toolbox sophisticated renormalization methods. Therefore it is trivial in physics to apply a triple renormalization to

and recover Newton’s authority:

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1. From Not Even Wrong [↩]

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They are called “anomalies”, I’d say, because to a large extent in physics the approach is to pretend that working locally is fine – until one happens to run head-on into global issues. A mathematician might say at this point: “We made a mistake at the beginning in assuming that everything is globally well defined, instead there may be obstructions to doing so”. The physicist says: “My naive approach of working locally is fine, but since it fails to work in this situation, it is the situation which is not normal: it is anomalous.”

So the physicist assumes that the local is the norm? Like all antonyms in physics local/global pair is a pun. Physicists always extrapolate the local to global by using this pun. Local is trivially boring, global in the sense of cosmic is what sells. And what obstructions? There are no obstructions in physics that can stop physicists from making the most absurd extrapolations. My apologies for totally ignoring the technical meanings, if any, of local, global and obstructions.

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There is an important concept evident in all three equations – the period, speed and the acceleration [i.e. the orbit] of the satellite are not dependent upon the mass of the satellite.

The same is also true for force. Physicists start their derivation of orbital motion by writing force equations and later cancel all force terms. Therefore, by the same reasoning above, orbital motion does not depend on force.

Yet, in the case of force physicists reject the authority of mathematics and uphold Newton’s authority and claim that orbits are governed by force. To me this is not a scientific conclusion that follows from the equations.

What do you think?

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Physicists start their derivation with

This statement may be meaningful to physicists but the truth is that all three terms, F, m and a, disappear during the derivation. None of these Newtonian terms enter the formula used to compute orbits. From this observation we must conclude that F, m and a are not quantities that play any role in orbital motion:

• Orbital motion is independent of force, mass and acceleration caused by a supposed tangential motion.

This is not surprising because force is occult and does not exist in nature. Physicists write F, m and a because it is a professional tradition and also to save Newton’s authority. But authority terms do not have a place in orbital motion. Below I demonstrate that physicists’ derivation is nothing more than writing Kepler’s rule with a conventional unit.

2. Acceleration

Let’s use the following figure to look at physicists’ derivation in more detail:

In F=ma we can expand a

Acceleration a refers to the supposed tangential motion of point B.¹ To make explicit that BC is tangential and not circular, let’s define BC = d and write a as

where

So F = ma is really

But we know that m will cancel and it’s silly to carry a term we know we will cancel, so, for unit mass,

2. Geometry of circular motion and Newtonian gravity

From the geometry of circular motion

or

Placing this acceleration into F = ma

Let’s invoke the other Newtonian F

and let both forces be reunited²

4. Rotation versus revolution

The velocity on the circle and orbital period T are related by

Now physicists make the hidden assumption that

and that

But according to this, for a given period T

but this describes a sling-type rotation where velocity increases with increasing r. But orbits obey a different rule

Therefore, the assumption that the planet has a tangential motion and that this tangential motion is converted into a dynamical orbit by the Newtonian occult force F = ma is an incorrect assumption that is contradicted by observations. This is why v(tan) cancels below.

But physicists equate v(tan) and v(orb)

and obtain

This eliminates the tangential component v(tan) from the equations. Now all of the Newtonian terms physicists started with are eliminated. Kepler’s rule, the true formula used to compute orbits, has no Newtonian term in it:

At this point physicists say that they have derived “Kepler’s laws” from “Newton’s laws.”

Conclusion

This derivation amounts to writing Kepler’s rule R3/T2 = k with a conventional unit

This replacement of the Gaussian constant of gravity k³ with the Newtonian G occurred in the 19th century. Later physicists elevated G to the status of “constant of nature.” But constant terms in a proportionality cannot be “constants of nature.” What is constant is the proportionality, what physicists call “proportionality constants” are arbitrary constants no different than arbitrary constants of integration.

Therefore, all of the Newtonian terms physicists wrote when they started their derivation turned out to be physics vaporware. F, m and a exists in physics solely for traditional reasons and to save Newton’s authority. They are not needed to describe orbits. And orbits are independent of the Newtonian occult force and animistic mass.

1. Physicists draw a picture over the geometric point B to represent the mass m. But this term cancels even though it is represented in the figure. So the mass is an occult, or hidden, scholastic dormitive virtue. [↩]
2. Here we’ve equated two forces, one proportional to 1/r and the other 1/r2. This seems absurd to me. [↩]
3. or k2 with proper units [↩]

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Classical Greek or Latin formed an important part of secondary education only 50 years ago, with motivations similar to those currently used for mathematics: studies in these subjects would help develop logical thinking and problem solving skills. Today, very few students take Greek and Latin with the motivation that such studies are both difficult and of questionable usefulness for the effort invested.

Why is it that Calculus is compulsory for the majority of students most of whom will never use what they are taught? Because Doctors of Philosophy control mathematics education in the name of the bureaucracy they work for.

Calculus is the teaching vehicle of a giant bureaucracy

Professional Doctors make their living by teaching. The more there is to teach, the more complicated it is and the more hidden it is, there will be more jobs available for everyone. This is the major reason mathematics education exists in the ugly state it is taught today.

Once a habit forms in a bureaucracy it cannot be removed. If so how come Calculus replaced Greek and Latin? Well, thanks to Newton.

The scholastic corporation is the bureaucracy who owns both Calculus and physics and Newton is the founder of both.

But the habit of sustaining doctoral monopoly on theoretical knowledge by designing, hiding and teaching a complex and proprietary language is a constant of history; its content may change but the habit will remain. This pro-unhuman system is perpetuated by universities who employ the Doctors and they take all the profit while doctors earn authority for accepting to work for substandard wages.

Newton’s calculus becomes the new Latin

Mathematics as a discipline was starting to infiltrate the curriculum in Cambridge a few years before Newton started there. The main instigator was Newton’s teacher Isaac Barrow.

Newton made good use of this emerging field by writing a book that put for the first time in scholastic history the traditional polemical philosophy and geometry under the cover of the same book. Newton named his new language Natural Philosophy or simply Science. Today this old branch of scholasticism is called physics.

Newton defined rival Doctors of Theology to be ugly scholastic Doctors who taught two dead languages while up and coming Newtonian natural philosophers studied the new sciences of rational mechanics and calculus. Rational mechanics was the string theory of its day.

When Doctors of Philosophy became all powerful in the academia and Newtonism spread to the continent they started to teach their own habit, the Calculus.

Modern mathematics

Euclid’s Elementa, with its axioms, theorems and the ruler and compasses as tools, was the canon of mathematics education for many centuries into the mid 20th century, until it quite suddenly disappeared from the curriculum along with Greek and Latin. Not because geometry ceased to be of importance, but because Euclid’s geometry was replaced by computational geometry with the tools being Descartes analytical geometry in modern computational form.

Calculus will disappear the same way. This doesn’t mean that mathematics will cease to be of importance but that Calculus of the classroom will be replaced with a whole new mathematics curriculum based on computer science concepts developed since Newton’s time. There is no room for the ugly bureaucratic code called Calculus in the post-Newtonian world.

Commentary

The point is that the content of human science, in this case Calculus, has been corrupted by unhuman organisms for teir own profit. The corruption is even worse in academic physics. The content of the science of physics has been corrupted to serve the purposes of unhuman organisms. This means that all physics concepts are fused with cultural elements that need to be eliminated to recover the scientific content.

1. Thanks to Misha for bringing this wonderful book to my attention. [↩]

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Physicists are very proud of the logo of the House of Newton but what does it mean to multiply two masses?

It is

1. absurd
2. physical

Type Newton

In the multiplication

both M and m are type Newton. Yesterday we saw that little m, the inertial mass, and the inertial force F, the twin sister of the gravitational force F, were type Newton. We now extend our collection of type Newton with the inclusion of big M, the mass in charge of gravitation.¹

A new multiplication operator

To solve the problem of dubious instances of multiplication invented by physicists to save Newton’s authority such as multiplying two case-sensitive masses we can define a new multiplication operator x-N for Newtonian multiplication:

An application of the Newtonian multiplication

This new multiplication operator can be used to multiply masses by an application of Newton’s authority:

Now the Newtonian multiplication

makes perfect sense in physics: it has Newton’s stamp of authority.

Conclusion

Since both M and m are physical quantities, they either cancel or fuse with other constants and disappear. Therefore, this has been an academic exercise making clear why physicists don’t care about data types: they introduce too much unwanted and unneeded precision.

1. The only category of data type strictly enforced in physics is typographical: all constants are case sensitive. So, don’t confuse G and g. [↩]

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