How can Mindless Mathematical Laws give rise to Aims and Intentions? by James A Putnam

The third mathematical example demonstrates that direct dependency upon empirical evidence for derivations of properties and their units, makes it clear that proportionality constants of important property relationships should be left to have their meanings revealed by the mathematics of equations that are not those of theoretical physics, but, rather equations that have been returned to their empirical forms. In their empirical forms they have fundamental unity and their empirically communicated meanings will be faithfully revealed by the mathematics. They can tolerate no intersession by anyone's mind. They are formed free of theorists' guesses and imaginings. They reveal what empirical evidence is communicating to us. What is the importance of this to proportionality constants? The answer to this question is made clear by my example:

Using the mks system of units, Coulomb's Law for two equally charged particles is:

f=k(qq/r2)

The proportionallity constant 'k' is found by experiment to be:

k=8.987x109((newtons*meters2)/coulomb2)

This constant must be found experimentally because: The units of force f, charge q and distance r in the mks system are defined independently of Coulomb's Law. Their meanings have been set before the advent of Coulomb's Law. The only source left that can contain and therefore reveal the new meaning that is represented by Coulomb's Law, is the proportionality constant. It is the only new source of information to be learned from experiment.

In the case of Coulomb's Law, it is usually written showing an inverse proportionality of force with the square of distance. Actually it is inversely proportional to the area of the surface of a sphere with radius r. The formula for the area of the surface of a sphere is:

S=4*pi*r2

Taking this into account, Coulomb's Law can be written as:

f=kf(qq/4*pi*r2)

Where, kf is the pure proportionality constant. As stated previously, when all the other terms in the equation are independently defined based upon previous empirical measurements, then, only the proportionality constant can bring new meaning into the equation that makes Coulomb's Law express unique new meaning.

It does not matter that the arithmetic values are relative. It does not matter that some of the units may be artificial. What is essential is that the proportionality constant be separate from each of these other properties. It then becomes possible to identify this new property. Within the framework of my work it is found to be:

kf=vsvc

Where vs is the speed of sound and vc is the speed of light in the specific medium. This relationship is approximate for a gas and accurate for solids.

James Putnam

Example 1 from above shows that Einsteins' idea that setting rest energy equal to zero leaves an equation for the energy of a photon.is wrong. Yet his solution does predict photon energy accurately. The reason is that energy is derived from force times distance. The rest energy term does not result from applying a force across a distance. The product of force and distance yields kinetic energy. The term that is left to apply to photon energy is the kinetic energy term. Even though I suggest that the form of his energy equation is not the best form, it will successfully predict kinetic energy whether for an object or for a photon. However when he divides his photon energy equation by the speed of light C, he does not get the correct form for photon momentum. That is why his photon momentum equation over predicts the amount of photon momentum. The equation that I provided for photon momentum will predict the correct momentum.

The second example shows an equation that makes no sense in any unit system of today's theoretical physics. After mass is defined, the equations of physics begin to be replaced by their empirical forms. Their empirical forms take their lead directly from empirical evidence leaving no room for theorists to add their ideas. The result is physics equations that have had theory removed from them. They are returned to their natural empirical forms where all properties are defined directly from empirical evidence. The units for all properties are formed from different arrangements of the units of empirical evidence. There are just two natural units for the two properties by which all empirical evidence is communicated to us. The equation introduced in my second example is a solution reached using the new units of physics properties, and, the immediate fundamental unity that they bring back to physics equations. The units for the equation in its empirical form do match; and, the equation makes great sense.

The third example shows that the practice of setting proportionality constants equal to unity, for convenience, can be a bad practice. In the case of Coulomb's law in the mks system, the proportionality constant is not set to one. Because of that, it is able to communicate to us the new meaning that arrives with the formation of Coulomb's equation. I also will stress that although I have provided no examples thus far, I am certain the the practice of 'normalization' suffers from the same risk. It can make it more difficult or nearly impossible to learn the new meaning that comes with new expressions. For example, the equation E=MC2 normalized so that it reads E=M, an apparent equation that is definitely not an equation, loses the potential for understanding the detailed physical information that is being communicated by E=MC2. That information is not yet recognized, but writing the non-equation E=M makes it impossible to learn the physics basis for the equation E=MC2.

James Putnam

This first quote establishes how to define a property in physics. It is then followed by a second quote from the 13th ed. The differences in these two introductions shows a decline in rigor that I think is part of what works against relatively recently trained professionals understanding what I write:

First quote:

College Physics; Sears, Zemansky; 3rd ed.; 1960; Page 1, Chapter 1:

1-1 The fundamental indefinables of mechanics. Physics has been called the science of measurement. To quote from Lord Kelvin (1824-1907), "I often say that when you can measure what you are speaking about, and express it in numbers, you know something about it; but when you cannot express it in numbers, your knowledge is of a meagre and unsatisfactory kind; it may be the beginning of knowledge, but you have scarcely, in your thoughts, advanced to the stage of Science, whatever the matter may be."

A definition of a quantity in physics must provide a set of rules for calculating it in terms of other quantities that can be measured. Thus, when momentum is defined as the product of "mass" and "velocity," the rule for calculating momentum is contained within the definition, and all that is necessary is to know how to measure mass and velocity. The definition of velocity is given in terms of length and time, but there are no simpler or more fundamental quantities in terms of which length and time may be expressed. Length and time are two of the indefinables of mechanics. It has been found possible to express all the quantities of mechanics in terms of only three indefinables. The third may be taken to be "mass" or "force" with equal justification. We shall choose mass as the third indefinable of mechanics.

In geometry, the fundamental indefinable is the "point." The geometer asks his disciple to build any picture of a point in his mind, provided the picture is consistent with what the geometer says about the point. In physics, the situation is not so subtle. Physicists from all over the world have international committees at whose meetings the rules of measurement of the indefinables are adopted. The rule for measuring an indefinable takes the place of a definition. ...

Chapter 15, page 286; 15-1:

To describe the equilibrium states of mechanical systems, as well as to study and predict the motions of rigid bodies and fluids, only three fundamental indefinables were needed: length, mass, and time. Every other physical quantity of importance in mechanics could be expressed in terms of these three indefinables., We come now, however, to a series of phenomena, called thermal effects or heat phenomena, which involve aspects that are essentially nonmechanical and which require for their description a fourth fundamental indefinable, the temperature. ...

Second quote:

Sears and Zemansky 13th ed.

Summary of Chapter 1 (page 26):

"Physical quantities and units: Three fundamental physical quantities are mass, length, and time. The corresponding basic SI units are the kilogram, the meter, and the second. Derived units for other physical quantities are products or quotients of the basic units. ... "

'Physical quantities' means the modern authors are speaking of rules of measurement. "Derived units for other physics quantities ..." means the same authors are speaking of a derivation process which is not the same as citing rules of measurement.

(Going back to pages 4 & 5)

"Some physical quantities are so fundamental that we can define them only by describing how to measure them. Such a definition is called an operational definition. Two examples are measuring a distance by using a ruler and measuring a time interval by using a stopwatch. In other cases we define a physical quantity by describing how to calculate it from other quantities that we can measure."

"Time

From 1889 until 1967, the unit of time was defined as a certain fraction of the mean solar day, the average time between successive arrivals of the sun at its highest point in the sky. The present standard, adopted in 1967, is much more precise. It is based on an atomic clock, which uses the energy difference between the two lowest energy states of the cesium atom. When bombarded by microwaves of precisely the proper frequency, cesium atoms undergo a transition from one of these states to the other. One second (abbreviated s) is defined as the time required for9,192,631,770 cycles of this microwave radiation (Fig. 1.3a)."

"Length

In 1960 an atomic standard for the meter was also established, using the wavelength of the orange-red light emitted by atoms of krypton in a glow discharge tube. Using this length standard, the speed of light in vacuum was measured to be 299,792,458 m s. In November 1983, the length standard was changed again so that the speed of light in vacuum was defined to be precisely 299,792,458 m s. Hence the new definition of the meter (abbreviated m) is the distance that light travels in vacuum in 1 299,792,458 second (Fig. 1.3b). This provides a much more precise standard of length than the one based on a wavelength of light."

[With no explanation there is a third "so fundamental" ... "physical quantitiy" introduced.]

"Mass

The standard of mass, the kilogram (abbreviated kg), is defined to be the mass of a particular cylinder of platinum-iridium alloy kept at the International Bureau of Weights and Measures at Sèvres, near Paris (Fig. 1.4). An atomic standard of mass would be more fundamental, but at present we cannot measure masses on an atomic scale with as much accuracy as on a macroscopic scale. The gram (which is not a fundamental unit) is 0.001 kilogram."

I knew textbooks had changed by becoming less rigorous. This introduction not only lacks rigor, but, is deliberately claiming it has presented material that it has not presented.

From the summary: "Three fundamental physical quantities are mass, length, and time."

Mass was not introduced as a fundamental physical quantity. It was placed, without explanation, following the "operational definitions" of length and time. It was given, by placement alone, the appearance of being associated with length and time. Length and time are the names used by physicists of the two properties of empirical evidence. Those two properties " ... are so fundamental that we can define them only by describing how to measure them." (The word define is an example of the adoption of layperson type of terminology.) There is not a third property involved in communicating empirical evidence. Mass is not associated with length and time. It is not a property that is " ... so fundamental that we can define it only by describing how to measure it. " It is associated with all other properties of mechanics that are learned from empirical evidence and must receive their definitions in terms of the only two fundamental physical quantities limited to being represented by their rules of measurement, length and time. The equation f/m=a gives us guidance that empirical evidence shows that the units of force divided by the units of mass must reduce to the units of acceleration. The properties of acceleration are length and time because acceleration is the form that empirical evidence arrives in. The 'a' in f/m=a is the empirical evidence.

James Putnam

My view of mathematics being either mindful or mindless depends on if there are any human decisions that result in choices or changes to the equations. Human interventions might be either helpful or harmful to the meaning of an equation, but, in either case the equation is no longer held in a mindless state. I did at times, in my essay use equations that had been affected in the past by human choice. Even so, I used the equation or equations as if they were mindless. The point is that they remained unchanged by human intervention during their present use by me. So, mathematics being mindless depends both upon the quality of the effects of human intervention and whether or not the point I want to make is practically independently valid and is not significantly affected by past human intervention. My own work comes very close to keeping mathematics mindless. Mindless mathematics has the best chance of revealing that which empirical evidence is communicating to us.

Human interventions, in physics equations, began at the beginning and immediately introduced human developed meanings that compete against those which empirical evidence is communicating to us. My repeated stressing of the importance of defining mass is a prime example of my reaching for learning its empirical description by relying upon mindless mathematics in opposition to the existing harmful human choice to make it a permanently undefined property. That harmful act turned f=ma into a partly human invention. The effect of that choice from the past was to prevent it and further physics equations from developing their empirical forms, forms that are learned directly from empirical evidence, and instead caused physics equations to become human guided vessels serving human inspired ideas and guesses that combine into theories.

The correct form for f=ma must include definitions for both force and mass. Those definitions must be formed from combinations of pre-existing properties. The units of force and mass must be defined by forming them from combinations of the units of pre-existing properties. The only pre-existing units are meters and seconds. The only pre-existing properties are length and duration, permanent substitutes that serve in place of the unmeasured indefinable properties of space and time. Length and duration are the two properties by which empirical evidence is communicated to us via photons.

James Putnam

The FQxi.org Essay Contests: There is an obvious over supply of the lowly 'one' votes available. Since each voter has just one vote per essay, that supply reflects a concerted effort on the part of a body of voters, not necessarily essay contributors. Does this matter? In a perfect world it would. However, in this world there is good reason to appreciate the opportunity for amateurs to submit essays alongside professionals.

It is an opportunity to put one's ideas on a record that remains permanent and is good as any other. Perhaps the most important plus about FQXi.org is that they are tolerant to a fault. You can express your views here and not be threatened with being banned for not being a puppet made to talk about physics the way that many theoretical physicists think we should. Here is an example of mine: Physics is not dumbness, but, it is about dumbness. It is about learning the most useful relationships between empirical evidence and mechanical activities. Yet its equations are loaded with intelligent input. There is value in a contest to show how aims and intentions emerge from theoretical physics. I say that they emerge because they have been added to it. It is of interest to learn all the ways that intelligent minds have molded physics equations and property interpretations to give opportunity for those equations to reflect back to us, as solutions, all those same ways that intelligent minds have molded physics equations and property interpretations. Seriously, here at FQXi.org there is mix of the fruits of intelligence that I know of nowhere else on the Internet.

James Putnam

I recommend a new Author and his Essay by Steven Andresen

Vladimir,

Your essay will receive a high rating before the contest closes. Agreement isn't necessary at all. I appreciate reading your opinion. My response is that it cannot be established that there is separation of the intelligence of physics' tools from the nature that gave rise to it. The potential in full had to already be provided for. This may sound creator like. It matters not whether it sounds that way or not. I follow where empirical evidence leads. the empirical evidence is that we are formed from parts of the Universe according to the properties of the Universe. There is nothing new added into the mix. If that was the case, then we would have evidence for the existence of miracles.

Computers will never be intelligent. They will always mimic intelligence. When I ask a computer to add 2+3 and it responds that the answer is 5, all that has happened is that electrons have changed places either moved to inputs to transistors or moved away from inputs to transistors. The computer is forced to display a meaningless figure and it is done. Only the observer can attach meaning to that figure of 5. Even for a computer that currently adds numbers, as it does when plotting the integral of a function, and does so far, far faster than a human ever will, it is doing something that we don't do. We do not add. We either remember the sum of 2+3=5 or we must resort to counting. Another important missing function of intelligence, for computers, is the use of emotion.

If it wan't for emotion, we wouldn't know the difference between a sensible thought and an insensible thought. Every conscious thought is a conclusion that was reached subconsciously after our subconscious mind searched for the best meaning to fit with patterns that our subconscious mind decided probably exist in the wildly mixed storm of photons that bombard us from innumerable sources. That mix is arriving as innumerable tiny increments of information about particles located throughout the Universe changing their velocities. They are arriving at the speed of light in formations that are never repeated.

From that storm we very quickly discern possible patterns and find meanings to fit with them. Just one of the things our subconscious mind does is it draws a picture of what it has concluded we should be seeing. That conclusion is presented to our conscious mind. Its conclusion is sometimes wrong. That is why optical illusions work. Even when we know that the conclusion is wrong, our subconscious mind continues to draw its own erroneous conclusion and we continue to see the wrong picture.

Too much said right? :) Please look forward to a high rating for your essay.

James Putnam