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Measurement And Perceptual Units

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In the section, "Concept-Formation as a Mathematical Process," (found in Chapter 3 of OPAR) Dr. Peikoff discusses the purpose of measurement, what Miss Rand identified as "a process of integrating an unlimited scale of knowledge to man's limited perceptual experience—a process of making the universe knowable by bringing it within the range of man's consciousness, by establishing its relationship to man." (Introduction to Objectivist Epistemology, p. 8) This means that every unit of measurement must, ultimately, be brought down to the level of man's perception.

Would someone illustrate this principle with an example or two of scientific units of measurement? How does a "light-year" get reduced to something easily perceivable?

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In the section, "Concept-Formation as a Mathematical Process," (found in Chapter 3 of OPAR) Dr. Peikoff discusses the purpose of measurement, what Miss Rand identified as "a process of integrating an unlimited scale of knowledge to man's limited perceptual experience—a process of making the universe knowable by bringing it within the range of man's consciousness, by establishing its relationship to man." (Introduction to Objectivist Epistemology, p. 8) This means that every unit of measurement must, ultimately, be brought down to the level of man's perception.

Would someone illustrate this principle with an example or two of scientific units of measurement? How does a "light-year" get reduced to something easily perceivable?

The perceivable concrete is the letters you use in writing "l-i-g-h-t-y-e-a-r." You don't have to project a distance of 9.4605284 × 10^15 meters. Just look at the visual-auditory symbols light-year.

I had begun to project how physicists would have done this over time when I found this.

I hope I answered your question.

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The perceivable concrete is the letters you use in writing "l-i-g-h-t-y-e-a-r."

Well, the word "lightyear" is certainly with man's perceptual range but that's not the answer that I was seeking. A unit is itself an instance of the attribute being measured, in this case length. A word is not a unit in this sense. Dr. Peikoff writes in OPAR:

In the process of measurement, we identify the relationship of any instance of a certain attribute to a specific instance of it selected as the unit. The former may range across the entire spectrum of magnitude, from largest to smallest; the latter, the (primary) unit, must be within the range of human perception.

What is the primary unit of length used by scientists to grasp the distance of a lightyear? If astronomists ultimately reduce lightyears to feet, I can live with that. I was just wondering if there was a readout on some instrument or some other observable phenomenon that gave us an easily perceivable unit of measurement in this case.

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It seems to me that you can relate light years to man, by relating it to smaller units, such as feet and yards.

I know what a foot is. I have a direct grasp of this. There are 5280 feet in a mile, so I can relate a mile to a foot. There are 93 million miles to the sun. That distance, IIRC, is referred to as an astronomical unit.

There are 6.32x10^4 astronomical units in a light year.

This sort of knowledge would allow us to build a star ship, with enough fuel to get to its destination, if we had that sort of technology!

You can check out my unit conversion engine, which gives several units for different types of measurements.

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What is the primary unit of length used by scientists to grasp the distance of a lightyear?

You have answered your own question: a light-year is primarily a measure of distance. Because it is used for unimaginably large distances, it becomes its own primary in the context in which it is used. One would never measure the distance to the grocery store in light-years, unless said store was on the other side of the galaxy. Epistemologically it would reduce the same way as the Earth to moon example in OPAR (pg. 81-82).

If you want to get more involved, then consider this: a light-year can be defined as the product of the velocity of light and a duration (time). The velocity is a vector composed of speed and direction. Since direction isn't important to your question, we will ignore it and focus on speed. Speed is distance per unit time. Therefore a light-year can be reduced to two components of time (in minutes, hours or whatever you can comfortably perceive) and distance, in inches if you like.

Is that more what you had in mind?

d_s

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Well, the word "lightyear" is certainly with man's perceptual range but that's not the answer that I was seeking. A unit is itself an instance of the attribute being measured, in this case length. A word is not a unit in this sense. Dr. Peikoff writes in OPAR:

What is the primary unit of length used by scientists to grasp the distance of a lightyear? If astronomists ultimately reduce lightyears to feet, I can live with that. I was just wondering if there was a readout on some instrument or some other observable phenomenon that gave us an easily perceivable unit of measurement in this case.

Oh, I see. I should have paid more attention to your use of the word "reduced" in your original post.

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In the section, "Concept-Formation as a Mathematical Process," (found in Chapter 3 of OPAR) Dr. Peikoff discusses the purpose of measurement, what Miss Rand identified as "a process of integrating an unlimited scale of knowledge to man's limited perceptual experience—a process of making the universe knowable by bringing it within the range of man's consciousness, by establishing its relationship to man." (Introduction to Objectivist Epistemology, p. 8) This means that every unit of measurement must, ultimately, be brought down to the level of man's perception.

Would someone illustrate this principle with an example or two of scientific units of measurement? How does a "light-year" get reduced to something easily perceivable?

Grace Hooper, the admiral that coined the term "computer bug" and had a major role in inventing the concept of a compiler had a problem. She was having trouble getting her head around the distances involved in a light year so she ordered one of her staff to cut a piece of wire the length that light travles in something like a pico-second. It was around a meter or so. She used to hand out lengths of wire when she'd speak so that people could concretize such an abstract and huge concept.

She even gave one to David Letterman during an interview. He completely failed to grasp the importance of what she handed him. No surprise there.

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Could you explain in different words what sort of example you want? What exactly do you want illustrated?

I would like a scientific illustration of this line from OPAR:

In the process of measurement, we identify the relationship of any instance of a certain attribute to a specific instance of it selected as the unit. The former may range across the entire spectrum of magnitude, from largest to smallest; the latter, the (primary) unit, must be within the range of human perception.

In science, there are very large scale or abstract units of measurement like lightyears. Following the principle that Dr. Peikoff writes about above, there must be a perceptual-level primary unit to which a lightyear can be reduced (since we can't directly perceive a lightyear).

I was wondering if someone could reduce a more abstract unit of measurement (perhaps ohms or something not as obvious as length).

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I was wondering if someone could reduce a more abstract unit of measurement (perhaps ohms or something not as obvious as length).

Okay, now I think I understand what you are after.

In physics we often define our units in terms of fundamental constants. The International System of Units (SI) has as its base seven independently defined units: second (time), meter (length), kilogram (mass), kelvin (thermodynamic pressure), mole (amount of substance), ampere (electric current), and candela (luminous intensity). These are usually considered to be human-scale units. There are also many derived units, meaning some combination and/or algebraic manipulation of the base units is performed. Therefore the general answer to your question is that derived units are always reducible to the base units, only differing in terms of scale and complexity.

So, as you suggest, to take "ohms" as an example: an "ohm" is a derived unit of electric resistance that is expressed in terms of the derived unit of electrical potential difference (V) and the base unit electric current (A). The relation is simply ohm = V/A. But V itself is a derived unit expressed in terms of energy (J) and electric charge ( C). This relation is V = J/C. But the derived unit J is expressed in terms of force (N) and and the base unit length (m), and the derived unit C is expressed in terms of the base units electric current (A) and time (s). These two relations are J = Nm and C = As. We are left then with one remaining derived unit, N, which itself is expressed in terms of the base units length (m), mass (kg), and time (s). That relation is N = m(kg)/s^2.

Therefore, starting from the derived unit ohm = V/A, if you do the algebra of substituting all of the derived units in terms of the base units that I showed above, and, if you get all of that algebra right!, you wind up with ohm being reduced to base units, expressed as ohm = (kg)(m^2)/[(s^3)(A^2)]. So the derived unit ohm is just a complex expression relating mass (kg), length (m), time (s), and electric current in a certain manner. We have reduced the more complex derived unit ohm to the human-scale base units.

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In my physics class, the professor told us that all physical quantities are reducible to a combination of mass (kilogram, kg), length (meter, m), time (second, s), and charge (coulomb, c).

An ampere is a coulomb per second, c/s.

Thus, if you reduce Ohms by this method, it becomes: Ohm = (kg^1)(m^2)(s^-1)(c^-2).

The professor also made the point that we know what mass, length, and time are, but we don't really know what charge is? To what extent is this claim true?

Also, can a coulomb be grasped on the perceptual level?

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The International System of Units (SI) has as its base seven independently defined units: second (time), meter (length), kilogram (mass), kelvin (thermodynamic pressure), mole (amount of substance), ampere (electric current), and candela (luminous intensity).

One thing that has always puzzled me about SI units is why the standard unit for mass is kilogram and not gram. It is strange that a standard unit of measurement is defined as a multiple of another unit. Is the reason for this that the already defined kilogram was recognized as a more useful unit to measure mass when The International System of Units was set up?

Here is another question that is semi-related. The candela is the unit of measurement for luminous intensity, is there a unit of measurement for intensity of odor?

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The sense of smell is based on receptors in the nose that detect certain chemicals. So I suppose an objective unit of measurement for odor might be based on the concentration of the chemical causing the odor. Beats me whether this has ever been formally done, though ...

Charge can certainly be perceived directly (e.g. static electricity). I'm not sure whether 1 coulomb of charge could be.

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In my physics class, the professor told us that all physical quantities are reducible to a combination of mass (kilogram, kg), length (meter, m), time (second, s), and charge (coulomb, c). 

I wasn't aware of this. That is a great insight!

I'll need to chew on it further. :(

Also, can a coulomb be grasped on the perceptual level?

From the standpoint of force? The answer is yes, as Godless notes, since you can observe electrostatic attraction, e.g. a sock that sticks to your pants after going through the dryer.

I coulomb of charge would result in some fraction of the perceivable force, or is probably perceivable with a torsion balance, ala Coulomb's experiment!

Btw, Millikan, with his oil drop experiment, was able to measure the charge on one electron, which is 1.6e-19 Coulombs!

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In my physics class, the professor told us that all physical quantities are reducible to a combination of mass (kilogram, kg), length (meter, m), time (second, s), and charge (coulomb, c).

Mass, length, and time are fundamental units, but charge is derivative, itself expressed in terms of the more fundamental ampere and time. He also left out thermodynamic temperature (kelvin, K) and others.

The professor also made the point that we know what mass, length, and time are, but we don't really know what charge is?  To what extent is this claim true?
The same can be said about mass as about charge. To "know" what these are is something different for different theories. The classical physics view of charge is not the same as charge in quantum chromodynamics, and the mass of classical physics is not the same mass of quantum field theory.

Also, can a coulomb be grasped on the perceptual level?

Not directly, but certainly by its effects. That is what Millikan did with his oil-drop experiments. Of course, now, you can purchase a nano Coulomb meter, a small digital device device with a pencil-type probe, and you can measure the dynamic charge on small semiconductor devices.

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One thing that has always puzzled me about SI units is why the standard unit for mass is kilogram and not gram.

It is an historical artifact dating back to the platinum standards developed in 1799. Each subsequent metrological meeting on standards for the next two centuries could have changed the unit, but by modern times it was so firmly ingrained that it remains the only base unit with a prefix.

Here is another question that is semi-related.  The candela is the unit of measurement for luminous intensity, is there a unit of measurement for intensity of odor?

No, at least not scientifically. The problems are severe. Each olfactory receptor can be stimulated by some small number of molecules that are chemically related, and each individual odorant molecule can be recognized by some small group of olfactory receptors. But in the olfactory mucosa the dynamics can change drastically, where different concentrations of the odorant molecule can change which group of receptors are stimulated. The intensity of the odorant molecule depends on this concentration, where electrical changes in the olfactory nerves are a measure of the receptor activity. In general, strong odorants generate more intense neural impulses, but the variations are so great as to defy quantification. There may be some hope in investigating an analogous effect to that of light adaptation, where the intensity of the light causes adjustments to light sensitivity. The olfactory neurons may likewise adapt to changing concentrations of the odorant molecule by adjusting certain aspects of its nucleotide-gated ion channels. Perhaps therein might lie the seeds of a unit, but that is pure speculation at this point.

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Stephen Speicher,

Considering charge to be derived from current and time (c=at) seems to me analagous to considering mass to be derived from momentum and time (m=pt); it would make more sense to derive current from charge and time (a=dc/dt) like we do momentum from mass and time (p=dm/dt).

Why do you think this is not so?

(And pardon me for asking, but how do you pronounce your last name?)

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Stephen Speicher,

Considering charge to be derived from current and time (c=at) seems to me analagous to considering mass to be derived from momentum and time (m=pt); it would make more sense to derive current from charge and time (a=dc/dt) like we do momentum from mass and time (p=dm/dt).

Why do you think this is not so?

Keep in mind that the context I have been talking about is the practical SI units as standards in measurements. When establishing the standards more than a century ago the cgs units in electromagnetism, which include the statcoulomb for charge, were not as practical as the ampere for current, which is why SI included the amp. The ampere can be measured to a much higher precision. However, note that when doing theoretical work in EM physicists frequently work in cgs (Gaussian or Heaviside-Lorentz) units for ease of manipulation, and only switch to SI when they need to quantify.

(And pardon me for asking, but how do you pronounce your last name?)

SPY-SHER

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