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Post 0

Thursday, November 24 - 4:43am

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My definition: "Measurement is a quantity in terms of real numbers and a standard of magnitude that serves as a unit, with multiples of the unit being additive and subtractive."

Does this allow for measurement systems that are non linier like decibels or the Richter scale?

(I'm asking, not being rhetorical)

Post 1

Thursday, November 24 - 6:02am

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Thank you for the excellent exposition, Merlin! I found it enlightening and edifying. I am smarter for having read it. This day was not going well, but you turned it around for me.

Keith: If I may, I might point out that via logarithms, etc., you can make anything "additive" and basically, the operations of exponentiation and multiplication are defined as kinds of repeated additions. (Likewise, subtraction is just a kind of addition.) But your point is well made and it occured to me, too, as I was reading the article.

Finally, perhaps my favorite example of errant psychology is William Sheldon's somatotyping. Sheldon also invented the bizarre 70-point grading scale loved by American coin collectors. He photographed college freshmen in the nude to develop metrics for psychological profiles. Somewhere are naked pix of Nora Ephron, Judith Martin, and Hillary Rodham. See here for how coins and nudes are intertwined.
http://www.maineantiquedigest.com/articles/shel0298.htm
or here:
http://tafkac.org/collegiate/ivy_league_nude_photos.html

Also, for those who believe that epistemology has moral consequences, Sheldon was posthumously condemned in court as a thief and his stolen property -- subsequently sold via auctions after his death -- was returned the American Numismatic Society.

(Edited by Michael E. Marotta on 11/24, 6:05am)

Post 2

Thursday, November 24 - 6:34am

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Keith Phillips asked if the Richter scale fits my definition of "measurement." Good question and one I expected. Based on what I know about it, I'm inclined to call it a borderline case. It is a ranking or scaling calculated from measurements of amplitudes of seismic waves that do fit my definition. Note that these amplitudes are found. My guess is that Richter decided that using a linear scale would sometimes give amplitude values so large they are inconvenient to use. Therefore, he decided to convert such values to a base-10 logarithmic scale for easier comprehension and expression. It seems he could have chosen scientific notation, e.g. NN.NN x 10^M (N and M numbers and ^ for exponentiation), which would have not masked the linearity. However, he did not choose that route.

You're welcome, Michael M!

Soon I will be preoccupied with Thanksgiving Day festivities for most of the rest of the day, so my replies will be delayed.

Happy Thanksgiving to all!

Post 3

Thursday, November 24 - 10:40am

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Merlin,

Thanks for the nice article. Interesting, I was talking to my wife Karen a couple of weeks ago and she was talking about the different ways they measure larger and larger parcels of land. At some point they run into trouble because of the curvature of the earth. She asked, what makes a measurement anyway? I said a true measurement has to have a reference unit, like feet, pounds, seconds, etc. If there's no reference, then it's not a true measurement.

Regarding decibels: You state "If P claims that X is measurement, then P should be able to name the unit."

This is true of the dB unit. However, dB values only make sense if you name the reference unit and the quantity of reference unit you are comparing a measured value to.

For instance we may define 1 milli Watt of RF power to be 0 dB. If we want to compare some other RF power to our 1 milliWatt reference we do the following calculation: X dB[1mW] = 10 times log X (milliWatts)/1milliWatt. A measurement of greater than 1mW is represented by a positive dB number, a measurement of less than 1mW is represented by a negative number. Many orders of magnitude of powers both less than and greater than our reference can be represented in simple comparable units. Quite convenient. It is not a borderline case at all because dB's are easily converted to real units of power (or voltage or whatever).

Post 4

Thursday, November 24 - 12:28pm

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The points in this article cannot be addressed without asking, what is essential in measurement - and how does measurement differ from other evidence obtained by the senses? As with much else recently, I'll address this when I have time to write about it at adequate length. I am grateful to Merlin for setting the stage.

Post 5

Thursday, November 24 - 5:59pm

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Keith wrote:

"Measurement is a quantity in terms of real numbers and a standard of magnitude that serves as a unit, with multiples of the unit being additive and subtractive.

Does this allow for measurement systems that are non linier like decibels or the Richter scale?"

I would disagree regarding "real" numbers. Imaginary or complex numbers measure a point on a circle.

The "standard of magnitude that serves as a unit" is confusing. I would say measurement is the non-arbitrary magnitude of the units being measured.

There are linear measurements, logarithmic measurements (decibels), even (contrary to the article) statistical measurements - "standard deviations". The more complex logarithmic measurements are transforms of the simpler, but are still true, as long as the relationship is defined.

In general relativity, measurements are in curved space along a path (geodesic) of least-action.

Adam wrote:

what is essential in measurement - and how does measurement differ from other evidence obtained by the senses?

That's the issue - what is essential. Some quantity to measure, and a standard unit to measure with.

Thinking about Goedel's theorem and Turing machines, I'm doubting the reality of "whole" or "integer" numbers!

Yea, sure it looks like you have one or two or three... discrete fingers or toes. But what defines the transition where one begins and the other ends?

What about particles? If you squeeze one or two or three... discrete particles close enough, there starts to become probabilities quantum states could begin blurring - you describe them as waves and probabilities of observing them as discrete or tangling entities.

Even quantum numbers like spin, particle charge or magnetic moment, though discrete for particles, are dictated by the nature of the geometry of interacting fields composing the particle.

So as the quantity of mass-energy increases distance in space and time, approximating the quantities with integers becomes valid.

AFAIK, no ultimate quantized "particle" is known.

Scott

Post 6

Friday, November 25 - 6:06am

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Scott Stephens wrote:

I would disagree regarding "real" numbers. Imaginary or complex numbers measure a point on a circle.

I have no idea what your second sentence means. Please elaborate. If you claim there is such a thing as a measurement in terms of complex numbers, please give a clear concrete example.

The "standard of magnitude that serves as a unit" is confusing.

What exactly do you find confusing? Consider a few concrete examples of measurement units and maybe it will be clearer.

I would say measurement is the non-arbitrary magnitude of the units being measured.

What qualify as units? Is that a definition? If yes, it's circular. Also, "units being measured" sounds strange. One measures an attribute in terms of units.

There are linear measurements, logarithmic measurements (decibels), even (contrary to the article) statistical measurements - "standard deviations". The more complex logarithmic measurements are transforms of the simpler, but are still true, as long as the relationship is defined.

Regarding logarithmic and statistical measurements, you are free to use "measurement" metaphorically. My article concerns literal meaning, not metaphors. About the logarithmic Richter scale, it's discussed above and note that it is called the Richter scale, not the Richter measurement. Suppose you calculate the standard deviation for a series of random numbers. The result is a pure number. My definition of "measurement" also requires a standard unit of magnitude, an analog to inch, gram, mph, etc. That's why I consider statistics quantities but not measurements. Of course, statistics may be about measurements.

Post 7

Friday, November 25 - 10:05pm

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Merlin,

No doubt there is much to analyze and discuss. I'd rather not get pedantic with semantics.

First, regarding examples of measurements of complex vs. real numbers, consider the electrical power grid. "Power Factor" is a measure of reflected power. In the most common application, flourescent or HPS lights in a warehouse. Some have many inductive ballasts that reflect energy, create a phase-shift between voltage and current.

http://en.wikipedia.org/wiki/AC_power

I don't have time to explain. Here:
http://www.google.com/search?sourceid=mozilla&q=%22power%20factor%22%20lighting

http://www.google.com/search?hl=en&lr=&q=%22power+factor%22+lighting+%22complex+numbers%22&btnG=Search
http://en.wikipedia.org/wiki/AC_power

Any further questions regarding complex vs. real power mesurement?

Scott

Post 8

Saturday, November 26 - 5:49am

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Scott, thank you for the links.

I thought my definition might be too restrictive.

1. I included "real number" to exclude ordinal numbers, which don't have arithmetic properties and are often subjective. The electrical power example ("apparent power") seems to warrant not excluding complex numbers. The drawback, of course, is it could much complicate the definition.

2. It could be construed to improperly exclude "derived measurements" like the Richter scale numbers, decibels, and apparent power. I favor including ones like the first two, since the exponent part has arithmetic properties. Also, underlying all three are (non-log, non-derived) measurements which do fit my definition. Again, it could much complicate the definition.

"Apparent power" seems to describe a potential value, in contrast to the real valued units of measure watt, volt and ampere that underlie it. Is that accurate?

Post 9

Saturday, November 26 - 3:35pm

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Merlin,

"Apparent power" seems to describe a potential value, in contrast to the real valued units of measure watt, volt and ampere that underlie it. Is that accurate?

I haven't heard the term "Apparent power" before.

There is another term VAR - volt-amps-reactive. Motor-start capacitors have that rating.

You see, an inductor or capacitor store current or voltage, then discharges it. There isn't anything "apparent" or "imaginary" about it! Its quite real, I assure you!

If you don't think so, try using an under-rated component in a high-power application and you will get a violent object lesson in the reality of reactively-stored energy!

"Real" power is absorbed power, power converted to heat by a resistor, or light, or kinetic energy by a motor. Reactive power is *REAL* electrical power bouncing around; taking the form of magnetic flux in an inductor, or electrostatic potential in a capacitor.

And if you whiz around an inductor or capacitor at relativistic speeds, the electric and magnetic fields change from one to the other, depending on reference frame.

Which demonstrates the real dimension of "charge" is displaced, and is defined according to reference frame.

Scott

Post 10

Saturday, November 26 - 4:12pm

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Scott Stephens wrote:

I haven't heard the term "Apparent power" before.

It was at the URL, http://en.wikipedia.org/wiki/AC_power, you gave in post #7.

There is another term VAR - volt-amps-reactive. Motor-start capacitors have that rating.

Yes, that is the unit for reactive power at the same URL.

You see, an inductor or capacitor store current or voltage, then discharges it. There isn't anything "apparent" or "imaginary" about it! Its quite real, I assure you! If you don't think so, try using an under-rated component in a high-power application and you will get a violent object lesson in the reality of reactively-stored energy!

I didn't say "real power" was "apparent" or "imaginary." The webpage used "apparent power", and the formula for it included an imaginary number. I did use "potential" (in regard to "apparent power"), but that does not mean imaginary or unreal.