6 - Operational Definitions

[MikeO]

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I mentioned earlier in "Generating the RIGHT Answer" that there was one word which was slippery and very difficult to define in the mirror riddle. That word was identified as "reverse" and I started working out operational definitions for that word without very much explanation as to WHY "reverse" was slippery, nor what operational definitions were all about.

This thread will address these issues, but it will start in a roundabout way.


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Very young schoolchildren often play a came called "Opposites" where one will call out a word, and the others have to name its opposite. This is fun for a while with simple words like "hot" and its opposite "cold," or "fast" and "slow."

It can keep kids occupied for a quite while on a long car trip with pairs like big/little, up/down, best/worst, tall/short and the like. But eventually a word can come up that has no obvious opposite.

What's the opposite of "New York"?

What's the opposite of "red"?

When this happens some clever kids will start bending and stretching what they think are appropriate answers. Sometimes, this works pretty well.

What's the opposite of a sweater?

Someone might say that an undershirt is the opposite of a sweater,
because a sweater goes OVER a shirt, while an undershirt goes UNDER a shirt.

But then someone else may say that sweat-pants are the the opposite of a sweater,
because a sweater covers the top half of the body, while sweat-pants cover the bottom half.

So who's right?

[MikeO]

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Here's another one:





What's the opposite of a tall, skinny man?





Think about it a little...





...at least one screen's worth.

[MikeO]

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So what IS the opposite of a tall, skinny man?


Here are the answers I've heard upon asking this question over a hundred times:


A tall, skinny woman

A short, skinny woman

A tall, heavy woman

A short, skinny man

A tall, heavy woman

A short, heavy man

A tall, heavy man

A short, heavy woman



Some of these answers are more frequently offered than others, but all seem to be legitimate opposites.


But which one is the really right answer?

[MikeO]

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Before giving up, let's analyze this situation a bit.



We might start by asking who wants to know?

Or how did this ever come up in the first place?

And what are we going to do with the right answer, anyway?


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If all this is but a children’s game, then it’s silly and we need not answer at all.

But what if it came up in some complicated technological situation, or as part of a deep theoretical physics experiment? In that kind of case we’d have to go back and examine the context in which it came up. Then we might come up with some kind of formula, or procedure, or operation to determine what the correct answer is.



Is this sounding at all familiar? .. It should! ..I designed it that way.



First of all, in “Generating the RIGHT Answer” we had to determine how people approach the mirror situation. We looked at how they behaved in front of a mirror pondering the mirror riddle. We reconstructed what was going on in their heads when they perceive and vocalize a left/right reversal.

For the "sweater" or the "tall skinny man" questions we would have to go back and interview whoever asked the question to see what kind of opposite they had in mind. If they were consistent in all their “Opposites" game questions, we’d have to ask of them what rule, or formula they are using.

THIS is what operational definitions are all about.

For the "sweater" question, one person thought in terms of layers of clothing, for the other it was visible location of clothing.

For the "tall skinny man" there are three paramaters that can be "reversed" individually, the first to "short," or the second to "heavy," or the third to "woman." There are nine permutations to go through, so eight different “opposites” emerge. In order to answer it, the asker of the question would have to supply us with some kind of context, or rule, or operational definition of what they mean by opposite in that case.


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Another similarity is that the word “opposite” is a lot like the word “reverse.” They have similar root definitions, and they’re both slippery in that there are sometimes multiple ways they can operate, depending on the application, or context, or the one asking.

I noted that in the mirror riddle there was no technological context in which the riddle was posed, and hence no big, immediate practical application for the answer. This is a lot like the “opposite” game.

It seems that the mirror riddle is a lot like a child’s game. It’s curiosity and the pure desire to make things fit that drives both. With the “Opposites" game it’s curiosity as to what fits in the rules of language. In the mirror it’s curiosity about how symmetry works out that we are after.

[MikeO]

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We were stumped when facing subtle words like “reverse” and “opposite” and the only way out was to come up with some kind of way to “pin down” those slippery words. We found that operational definitions were very useful.

A little over a hundred years ago Einstein was facing some similar situations. It seemed that the way light rays behaved was very odd. When there was motion involving the source of the light or the observer of the light, then the velocity of the light rays was a big problem.

It seemed that no matter what combinations of source motion or observer motion, the speed of light measured always the same.


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When we think about a jet plane firing a bullet forward, we would expect (and rightly too) that the airplane's velocity gives more oomph to the bullet, and that the bullet would go faster than normal. We might think that the bullet would be moving at the airplane speed PLUS its normal muzzle velocity. In this case the source velocity (airplane speed) affected the bullet velocity.

But with light it's different. The velocity of a source of light was found to NOT affect the light speed at all. Not even a little.

Consider now a bullet fired from a gun pointed East on the ground at the normal muzzle velocity. A jet plane with a Highway Patrol Radar Gun, and moving West, headlong toward the bullet, would see that bullet coming at it with additional velocity, again higher than mere muzzle velocity. This is a case of the observer’s motion affecting the measured speed of the bullet.

But, again, observer motion had NO effect on light ray velocity. NONE at all! This was a HUGE puzzle in the late 1800’s. The velocity of light was absolutely always the same, in vacuum that is. Air or glass will always slow it down some, but that was avoided.


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Two physicists named Lorentz and FitzGerald found a solution, but it was pretty quirky. They found that the math worked out better if space shrunk (whatever that means) when motion was involved. Then they noticed that they also should fiddle with time to get their equations to look neat.

So, the situation was one of “space” and “time” behaving in a very slippery fashion, and light was absolutely stuck in a rut, unaffected by any motion. It was a huge riddle, and THIS riddle had plenty of practical applications that made it worth solving. But no one could.

Then Einstein came along and proposed using operational definitions to pin down space and time.

See where I got my ideas from?


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Light velocity, like all velocities, is found by measuring miles per hour. The miles traveled divided by the hours it took, or the meters divided by seconds it took, or whatever, all are measures of space divided by time. Einstein’s theory started out with a very new way of thinking about the peculiar behavior of light velocity measurments.

He simply accepted it.

Einstein thought that the strange un-affectability of light velocity should be his starting point, instead of at the end of some long winded explanation. It made things much more simple to think this way.

Then he came up with another incredible simplification. It was an operational definition for how to think about time. Up until then time was something philosophers, poets, and songwriters thought of as fertile ground for the imagination. And it WAS! Time was a VERY slippery idea and very difficult to define.

Einstein’s definition for time was astoundingly simple:

Time is that which is measured by clocks.

End of story, end of song, end of essay.

He then came up with a very useful operational definition of a clock. It was a yardstick
with a mirror at each end. Yes, that’s right MIRRORS at either end! And then he asked
why did his mirror clock reverse time but not his mortgage rate!




;D Sorry, I couldn’t resist.


Seriously, Einstein’s clock went tick-tock every time this trapped light ray bounced back and forth.
The amount of ticks was the measure of the amount of time.


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He then operationally defined space, or length as that which is measured by the following simple procedure:

1 - Set the clock tic-tock count to zero and send out a second light beam from point A.
2 - Count how many tic-tocks it takes (there’s a tongue twister!) for the second beam to reach point B.
3 - The length between points A and B is calculated by. L= c * t., .or c multiplied by t, where c is the
......unchanging speed of light and t is the time it took for the second beam to get there.



And, with his operational definition of a clock (yardstick with bouncing light),
and with his operational definition of time (that which is measured by the clock),
and with his operational definition of space (that 3 step procedure above),
Einstein "did the math" and was able, after a just few pages of Physics,
to come up with his most famous formula of E = mc squared!


His operational definitions took the slippery stuff and nailed it down.


So in how many OTHER situations would we benefit by the use of operational definitions?


Something to think on...

[MikeO]

Under construcfion




...including spelling checks ;D

[MikeO]

At some time I'd like to add to this thread, some ARTISTIC applications of these ideas of opposite and reverse.

Already mentioned is the apparent fact that there are no technological applications to the "right" answers to questions regarding opposite and reverse, and HENCE few logical big guns were ever aimed in this direction.

But ARTISTIC applications are out there. They may, or may not, be extensions of the childrens games discussed.

The two most prominent art pieces I can think of in this area are literary works of fiction: Lewis Carrol's "Alice in Wonderland" and the comicbook character named "Bizarro Superman."