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Mondo Fuego™
Mondo Friday Blog
Fri Nov 10, 2017 5:34am
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The word "triangle" ... is to a triangle ... as the word "elephant" is to the animal that we call an elephant.

It's not a definition of the object ... it is the word in our language that verbally and visually represents the object ... even without the object being in sight.

Of course, although a (planar) triangle has the universal property that the sum of the interior angles is 180o, it is not fixed in shape, so we have additional words to more precisely define the shape of a particular triangle ... "equilateral" (all 3 sides of same length), "isosceles" (2 sides of same length), or "scalene" (all 3 sides of different lengths) ... "right" (one interior angle is 90o) or "oblique" (each interior angle is either < or > 90o) ... "oblique" triangles can be "acute" (all interior angles < 90o) or "obtuse" (one interior angle > 90o).

It is interesting to note that, while words which represent objects are not "truths" in and of themselves, we can deduct "rules" or "truths" in connection with the "relationships" among words that relate to an object ... an "equilateral" triangle is "acute" and can never be "obtuse" ... a "right" triangle can never be "equilateral" or "acute" or "obtuse" ... an "isosceles" triangle can be "right", "acute" or "obtuse".

Then, we can add quantitative words and values to exactly define the physical shape and size of any given triangle ... length ... angle in degrees, grads, radians, etc. ... sine, cosine, tangent, cotangent, secant, cosecant, arcsin, arccos, arctan, etc.

Then, to shake things up a bit and cause mass hysteria and confusion in the classroom, we have non-planar triangles ... "hyperbolic" (sum of interior angles < 180o) and "spherical" (sum of interior angles > 180o) ... which bend and twist the rules and properties of their "straight" planar cousin.

Of course, we may have several different words which refer to the same object ... e.g., "violin" and "fiddle".

And, we may have different words that refer to the same object at different points in time, thus adding a time-oriented dimension to the word which refers to the object ... e.g., "boy" and "man" ... or "filly" and "mare".

Furthermore, we may have different words that refer to the same object based on an event in their life, such as bearing offspring ... e.g., "heifer" and "cow".

And, we can have different words that refer to the same object based upon whether they still have their (*snicker*) balls ... e.g., "bull" and "steer". (LMAO)

And, we may have different words which connote the physical characteristic of an object, such as size ... e.g., "pebble", "rock" and "boulder".

No wonder it is difficult for some (or all) of us to determine precisely where and when words which represent objects leave off doing that and that only, and become data, rules, laws and/or truth. Each and every time another word is tossed into the pot of words relating to a discussion, idea, observation, or phenomenon, it's just another opportunity for someone to get confused and/or disagree. ;)


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