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Veritas
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A person that age would have a difficult time grasping a concept that is so far removed from the perceptual level. The concept of "length" itself would come before "mile", perhaps "foot" would come next. "Mile" can only be grasped after lower level concepts that are closer to a childs perceptual awareness, and can be grasped spatially are automatized.

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A person that age would have a difficult time grasping a concept that is so far removed from the perceptual level. The concept of "length" itself would come before "mile", perhaps "foot" would come next. "Mile" can only be grasped after lower level concepts that are closer to a childs perceptual awareness, and can be grasped spatially are automatized.

Would a more complete order go something like:

concepts of entities

concepts of attributes

concepts of relationships (spatial, temporal, etc.)

concepts of quantitative relationships

concepts of measurement-units, such as "foot"

?

I am not a cognitive scientist.

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I wouldnt try to put a specific order to it. Knowledge is contextual, A child may define "mile" as, "the distance moms car drives in about 2 minutes" and still not have any idea what a narwhal is. We're constantly learning new concepts, and refining our definitions of old ones.

Before yesterday, I had no idea what a "Planck time" was, its a new concept for me, I imagine my definition of it will change greatly as I continue to study cosmology. Imagine the types of concepts that a child learns growing up on a farm in Africa, and in what order he learns them. Compare that to a child growing up and learning in Los Angeles.

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"From A to B" is not a question of distance, but of travel, i.e., of getting from here to there.

Travel has two aspects: displacement and duration.

Any path of travel can be broken down into shorter paths that connect end to end.

In general, a path of travel consists of a sequence of displacements with associated durations.

Distance is not a fundamental observable, only sequences of displacements with associated durations can be observed in fact.

Distance is contextual, and must be defined with respect to a measurement framework. And a measurement framework must use sequences of displacement/duration pairs as its basis, even if only implicitly.

All we have to work with, in processing the experience of travel, is such sequences. Distance a la Euclid is one metric assumption, relevant to simple macroscopic geometric problems. But to assume that Euclid's notion is generally applicable is to drop context.

- ico

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"From A to B" is not a question of distance, but of travel, i.e., of getting from here to there.

Travel has two aspects: displacement and duration.

But "displacement" is distance, right? By "duration", I take you to mean, for a concept like 'mile' duration is an implicit characteristic. I think I agree with that. Otherwise, without explicit knowledge of what a mile is, (knowledge a child doesnt have) you'd be lacking distinguishing characteristics, and measurements to omit when first grasping the concept. Is that what you mean?

Well, how are concepts of measurement, like 'mile' formed? . A concept is "a mental integration of 2 or more units" (this mile, that mile, any mile) "possessing the same distinguishing characteristics" (5,280 feet, the distance moms car travels in 'x' time or 'duration', how tired I am after walking, how long it takes to walk) because definitions are contextual, "with their particular measurements omitted" heres where it gets good, (all miles, uphill, downhill, 4 laps around this track, one lap around that track). Once we realize that "mile" represents more than just 4 laps around Marshall park in Lunenburg Massachussetts, we've put ouselves on a new conceptual policy through a process of measurement omission and fundamentally, induction.

Any path of travel can be broken down into shorter paths that connect end to end.

You sound like Zeno.

Edited by JayR
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I wouldnt try to put a specific order to it. Knowledge is contextual, A child may define "mile" as, "the distance moms car drives in about 2 minutes" and still not have any idea what a narwhal is. We're constantly learning new concepts, and refining our definitions of old ones.

In that example, the child knows "distance" and "minute" before "mile" AND indicates a grasp of quantitative relationships.

But I agree that the child doesn't have to know "feet".

Not to mention that definitions will change as the child's knowledge base grows.

I think that what you will find universally is that a grasp of quantitative relationships is a prerequisite for definitions of measurement-units.

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Distance is not a fundamental observable, only sequences of displacements with associated durations can be observed in fact.

Distance is contextual, and must be defined with respect to a measurement framework. And a measurement framework must use sequences of displacement/duration pairs as its basis, even if only implicitly.

Q: What is the distance between the two endpoints of a footlong ruler?

A: 12 inches.

All that is required to answer the question is a standard unit of length (the inch). You do not need concepts such as "time" or "duration" to observe and conceptualize length or distance. In fact, I would argue that the concept of time arises because one perceives changes in more fundamental observables (e.g. length, weight, color, etc.)

Unless you are using esoteric mathematical definitions of the terms which I don't know, I would say that "displacement" is a qualified instance of "distance". The qualification being that the distance was traversed during a duration.

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Yes, but initially a baby's distance measurement is perceptual - the short distances.

I think I'm right in saying that only with increased intelligence and language does the concept of long distance develop.

I have a pet theory that an infant is learning short distances by using a standard reference.

Have you observed that a baby constantly has his arms or legs in the air?

How about this one - that he is 'judging' distance and scale against his hand, or his foot?

i.e., when his father holds his hand, he is estimating the relative size of the two hands. Or, when his mother walks towards him from across the room, he is absorbing the fact that she started out, let's say, twice as big as his hand (in front of his face), and grows in proportion to his hand, as she nears him.

Developing binocular vision of his eyes also adds to this perceptual sense of distance.

Sounds crazy? I like it!

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