Thomas Hobbes Hour and Fifteen Minutes of Fame

Merlin,

Does this dog implicitly and perceptually do calculus?

That dog, like all animals, alters its response to the environment -- rather than altering the environment. What the dog is doing can be re-formulated by man in the form of a calculus, but that's just because math is something that fits in with, or "works in", reality. If math didn't hold up in reality, then men couldn't re-formulate the optimized behavior of the dog in mathematical terms. The dog is optimizing, our method of conveying this optimized behavior is called "calculus."

And what about puny-brained spiders? Spiders are pretty dumb (compared to humans). Yet spiders create perfect webs (even on their first try!). And here's the kicker: it's not because they excelled in high-school geometry or carpentry or, and I know this is going to make SOMEONE wince, or ... 'web-design.'

:-)

Ed

Post 21

Saturday, June 28, 2008 - 3:00am

query to post #19

Would you conjecture how Rand might have reacted to the fact that the diagonal of a square is not co-measurable with the side of that square. There is no common unit that measures both.

The diagonal is longer than the side, but there is no common unit to both. In short there is no unit to omit.

Bob Kolker

Post 22

Saturday, June 28, 2008 - 7:09am

Ed, our conversation seems to be heading toward a dead end, but here's a challenge for you. Define measurement. Then tell us how every example you have used satisfy that definition, literally, w/o resorting to hand-waving, equivocation or bad analogies.

Post 23

Saturday, June 28, 2008 - 7:20am

Measurement.

I can see four kinds of measures:

1. Ordinal

A is compared to B in some ranking scheme. Such as win, place and show.

2. Cardinal

A measure which answers the question: How many? Simple counting applies here

3. Extensive

This is a measure defined on some kind of linearly ordered compact space. For example real value measures like length, area and volume or weight.

4. Ratios

Ratios of cardinal or extensive measure. Speed for example. The ratio length to time elapsed. Or density, the ratio of mass to volume.

Can anyone come up with any other kind?

Bob Kolker

Post 24

Saturday, June 28, 2008 - 8:23am

Replying to post 23.

"Ordinal" is not a measurement at all. It's simply ranking. It can be done without numbers and there is no standard unit such as inch, gram, or second.

"Cardinal" is not a measurement at all. It's simply counting. There is a unit, 1, but there is no accompanying standard magnitude such as inch, gram, or second.

The two you classify as ratio and extensive are usually classified as just ratio. Speed is 2-dimensional, combining 2 other ratio measures -- distance and time. Volume is 3-dimensional.

A type you did not mention is "interval". Contra ratio measures, the lower limit is not zero. Examples are temperature in Centigrade and Fahrenheit. A ratio of +30 degrees to -10 degrees doesn't make sense. Temperature in Kelvin is ratio.

Arguably the Richter scale is different because the numbers are exponential. However, underlying it are non-exponential numbers (wave amplitude).

Post 25

Saturday, June 28, 2008 - 12:44pm

Bob,

query to post #19

Would you conjecture how Rand might have reacted to the fact that the diagonal of a square is not co-measurable with the side of that square. There is no common unit that measures both.

The diagonal is longer than the side, but there is no common unit to both. In short there is no unit to omit.

She'd say that diagonals of squares require their own concept. She'd say that the concept of squares is transcended as soon as you start talking about diagonals of squares. When you bring up the idea of a diagonal of a square (as it relates to a side of that same square), then you have shifted the discussion from the concept of a square to the concept of the triangle; specifically, a right triangle.

Now that the discussion has shifted off of squares and onto right triangles, we can use the Pythagorean theorem (a^2 + b^2 = c^2) to discuss how the length of the "diagonal" (now "the hypotenuse") relates to the length of the sides.

Ed

Post 26

Saturday, June 28, 2008 - 1:11pm

Merlin,

Define measurement. Then tell us how every example you have used satisfy that definition, literally, w/o resorting to hand-waving, equivocation or bad analogies.

Measurement is: An act which results in a ratio to a standard

The 1st example I have used (post 10) is Rand's match, pencil, and stick example for forming the concept of "length." If the match was half the length of the pencil, and if the stick was twice the length of the pencil, then a child could grasp the pencil as "worth" 2 matches, and the child could grasp the stick as "worth" 2 pencils (or, for more clarity, 4 matches). In this case, the heuristic or operational unit of length would be one "match-length" and the match would be assigned the value of "1," the pencil would have the length-value of "2," and the stick would have the length-value of "4."

The 2nd example I have used (post 17) is the perceptual measurement a lion uses successfully in order to chase down a gazelle. The measurement is continuous rather than discreet, and the unit is the current length between the lion and the gazelle. As the gazelle speeds away, the lion gauges that the distance between her and the gazelle is increasing, so the lion steps it up a notch in the velocity department.

Sometimes, the lion may -- as a result of measurement -- give up on the chase, recognizing that she is not able to close the distance between her and the gazelle. At other times, the gazelle may be forced to run at a tangent to the lion (as when near the edge of a cliff). At these times, the lion will make subtle corrections to her attack angle, in order to close the distance -- in order to reduce the measurable length between her and the gazelle.

Those examples were easy, and the next example I used (of love, hate, and indifference) is harder. In order to prevent myself from wasting my time on a lost cause, I am compelled to ask you whether I have already succeeded twice (in the 2 examples above) in showing how these 2 examples really do satisfy my definition of measurement.

I will pause and wait for your answer.

Ed

Post 27

Sunday, June 29, 2008 - 6:08am

Ed, I think your definition is far too broad.

I assume by "ratio" you mean of one number to another, which implies at least the ability to count.

Your first example includes hand-waving and unwarranted leaps like Rand's example in ITOE. There are children who are unable to count at all and can compare two things, e.g. a pencil and a match, and say which one is "bigger", provided the difference is large enough and they aren't confused. Note I said "bigger", not "longer", because the latter requires a more specific focus.

Once a child gets the idea length (to some extent) and can show some success in understanding it (X is longer than Y), they can still misuse it. For example, show a child two rectangles, e.g. 1x8 and 6x7, ask which is longer, and the child may respond the second (which is "bigger") because they do not sufficiently understand it.

Experiments with children clearly show a stage during which they know how to count but not how to measure. Rand's example using length is less detailed than yours, but yours more clearly makes the unwarranted leap that a child who knows how to count necessarily knows how to measure. Numerous experiments, such as those performed by Jean Piaget, prove this is false. Many younger children are incapable of measuring even when given hints or training on how to do it. Also, your example is "cherry-picked". What if, for example, the pencil were 1.5 times the length of the match?

You give zero evidence that a lion can count, let alone measure. You also say "the unit is the current length between the lion and the gazelle". In measurement the unit, once chosen, is invariant. If not, it's useless. There is a far simpler and more plausible explanation as to what the lion does. It moves toward its prey, period. As the prey moves, the lion adjusts its direction, always toward the prey (allowing for obstacles, of course).

So both your examples include hand-waving and/or unwarranted assumptions. They don't even pass your definition of measurement, let alone mine.

Post 28

Sunday, June 29, 2008 - 8:48am

Jetton:

You give zero evidence that a lion can count, let alone measure. You also say "the unit is the current length between the lion and the gazelle". In measurement the unit, once chosen, is invariant. If not, it's useless. There is a far simpler and more plausible explanation as to what the lion does. It moves toward its prey, period. As the prey moves, the lion adjusts its direction, always toward the prey (allowing for obstacles, of course).

Me:

Lions and other members of the cat family (including the domestic feline) show strong behavioral evidence of judging timing and distance which is a form of measuring.

My pet kitty cat (may she be chasing string in cat heaven) was an expert huntress. I saw her poised and looking sharp eyed at her targets. I once saw her take down a bird from mid-air flight. She could just distance a lot better than I can. And her timing was precise and virtually flawless.

Just a side remark: Cats are the perfect pets for Objectivists. They are very ego-oriented, they look out for themselves, they keep themselves clean and don't make a mess and they knew which side their bread is buttered on and where the cat-dish is located.

Bob Kolker

Post 29

Sunday, June 29, 2008 - 9:34am

Merlin,

I assume by "ratio" you mean of one number to another, which implies at least the ability to count.

By ratio I mean one thing to another (ala philosophy), not one number to another (ala math & science). When an adult compares a short vehicle like the Chevy Aveo to a long vehicle like the Chevy Suburban, the adult doesn't explicitly measure their length difference by saying that the Suburban is 1.93 Chevy Aveo's. They say it's almost twice as long. The ratio consciously used by the adult is in the virtual twice-ness, not in the decimal value (which we can reach by being more exacting than normal).

So no, ratio doesn't imply the ability to count -- but to compare. It's all in the ability to grasp difference (and therefore, similarity).

There are children who are unable to count at all and can compare two things, e.g. a pencil and a match, and say which one is "bigger", provided the difference is large enough and they aren't confused.

Right, because of what I said above.

Once a child gets the idea length (to some extent) and can show some success in understanding it (X is longer than Y), they can still misuse it. For example, show a child two rectangles, e.g. 1x8 and 6x7, ask which is longer, and the child may respond the second (which is "bigger") because they do not sufficiently understand it.

This is the problem with interpretation of research, like when Game Theorists interpret their research to say that man isn't a rational being (because they pre-stipulated what "rationality" would have to look like in a game, incorporating their false view of morality, etc). Logical positivists suck. They take their carefully partitioned and re-created reality to just "be" reality. That confuses many of the rest of us. It could be said that their scientific research -- while adding information to the world -- is decreasing the aggregate understanding of reality. That sucks.

An alternative explanation for the rectangle conundrum you mention -- one which doesn't toss out the hypothesis prematurely, like Game Theorists did with rationality in games -- is that the children above can "see" that the perimeter of the 6x7 rectangle is indeed longer than the perimeter of the 1x8. On this explanation, the problem is in the researcher's carefully partioned re-creation of reality in the lab, not in the children's ability to grasp the longer thing. The solution boils down to the tactics and antics of the visual illusionist. Is the picture a pretty young girl, or an old wretched person?

Experiments with children clearly show a stage during which they know how to count but not how to measure.

Addressed above.

... yours more clearly makes the unwarranted leap that a child who knows how to count necessarily knows how to measure.

Addressed above.

Numerous experiments, such as those performed by Jean Piaget, prove this is false.

Addressed above.

Many younger children are incapable of measuring even when given hints or training on how to do it.

Addressed above.

Also, your example is "cherry-picked". What if, for example, the pencil were 1.5 times the length of the match?

This criticism is inconsequential. The point is whether difference (like length difference) can be grasped accurately. The point is not in how precise these measurements of difference have got to be -- as long as they are accurate in context. I have a quote about this kind of argumentation, and have coined it as a fallacy (the Fallacy of Super-Contextual Precision, or the Heisenberg Fallacy).

You give zero evidence that a lion can count, let alone measure. You also say "the unit is the current length between the lion and the gazelle". In measurement the unit, once chosen, is invariant. If not, it's useless. There is a far simpler and more plausible explanation as to what the lion does. It moves toward its prey, period. As the prey moves, the lion adjusts its direction, always toward the prey (allowing for obstacles, of course).

If a lion couldn't measure the varying distance between it and the gazelle, then how come it sometimes gives up the chase, even when it has energy left -- upon seeing that the gazelle is "pulling away"? According to you, it just moves toward its prey -- i.e., it won't ever stop moving toward its prey until it gets tired or sees closer prey. Simpler, yes, but NOT more plausible. Regarding the unit of instantaneous distance between the lion and the gazelle, you are saying that if the distance (unit) varies, then it's useless for measuring the progress of the chase. Not only is that not more plausible, it's not even more simple -- its absurd, actually.

Like a logical positivist, you are pre-conditioning not only what is to be looked for, but what counts or doesn't count as evidence that is to be either:

(1) integrated with results in forming the research conclusion
or
(2) subsequently explained-away as irrelevant, unacceptable, or inconsequential

That might be good science, but it's not good philosophy.

Ed

Post 30

Sunday, June 29, 2008 - 10:38am

Ed,
Let me get this straight. You use "measure" simply as a synonym for "compare". In your view all of the following are acts of "measuring."
1. You like movie X more than movie Y.
2. A toddler notices that daddy is bigger than itself or a sibling.
3. A cat likes one toy more another.
4. A lion chases as prey one gnu (a young one) rather than a different gnu.
5. With regard to books whether one is written in English, German, Spanish, Russian, or some other language is a "measurement".

It seems to me the word "standard" in your definition of "measurement" (post 26) adds nothing at all to it, since either thing, attribute or relation being compared can be taken as the standard.

In other words, many times you use "measure", you aren't using "measure" literally -- what I mean by it -- but as a metaphor or some vague approximation of what I mean by it. Is that correct?

And here is a follow-up question. As you use "measure" is it also a synonym for "identify"?

You wrote:

An alternative explanation for the rectangle conundrum you mention -- one which doesn't toss out the hypothesis prematurely, like Game Theorists did with rationality in games -- is that the children above can "see" that the perimeter of the 6x7 rectangle is indeed longer than the perimeter of the 1x8.

This seems like a very weak hypothesis. If true, then it seems children should have no problem comparing the lengths of straight lines with bent ones or two bent ones. But the fact is many do.
(Edited by Merlin Jetton on 6/29, 2:56pm)

Post 31

Sunday, June 29, 2008 - 8:56pm

Merlin,

Let me get this straight. You use "measure" simply as a synonym for "compare". In your view all of the following are acts of "measuring."

1. You like movie X more than movie Y.

I agree that -- according to my definition of measurement -- comparison is measurement. In this case, I can measure whether I like movie X over movie Y by the standard of how much visual or thematic pleasure they each differentially provide me, but this example is poor grounds for forming concepts. I'm comparing movie X, which is a proper noun (the only one of its kind), with movie Y, another proper noun; and my personal preference (my "like" -- as you put it) is likely to be less than completely objective.

2. A toddler notices that daddy is bigger than itself or a sibling.

Now this is fertile ground for forming the concept of "size." The toddler is able to compare the different sizes of itself, an older sibling, and Daddy. Notice how the toddler could have used the variable sizes of toys, or houses, or cars (because actual measurements don't matter, but can instead be omitted without giving them a second thought). The toddler could have used any 3 things with some kind of a size difference between them -- as long as the difference is perceptive to the naked eye -- in order to form the very same concept of "size."

The reason that the toddler could have used any 3 things, without having a clue about how to go about explicitly measuring their sizes (by using numbers), is because in forming the concept of size, itself, "size doesn't matter." Any measureable differences in size are omitted during formation of the concept. Explicit measurements, numbers and counting are not required in forming basic concepts. Only the ability to view a shared difference is.

3. A cat likes one toy more another.

Same as #1.

4. A lion chases as prey one gnu (a young one) rather than a different gnu.

That's a trick question. On the one hand, it could be argued that young gnus are simply instinctually preferred by lions. On the other hand, it could be that young gnus are identifiably slower, or more awkward, or more tasty, or whatever. At any rate, a lion's choice to chase the newest gnu isn't relevantly revealing.

5. With regard to books whether one is written in English, German, Spanish, Russian, or some other language is a "measurement".

This is worded poorly. The very fact of differing languages isn't, itself, a "measurement" -- though when viewed by a consciousness, yes, measurement exists in the comparison. Take Rand's talk of differing geometrical shapes: "... differences of shape ... are a matter of differing measurements ..." There are different shapes in certain German letters (e.g. when an "OOM-lah-owt" is used). Even words themselves, can be view as being of a certain shape, so that languages with no shared words have (essentially) no shared shapes -- though they all have a shape.

It seems to me the word "standard" in your definition of "measurement" (post 26) adds nothing at all to it, since either thing, attribute or relation being compared can be taken as the standard.

The word "standard" in my definition of "measurement" wasn't MEANT to add something, but to limit the comparisons performed -- so that folks don't try to make a concept by comparing "long" things with "green" things (like Rand warned against).

... many times you use "measure", you aren't using "measure" literally -- what I mean by it -- but as a metaphor or some vague approximation of what I mean by it. Is that correct?

Yes, my use of "measure" -- when compared to (or measured against!) your use of measure -- is either only metaphorical, or only approximate.

As you use "measure" is it also a synonym for "identify"?

No. But it is a synonym for identifying a relationship.

This seems like a very weak hypothesis. If true, then it seems children should have no problem comparing the lengths of straight lines with bent ones or two bent ones. But the fact is many do.

You may refer to this as some kind of Red Herring hand-waving, but an alternative explanation exists. On the alternative explanation, the child is having trouble with the directions and is taking the word "line" literally as a straight line. On this interpretation, the child follows the bent line until the bend -- and then views the bent part as a new line. Instructing that child by telling her that sometimes lines bend doesn't necessarily resolve the ambiguity in the child's mind. The child could merely interpret that to mean that sometimes connecting lines bend.

Common language and even math classes can also be guilty here. Heck, I remember a few decades ago in geometry class calling the connecting lines of a square different names like:

Line A-B, Line B-C, Line C-D, and Line D-A (or A-D)

The corners were labelled A, B, C, and D. The lines were taught to us as separate lines, even though they were actually merely one line ... bent on itself.

So, now, here is my follow-up question to you:
Did these child researchers take (remember) geometry class? It seems that they are making shaky assumptions about the young childrens' ability to conceptualize instructions.

Ed

(Edited by Ed Thompson on 6/29, 8:59pm)

Post 32

Monday, June 30, 2008 - 6:33am

Did these child researchers take (remember) geometry class? It seems that they are making shaky assumptions about the young childrens' ability to conceptualize instructions.

Do you really expect me to know the educational background of the researchers? Do you really expect researchers asking children questions about areas, volumes, and speeds are ignorant of geometry? Moreover, the researchers don't simply make assumptions about why a child fails. They ask the child questions why it answered as it did. In the 2-rectangle problem and similar ones, they get answers like "it's bigger" or "it takes up more room." Oddly enough, in the literature I've read I have never read a response like "I compared the perimeters" or its equivalent in other words and/or with pointing.

Changing the topic some, maybe the following will better convey my view of measurement.

Case 1: A pet cat jumps onto the kitchen counter and then on top of the refrigerator. Done exploring, the cat looks down to the floor and considers jumping. It apparently judges "too far" and doesn't jump from there. It decides to jump back down to the counter and then jump to the floor.
Case 2: A toddler, who is just learning to count but has no competence with a yardstick or seen anybody use one, is shown side-by-side a pencil and a match, and asked which is longer. The child answers correctly. The match and pencil can be compared perceptually. No ruler is required.
Case 3: An older child is asked how long a given pencil is. Using a ruler, she says 5.5 inches.
Case 4: An older person is asked which of two rooms is longer and handed a yardstick. The rooms cannot be seen in one view and their lengths differ little, e.g. 16 feet and 17 feet. The person uses the yardstick to measure them and answers that the second room is longer, by one foot. This is a conceptual comparison, which cannot be done perceptually.
Case 5: An older person is asked how many square feet of carpet will be required to cover an L-shaped room. The person measures and calculates to arrive at the correct answer. This cannot be done with a simple perceptual comparison like case 2.
Case 6: A runner is clocked in the 100-yard dash at 11.5 seconds with a stopwatch.
Case 7: A driver fills up the gas tank, notes the miles driven since the last fill-up and divides by the number of gallons to get a mpg number.

To me there are vast differences between these cases. All are identifications, all involve comparison, but only cases 3-7 are measurement in my view. Note that 3-7 involve using tools based on an explicit unit to get a (not ordinal) number. Yet everything you have written here implies all seven cases satisfy your concept "measurement", like the particular differences between them, including mental operations, are negligible enough to be disregarded ("measurements omitted" in Rand's words).

Suppose I say: "Rand said that a concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular comparisons omitted." Do you object? If yes, why? You wrote "comparison is measurement", and I did not say she said this verbatim.

Post 33

Tuesday, July 1, 2008 - 1:31pm

Merlin,

Suppose I say: "Rand said that a concept is a mental integration of two or more units possessing the same distinguishing characteristic(s), with their particular comparisons omitted." Do you object? If yes, why? You wrote "comparison is measurement", and I did not say she said this verbatim.

I wouldn't necessarily object, if it had been made clear to me that a comparison did in fact precede the "mental integration" performed by the conscious subject who is forming this concept.

There are 2 valid ways to use the word: measure. Things "have" measurements, and humans measure things. But the 1st requires the 2nd. If there were only 2 objects in reality, nothing but these 2 things (no humans), then they'd have the capacity for being measured -- but they wouldn't have measurements. The upshot here is that measuring involves consciousness as a logical genesis. Measurement is not some intrinsic thing that is signified by number and exists in a consciousness-free realm.

When young kids form basic concepts, they do it on the perceptual basis of being able to see 2 things as similar in a respect in which a 3rd thing is different. The only kind of measurement needed for that is the "eye-ball method" of simple comparison. You don't need a rich background of numbers or words in order to form basic concepts. As humans, we already "come with" every needed mental tool required.

Ed

Post 34

Tuesday, July 1, 2008 - 4:14pm

There are 2 valid ways to use the word: measure. Things "have" measurements, and humans measure things. But the 1st requires the 2nd.

Wow! Maybe you are finally starting to get it. However, the 3rd sentence gives me pause. A stick has an attribute length independent of human consciousness. That a stick has a length of 6 inches is dependent on a human consciousness to identify it as such, more exactly one that has reached a particular stage of development. But the 1st does not require the 2nd. Indeed, the 2nd requires the 1st.

Measurement is not some intrinsic thing that is signified by number and exists in a consciousness-free realm.

Did you intend this to be relevant to anything I have said? Regardless, it seems to support what I said in my last paragraph.

Post 35

Tuesday, July 1, 2008 - 4:57pm