Length of a Line...

I taught my son the concept of addition when he was about 4. I placed 2 Lincoln logs in one spot and 3 in the other and we counted them. Then I put the two groups together and counted 5. Then 1 and 1 gathered them and counted two.

Soon he just started yelling out how many there are together without counting. Then we counted and saw he was right. I said how do you know before we count? I would tell him how smart he was for knowing before we counted. He would laugh because he knew and I did not.

@eladar said
The brain is ready when it is ready.

Try this famous experiment. Find a wide glass cup and a narrow cup. Pour water from the wide cup into the narrow cup and ask which glass holds more water. Both cups must be clear to see the level of the water.

Thanks for the idea! I'll test it out.

@joe-shmo said
I'm not teaching her about that. That is just my own thought on the "absolute ruler" when you were bringing up various things. But my point was that IF it is an observable scale then then it cannot be absolute. What I don't know is if the plank scale is observable. If its not, then I suppose it could be absolute.

The length is absolute. How many units you use to measure the length is relative.

1 yard, 3 feet, 36 inches are all the same length.

@eladar said
I taught my son the concept of addition when he was about 4. I placed 2 Lincoln logs in one spot and 3 in the other and we counted them. Then I put the two groups together and counted 5. Then 1 and 1 gathered them and counted two.

Soon he just started yelling out how many there are together without counting. Then we counted and saw he was right. I said how do you know befor ...[text shortened]... ll him how smart he was for knowing before we counted. He would laugh because he knew and I did not.

We do lots of puzzles. 3D block counting is also a good one. I like to put pockets and such within the structure so that it outwardly appears to be full, and have her discover that though they look like the same structure they have different amount of elements. They think its magic at first!

@joe-shmo said
We do lots of puzzles. 3D block counting is also a good one. I like to put pockets and such within the structure so that it outwardly appears to be full, and have her discover that though they look like the same structure they have different amount of elements. They think its magic at first!

You are trying to teach a different concept. Try that experiment on a 15 year old and see what reaction you get.

@eladar said
The length is absolute. How many units you use to measure the length is relative.

1 yard, 3 feet, 36 inches are all the same length.

I don't believe there is any line which has any length that is free from ones perception of that length. So its "length", whatever that is, can't be absolute in those terms. In reality we only agree on these things in a narrow band of common circumstances. "Time" is another one of those constructs, and in fact is inextricably meshed into "length".

“If the doors of perception were cleansed every thing would appear to man as it is, Infinite." - William Blake

I would only add that it could also appear to be infinitesimal!

Perhaps even further still it simply can't appear...

@joe-shmo said
I don't believe there is any line which has any length that is free from ones perception of that length. So its "length", whatever that is, can't be absolute in those terms. In reality we only agree on these things in a narrow band of common circumstances. "Time" is another one of those constructs, and in fact is inextricably meshed into "length".

“If the doors of p ...[text shortened]... it is, Infinite." - William Blake

I would only add that it could also appear to be infinitesimal!

So you are arguing that if a tree falls in the forest and nothing is there to hear it, the tree made no sound waves.

@eladar said
So you are arguing that if a tree falls in the forest and nothing is there to hear it, the tree made no sound waves.

I guess...

@eladar said
So you are arguing that if a tree falls in the forest and nothing is there to hear it, the tree made no sound waves.

More importantly, if a line segment is a non-physical object...an idea. If you were thinking of a line segment of length 42 and you got into your spaceship and shot off would you be thinking it was 36 perhaps? I'm kind of confused by this because that is kind of what is happening. Your perception of the length of a physical object, which is just an "idea", seems like would change. Does that mean that ideas are in fact physical also?

@joe-shmo said
More importantly, a line segment is a non-physical object. If you where thinking of a line segment of length 42and you got into your spaceship and shot off would you be thinking it was 36 perhaps?

So you are trying to deal with relativity. I think that has to do with time, perhaps distance as well.

For practical purposes, we should deal with that bridge when we cross it.

@joe-shmo
You might say the rulers we use are arbitrary, show them Metric ruler and how long 1 Cm is V one inch on an inch ruler and maybe a bit about how those lengths came about. I think the inch was some English king and they used his thumb as the measure, and it became 1 inch.

@sonhouse said
@joe-shmo
You might say the rulers we use are arbitrary, show them Metric ruler and how long 1 Cm is V one inch on an inch ruler and maybe a bit about how those lengths came about. I think the inch was some English king and they used his thumb as the measure, and it became 1 inch.

English is unique among Germanic languages in that our word for an inch is not related to our word for thumb. In English it's the Roman word ounce mispronounced by my ancestors. It's not to do with an English King. The oldest reference to the inch is in the Laws of Aethelberht where it is defined as three barleycorns in length. This is a copy and paste from Wikipedia:

The earliest known reference to the inch in England is from the Laws of Æthelberht dating to the early 7th century, surviving in a single manuscript, the Textus Roffensis from 1120. Paragraph LXVII sets out the fine for wounds of various depths: one inch, one shilling, two inches, two shillings, etc.

An Anglo-Saxon unit of length was the barleycorn. After 1066, 1 inch was equal to 3 barleycorns, which continued to be its legal definition for several centuries, with the barleycorn being the base unit. One of the earliest such definitions is that of 1324, where the legal definition of the inch was set out in a statute of Edward II of England, defining it as "three grains of barley, dry and round, placed end to end, lengthwise".

Similar definitions are recorded in both English and Welsh medieval law tracts. One, dating from the first half of the 10th century, is contained in the Laws of Hywel Dda which superseded those of Dyfnwal, an even earlier definition of the inch in Wales. Both definitions, as recorded in Ancient Laws and Institutes of Wales (vol i., pp. 184, 187, 189), are that "three lengths of a barleycorn is the inch".

https://en.wikipedia.org/wiki/Inch

@deepthought said
English is unique among Germanic languages in that our word for an inch is not related to our word for thumb. In English it's the Roman word ounce mispronounced by my ancestors. It's not to do with an English King. The oldest reference to the inch is in the Laws of Aethelberht where it is defined as three barleycorns in length. This is a copy and paste from Wikipedia: ...[text shortened]... are that "three lengths of a barleycorn is the inch".[/quote]

https://en.wikipedia.org/wiki/Inch

Just contrast that to how much we have moved on with how distances and other physical quantities are defined in science compared to the old style of defining physical quantities (both for in and outside science) like with that above "three grains of barley, dry and round, placed end to end, lengthwise" for a unit of distance (an inch in this case). The old style of doing it has its own special charm but it wouldn't work well for in science.

@humy said
Just contrast that to how much we have moved on with how distances and other physical quantities are defined in science compared to the old style of defining physical quantities (both for in and outside science) like with that above "three grains of barley, dry and round, placed end to end, lengthwise" for a unit of distance (an inch in this case). The old style of doing it has its own special charm but it wouldn't work well for in science.

The style hasn't changed. They are just smaller barleycorns.

@joe-shmo
So one cm could be just one barleycorn. 2.4 cm=1 inch.