Length of a Line...

I was exploring ways to introduce measuring lengths of line segments to one of my children the other day and I realized I'm not sure how to approach it. Should I show that its length is symbolically indistinct by using different rulers to measure it a segment? or stick with the single measurement unit? What is the reality I wish to teach...

Anyhow, it got me to thinking. Does a line segment in fact have a length or is it truly unknowable. Even physically, if you draw a line segment you cannot perceive it's length without making a measurement. The simple act of observation seems to bring its length property into existence, but even then its not absolute. What I'm thinking is there is no way to decouple a line length from our own personal ruler which is forced upon it in the act of observing it, but even then it has no absolute length, it only has relative length. Does this make sense?

@joe-shmo said
I was exploring ways to introduce measuring lengths of line segments to one of my children the other day and I realized I'm not sure how to approach it. Should I show that its length is symbolically indistinct by using different rulers to measure it a segment? or stick with the single measurement unit? What is the reality I wish to teach...

Anyhow, it got me to thinki ...[text shortened]... eems to bring its length property into existence, but even then its not absolute. Is that correct?

It only has actual length when compared to another thing, such as wavelength of light, the diameter of a neutron, or an apple.
A line in the absence of stuff, or space, would have no reference to measure its length.

@bunnyknight said
It only has actual length when compared to another thing, such as wavelength of light, the diameter of a neutron, or an apple.

Even still, it has no "actual length". It only has "relative length".

@joe-shmo said
Even still, it has no "actual length". It only has "relative length".

In this universe it would have "actual length" in reference to natural wavelengths in our universe.

@bunnyknight said
It only has actual length when compared to another thing, such as wavelength of light, the diameter of a neutron, or an apple.
A line in the absence of stuff, or space, would have no reference to measure its length.

How do we know that space is spacious? Again...our internal ruler is forcing its will upon the universe as we know it, and there is no way to decouple it.

@bunnyknight said
In this universe it would have "actual length" in reference to natural wavelengths in our universe.

The smallest thing in the universe is the plank scale...forget about various wavelengths and all things alike. Is the Plank scale absolute? What I'm saying, Is the Plank scale as we know it free from the decoupling of our internal rulers? I don't believe it is, but I'm not a physicist so...

@joe-shmo said
How do we know that space is spacious? Again...our internal ruler is forcing its will upon the universe as we know it, and there is no way to decouple it.

Well, if you really want to confuse yourself, consider that your ruler will not stay the same length if exposed to different gravity fields, or different speeds of travel.

@joe-shmo said
I was exploring ways to introduce measuring lengths of line segments to one of my children the other day and I realized I'm not sure how to approach it. Should I show that its length is symbolically indistinct by using different rulers to measure it a segment? or stick with the single measurement unit? What is the reality I wish to teach...

Anyhow, it got me to thinki ...[text shortened]... ving it, but even then it has no absolute length, it only has relative length. Does this make sense?

How old is the child you are trying to teach? 5 year old or younger? Stick with the same units, perhaps Lego blocks or Lincoln logs?

12 year old the use both inches and cm, perhaps Lincoln logs as well.

From this you can see the length is absolute, but how many units you describe the length in depends on the units you choose.

@eladar said
How old is the child you are trying to teach? 5 year old or younger? Stick with the same units, perhaps Lego blocks or Lincoln logs?

12 year old the use both inches and cm, perhaps Lincoln logs as well.

Yeah, 4 years old. So what is the philosophy here? That we teach practicality first before all else. Is there harm that can be done by teaching the mailability of it all simultaneously? I think she is more than capable the understanding. She is doing semi complex color patterns like 2D arrays of color where both the sequence is changing as well as the number of elements in each row etc...So I guess, why shouldn't I introduce a deeper version to her?

@joe-shmo said
Yeah, 4 years old. So what is the philosophy here? That we teach practicality first before all else. Is there harm that can be done by teaching the mailability of it all simultaneously?

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.

@joe-shmo said
I was exploring ways to introduce measuring lengths of line segments to one of my children the other day and I realized I'm not sure how to approach it. Should I show that its length is symbolically indistinct by using different rulers to measure it a segment? or stick with the single measurement unit? What is the reality I wish to teach...

Anyhow, it got me to thinki ...[text shortened]... ving it, but even then it has no absolute length, it only has relative length. Does this make sense?

Is this an exercise in Mathematics or Physics? In his book Elements, Euclid introduces points, lines and plane objects as having no length, length but not breadth and so on. Basically you pick a reference line and that has length 1. As an exercise in Physics you'd need to consider strengths of various couplings, so it's probably better to stick with the Mathematical approach.

@joe-shmo said
The smallest thing in the universe is the plank scale...forget about various wavelengths and all things alike. Is the Plank scale absolute? What I'm saying, Is the Plank scale as we know it free from the decoupling of our internal rulers? I don't believe it is, but I'm not a physicist so...

If you're teaching your child about the Planck scale, then that child is already way smarter than me, and will soon leave Einstein in the dust.

Here is a little pedagogy theory.

There are three levels of understanding.

The lowest level is objects that you can handle.

The middle level is pictures of objects.

The top level is theoretical which means symbols that represent numbers.

By sticking with legos and Lincoln logs you are introducing the concept at the lowest level, most easily understood.

@bunnyknight said
If you're teaching your child about the Planck scale, then that child is already way smarter than me, and will soon leave Einstein in the dust.

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.

@deepthought said
Is this an exercise in Mathematics or Physics? In his book Elements, Euclid introduces points, lines and plane objects as having no length, length but not breadth and so on. Basically you pick a reference line and that has length 1. As an exercise in Physics you'd need to consider strengths of various couplings, so it's probably better to stick with the Mathematical approach.

I'm not sure on that. I think it will be mostly on the Mathematics side for them. The observational stuff was more for my own musings on the subject.