Phi

[klypp]

Tried that. The judge seemed to agree with me by constantly calling the plywood "exhibit one". Still got 6 months though...

[altonhare]

Tried that. The judge seemed to agree with me by constantly calling the plywood "exhibit one". Still got 6 months though...

Klypp, is the hypotenuse of your triangle like this:

line.JPG (6.28 KiB) Viewed 13153 times

or like this:

trapezoid.JPG (5.33 KiB) Viewed 13153 times

[webolife]

Altonhare, you didn't answer Grey Cloud's question...
Does his tin triangle not have an edge?
If it indeed has an edge, does that edge have a length?
If so can it be measured?
If not, is it because of the finitude [let's call it rationality] of the measuring device?
If so, is it possible that the length of the edge is irrational, but our finite measuring device is limited to a rational approximation?

[klypp]

Altonhare:

Klypp, I'm afraid you have been duped by the establishment. Nobody learns physics in school anymore, nobody learns what an object is or what numbers mean. As rcglinsk so cogently pointed out, you will never be able to mark phi or pi on your stick.

I'll have to give in on the hypotenuse and admit that "the establishment" never told me about the trapezoid brick.
Another thing they duped me with was this:


Please, help...

[altonhare]

Altonhare, you didn't answer Grey Cloud's question...
Does his tin triangle not have an edge?
If it indeed has an edge, does that edge have a length?
If so can it be measured?
If not, is it because of the finitude [let's call it rationality] of the measuring device?
If so, is it possible that the length of the edge is irrational, but our finite measuring device is limited to a rational approximation?

I answered that length is what an *object* has. An edge is not an object, an edge is not a stand-alone geometric figure. So no, you cannot measure an edge. It makes no sense to talk about the "length of an edge". You talk about the length of a line or a box.

If you're "measuring an edge" what are you measuring? Whatever you put on the paper, whatever you measure, will end up being a shape, a line, a trapezoid, an octagon, etc.

It's not a matter of the "finitude" or the "rationality" of the measuring device per se. It has to do with using incompatible units. You can use a line to measure other lines. You can use something with uniform length only to measure other things with uniform length. So you have a standard-line A1. You measure another line A2 and say it is 3 A1's or 4 A1's or whatever. You're always expressing length in terms of standard-line A1, which has uniform length. You have consistent units, A's measure A's (uniform length objects measure uniform length objects).

What if you take your standard-line A and try to measure a trapezoid? You will be unable to do so accurately because the trap's length is not uniform. Trapezoid has a length of "trapezoid B1" which is an incompatible unit. You're trying to compare apples and oranges. You're trying to measure A's with B's. B is not A! As long as you use A's (lines) to measure lines you're using consistent units. As long as you use B's to measure B's you're using consistent units.

But we know that "trapezoid" doesn't refer to something as specific as "line". Line refers to uniform length. Trapezoid doesn't say anything specific about the object's length other than it is nonuniform. So if trapezoid B1 is your standard you can only measure trapezoids with relative length, width, and height identical to trapezoid B1. By relative I mean that trap B1 may have bottom length 1, top length 2, height 1, and width 1. Now you can only use it to measure trapezoids whose top length is twice its bottom length and whose bottom length is equal to its width and height.

This is a lot more complicated than the line right? With the line the relative dimensions didn't matter for measuring length because the length was always uniform. The trapezoid measurement makes a lot of additional demands and generally makes things messy. In math we get around this by saying that a very very thin trapezoid looks a lot like a line. So we can approximate it as a line. The irrational result is purely an artifact of the initial assumption. The irrational indicates that, no matter how thin/small we make our trapezoid we can never quite measure the trapezoid with a line. They are incompatible units.

The result sqrt(2) is *useful* because measuring things in units of trapezoids or octagons is not only hard in itself, but makes it impossible to compare nonidentical shapes. But this is the difference between mathematics and physics. In mathematics we are interested in calculating a quantity. In math we will treat everything as a line for the sake of getting an easily calculated and communicable answer.

In physics we are interested in shapes. In physics we know that a trapezoid has nonuniform length and that this is fundamentally different than a line with uniform length, despite what the mathematician says. Just because the mathematician is approximating a thin trapezoid as a line does not mean that a trapezoid IS a line. This is a big, big leap!

No length is irrational. Again the reason for the irrational result sqrt(2) is because the mathematicians are assuming the hypotenuse is a line (uniform length) when a *physical* triangle composed of lines is impossible. They try to assign a single value to the hypotenuse and are surprised when they reach a contradiction. A physicist could have told them that a line is not a trapezoid at the outset and saved the mathematician a good deal of work.

EVERY irrational is a result of measuring that which does not have uniform length with lines (with uniform length). Indeed, pi is a result of inscribing polygons composed of lines. The mathematician is trying to tell you that if you measure the circle with lines you will never get the right answer! Obviously not! The circle's diameter and circumference are just exactly what they are, despite your insistence on using the convenient line to approximate them.

[altonhare]

Altonhare:

Klypp, I'm afraid you have been duped by the establishment. Nobody learns physics in school anymore, nobody learns what an object is or what numbers mean. As rcglinsk so cogently pointed out, you will never be able to mark phi or pi on your stick.

I'll have to give in on the hypotenuse and admit that "the establishment" never told me about the trapezoid brick.

Please, help...

I will be glad to help. In your video it is assumed that an object with uniform length (a line) can be wrapped around to connect itself perfectly. In fact it cannot. The mathematicians approximate tiny chunks of the circle as lines to get an easily quantifiable answer. Just because they insist on calculating/measuring everything with lines doesn't mean everything's made of lines!

[Grey Cloud]

Hi Alton,
You are averse to irrational numbers but are quite willing to use irrational words. You missed your vocation; you should have been a lawyer.

[klypp]

I will be glad to help. In your video it is assumed that an object with uniform length (a line) can be wrapped around to connect itself perfectly. In fact it cannot. The mathematicians approximate tiny chunks of the circle as lines to get an easily quantifiable answer.

Ouch...
I didn't see those tiny chunks of the circle.
I'll immediately claim my money back for the bicycle!
To think that the bastards tricked me into believing that an object with uniform length can be wrapped around to connect itself perfectly...
Bastards! What has become of the world!

[rcglinsk]

I just looked up the definition for plywood. It says:

a board made of thin layers of wood glued together under pressure, with the grain of one layer at right angles to the grain of the next

There are no such thing as "right angles". So I guess that rules out plywood. It's just some kind of mathematical construct...

LOL, I bet they mean perpendicular in that case. At any rate, mathematical concepts strike me as being nouns for the purpose of math and adjectives for the purpose of English. So we can have a triangular, square or circular table. Or If I wrote down "30 degrees" and "60 degrees" on a sheet of paper and asked to add the angles together you could write "90 degrees" or "a right angle" and everything would be cool. But if I handed you two circle drawing compasses, one stretched to thirty degrees and the other stretched twice as much and asked you to "add the angles together" you'd look at me like I was crazy. In the case of the piece of paper the angle is a noun, a number that can be manipulated by the rules of math. But when I hand you the compass, the angle is a way to describe the shape of the object; an adjective. The noun "right angle" of math doesn't exist in the real world.

[rcglinsk]

I just looked up the definition for plywood. It says:

a board made of thin layers of wood glued together under pressure, with the grain of one layer at right angles to the grain of the next

There are no such thing as "right angles". So I guess that rules out plywood. It's just some kind of mathematical construct...

Try walking out of your local timber merchant without paying for the ply. And then try using your argument with the judge. [See you in six months ]

Ha ha. No way. I'd make the argument, have my lawyer tell the judge I was crazy, and walk away free.

[rcglinsk]

Hi Klyph, you said,

I'll have to give in on the hypotenuse and admit that "the establishment" never told me about the trapezoid brick.
Another thing they duped me with was this:

And then had that picture of the circle. Anyway, the problem with your movie is the area of the red hoop changes when you stretch it to a line.

When it's wrapped around the circle the area = pi(1+dr)^2 - pi(1)^2 = pi(2dr+dr^2);
in the case of the line the area = pi(dr).

So the area of the second line is pi(dr+dr^2) smaller than the first, where dr is the width of the hoop and the line.

[klypp]

Or If I wrote down "30 degrees" and "60 degrees" on a sheet of paper and asked to add the angles together you could write "90 degrees" or "a right angle" and everything would be cool. But if I handed you two circle drawing compasses, one stretched to thirty degrees and the other stretched twice as much and asked you to "add the angles together" you'd look at me like I was crazy.

Yes I would!
My first thought would be:
How can this guy think he can add 30 degrees to 30 degrees ("twice as much") to his compass angle, and then - within the same breath - think he poses some kind of unresolvable problem when he asks someone to add another 30 degrees to his compass angle?
My second thought would be:
Someone must have dropped a brick on his head...

[klypp]

Anyway, the problem with your movie is the area of the red hoop changes when you stretch it to a line.

Brilliant! You're absolutely right! The video becomes nonsense if you conceive the red hoop as an area!
The nice doctors now think you can be absolutely cured from the damage the brick caused. They are very pleased with your progress!
If you can conceive the concept of an area, there's a very good chance you'll soon be able to conceive the concept of a line as well!
Just rest your head, take your medicine, and I'll bring flowers and chocolate at my next visit!

[altonhare]

Anyway, the problem with your movie is the area of the red hoop changes when you stretch it to a line.

Brilliant! You're absolutely right! The video becomes nonsense if you conceive the red hoop as an area!
The nice doctors now think you can be absolutely cured from the damage the brick caused. They are very pleased with your progress!
If you can conceive the concept of an area, there's a very good chance you'll soon be able to conceive the concept of a line as well!
Just rest your head, take your medicine, and I'll bring flowers and chocolate at my next visit!

Show us your line without area Klypp.

[rcglinsk]

Or If I wrote down "30 degrees" and "60 degrees" on a sheet of paper and asked to add the angles together you could write "90 degrees" or "a right angle" and everything would be cool. But if I handed you two circle drawing compasses, one stretched to thirty degrees and the other stretched twice as much and asked you to "add the angles together" you'd look at me like I was crazy.

Yes I would!
My first thought would be:
How can this guy think he can add 30 degrees to 30 degrees ("twice as much") to his compass angle, and then - within the same breath - think he poses some kind of unresolvable problem when he asks someone to add another 30 degrees to his compass angle?
My second thought would be:
Someone must have dropped a brick on his head...

Imagine you had to actually put the two compasses together to make a 90 degree angle. You could adjust one of them to be shaped like a right angle and discard the other, but the angles of the compasses cannot be added together directly the way that numbers can.