Season's Greetings

[Trev]

I have given your hypotheses some considerable thought and come up with the following counter claims.
In the case of thick and thin 'lines', they have width so they are not lines they are, assuming constant width, rectangles. I use the tem width because thickness is usually associated with depth and if a line has length, width and depth, it becomes a rectangular solid.
Lines are straight and of infinite length with no thickness/width.
Lines of people are actually queues.
Power lines are actually cables or wires.
Spectral lines are in fact lines on a spectrum, so do qualify as lines of zero width (multiple spectral lines may be close enough together to give the impression of having width).
If a line has no length then surely it's a point as a line passes between two or more points.
You are correct in your statement that by my definition a line has zero height (which was my original hypothesis). But as the line is describing a wavelength of infinite length, it must have a value at every point along it, but its average value must be zero.
I'm still working on its RMS value though which is a bit difficult as we have not yet defined the peak value of this infinitely long waveform.

 

[Black Hole]

There is no such thing as an infinite wavelength, just to be pedantic.

That's just getting silly. Lambda tends to infinity as f tends to zero, so unless you take the position that f can get as close to zero as makes no difference but never actually zero then of course lambda can equal infinity.

 

[RobH1]

Referring to the thread title, I sincerely hope you chaps don't get around to Xmas card verse writing. Second thoughts- they may be more interesting, though indecipherable, than the guff usually within.
Any takers?

 

[Black Hole]

Jingle bells, Batman smells, Robin's gone away...

 

[Luke]

In the case of thick and thin 'lines', they have width so they are not lines they are, assuming constant width, rectangles.

A rectangle should have 4 straight sides, with opposite sides being of equal length.
A 'line' can be curved and therefore the two longest sides of a non-straight line could not form a rectangle. The two shortest sides may form part of a circle if drawn with a pencil and therefore may not be straight either. I wouldn't describe my washing line as being rectangular, although the people who previously lived where I am now had a multi-square washing line being of the rotary variety.

 

[Black Hole]

Nah, what defines a rectangle is four corners of 90 degrees each. It will only have straight sides if the geometry is Euclidean. My rotary washing line is hyperbolic (and when the wind blows it has curved space-time).

 

[Deleted member 473]

Lines are straight and of infinite length with no thickness/width.

Only true for flat, Euclidean geometry. Not true in the real world. In the real world, straight lines are the paths of light rays and in or near a Black Hole they could be of finite length. A straight line on the surface of a mathematical sphere of radius r has length 2πr.

 

[Deleted member 473]

That's just getting silly. Lambda tends to infinity as f tends to zero, so unless you take the position that f can get as close to zero as makes no difference but never actually zero then of course lambda can equal infinity.

I agree that frequency can be zero, but 1/0 is not defined mathematically. Yes, wavelength tends to ∞ as f tends to zero, but there is all the world of difference between a limit and a value. If you ignore this then all sorts of paradoxes emerge in mathematics. You can't reliably deduce anything then.

“Two things are infinite: the universe and human stupidity; and I'm not sure about the universe.”
― Albert Einstein

 

[Black Hole]

Yes, but in this case...

 

[Deleted member 473]

Referring to the thread title, I sincerely hope you chaps don't get around to Xmas card verse writing. Second thoughts- they may be more interesting, though indecipherable, than the guff usually within.
Any takers?

(Not original)

I'll count to a hundred,​

Said John-Jay-Joe-Ray,​

I'll count to a thousand,​

Said Stacey-Grew-Gray...​

That's too easy,​

Said Mike Jeffrey-Binadee,​

I'll be counting,​

Right up to infinity!​

No way!!, ​

Yelled John,​

Stacey just laughed,​

But Michael was counting,​

And time?​

It just passed... ​

He counted all day,​

Mike counted all night,​

He counted in dark,​

He counted in light... ​

He counted for minutes,​

For days, and for weeks,​

Mike counted so long,​

His mouth got the creaks...​

He got to a thousand,​

Ten thousands too,​

Mike was determined,​

He even missed school...​

Two weeks to a million,​

He kept counting more,​

Ten years to a Trillion!​

His tongue was so sore!!!​

His friends were in college,​

Mike stuck to his goal,​

To count to his number,​

Mike had grown old... ​

His beard was quite long,​

His hair was quite white,​

But he kept up his counting,​

Mike's goal was in sight! ​

But Mike found out,​

It just wouldn't quit,​

And he'd never quite get there,​

But still there he sits ... ​

Can you hear him counting?​

In the place that he lives,​

Saying large numbers,​

Like Santa Claus gives...​

Mike's still on his mission,​

To count to the top,​

But I'm just wishing,​

One day he might stop...​

​

​

​

"MERRY XMAS! AND A HAPPY ETERNITY!"​

 

[Wallace]

Oh how I am looking forward to Easter....

 

[Trev]

Lines are straight and of infinite length with no thickness/width.

Only true for flat, Euclidean geometry. Not true in the real world. In the real world, straight lines are the paths of light rays and in or near a Black Hole they could be of finite length.

Firstly, it was of course plane geometry to which I have been referring all along. All lines are straight and of infinite length (with the possible exception of those approaching a black hole or a space/time discontinuity). If a 'line' start at a point and proceed to infinity, it is a ray, and if the 'line' starts at a point and ends at a point then it is a line segment. I'm still working on the RMS value though.

 

[Deleted member 473]

Firstly, it was of course plane geometry to which I have been referring all along. All lines are straight and of infinite length (with the possible exception of those approaching a black hole or a space/time discontinuity).

Make your mind up! First it is 3D space, then it is 2D plane Euclidean space, then it isn't Euclidean, it has black holes in it, and could I respectfully point out that we are in the Near Vicinity of a Black Hole on this forum?

 

[Black Hole]

That's why everything gets warped.

 

[Trev]

You pinched my line BH

@Mike. Ok, you win. Up 'till recently, I thought that I knew everything about everything. Now I'm just confused

 

[4291]

You pinched my line BH

@Mike. Ok, you win. Up 'till recently, I thought that I knew everything about everything. Now I'm just confused

It's either till or 'til.

 

[Black Hole]

Or even til'.

 

[Deleted member 473]

@Mike. Ok, you win. Up 'till recently, I thought that I knew everything about everything. Now I'm just confused

No, you are right. I concede victory. I insist! It's just the influence of that BH making us all confused.

 

[Trev]

Dam speelin misteaks {'till}. Don't you just hate it when that happens in the Arms?
What is til' an abbreviation of? Wikipedia has let me down.

 

[Black Hole]

It's only the last l got sucked over the event horizon, leaving a ' in its place.

BTW, I didn't know "till" was valid until I had a similar conversation.