[2013-Mar-26] 2927

[Gila]

That depends on the definition of "emptiness". If it's how much white space then it'd be just a simple square curve (unless it's filled in under the curve). If it's how empty it is of data then it's a horizontal line at 0 (a value of 0 is still data).

[Soylent Plaid]

Ah, but the answer is simple: emptiness is a function of area. The wider the graph is, the larger the area, so the proper answer is a straight line starting in the bottom corner going diagonally up to the right.

[chaoservices]

I agree and add that since the domains are vaguely defined so the answer can vary but is not a difficult one.

[gost]

I think it means total emptiness within the graph defined as far as where you are on the X axis, filling in everything below the line. So the joke is that an approach like going from the lower bottom corner to the upper right corner would be wrong, since in the process of indicating that the graph gets more and more empty as you go right, you would make the graph more and more non-empty as you went right.

If it was percent emptiness, that wouldn't be too hard (just have a slope 0 line starting halfway up the y-axis), but as total emptiness as a function of width I don't see a solution.

[Opus_723]

If you define emptiness to be the area between the top of the graph (assuming it doesn't go up to infinity), the y-axis, and the curve you are drawing, out to the x-value you're at, (like the poster above me) then I think it's still pretty simple. It's a differential equation that you can do in your head. Like everyone else said though, you can define "emptiness" however you like and get totally different answers.

Anyway, don't laugh if I did this wrong, but:

h= height of graph
E(x) = Empty area as defined above.

Then,

E(x) = Int(h-E(t))dt from 0 to x

Which leads to:

d/dx(E(x)) = h-E(x)

With initial condition E(0) = 0
(The graph can't be empty if the graph has no width)

So we just draw the curve:

E(x) = h-h*(e^-x)

Edit: And of course, we fill in the graph below this curve, if that wasn't clear.

[Gorbax]

the trivial answer is to fill in the entire graph, making it entirely non-empty for each width of x-axis.

[gost]

[Gorbax]

[Guest]

Just measure emptiness as a percentage, then have a horizontal line at 50% (with the area underneath the line filled in).

[Guest]

[Wufnu99]

For each dwidth, the width of ink of the graph line will account for some percentage of the total dA. As the line width is relatively unchanging, and dwidth could be chosen small enough that graph line direction appx horizontal, the percentage of filled in graph will be approximately constant. There will be a vertical asymptote at width = 0 (which will fall so sharply that it would be nearly imperceptible) due to the space used for the axes and a horizonal asymptote at some % value (depending upon pen used). In general, it will look like a horizontal line however due to the boundary conditions will have an effectively zero but not zero negative slope.

[Wufnu99]

You could program this, btw. I'm not a programmer but maybe you can try. Take the graph .gif file and analyze it pixel by pixel vertically. Add 3 pixels for the line (assuming a line weight of 3 pix, or you can choose your own). Assume a pixel is either white or black. Add up white for a vertical column, add up black, add 3, and divide by total vertical pixels. Do that for each column in the picture, adding in 3 black pixels at the appropriate % for each column.

Width should be defined as the abs value of horizontal distance from the origin, thus no negative width.

[Lethal Interjection]

Here's a better graph idea.

Posting in this thread on the one axis, emptiness of the poster's lives on the other.

And before you 'OH-HO!', I'm well aware of the emptiness of my life. And yet I'm still not contemplating a stupid graph joke.

[mdsimeone]

1) How does emptiness work? The easiest way to think about emptiness is as the opposite of fullness. Does fullness increase when you have a larger bucket or glass of water? No, fullness goes up to 100% full and down to 0% full and that's it. No going above 100%. Thus emptiness is the same way. Something can only be between 0-100% empty.
2) A line is 1-dimensional, and in a 2-dimensional space like this graph, a 1-dimensional line takes up no area, aka no space. Thus a 1-dimensional line fills 0% of a 2-dimensional area. So if you were to graph a line on this graph, it would still be 100% empty because the line takes up no space. You could start to think about the area below the line as taking up space, which is true, but that'd be the integral of this graph, and that's not what it's asking for. It's asking for the emptiness and the emptiness is 100% throughout all widths, thus the graph would have a straight line across at 100% emptiness for all widths because the line takes up no space and the graph is empty at all widths.

[windytan]

The graph is a static image, which means its width is constant. Also, the amount of emptiness is constant in a static image, whichever definition of "emptiness" we use. Since quantities have been omitted on the axes, an arbitrary dot anywhere on the graph is correct.