I call our world Flatland, not because we call it so, but to make its nature clearer to you, my happy readers, who are privileged to live in Space.

function main(){ var foo = 123 var bar = 456 return foo + bar }

Imagine a vast sheet of paper on which straight Lines, Triangles, Squares, Pentagons, Hexagons, and other figures, instead of remaining fixed in their places, move freely about, on or in the surface, but without the power of rising above or sinking below it, very much like shadows โ only hard and with luminous edges โ and you will then have a pretty correct notion of my country and countrymen. Alas, a few years ago, I should have said "my universe;" but now my mind has been opened to higher views of things.

In such a country, you will perceive at once that it is impossible that there should be anything of what you call a "solid" kind; but I dare say you will suppose that we could at least distinguish by sight the Triangles, Squares, and other figures, moving about as I have described them. On the contrary, we could see nothing of the kind, not at least so as to distinguish one figure from another. Nothing was visible, nor could be visible, to us, except Straight Lines; and the necessity of this I will speedily demonstrate. Similar to Laplace of Gaussian, the image is first smoothed by convolution with Gaussian kernel of certain width $\sigma_{1}$:

\[ G_{\sigma_{1}} (x,y) = \frac{1}{\sqrt{2\pi\sigma_{1}^2}} e^{-\frac{x^2 + y^2}{2\sigma_{1}^2}} \]Place a penny on the middle of one of your tables in Space; and leaning over it, look down upon it. It will appear a circle. When $a \ne 0$, there are two solutions to $\sqrt{ax^2 + bx}$ and they are

$$x = {-b \pm \sqrt{b^2-4ac} \over 2a}.$$Commutative Diagrams:

$$ \newcommand{\ra}[1]{\kern-1.5ex\xrightarrow{\ \ #1\ \ }\phantom{}\kern-1.5ex} \newcommand{\ras}[1]{\kern-1.5ex\xrightarrow{\ \ \smash{#1}\ \ }\phantom{}\kern-1.5ex} \newcommand{\da}[1]{\bigg\downarrow\raise.5ex\rlap{\scriptstyle#1}} \begin{array}{c} 0 & \ra{f_1} & A & \ra{f_2} & B & \ra{f_3} & C & \ra{f_4} & D & \ra{f_5} & 0 \\ \da{g_1} & & \da{g_2} & & \da{g_3} & & \da{g_4} & & \da{g_5} & & \da{g_6} \\ 0 & \ras{h_1} & 0 & \ras{h_2} & E & \ras{h_3} & F & \ras{h_4} & 0 & \ras{h_5} & 0 \\ \end{array} $$The DoG as an operator or convolution kernel is defined as:

\[ DoG = G_{\sigma_{1}} - G_{\sigma_{2}} = \frac{1}{\sqrt{2\pi}} \left( \frac{1}{\sigma_{1}} e^{-\frac{x^2 + y^2}{2\sigma_{1}^2}} - \frac{1}{\sigma_{2}} e^{-\frac{x^2 + y^2}{2\sigma_{2}^2}} \right) \]