It is well known to mathematicians that it takes an infinite amount of paint to cover a surface-relief fractal. To foil grafitteers, create such a fractal topography on the outside wall of a building.-- sqeaketh the wheel, Dec 18 2010 IMB.
Seriously though, you could just decorate all the walls with multicoloured Mandelbrot and Julia sets to make the graffiti invisible.-- nineteenthly, Dec 18 2010 I would think that this would only work if the graffitieers use infinitely viscous paint.-- pocmloc, Dec 18 2010 //infinitely// Infinitessimally?
And better make sure the surface doesn't adsorb gas, otherwise the Earth's entire atmosphere might disappear onto it.-- mouseposture, Dec 18 2010 Hmmm... Infinitessimally viscous paint would be less viscous and therefore more solid. i.e. a brick.-- pocmloc, Dec 18 2010 [pocmloc] "viscosity is the quantity that describes a fluid's resistance to flow" is it not?-- mouseposture, Dec 18 2010 It would only work if they used liquid helium-based paint and i doubt helium is a good solvent. A suspension would presumably make it more viscous.-- nineteenthly, Dec 18 2010 It's a risky idea. If the bastards found a way to graffiti it, you'd need an infinite amount of solvent even to remove a small part of the graffiti.-- MaxwellBuchanan, Dec 18 2010 [mouseposture] Right, we would need to train the grafitteers to use zero-viscosity paint. Perhaps viscous paint would not be available to purchasers under the age of 29, or without a prescription.-- sqeaketh the wheel, Dec 18 2010 By the way, there's a word for this, coined by Ian M. Banks: the surface is said to be "baroqued."-- mouseposture, Dec 18 2010 Yes, hence my initial anno.-- nineteenthly, Dec 18 2010 O Squeakey One, I have to admit you may, in this instance, be correct. It is I who am a brick.
I have just realised, that if the paint is infinitessimally viscous, then only a small amount (e.g. one spray can full) should spread itself with infinitessimal thin-ness over a significant part of the surface - plenty enough to write one's “tag”.-- pocmloc, Dec 18 2010 One problem. Some idiot will end up getting consumed by the wall and their family will sue. It's inevitable.-- Joolin, Dec 18 2010 [pocmloc] Not at all. A finite volume of paint means a finite number of paint molecules. so they would get too dispersed on "The Infinite Surface" and not show up at all. (Note - any sub-set of the surface is also infinite.)-- sqeaketh the wheel, Dec 19 2010 Unless the material had an emissivity of 0, it would be a perfect black body. If it did have an emissivity of 0, a vanishingly small change in spectral emissivity would cause an apparent change in colour; a finite amount of paint would therefore be visible, despite being spread infinitely thin.-- spidermother, Dec 19 2010 //finite number of paint molecules. so they would get too dispersed on "The Infinite Surface" and not show up at all// If you can have a surface that is not made of separate molecules, why can’t I have a paint like that too?-- pocmloc, Dec 19 2010 Good to see so many people committed to hylomorphism in this day and age.-- nineteenthly, Dec 19 2010 The trouble would be building it, as an infinite area would take an infinitely long time to detail. On the other hand, if the detail on the surface was done right (not fractal, but on a very small scale), the wall could be made so the paint wouldn't stick to it at all (some non-stick pans, various insects and plants have the right texture), and the paint would always end up as a puddle at the bottom of the wall.-- neutrinos_shadow, Dec 19 2010 // a finite amount of paint would therefore be visible, despite being spread infinitely thin. //
How can a single molecule of pigment be spread "infinitely thin" ?-- 8th of 7, Dec 19 2010 Easy. Measure its momentum accurately.-- mouseposture, Dec 20 2010 But how will you then know its position ... ?-- 8th of 7, Dec 20 2010 That's my point. Its position will be a probability distribution spread out very thin over a wide region. It's true, I'm conflating "arbitrarily thin" with "infinitely thin." I'm also postulating some QM legerdemain which ensures that the spread is in a subspace of more than two, but less than 3 dimensions.-- mouseposture, Dec 20 2010 I'm not sure if the uncertainty principle is well formulated in fractional (Hausdorf) dimensions.-- sqeaketh the wheel, Dec 20 2010 //I'm also postulating some QM legerdemain which ensures that the spread is in a subspace of more than two, but less than 3 dimensions.//
Does that work straight out of the fridge?-- pertinax, Dec 20 2010 // fractional (Hausdorf) dimensions //
Sp. "Hausdorff"-- 8th of 7, Dec 20 2010 Use a hard object to bash shapes into the infinitely flexible, infinitely weak structure.-- GutPunchLullabies, Dec 20 2010 // hard object to bash ... the infinitely flexible, infinitely weak structure //
The Conservative Party are ahead of you, that's exactly what they've been doing to the Liberal Democrats for the last few months ....-- 8th of 7, Dec 20 2010 //How can a single molecule of pigment be spread "infinitely thin" ?// I meant that if a finite number of pigment molecules were scattered over a fractally infinite area, remaining as discrete molecules, then either
(a) the surface would appear black, paint or no paint, or
(b) there would be a non-zero probability that a given photon incident on the painted region would interact with at least one pigment molecule, so the graffiti would be visible.-- spidermother, Jan 01 2011 random, halfbakery