Gabriel’s Horn and the Painter’s Paradox

Post 364

Come Judgment Day, it is said that Gabriel will sound a mighty horn, to announce the end is nigh. The day of reckoning is upon us. This sense of divinity is considered infinite, and the horn is the connection with finite. Hence the name of this paradox. Gabriel’s Horn is the name of a three dimensional horn shape. Using rather complicated maths, the interior of this shape has finite volume yet has an infinite surface area. This isn’t magic, this has been proven in the real world to be true. It’s a quirk of mathematics. Imagine, then, a tin of paint. It would be impossible to paint the shape because one would need an infinite amount of paint, but one could fill the entirety of the shape with paint because it has a finite volume. How can one be unable to paint the surface of Gabriel’s Horn but, at the same time, be able to fill it with paint? ‘Tis the question, readers.

The properties of this object were first studied by Italian physicist and mathematician Evangelista Torricelli. The apparent paradox caused great argument about the nature of infinity among great minds of the time. It’s an interesting paradox. If you fill the shape with paint, you’ll have covered the entire surface area. This is true because the paint will touch the sides. Heck, you bought more paint than you needed. Your filling of the shape reaches the surface. You have filled the volume of the shape. You have painted the horn. The volume is filled and the surface is covered. But what have you done? You’ve painted an infinite surface with a finite amount of paint. And remember that paint left over? Yes, you still have paint to spare. This is a paradox.

Of course, this paradox is easily solvable. Whilst the shape may be real, the idea of painting the entirety of it is impossible. Remember, this horn will narrow to the point that even one molecule of paint can’t get through. So whilst the paradox is true, in that you could, theoretically, fill the volume whilst not being able to paint the entire surface area, it’s not true that it’s actually possibly to do that. Paint isn’t, unfortunately, as paradoxical as this horn. The answer to this puzzle, remarkably, is paradoxical in itself. The paradox holds true whilst not holding true whilst answering the bit that is true by not actually being true.

It’s a wonderful headache, isn’t it readers?

Gabriel’s Horn. The paradox that just keeps giving.

Toodle-pip :)(:

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The Indelible Life of Me
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