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How can we push our minds to grasp infinity?

Digital infinity is the same size as the infinity contained in the ellipsis of "1, 2, 3, 4, 5, … ". One purpose in pointing this out might be to underscore just how big infinity is.

Rarely do we push our minds to contemplate large numbers and vast accumulations. Perhaps we are poorly equipped to comprehend endless enumeration. The vastness of digital information provides one tool for grasping at such bigness.

As ones and zeros compound into kilobytes, megabytes, gigabytes, and terabytes, stored in devices that become smaller and smaller, we have a gauge for what it feels like to grow our digital footprints.

As millions, then hundreds of millions, then billions of people upload photos and videos and text, the expansion of digital information really feels like something, reaches into our deepest sense of who we are and how the world works.

Just as with the measured scaling up from atoms to molecules to bacteria to organ systems to bodies to communities to earth to solar system to galaxy… global digital accumulation gives us access to contemplation of ever more orders of magnitude.

Imagining endless such digital growth -- larger and larger storage, finer and finer resolutions, more accurate documentation of more aspects of the lives and knowledge and art of more and more people -- similarly pushes open our minds to make space for the vastness of infinity.

Digital infinity.

In this section we learn that digital infinity is the same size as countable infinity. In other sections, we learn that this infinity is actually the smallest infinity; there are others that are larger -- much, much larger.

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You can read a short explanation of why \(|\mathbb{N}\times\mathbb{N}|=|\mathbb{N}|\), or an in-depth explanation (a rigorous proof), or you can take our word for it, and go read the story or the meta-discussion.

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