Math is like the Hawaiian islands

Keith Kendig compares math to the Hawaiian islands:

Hawaii may look like a group of separate islands, but actually the islands are just the highest peaks of an immense, mostly-submerged mountain range. All that water hides their underlying connectedness, their oneness. Mathematics may similarly seem like an archipelago of different areas — geometry, analysis, topology, number theory, applied math, and so on. My philosophy is that we’re really just seeing a few peaks of a huge mathematical mountain range. Our ignorance is like the water surrounding Hawaii and hiding its true mountain-rangeness. In mathematics, when we remove ignorance by making discoveries and advances, the water level in effect goes down, and when it drops far enough, separate islands are connected.

Source: Conics

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2 thoughts on “Math is like the Hawaiian islands

  1. Most people can only think, visualize and explain in 2 or 2+ dimensions; like an overhead view of Hawaii. 2 dimensions/coordinates typically explains 50-70% of any subject/issue. Add a 3rd dimension/vector/coordinate and you get 95% of the story. 3D constructs can become more pervasive with new computers, screens, algorithms. I like to map industries and companies (macro/micro) along 3 vectors. It is important that each vector have a definable and measurable gradient. What are the 3 axii for math?

  2. Arjun (@wicknicks)

    Nice! Take all the water out. You will get one fully connected Earth. Maybe taking a step back to look at the big picture does indeed help.

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