Author Archives: Marcello Herreshoff

Use the Native Architecture

Imagine writing two versions of the same computer program. The first represents its integers as 32-bit binary numbers.  The second writes the numbers in base 10, ASCII strings with each byte used to store one digit.

The second version has its upsides.  Thirty-two bit numbers max out at several billion, but you can keep tacking digits onto the string until you’re out of memory.

That said, the program that uses 32-bit integers runs faster because it uses the native architecture of the CPU.  The CPU was designed with this more compact format for numbers in mind, with special-purpose circuits like 32 bit adders.

The same principle applies to using one’s brain:  Some things the brain can do quickly and intuitively, and some things the brain has to emulate using many more of the brain’s native operations.  Sometimes thinking in metaphors is a good idea, if you’re human.

In particular, visualizing things is part of the brain’s native architecture, but abstract symbolic manipulation has to be learned.  Thus, visualizing mathematics is usually a good idea.

When was the last time you made a sign error?

When was the last time you visualized something upside-down by mistake?

I thought so.

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