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> Would it be possible to develop a computer from linear transformations? No, a program consisting of a billion linear transformations could be simplified to a
by Buttons840 5y ago
> Would it be possible to develop a computer from linear transformations?
No, a program consisting of a billion linear transformations could be simplified to a single linear transformation. The halting problem would be solved, all programs can halt. All calculations, no matter how many linear transformations they consist of, could be simplified to a single linear transformation. This would be absurdly good, but still absurd, thus impossible.
- Buttons840 5y agoA key insight is that any combinations of linear transformations is a linear transformation. Got a sequence of a billion linear transformation? The entire sequence can be expressed as a single linear transformation. Thus, no matter how many linear transformation you perform, you're never able to exceed the abilities of a single linear transformation.