External and internal direct sums

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## External and internal direct sums

To give a slightly different intuition, there are two views of a vector space formed by the direct sum of component spaces. These views are isomorphic when the space is considered as an algebraic entity. In the internal view, the space is made up of several subspaces that we see as individual components. The components are entities in themselves and can be directly manipulated. This is the view taken by conventional block structured languages. No local copies of state variables are made automatically. The block is internal to the state space.

In the external view, the vector space is a single entity having different components, and it is this latter view that AFL blocks have of the total audio space. Blocks are external to the state space, so whenever a new block is executed, the local state is a copy of the current point in the total space. This means that local copies are made of all the component states.

TV Raman
Thu Mar 9 20:10:41 EST 1995