Hartmanis and Simon demonstrated that parallelism can yield exponential speedups, meaning first machine class membership fails to capture the true cost of physically realizable computation.

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Exponential speedups(in describing computational performance improvements): When adding more parallel workers makes a task dramatically faster—not just twice as fast with twice the workers, but potentially thousands of times faster.
Hartmanis and Simon(as referenced in computer science and computational complexity): Juris Hartmanis and Herbert Simon are computer scientists who studied how different ways of measuring computer performance can give different results depending on the machine you're using.
Machine class membership(in computer science classification): A way of categorizing or grouping different types of computers or computational systems based on their basic capabilities.
Parallelism(as the claim being refuted): The property or concept of lines (or things) being parallel—existing alongside each other without ever meeting.

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