Measuring large numbers: Difference between revisions
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The Busy Beaver function is known to grow faster than any computable function, as do many of it's variants. Because of this, values of the function or lower bounds on the function can be very, very large, so it is important to find ways of representing these numbers; this article will cover these methods. | The Busy Beaver function is known to grow faster than any computable function, as do many of it's variants. Because of this, values of the function or lower bounds on the function can be very, very large, so it is important to find ways of representing these numbers; this article will cover these methods. | ||
Paradoxically, although the Kolgomorov complexity of stating "The runtime of program X" for the program X is typically very low, it is often not useful as it does not give us good information on | Paradoxically, although the Kolgomorov complexity of stating "The runtime of program X" for the program X is typically very low, it is often not useful as it does not give us good information on the size of the number. Informally, more "natural" or "combinatorial" ways of measuring large numbers are desired. Tools like the [[Fast-Growing Hierarchy]] can help us achieve this, as do Laver tables, or the diagonalization of an axiomatic foundation of mathematics. | ||
The Googology wiki hosts good information on methods of describing large numbers or large upper bounds for numbers. | The Googology wiki hosts good information on methods of describing large numbers or large upper bounds for numbers. | ||
Revision as of 01:58, 13 September 2026
The Busy Beaver function is known to grow faster than any computable function, as do many of it's variants. Because of this, values of the function or lower bounds on the function can be very, very large, so it is important to find ways of representing these numbers; this article will cover these methods.
Paradoxically, although the Kolgomorov complexity of stating "The runtime of program X" for the program X is typically very low, it is often not useful as it does not give us good information on the size of the number. Informally, more "natural" or "combinatorial" ways of measuring large numbers are desired. Tools like the Fast-Growing Hierarchy can help us achieve this, as do Laver tables, or the diagonalization of an axiomatic foundation of mathematics.
The Googology wiki hosts good information on methods of describing large numbers or large upper bounds for numbers.