| Title | The Busy Beaver That Ate the TREE |
|---|---|
| Contributor | David H. Silver(author) |
| DOI | https://doi.org/10.11647/OBP.0526.17 |
| Landing page | https://www.openbookpublishers.com/books/10.11647/obp.0526/chapters/10.11647/obp.0526.17 |
| License | https://creativecommons.org/licenses/by-nc/4.0/ |
| Copyright | David H. Silver |
| Publisher | Open Book Publishers |
| Published on | 2026-04-08 |
| Long abstract | Imagine you are given pen with enough ink to write 20 centimeters and you are to write the biggest number you can think of. You can start by a tower of exponents 10^10^...^10, but it is not that big. In this chapter we explore the hierarchy from computable functions to TREE(3) — a number so immense that even if you built a tower of exponentials starting with a trillion raised to the power of a trillion, and then repeated that construction every attosecond for a trillion years, the result would still be vanishingly small in comparison. Yet even TREE(3) sits as close to infinity as the number 8, placing us in an infinity zoo where sizes exceed the categories brains evolved to handle. |
| Print length | 10 pages |
| Language | English (Original) |
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| Landing Page | Full text URL | Platform | |||
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| https://www.openbookpublishers.com/books/10.11647/obp.0526/chapters/10.11647/obp.0526.17 | Landing page | https://books.openbookpublishers.com/10.11647/obp.0526.17.pdf | Full text URL |
David H. Silver is an industrial researcher whose career bridges computer vision, computational biology, and science communication. He studied mathematics, computer science, and biology at the Technion — Israel Institute of Technology as a Rothschild Scholar, and was awarded a Microsoft Research PhD Fellowship for his doctoral work in computational biology at Cambridge, UK. Silver’s peer-reviewed publications span multiple domains: computational biology in Nature and PNAS; computer vision systems in IEEE Transactions on Pattern Analysis and Machine Intelligence; medical AI in Human Reproduction and MIDL; and entertainment analysis in PLoS One. He holds over a dozen patents in depth sensing, medical imaging, and generative AI. His industry positions include Algorithm Engineer at Intel Corporation, ML Researcher at Apple, and CTO/co-founder roles at several technology startups. Silver maintains academic collaborations with researchers worldwide and serves as a peer reviewer for Image and Vision Computing and PNAS.