Mathematical highload: big, very big, and unimaginably large numbers
summary
A mathematical perspective on what “big” really means: compares common IT scales (billions of users, terabytes) to much larger mathematical magnitudes and orders of magnitude. Uses concrete large-number concepts from mathematics to show how typical big-data and high-load figures stack up against extremely large and unimaginable numbers.
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chapters (15)
- 0:00Introduction
- 3:44Why we're stuck
- 5:31Small and large numbers
- 11:16Knuth up-arrow notation
- 14:48Graham's number
- 17:40Conway chained arrows
- 20:36Mathematical highload begins
- 23:46Super-dimensions and massive numbers
- 25:59Computable vs uncomputable numbers
- 28:54Busy beaver problem
- 30:20Infinity and ordinals
- 35:19Inaccessible cardinals
- 36:45Dead ends and euphoria
- 39:10Routine past and future
- 40:35Embracing the moment
