Kastalia Knowledge Management System · Glasperlenspiel template · knot 3994
Alles ist Zahl!
Pythagoras, Latin numerals, Invention of Zero, Leibniz, Decimal / Binary / Hexadecimal Codes, int8 / fp16 / bf16 &c.
Ancestors (1 superordinated path)
Descendants (at least 19 branches originate here)
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Alles ist Zahl!
Pythagoras, Latin numerals, Invention of Zero, Leibniz, Decimal / Binary / Hexadecimal Codes, int8 / fp16 / bf16 &c.
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Pythagoras's Claim
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“All is number.” (πάντα αριθμός) — attributed to Pythagoras, 6th century BCE.For Pytha -
is_parent Why It Mattered ·
Here is the thread we will follow: a number can be written down in many different ways — and the way you write it changes what you can do with it.That was -
is_parent Counting Before Zero ·
Rome counted like this: I, V, X, L, C, D, M.No zero. No place value — the position of a symbol barely matters, only which symbols appear and in what combi -
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An Older Theorem
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Centuries before Pythagoras, the Baudhayana Sulba Sutra (India, c. 800 BCE) already states the same relationship between the sides of a right triangle.The mathe -
is_parent The Missing Symbol ·
Every numeral system so far shares the same gap: no symbol for nothing.Without a zero, there is no clean way to write a number as a position-dependent code &mda -
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The Invention of Zero
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Zero emerges independently more than once: among the Maya of Mesoamerica, and in India, where the mathematician Brahmagupta (7th century CE) is the first to giv -
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Zero Reaches Europe
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In 1202, Leonardo of Pisa — better known as Fibonacci — publishes Liber Abaci, introducing Hindu-Arabic numerals (zero included) to European merchan -
is_parent Positional Notation ·
Here is the real leap: the same ten symbols, re-used, mean something different depending on where they sit.106 and 160 use identical digits. Position alone carr -
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Leibniz's Dream
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Gottfried Wilhelm Leibniz takes positional notation somewhere further: in 1703, he formally describes arithmetic in base 2 — binary.He was reportedly deli -
is_parent Why Base Two? ·
Binary is just another positional system — base 2 instead of base 10. Only two symbols: 0 and 1.That turns out to be the whole point. Building a reliable -
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From Numbers to Logic
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George Boole (1854) notices that 0 and 1 can represent more than quantity — they can represent truth: false and true.Boolean algebra — AND, OR, NOT -
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Bits, Bytes, and Beyond
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One binary digit is a bit. Group eight of them and you get a byte — 256 possible values.Hexadecimal (base 16) exists purely as a convenience: one hex digi -
is_parent A New Question ·
So far: how a culture chooses to write a number. Now: how a machine chooses to store one — and why, in a modern AI system, that choice is no longer a hist -
is_parent Integers vs Floats ·
Integer formats store whole numbers exactly. int8: one byte, 256 distinct values — typically -128 to 127.Floating-point formats trade some of that exactne -
is_parent f16 vs bf16 ·
Both fp16 and bf16 use 16 bits total — half the size of ordinary fp32 — but split those bits differently.fp16 (IEEE half precision): 1 sign + 5 expo -
is_parent Why int8 for Inference ·
Models are usually trained in fp16, bf16, or fp32 — the precision that stability during training needs.Once trained, they are often quantized down to int8 -
is_parent Case Study: NVIDIA Jetson Orin ·
Take a real, current piece of edge-AI hardware: NVIDIA's Jetson AGX Orin (64GB module).NVIDIA's own published figure: up to 275 TOPS (trillion operations per se -
is_parent Closing: Same Question, New Stakes ·
Pythagoras claimed number was the hidden structure of reality.Three thousand years later, the question "what exactly is this number, and how many bits does it c
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