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Computers use base two because their most natural unit can occupy one of a couple states: 0 or 1. One, two, base two. Human hands, on the other foot, have ten fingers. Since our favorite mapping between things and integers is finger counting, we naturally end up with more than two states. Zero, one, two, three, four, five, six, seven, eight, nine, and the fully-extended state, ten. That's eleven states, which is why…
Computers use base two because their most natural unit can occupy one of a couple states: 0 or 1. One, two, base two. Human hands, on the other foot, have ten fingers. Since our favorite mapping between things and integers is finger counting, we naturally end up with more than two states. Zero, one, two, three, four, five, six, seven, eight, nine, and the fully-extended state, ten. That's eleven states, which is why…
To my non-mathematically trained ears this doesn't sound like a binary system at all, but more like the highly inefficient Roman system. Am I missing something?
Of course, we all know what they would have used if they were real pros: https://en.wikipedia.org/wiki/Factorial_number_system
Hi, Peter. Welcome to Hacker News! If you get downvoted, it's because HN community takes a somewhat strict approach when moderating comments that contribute noise to the conversation. "Nice article!" comments are routinely downvoted. As is sarcasm, witticisms, memes, references and other styles of comments that occur frequently but do not contribute to the discussion. It's a knowingly doomed attempt to hold back the…
Computers use base two because their most natural unit can occupy one of a couple states: 0 or 1. One, two, base two. Human hands, on the other foot, have ten fingers. Since our favorite mapping between things and integers is finger counting, we naturally end up with more than two states. Zero, one, two, three, four, five, six, seven, eight, nine, and the fully-extended state, ten. That's eleven states, which is why…
In other words, the "fist" symbol was a reserved word for a very different purpose than counting.
Or possibly more realistically: if the way you communicated numbers didn't rely on position to indicate magnitude, you didn't need zeros as place holders. You could just "sign", 3 * 100 + 5 * 10 (whatever the symbols for those were ). Hell, maybe the symbol for 10 was 1 x "fist" and 100 was "pump your first twice."
Of course, we all know what they would have used if they were real pros: https://en.wikipedia.org/wiki/Factorial_number_system
Hi, Peter. Welcome to Hacker News! If you get downvoted, it's because HN community takes a somewhat strict approach when moderating comments that contribute noise to the conversation. "Nice article!" comments are routinely downvoted. As is sarcasm, witticisms, memes, references and other styles of comments that occur frequently but do not contribute to the discussion. It's a knowingly doomed attempt to hold back the…
The ability of the Polynesians to settle huge stretches of the Pacific might be one of the most impressive human achievements ever. Odds are they reached South America even if we never find direct evidence (there is some).
There's a study that found Polynesian DNA markers in indigenous Brazilian remains. It's probably what you are referring to by the some evidence. https://www.nature.com/news/dna-study-links-indigenous-brazi... I've visited Mangareva. It's a lovely island and a step in the journey to get to Pitcairn Island.
While not intended to be used mathematically, the I Ching hexagrams developed around 1000AD represented the binary numbers from 0-63 (2^6), as discovered by Leibniz who was quite fond of binary himself.
They had number words for 1 to 10, and then for 10 multiplied by several powers of 2. The word takau (which Bender and Beller denote as K) means 10; paua (P) means 20; tataua (T) is 40; and varu (V) stands for 80. In this notation, for example, 70 is TPK and 57 is TK7. To my non-mathematically trained ears this doesn't sound like a binary system at all, but more like the highly inefficient Roman system. Am I missing…
n = 10 * q + k, where 0 q = 1 * K? + 2 * P? + 4 * T? + 8 * V?
where K?, P?, T?, and V? are 0 if the letter is absent and 1 if the letter is present. n is a textbook base 10 decomposition, and q is a sparse binary representation.
Roman numerals didn't use quotient/remainder or a geometric expansion at all. Since the 'base' seems to switch between 2 and 5 each time, you can't cleanly decompose it. And there was that weird subtractive case.
Computers use base two because their most natural unit can occupy one of a couple states: 0 or 1. One, two, base two. Human hands, on the other foot, have ten fingers. Since our favorite mapping between things and integers is finger counting, we naturally end up with more than two states. Zero, one, two, three, four, five, six, seven, eight, nine, and the fully-extended state, ten. That's eleven states, which is why…
Imagine you had two fingers and not ten. Try counting in binary. That should clear up the anomaly.