4 ms·
Actually if you think in the sense of informatics...base 3 is more efficient than base 2, but natural base (base e = base 2.718...) is the most efficient, and 3
by stevefan1999 3y ago
Actually if you think in the sense of informatics...base 3 is more efficient than base 2, but natural base (base e = base 2.718...) is the most efficient, and 3 - e is closer to e than e - 2. So it is more natural for computers to go in multiple bases but unnatural to human.
- davidw 3y agoSee: https://en.wikipedia.org/wiki/Ternary_computer https://en.wikipedia.org/wiki/Ternary_computer
- stevefan1999 3y agoYes -- The soviets did the right thing, but it was too costly.
- deleted 3y ago[deleted]
- aYsY4dDQ2NrcNzA 3y ago> 3 - e is closer to e than e - 2 I don't get it.
- hulahoof 3y agoI assume they mean absolute distance abs(3-e) < abs(2-e)
- dismalpedigree 3y agoI still don’t understand why base e is the most efficient ideal. There has to be some more info on this.
- gretch 3y agoYeah I don’t even understand non-whole bases. For example, how does someone express the number 5 in base e…
- davidnc 3y agohttps://en.m.wikipedia.org/wiki/Radix_economy https://en.m.wikipedia.org/wiki/Radix_economy The idea is that if it costs $r to store a base-r digit, then base 3 (or e in a continuous scale) turns out to be the most efficient. Obviously, there's no a priori reason to think that a 3-level gate is exactly 1.5x more expensive than a 2-level gate, so this is mostly of theoretical interest.
- joe__f 3y agoThis was a really interesting article, thank you. I'm thinking about how this would apply to human psychology of reading and writing numbers. Then it doesn't make sense to measure economy as b floor(log_b(n)+1), because adding in more symbols doesn't increase the complexity linearly for people reading or writing numbers. Maybe something like E(b,n) = f(b) g(floor(log_b(n)+1)), where f stays constant up to 10 or 20 symbols, and then increases after, and g increases faster than linearly because it's easier to read shorter numbers than longer ones.
- rlpb 3y agoHow are you measuring efficiency? Why is base 3 more efficient than base 2? Why is e the most efficient?
- ravi-delia 3y agoThere is a particular notion of "radix economy" which takes into account both the length of a number compared to its size and the informational complexity of more symbols. It doesn't really have anything to do with data storage though. If you could create a device to store 1000 10-bits (10its?) for exactly the same cost as one that stores 1000 3-bits you'd obviously pick the base 10 one, no matter what radix economy says.
- joe__f 3y agoWhat does it mean to have a transcendental base? I understand algebraic bases but I don't see how you could use a transcendental base to represent integers with a finite number of symbols