On the plus side, people can pick the point at which the day changes. For example, 1am Thursday is really an extension of Wednesday night for most people.
On the minus side, the time becomes required for meaningful conversation. In your system, saying "Let's get together Tuesday" would be ambiguous. People have a sense of what a day is, and what day it is. Messing with that will lead to... unintended consequences.
> qntm.org/abolish
Yeah, I've seen that. My idea would hopefully solve the day-related problems (days changing at midnight); otherwise, it would require changing our way of thinking about things from "What time is it there?" to "What time do they work/eat meals/go to bed/etc. there?"
> On the minus side, the time becomes required for meaningful conversation.
Not necessarily. People close to each other in longitude would probably tend to be in the same day during the day, differing mostly during the night, except perhaps people who work night shifts or are otherwise nocturnal. People in different parts of the world will be in different days, but that's not any different than it is now.
> People close to each other in longitude would probably tend to be in the same day during the day, differing mostly during the night...
Differing during the night is... significant. Also anything written will be stripped of the needed context, leading to ambiguity later (if not also sooner)
> People in different parts of the world will be in different days, but that's not any different than it is now.
It is different from now, because at least now we know what day they are in wrt the day we're in. If everyone gets to define their own day, all bets are off.
Tuesday isn't Tuesday anymore.
The "shrink" command just works by remembering all previous iterations, but I *did* realize after I implemented it that it *is* reversible. (Just remove every pair of dominos pointing apart, move everything backwards, and fill the remaining spaces with pairs of dominos pointing towards each other, in either orientation.)
I know this looks like spam, but please add:
Fibonacci {option: Starting numbers: _number_, _number_; presets: Fibonacci {1, 2}, Lucas {2, 1}} [The starting numbers (values of last 2 digits).]
Factors {option: Recursive: _checkbox_} [If it is recursive, the exponents are displayed in Factors notation.]
Transfinite ordinals {option: ω=: _number_} [Defines ω (the first transfinite ordinal) as a number, and then works upwards from there. ε_0 is defined to be ω^^ω (a power tower of ω ω's).]
Roman {option: Custom: _checkbox{yes @ Custom numbers: _list⁄_number_ = _text_⁄_, Allow subtraction rules: _checkbox_}_} [If custom numbers are turned on, you can set any number to any string, and toggle subtraction rules.]
Transfinite ordinals aren't a representation of the real numbers, so they wouldn't make sense for this page (there isn't really a way to show them in different bases etc.). However, I do have an ordinal number calculator: https://chridd.nfshost.com/calc/number-types#ord. It doesn't support ε₀ yet, I think because I couldn't figure something out.
I can't find information about that particular generalization of Fibonacci coding; I'll have to think more about whether that can work. (I know about the Lucas numbers, the question is whether/how they'd specifically work with Fibonacci coding.)
Just making sure this is clear: I don't actually guarantee any new features for this. This is just something I'm doing in my spare time (and sometimes I have other stuff I want to do), and also I'm not an expert on the stuff here; I'm only going to work on this if I'm sufficiently interested, have time, etc. I don't have an issue with suggesting features, as long as you understand that I don't have an obligation to add them.
ε₀: It's been a while since I worked on the ordinal numbers part, but from what I can remember, I had trouble finding information about how exactly to do what I'm trying to do here (take an arbitrary expression and simplify it to some canonical form); like, the definitions weren't worded in a way that makes this easy, and there were examples, but not enough to cover all the cases. I figured out enough to be confident about expressions involving ω, but not enough to be confident about expressions involving ε₀. (I could look at it again at some point, but again, I don't guarantee anything.)
ג_n: Gimel? I'm not familiar with that notation.
real number imprecision: because computers can't actually perform exact calculations on real numbers. I included "real numbers" mostly for completeness, but everything involving real numbers is still doing calculations using floating point numbers. I did start a rewrite that would give more exact answers *sometimes*, but I never got around to finishing it.
suggestion for addition: the plastic number base ("plastinary"?), which shares interesting properties with phinary.
> "It was proven by Aarts et al. (2001) that P and the golden ratio phi are in fact the only such numbers."
also corresponding mixed-base but we have perrin sequence and padovan sequence... maybe forget about this.
there might also be primorial base and its recursive version that seems somehow more elegant than factorial.
my idea about some "bijective factorial/combinatorial": 0->0 1->1 2->10 3->102 4->120 5->201 6->210 7->1023 8->1032 9->1203 ... but not sure if the shift-by-one is good.
also i'd prefer showing bijective binary by default.
also in case you're interested, the chinese ordinals 天干(decimal) 地支(duodecimal) 干支(sexagesimal, a tuple of two characters as a digit, starting from 甲子 乙丑, seems that's not yet supported in customization, unless unicode allocates 60 code points for them) may be used to form bijective systems. (though historically in reality the usage is just use one tuple as elements of (Z/60Z)+0.5)
in the binary section, a recent format called posit might be notable. though it's parameterized, there'll be some work on rounding and denormals. however there's plenty of official demo in js and i've heard that some hardware ALU has been produced.
further, i've made a dedicated Chinese huge number reading generator at farter.cn/number that supports several schemes. though it might be bit of out of scope, what i want to say here is that repeating the highest unit is widely accepted (in modern daily life, it's 亿. it's also acceptable to repeat 载 if we pretend to speak like our ancestors.)
about factors-like, here's my invention some years ago (turns out invented by someone else) oeis:A153013 (just ignore this)
finally, this page just completed (some of) my dream. it's just holy. i can safely delete my new folder now.
a suggestion that should be rather easy to implement but makes a lot of convenience:
in the "sequence" part, add a type "list" that allows just input of numbers to convert. basically decimal input should be sufficient.
thx for the tool as always, and hope this will happen!