trying to figure out a title for this "how your CPU represents integers and floating point numbers" zine

so far the best idea is "inside the machine: integers and floating point" but that's not great

@b0rk "Numbers Considered Harmful"
@b0rk Bit Twiddling? 😁
@derickr @b0rk We all float down here
@derickr @b0rk Would totally be a great title if the CPU stored all numbers as floats, but alas.
@b0rk
maybe something along the lines of "counting with 64 fingers" ? but not really a perfect analogy maybe

@b0rk Whatever you do, make it count!

*ducks* 😁

@b0rk “Get to the point: Fixed vs Floating point numbers and you”
@b0rk A layer deeper it's all integers, and underneath that it's nothing but ones and zeroes. And those are just abstract notations for electrical charges in wee bits of crafted beach sand!
@b0rk It's as easy as 0.1, 0.2, 0.30000000000000004
@b0rk Maybe something like, "Chopped to Bits: fitting all the numbers into a tiny CPU"?
@b0rk “I _Can_ Count the Ways”

@b0rk How about:

"When 1+1 doesn't equal 2"

"It's just a 1. How hard can it be?"

"What's the (floating) point?"

"I do not think the floating point representation means what you think it means" (Princess Bride!)

"Numbers: a bit of this, a bit of that"

@b0rk see? pee-yew; how computers math it up
@b0rk “I’ve got your number.”
@b0rk I was explaining Turing machines to my sister, and how every bit of memory is just
 an integer. Everything else is just fancy interpretation. Everything.
@b0rk "How bits become numbers"
@b0rk "How CPUs have got your number"
@b0rk Probably best to avoid "Representation Theory" because https://en.wikipedia.org/wiki/Representation_theory
Representation theory - Wikipedia

@b0rk "The 1, 2, 2.99999 of How Computers Count'
@b0rk "The anatomy of numbers: how numbers inside the machine look like"
@b0rk Computers, me and numbers?
@b0rk The Guts of your Computer: integers and floats dissected!
@b0rk The beginning and the endianness of numbers in computer hardware
@b0rk "Int internals and floating bits: How does your computer store numbers?"
@b0rk
“Float like a point and sting like an Integer: How a CPU Maths”
@b0rk From bits to billions: How computers represent numbers
@hanshuebner @b0rk that's actually really good :)
@b0rk hmmmmm. “ A NaN, A plan, how your computer does math” 
I couldn’t make the palindrome :-)
@b0rk One point at a time
@b0rk “IEEE Except Before C: A History of Numerical Representations”
@b0rk numbers in the CPU: the long and the short of it, and everything intbetween â˜ș
@b0rk "Floating integers pretending to be numbers"
@b0rk “A Field Guide To Numerical Phenotypes in CPUs”
@b0rk Dots & Digits: how computers store numbers

@b0rk
Some random ideas:

How Numbers Are Made
Inside Numbers
The Bits of Numbers
Numerical Bits

I hope these might be helpful.

@b0rk Something I’ve been trying to figure out about big- and little-endian designs: The reason I’ve always felt weird about little-endian integers is that the most-significant bit is on the right and most-significant byte is on the left.

But
 is that just because of the convention of writing left-to-right? Could you write a 16-bit little-endian int containing “1” as

10000000 00000000

?

Does the hardware fundamentally care or is it just writing convention?

@b0rk Short & simple: "How Computers Count". Catchy: "The Trouble with Numbers". Funny(?): "Entirely Integer & Double Trouble".
@b0rk #spitballing -- something with Schroedinger's Cat maybe, inasmuch as: you never know what the float is until you try to use it?
@b0rk The Point of Floats : A Deep Dive into How Computers Represent Numbers

@b0rk I think "how your CPU represents integer and float numbers" is good as is!

maybe "how your CPU sees ints and floats" if you want something shorter

@b0rk
"Inside the CPU: A tale of numbers... and more"
@b0rk Knuth’s book on it was “Semi-numeric algorithms”, which I didn’t understand and didn’t read it for years because I thought it wasn’t numbers, but true numbers to a mathematician aren’t the finite approximations we have inside the machine. It is a great read on numbers in computers tho.
@b0rk "A Short History of Lies We Tell Ourselves In Order to Continue Pretending the Integers and the Reals Are Implementable Within Finite Space and Time"

@b0rk I remember having trouble explaining numeric-resolution problems to a nontechnical friend and I finally realized the key issue they didn't know but we all do is that we want to fit numbers into fixed-size slots. 16/32/64/128 bits. So maybe something like "numbers as bits in slots" or some such.

(Then this smart person asked "what if they won't fit?" and I had to explain about BigNumbers etc, but that's maybe a distraction)

@timbray yeah the zine talks about big integers! I don't think it's a distraction
@b0rk
Keep it short: "numbers in your computer"
@b0rk "Why Numbers Sink, Unless They Float"

@b0rk

Hey, I just `ADD` you.
And this is Craaaazy.
Bits make these numbers.
So `CALL` me Maybe!

@b0rk „byting numbers“?
@b0rk "How your computer stores Pi, and other numbers"? Start with a concrete example of a floating point number people know about?
@b0rk "Bits of Numbers"?
@b0rk "12.000000000004 things you didnt learn in grade school math"
@b0rk values beyond (and between) zero and one.