=== ANCHOR POEM ===
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@user-36 Question - how do you do those cool superscript and subscript
notations?
Also: I don't think base 1 falls apart with negative exponents, for example
consider 1^-1 ----- it would evaluate to 1/10 in this system, which is not
1/1. Another example, 1^-3 would evaluate to 1/1110, which seems accurate to
me.
As for 0^0, I guess I think it does equal 1? Bear with me:
for any number n raised to an exponent e, you can write it like this:
1 * n * n * n ... with as many "* n"s as you have n's. for example:
1 * 3 * 3 * 3 = 9
or
1 * 5 * 5 * 5 * 5 * 5 = 625
in each case there's 3 or 5 instances of "* n" tacked onto the end. I don't
know the math notation for that.
now, when you raise something to the power of zero, it looks like this:
1
because there's zero "* n"s added to the end.
For negative exponents of course you divide instead of multiply, which is why
it ends up looking like a fraction.
So, it makes sense to me that 0 ^ 0 would equal 1, because it'd look like this:
1
while 0^1 would be
1 * 0
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=== SIMILARITY RANKED ===
--- #1 fediverse/286 ---
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│ CW: re: mathematics │
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@user-211 I agree! The problem is the limit as x->0 from the left and right
trend toward different infinities, meaning it's neither -infinity nor
+infinity. Which makes me think that it's the value that's exactly in the
middle, AKA zero.
Why wouldn't 1/0 be zero? Division is just inverse-multiplication, and
multiplying anything by zero is zero. Why wouldn't division use the same
rules? I don't understaaaaaand T.T
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--- #2 fediverse/42 ---
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@user-36 I always conceptualized bases as "the amount of numbers you can stuff
into a bucket before you spill over to the next bucket". Call it a holdover
from learning binary a bit younger than most people would consider normal...
Anyway with base 2 it makes sense. Put one thing in the bucket, and if there's
something there then it spills over.
But if the bucket is ALWAYS full, as in base 1, then you'd have to do a tally
system like you said: essentially counting from 0, then adding one to the end
making 10, then 110 for two, and 1110 for three, and 11110 for four, etcetera.
The reason you leave 0 at the end is because zero is a number and must still
be represented as a tally - it just uses a different symbol for our human
interpretation. Zeroes deserve respect in base 1 just the same as any other
number! zero rights are human rights... no that doesn't quite work, zero
rights are number rights? nevermind that joke is stupid
(continued)
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--- #3 fediverse/46 ---
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@user-36 neat thanks
when I said 1-1 = 1/10 I meant 1/1 in decimal except the denominator is in
base 1 meaning it's represented as 10 (since 10 in base 1 equals 1 in base 10.
Or pretty much any other base.)
I'm trying to figure out why 00 is undefined. There's a lot of math notation
in that wikipedia article and I'm working through it bit by bit... I feel like
there's a bug in the code of the universe and I'm trying to understand it.
Like... why is dividing by zero undefined? That seems like a bug to me.
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--- #4 fediverse/3030 ---
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@user-570
ooooo separating additive and multiplicative, I love that. I do like
specificity unless "increased" and "more" always corresponds to +10% and +50%,
or if the "rate of increase" is a stat stored on the character then
"increased" could increase quality by however-many percentage,, while "more"
could be "more soldiers" x(charisma_stat)
I tend to think of percentages like "0-100 (or more) stacks" of a particular
effect, so I think that's just how my brain works... xD clumping them up into
discrete groups - like, anti-abstracting, or measuring things that are just a
few.
"is this belt better than this one?"
"is this pair of tongs
even for larger buffs like +10% or +50% or whatever, those are just... 10
stacks, or if percentages are usually round numbers like +10% and +50% then
like... +1 stack which calculates to +10%
the hard limit vs math limit thing you said is amazing ^_^
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--- #5 fediverse/43 ---
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@user-36 now base zero is interesting because it means there's NO BUCKETS AT
ALL, which means that any numbers you try to stuff nowhere don't overflow to
anywhere. Meaning each number is it's atomic value, and represented with a
different character. So 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H,
I, etc etc until we run out of symbols, in which case we'd need to start
making more.
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--- #6 fediverse/227 ---
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│ CW: mathematics-and-socio-economics │
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humans are notoriously bad at large scales. tack a couple zero's onto the end
and it increases in value to them as much as if you had given them two.
10+1010. but hey it's all 10's right?
I think we severely overestimate the number of bad people in the world. I'm
basing that on nothing but my feelings. I think people generally are just
doing the best they can. that's what happens when you're oppressed in a
livable way. in a time of peace you can be merry, but these days it's always
been war. what can you do if your government disagrees with you?
hey, what's the 10th root of 10? 0.1? dang that's so close to zero. I wonder
if there's a calculation we can make that would end on a zero, but be unable
to return? is that what dividing by zero is? just... casting it into the void?
sure would make a lot of calculations easier if we could just return NULL
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@user-246
It's interesting to me that we can divide by infinity, but not zero. I feel
like it's true that dividing by zero would equal infinity (or maybe zero too
lol) but I don't know how to prove it T.T
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--- #8 fediverse/3325 ---
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@user-246
so... if infinity is the inverse of zero, then when inverted would infinity
also be zero?
if so, it follows that the [spectrum/dimension/cardinality/direction] that the
inversion is occurring upon might also have other steps inbetween. Unless it's
a binary thing, like "top and bottom" or "present and absent".
I wonder what those steps might look like? Clearly, since infinity minus
infinity does not equal zero, the steps inbetween (if they exist) would not be
numbers. If they were, then one single step from inverting infinity would be
1, but I don't believe that would be true.
On the topic of rings, the axioms would be things like "a ring is a ring if
you can trace a continuous line with a length of infinity across it's
ring-like-surface"? I wonder what the inverse of a length is... Or perhaps you
cannot invert a length, as to do so would give you a length of zero (in this
particular ring-like-case)
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--- #9 notes/division-by-zero ---
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--{{{ introduction
When division is explained at the elementary arithmetic level, it is often
considered as splitting a set of objects into equal parts. As an example,
consider having ten cookies, and these cookies are to be distributed equally
to five people at a table. Each person would receive 10 / 5 = 2 cookies.
Similarly, if there are ten cookies, and only one person at the table, that
person would receive 10 / 1 = 10 cookies.
So, for dividing by zero, what is the number of cookies that each person
receives when 10 cookies are evenly distributed among 0 people at a table?
Certain words can be pinpointed in the question to highlight the problem.
The
problem with this question is the "when". There is no way to distribute 10
cookies to nobody. Therefore, 10 / 0 —at least in elementary
arithmetic—is
said to be either meaningless or undefined.
- wikipedia, division by zero, 7-12-23
alright I have several problems with this. I like the idea of dividing
cookies, but I disagree with their conclusions. So dividing by integers works
as
they say, but division by zero is a little different - they say "the problem
with this question is 'when'" when in reality 'when' is the same for this
question as it is for any of the others. Obviously, zero is just a number. Why
would this be any different? The computational actions necessary to complete
this statement all occur at the same time, because they are by definition
immutable. You cannot change any equation, you only generate new ones.
Okay so here's my thinking. To answer the question "what is the number of
cookies that each person receives when 10 cookies are evenly distributed among
0
people at a table?" we simply have to answer the question. "How many cookies do
I get?" well, none, because you weren't at the table. In fact nobody was at the
table, so the result is that nobody got zero cookies.
You might even say you have a remainder of 10 cookies, as none of them were
distributed.
10 / 0 = 0 remainder 10
^^^ that's how I think it should be. I have an algorithmic justification, and
excuse me as I don't have a mathematical proof or anything. Math was never my
strong suit, there's too many symbols and strange names for obvious operations
that get in the way of the abstract big picture.
ahem...
abstract:
Given: x = 13 / 3 what is x?
step 1: convert 13 to base 3
step 2: digit shift right by 1
step 3: convert back to binary
--}}}
--{{{ step 1:
v
start with the binary number 1101 which is 13 in decimal. To convert to a base
3
number, \___________________.
\ |
first start with the Least Significant Bit (LSB) which is 1. So our
base-3 number starts with 0001.
v
Next, move to the next bit: 1101
^-----It's a zero so we can skip it.
Which means our
base 3 number remains unchanged as "0001"
v
Next, move to the third bit: 1101
^-----It's a 1, which evaluates to 4 in decimal,
meaning we should add 4 to our base 3
number
base 3
4 in base 3 is "11", which means we 0001 <----- 1 in decimal
should have a base 3 number of "12" now. +0011 <----- 4 in decimal
=0012 <----- 5 in decimal
\_________ 2? -> yes,
base 3
remember?
Next, move to the fourth and final bit: 1101
^ --it's a 1, which evaluates to 8 in
0012-----.____________ decimal. 8 in decimal is "22"
in
+0022-----. \ base 3, which means we
need to
=0111 \ T---- add "22" and "12" in base 3
\__________/ to get our final number
of
13. Which should evaluate
step 2: to 0111 in base 3.
.____.
bit shift |0111| to the right,
|>>>>|
|0011|--->1 underflow
.----.
meaning the base 3 number is now 0011 with an underflow (remainder) of 1
step 3:
convert back to binary, meaning 0011 in base-3 becomes 4 in decimal or 0100 in
binary. Store the underflow as the remainder.
===============================================================================
=
okay that's great and all, but what does this have to do with dividing by zero?
great question, me. I have two questions I want to pose to you:
1. what happens when trying to divide by 1 with this algorithm?
- you convert to base 1
\
wait hang on base 1? Sounds made up... Well, its
not!
or at least if it is, then I'm the one who made it
up
so... yeah
|
okayyy how does base 1 work?
\
glad you asked.
--}}}
--{{{ bases
--}}}
--{{{ decimal (base 10)
--}}}
--{{{ binary (base 2)
--}}}
--{{{ digit shifting
--}}}
--{{{ bases higher than 2 and not 10
--}}}
--{{{ base 1? base 0?
--}}}
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EDIT: Ooops, sorry, should have content warning'd this post
two incredibly useful tools I found for boolean logic in mathematics:
| f(x) | / | f(x) |
or more visually:
| f(x) |
---------
| f(x) |
this will return a 1 if f(x) evaluates to a non-zero value, and 0 if f(x)
evaluates to zero. Pretend there's an infinitesimal at the bottom if you're
one of those weirdos who think dividing by zero doesn't equal zero...
the other tool is this:
( A * B ) + ( (1 - A) * C )
or more visually:
( (0 + A) * B)
+ (1 - A) * C)
This will evaluate to B if A is 1, and C if A is 0, essentially creating an
"if true" check. Note that it doesn't work if A is neither zero nor one, but
that's what the first tool's for.
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@user-36 So, you're saying the tally system doesn't make sense, and instead
what I suggested for base zero is instead base 1?
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@user-209
I think you're right. Every letter in the variable name is another byte the OS
has to keep track of, which was a bigger problem in the past than it is today
(when it's been made irrelevant)
it's interesting how habits persist though the conditions that caused them
have faded. like a personal reflection of the environment you learned in.
"A a = new a();" is much more concise and (crucially) you can fit more words
to the right.
"a + b = c; c -= 2; f_z.write(c); f_z.close();" could conceivably be written
on a single line if you have short variable names. and when you only have so
many lines...
glad we're not constrained by those things anymore. the skeletal code that we
look at daily is much clearer - scope is more important, and so it makes sense
to encourage a coding style that illustrates it. however I can't help but
think block formatting like this could be useful in some situations, such as
when you'd normally be compelled to write a function for an operation that
runs once or more.
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the reason the right is hurt that you'd celebrate charlie's death is because
they hired an actor to perform him to one side and he does his natural self to
the other. maybe he was a really big cutie, nobody can tell, because it's
pretty much like hand-waving on narkina 12.
it's okay to hate the version you've been shown
fuck that kind of cowardly assault
propaganda? and at this hour?
she's made out of midnight, she's suffused in the stuff. it permeates her form
elementally, because she's a witch, tee hee.
why would magic work if it wasn't a performance? there always is a source from
where it must flow.
== jeez I just got mind controlled, wacky ==
*she's **essential* izing**. usually that means she's been playing dominions.
my family and I always used to fight. we got so good at navigating it. like,
storms, that the earth called, that we had to sail through to maintain our
relation orbits.
== stack overflow =======================================================
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--- #14 fediverse/3324 ---
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@user-246
If I follow correctly, the reason it's not is because you're dividing zero by
two? meaning the magnitude of infinity would be zero.
... chat, is infinity just... zero, viewed from a different perspective?
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║ @user-246 │
║ │
║ yes, when defining with numbers it's easy because one is one and that's done. │
║ │
║ with concepts such as infinity or direction or cardinality, it's more │
║ difficult because you need more than just a "magnitude from zero" to describe │
║ them. Rules means more contradictions, which is totally okay! It just means │
║ you need more than one definition of "infinity" for example, for different │
║ contexts. │
║ │
║ use a scalpel for surgery or art, when precision is needed, use a pocket-knife │
║ like a leather~~man~~daddy for tougher tasks like whittling a spear or │
║ throwing a spear or stabbing fascists with spears - where was I going with │
║ this? oh yes: │
║ │
║ when thinking of sets, to me infinity is more like... "too many numbers" like, │
║ the meme with the guy who is having difficulty holding too many limes. They │
║ overflow and spill out of your set-like-container, no matter how you define │
║ the boundaries of the set. "does the set of all sets include itself or does it │
║ overflow" kinda vibe. │
║ │
║ the idea of a chesspiece disagreeing with math lol! │
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║ @user-941 │
║ │
║ well, your computer only has so many 1s and 0s that it can use at once. Like, │
║ having a trillion hands that can each hold a single grain of rice. Every │
║ character in that txt file would be like, 8 grains of rice, minimum, meaning │
║ you'd need at least 8 "hands" (or spots to put a zero or a one) for each │
║ letter! │
║ │
║ Hmmmm that's a lot of bits and bytes if everyone's writing to the same file. │
║ Maybe if we split the file up into smaller sections, then we could just read │
║ part of it at once. Then we could "scroll" through it to make sure we've read │
║ the whole thing, starting from the top and going to the bottom. │
║ │
║ ah but if everyone's SSHing into the same computer and reading it there, then │
║ that computer will have to present different parts of the file at different │
║ times to different people, as they read from the top to the bottom. Maybe we │
║ could just send them the file, so they can read it at their leisure? │
║ │
║ Yeah! And we could use tags to organize it and make it look pretty, like an │
║ HTML file except... wait hang on │
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--- #17 fediverse/5217 ---
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a float is a number between 0 and 1 like 0.5
they don't store the exact valyue, they just guesstimate
for some reason computers are designed such that 100% is represented as
1.175494351 E - 38: 3.402823466 E + 38 ->source/microsoft/learn/"cpp
(lol)"/type-float
... which is weird because, that's such an arcanely obscure number, who's
gonna remember that? meaning you gotta go to their website everytime, called
google.com, and search through microsoft for the answer to life's common
mysteries.
emphasis on common
so yeah you gotta write a conversion library which turns every single instance
of e to the whatever into a 100 and all the other numbers get converted too.
but you gotta do it without doing any hardware division, because that one's
too expensive. it's gotta be a true natural doubling representative, except,
without doubling the hard-drive space, leading to a distribution of only one
half of the results of the metghoid. [[ type ohhhhhhs ab ound] ]
I swear I'm not an LLM I just think embiggeningly
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if you want to "not think about a purple elephant", the first step is to
imagine yourself slaying it
... okay how about cthulu - if you don't want to imagine cthulu nomming on our
gravity well, then picture yourself wielding a bright burning blade of fire
and vengeance and pay special attention to the way that you cauterize each
tentacle as you slice them one by one at first, and then in a massive flurry
at best, ultimately leading to the incomparable brightness that radiates out
from your shining blade of the sky, which blinds the poor beast who can't see
you as you approach, piercing the skull and then going home for some toast
if you can get good at that, then you can wield magic
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claude-code is like programming, but for executives.
when everyone has FUCK I'M TOO HUNGRY I can't think right
when everyone has the power of an executive, that's communism.
something something futurism is when everyone is elevated without diminishing
others
gah I need to live in a palace or something where everyone does the normal
stuff and I can focus on magic and the gods
I wondeer how much the oracles at delphi did for themselves? weren't they
blinded at a young age, to better hear the voices of the gods? ... oh that
suddenly makes sense now. I always thought that pretender chassis in Dominions
5 was pretty cruel, but, now I know *how* it works and yeah. ancient peoples
were smart. but also sharp. they had to work with what they got, and we got
computers now, so.
I am nothing but hopeful for the future! I'm convinced that everything's going
to be alright. I've thought about it at length, and I think we're winning
against the dark. We're on the right track, and there aren't many things that
could go wrong at this stage.
... okay there are always things that could go wrong. But I don't see what I
could do to help. Maybe I should go walk around a bit, and see what's changed
in the past few months, as I've been sleeping in my room for most of it.
Haven't gone on a proper walk since summer. It's winter now...
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left stick is grab a target and bring it into context, right stick is for
drawing a pointer, a to group things together and b is to separate, etc etc
--
I remember coding it to be designed around two dimensional arrays. It used
lateral numbers, AKA "imaginary" numbers (they aren't imaginary they're just
orthogonal to regular numbers - hence, lateral)
and like... the math worked, and it was all on a T9 keyboard.
I figure each memory location would be like, a function written in the
program, or perhaps a binary or script file in a nearby directory. by writing
a value to a certain coordinate, you are giving an input value to a function.
and if nothing is stored for that particular coordinate, then the command
fails to execute and nothing happens.
pointers to functions which may or may not exist.
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|