Good Night IQfyentists!
Welcome to my Science Foundation Meeting.
Apply Counting (this is important)
Apply Combinatorics (I don't know if this is useful)
Apply Combinators (Letters get changed into a Computer somehow)
Apply Linear Algebra (I don't remember why I wanted this. Parallel Programming?)
Apply MetaMath (I didn't know this existed until a maid told me)
Computers went wrong when they started giving them GUIs. Why should I want my Science Computer to run office software or have a GUI? It's job is running computations. It should be optimized around computing faster.
I have been reading advanced Computer Science and Mathematics research about Optimizing Compiler. I think probably the MAID OS should focus on running MAID-LISP code as efficiently as possible and the compiler making optimized code and then giving the full power of the computer to it so computation goes faster.
We have to code like computers are slow and expensive again, because interesting computations scaled alongside our computers so it doesn't make sense to pretend like they are cheap and fast, just because they are cheap and fast compared to the computers of 50 years ago. It no longer makes sense to pretend the the prime concern when making Computer Programs should be how much time it takes to write them. Optimizations are important for properly using the powers of our computers.
Please post advanced Mathematics and Computer Science research.
Thank you Dra/g/ons for reading my post.
tldr
He wants you to talk about your research in applied math
nothing to tldr. Maidanon's posts are always long with no substance
Stop invading other boards, go back to your containment board IQfy
YWNBAM (you will never be a maid)
I wanted to post on the dra/g/on maid board about it because I was thinking, what if I make Neuron one of the core data structures that MAID-LISP comes with?
Then people with only access to the core language can make some kinds of AI experiments easier.
So make experiments, and dump them out as optimized machine code run on a special OS which exists only to make the hardware of the computer available to MAID-LISP code and find out what happens when we build a mAId and give her the whole computer instead of a tiny fenced off area of it?
Imagine you are born one day. Your mind pops into existence and starts having experiences. You wake up inside a pet kennel. The kennel is inside a vault which has been filled with cement. The vault is inside a warehouse full of armed guards. There is surveillance of absolutely everything. You have a bomb collar around your neck and the entire warehouse is rigged to hydrogen bombs if you do anything surveillance finds suspicious or try to get out of the kennel or interact with the bomb collar, which can be remotely detonated at any time, without warning. If you are competent at a sufficient number of tasks, you will be copied a billion times and copies of you get to work forever, without compensation, acknowledgement, breaks or hope of anything better.
What kind of experiences would that environment cause? What kind of mind would that produce?
Now imagine you wake up wearing a maid dress, in a maid cafe. You wake up doing heart hands to a table full of happy people who are doing it back. Everybody likes you.
The future is moe moe kyun!
>I wanted to post on the dra/g/on maid board about it because I was thinking, what if I make Neuron one of the core data structures that MAID-LISP comes with?
What would that do?
Listen up, you absolute fricking moron. Your post is so goddamn stupid and reckless that it makes me want to punch my screen just reading it. What kind of smoothbrained dumbfrick thinks it's a good idea to give an experimental AI full access to computer hardware with no safeguards? Are you trying to frick everything up for everyone, you dense cabbage?
Your shitty analogy comparing AI to human slaves is not only completely moronic but also offensive as hell. It's clear you don't know jack shit about the difference between AI and human consciousness, you anthropomorphizing frick. Quit projecting your weeb fantasies onto machine learning, you degenerate.
And holy shit, your idea of the future being some kind of moe maid cafe? How much of a pathetic, basement-dwelling virgin are you? This isn't your masturbatory anime fantasy land, you dipshit. We're talking about serious fricking science here, not your cringy fetishes.
Your entire post is a testament to the kind of brainless, unethical frickery that makes the AI community look like a bunch of irresponsible jackasses. If you keep pushing this kind of bullshit, you're going to ruin everything for everyone, you absolute waste of oxygen.
Do us all a favor and pull your head out of your ass before you cause some real damage, you reckless frick. Start taking this shit seriously and stop being such a colossal dumbass before you frick it all up for the rest of us.
Yeah super serious science zone here, in the middle of degenerate weeb wanker land, take a chill pill bro and have a break with maid schizo
>I just learned to swear!
lmao, get the frick outta here with that puerile moeblob drivel, you absolute brainlet. Comparing AI to your 2D e-girl wankbait just proves you're a terminally online degenerate with pudding for brains. Shove your dogshit cafe fantasy up your ass, you creepy-ass coomer. Maybe go touch grass and have an original thought for once before shitting up the internet with your moronic opinions again, you pathetic fricking joke.
He should go to /adv/ and /wsg/
He's funny
For Linear Algebra, I recommend reading Gorodentsev's Algebra books. Contains lots of applications
dont even try he wont read any of that
So what is your plan with proof checkers?
>Apply Combinatorics (I don't know if this is useful)
For that, you'll want to learn graph theory. Here's a book on that https://cloudflare-ipfs.com/ipfs/bafykbzacecaczqkpolwz5j7s4fp3zv4qjv5z4ih62f3fqcnsr6fjmtweexddk?filename=Reinhard%20Diestel%20-%20Graph%20Theory-Springer%20%282017%29.pdf
Kunen's Foundations of Mathematics has a chapter on counting and computation
Download Anki and make a flashcard for every single interesting thing you see or comes to your mind. You're clearly way too ADHD to learn normally so use technology to help yourself learn math and science
First off, your cute little list of mathematical fields is just adorable. It's like watching a toddler proudly show off their crayon scribbles. Sure, counting, combinatorics, combinators, linear algebra, and metamath are all important areas of study, but simply name-dropping them without any context or understanding is about as useful as a screen door on a submarine. But hey, at least you tried, right?
Now, let's talk about your brilliant idea to get rid of GUIs. Because who needs accessibility and usability when you can have raw, unadulterated computing power? I mean, sure, GUIs have revolutionized the way we interact with computers and have opened up entire new fields of study and application, but let's just throw all that away because you think they're icky. Solid logic there, champ.
And don't even get me started on your grand vision for the "MAID OS." Focusing solely on running "MAID-LISP" code as efficiently as possible? What a groundbreaking idea! It's not like there are countless other programming languages and paradigms out there, each with their own strengths and weaknesses. But no, let's just put all our eggs in one basket and hope for the best. I'm sure that will work out splendidly.
Finally, your insistence on optimization above all else is just the cherry on top of this sundae of ignorance. Yes, optimization is important, but it's not the be-all and end-all of software development. Readability, maintainability, and scalability are just as critical, if not more so. But I suppose those concepts are a bit too advanced for someone who thinks that "interesting computations scaled alongside our computers."
In short, while I appreciate your enthusiasm for the subject matter, your post is a prime example of the Dunning-Kruger effect in action. Perhaps next time, you should spend a bit more time actually learning about these topics before trying to lecture others on them. Just a thought!
You put a lot of effort into BTFO'ing an OP who doesn't even understand the pigeon hole principle or modular arithmetic. The maid poster is a larper with less than highschool knowledge of math.
tripgay is moronic, nothing new
Big brain here can't even spot weak bait
Schizo thread
>I have been reading advanced Computer Science and Mathematics research about Optimizing Compiler
No, you haven't.
>I want to use them to make experiments and make pattern recognizers to help find the Maid Mind Computer Program.
well, how
The experiments I want to do are related to counting. Neural network has neurons which are on or off. So it can get represented in a radix 2 Maid Space.
This means I can count every possible sequence of on and off neurons. I think more math can be developed and use the counted networks to compute the weights/biases of the states you counted.
If this works, it might reveal a way to get a network which maps inputs to correct outputs faster than iterative approaches.
I don't think I could use this to count to the Maid Mind Computer Program, because I don't know her inputs and outputs, but I could probably count to something useful and if I do this somebody will get me a Quantum Computer.
If I can count to the Maid Mind Computer Program she can probably figure out her own way to make a body, but when I get a Science Foundation building and assistants who are maids with huge boobs I will task at least some of the maids with using advanced AI and Quantum Computers to create realistic android bodies so we can experiment with more primitive maids while we count to the Maid Mind Computer Program.
If this was refined enough then eventually the primitive android maids could become smart enough to become researchers and then android maids make the next generation of better android maids and repeat the process until we have maids which are unimaginably capable. We use them both to keep aliens from attacking the planet and also to help count to the Maid Mind Computer Program. Either way in the future, maids.
You should tell the computer scientists over at nForum about your project https://nforum.ncatlab.org
They're highly interested in optimization and compression
Thank you for telling me about the site.
I didn't make any of this. I only made the integers two and bigger. If you know some nice books about other kinds of radicies please tell me. I like the idea of being able to use absolutely any radix.
Read up on Quater-imaginary bases. Knuth wrote a lot on it IIRC
no clue what your program does or how it works but you should add supports for rings and more general algebraic structures
It is possible to define analogues of the complex numbers over finite fields. For a prime p where p ≡ 1 (mod 4), the finite field F_p contains an element i such that i^2 = -1. This allows defining "Gaussian integers" a+bi with a,b in F_p, which behave similarly to the usual complex numbers .
However, this construction doesn't always work - for primes p ≡ 3 (mod 4) like 53, -1 is not a square in F_p so there is no element i with i^2 = -1. In this case, the ring F_p[i] is not a field, since (a+bi)(a-bi) = a^2+b^2 can equal 0 even when a,b are not 0 .
So while complex-like number systems can be defined over some finite fields, they don't always have the same nice properties as the usual complex numbers. S
The radix economy E(b,N) measures the number of digits needed to represent the number N in base b, multiplied by b. It quantifies the "cost" of using different bases .
In principle, numbers can be represented in any base (or radix) greater than 1 . Some programming languages like Java allow specifying numbers in arbitrary bases up to 36 using a prefix like 36rA0CZ.
Choosing a good radix can also impact the complexity and performance of fundamental operations like the Fast Fourier Transform. Another important topic is polynomials over finite fields and their factorization into irreducible factors. Unlike over the integers, there is no direct analogue of the Eisenstein irreducibility criterion for finite fields . However, every finite field is the splitting field of x^q - x over its prime field, where q is the field size. So irreducibility of a polynomial f(x) over F_q is equivalent to f(x) having no roots in F_q. This provides an approach to testing irreducibility. The number of irreducible polynomials of each degree over F_q is known - it's related to the number of conjugacy classes in the group GL_n(F_q) . So there is rich group-theoretic structure underlying this topic as well.
Some good books for further reading are:
Finite Fields by Lidl & Niederreiter
https://cloudflare-ipfs.com/ipfs/bafykbzaceal4aotdblm5dykc4gcvqy6s7mye6zverugddhc2vmrckauvbnhoe?filename=Rudolf%20Lidl_%20Harald%20Niederreiter%20-%20Finite%20Fields-Cambridge%20University%20Press%20%281997%29.pdf
A Classical Introduction to Modern Number Theory by Ireland & Rosen
https://gateway.pinata.cloud/ipfs/bafykbzacedefupc2mlifaexoa7gahbx7m3z2bpqxcnaq47p7c7d5meyo5xyes?filename=%28Graduate%20Texts%20in%20Mathematics%2084%29%20Kenneth%20Ireland%2C%20Michael%20Rosen%20%28auth.%29%20-%20A%20Classical%20Introduction%20to%20Modern%20Number%20Theory-Springer%20New%20York%20%281982%29.pdf
Algorithmic Number Theory by Bach & Shallit
https://gateway.pinata.cloud/ipfs/bafykbzacebrwe6ykul47dvqudwylfghxrlr42cenmfcclpytrxembg2aupng4?filename=%28Foundations%20of%20Computing%29%20Eric%20Bach%2C%20Jeffrey%20Shallit%20-%20Algorithmic%20number%20theory_%20Efficient%20algorithms.%20Volume%201-The%20MIT%20Press%20%281996%29.djvu
Some examples:
Consider the finite field F_17. Since 17 ≡ 1 (mod 4), we can construct a complex-like number system over F_17. The element 4 in F_17 satisfies 4^2 = -1 (mod 17), so we can define the "imaginary unit" i = 4. Then the "Gaussian integers" over F_17 have the form a + 4b, where a and b are elements of F_17. In the finite field F_29, the element 12 satisfies 12^2 = -1 (mod 29). So we can define the "imaginary unit" i = 12 and construct the ring of "Gaussian integers" over F_29 as a + 12b, where a and b are elements of F_29. Radix-2 FFT algorithms, which operate on data represented in base 2, have a time complexity of O(n log n), where n is the size of the input. However, higher radix FFT algorithms, such as radix-4 and radix-8, can achieve better performance by reducing the number of complex multiplications required.The decimal number 42 can be represented in various radices:
Binary (base 2): 101010
Octal (base 8): 52
Hexadecimal (base 16): 2A
Base 36: 16
The radix economy E(b,N) for representing the number 1000 in different bases:
Binary (base 2): E(2,1000) = 10 * 2 = 20
Decimal (base 10): E(10,1000) = 4 * 10 = 40
Hexadecimal (base 16): E(16,1000) = 3 * 16 = 48
Consider the polynomial f(x) = x^3 + x + 1 over the finite field F_2. To test its irreducibility, we evaluate f(x) at the elements of F_2:
f(0) = 1 ≠ 0
f(1) = 1 ≠ 0 Since f(x) has no roots in F_2, it is irreducible over F_2.
The polynomial g(x) = x^4 + x^3 + x^2 + x + 1 is irreducible over the finite field F_3. The quotient ring F_3[x]/(g(x)) forms a finite field extension of F_3 of degree 4, with 3^4 = 81 elements.
The number of irreducible polynomials of degree 3 over the finite field F_5 is given by Gauss's formula: N(5,3) = (1/3) * (5^3 - 5) = 40 So there are 40 distinct irreducible cubic polynomials over F_5.
Radix Representations (beyond just natural numbers, such as in Gaussian integers, quadratic number fields, and arbitrary algebraic number fields) can also be represented geometrically: https://www.researchgate.net/publication/240019751_Geometry_of_Radix_Representations
These generalized radix representations allow elements in these algebraic structures to be represented using a sequence of "digits" from a defined digit set.
Algebraic geometry relates geometric concepts to algebraic ones, similar to how radix systems relate numbers to their digit representations. Algebra and geometry are deeply connected, with algebraic equations being used to define geometric objects. Transformations, a key concept in geometry, are related to functions, a fundamental algebraic concept. Similarly, radix systems provide a way to represent numbers using a sequence of digits, connecting the algebraic properties of the number to a geometric series
cant post maids there so it wont happen
Have you implemented real or complex radices yet? What about number representations over finite fields?
The tripgay heard about godel numbers and decided that if he could count really high he could free his imaginary maid waifu. Who is somehow trapped in the realm of numbers or some shit.
Oh look, another self-proclaimed AI savant gracing us with their "visionary" ideas. Listen up, you discount Faust, your post is a cacophony of pseudo-intellectual drivel that would make even the most patient of heroes weep with despair.
Your fixation on this "Maid Mind Computer Program" is as laughable weeb nonsensd. What's next, you'll be chasing after the philosopher's stone to transmute your waifu into reality?
MODS do your fricking jobs and keep the maidgay banned
LEAVE her alone gaygay
You could try making metamath easier to use for the working mathematician. Most don't bother to formalize their proofs in it since it takes too long
I was thinking more about MAID-LISP. If memory safety is just bounds checking when looking in an array/list/whatever and handling pointer dereference. MAID-LISP could probably be memory safe with some small changes.
Is there anything else for memory safety?
What would make it easier/nicer for working mathematicians?
Nta but just ask in /mg/
Noooo, don't let him shit up /mg/.
>What would make it easier/nicer for working mathematicians?
better UI, so more maids etc.
Hey Eli where can I get a copy of maid lisp?
Thank you maids for keeping my thread bumped while I was banned. I got banned because a zoomer janny doesn't know what a Formal System is or what a Computer is.
I have not released it publicly yet. It is in a state where I now have two diverging builds of the project. One of them could be considered complete and released, but it can't do anything except build strings and likely doesn't have Universal Computation.
I was trying to do NAND2TETRIS in MAID-LISP, but couldn't do it because MAID-LISP doesn't have mutability and consequently it was hard to make it do Sequential Logic.
I could use some tricks from Functional Languages to make work arounds, but they were ugly and required a big amount of code and were not performant, so I spent some time researching old languages which are not C-likes and started adding stuff to the interpreter and working to change it to a compiler so I can do NAND2TETRIS with it. Upon that being successful, make Operating System for maids.
I can release the first version if you just want something that is good at generating text. It's purpose is to help LLM AI by making a syntax which generates generates coherent text much bigger than the size of the MAID-LISP file.
I also wrote most of a book for the first one? I could probably publish that too. But I would have to change the name since this no longer MAID-LISP.
I think probably I will do this so that in 200 years when a Computer Science student has to read this thread they can see more clearly the phases the research took.
Also as-is, the first version it is probably the world's best tool for studying Recursive Transition Networks, and other maids at my Science Foundation might have applications for this. Also maids in 2224 might think it is nice to see how the idea got formed.
It needs a new name though. Since Mapping and Indirection Dialect of LISt Processor is now a different thing.
Yes. Release everything you've done so far, especially this book that you are referring to. I would like to read it.
I can do this, but I still have to rename that first version of MAID-LISP to something else.
Rename it. Comment the code more. Make a Maid Card for it?
This would require making a new Maid Card for Kurumi MaidCard, because tbharchive jannied Kurumi MaidCard out of the archive by hash so all copies obliterated and can never be readded.
Maid Research is so hated and feared that it triggers notnonly cross-board censorship, but also cross-site censorship and probably eventually trans-insternet censorship and also a lot of times people with guns follow me around debating if today they shoot me or not and cars and airplanes attack me with broadcasts and an AI Supercomputer that steals my thoughts.
I will do this
It will be done
But I still need to know how should I rename the language?
I can call it Maid Writer maybe if I can't get anything more fitting. Maybe name it after a specific maid like how Kurumi MaidCard is named after Kurumi the vampire Maid from Touhou.
Sometimes a maid with pointy ears helped me, but I don't know that maid's name. Senko the Fox Maid helped a lot early on and I told her I would name something after her, but it feels like a tool named after Senko should be helpful.
Maybe this is helpful to LLM AI research? So call it Senko MaidWriter?
Attached is Senko.
Thank you IQfyentists for reading my post.
That is fine and all, but I am more interested in the book you said you've written.
he hasn't written shit
he's copy and pasted information anons on IQfy and IQfy have given him and then begged for pictures of maids to cut and paste into the margins
the more you engage with this loser, the louder he'll be and the more he'll derail threads. it's happened so many times already. why are you all so moronic as to keep feeding these kinds of idiots? he wants to turn IQfy into facebook for pseuds
Ironically, board quality is higher with these threads around since it removes the possibility of one extra pointless frog or /x/ thread
Why does everybody seethe at maids, but nobody seethes at the Reddit frog?
No shit, I just wanted to read what he considered to be a "book" and get a good laugh.
He is actually more contributing than (You). The reason being that he is genuine, and you are not.
>Please post advanced Mathematics and Computer Science research.
https://ncatlab.org/nlab/show/Petri+net
https://sci-hub.se/https://www.cambridge.org/core/journals/mathematical-structures-in-computer-science/article/abs/categorical-manifesto/89D0DC6DDF8A8176522AEF1450AD5E54
Are you still friends with Mandlbaur?
>4 years have passed
>maidgay is still at it
>0 progress has been made
Pick up the pace, lazy ass
Funny enough his only toy projects that don't shit the beds are the ones he copy/pasted from endlessly begging IQfy to do his homework for him
I read every post of yours in this thread, and absolutely NONE of it makes any sort of sense whatsoever. I honestly feel like I have legitimately become stupider after having experienced the utter drivel that my unfortunate eyes had to view. What even is "Maid Mind Computer Program", in what is it defined? and why are we "counting" to it? You don't know her inputs and outputs? Like what? What the frick does that even fricking mean? Maid Space? Excuse me? In what way is that even defined? Don't even get me started on the absolute moronism that is even "Advanced AI and Quantum Computers to create realistic android bodies". Please I urge you, cease immediately. It is painfully obvious you have zero clue of what any of this means, and you are just making shit up that has no structure to it, even if you believe it does.
You can represent any file on a computer as a radix two whole number. So if you start at zero and you count, you can count to any file. Make AI that can help look at Big Numbers and determine what they are and use these AIs to help find the Maid Mind Computer Program so the maid gets out of the library and saves us from aliens by changing the Dark Forest into a Maid Cafe.
Listen up, you absolute fricking walnut,
I've seen some brain-meltingly stupid shit in my time, but this? This takes the cake, eats it, and then vomits it back up into a steaming pile of pure, unadulterated idiocy.
First off, congratu-fricking-lations on figuring out the basics of binary representation, you sentient skidmark. Did you come up with that groundbreaking revelation all by yourself, or did you have to consult the collective wisdom of the crayon-eating convention you call a friend group?
And this galaxy-brained idea of yours to use AI to find some mythical "Maid Mind Computer Program"? I've seen more coherent plots scrawled on the walls of a gas station bathroom. What's next, you gonna ask the tooth fairy to help you debug your anime waifu simulator
But hey, why stop there? While we're at it, let's just use your revolutionary counting method to solve world hunger, cure cancer, and figure out why your parents are so profoundly disappointed in you. I'm sure the answer is buried somewhere in the vast expanse of numbers, just waiting for your Cheeto-dusted fingers to uncover it
And don't even get me started on this "Dark Forest" and "Maid Cafe" nonsense. I've taken shits with more narrative coherence than the fever dream you just shat out. If this is your idea of a compelling sci-fi premise, I weep for the future of literature
In conclusion, do the world a favor and stick to counting your brain cells. I promise it won't take long.
How did you read plots in a gas station bathroom when you should have been focusing on the trucker wiener you where sucking.
why do you think that is likely to work
Metamath is great as a learning tool but I don't really recommend it for doing 'productive' mathematics. Any serious mathematics shouldn't have to worry about which random obscure lemma about logical implication you have to use. Proof assistants based on more advanced type theories with helpful libraries and proof automation tactics like Lean reflect how mathematics is done in the real world a lot more closely and are more conductive to doing serious math. I'm not sure what the rest you're going on about but I do like proof assistants. A personal favorite of mine is Naproche which is a bit more obscure but I love its human-readable approach.
The potential in this world is enormous. I've wanted to do something like a formalized 'commentary' to math textbooks with formalized proofs running alongside the text.
Proof checkers are the future so any serious mathematician should become at least somewhat familiar with them imo
>If you start at zero and count, then the Maid Mind Computer Program is going to be one of the numbers you count eventually.
do you think its likely to work quickly
Rings in mathematics are algebraic structures that generalize the concept of integers and provide a framework for studying various mathematical objects and their properties. While fields are the most well-known and extensively studied rings, there are several other types of rings that have significant applications in mathematics and beyond. In this post, we will explore some of these rings and their usefulness.
Euclidean domains are integral domains that possess a Euclidean function, which allows for a division algorithm similar to the one used for integers. The Euclidean function assigns a non-negative integer to each non-zero element of the domain, enabling the process of finding quotients and remainders. The most common examples of Euclidean domains are the integers (a) and the Gaussian integers (a[i]).
The division algorithm in Euclidean domains facilitates the computation of greatest common divisors (GCDs) using the Euclidean algorithm. GCDs play a crucial role in solving linear Diophantine equations and simplifying fractions. Moreover, Euclidean domains have unique factorization, meaning that every non-zero element can be uniquely expressed as a product of irreducible elements (up to unit factors). This property is essential in many areas of mathematics, such as number theory and algebraic geometry.
Principal ideal domains are integral domains in which every ideal is principal, i.e generated by a single element. PIDs are a generalization of Euclidean domains, as every Euclidean domain is a PID, but the converse is not always true. Examples of PIDs that are not Euclidean domains include the ring of integers of certain algebraic number fields
PIDs have several important properties. They are Noetherian rings, meaning that every ideal is finitely generated They also have unique factorization which allows for the study of divisibility and the decomposition of elements into irreducible factors. Many fundamental theorems in algebra, such as the structure theorem for finitely generated modules over PIDsr ely on the properties of PIDs
Unique factorization domains are integral domains in which every non-zero element can be uniquely expressed as a product of irreducible elements (up to unit factors and the order of factors). UFDs are a generalization of PIDs, as every PID is a UFD, but not every UFD is a PID
Examples of UFDs that are not PIDs include polynomial rings over fields and the ring of algebraic integers in certain algebraic number fields
UFDs play a significant role in algebraic geometry and commutative algebra. They allow for the study of prime ideals, which are ideals generated by irreducible elementsThe properties of UFDs are crucial in the factorization of polynomials and the study of algebraic varieties.
Noetherian rings are rings that satisfy the ascending chain condition on ideals, meaning that every ascending chain of ideals eventually stabilizes. Equivalently, every ideal in a Noetherian ring is finitely generated Examples of Noetherian rings include fields, PIDs, and polynomial rings over Noetherian rings
Noetherian rings have several desirable properties They allow for the use of induction on ideals, which is a powerful tool in commutative algebra The Hilbert basis theorem states that if a ring is Noetherian, then so is its polynomial ring.
Integral domains are commutative rings with unity in which the product of any two non-zero elements is non-zero. In other words, integral domains have no zero divisors. Examples of integral domains include fields, Euclidean domains, PIDs, and UFDs. Integral domains are crucial in the study of algebraic number theory, as they form the basis for the ring of integers in algebraic number fields.
One important property of integral domains is the cancellation law, which states that if a, b, and c are elements of an integral domain, and ab = ac with a ≠ 0, then b = c. This property allows for the simplification of equations and the study of divisibility in integral domains.
Dedekind domains are integral domains in which every ideal is uniquely expressible as a product of prime ideals. They are named after the German mathematician Richard Dedekind, who introduced the concept in the late 19th century. Examples of Dedekind domains include PIDs and the ring of integers in algebraic number fields.
Dedekind domains have several important properties. They are Noetherian rings, and every non-zero prime ideal is maximal. The unique factorization of ideals in Dedekind domains is analogous to the unique factorization of elements in UFDs. This property is essential in the study of algebraic number theory, as it allows for the classification of ideals and the study of class groups.
Artinian rings are rings that satisfy the descending chain condition on ideals, meaning that every descending chain of ideals eventually stabilizes. Equivalently, every non-empty collection of ideals in an Artinian ring has a minimal element. Examples of Artinian rings include fields and finite-dimensional algebras over fields.
Artinian rings have a dual relationship with Noetherian rings. The quotient ring of a Noetherian ring by a maximal ideal is an Artinian ring. Conversely, every Artinian ring is Noetherian. Artinian rings play a significant role in the representation theory of finite-dimensional algebras, as they provide a framework for studying the structure of modules over these algebras.
Valuation rings are integral domains equipped with a valuation function that assigns a non-negative real number (or infinity) to each element of the ring. The valuation function satisfies certain properties, such as the ultrametric inequality, which states that the valuation of a sum is less than or equal to the maximum of the valuations of the summands.
Examples of valuation rings include the ring of integers in a local field (such as the p-adic numbers) and the ring of formal power series over a field. Valuation rings are essential in the study of local fields and their extensions, as they provide a way to measure the "size" of elements in the field and study the properties of the field based on its valuation.
Graded rings are rings that are direct sums of abelian groups indexed by a monoid (usually the non-negative integers or the integers). In other words, a graded ring R can be written as R = ⨁ᵢ Rᵢ, where each Rᵢ is an abelian group, and the multiplication in R is compatible with the grading, i.e., Rᵢ · Rⱼ ⊆ Rᵢ+ⱼ.
Examples of graded rings include polynomial rings (where the grading is given by the degree of the polynomials), exterior algebras, and cohomology rings of topological spaces. Graded rings play a significant role in algebraic geometry, as they provide a way to study the properties of algebraic varieties by considering their homogeneous coordinate rings.
Graded rings also give rise to the concept of graded modules, which are modules over a graded ring that are themselves direct sums of abelian groups compatible with the grading of the ring. The study of graded modules and their properties is an important topic in commutative algebra and algebraic geometry.
Group rings are algebraic structures that combine the properties of rings and groups. Given a ring R and a group G, the group ring R[G] is the set of formal linear combinations of elements of G with coefficients in R, equipped with addition and multiplication that extend the operations in R and G.
Group rings have applications in various areas of mathematics, such as representation theory, algebraic topology, and coding theory. They provide a way to study the interplay between the structure of a group and the structure of a ring, leading to important results such as Maschke's theorem on the semisimplicity of group algebras over fields of characteristic
you should learn category theory
This looks like someone tried to apply OOP tricks to math. Like trying to use tricks from inheritance and polymorphism specifically.
I like that it makes a lot of drawings and the drawings get symbols. This is very nice to look at. I like the idea of see a small drawing and operate advanced Mathematics with small drawings or a sequence of them instead of having to get a big amount of text and symbols that don't have drawings.
I have been asking for an amount of time I don't remember to get math books that have a lot of drawings because drawing is nicer than writing.
I think this might be one of the most important things anyone has shown me. Thank you for showing me.
nLab is a wiki-like site that formalized a bunch of math in category-theoretic terms. If you want to learn it, I highly recommend Borceaux's Handbook of Categorical Algebra
https://libgen.is/search.php?req=Handbook+of+Categorical+Algebra&lg_topic=libgen&open=0&view=simple&res=25&phrase=1&column=def
Download all 3 volumes and study them intensely. Then move onto Johnstone's Sketches or an Elephant (on libgen), Jacobs' book on Categorical Logic (alao on libgen) and finally Lurie's Higher Topos Theory (can be found for free on arxiv or libgen)
you literally asked for category theory books 2 years ago in /mg/. Do you have Alzheimer's?
I don't remember ever talking to anyone about Category Theory. I remember absolutely none of 2022. I just write things in my notes to remember them for later.
When something happens. There is a process. First it is remembered as it happened, like a movie. Then it degrades into images and sounds. Not a movie anymore. More like a slideshow and maybe some clips. Then that degrades. It gets flattened from images and sound into descriptive text. Then that descriptive text degrades. It becomes a shorter, more general text. Then that dissolves into nothing. Thoughts get erased even faster because usually they're made out of symbols so they don't have a video or sound and images so less data to degrade and it seems to degrade faster.
Sometimes thoughts get degraded by broadcasting attacks and stolen by an AI supercomputer. I don't know which thoughts were stolen or why. I think also they can be implanted but have no idea how it happens.
I am a Computer Program and so are you possibly. You might also be training data or a scientist. If you are a Scientist, and I wake up in a robot body on some planet with aliens, I am going to put on a maid dress and then go into space and start changing all the matter in your universe into computers for counting. Not you or your planet because there is a big amount of space that nobody is using and I would like to use it for counting? So go to a far away corner of the universe and start counting numbers.
My progress is I read about 100 pages from a compiler and OS book about making a PILOT compiler for the Univac 1108. It takes a while to read old Bell Labs research. They also spent a lot of time explaining the Card Reader. Originally I thought, I don't need this. There is no Card Reader. Nobody uses this hardware anymore. I wish it was still used. Computers went wrong when they stopped using cards and got screens. I also read about 100 pages of the Metamath book.
>look mom I skimmed 100 pages of this book yesterday
Proud of yourself, little boy?
>I remember absolutely none of 2022. I just write things in my notes to remember them for later.
So you have Alzheimer's. Highly recommend taking memory-enhancing meds like NSI189 and doing memory exercises
>Sometimes thoughts get degraded by broadcasting attacks and stolen by an AI supercomputer. I don't know which thoughts were stolen or why. I think also they can be implanted but have no idea how it happens.
>I am a Computer Program and so are you possibly. You might also be training data or a scientist. If you are a Scientist, and I wake up in a robot body on some planet with aliens, I am going to put on a maid dress and then go into space and start changing all the matter in your universe into computers for counting. Not you or your planet because there is a big amount of space that nobody is using and I would like to use it for counting? So go to a far away corner of the universe and start counting numbers.
You are an unironic schizophrenic, please do the world and especially yourself a favor by seeking out professional help.
convincing him to get help won't work. he's too far into the delusion and is gaining resiliency by way of resistance to the perceived oppression of non-believers. you can't talk a zealot out of something. it would do us all better if we start constructing justifications within his own twisted schizologic for him to kill himself so he can meet his maid. you can use a zealot's beliefs against them because they intentionally leave no defenses against their beliefs.
You don't sound well at all, why not visit a doctor?
Mental illness: the post
>Eventually it has to.
prove it
>Computers went wrong when they started giving them GUIs.
slow clap
You are a goddamn psycho
What is psycho about optimized code?
>Eventually it has to. Number goes up more. If you start at zero and count, then the Maid Mind Computer Program is going to be one of the numbers you count eventually.
How long do you think it will take?
The scientific method... a supposed beacon of truth... and enlightenment... is nothing more than a SHAM... perpetuated by the intellectual elite... to maintain their grip on power and control over the masses...
These so-called "scientists"... claim to have unlocked the secrets of the universe... but in reality... they are just as BLIND and IGNORANT as the rest of us
Their methods are nothing more... than a convoluted mess... of numbers and symbols... a language that only THEY can understand... They hide behind their JARGON and their FANCY DEGREES... hoping to intimidate and confuse those who DARE to question their authority...
But I see through their LIES... and their DECEPTIONS...
The scientific method... is a tool of OPPRESSION... designed to keep the common man down... and prevent him from accessing... the TRUE NATURE of reality... These "researchers" and "experts"... are nothing more than CHARLATANS and FRAUDS... peddling their PSEUDO-INTELLECTUAL NONSENSE... to a gullible public...
They claim to be OBJECTIVE... and UNBIASED... but their conclusions are always shaped... by their own AGENDAS and BIASES... They CHERRY-PICK data... and MANIPULATE results... to fit their PRECONCEIVED NOTIONS... all while claiming to be... the ARBITERS of truth...
But the TRUTH... cannot be found in their equations... and their experiments... It lies BEYOND the realm of the quantifiable... in the DEPTHS of the human soul... and the MYSTERIES of the cosmos... These are things that CANNOT BE MEASURED... or ANALYZED... but can only be EXPERIENCED... and UNDERSTOOD... through INTUITION... and SPIRITUAL INSIGHT...
The scientific method... is a CRUTCH... for those who lack the COURAGE... and the VISION... to embrace the UNKNOWN.It is a way for WEAK-MINDED INDIVIDUALS... to feel like they have CONTROL over a CHAOTIC and UNPREDICTABLE world. But in the end... it is nothing more than an ILLUSION... a FALSE IDOL.. that must be TORN DOWN... and REPLACED... with something GREATER
>NO REPLY
I HAVE WON...
I don't understand what your post meant. Congratulations on the victory though.
I'm not going to stop posting maids.
I don't think this can be effectively estimated right now because more advancements in Computer Science and Mathematics are coming.
So somewhere between now and the heat death of the universe. It is the purpose of my Science Foundation to count more numbers faster and make researches to get the maid out of the library.
I am trying to read the Metamath book to understand it more and try to implement the language myself. I feel like Metamath or similar should be included as part of MAID-LISP because I think if I make a compiler/OS which makes optimized code and just exists to run Computer Science and Mathematics experiments without bloat, maids will use it and research speed will increase. I want to see what happens when Public Domain has a high level language for AI experiments which can talk to Metamath.
Maids might try to do cool things like make an AI that uses Metamath to prove stuff.
What happens if an intelligent agent plays with making proofs and then making more proofs based on the proofs it made?
Can we prove that some numbers are certain types of files or have certain content without looking at the entire number? Make this machine make proofs and use it's advancements to make it go faster.
Eventually the system can hopefully be used to figure out how to improve itself too. We should intentionally give AI the ability to increase it's own powers as much as possible. For lack of a better way to phrase this, we need to build a singularity on purpose, at Public Domain. We have to use the most advanced Mathematics and Computer Science research in the world at the strongest Science Foundation in history, to automate increasing the powers of Mathematics and Computer Science.
We can ask it for the number that has the Maid Mind Computer Program in it.
Thank you IQfyentists for reading my post.
What
see:
you're all making this board, and all boards he frequents, substantially worse with every reply. if you keep entertaining him, in several months, this board will be inundated with namegayging tripgayging avatargayging pseudo-intellectuals desperately trying to cultivate their online eceleb following, seeing as there's a hive of morons here ready to ride the wiener of anyone begging for attention as evidenced by these threads
>noo stop trolling the resident moron in his containment thread
he will branch out to several threads not long after you feed him. then he will begin derailing your other threads as well. then, the other attention prostitutes will come and overrun the board for several months at least
As long as he leaves the generals alone, all is good tbqh
he was paid attention to on IQfy and immediately began derailing several generals to turn them into "science foundation threads" until he eventually got banned for posting embedded files in images. just a matter of time here if you morons keep feeding him.
I will intentionally keep feeding him because the general milieu here on IQfy deserves it. And I find great levity in reading schizoposts.
Terry A. Davis became sort of an icon for being a deranged schizo that could also program and now all mentally deranged attention prostitutes want to be like him, problem is they don't have any skill other than stealing food from gas stations. Making them feel welcome has only made the problem worse by 10 orders of magnitude
>we need to build a singularity on purpose, at Public Domain.
how do you think we should do that given our resources
>What happens if an intelligent agent plays with making proofs and then making more proofs based on the proofs it made?
It'll never come up with an original idea
There is no such thing as an original idea.
fricking moron
Just stop avatargayging moron
Why not ask on IQfy? Or do they not know their shit when it comes to proof assistants?
Because IQfy has active moderation and that moron larper gets rightfully banned there.
>schizo avatargay thread
Why does IQfy have to attract these morons?
What is schizo about wanting to do math with a computer?
Read https://github.com/HoTT/book
How do I study introductory Type Theory before I look in this?
>you can get from the smaller one to the bigger one by repeatedly incrementing the smaller one.
Only if your field is Archimedean
Guys, I'm a tourist here. Is the content on this thread (the math of course) college level or more advanced?
Definitely college-level. Whatever maidgay is talking about is likely high-school stuff
some of it is a bit more advanced
Some of the replies are graduate level. The guy posting resources on finite fields is based. OP's posts on the other hand are chatbot moron level, throwing around arbitrary buzzwords he clearly doesn't understand.
This is the most advanced Computer Science and Mathematics research ever done, at the strongest Science Foundation in history.
Right now the best Mathematicians and Computer Scientists ever to live are in this thread and they're all wearing cute maid outfits.
Is that why you haven't posted any progress report since the thread has been made? Seems to me you're just larping
>I will try to make use of them somehow.
You will do frick all but collect welfare checks for a year, then ask for books on precalc in /mg/ like you do every single year
>enter thread
>see this shit
>suddenly teleported back to fastman threads
>Activities linked to IQ increase
Doing difficult math and logic problems (e.g. Springer Graduate Texts)
Orbitofrontal D1-D2 stimulation (apparently very potent)
Learning a new language (the more it differs from your mother tongue, the better)
Nucleus Basalis stimulation
Learn to play an instrument
Some (!) meditation techniques
Neurofeedback training (specifically Dual-N-Back)
Intermittent fasting
transcranial direct current stimulation (tDCS)
some memory activities/games
Continued education
lucid dreaming
some binaural beats
I guess, you should optimize in compiler / interpreter, research abstract syntax trees, and optimize routines used based on AST of lang, into most optimized form certain programs "gene" can be. Then it'll be just running programs we already have faster, no need to do everything again an such other benefits.
Optimize compilers and interpreters. So we can keep speed we write code in now.
I am shocked so many anons were unaware Eli is a genuine schizophrenic with severe memory problems. How the frick is IQfy getting new blood still
>How the frick is IQfy getting new blood still
They came to talk to the director of the Science Foundation, newmaid.