A list of puns related to "Algebraic Language"
Two passages from The Science of Logic in which Hegel expresses his strong reservations against the use of spatial figures, algebraic signs and symbols in philosophy:
>Since the human being has in language a means of designation that is appropriate to reason, it is otiose to look for a less perfect means of representation to bother oneself with. It is essentially only spirit that can grasp the concept as concept, for the latter is not just the property of spirit but its pure self. It is futile to want to fix it by means of spatial figures and algebraic signs for the sake of the outer eye and a non-conceptual, mechanical manipulation, such as a calculus. Also anything else that might be supposed to serve as symbol, like the symbols for the nature of God, can at best elicit only intimations and echoes of the concept; if, however, one insists on employing such symbols for expressing and cognizing the concept, then it is not their external nature which is fit for the task; the reverse relation applies, namely that what in the symbols is the echo of a higher determination is recognized to be such only by virtue of the concept, and it is only by shedding the sensuous standbys that were supposed to express it that one comes closer to the concept.
>There is nothing much to be said against the symbolic use of the language of “power,” no more than there is against the use of numbers or any other kind of symbols for concepts. But there is also everything to be said against it as there is against any system of symbols that pretends to convey pure conceptual or philosophical determinations. Philosophy has no need of any such aid, either from the world of the senses, or from the representations of the imagination, or also from spheres which belong to its own realm but are subordinated, and whose determinations are therefore unsuited to higher circles and to the whole (...) If one is to use numbers, powers, the mathematical infinite, and the like, not as symbols but as forms of philosophical determinations and consequently as themselves philosophical forms, then one must start by defining their philosophical meaning, that is, their conceptual determinateness. But the moment this is done, they become superfluous designations, for the determinateness of the concept is its own designation, and this alone is the one which is both correct and fitting. The use of those forms is, therefore, nothing more than a convenient means for sparing oneself the task of grasping
... keep reading on reddit ➡like Qxf7# becomes Zxf7# where Z is whatever letter your language's word for queen starts with? or does everyone use the english initials?
Apologies if this is not the right place to ask (I would argue that it tangentially hits design), but is there a programming language that has/is:
Easy to script with (think Python with lots of built-in convenience modules for regex, FS access, and CSVs)
Statically typed (I've been screwed over by dynamic typing too many times; lint aids such as Elixir's typespec aren't enough for me)
Immutability-first with native functional programming support (I don't want to depend on third-party FP libraries; hopefully with partial application and currying)
Algebraic data types or similar (I love the level of expressivity and soundness I can get with OCaml's algebraic type system)
Stable (enough community and developer support)
I do know a bit of OCaml, but there's a lot of friction regarding its scriptability (i.e., how fast you can churn single-use data processing scripts); it's otherwise perfect.
Reason is in the same camp as TypeScript; I find the filesystem access API to be inconvenient; I can do the same in Python much faster with glob (i.e., scripting friction). Elm is cool, but it can't be used for scripting.
I love Elixir; it has most of I want except static typing and ADTs with typespecs not being enough for me. There are Elixir + Elm language projects which I think are perfect for me, but they all look dead as of 2021.
F# is probably the closest language to what I want after Elixir and OCaml, but the extra baggage from depending on the CLR makes the language relatively dirty (Mono seems like a pain to quickly deploy too).
I'm looking at Scala right now, but I have personal biases against JVM-first languages. Kotlin doesn't seem to be functional-first. On that note, Swift doesn't seem to be scripting-friendly, but I have to explore that further.
I might be wanting too many things; if so, maybe you can just point me to languages satisfying a subset of my criteria then maybe I can work from there.
If you think I have misconceptions about the languages I mentioned, then maybe you can correct me too.
Trying to build a lazy, not statically typed, purely functional programming language and I find myself being unable to find a way to make ADTs fit into the design.
I’ve been learning Algebraic Geometry, working through Hartshorne, and supplementing with Vakil’s notes as needed. One thing really bothers me however, and I’ve asked numerous people and never could get a satisfactory answer. It has to do with how people talk about an affine open in a scheme.
The definition of a scheme is a locally ringed space (X,O_X) with a cover by U_i’s such that (U,O_X|_U) is affine, i.e. isomorphic as a locally ringed space to Spec A for some ring A. This is fine, but often I see people write things such as “let X be covered by {Spec A_i}”. Now sure, one could say that this just implicitly identifies a cover U_i with the affine schemes they are isomorphic to, that’s fine. If the proofs people presented seemed to work with these natural identifications fine, then I wouldn’t mind, but people make statements that don’t really make sense. Here’s an example.
Nike’s lemma as some people call it is the statement that two affine opens of a scheme can be covered by sets that are simultaneously distinguished opens in both. The proof in Vakil’s notes seems to treat a Spec A, Spec B as an actual subset of X. He grabs ring elements in A, B, considers the distinguished opens for them, and does some more stuff. If you wanted to be pedantic I imagine the proof would look more like
Let U,V subset X be two affine opens, U isomorphic to Spec A via f, V isomorphic to Spec B via g. Then U \cap V can be covered by sets W_i such that f(W_i) = D(a) for some a in A, and g(W_i) = D(b) for some b in B. Now this is ridiculously weighty, I’d much rather just treat affine opens of a scheme as actually “physically” (in the sense that as a set, their topological space is literally equal to the spectrum of a ring with the same topology) being Spec A for some A, but to me I have no reason to believe one can do this!
A lot of people have told me that “everything is canonical” in the sense that with respect to some maps things are uniquely isomorphic, but when pressed for why that would imply that things magically smooth over and you can just pretend that these sets exist as a subset no one can give me a response. An example is that if U is an affine open of X, that “since any open subset has a unique structure as an open sub scheme” that U = Spec O_X(U). Now I buy that (U, O_X|_U) is isomorphic to Spec O_X(U), and maybe it’s even unique with respect to the inclusion map into (X,O_X). But to say that U = Spec O_X(U) suggests to me that U, as a set which is a subset
... keep reading on reddit ➡Sorry this is not strictly a PL topic (because it can sometimes be solved in library level).
One of the most exciting developments in PL is algebraic effects and handlers, ala "Frank" (language) or Oleg et al's "freer" (library).
However most of the research seem to just ignore concurrency as an effect. For example, neither Frank paper nor freer paper mention concurrency. Multicore OCaml papers combine these words but what they mean is entirely different (and not something that I'm interested in).
I'm wondering if anyone know any publication on this. Any pointers would be much appreciated.
Are there any journals/conferences I should read to get a better idea of what's going on? The only things I've found on the internet so far are books/primers about it (and some of them are quite old). Thanks!
This is an automatic summary, original reduced by 68%.
> Galileo called mathematics the "Language with which God wrote the universe." He described a picture-language, and now that language has a new dimension.
> Though not the first pictorial language of mathematics, the new one, called quon, holds promise for being able to transmit not only complex concepts, but also vast amounts of detail in relatively simple images.
> "It seems to be the tip of an iceberg. We invented our language to solve a problem in quantum information, but we have already found that this language led us to the discovery of new mathematical results in other areas of mathematics. We expect that it will also have interesting applications in physics."
> The new language relies on images to convey the same information that is found in traditional algebraic equations - and in some cases, even more.
> "For centuries there has been a great deal of interaction between mathematics and physics because people were thinking about the same things, but from different points of view. When we put the two subjects together, we found many new insights, and this new language can take that into another dimension."
> In their most recent work, the researchers moved their language into a more literal realm, creating 3-D images that, when manipulated, can trigger mathematical insights.
Summary Source | FAQ | Theory | Feedback | Top five keywords: Language^#1 mathematics^#2 new^#3 image^#4 Jaffe^#5
Post found in /r/science and /r/citral.
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i'm working on a hobby project for educators and students alike and i was wondering if it was possible to convert algebraic notation (if that's the right term), (2x^2+3y)/2, for example, to latex or mathml so that it can be rendered much more smoothly/nicely.
I'd love to learn some ANT, but ideally I'd like to see it geometrically from the angle of schemes and AG.
Does anyone know what language is used in this course? Python (numpy), Julia, C++? I'm thinking Python is the obvious choice here, but heard rumors of Julia.
Just realized MAS3114 says that a prereq is to have knowledge of a programming language, that which I have none of. I was planning on taking this class next semester, but do I actually have to postpone it or would I be fine with no experience. Thanks :)
New to PLCs and wondering if there is any PLC language that makes direct use of boolean algebraic equations instead of having to draw through ladder diagrams? I had a feeling that Function Block Diagrams (FBD) sounds like a logic gate diagram but just wanted to get some inputs from this sub
While there's plenty of resources on ladder programs, I am able to only find introductory materials for FBD. Is ladder programming the most widely used language for PLCs in industries?
Trying to build a lazy, not statically typed, purely functional programming language and I find myself being unable to find a way to make ADTs fit into the design.
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