Thin slice : on "epiplexity" ( Jiang, et al. 2025, 2026 )

Leon commented on this paper.

Thin slice : the paper's paradoxes seem to come from a confusion definitions of "information". Perhaps, there is a confusion between : the accuracy of information transfer ("surprise") and the accuracy of representing originating knowledge ("semantics").

Information theory is concerned with "already quantified" data, and not about "quantifying unquantified states". So entropy is meaningful as a descriptor of quantified data, and not meaningful as a descriptor of how accurate a quantification operation was upon an unquantified substrate.

Vis-a-vis LLMs, whether the input data is the traditional "verbal / just text" or multimodal "multi/sensory" ... these are "already quantified data" at the point of ingestion, and information is preserved as the LLMs compute any egestions.

For those of US OBSERVING the LLMs, we may find that the LLMs produced "new information", but that does not refer to insight about the ingested data (stateT=0), but rather about the the UNQUANTIFIED WORLD STATE prior to the creation of the ingested data (stateT=-N).

Please forgive my unfamiliarity with the underlying material, and my faint disgust at seeing 50+ comments applauding without adding much to conversation ( I think I saw few dissenters haha ).

maths has an ISO notation

Day 1 back at elementary number theory ( day 1155 of sabbatical2, day ~15,547 on earth ). I am revising this slide on the notation for exponentiation and logarithms which I made year ago.

• after a bunch of catch up on software engineering, I am finally turning to focus on remediating my poor foundations in number theory
• a quick look around the internet will show you that this "has always been, and continues to be" an issue for many students of maths; folks also decry other notations like dx/dy, and the visual non-symmetry of notation for differentiation and integration
• I think, a pet idea of mine henceforth will be  : someone should make an ISO standard for canonical mathematical notation, and then republish all past mathematical texts ( or have a way of translating them automatically ) to the canonical mathematical notation; all mathematicians would be of course free to use non-ISO notation anywhere they liked. ( oh wait, they've been doing it since 1992, and the latest is here : https://en.wikipedia.org/wiki/ISO/IEC_80000 )

TIL :(or am reminded, because I probably forgot) : 

• (1) there's an ISO for maths notation, so speculation about notation optimisation should just target that, 
• (2) the notion of "antilogs" we studied in highschool are already deprecated in scientific writing, 
• (3) the etymology of "logbooks" is the same as that of "knots"

Mathematics as an Information Process

 ... or "how any brains, human or artificial, can do maths" : including the creation of novel concepts for nouns, verbs, and adjectives in maths.

I started writing this as a comment on Valerio's post, but it overflowed so I made it a repost, then it overflowed, so I had to articleise it.

What the hell is maths?

I think categorically, "mathematics" isn't "a thing that can be solved" as a whole. Mathematical QUESTIONS yes, but there is no end to the questions.

Mathematics ITSELF is a [ software program ], for [ representing ways to reason about phenomenology in general ] - in other words, maths is a programming language, or compiler toolchain - with specific focus on [ phenomenology that is objective ].

( This applies to mathematics as a social activity - in private, any mind can perform subjective quantification upon phenomena it perceives, even though that activity is not directly observable by other minds. Because at this point in history, we still do not have [ social / common access ] to the [ subjective phenomenological experience of humans ], since that memory space is embedded within an ill-understood meat net. )

I think the matter of coming up with new [ mathematics, and science in general ] is really just a generative process of creating ontologies of language where existing ontologies are insufficient. It's just mutate, and cull, loop. What gives rise to the DEMAND for new ontology / concepts, depends a bit more on the field.

PHYSICS :

In physics, ontological DEMAND is a matter of "we have some observational SENSORY data that does a quantifiable pattern, but we don't have a name for the pattern, though we can point at the pattern. Also we don't know how this new pattern relates to old patterns, and we need to do more tests to find out."

MATHEMATICS :

In mathematics, ontological DEMAND is a matter of "basically everything that physicists do, but swap the object of research from SENSORY phenomena in general to [ formal INSENSIBLE verbal concepts, attached to some SENSIBLE notation that we use to represent it ]".

THE DIFFERENCES :

While physicists have to tolerate the limit of "hypotheses are falsifiable, and resistant to falsification under duress," mathematicians tend to need to show that "theses are necessarily true/false".

In the realm of testing the combinatorial play-niceness of known fundamental relations and entities, that's fairly straightforward.

THE COMMONALITIES :

The discovery of new fundamental relations and entities ... is also driven, from the same sensory source that drives such discovery in physics.

Physics and mathematics are both "sensory", it's just that in physics the sensory data is of [ intrinsic ] interest, whereas in maths the sensory data is [ just symbolic of insensible interests ].

So, in the same way machines can be programmed to be creative in hypotheses about [ intrinsically interesting sensory data ], they can do the same for [ sensory data, i.e. language morphemes and syntax, which are extrinsically interesting ].

THE MENTAL MODAL :

After all, in and of itself, [ the latent intuition about how logic, space, and time, work ] is essentially the brain's physical activity, as a [ subconscious memory space ]. Data from there then intrudes, from time to time, upon our also physical [ imaginations, as conscious memory spaces ].

Both memory spaces simply process [ sensory data structures, which we may call qualia when they move into the conscious memory space ].

A practiced thinker knows how to completely map, FROM qualia, TO analogous signals or other data structures which are known to be objectively quantifiable, through the social practice of science.

Of course, I might be venturing a bit too far here, in terms of asserting that meat brains are just sub/conscious physical information processes.

Haha

- - -

Discussion

2026-05-26 :

• the concept of "well if X is in conscious memory, then X must be an instantiation of the data types supported by your conscious memory" is from COPR, as mentioned to Alex : might be worth a wiki; or see the Sophie's World version of Transcendental Idealism / t-analytic / t-aesthetic. Ofc in LeCun's phrasing, this is a "world model".
• I think the insight on maths is : "the only way to handle maths is via sensible symbols, and we are quite sure the LLMs can handle symbols + rules + rules of replacement", so an LLM can look at "any N-dimensional field of raw noise" and formally hypothesise any new set of rules that applies to the field. Given a less noisy field the LLM can run formal or empirical tests against the field, to see if the rules still apply, just for example. This is literally all it takes to invent new science, in a very thin slice lol. And for maths, the bot doesn't even need a noise field for sensory data - it just has to check rule coherence.

2026-05-29:

It is remarkable, after all this time, that mathematics remains as much a veil, to the mode practicioner, in the same way that other conscious macrophenomena are to the mode person. Some people are ontologically committed to the notion of persons, some are committed to the notion of emotions, some are committed to the notion that food is yummy, and travelling is fun. Mathematics likewise is broadly appreciated macroaesthetically.

But if you tear apart the qualia, and isolate the categories of sensational units in every sense modality, then you are left with only a few kinds of lego, so to speak. Mathematics reduces to a sensible language, with insensible referents, and so the treatment of the language can only be tested with regards to the rules employed about the sensible language.

I guess?

2026-06-02:

It's astonishingly stupid, that some professional mathematicians can't understand how it is possible to teach a machine how to discover novel mathematics.

Simply stepping through the history of maths, demonstrates each point of "ontological demand" , where existing linguistic constructs were insufficient for a formal representation of some sensory dataset, thereby leading to the designation on new linguistic constructs as hypothetical frameworks, then affirmed as practically useful via coherence testing.

It is just a special case, of the development of languages in general. Perhaps it is because mathematicians are not often trained as philologists, even though these are both primarily about language use and development. Just as grammar teachers or English professors are not expected to be philologists, as a rule. 

2026-06-07:

Humans spend 150 years making a machine that does weird stuff really fast - because weird stuff is enriching, but humans are slow at it.

Someone figures that the machines could be a little less weird, so makes the weird machine do less weird things, but in a slow way.

Someone then figures out that if you get enough weird machines doing less weird things, in the slow way, you can approximate a human in all its slowness at doing the weird thing. 

Ladies and gentlemen : a neural network doing maths ... instead of outsourcing it to an ALU.

STEM atau KESENIAN

Dorang tanya, STEM atau KESENIAN, lebih penting?

Dengan terperinci.

0. Seni

Secara am, semua kegiatan itu ada perseniannya.

KEMAHIRAN = KESENIAN LAH XD 

1. Sains (Stem)

Ilm mengutamakan pemantauan zahir / empiris. Jadi kesenian STEM senang mula dikaji dari sini.

2. Matematik + Logik (steM)

Kesenian hisab + mantik adalah kerangka batin, yang menyekat Sains.

3. Kejenteraan (stEm)

Inilah seni kerja amal.

4. Teknologi (sTem)

Sina'ah hanya istilah am bagi kesemuanya.

Yunani, "tekne" => technology;

Latin, "ars" => art. 

Rough epistemic model

 Rough epistemic model : 

• 1. Truth, to an individual human, is a hormonal cascade which stabilises a neural holding pattern, and subsequently a broader physiological holding pattern, associated with positive well-being ( 'pleasure' ). 
• 1.1. It results from recognition of semantic coherence, between the expectation of what a sign means, and the reified discovery of what a sign means. ( Phew, anxiety alleviated, risk-off, etc. )
• 2. Truth, to groups of humans, is determined by the establishment of semantic coherence in communication within the group, synchronising each individual's notion (1.) of truth.
• 3. Truth, to an anthropomorphic machine, is a model of (1.)

Sometimes the discipline of maths is stupid.

Today's research into the historical and contemporary use of [proof assistants] and [automated theorem provers] is a sobering reminder of certain idiocies which annoyed me as an undergraduate :

• 1. many professional mathematicians are not practitioners of formal mathematics - this may not be news for many, but it was certainly an irritating discovery for me  back in the day ( and it remains irritating to be reminded of this today )
• 2. the entire concept of relying on intuition and a closed community-of-the-intuitively-attuned to uphold norms of any sort, let alone scientific norms, is just ass-backwards and needs to die; or you know, it should be made explicit who is a low-context/explicit mathematician, and who is a high-context/intuitive mathematician, so that others can pick their associations, pedagogical paths, and strategise about any other work appropriately

I am happy with my decision at the time to set all of this aside, and to focus the first part of my career on accumulating other knowledge. Now the time has come for me to do the harder work. Hopefully something will come of it, which I will be happier with, than I am with the state of the world as it is.

math words for matchy things

 disambiguation : 

• : mappings : the most ambiguous term for "matching things"
• : morphisms : a formally defined mapping in category theory
• : functions : a morphism that applies to sets

I think 1999 me would be very disappointed with 2025 me, having added trivial detail to my understanding of functions. But 2005 me was rather different than 1999 me in having acquired a paradigm shift in some dimension A, and so an expanded requirement to balance A with more exposure in B, where I spent the next 18 or so years.

Type Systems and Politics : prejudice

#### Types, Kinds, Classes, hinting

-   Types may affect different layers of data flow. The economics of
    type systems ( policy design and enforcement ) comes down to the
    trade-off between PREEMPTIVE and AD HOC checks.
    -   Lexing : Lexical layer : specific graphemes may indicate tokens which are
        about the type system. 
    -   Parsing of semantics : Abstract syntax layer(s) : Tokens may indicate 
        1.  that specific data is of a specific type,
        2.  that specific types are related in certain ways, or
        3.  that specific types are required, allowed, or prohibited,
            from any operation.
        This is essentially a "compile time" opportunity to find data
        that is not where it is wanted. The complexity of analysis at
        this phase may vary, throughout various stages before the final
        machine code is produced.
    -   Runtime type checking : this may be implemented in both
        interpreted or compiled runtimes. The most performant code is of
        course, compiled code with no runtime checks, WHEN CODE IS
        PREDICTABLE. Whereas, CODE THAT BRANCHES HEAVILY may be more
        performant with just-in-time type checking, depending on the
        specific nature of the code.

Going Global : after a hiatus of nearly 20 years

Reddit was founded in 2005, the year I graduated. HackerNews was 2007.

At those times, I had very little working knowledge of the software engineering industry, and I was in no rush to pick it up since I was under the impression that I was far-far-far behind everyone else, and should just focus on anthropology in Malaysia for some years. ( Moreover it was a known quantum that documentation would improve over time, and that quant work being more deskbound than anthro, would be something more suitable for older than younger age. )

I really didn't get into Reddit and HN for a very long time. I might have chucked a few fanciful posts at it, but there was no need to plumb the network very seriously - even my hipster colleagues used Reddit more than I did, for their non-technical interests. Anyway, in 2025 I'm amused to be finally more active on these two sites. As I frequently tell folks in my circles ... Malaysia is where STEM goes to die, and since I'm looking into very upstream stuff like Programming Lanaguage Design, Type Theory, Set Theory, and Foundations of Logic and Mathematics ... I pretty much have no local groups to harass, not even online.

On we go ... such is the student life.

Common : Matrices as Lenses upon Graphs

Adjacency List

• X : single-column
• Y : node-pair list -> fairly dense

Adjacency Matrix

• X : node list
• Y : node list
• Z : edge count -> a sparse matrix

Incident Matrix 

• X : edge list
• Y : node list
• Z : properties of edges, e.g. weight -> a sparse matrix

Degree Matrix

• X : node list
• Y : node list
• Z : degree of each edge -> a diagonal matrix

Laplacian Matrix

• [ Degree Matrix ] minus [ Adjacency Matrix ]

Rudiments of Computer Programming for K12 Education : Malaysian Model

The Malaysian Ministry of Education should make these mandatory in public schools  ( there are 13 years ) :

• Years 1-3 : maths, must be taught with spreadsheets.
• Year 4-6 : maths, must include coding in the Forth language ( it is very simple, and used it in electronics ).
• Years 7-9 : maths, must include coding in the Python language.
• Years 10-11 : an SPM elective, for the C language, must exist
• Years 12-13 : an STPM C++ elective, must exist

Gaussian Elimination

Gaussian elimination : this was missing in the 1990s Sijil Pelajaran Malaysia syllabus ... leading to a bit of a curiousity, where we studied matrix operations without being told wtf they were for. I only learnt that matrices were related to simultaneous equations several years later, as I was not focused on the study of math in my 20s and 30s. 

Gaussian elimination is demonstrated in Chinese texts dated 0 +/- 180 CE.

---

I was wondering where "elementary row operations" come from, and couldn't find any historical study of this. Then I watched a YouTube video by Jeff Suzuki, and realised they are indeed elementary ... and merely the arithmetic analysis of simultaneous linear equations covered in secondary school ( should be in primary, since it's just arithmetic ), but applied within the notational box of a matrix.

Now that after 25 years I have bothered to figure out what linear algebra is about, it makes a lot of sense that some countries teach this in elementary school. It's not that hard, when minimally approached from first principles.