Syllabus design in the age of AI

 A suggestion for educators, on syllabus design, in the age of AI :

- let D, delta, be the difference in student, S', performance; before a course, vs after a course

- D should be stated precisely, in terms of memory recall methodologies, M

- for example when a course guarantees that S will be able to execute M_1, the AI assisted processing of relevant documents, it should be distinct from M_2, the unassisted processing of relevant documents

a simple concrete example would be :

• MATHS 101 : calculus with scientific calculators
• MATHS 101b : calculus without scientific calculators

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.

getting started on computer vision

Brief dip into computer vision jargon. Anthropomorphism. Humans learn to recognise gross gestalten, before understanding mereology ... and humans learn to recognise 2D persistence before 3D persistence. But as conscious processes develop, they discover more efficient storage formats for data, by relying on 3D persistence graphs.

So while we could train a vision system to be more human like by beginning with gross gestalten, we may want to skip forward a little bit to endow the system with the capability to immediately begin forming a database of 3D graphs, representing object topologies in the wild.

LFG :

0. Statistical globbing via neural networks should be used as a final optimisation technique, only after all known structural optimisations ("physics") have been ("logically") programmed into the system - not as a lazy shortcut from zero.

1.

1.1. Let us throw away the concept of colour, and begin only with one dimension of magnitude per unit of space - luma / luminance / brightness.

1.2. Let is ignore 3D structure and begin only with the gross phenomenology of the field of vision. 

2.

2.1. Now, mereology : we must have a way to describe subsets of any field which are interesting. The smallest item is a point of brightness.

2.2. SCALE invariance : the concept of an item growing to take up a larger fraction of the field, or shrinking to take up a smaller fraction, must exist. See SIFT, SURF, ORB, et al.

2.3. Location : the field of vision must be referenced by an address space.

2.4. Multiplicity : there may be many items of interest.

2.5. Extension in 2D : items may be linked, giving them 2D structure in the field. See "graph convolution networkS / GCNs"

2.6. ROTATIONAL invariance : the 2D structure is different if you spin it around with respect to the address space. Where you apply this to spinning everything around the system, see "sphere node graphs", though in 2D that's probably a "cylinder node graph".

... at this point we have five to six concepts that must be uniquely addressed in the cognitive space of the system. A sort of introductory transcendental aesthetic.

3.

3.1. Extension in 3D : Now we can revisit the notion of 3D space. 

3.2. Location ("distance") in 3D is associated with scale in 2D (2.2.).

3.3. Occlusion in 2D is associated with rotation in 3D. See "aspect graphs".

... and, I think that's all we need to get starting building a computer vision system, to undergird the visual ontological comprehension of any anthropomorphic computer.

4. Oh yes, we can then revisit colour and motion in the end.

Reifying one's understanding of large geosocial phenomena

 __TRAVELLER__

"How do I find something firm to latch my feelings and understanding to, on the [ war in Iran ]* ?"

( Where * can be replaced with any complex geosocial phenomena. )

__GUIDE__

There are some separate "planes". You can cluster your study of each plane, then combine them. 

Plane 1.

Abstract concepts in : sociology / psychology / anthropology : such as "The Clash of Civilisations", someone mentioned ( in chat ).

Plane 2. 

Linear narrative of time's arrow of geopolitics : today, Google gives great bullet point summaries, and links to wikis or academic literature. ( Evaluating academic sources is a separate question, which can spin off to a new chat. )

Plane 3.

Lens of each tribe ( non-linear time, the subjective experience ). Or the effect of 2 upon the fabric of 1. Reading method can be similar to 2. 

__PROMPT EXAMPLES__

Plane 2 :

"Who are the main groups of stakeholders, and actors, in [ the current war in Iran ]*"

ANSWER : ABC; now you have to keep your own notes! So ...

Plane 3 :

"What is the history of A's view on topic-X. List major events and shifts in perspective over the last 2000 and 200 years."

ANSWER : DEF

"Tell me more about the details of D." 

ANSWER : HGI

__MAP-REDUCE__

So ... your reading will be this huge cube of :

( parties : A+B+C )

* ( Abstract Issues : X+Y+Z )

* ( ( Concrete events : D + E + F ) + ( Details : H+G+I ) )

__APPROACH__

No need to rush. Understanding people takes time.

Avoidance of intellectual tasks. Algorithm for mechanistic resolution.

• 1. Reify the abstract model at the napkin level.
• 2. Review the napkin model, until its physical form becomes consciously boring - this consolidates in subconscious, the conscious form of the model in its current state, and its evoked subconscious implications.
• 3. Then reiterate from 1, with improvements. Stop when the model complexity is diverging on a trajectory to exceed known cognitive limits : increase reductive prejudice, or assume complete non-feasibility.

gamification of the art of law

Why does it seem like [ the legal system ] lacks [ a pedagogical computer game ] ... which simply shows

•  - every entity and their possible states
• - the state-transitions, timeouts, and sufficient triggers
• - the logistics of triggers ( "events" ) ?

If I had a kid, I'd probably try to write a simply game for them to play about this. Probably would make for an interesting open-world MMORPG.

moderating the pace of operational development with AI

AI in the weeds ... in the development of operations ( or organisations ) I think we all agree that a small team of highly-predictable ( definition of "elite" ) staff can move quickly without formal guardrails. The corollary to this is that we will probably also agree that AI is not presently trusted to be this predictable, so using AI like this ( which is a common lunge ) is a [ governance ] error.

The organic approach of micromanaging tiny workflows with a high degree of oversight, and then gradually removing oversight, is precisely the traditional approach to conservative development. The corollary to this is that given the current state of AI reliability, operational AI should be treated as an army of idiots to be minded, and not as some [ elite intern ] to be [ relied on to run a multi-factor operation ]  LOL

Avoiding Disappointment : advice most people need

 Tips to avoid disappointment, and unnecessary sadness which will limit your productivity :

• 1. Your memory is not reliable - don't expect it to be. Install guardrails.
• 2. Your instincts are not cultured - don't expect them to be. Review culture frequently.
• 3. Your society is not safe - don't expect it to be. Make it more what you wish.
• 4. Other people face the same limitations 1,2,3 - don't expect otherwise. Work together to address common concerns.

Models and their Verbal Expression

It's amusing how "JSON output" as a line-protocol between LLMs is a hot topic in some circles. Some have rightly pointed out that this is merely a selection of grammars. But more broadly it is a selection of languages. When teaching languages to children ( meat or machine ), one must first teach the child to build internal models, before worrying about external grammars. What does that mean? 

Well, for any sensory dataset, there is a "cognition" of its informative value ... ( "difference from null" is the definition of information ) ... this is discussed to a great extent in the study of gestalt psychology, which fortunately for formalists, is very easy to model mathematically. 

Now here comes some differentiation. Of the children who can recognise a sensory pattern, NOT everyone can imagine it internally, due to limitations of their conscious sensory imagination : and those who cannot, must use external modelling, via gestures, or pen and paper, to visualise what they want to think about.

However, once a child demonstrates a consistent ability to recognise and manipulate a sensory model, ONLY THEN is there a question of how the child should verbally express it.

This is a fundamental matter in semiotics, and language in general.

Imprint Engineering : Labour must be Led

A bestie's friend is closing their cafe. Bestie recanted that it was difficult to find staff who were neither too dumb nor too smart, who would leave for better opportunities. I am reminded that the service industry's main supply-chain is talent management. The European canon contains quite a bit about "how to govern men", and I'm sure the other literary traditions do also.

Every individual staff requires a leader to imprint upon ( see Jurassic Park, Chris Pratt ). Either they imprint on their colleague, their line manager, a senior leader, or the abstract brand as a person. This is why I put so much emphasis on brand development when I launched a cafe in 2015. I prefer not to be followed as an individual, but the staff need something to follow, so brand equity is essential.

However, I resorted to personality-based leadership of the staff after shareholders turned off our core brand's distribution channels in the third year of operations, throttling our brand equity. It was an inconvenient corporate duty, but such was the business environment. I came from a family of pastors, so it was not difficult, though it took time away from other forms of corporate development that I could have worked on if we had retained social media distribution of the brand.

Why you suck at ordinary conversation, teaching kids, and building AIs

Phenomenology. Most people suck at it. As a result, they don't understand other people, and they don't have good communication skills. When they are thinking about building machine intelligences, they get stuck because they don't have a good grasp on what their own thought process is. Such is the plight of man(kind).

Typical example : today I'm reading about how linguists make a distinction between the 'reference' of a sign and the 'denotation' of that sign. This is just sloppy language which reflects sloppy thinking, over a century.

Try this instead :

• 0. Any semantic expressions in empirical space ( signs, words ), are only dereferenceable in the context of a cognitive system ( mind ).
• 1. The first mind to consider, is the mind of the observer of the expression ( reader ), not the mind of the expression's expressor ( writer ).
• 2. The second mind to consider, is the mind of the writer.
• 3. The bare minimum requirement for a mature reader, therefore, is to be able to form cogent internal models of [ readers' mental models ], and [ writers' mental models ]. ( While this is sometimes referred to as 'empathy', that terms is loaded and may or may not be a good inclusion at this point. )

The PROBLEM : 

Many people engage in daily reading ( and listening ), and writing ( and speech ), therefore conversation in general, and even the business of constructing minds in children of various media ( both meat and machinery ), without paying due consideration to 0-1-2-3.

This is why you suck at ordinary conversation, teaching kids, and building AIs.

link

Unsupervised Learning is mainly good for Feature Detection

Unsupervised learning is useful for low-level wetware emulation ... feature detection, signal recognition, etc. 

However, most of what we call civilisation and social life, depend on higher-level constructs which are maintained by supervised learning in humans, so it is only reasonable that we should teach anthropomorphic machines using the same methods which we already apply to humans.

I can never understand people who believe it is more efficient to do otherwise - though I would be happy to consider proofs.

( Updated my vocabulary today, with 'feature' and 'blackboard' : for concepts which I am already quite familiar with. ) 

Discussion : 

• 2026-06-24 : I've generally been of the view that USL is inefficient for small things because that's just not how humans are educated. A refinement of that view is that USL/SSL captures how meat brains learn, but that's pretty low-level. Higher-level culture is built upon that, and relies on things that are rather much like logic programming and SL. IDK - maybe I'm just wrong about all of this.

Canon : the lexicon of possibility

Frege's Über Sinn und Bedeutung ( Sense & Reference ) can be summed up as

• 1. any signal, takes a form
• 2. the form may have loose connotations ( sinn, sense )
• 3. the form may have firm connotation ( bedeutung, reference )
• 4. the connotations, may be interpreted differently by any emitter or receiver of the signal

Further canonical efforts to nail this down to tighter language may just make it worse : see Kripke's 'possible worlds' bike shedding 

Textual Interpretation in Machines

 'A turn of phrase' is a metaphor, which refers to metaphors in general. In the resolution of indirect pointers, perhaps the machine architecture for this is pretty similar to the machine architecture for banal memory address and final data resolution. That is insightful. 

So we can have sensory data structures which depict an interpretation of a sign, let's call them 'visualisations' or 'imaginations' and then we can have pointers from imaginations to imaginations which eventually resolve to a reified state. The meaning of the original sign ( 'text' ) however, is not merely the final reified interpretation, but the entire chain of interpretations, in a possibly cyclic digraph.

The iteration of imperfect lives

• In friendship ( or therapy ) we iteratively use imperfect thoughts to fix themselves.
• In civilisation ( or government ) we iteratively use imperfect policies to fix themselves.
• In science ( or epistemology ) we iteratively use imperfect concepts to fix themselves.
• In scholarship ( or academia ) we iteratively use imperfect history to fix itself.

Such is our commitment to dogfood.

Things you are allowed to say, when someone dies.

• To an enlightened person : why so serious?
• To a pleb : you have my condolences.

That is politics. And business is built on politics.

Plebs & the study of culture : on Zero Trust

• 1. Trust is a device for control.
• 2. Trust with verification, is robust. This is abbreviated as ZERO TRUST.
• 3. Trust without verification, is PLEB TRUST.
• 4. The behavioural incentives to be pleb, are varied.
• (a) subject is lazy, hence pleb
• (b) subject is conned, hence pleb ( POSSIBLY incepted with control mechanisms, prior to autonomy )
• (c) subject has no capital, hence pleb ( synonymous with power, leverage, etc. )
• (d) other?

Culture is by definition, a control mechanism. The study of culture is simply a variety of cybernetics.

Don't be a pleb.

20-80 : catch-pull : money management

 20-80 : catch-pull : applies to investment management too

taking money off the table takes 400% the effort of getting money on it

structuring math at the primary school level

• 1. Point : intuition of existential quantifier. D0
• 2. Line : intuition of physical tension. D1
• 3. Circle : intuition of planarity. D2
• 3.1. Radian : intuition of angular ratio. D2
• 2.1. Right-angle : intuition of physical compression. D2
• 2.2. Hypotenuse : intuition of loss minimisation. D2
• 4. Numbering : intuition of linear ratio. D1
• 4.1. Trigonometric ratios : intuition of complex plane. D4
• 5. Spirograph : intuition of modular forms. 

... some notes on structuring math at the primary school level. It turns out that throwing symbols at kids is a lot harder to digest than throwing reified geometry.

Adolescent Development of Pain Tolerance

Emotional regulation is a skill poorly performed by folks of all genders. We make fun of man-babies, and crazy bitches alike. Perhaps it is a virtue to maximise one's ratio of (irritating-to-others)-to-(irritability-of-self) ... we're not all trolls, though I am clearly predisposed to be one, myself.

Trolling and the manosphere are light and dark sides of the same coin. Trolling is a lens on the adolescent activity of competitive pain tolerance. Adolescence approach this rite of passage in more or less gendered ways of course. Sports are generally understood as athletics of the developmental sort.

It is probably well documented how the rituals of both antagonisation, and support, are practiced by groups of young and old, women, men, and those who find themselves in between this crude dichotomy.