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To the author's credit, he has this in the first line, ie, that the article was not intended for others to read and enjoy.

> This is mostly a bunch of notes to myself

As Bessis has described in his book [1], it is extremely difficult to understand math someone else has written. The words and symbols dont convey imagery or ideas that the author has in their mind. I was surprised to read in that book that this applied to mathematicians just as it applies to you and I.

Coming back to this article, I wish it were written in the spirit of the essence of linear algebra [2] - conveying the essences in images and pictures instead of words. I am curious to hear from others if they feel this way or is it just me.

[1] Mathematica: A Secret World of Intuition and Curiosity

[2] Essence of linear algebra (3Blue1Brown, youtube)


There are lots of people who write math in a way that is very easy for others (of an appropriate level of experience let’s say) to understand. I also didn’t find this particularly hard to follow, although some of it is I think a little fast and loose. eg

   > In general, given two finite-dimensional vector spaces U and W, then U ≃ W exactly when dim(U)=dim(W).
Is that really true? I don’t think it is. Specifically surely at least they have to be vector spaces either over the same field or over fields which are themselves isomorphic. I’m thinking say U is a vector space over R and W is a vector space over Q. Dim(U) = Dim(W)=1 but U and W are not isomorphic because there exists no bijection between the reals and the rationals.

yes, definitely some of it is (purposefully) fast and loose, though (ideally!) mostly unambiguous with reasonable assumptions

I think that part should've been "vector subspaces" rather than vector spaces since that is how U and W are defined in the paragraph prior.

I'll add this as a note, thanks!


It’s a cool article. I love linear algebra, particularly in settings like the polynomials.

ha, thank you! it's very fun to write these

hopefully you also enjoy the next one which imo makes a fun connection between the linear algebraic CRT and the fourier transform :)


I don't want everything to be images and pictures. Often, I enjoy words for communicating math.

Fair on all accounts! Surely, this could be made way more lively if I were in front of a blackboard waving my hands and drawing images, but alas, the medium is what it is :)

Thanks for reading though!


> anthropic messed up big time harness works with any muh commodity LLM

that surprised me too. The intelligence is at the client, and by making that open, anthropic has commoditized the coding agent.


I mean, it's not like claude code is the most impressive agent of the pack.

> AI models are the new virtual machines

Deepseek v4 flash is priced at 1/10 that of openai/anthropic. I can see a race to the bottom - or perhaps an android vs iphone split - where, the premium market is served by openai/anthropic and there is a long-tail of commodity vendors.


It's priced at 1/10, but deepseek is probably not profitable, also it's slow.

Even more interesting is the question if we would have a deepseek model without the US frontier models.

And then what's the value of the advantage that the frontier models have. It's definitely 100x more valuable to find zero days 3months earlier. Probably not in every domain but in enough domains having the smartest model is valuable.


False. Deepseek and other providers who host deepseek have no incentive to subsidise. They also price it similarly. So it is the true value.

iPhone is a consumer brand, and to some extent a fashion/status signalling choice. The market pressures in the B2B space are quite different, I expect lots of cheap good-enough models (Deepseek and others) will end up powering customer service chatbots and the like.

Who will pay 500x the price for a 1% better model? Quants and traders?


Much of the agentic intelligence is at the client. The llm backend is largely swappable. For instance, claude-code paired with any model performs well enough for many usecases. In fact, the real breakthrough is how an agent paired with an unreliable llm could perform well. Given this dynamic, I see llm tokens as the electrons or electricity, and agents as the toasters, and appliances using those electrons. If you extend this analogy, value will bubble up into the appliances which would each have consumer preferences. A token is a token no matter who produces it, just as an electron is, but I like my KitchenAid toaster, whats your preference ?

But Claude Code works about as well as Codex and roughly the same as Github Copilot. So what part of this pipeline is supposed to command premium pricing?

You might prefer your KitchenAid toaster but I'd wager you won't pay enough to support a trillion dollar valuation.


> consumer grade local models are getting good enough for local inference

I am waiting for that. Perhaps a taalas kind of high-performance custom hw coding llm engine paired with an open-source coding-agent. Priced like a high-end graphics card which would be pay off over time. It will be a replay of the ibm-mainframe to PC transition of a previous era.


> I am waiting for that

Same, and I think we're close. "The original 1984 128k Mac model was $2,495, and the 1985 512k Mac was $2,795" [1]. That's $8 to 9 thousand today. About the price of a 32-core, 80-GPU M3 Ultra Mac Studio with 256 GB RAM.

[1] https://blog.codinghorror.com/a-lesson-in-apple-economics/

[2] https://www.bls.gov/data/inflation_calculator.htm


The maxed out 512GB RAM Mac Studio is no longer available from Apple and is now pushing $20 thousand in the secondary market. And we might not even see a new Mac Studio release from Apple before October.

> and is full of empty LLMisms

I dont have an llm-radar like you but I felt some anxiety reading through it. Cant explain why but the logic was not linear and this strained me as a reader. It didnt have the obvious llm-isms i see on youtube videos "not this but that". My natural instinct is to make sense of what I read, and if presented with a word-salad, it strains me. What are the empty LLMisms so my radar can be calibrated ? These are some giveaways I could spot.

> The timeline is genuinely absurd

> The timeline sequence description (Feb/March/April) is abstract and does not depict specifics reflecting human understanding.


> you would expect to see a lot of different opinions about the world.

It is an age-old debate between know-that and know-how. Understanding the world around us is the point of education, and this means ways of looking at it, insights or theories, and how these insights and theories come about which is the critical thinking process. I would like to call it thinking from first assumptions since critical thinking as a term is overused and I would argue that AI is great at critical-thinking in the shallow definition of the term.


> A good percentage of cybersecurity has always been theater

It is great to be in a "best-effort" business where there are no consequences for bad things happening. Cybersecurity is one of those businesses. Web search, feeds and ads are another.

Imagine you are selling locks to secure homes. A thief breaks the lock. The lock-maker is not held liable. In fact, they now start selling stronger locks, and lock sales actually improve with more thefts.


Not surprising given that they dont even know why claude-code works as before or doesnt work [1] ie, there is no known theory of operation. Explains why they are afraid of it.

[1] https://news.ycombinator.com/item?id=47660925


I think Boris will come and say there is no issue with claude code.


> I can't believe that's where we're at, as software devs

Agree wholeheartedly.

The premise of the bug did not make any sense to me. For instance, "unusable for complex engineering tasks", why would someone who understands these tools use them for complex engineering tasks ? Also, this phrase in the bug appears too jargon-ny "Extended Thinking Is Load-Bearing for Senior Engineering Workflows" - what does this even mean ? Am I the only one who is looking at this with bewilderment. I think there is group of folks producing almost-working proof of concept code with these tools, and will face a reckoning at some point - as the bug illustrates. I see this as a storm in a teacup with wonder and amusement.

There is also a larger commentary on: when you dont understand why things work (ie, have a causal model), you wont know why they broke (find root causes). We are at a point in our craft where we throw magic dust and chant spells at claude and hope and pray it works.


Imagine a team of human engineers. One day they are 10x ninjas and the next they are blub-coders. Not happening.

Put Claude on PIP.


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