havercosine

In case if any Physics learner finds this useful: Susan Rigetti's list is great if you are planning to do a late life PhD in Physics but not if you are re-learning it on the sideline of normal career as a hobby.

I've found many hard-core Physics textbooks to be off putting. Because the syllabus and its progression makes it seems like we are jumping from one special formula to another and there's just so much to learn! I was trying to search for a physics book that will try to cover as much ground as possible in fewer ideas and mental models. Roughly similar to Elon's idea that knowledge is a semantic tree and one should focus on trunk and big branches first.

Thomas A Moore did this experimental syllabus / series called "six ideas that shaped Physics". Each textbook takes one idea like "conservation laws constrain interactions". It's an excellent series, each book is relatively short and has amazing explanation. Especially look out for 2nd edition because later editions were probably "mainstreamed" by editors / publishers. The series is great choice for self learners. It uses non-standard notation and terminology at places to get the point across effectively so maybe not a great textbook lol.

2 standout examples for me : the first unit starts from the idea of interactions -> change in momentum -> to talk about change in kinetic energy. This motivates the idea of work done from first principles instead of directly throwing a definition "force . displacement". The unit on electromagnetic fields similarly has a beautiful discussion to motivate why one would use the ideas of curl and divergence.

It is honestly hard to predict. We are currently in everyone is building website/mobile app/gadget era of AI. Very few places are questioning what is worth building.

Short term, we can compare this to 2-3 recent (mini) revolutions: internet, mobile, cloud. Then the answer is somewhat predictable and (somewhat sad personally). Companies owning the main distribution of intelligence (big labs) or distribution of the app/cloud layer (Google, MSFT, AWS) will make most of the money. In fact Google looks well positioned that way with owning intelligence, cloud (and even hardware, if they can get TPUs right as commercial product).

Long term view is interesting and somewhat satisfying (again, personally). We can compare this to industrial revolution, but for intelligence instead of physical labour. I hope, to borrow from Alan Kay's words, the total value generated will be more than what few big labs can capture. Though we will also see normal market dynamics of boom and bust in play. Companies building something useful, patiently will keep winning the markets. But only to get challenged by newer modes of the technology emerging.

In this long term view, the technology per se doesn't offer monopolistic profits to big labs. I think Anthropic is well aware of this and they are trying to extract as much cash from white collar work automation as they can before things are democratised. Contrary to popular opinion, they are also trying to seek a regulatory capture here by to maintain monopolistic position in the US market by scare mongering about China and open source. Its a case study how they managed to keep the good boy image of themselves while doing this.

In the end, I hope the technology emerges as electricity or combustion engine cars. Yes early pioneers (e.g. Ford) were perhaps able to make lot of money. But eventually, the technology was too important to allow one party to have monopoly and we had an abundance market which enabled jobs and money for a lot more people.

Edit, postscript : Dario, Sam and even Jensen will end up looking like the new the John D. Rockefeller's of this era. I'm personally hoping Demis Hassabis actually solves something much more important (problems in diseases, biology etc) with AI.

That is the ideal solution. I'll tell you an incident that seems from a black humour novel. A state government in one of the highest populous state in India decided to make biometric attendance for government school teachers, to ensure they are in school. Large number of so called "teachers" started protesting against state, egged on by opportunistic opposition. Because many of them were drawing salaries from government and _not even showing up in school_. That's the ground reality of government funded education.

I'm open to the idea that market forces or reality _might_ tilt the favour in more investment in AI in education and tutoring. Think about developing economies or under developed economies of the world. The state / government has to think how should they allocate budget: on agriculture subsidies or pay teachers better or spend it on energy security in increasingly hostile multipolar world or invest it in infrastructure. There are no good answers.

I hear you, and I know every project being dissed here is not going to be Dropbox. Perhaps some projects deserve the reality check they get. Though I still believe that HN crowd telling that just pay teachers more or kids need to be taught by good human teachers are underestimating the scale of the problem.

Some real experience of school in my part of the world (India). My child goes to a somewhat costly private school. Still, each class has 35-40 kids. The teacher is over-worked : checking home work, prepares kids for upcoming random extra curricular activity, has to teach AI because someone suddenly thought it is important to teach it in grade 3. I know multiple teachers in that school who landed the job after doing just a 6 months course after a career break. Forget research on teaching, hardly any one of them read anything beyond curriculum. None of the teachers have enough time to give personalised attention to _any_ kid. Its a sorry state of affairs.

Personalised tutoring produced geniuses in last century but was affordable only for a wealthy few. It is my belief that AI might help democratise the idea. I know it is somewhat hard to think that a mere machine might have more patience and time to explain a concept 100 times to a student, instead of a human.

This still doesn't take away from the fact that teachers deserve to be paid more. I was a passionate for becoming a teacher, but knew I can't make enough money from it. I'm seeing a possibility in emerging markets that India / China might find it cheaper to deploy AI en masse for better educational outcomes because it will be much cheaper for the state than paying high wages (and subsequently pensions) to human teachers, however unfair it might look.

Thanks for taking time to write this. HN is showing (expected) dismissing attitude towards this idea. That tells me it might work :) ! Folks here are wildly overestimating (or ignoring!) how many adults are qualified to be good teachers and how many of them further have enough incentives (money, time, resources) to do it well. Its a _very_ small number.

In my part of the world, "become a teacher" is often a job advised to people who are not able to find other jobs or are looking for a safe way back after career break. None of them are looking forward to engaging 5 year old with life's curiosities. To add the famous quip from WorryDream/Bret Victor : most of the teachers teaching calculus etc. have never ever used it in real life.

Working parents with STEM backgrounds likely know that schools are glorified day-cares and probability of your child having access to a life changing tutor is very low.

I tried building an edtech venture frustrated precisely with these problems. Failed, but would def do it again with AI in the mix. I'm for one rooting for this to succeed!

Though, Modular should have been the team to do it. My theory is that they raised too much money too soon. With that kind of money, you get anxious investors waiting to see some magic on quarterly timelines. So Modular was forced to be compatible with Python as there's no other way to win quick developer mindshare. (Though I don't think they managed to do that either).

A closest counter path I would have expected Modular to follow was Zig or Oxide computers (I know not apples to apples comparision). Start actually attacking the problem with hindsight and lessons of 30 years of Python, build something fresh, and try to patiently win the market.

Rust is not going to win this market. The language has too much syntax friction to win over data science/AI folks and doesn't offer too much in parallel programming world. Julia, although beautiful attempt, couldn't gather enough support outside academia.

In fact, if Nvidia cuTile, Triton, Jax keep delivering, Python seems unmatched at the moment. It is likely to be in the similar position that C/C++ have been in embedded and firmware world.

Well spotted but I don’t think it’s bad trade off. A beefy postgres instance (with standby configured), couple of worker nodes running dbos / river directly as a library backed by same db . This system can go surprisingly far.

I’ve seen and used airflow , spark , temporal for many systems. I’d def pick this simpler choice for 95% workloads these days.

Yes and yes. DBOS self hosted , pointed to same application DB. Systems like these (durable execution) fit well with agents or LLM driven on demand workflows. You might be attaching multiple flaky local or remote api call tools. Many complex LLM workflows that you don’t want to one shot but break down into chain of prompt can be added to river/dbos + LLM , providing much needed retries and bit of concurrency control.

Airflow perhaps fits better with scheduled recurring ETL workflows.

Well done! I couldn't understand how you are building reels out of it via the agent. Is it some sort of AI tool calling that takes image links and builds a reel via some video editing tool ? Or +/- time delta around the timestamp returned from the indexed from a given query + join them together?

Not Op. I have production / scale experience in PyTorch and toy/hobby experience in JAX. I wish I could have time time or liberty to use JAX more. It consists of small, orthogonal set of ideas that combine like lego blocks. I can attempt to reason from first principals about performance. The documentation is super readable and strives to make you understand things.

JAX seems well engineered. One would argue so was TensorFlow. But ideas behind JAX were built outside Google (autograd) so it has struck right balance with being close to idiomatic Python / Numpy.

PyTorch is where the tailwinds are, though. It is a wildly successful project which has acquired ton of code over the years. So it is little harder to figure out how something works (say torch-compile) from first principles.

Bifrost is the fastest LLM gateway on the market. Built in Go with careful garbage collection, it adds just about 11 microseconds of overhead at 5,000 requests per second (with 4,100 RPS throughput) on a t3.xlarge instance.

The benchmarks are here: https://github.com/maximhq/bifrost/blob/main/docs/benchmarks...

Some features: • Built-in governance and routing rules • Supports over 1,000 models from different providers • MCP gateway included (HTTP, SSE, and console transport) • Out-of-the-box observability and OTel-compatible metrics

A fellow Godot enthusiast here. Love to see Godot being used in commercially successful indie game like this. In 2021-22 time, I tried (unsuccessfully!) building educational video games for maths using Godot and I have fond memories of being in the flow state while working with Godot. IMO Godot fits well with programmer's brain much better than Unity etc.

I'm honestly in two minds on this one. On one hand, I do agree that valuations have run a bit too far in AI and some shedding is warranted. A skeptical position coming from a company like MSFT should help.

On the other hand, I think MSFT was trying to pull a classic MSFT on AI. They thought they can piggyback on top of OpenAI's hard-work and profit massively from it and are now having second thoughts, thats better too. MSFT has mostly launched meh products on top of AI.

Paras, as a an Indian founder, I've watched your journey for few years now. You are an inspiration and a thoughtful leader. Your "Mental Models for Startup Founders", is a very well written mirror for every founder to look into.

Hope you get some nice time off and go back with vigour to Turing's Dream now...

Andy's collaborator Michael Nielsen has a nice blog post, "using space repetition system to see through a piece of maths"[0]. He makes a point that the idea is to commit more and more higher order concepts to memory. But he does emphasise that Anki is one way to achieve his and a more simpler pen-paper method that you wrote might work.

[0] https://cognitivemedium.com/srs-mathematics

I was going to say the same thing. For some real world estimation tasks where I don't want 100% accuracy (example: analysing working capital of a business based on balance sheet, analysing some images and estimating inventory etc.) the job done by GPT-4o is better than fresh MBA graduates from tier 2/tier 3 cities in my part of world.

Job seekers currently in college have no idea what is about to hit them in 3-5 years.

Disagreeing here! I think we often overlook the value of excellent educational materials. Karpathy has truly revitalized the AI field, which is often cluttered with overly complex and dense mathematical descriptions.

Take CS 231, for example, which stands as one of Stanford's most popular AI/ML courses. Think about the number of students who have taken this class from around 2015 to 2017 and have since advanced in AI. It's fair to say a good chunk of credit goes back to that course.

Instructors who break it down, showing you how straightforward it can be, guiding you through each step, are invaluable. They play a crucial role in lowering the entry barriers into the field. In the long haul, it's these newcomers, brought into AI by resources like those created by Karpathy, who will drive some of the most significant breakthroughs. For instance, his "Hacker's Guide to Neural Networks," now almost a decade old, provided me with one of the clearest 'aha' moments in understanding back-propagation.

Most countries in South, South East Asia have made exams as a make and break deal for every student. In India, there are so many kids staying away from home in cities which are just exam preparation centres, with routine news of suicides.

Looking back on my life I think we asians have definitely stretched this way too far. Unfortunately, in high & young population countries like ours these exams are perceived as the only non corrupt way of moving out of low income trap. So this will go on :-(

Spot on! Lot of voice assistants have been following "if we could" line instead of "if we should line". For many straightforward applications, clicking through well defined interface can be the least error prone way to get the job done.

Overall there's very little to understand from the page in terms of motivation, sample examples etc. But, one interesting thing: The math module allows choosing between radians, degrees and more importantly cycles. I only know of one more project, Pico8 fantasy console, which offers this correct "API" for trigonometry.

Daniel Fleisch has written a series of books "Student Introduction To.." for maxwells equations, waves, tensors. All his books are famous for explaining everything step by step and making it informal but super clear.

`why rock the boat` is spot on! Most large organisations eventually go into a mode of maximising the free cash flow for shareholders. I guess more or less this is by design. Investors, Founders and early employees take risks in short run for the rewards in the long run. A company cannot keep saying the promised green land is delayed by another 5 years.

Some criticism of CEO might be warranted. But remember that CEO compensations tied to profit after tax. I guess the only way to get back old Google is to start one!

Once number of employees hits a certain inflection point (roughly when one can't identify everyone with name), the focus for a lot of people is to keep their manager happy. Because any other goal is too abstract. Safi Bahcall's book Loonshots had some nice discussions on this point.

Naive question. In my part of the world, board meetings for such consequential decisions can never be called out on such short notice. Board meeting has to be called ahead of time by days, all the board members must be given written agenda. They have to acknowledge in writing that they've got this agenda. If the procedures such as these aren't followed, the firing cannot stand in court of law. The number of days are configurable in the shareholders agreement, but it is definitely not 1 day.

Do things work differently in America?

It is an interesting thought experiment to wonder if certain things were discovered earlier or later owing to a particular type of maths that we practiced.

I was amused to learn that there are societies dedicated to the cause of dozenal system who write papers and books urging everyone to switch. On the other hand, I don't know if it is exaggerated but French revolutionist had grand ideas of creating decimal based systems even for time. But better sense prevailed in the long run!

It is interesting to think how can changes of the form "if we can align everyone to change and adopt this new way" can be brought about at any scale beyond a few thousand folks. I think large mass adopted switches (horses to cars, smart phones) have been about incentives and convenience demonstrated by some early adopters. But for basic arithmetic this seems impossible to pull off!

These notes are excellent. One good thing is how often Terence Tao gives real life examples and analogies, contrary to what one may expect from a fields medal winner. From utilitarian perspective, reading Axler's book looks like comically bad use of one's time.

It might have been a reason, mathematicians wanting everything well defined etc. But here's a better way to think about it: On real number line, addition defines shifts and multiplication defines scaling. If you are in two dimensions, what is the equivalent? We define a 2 dimensional number such that multiplication defines scaling + rotation. The complex in complex number should not be read as complicated but like duplex or two things intertwined together.

The next question is why bother? What's the point? Turns out that important real life signals, like AC voltage and current, are sinusoidal. And real life electrical machines shift the phase of these signals. By using complex numbers to represent these signals, you can continue to use simple maths of DC circuits to analyze AC circuits. So you'd can still use V = IR, but R of a AC machine like motor will be impedance (generally called Z), represented by a complex number.

I found first few pages of MD Alder's complex analysis for Engineers indispensable in demystifying this complex stuff. Here's a quote from first paragraph "If Complex Numbers had been invented thirty years ago instead of over three hundred, they wouldn't have been called `Complex Numbers' at all. They'd have been called `Planar Numbers', or `Two-dimensional Numbers' or something similar, and there would have been none of this nonsense about `imaginary' numbers"

Solid post. It also shows how powerful Julia is: allowing to operate at different levels of abstractions (down to seeing the assembly) using the same set of tools.

The most badass story related to 'using basic tools and a steady hand in a pinch' is Buzz Aldrin pulling out a sextant and sliderule to do some calculations in Gemini XII. The description in the article reads "Aldrin pulled out a sextant and his slide rule and put his MIT doctoral research to work."

More details on the link here: https://www.nasa.gov/feature/gemini-xii-crew-masters-the-cha...

This is a great post. Another aha! moment I had in understanding Kalman Filter came from a short note by John D. Cook (link: https://www.johndcook.com/blog/applied-kalman-filtering/) . A traditional calculus/differential equations based modelling of systems takes a view that there is no uncertainty in the data and everything is captured by system model. OTOH, data driven estimator will say that "it is all in the data", completely ignoring the model of the physical process that is generating the data. Beauty of Kalman filters is that it combines these two approaches.

I agree with the observation (most people do not contribute to libraries), but I think the arrow of causality is little different. Python is used as a glue code in scientific computing on top of libraries written in C/C++. The development ergonomics of these languages are intimidating for many people, with both languages having enough footguns. The net result is no-one wants to peek under the hood and see how things are working.

A fresher take on scientific computing like Julia, if it is mainstream, might enable more contributions and in general understandability of the black box algorithms.