fidzu : software

My productivity has increased by at least 300% with AI assistance. You can get amazing results nowadays. If you use the tools right. Discover 4 key ingredients that make the tools work for you in this post.

Many people have only tried free AI via ChatGPT or similar web chatbots. It's easy to dismiss those tools, since they lack all 4 ingredients.

1. Context. If I ask you how I could improve my business, you won't be able to provide a good answer. You don't know all the details about my business that matter. All you can do is offer generic advice or make guesses (hallucinations). It's the same with AI tools. Don't rely on the knowledge baked into the LLM base models. Either provide this knowledge, or provide the tools to obtain that knowledge. You can include "all relevant knowledge" in the prompt, but this is labor-intensive. This is why you want an agentic tool.

2. Agentic tools. I've been using Claude Code, a CLI tool that provides agentic AI for knowledge tasks (not just coding). There is also Claude Cowork, a desktop tool, and alternatives from vendors besides Antrophic. These tools use a loop in which the AI determines whether it needs more information and then goes looking for it. You can give these tools a task or a question, and then they will, if called for, run hundreds of searches and commands. They can look at your documents, codebases, and web resources. Tell these tools "Fix GitHub issue $link", and they'll look at the issue, anything references on the issue, as your codebase, make changes, run tests, make more changes, check results via the browser, fix some final issues, create a draft pull request, and provide you with a summary of what was done and possible next steps.

3. Feedback harness. When writing code, you often don't get everything correct the first time. Which is why automated tests are great. More generally, fast feedback loops are great, regardless of whether you're doing software development. For software development, you'll get much better results if the AI tools can actually run the code and run tests and other CI tools to verify everything is correct.

4. Model. AI capabilities are increasing at an incredible pace. If you're using the latest models, your experience will be worlds apart from those using 2-year-old models. For maximum quality, there are 3 metrics to max out: model size/capability, model version, and effort parameters. In other words, use the latest version of the biggest model with "max effort". At the time of writing this post, that is Claude Opus 4.7 with max-effort when using Antrophic, or GPT-5.4 Pro with heavy thinking when using OpenAI. These settings eat tokens, so you will quickly run into your subscription limits of the basic tiers. Then again, paying 200 USD a month for the higher tiers so you can 5x your productivity is quite the bargain.

Those 4 points provide a conceptual framework. There is more to learn, and the AI space is evolving quickly. Ask your favorite AI tool how you can improve your AI workflows, starting from this post, to get specifics.

Some more tips:

• Know how to use CLAUDE.md / AGENTS.md
• Create sandboxed environments so you can let agents run autonomously for longer periods of time
• Mind the current model's tendency to sycophancy when prompting. If you go, "Here is my idea, is it good?" LLMs will often say yes even if there are issues. Adding "Be brutally honest" to your prompt or CLAUDE.md helps. It takes some practice to build up an understanding of how to prompt and in which ways responses should be distrusted. As a starting point, treat current LLMs as overeager sycophantic juniors with an inhuman, jagged skill profile, who tirelessly work at superhuman speeds.
• Claude Code (or similar) plus local files in a text format works well. I've been enjoying Obsidian + Claude Code for personal knowledge management.

You can stay up to speed with AI capabilities development via Don't Worry About the Vase and Astral Codex Ten, which I both highly recommend.

Shameless plug: my company provides an AI Assistant for MediaWiki, giving you AI capabilities on top of collaborative knowledge management, ideal for organizations.

The post Boot Your Productivity With AI appeared first on Blog of Jeroen De Dauw.

18 Apr 2026 3:55am GMT

Ik ben niet zo voor lijstjes, maar als ik onder dreiging van foltering een boeken top 3 zou moeten geven, dan zou "Max, Micha & het Tet-offensief" daar zeker in staan. Van auteur Johan Hardstad verscheen in 2024 al een nieuwe roman in het Noors onder de titel "Under brosteinen, stranden!" en volgens doorgaans goed ingelichte bronnen (ik mailde met de uitgever) zou in het najaar van 2026 de…

Source

18 Apr 2026 3:55am GMT

This post was co-authored with Nicholas Gates, senior policy advisor at OpenForum Europe. It was originally published on EUobserver, an independent online newspaper widely read by EU policymakers, journalists and advocacy groups. The article summarizes a series of posts I've been writing about digital sovereignty.

European digital assets have a habit of not staying European - a problem current discussions about sovereignty are overlooking.

For example, Skype had Swedish and Danish founders, Estonian engineers, a Luxembourg headquarters, and proprietary code.

Every sovereignty credential was correct on the day it would have been assessed - and meaningless after eBay acquired it, Microsoft bought it, and eventually shut it down in 2025.

This speaks to a core tension at the heart of Europe's digital sovereignty moment. The real story has to do with licensing, dependencies, and supply chains more than it has to do with ownership or operational control - both of which can (and often do) change in Europe.

The current conception of cloud sovereignty asks the right questions about where data is stored, where companies are headquartered, and whether supply chains are European.

What they don't yet ask is whether the sovereignty they are assessing is durable and resilient - for example, whether it will survive a change of ownership, a corporate acquisition, or a disruption in the infrastructure the software depends on.

The European Commission's Cloud Sovereignty Framework provides a non-legislative assessment tool designed to evaluate the digital independence of cloud services in Europe.

It enables public authorities to rank services based on factors such as immunity from non-EU laws, operational control, and data protection.

The forthcoming Cloud and AI Development Act (CAIDA) - expected at the end of May - will possibly go further.

That said, while both are serious and welcome efforts, they are likely to solve only part of the problem.

'Buy European' is a fragile concept

Europe's 'Buy European' strategy is being built on two fragile foundations it hasn't yet explicitly addressed, and this could have disastrous implications in the cloud domain in particular.

Proprietary software with a perfect sovereignty score today is one acquisition away from a different answer tomorrow. Open Source software means the question doesn't arise.

The legal right to fork changes the power dynamic entirely: it gives you leverage, lets a community step in, and means the technology cannot be held hostage.

This is the distinction the Cloud Sovereignty Framework currently misses.

When Oracle acquired Sun Microsystems in 2010, governments running MySQL faced an immediate question: what happens to this software now?

The answer turned on one thing - the licence. Because MySQL was GPL-licensed, the right to fork and maintain it independently was already being exercised before the acquisition even completed.

MySQL's creator, Monty Widenius, forked it in 2009 precisely because he saw the acquisition coming - that fork exists today as MariaDB. The licence didn't prevent Oracle from buying Sun. It meant the acquisition couldn't end the software, and anyone paying attention could act on that right before any harm materialised.

Getting the licence right is necessary, but it is not sufficient.

In 2024, a conflict between WordPress co-founder Matt Mullenweg and WP Engine disrupted updates for millions of websites.

The code was Open Source. The delivery infrastructure had a single point of control. Most programming languages rely on a single central registry and most are controlled by US companies.

In 2019, GitHub restricted access for developers in sanctioned countries; since GitHub also owns npm, the JavaScript ecosystem's delivery infrastructure became subject to the same trade controls. These aren't interchangeable download sites you can swap out.

Sovereign software on fragile infrastructure is not sovereign. It is software waiting for a supply chain to break.

Both fragility problems point to the same conclusion: a 'Buy European' label is not a sovereignty guarantee unless it embraces licensing as a tool and helps to safeguard the supply chains the software depends on.

Consider two scenarios. A government running proprietary software on a European cloud has jurisdiction, but no exit if the provider is acquired - replacing the software could take years.

A government running Open Source software on Amazon Web Services (AWS) in Europe can move the same software to a European provider whenever it wants. Neither is ideal, but they are not equal.

Europe's sovereignty frameworks need to internalise this asymmetry. Structural sovereignty - the kind that survives change - requires open foundations that flow from licensing through the critical supply chains on which that software depends.

A call-to-action for the Cloud and AI Development Act

CAIDA should not make the same mistakes as the Cloud Sovereignty Framework. It would be a mistake to simply extend a 'Buy European' checklist. The legislation should instead define what makes sovereignty durable.

Two concrete steps would make an immediate difference.

First, it can make Open Source licensing a pass/fail gate for mission-critical procurement under the Cloud Sovereignty Framework - a condition of eligibility at the highest assurance levels, not a weighted factor in a composite score.

Second, it should require supply chain resilience assessments that distinguish between dependencies switchable in weeks and those that would take an entire language community years to replicate, with federated or mirrored European alternatives required where no fallback exists.

Yes, requiring Open Source for mission-critical systems narrows the field in the short term.

But the providers you lose are the ones whose sovereignty credentials don't survive change.

In the longer term, these requirements push European companies toward Open Source software - technology that no one can take away.

18 Apr 2026 3:55am GMT

A while ago, CommBank started asking for MFA confirmation on its mobile app for every NetBank login on a browser. Previously, there was an option to use SMS for MFA, which isn't as secure as I would like, but it was at least usable. Since I'm switching away from Android to Mobian and won't be able to use the CommBank app for much longer, I applied for a physical NetCode token.

The letter that came with it has the wrong link for activation, the correct link is under NetBank -> Settings -> NetCode (under the Security section)

To apply for a physical token, call the NetBank team, mention you can't use the app and need a physical NetCode token, and make sure they actually submit your request for a token. It took me 2 calls to get them to ship me a token. The hardware is free of charge but can only be applied for via phone call; unfortunately staff members at my local branch are unable to do anything in relation to NetBank. I was told privately by a CommBank employee that they are deprecating the hardware token in favor of the mobile app, I hope that won't happen anytime soon, or that they add support for passkeys before they do. The last time I checked, the CommBank app was LineageOS-friendly, but I don't want to configure WayDroid just to do online banking.

PayID, the thing that allows you to receive payment via a phone number or email address, is not compatible with the hardware token, and existing PayID will be silently deactivated if you use hardware token. This looks to be an artificial restriction; I don't see why it has to be this way.

Regular CommBank mobile app sessions will also be de-activated once the hardware token is activated (I was told so but my sessions weren't deactivated until I wiped my Android phone), and you won't be able to sign into mobile app again until you manually disable the NetCode token.

Online banking has been getting progressively more invasive and anti-user over the last decade, from demanding remote attestation to requiring real time location data, each time locking certain features when those demands are not satisfied; all based on the flawed assumptions that everyone owns a phone running a certain flavor of iOS or Android, and has it ready all the time. I'm not sure what can be done to reverse this trend, but on the personal level I will use NetBank less and go back to cash.

18 Apr 2026 12:00am GMT

Prices

On the 19th of March I got a home battery system installed. The government has a rebate scheme so it had a list price of about $22k for a 40kWh setup and cost me about $12k. It seems that 40KWh is the minimum usable size for the amount of electricity I use, I have 84 cores running BOINC when they have nothing better to do which is 585W of TDP according to Intel. While the CPUs are certainly using less than the maximum TDP (both due to design safety limits and the fact that I have disabled hyper-threading on all systems due to it providing minimal benefits and potential security issues) given some power usage by cooling fans and some inefficiency in PSUs I think that assuming that 585W is accounted for 24*7 by CPUs is reasonable. So my home draws between 800W and 1KW when no-one is home and with an electric car and all electric cooking a reasonable amount of electricity can be used.

My bills prior to the battery installation were around $200/month which was based on charging my car only during sunny times as my electricity provider (Amber Electric) has variable rates based on wholesale prices. Also the feed in rates if my solar panels produce too much electricity in sunny times often go negative so if I don't use enough electricity. I haven't had the electric car long enough to find out what the bills might be in winter without a home battery.

Before getting the battery my daily bills according to the Amber app were usually between $5 and $10. After getting it the daily bills have almost always been below $5. The only day where it's been over $5 since the battery installation was when electricity was cheap and I fully charged the home battery and my car which used 50KWh in one day and cost $7.87 which is 16 cents per KWh. 16 cents isn't the cheapest price (sometimes it gets as low as 10 cents) but is fairly cheap, sometimes even in the cheap parts of the day it doesn't get that low (the cheapest price on the day I started writing this was 20 cents).

So it looks like this may save me $100 per month, if so there will be a 10% annual return on investment on the $12K I spent. This makes it a good investment, better than repaying a mortgage (which is generally under 6%) and almost as good as the long term results of index tracker funds. However if it cost $22K (the full price without subsidy) then it would still be ok but wouldn't be a great investment. The government subsidised batteries because the huge amount of power generated by rooftop solar systems was greater than the grid could use during the day in summer and batteries are needed to use that power when it's dark.

Android App

The battery system is from Fox ESS and the FoxCloud 2.0 Android app is a bit lacking in functionality. It has a timer for mode setting with options "Self-use" (not clearly explained), "Feed-in Priority" (not explained but testing shows feeding everything in to the grid), "Back Up", "Forced Charge", and "Forced Discharge". Currently I have "Forced Charge" setup for most sunny 5 hours of the day for a maximum charge power of 5KW. I did that because about 25KW/day is what I need to cover everything and while the system can do almost 10KW that would charge the battery fully in a few hours and then electricity would be exported to the grid which would at best pay me almost nothing and at worst bill me for supplying electricity when they don't want it. There doesn't seem to be a "never put locally generated power into the grid unless the battery is full" option. The force charge mode allows stopping at a certain percentage, but when that is reached there is no fallback to another option. It would be nice if the people who designed the configuration could take as a baseline assumption that the macro programming in office suites and functions in spreadsheets are things that regular people are capable of using when designing the configuration options. I don't think we need a Turing complete programming language in the app to control batteries (although I would use it if there was one), but I think we need clauses like "if battery is X% full then end this section".

There is no option to say "force charge until 100%" or "force charge for the next X minutes" as a one-off thing. If I came home in the afternoon with my car below 50% battery and a plan to do a lot of driving the next day then I'd want to force charge it immediately to allow charging the car overnight. But I can't do that without entering a "schedule". For Unix people imagine having to do everything via a cron job and no option to run something directly from the command-line.

It's a little annoying that they appear to have spent more development time on animations for the app than some of what should be core functionality.

Management

Amber has an option to allow my battery to be managed by them based on wholesale pries but I haven't done that as the feed-in prices are very low. So I just charge my battery when electricity is cheap and use it for the rest of the day. There is usually a factor of 2 or more price difference between the middle of the day and night time so that saves money. It also means I don't have to go out of my way to try and charge my car in the middle of the day. There is some energy lost in charging and discharging the batteries but it's not a lot. I configured the system to force charge for the 5 sunniest hours every day for 5KW as that's enough to keep it charged overnight and 5KW is greater than the amount of solar electricity produced on my house since I've been monitoring it so that forces it to all be used for the battery. In summer I might have to change that to 6KW for the sunniest 2 or 3 hours and then 4KW or 5KW surrounding that which will be a pain to manage.

Instead of charging the car every day during sunny times I charge it once or twice a week, I have a 3.3KW charger and the car has a 40KWh battery so usually it takes me less than 10 hours to fully charge it and I get at least 5 hours of good sunlight in the process.

There are people hacking on these devices which is interesting to get direct control from computers [1], and apparently not banned from the official community for doing so. I'm not enthusiastic enough to do this, I've got plenty of other free software things to work on. But it's good that others are doing so.

• [1] https://foxesscommunity.com/viewtopic.php?t=2397

17 Apr 2026 12:58pm GMT

It started with a thought: to understand people's perspectives on life and its meaning. So I texted folks, "What is life (to you)?". Each of the following list items (-) is a response from a different individual, mostly verbatim.

- A lot

- Everyone has a few universal basic qualities, and some special qualities. To me life is pursuit of exploring world based on those qualities and maturing those qualities as one goes on about exploring world/life with those qualities.
Discovering and enhancing experiences as one goes through them.

- life is endless suffering

- my answer might change daily, but this is what I've noticed and feel recently. Life is a spectrum with two distinct ends: what we control and what we don't. At birth, the spectrum is largely tilted toward control, but throughout our lives, it gradually shifts toward the other side. Ultimately, as we approach death, we lose all control over any aspect of our existence, reaching the other end of the spectrum.
tho this isn't universal, privilege plays a huge part in what you control tho i believe it holds true for the majority
but yeah man, meaning and purpose are dynamic, it's in their nature to change i can give you a different answer this evening itself xD

- Funeral Monologue from Synecdoche, New York. https://www.youtube.com/watch?v=Z9PzSNy3xj0

- Zindagi ek nadiya hai, Aur mujhe tairna nahi aata
(translation - Life is a river, and I don't know how to swim)
On a more serious note, Life is what you make it out for yourself. The only established truth is that it will end. We can never know if there is something after or if there was something before. So try to live a life that you feel aspired by? But this question was beautifully answered by that book which you had about that dying professor
(Me - He was talking about Tuesday's with Morrie)

- My answer is 42

- One, it's living on your own terms, you define everything for yourself, success, normal, whatever. You get to curate your version of it no matter the societal norms.
It's an accumulation of experiences - friends, parents, work, activities, doing shit loads. Sab try karo- travel, zumba, art, music, workout, sports, dil kara ye karna hai karlo. (translation - If your heart wants to do it, just do it.)
Then I think relationships - all that you've nurtured, people forget maintaining people because of work. It takes efforts to keep people in your life, everyone that comes has a place in yours, how well thats stays is upto you. You also get to curate your people, who stays who don't. Family toh hai hi (translation - family is there) but everyone else that comes along can make it pretty good.
So I don't want to be 50 and be like chalo ab kuch apne liye karte hai… (translation - Come on, now let's do something for ourselves) Do whatever shit you want today. Not everything costs money, and if it does get thrifty
But do keep healthy while doing all of that

- Being alive so that my daughter can grow up and i can help raising her kids as well. Raising kids without mother is tough :P

- Definitively, I feel like Life is a by product of proteins and energy working together. But in a more personal sense, Life is a dumb joke played onto us. It's a rat race. But rats exists because of life and then it becomes a chicken-egg problem
Honestly, I don't give good answers to life questions. I'm generally the one asking
Life can be like a box of chocolates, you don't know what you're gonna get untill you experience the chocolate(assuming the chocolates are heterogenous and contains a mix of everything)
Camus once said, "Life is a revolt", and one of his students added more spice to it like "Life is a revolt against the meaninglessness of existence"
I kinda feel like Life is the pursuit of every person's search for meaning

- Imprisonment waiting for execution 😄
I have one more thought while we are on the topic , game with pre defined starting position and predefined destination , path to reach is a maze

- Life to me is to live without regrets and live with freedom.
Life is always unpredictable and this unpredictability makes it more interesting and worth it.

- As of now, for the state of mind that I am in , I think for me life is about subtle struggle, subtle inconveniences and yet moving forward cause that's all I know.
I am not sure if any of this has any meaning, but sometimes I feel I was born of a purpose and that the universe has my back.
For me it's about raising my consciousness, understanding people to their depths, gaining moderate material success and helping people to some extend.
I have tried to seek a grander meaning but I have failed.
Life for me is what I make out it.
In my times of great success i rarely think about life for I am busy enjoying it, whatever you may call that state of mind.

- For me its the little things that you enjoy with YOUR people

- Life to me is about living and loving, and doing it in a way that sustains. It's the people who shape you, the work you get absorbed in, the quiet moments in between. There's also the wanting, the drive to figure out what's worth going after and how to get there, but that's just one part of it, not the point of it. And none of it happens in a vacuum. I'm aware of the privileges that let me live this way, and I try to hold on to that gratitude. In the end, life has both a material and a non-material side, and a lot of what we do is chasing material things in an attempt to satisfy something non-material within us

- Mere liye (translation - for me) life is staying at my home and studying random economics papers. That's when I enjoy myself the most.

- Very complicated
Some days I wish this life never ended and some time I feel it would be better if it stopped at that moment.
It all depends on the events that happen in the so called "life".
So life to me is a string of events that happen anyway and you get to make some decisions which can turn it in any direction and then you wonder how did that happen.

- not forgetting to breathe, learn, eat, game, take a good shit, love, sleep.

- To be honest it changed with time! At 19 it was about freedom, wasn't sure what freedom meant but i wanted that! To be free from everything, maybe because parents still controlled a part of my life. Then came 22-24 where i was working, trying to figure out what i want, the meaning changed from freedom to living for myself. To earn more, to be greedy about myself and pursue whatever would help me gain more steps in my career.
Came my mba life, switched my life from doing for myself to trying everything out to have no regrets. Life meaning was just about living with no regrets, invested, gambled, did everything to earn that tag of "yeah, have tried that". Now it has all switched to, it was all just a fake facade. Life turned to having a meaningful life rather than finding meaning in what i am doing. Living for people around me, chhoti chhoti cheezo m khushi (translation - happiness in small things(?)) isn't really a topic of conversation but more of happy thing for me. So it changed, and m quite happy to be honest. Life did show me a lot of failures, but was privileged enough to face those failures. Gained a lot of learnings if not money😂
Hopeful for more learnings and change meaning of life with time

- A task.

- You have different answers at different times You learn different meanings at different times When you are studying, basically it is about job, finding a partner then it becomes, house, car other things based on your income in between, there can be passion too
Free Software was a passion, electoral politics too, but both kind of faded and I want cooperative and user driven development now (prav - something that motivates me every day) and these days learning Chinese and watching Cdrama takes a huge part of my leisure time it is heavily subjective and also influences by previous experiences people around you, how much influence they have on you
it also depends on if they had to struggle in their life or not, for some life did not give much troubles and trouble itself can be relative people who never had to struggle may find even smallest challenges as troubles like if you own a car, your worry is finding a parking slot

- I am too young to think about lyfe

- A ticket to see the show on earth, I guess 😀
I guess life is different depending on the mood. It is a very broad question.
(Me - What is it in this present mood?)
Learning stuff (like I am learning a new language) and being happy but also to regulate emotions in a world where being optimistic is getting harder each day.
Life is also having a unique set of glasses you wear. Both in terms of looking from your eyeballs and your psychological perspective. Both are unique and cannot be replicated.
It is interesting what people on their deathbed think of life. If I know I am dying, my perspective would change a whole lot.
Life is finishing reading books while we are alive 😉
Life is sleeping after a good XMPP chat 😉

- Dukh dard peeda (translation - surrow pain suffering)

- uhh to word it? life is just like a journey from A to somewhere and its all about what paths you take and what line you get on to me, just a series of short adventures that all connect to a larger sequence until you can't have any more adventures-
(Me - eee, THE END. drop dead, like a coin)
yeaaaah- I am not really for spirituality of an afterlife, to me life just ends at some point, after which point there fails to remain a discernable you, and some X time after which, you will be last remembered, try to make that last time a good one I guess?
(Me - no soul?)
uhhh not in the way most people think of it i guess?
theres just a lot of yous, theres the physical you, there is the idea of you, there is the expectation of you, and one of the undefinable you I would label as the soul maybe? like the part thats not physically you, but also certainly you
(Me - can't say I understood part, but I get you in this sense)
mhm- well its about just questioning who you are more so questioning what life is-, I have sadly spent way too much time trying to figure that out

- Making the best of the time you have

- living a full range of experiences and embracing the good ones, seeing all that the world has to offer. In the end we were always just stardust. Might as well enjoy it when we are stardust with a consciousness of our own.

- Life is being fucked by everything and you just have to figure out and try to stick to the things worth being fucked for

Note: Following was transcribed from a audio message.

- There are five conditions to become a life to survive in the environment. I think there's five conditions by the biological definitions and reproduction is one of the factor virus is not considered a life form because it cannot reproduce on its own but technically it's kind of a life because it reproduces using the DNA ability this is the biological definition. Do you want a philosophical definition?
My definition is kind of the same except that you get life experiences along with it as a human. Extra benefits is that you are not an NPC. All other organisms are NPCs. But humans can interpret the world and change it to their liking. That is life in the case of a human. But then many humans are mostly NPCs. But they still can change the life. Okay, fuck this. Where is this even going?
A human is an exception in the case of life, because human is not an NPC. Human can interrupt the world, human can change it to its liking, which is why we are such a successful organism on this planet. That is life to me. That's a human. But all of this is kind of meaningless, because the biological impurity of a human being still exists, so you still have the urges to reproduce, which kind of makes it like just another organism. But then, humans are yet to evolve to overcome that biological imperative.

I'm grateful for all the replies, outlooks, and subsequent conversations I got to have after this question with everyone. After all, it was a deeply personal question. It does fit in nicely with my definition of life:
"Life is all about experiences and all the transient relationships one gets to have with folks we meet on the way."

PS - I would love you hear you on this. Feel free to text or email on sahil AT sahilister.in

16 Apr 2026 5:59pm GMT

Or, second system.

A while ago, I decided that I'd like to test my intuition that Lisp (specifically implementations of Common Lisp) was not, in fact, bad at floating-point code and that the ease of designing languages in Lisp could make traditional Fortran-style array-bashing numerical code pretty pleasant to write.

I used an intentionally naïve numerical solution to a gravitating many-body system as a benchmark, so I could easily compare Lisp & C versions. The brief result is that the Lisp code is a little slower than C, but not much: Lisp is not, in fact, slow. Who knew?

The point here though, is that I wanted to dress up the array-bashing code so it looked a lot more structured. To do this I wrote a macro which hid what was in fact an array of (for instance) double floats behind a bunch of syntax which made it look like an array of structures. That macro took a couple of hours.

This was fine and pretty simple, but it only dealt with a single type for each conceptual array of objects, there was no inheritance and it was restricted in various other ways. In particular it really was syntactic sugar on a vector: there was no distinct implementational type at all. So I thought well, I could make it more general and nicer.

Big mistake.

The second system

Here is an example of what I wanted to be able to do (this is in fact the current syntax):

(define-soa-class example ()
  ((x :array t :type double-float)
   (y :array t :type double-float)
   (p :array t :type double-float :group pq)
   (q :array t :type double-float :group pq)
   (r :array t :type fixnum)
   (s)))

This defines a class, instances of which have five array slots and one scalar slot. Of the array slots:

• x and y share an array and will be neighbouring elements;
• p and q share a different array, because the group option says they must not share with x and y;
• r will be in its own array, unless the upgraded element type of fixnum is the same as that of double-float;
• s is just a slot.

The implementation will tell you this:

> (describe (make-instance 'example :dimensions '(2 2)))
#<example 8010059EEB> is an example
[...]
dimensions      (2 2)
total-size      4
rank            2
tick            1
its class example has a valid layout
it has 3 arrays:
 index 0, element type double-float, 2 slots
 index 1, element type (signed-byte 64), 1 slot
 index 2, element type double-float, 2 slots
it has 5 array slots:
 name x, index 0 offset 0
 name y, index 0 offset 1
 name r, index 1 offset 0
 name p, index 2 offset 0
 name q, index 2 offset 1

This is already too complicated: the ability to control sharing via groups is almost certainly never going to be useful: it's only even there because I thought of it quite early on and never removed it.

The class definition macro then needs to arrange life so that enough information is available so that a macro can be written which turns indexed slot access into indexed array access of the underlying arrays which are secretly stored in instances, inserting declarations to make this as fast as possible: anything slower than explicit array access is not acceptable. This might (and does) look like this, for example:

(with-array-slots (x y) (thing example)
  (for* ((i ...) (j ...))
    (setf (x i j) (- (y i j) (y j i)))))

As you can see from this, the resulting objects should be allowed to have rank other than 1. Inheritance should also work, including for array slots. Redefinition should be supported and obsolete macro expansions and instances at least detected.

In other words there are exactly two things I should have aimed at achieving: the ability to define fields of various types and have them grouped into (generally fewer) underlying arrays, and an implementational type to hold these things. Everything else was just unnecessary baggage which made the implementation much more complicated than it needed to be.

I had not finished making mistakes. The system needs to store some metadata about how slots map onto the underlying arrays, element types and so on, so the macro can use this to compile efficient code. There are two obvious ways to do this: use the property list of the class name, or subclass standard-class and store the metadata in the class. The first approach is simple, portable, has clear semantics, but it's 'hacky'; the second is more complicated, not portable, has unclear semantics¹, but it's The Right Thing². Another wrong decision I made without even trying.

The only thing that saved me was that the nature of software is that you can only make a finite number of bad decisions in a finite time.

More bad decisions

I was not done. Early on, I thought that, well, I could make this whole thing be a shim around defstruct: single inheritance was more than enough, and obviously I could store metadata on the property list of the type name as described above. And there's no nausea with multiple accessors or any of that nonsense.

But, somehow, I found writing a thing which would process the (structure-name ...) case of defstruct too painful, so I decided to go for the shim-around-defclass version instead. I even have a partly-complete version of the defstructy code which I abandoned. Another mistake.

I also decided that The Right Thing was to have the system support objects of rank 0. That constrains the underlying array representation (it needs to use rank \(n+1\) arrays for an object of rank \(n\)) in a way which I thought for a long time might limit performance.

Things I already knew

At any point during the implementation of this I could have told you that it was too general and the implementation was going to be too complicated for no real gain. I don't know why I made so many bad choices.

The whole process took weeks and I nearly just gave up several times.

The light at the end of the tunnel

Or: all-up testing.

Eventually, I had a thing I thought might work. The macro syntax was a bit ugly (that macro still exists, with a different name) but it seemed to work. But since the whole purpose of the thing was performance, that needed to be checked. I wasn't optimistic.

What I did was to write a version of my naïve gravitational many-body system using the new code, based closely on the previous one. The function that updates the state of the particles looks like this:

(defun/quickly step-pvs (source destination from below dt G &aux
                                (n (particle-vector-length source)))
  ;; Step a source particle vector into a destination one.
  ;;
  ;; Operation count:
  ;;  3
  ;;  + (below - from) * (n - 1) * (3 + 8 + 9)
  ;;  + (below - from) * (12 + 6)
  ;;  = (below - from) * (20 * (n - 1) + 18) + 3
  (declare (type particle-vector source destination)
           (type vector-index from)
           (type vector-dimension below)
           (type fpv dt G)
           (type vector-dimension n))
  (when (eq source destination)
    (error "botch"))
  (let*/fpv ((Gdt (* G dt))
             (Gdt^2/2 (/ (* Gdt dt) (fpv 2.0))))
    (binding-array-slots (((source particle-vector :check nil :rank 1 :suffix _s)
                           m x y z vx vy vz)
                          ((destination particle-vector :check nil :rank 1 :suffix _d)
                           m x y z vx vy vz))
      (for ((i1 (in-naturals :initially from :bound below :fixnum t)))
        (let/fpv ((ax/G zero.fpv)
                  (ay/G zero.fpv)
                  (az/G zero.fpv)
                  (x1 (x_s i1))
                  (y1 (y_s i1))
                  (z1 (z_s i1))
                  (vx1 (vx_s i1))
                  (vy1 (vy_s i1))
                  (vz1 (vz_s i1)))
          (for ((i2 (in-naturals n t)))
            (when (= i1 i2) (next))
            (let/fpv ((m2 (m_s i2))
                      (x2 (x_s i2))
                      (y2 (y_s i2))
                      (z2 (z_s i2)))
              (let/fpv ((rx (- x2 x1))
                        (ry (- y2 y1))
                        (rz (- z2 z1)))
                (let/fpv ((r^3 (let* ((r^2 (+ (* rx rx) (* ry ry) (* rz rz)))
                                      (r (sqrt r^2)))
                                 (declare (type nonnegative-fpv r^2 r))
                                 (* r r r))))
                  (incf ax/G (/ (* rx m2) r^3))
                  (incf ay/G (/ (* ry m2) r^3))
                  (incf az/G (/ (* rz m2) r^3))))))
          (setf (x_d i1) (+ x1 (* vx1 dt) (* ax/G Gdt^2/2))
                (y_d i1) (+ y1 (* vy1 dt) (* ay/G Gdt^2/2))
                (z_d i1) (+ z1 (* vz1 dt) (* az/G Gdt^2/2)))
          (setf (vx_d i1) (+ vx1 (* ax/G Gdt))
                (vy_d i1) (+ vy1 (* ay/G Gdt))
                (vz_d i1) (+ vz1 (* az/G Gdt)))))))
  destination)

And it not only worked, the performance was very close to the previous version, straight out of the gate. The syntax is not as nice as that of the initial, quick-and-dirty version, but it is much more general, so I think that's worth it on the whole.

There have been problems since then: in particular the dependency on when classes get defined. It will never be as portable as I'd like because of the unnecessary MOP dependencies³, but it is usable and quick⁴.

Was it worth it? May be, but it should have been simpler.

---

16 Apr 2026 11:01am GMT

By Robert Smith

All Elementary Functions from a Single Operator is a paper by Andrzej Odrzywołek that has been making rounds on the internet lately, being called everything from a "breakthrough" to "groundbreaking". Some are going as far as to suggest that the entire foundations of computer engineering and machine learning should be re-built as a result of this. The paper says that the function

$$ E(x,y) := \exp x - \log y $$

together with variables and the constant $1$, which we will call EML terms, are sufficient to express all elementary functions, and proceeds to give constructions for many constants and functions, from addition to $\pi$ to hyperbolic trigonometry.

I think the result is neat and thought-provoking. Odrzywołek is explicit about his definition of "elementary function". His Table 1 fixes "elementary" as 36 specific symbols, and under that definition his theorem is correct and clever, so long as we accept some of his modifications to the conventional $\log$ function and do arithmetic with infinities.

My concern is that the word "elementary" in the title carries a much broader meaning in standard mathematical usage. Odrzywołek recognizes this, saying little more than "[t]hat generality is not needed here" and that his work takes "the ordinary scientific-calculator point of view". He does not offer further commentary.

What is this more general setting, and does his claim still hold? In modern pure mathematics, dating back to the 19th century, the definition of "elementary function" has been well established. We'll get to a definition shortly, but to cut to the chase, the titular result does not hold in this setting. As such, in layman's terms, I do not consider the "Exp-Minus-Log" function to be the continuous analog of the Boolean NAND gate or the universal quantum CCNOT/CSWAP gates.

The rough TL;DR is this: Elementary functions typically include arbitrary polynomial root functions, and EML terms cannot express them. Below, I'll give a relatively technical argument that EML terms are not sufficient to express what I consider standard elementary functions.

To avoid any confusion, the purpose of this blog post is manifold:

1. To elucidate what many mathematicians consider to be an "elementary function", which is the foundation for a variety of rich and interesting math (especially if you like computer science).
2. To prove a result about EML terms using topological Galois theory.
3. To demonstrate how this result may be used to show an elementary function not expressible by EML terms.

This blog post is not a refutation of Odrzywołek's work, though the title might be considered just as clickbait (and accurate) as his, depending on where you sit in the hall of mathematics and computation.

Disclaimer: I audited graduate-level mathematics courses almost 20 years ago, and I am not a professional mathematician. Please email me if my statements are clumsy or incorrect.

The 19th century is where all modern understanding of elementary functions was developed, Liouville being one of the big names with countless theorems of analysis and algebra named after him. One such result is about integration: do the outputs of integrals look the same as their inputs? Well, what does "input" and "look the same" mean? Liouville defined a class of functions called elementary functions, and said that the integral of an elementary function will sometimes be elementary, and when it is, it will always resemble the input in a specific way, plus potential extra logarithmic factors.

Since then, elementary functions have been defined by starting with rational functions and closing under arithmetic operations, composition, exponentiation, logarithms, and polynomial roots. While EML terms are quite expressive, they are unable to capture the "polynomial roots" in full generality. We will show this by using Khovanskii's topological Galois theory: the monodromy group of a function built from rational functions by composition with $\exp$ and $\log$ is solvable. For anybody that has studied Galois theory in an algebra course, this will be familiar, as the destination here is effectively the same, but with more powerful intermediate tooling to wrangle exponentials and logarithms.

First, let's be more precise by what we mean by an EML term and by a standard elementary function.

Definition (EML Term): An EML term in the variables $x_1,\dots,x_n$ is any expression obtained recursively, starting from $\{1, x_1,\dots,x_n\}$, by the rule $$ T,S \mapsto \exp T-\log S. $$ Each such term, evaluated at a point where all the $\log$ arguments are nonzero, determines an analytic germ; we take $\mathcal T_n$ to be the class of germs representable this way, together with their maximal analytic continuations.

Definition (Standard Elementary Function): The standard elementary functions $\mathcal{E}_n$ are the smallest class of multivalued analytic functions on domains in $\mathbb{C}^n$ containing the rational functions and closed under

• arithmetic operations and composition,
• exponentiation and logarithms,
• algebraic adjunctions: if $P(Y)\in K[Y]$ is a polynomial whose coefficients lie in a previously constructed class $K$, then any local branch of a solution of $P(Y)=0$ is admitted.

What we will show is that the class of elementary functions defined this way is strictly larger than the class induced by EML terms.

Lemma: Every EML term has solvable monodromy group. In particular, if $f\in\mathcal T_n$ is algebraic over $\mathbb C(x_1,\dots,x_n)$, then its monodromy group is a finite solvable group.

Proof: We prove by induction on EML term construction. Constants and coordinate functions have trivial monodromy.

For the inductive step, suppose $f = \exp A-\log B$ with $A,B\in\mathcal T_n$, and assume that $\mathrm{Mon}(A)$ and $\mathrm{Mon}(B)$ are solvable. We argue in three steps.

Step 1: $\mathrm{Mon}(\exp A)$ is solvable. The germs of $\exp A$ are images under $\exp$ of the germs of $A$, with germs of $A$ differing by $2\pi i\mathbb Z$ collapsing to the same value. So there is a surjection $\mathrm{Mon}(A)\twoheadrightarrow\mathrm{Mon}(\exp A)$, and a quotient of a solvable group is solvable.

Step 2: $\mathrm{Mon}(\log B)$ is solvable. At a generic point $p$, germs of $\log B$ are parameterized by pairs $(b,k)$ where $b$ is a germ of $B$ at $p$ and $k\in\mathbb Z$ selects the branch of $\log$. A loop $\gamma$ acts by $$ (b,k)\mapsto\bigl(\rho_B(\gamma)(b), k+n(\gamma,b)\bigr), $$ where $\rho_B(\gamma)$ is the monodromy action of $\gamma$ on germs of $B$, and $n(\gamma,b)\in\mathbb Z$ is the winding number around $0$ of the analytic continuation of $b$ along $\gamma$. The projection $\mathrm{Mon}(\log B)\to\mathrm{Mon}(B)$ onto the first component is a surjective homomorphism. Its kernel consists of the elements of $\mathrm{Mon}(\log B)$ induced by loops $\gamma$ with $\rho_B(\gamma)=\mathrm{id}$, which then act only by integer shifts on the $k$-coordinate. Let $S_B$ be the set of germs of $B$ at $p$. For each $b\in S_B$, such a loop determines an integer shift $n(\gamma,b)$, so the kernel embeds in the direct product $\mathbb Z^{S_B}$. In particular, the kernel is abelian. Hence $\mathrm{Mon}(\log B)$ is an extension of $\mathrm{Mon}(B)$ by an abelian group, and extensions of solvable groups by abelian groups are solvable.

Step 3: $\mathrm{Mon}(f)$ is solvable. At a generic point, a germ of $f=\exp A-\log B$ is obtained by subtraction from a pair (germ of $\exp A$, germ of $\log B$), and analytic continuation acts componentwise on such pairs. This gives a surjection of $\pi_1$ onto some subgroup $$ H \le \mathrm{Mon}(\exp A)\times\mathrm{Mon}(\log B), $$ and, since $f$ is obtained from the pair by subtraction, this descends to a surjection $H\twoheadrightarrow\mathrm{Mon}(f)$. So $\mathrm{Mon}(f)$ is a quotient of a subgroup of a direct product of solvable groups, hence solvable.

The second statement of the lemma follows: an algebraic function has finitely many branches, so its monodromy group is finite; a solvable group that is finite is, well, finite and solvable. ∎

Remark. This is the core of Khovanskii's topological Galois theory; see Topological Galois Theory: Solvability and Unsolvability of Equations in Finite Terms.

Theorem: $\mathcal T_n \subsetneq \mathcal E_n$.

Proof: $\mathcal E_n$ is closed under algebraic adjunction, so any local branch of an algebraic function is elementary. In particular, a branch of a root of the generic quintic $$ f^5+a_1f^4+a_2f^3+a_3f^2+a_4f+a_5=0 $$ is elementary.

Suppose for contradiction that at some point $p$ a germ of a branch of this root agrees with a germ of an EML term $T$. By uniqueness of analytic continuation, the Riemann surfaces obtained by maximally continuing these two germs coincide, so in particular their monodromy groups coincide. The monodromy group of the generic quintic is $S_5$, which is not solvable. But by the lemma, the monodromy group of any EML term is solvable. Contradiction.

Hence $\mathcal T_n$ is a strict subset of $\mathcal E_n$. ∎

Edit (15 April 2026): This article used to have an example proving that the real and complex absolute value cannot be expressed over their entire domain as EML terms under the conventional definition of $\log$. I wrote it to emphasize that Odrzywołek's approach required mathematical "patching" in order to work as intended. However, it ended up more distracting than illuminating, and was tangential to the point about the definition of "elementary", so it has been removed.

14 Apr 2026 12:00am GMT

A couple of weeks ago I released FSet 2.4.0, which brought a CHAMP implementation of bags, filling out the suite of CHAMP types. 🚀 FSet users should have a look at the release page, as it also contained a number of bug fixes and minor changes.

I've since released v2.4.1 and v2.4.2, with some more bug fixes.

But the big news is the book! It brings together all the introductory material I have written, plus a lot more, along with a complete API Reference chapter.

FSet is now in the state I decided last summer I wanted to get it into: faster, better tested and debugged, more feature-complete, and much better documented than it has ever been in its nearly two decades of existence. I am, of course, very much hoping that these months of work have made the library more interesting and accessible to CL programmers who haven't tried it yet. I am even hoping that its existence helps attract newcomers to the CL community. Time will tell!

13 Apr 2026 6:21am GMT

Are you ready for another challenge? We're excited to host the second yearly edition of our treasure hunt at FOSDEM! Participants must solve five sequential challenges to uncover the final answer. Update: the treasure hunt has been successfully solved by multiple participants, and the main prizes have now been claimed. But the fun doesn't stop here. If you still manage to find the correct final answer and go to Infodesk K, you will receive a small consolation prize as a reward for your effort. If you're still looking for a challenge, the 2025 treasure hunt is still unsolved, so舰

29 Jan 2026 11:00pm GMT

If your non-geek partner and/or kids are joining you to FOSDEM, they may be interested in spending some time exploring Brussels while you attend the conference. Like previous years, FOSDEM is organising sightseeing tours.

26 Jan 2026 11:00pm GMT

With FOSDEM just a few days away, it is time for us to enlist your help. Every year, an enthusiastic band of volunteers make FOSDEM happen and make it a fun and safe place for all our attendees. We could not do this without you. This year we again need as many hands as possible, especially for heralding during the conference, during the buildup (starting Friday at noon) and teardown (Sunday evening). No need to worry about missing lunch at the weekend, food will be provided. Would you like to be part of the team that makes FOSDEM tick?舰

26 Jan 2026 11:00pm GMT