Recent Pandemic Scares

There have been several pandemic scares in the past few years. We had the meningitis episode in the UK (Kent, March 2026). Then the cruise ship debacle (April–June 2026). Right now, the plague situation in Irkutsk (October 2026) is unclear. The future trajectory is blurry. Information noise is making it hard to tell what foreign actors are doing, and it is possible that we get more scares like this in the future. There are debates around whether we should aerosolise Ebola for research purposes. There are quite a few routes to a pandemic risk.

How can I help to reduce the risk of engineered pandemics? There are lots of unknowns, and it is unclear who is doing what. At the moment, I'm just a nobody who happens to blog about biosecurity. Is there any way I could make a meaningful contribution? One way that I think I can help is to write more about questions that I think the public is ignoring. And then maybe try to tease out an answer.

One question is what exact information set we need to make decisions during a crisis.

The first instinct of a policy maker might be to try and collect lots and lots of data. After all, more information is usually a good thing. But what data do we collect? Pandemic prevention is an undefined problem with so much uncertainty, and it is unclear what data might help us make better decisions. For example, one might imagine a scenario where we have a state of the art intelligence system that warns us when pandemic risk is more likely. But what exactly would be on those screens? Wastewater samples? PPE stockpiling lists? Sure, we could try to collect as much data as possible, but data collection has a cost.

Because of that, I'm focused on figuring out questions that point us to what useful data is missing. In a perfect world, the amount of data a government could collect is infinite. But we live in a world with human and financial constraints, which means we need to ask what data is actually useful for our aims.

In this essay, I will argue that estimating the immediate supply of elastomeric respirators is an important question, and offer a way to estimate it with some bounds in Greater London (tldr; 2,000 to 20,000 immediately available respirators, but it's very uncertain).

A Brief Taxonomy of Workers During a Pandemic

To motivate this, let's ask how we would reason about society in a pandemic scenario. One approach might be to triage, which is something that hospitals do in an emergency. A naive triaging strategy would be to divide society into two blurry categories, and then make decisions based on these two categories.

The first category would be the set of critical workers. It is unclear what the exact set of critical workers is. But, from just human intuition, it should at least include critical healthcare, electricity networks, agriculture, water sanitation plants, logistics and government.

The second category is non-critical workers; people who don't really fit the bill above. But as I will explain, the boundary is blurry.

First, it is unclear what exactly constitutes the set of critical work. It is almost certain that a doctor is a critical worker. It is almost certain that a water plant manager is a critical worker. It is almost certain that an electrical grid maintenance officer is a critical worker. On the other hand, a professional e-sports gamer is almost certainly not a critical worker. It is morally fine to not be a critical worker (I am not), it's just that in an emergency scenario this division might be useful.

Annoyingly, there is also a huge grey area in and between critical and non-critical workers. Consider truck drivers. They are essential to society functioning. However, in a pandemic scenario, which truck drivers are essential? Is it just the ones carrying food? What about medical equipment? Are the people who run financial infrastructure important? What about government and leadership? Do we need to give the department of culture and tourism critical worker status, or just defence and healthcare?

What a critical worker actually is in a full-blown crisis scenario is unclear. During the covid pandemic we had some guidance from the UK government here, but again this list doesn't really make the distinctions required in a full-blown scenario. GPT Astra estimates a range of 7 to 11 million, but again this number could be orders of magnitude wrong because of how logistical systems are so entangled.

Secondly, it is unclear which critical workers require person-to-person contact. If you considered the government as a part of the critical workforce, it's also possible that they could function entirely remotely. We could have the president or prime minister acting in a clean zone and governing through a video conference. It might be possible that groups could have some VR way of interacting with each other better than through a laptop screen. On the other hand, it would be impossible to be a healthcare worker without in-person contact.

If a pandemic was only airborne transmissible, we might have a way to make a system such that truck drivers may never need to be in person-to-person contact. For example, we could change shifting schedules so that loading times in big stores never overlap.

For the people that are not critical workers, it's also likely that they will eventually need to have contact with other humans during a pandemic. To survive, they need to go to stores to buy food. They need to go to doctors for healthcare. They should probably go outside to exercise. On the whole though, if a pandemic was catastrophic, it's possible that we could use technology to find a way to get the public to avoid going outside. For example, we might have robots do deliveries like they do in Milton Keynes (?). We could transport a treadmill or walking pad to each household so that people could get exercise.

And so this makes me think that we should prioritise one subset of people when it comes to pandemic preparation: critical workers who require in-person contact. The number of such people in the UK is unclear, and probably depends on logistical assumptions. I would like to try and estimate this in a different post.

Would elastomeric respirators satisfy critical worker need?

What is inevitable though is that critical workers would require masks of some sort. In my previous post, I bought and talked about elastomeric respirators. Elastomeric respirators are the dust masks that tradespeople wear. They have strong filters, and a rubber seal around the face to ensure a tight fit. They are also reusable. This potentially makes them better protection in the long run. The CDC says that they are likely to be at least as effective as N95s.

The dominant uncertainty though is that their effectiveness is heavily dependent on their fit quality. It could be possible that, on average, based on fit, N95s are better. But including average number of use and degradation, it's unclear.

But suppose that on average, the reusability does make elastomeric respirators more effective. So this leads me to the question...

How many elastomeric respirators would there be available in a pandemic?

Elastomeric respirators in the UK would probably be housed in warehouses, government stockpiles, or retail stores. DIY stores keep them in stock, since tradespeople use them as dust masks. As for warehouses or government stockpiles, it's hard to guess where those are, since this is likely to be confidential information. Warehouses would be owned by private companies, and so public-facing data is not available on how much stock mask companies would have.

It could be the case that government or warehouse stockpiles never get used. Suppose we had an extremely dangerous pandemic which was highly transmissible. We would then probably have mass paranoia, like from a psychological aftershock from Covid. In this case, a pandemic crisis might cause our logistical systems to fail. If so, private companies might be worried about their future businesses, and might elect not to distribute PPE if it's too expensive. On the government side, I have no visibility on how the government would plan to distribute their own stockpiles, and so I make no judgements there.

In that case, we have a worst-case assumption in case of logistical failure; the elastomeric respirators that are immediately available would only be those available in retail stores at that time. This assumption might be too strict for many reasons. For example, it could already be the case that hospitals and other places of work have their own PPE stockpiles. It's not clear to me how much NHS trusts keep reusable elastomeric respirators, so for now let's assume there are none.

Counting what's in London's stores

If stores are the only places which have elastomeric respirators, then how many elastomeric respirators are in stock, in retail stores, right now in London? To begin to solve this problem, I leaned heavily on AI to build some datasets that would help inform a subjective estimate of how many there are. Claude code seems particularly suited to this flavour of work.

First, I got Claude Fable to use OpenStreetMap data for the major hardware stores in greater London. The stores it got seem sensible; the stores it identified are Screwfix, B&Q, Arco, Wickes, and a handful of small independent stores. The image below is a generated map of those DIY stores in the greater London area: the colours of the dots are meant to show the rough probabilities of that DIY store actually carrying an elastomeric respirator.

And then I just got it to estimate the number of elastomeric respirators by having it look at the websites, and then estimating the low to high bounds for each one, based on inventory space and a best guess. Looking at the estimates, these seem reasonable. I've been to my local Screwfix and it seems reasonable that they stock probably a hundred units elastomeric respirators at a given time.

Multiplying the lower, central and upper bounds by the number of stores on OpenStreetMap gives a lower and upper bound estimate on the number of elastomeric respirators currently available in retail stores in Greater London. It gives us a range of 2,000 to 20,000.

Caveats

Ok, so let's think about this number of 2,000 to 20,000 respirators carefully. We might be being too generous. Even if these estimates were valid, it is possible that zero stock goes to critical workers. In a panic scenario, it is plausible that everyone lines up for elastomeric respirators and gets them first before critical workers. That would render this estimate pretty useless.

Then we have the dominant uncertainty, which comes from the point estimates of how many masks are kept at each store. Claude helped me guess some bounds but we won't really know until we ask. Maybe there's an efficient sampling method, where we could go to a subset of stores and then Bayesian update our guess. Or maybe we could get a local LLM to cheaply and continuously poll DIY store stocking lists to keep a monitor of where the elastomeric respirators are.

The second uncertainty I am worried about is the quality of OpenStreetMap data. Maybe Claude did not actually get the complete list of DIY stores. I can't think of any other significant DIY stores in the UK. But maybe art stores sell elastomeric respirators? What about those homeware stores?

But for now, let's draw a mild conclusion. Even taking the upper bound of uncertainty, 20,000 does seem low and it is mildly worrying. It seems likely that Greater London would need more elastomeric respirators, conditional on them being better than N95s. If you did index on elastomeric respirators being important, and these estimates were correct, then it's also surprising how relatively cheap they are to double in capacity.

Is there a way to circumvent this problem entirely? Well one thing we could do is just encourage people to buy elastomeric respirators over time. People buy condoms 'just in case', and so why couldn't we do the same for elastomeric respirators? And given how dependent the efficacy of respirators is on training, shouldn't there be public service announcements and schools training people how to put these on?

I heard of the quarantine situation in Irkutsk a few hours ago. The quarantine involves a pathogen of some sort. There are photos of staff in hazmat suits on the street. There are estimates of hundreds of people in quarantine. The incident seems to be related to the Antiplague Institute, although that is unclear. The nature of the pathogen is unknown. It is unknown if it was a lab leak. It is unknown if it is plague, what type of plague it is, or if it is an engineered strain of plague. The transmission mechanism is also unknown.

The situation remains unclear. I have no reasons to trust completely what media is saying, nor what people on Twitter are saying. Reports from Russia have been heavily edited. Russian news is incoherent and confusing. I am not confident enough to say things publicly on Twitter or Substack about the incident; I do not want to cause harm by saying the wrong thing. But also, I have tried to make people aware that there is a situation.

Because of this uncertainty, there are two actions I have taken. These actions are cheap and don’t cause harm. They pertain to my own sphere of influence, and I am comfortable executing them.

First, I have dug out my elastomeric respirator that I got from my local ScrewFix. Elastomeric respirators have a rubber seal and are reusable. This makes them more effective than N95s. I am to get another one tomorrow for my girlfriend. One uncertainty is what size of mask would be appropriate for her, so I will get her multiple sizes.

Secondly, I got ChatGPT to make a list of provisions for a month for a stockpile scenario. The list is reasonable, although I am worried about the lack of fruit and vegetables. I am not a fan of tinned fruits but whatever.

I live very close to a grocer, so I spent 50 pounds on what I could carry. Everything that was in this stockpile list was available at the store. I didn’t get the whole list, but aim to buy more tomorrow. Admittedly it was a bit of a struggle carrying what I bought. The whole process could have been smoother. I spent a lot of time debating in my mind whether I should even bother to go. So if this thing does blow over, I need to have a better stockpile ready to go.

I also thought in my mind about where I would go during a situation like this. For now, I’ve decided to stay at home. Uncertainty is high, going to an airport would increase entropy of a situation. It would also increase infection risk.

That being said, my car does have fuel and is ready to go. I live in London, but I have an option to go to a less crowded place. Overall though, I loathe to attempt to leave my house. If I went and my car broke down, I risk being stranded in a situation that could get rapidly worse. I will likely increase my infection risk if I was caught in that situation. So for now, I chose to stay at home.

But sometimes I have a lot of fun things to try, and I want to optimise my scientific choices. If you have experiment ideas that seem equally promising, how do you select which ones to start with?

One way might be:

1. List out all of your experiments.

2. Rank them on different factors.

3. For each experiment, average the rankings.

4. Start with the ones with the highest average ranking.

The initial guess is unlikely to be right, but it's better than guessing. A few months ago, it would have been unreasonable to do this because of the work it would take to rank many factors across experiments. But now we have LLMs. In my experience, they have at least been able to estimate costs well.

Here is a preliminary prototype of what I made to estimate the average ranking of each choice.

I fed the following factors for Claude to rank. I got it to rank interestingness from what I’ve written about before.

Cost

Most independent scientists are self-funded, myself included. Probably less than 5% of us with self-funded home labs spend more than $1000 a month. Most of the community is constrained by cost. Even for those who aren't, it is worth getting bang for your buck. Even though hardware costs are decreasing, the cost of living and real estate are increasing. Therefore, personal savings are useful to have in a world with intense debate around LLMs and jobs. All the more reason to keep costs low.

This gives us constraints to work with, since indeps have more reason than other labs to minimise cost. But constraints often give rise to creativity! Again, this may give us an edge.

Feasibility

An experiment is less feasible if it is long and complex to do. Oftentimes this applies to biological experiments because of contamination risk (although this is something I am trying to solve). If two experiments are equally interesting, then shouldn't you want to do the simpler experiment? A long and complex experiment is likely to give more uncertainties and errors than a simpler one. Uncertainties are not necessarily bad - I have talked about type B uncertainty in a previous post - but the experimenter needs to put effort into communicating both measurement and subjective uncertainties.

Interestingness

Interestingness can be defined however you'd like. This factor is likely to be the only one where an LLM can't really help, and you should rank based on your feelings. Alternatively, you can ask LLMs to proxy you from your previous writings. For me, things are interesting when there is beautiful mathematics involved. For example, the dripping water experiment uses methods from chaos theory.

Experimental uncertainty

When taking fine measurements, or using complex sensors, it is likely that there is going to be uncertainty involved. There is likely to be measurement uncertainty, such as from the calibration of your digital calliper or your thermal probes. There are also subjective uncertainties that are less obvious. For example, the well-mixedness assumption in a thermal experiment may or may not hold true. There may be turbulent effects in your fluids experiment that affect what you want to study. There may be unknown unknowns that you can't even quantify, but that you suspect. Given your equipment, it is prudent to minimise experimental uncertainty where you can.

Moral expected value

It would be bad if your science could be used for bad things, so experimenting with things that are obviously bad is bad. I did work on DIY biosecurity measures because I didn't think it would be harmful. There was a chance that the work might even have been useful.

That being said, most science is dual-purpose and initially feels morally neutral. In those cases, it is unclear what the long-term moral outcomes of those scientific actions are. Here, the experimenter is in a situation of moral uncertainty, which is a topic I don't think is written about enough. We usually talk about how to act in cases where we know what the right and wrong things are. But the decision theory for cases where right and wrong are unclear, or where moral frameworks are not obvious, is not that developed.

Contrarian-ness

Experiments that have the potential to disprove a well-known dogma or paradigm always feel strong. I have more conviction that if you’re going to spend time on stuff, then it’s probably worth trying to find something that would up-end literature in some way. Kuhn writes about this in The Structure of Scientific Revolutions.

For example, senior academics in Cambridge wear gowns to dinner. Do you need to do that to be a scientist? Obviously not. However, there are other things that blur the lines between doing good science and appearing to do good science. Peer review is likely to be useful in some ways, and genuinely positive for the scientific process. Feedback from others helps in spotting mistakes. But my academic friends find frustrations with other parts of the process. Could peer review simply be the best option out of a set of bad options? It's unclear, and first-principles thinking is required to untangle signal from noise. We think about this at the Independent Science Society.

I've been reading books on the philosophy of science to understand what good scientific reasoning really is. I wrote about my method for reading things in my previous post. I've been following that method for Peter Godfrey-Smith's Theory and Reality (2003) and Karl Popper's The Logic of Scientific Discovery (1934, English translation 1959). Admittedly, the style of these philosophy books is hard to digest. They tend to include a lot of propositional logic. I aim to simplify them and give my thoughts here.

First, Godfrey-Smith has convinced me that the word 'science' is ill-defined. Several fields have both entered and left the perception of being scientific. Theoretical physics in the 1950s was unmistakably a science geared towards understanding particle physics. Today it's less clear. Tests of string theory need energies far higher than the Large Hadron Collider can provide. Sabine Hossenfelder, in Lost in Math (2018), has argued that some theoretical physics departments now focus on inspiring new mathematics, seeking aesthetics instead of empirical results. On the other hand, economics and the social sciences seem to have taken on semi-scientific status. They have incorporated mathematics, use weird things called p-values and t-tests, and have put the word 'science' in their names.

So it's not clear what the meaning of science actually is. The word is probably abused. A better question, then, is how one can model the natural world. Godfrey-Smith's book is a review of such methods. The chapters are names of philosophies that I have heard of but have never taken the time to properly understand: empiricism, logical positivism, induction and Kuhnian revolutions.

Empiricism is the philosophy that all knowledge about the world is born of experience. In this framework, knowledge is created downstream of observation. Observation is done through the senses: sight, sound, touch and taste. The senses can be enhanced through instrumentation, like the microscope. In Godfrey-Smith's view, the difference between the scientific method and everyday empiricism is the detail and extensiveness of the practitioner's observations. This separates a scientist from someone who casually notices that you shouldn't touch a boiling cauldron. Da Vinci painstakingly drew what he saw. Darwin wrote down everything he noticed in the Galápagos Islands. Mendel collected a lot of data about peas.

Empiricism as a method is encouraging because there is no qualitative difference between a scientist and a non-scientist. It is merely a matter of degree. Anyone can aspire to the scientific rigour of the legends of past centuries. I aim to look closer at what I am doing, and record my observations in greater detail.

Pure empiricism feels different from knowledge about the world being born of logic. In mathematics, I can claim that 2+2=4 without any prior experience. And sometimes mathematically true things can later be confirmed by experience. The discovery of antimatter was born of Dirac's mathematical arguments. Similarly, the properties of black holes were predicted from Einstein's equations on mathematical grounds long before the LIGO experiments confirmed them. Being trained as a mathematician has biased me in favour of this style of thinking.

That being said, I'm starting to accept that a lot of good can be done from experience. Theories will ultimately turn out wrong in some way. And even if the underlying theory is replaced in the light of new evidence in the future, the observations can still take you far. Caloric theory was used to explain thermodynamics well before Boltzmann. The miasma theory of disease turned out to be wrong, and yet it was still effective at preventing deaths before germ theory was discovered.

The book argues that whilst empiricism may feel obvious as a theory, we have plenty of examples where humans have acted contrary to experience. History has had human sacrifices and witchcraft. Godfrey-Smith references Carl Hempel's account of Ignaz Semmelweis's ousting from Viennese hospitals when he tried to push his empirical study of hand washing preventing deaths from childbed fever. We have ideologies that prevent us from looking at the best evidence. Isaac Asimov's short essays in The Roving Mind (1983) on creationism in education serve as a particularly good example of humans acting against experience.

Sometimes we might act contrary to experience because of flawed statistical reasoning. In The Art of Uncertainty (2024), David Spiegelhalter lists several cases of mothers being tried for the deaths of their children due to expert witnesses and lawyers arguing on the basis of 'coincidence', rather than physical evidence.

In any case, I've increased my prior that the phrase 'see it to believe it' is useful. A purple duck is a purple duck, baby!

Books mentioned

• Peter Godfrey-Smith, Theory and Reality: An Introduction to the Philosophy of Science (University of Chicago Press, 2003)

• Karl Popper, The Logic of Scientific Discovery (1934; English edition 1959)

• Sabine Hossenfelder, Lost in Math: How Beauty Leads Physics Astray (Basic Books, 2018)

• Carl Hempel, Philosophy of Natural Science (Prentice-Hall, 1966), on Semmelweis

• Isaac Asimov, The Roving Mind (Prometheus Books, 1983)

• David Spiegelhalter, The Art of Uncertainty (Pelican, 2024)

In an experiment, the selection of acceptable temperature bands is a subjective choice made by the experimenter. For example, one might choose to say that a range of +- 1C might be acceptable for a biological growth rate experiment. A temperature range of +- 10C might be acceptable for a gravitational experiment. And on top of that, there is also uncertainty in the measurement of that temperature; it could be calibration uncertainty, or the declared uncertainty from the equipment.

But there could also be deeper causes of uncertainty at hand, which may not be obvious unless we thinking about them actively. For example, if you measure the temperature of a room, and there is a source of heating, then a point estimate of the temperature of the room may not be sufficient. This is because the room isn't well mixed, and there could be a temperature fluctuations throughout the room. I had to face a similar type of uncertainty when measuring the concentration of smoke particles for my air purification experiments Or suppose that you are heating up some liquid, and you want to measure the temperature of that liquid. In the process of heating, there is also likely to be a temperature gradient there, and you can't assume even-ness in temperature through out.

Again, these uncertainties may not matter, and their relevance feels like a subjective choice for the experimenter. In many experiments, temperature uncertainty is unlikely to matter at all; if you were looking at the dynamics of a double pendulum, who cares about what its temperature is! But on the other hand, there are examples of temperature variations possibly causing flukes in historical experiments, like in Fleming's discovery of penicillin. In any case, if temperature likely bears even so much as a marginal effect, then temperature ranges should be declared as a relevant uncertainty in an experiment. It feels that a quality of a skilled experimenter is nailing down the suite of subjective uncertainties that may be overlooked by others.

In my last post I tried to to control the temperature of the bioreactor David Jordan made for me. And again, it's boring, but controlling environment and calibrating my equipment remain to be the biggest technical challenges. My solution to this was to put the bioreactor in a mini-fridge and drill some holes, and use an Inkbird to control the ambient temperature of the fridge at 21C. I would then use the heating element in the bioreactor to control its actual temperature.

And so since the bioreactor had a heating element, I wanted to see if I could calibrate it at different set-point temperatures between 21C and 27C. In my last post I mentioned how the bioreactor had an api to control its temperature.

So, I let Claude try to write a script to control the temperature with some error around different setpoints. I made the judgement to let AI do this one because I'm no expert in temperature calibration, and the problem itself was a fairly standard one (just some basic optimisation and control). And I guessed that it would be good enough to calibrate things at around +-1C. I expected that several experiments would be necessary for it to learn how to get the calibration right.

This was the initial run that Claude did. In the first run, you can see that kept overshooting when it went to increase the temperature, and so it took time for the fridge to cool it back down. The dotted line is the setpoint, and the bottom graph shows the heating duty. Again, bear in mind that this is only the temperature at where it's measured, there's no guarantee that this was uniform in the actual vial.

In the next run it was still overshooting at the different temperatures.

In the run after that, it got the bounds a little tighter, so all I had to do was just tell Claude to use that as feedback to try to make the cycle tighter.

Then in the next run it was working pretty good, within +-, which you can see in the oscillations 1C

And this was the final run - I have suspicions that this one was overfit, and wouldn't really generalise to other situations. More on that later..

The final that set up Claude chose to do was a feedfoward duty cycle control. And the calibrations above lead to the following parameters.

Here is some extra stuff that it added on the implementation, including a safety break if the temperature gets too hot. The actual code is in the links on my other website.

Thanks as always to David Jordan for the support.

Links

• Write-up on the site

• Controller code

• Findings

• Session transcript

One of the chapters mentioned the Lorenz water wheel, an example of a system that is in-principle deterministic, but exhibits non-periodic oscillations that appear random. Another property of this system is that if you traced out its phase space, by plotting the value of observable quantities in real time, you'd find that the line you trace out never overlaps on itself. Harvard did a real life build of this experiment here.

This is a simulation of one made by Claude

I find such demonstrations of chaotic phenomena really interesting because they seem to happen in this weird area of physics that produces random-like behaviour from deterministic laws. People in modern times might like to call it emergent complexity, other people call it chaos, but I personally think that each different kind of system that exhibits behaviour like this is unique and cool, so theres no point giving a single label! Other things that make complex behaviour from simple rules are cellular automata like Conway's game of life.

To be clear, there is overwhelming evidence that nature, in some aspects, is genuinely random, in the deepest sense of that word. Not like the complexity that causes a dice roll to appear random; I mean genuinely indeterminate. To the best of our knowledge, quantum mechanics is fully indeterminate - if you prepare an electron in a neutral state, then you would observe it either spin up or spin down with equal probability. But just because the micro-scale atoms indeterminate through quantum mechanics, it doesn't mean that we can't predict things. Thermodynamics allows us to make general rules from aggregates of many atoms, like the ideal gas law.

Chaos, on the other hand, works in the opposite direction. Classical physical laws like Newton's theory of gravitation and relativity are determinate in their formulation. But from them, we still can get chaotic phenomena - the Lorenz water wheel, the three body problem, and much more, which behave essentially at random even though they obey clockwork physical laws. And so, because we so far have not been able to accurately forecast chaotic things, there is subjective uncertainty that humans have to deal with when it comes to forecasting chaotic systems. This subjective uncertainty is distinct from the genuine indeterminacy that we think govern quantum systems (although admittedly, its hard to distinguish the two).

This mix of the subjective, observer dependent view of uncertainty alongside objective physics is something I want to think about a bit more. I've been reading more about Bayesian probability and how subjective probabilities are involved in uncertainty of measurement. I also learned recently from David Spiegelhalter's book *The Art of Uncertainty* that institutes in metrology (the science of measurement) also allow for the inclusion of something called Type B uncertainty, an uncertainty that comes from judgement rather than from repeated measurements. I would like to get a handle about distributions of observables in chaotic systems. Indeed, Lorenz himself was a meteorologist!

I am trying to find demonstrations of such complex phenomena on a table top. I've written a list of cool experiments which might fit this kind of bill in a previous post. In the best case, maybe I might be able to discover some dynamics that are overlooked. Failing that, it's still cool to try and find stuff that can be used as a demonstration. For example, the traditional chaos demonstration with rotating buckets of water feels quite impractical.

In my last post I got claude to make a list of similar kinds of experiments using the list of equipment that I assembled in my lab. One of the things that caught my eye was observing convection currents and the plumes that you get when you apply a temperature gradient to a fluid. Previously I visually looked at Rayleigh–Bénard convection cells with mica powder and silicone oil, but I wanted a more quantitative way to track convection phenomena, so I tried this experiment.

Conduction is when heat is carried across stationary matter, like a metal. Convection is when heat is carried by parcels of moving matter, which happens in fluids. When the heat gets high enough, things become turbulent and unpredictable. But I wanted to straddle an area that wasn't too crazy, with some dynamics that are regular but not too regular. So I wanted to see if I could measure what I think are convection plumes that would come with slowly heating up a beaker of water. You apply heat at the bottom, and then you have parcels of water that are carried in these plumes which rise due to the decreased density of water, which causes the temperature measured to fluctuate.

I think this is cool because we always assume things heat up evenly when you apply heat to something. But that's not true, there seems to be a whole set of indeterminate phenomena that you can get in as simple as heating a cup of water! Biosecurity / building engineers / weather people / chefs take note. I also think there is this plume-type behaviour that you get in the Earth's crust, but I don't know too much about that.

An infrared camera is too expensive for me. So the experiment I decided to test if plumes occur was a lot cheaper and a lot simpler. I first got a pair of thermocouples, and then wired them up to a set of adafruit thermocouple chips. Thermocouples convert temperature into a differing electric current, and are one way of probing temperature. And then I decided to put one above the other in a heated beaker and then try to record the temperature difference. If there was a plume, we would see a temperature dip as the plume dissipates. Here is a simulated animation of the convection plumes that I wanted to capture;

And here is what I actually ended up building

Here are the results when I ran the experiment. The first graph shows the temperature of the thermocouples separately, and the second graph shows their difference. The blue line is the temperature of the bottom thermocouple nearest to the heater, and the red line is the one at the top.

In the diagram, you can see the oscillation in the temperature difference. It wangs around, even becoming negative, showing that the tempeature at the top at some points becomes higher than at the bottom.. This is evidence for what I think is convective behaviour, because otherwise, we should see the temperature difference being mostly constant. Whilst the amplitude of the oscillations look quite janky, the period looks kind of regular, which I think is cool, but there is no real pattern (note to self to check on this later - maybe there are cool patterns to be found here).

There are some subjective uncertainties here though. Are these spikes the result of some noise or systematic error? Seems unlikely, because the noise in the initial measurements when the heating was off is small, but who knows. Also, something that could be causing the oscillations could be the heating duty cycle of the heater itself - after all, it's a cheap heater that I got from China. So next time I'm going to try and check this with open flames under a candle.

To our knowledge, this discord is one of the biggest networks of independent scientists in the world, where we have people doing everything from the microscopy of inks, to reselling open source lab equipment, to detecting muons, to hosting podcasts. Currently there is no Royal Society-like space for people to just hang out and chat about their experiments. Within the discord we also make an active effort to connect them to people doing similar things. We take no credit at all for the work done in our circles, nor do we require any attribution. We just want to see cool stuff happen.

I have met quite a few independent scientists as part of my role at the Independent Science Society, on discord, or Substack or otherwise. In an effort to map the frontier of independent science, I am excited to write more reviews of the stuff members are up to. As empiricism and experimentation become cheaper to do, it feels like there should be work to map out the frontier of what's going on in our circles. I want to write these reviews because I hope that they could act as signposts for people to collaborate with each other, or offer constructive feedback, or to just build a community.

These reviews will be my own feelings about their work, and all mistakes in representation are mine, and I really encourage you to check out the links yourself.

Featuring

One such person I wanted to review is Tiffany Longfield. Again, neither the society nor I take ANY credit for Tiffany's work; we just wanted to share it.

Tiffany Longfield is an ex-Cornell PhD, ex-NASA, materials scientist and analytical chemist. In a lab at home, Tiffany does optical microscopy of a wide range of complex materials phenomena. The tools of choice are a stereomicroscope, which allows the user to easily place samples on a surface and zoom in, as well as an array of compound microscopes.

I am amazed at how much Tiffany has been able to do with these tools. Most recently, Tiffany's work has involved using a microscope to film the dynamics of inks and dyes, and the material failure of commercial sanitary pads. But there is a whole library of other stuff that Tiffany has observed, like videoing cryogens, the fluid turbulence of coffee in milk, mixing, and crystallisation. Tiffany posts results and videos on Reddit, TikTok, Substack, and also shares results on the Independent Science Society discord.

Over here at the society, we have been excited about folks who centre their science around experiment and observation at low cost, microscopy being one of them (temperature and gas probing are other forms of observation we are also excited about). I am personally excited about Tiffany's use of general microscopy because I never realised that it was such a versatile form of observation, and how much you can do with it - one can watch things from biological behaviours all the way to colloidal particles in fluids, all the way to the effect of cryogens. In addition, it is easy to record things, and we have more reason to expect that video as a form of data and evidence is going to get more important - there is a lot of data you can get out of video with image processing algorithms.

One of the streams of work that Tiffany does is observing the material and optical physics of inks and dyes. This field is rich with striking visual phenomena such as sheening, crystallisation, and the interaction of inks on substrates. For example, how does ink look as it dries on the different types of cellulose surfaces on paper? After reading Tiffany's posts on Reddit I was surprised to learn that the theory behind some behaviours in inks is not very well understood.

Here is a catalog of some stuff from Reddit posts. My words can't really do justice to how unexpected and visually striking some of these are, so here are a bunch of links from Tiffany's website:

• Inks on various substrates under the microscope (figures of dried ink, video of drying inks)

• Kiwi Inks’ Treasures of Atlantis drying timelapse under the compound microscope

• Wet Herbin Emerald de Chivor ink under the compound microscope (reflected/transmitted lighting)

• Various dried fountain pen inks on glass, acrylic substrates under the compound microscope

• Pilot Iroshizuku Kon-Peki Ink undergoing Marangoni effect under the stereo microscope

Microscopy experiments at home have been historically expensive, but I expect this to change due to a more liquid market in second hand scientific equipment and decreasing hardware costs. The philosophy of observing science as an act of spectacle is a fruitful approach that I also feel has been neglected, and I am happy to see Tiffany carrying on this tradition that was the de facto way of presenting scientific evidence in the Renaissance period. After all, all that Galileo did to prove that the moon was imperfect was to show his peers the moon through the newly invented telescope.

Tiffany was also nice enough to show me live footage of drops of water freezing in a gradient under the effects of cryogens. I find this exciting because materials like these are readily available, and yet the work shows a whole world of interdisciplinary science that seems to have been ignored from a 'come and see it!' perspective.

Tiffany has also observed a range of complex behaviours in a range of fluids that can be observed with a microscope. I have been particularly enamoured with the images of tendrils of brilliant blue dye in distilled water, a phenomenon that could be either Saffman-Taylor instability, viscous fingering, or something else. I am also trying to replicate this myself at home, since it's also within my research interest. I'm currently looking at papers like Bensimon et al. Bensimon, Kadanoff, Liang, Shraiman & Tang, *Viscous flows in two dimensions*, Rev. Mod. Phys. **58**, 977 (1986)

Another stream of work that of Tiffany's is the science of why commercial sanitary products fail, through hydrodynamics and microscopy in pad testing at home. One thesis is that the saline water used to test these products doesn't accurately reflect the viscosity and physical dynamics of menstruation. And so Tiffany is looking at how absorbance and wicking effects vary across different pads using fluids that more accurately mimic menstruation.

So, I spent a few hours reorganising things into different shelves to do with their purpose, like temperature, probes, and glassware. And then I spent a bunch of money on IKEA furniture. And then I spent like 4 hours building the shelves and desks, with my lower back hurting from bending over and screwing things.

Before:

After:

But in the process of cleaning up my lab, I kept a list of every component or piece of equipment that I had. I was hoping to eventually be able to give this list to Claude so that I could find stuff easily later, given how much time I’ve wasted losing stuff and then trying to find it again. I wrote a notes of everything I had. Stuff like the things I use to measure temperature, my probes, David Jordan’s bioreactor, and other stuff like

• pressure manometer for biosecurity experiments

• temperature, CO2, and particle concentration monitor for biosecurity experiments

• ammeter / voltmenter / multimeter

• cooking temperature probes

I also wrote all of the chemical samples that I had, down to the different types of geological samples that I own.

• magnesium chloride

• silver nitrate

• dilute hydrogen peroxide

• caustic soda

• agar jelly

• silicone oil

Most of the time, I buy things to replicate a certain experiment online. But I wondered what would happen if I tried to flip this on its head and tried to come up with stuff based on what I had already. Would this allow me to do interesting science more cheaply? If I did things this way, I wouldn’t need to buy things in the first place!

So just to see what would happen, I gave Claude this list of equipment. I then asked it to make a QtPy app of the state space of possible experiments that I could do with my equipment. I told it that the experiments should try to probe at complex phenomena that feels unexplored in literature, and could potentially be recreated in a home setting. In other words, I wanted the experiments to be amenable to independent scientists, and have the quality of ‘table-toppiness’ that I wrote here. The stuff right now I’m looking at is noisy phenomena, quantifying theory in biology, and organised structures like Rayleigh-Bernard convection cells.

I also got it to tell me what kind of dynamics each experiment would try to explore, and it also ranked each experiment by difficulty and time it took to set up. I also gave it the link to my blog, so that it As you can see, the left column is the list of stuff that I have. The middle column is the list of suggested experiments, and when you click on one you get a protocol to try and test out.

I think this is super cool, it also just makes organising my experiment ideas much easier, and I can update the equipment list as I buy more stuff. I’m keen to integrate this tool with learning tools, so I can get a better handle of the theory behind each dynamical system I am exploring. I also wanted to get better integration with literature review so that I could spot which phenomena feels really unexplored.

In the ideal case, this tool solves some optimisation problem where we maximise for novelty, diverge from current literature, but minimise cost and complexity of setup. There should also be a metric for the likelihood that a given experiment might agree or disagree with other experiments out there in current literature. And then maybe the user should also be able to subjective rank each experiment for interestingness. At the Independent Science Society we’ve been thinking a lot about how to optimise experiment quality with low resources, whilst still being curiosity driven, so I enjoy thinking about this problem a lot.

I’m not sure what you call this kind of kung-fu; experiment meta-strategy? In any case, there’s definitely some philosophy to dig into here.

This convection oscillation one really excites me. You heat up a beaker of water, and measure the temperature at the top and the bottom. I wonder if I can find a regime of heating where I can observe temperature oscillations from convection, and then find the regime when it goes crazy, and try to predict it. So I actually did end up buying some better temperature probes that were more loggable than what I had!

The Millennium prize problems are something that have inspired me to do math since I was thirteen. It’s why I tried hard to go to Cambridge and learn about analysis and fluid dynamics, and their aesthetic appeal have always enchanted something in my soul. Life has pushed me away from professional academia, but I still am trying to do research math precisely because of those feelings of wonder.

But regrettably, I was surprised at myself when I woke up a few days ago, and the discovery of the counter-example seemed to stir almost no passion nor excitement within me. Rather, it accelerated what my mind has already been thinking about. Questions about AI.

Apart from the economic side of things, like jobs, recent progress has raised questions within me that range from the philosophy of how science is going to move forward, all the way to the social aspects of research. What is math research going to mean? How can I do meaningful work if all the answers are known by an oracle-type computer? Where are the meaningful questions in math going to come from? What is the point of scientific community? Are rich people going to be the only ones able to solve problems with the compute they acquire?

Bear in mind, I’m thinking about this from the viewpoint of a simple math enjoyer, someone who does math in my house for fun. I can’t imagine how the pros are taking things right now.

I am using the word side-effects carefully here, it’s not clear to me that we have problems, nor advances (in the long run, which I’ll explain later) coming from AI assisted proof. It is also not clear if AI assisted proof is net good or net bad for research in the long time limit. In math at least, the realm of theory, success metrics are subjective and its not clear that beating a bunch of benchmarks or winning prizes counts as success in the theory realm. But we do have side effects nonetheless.

As a side note, last year, I thought these side effects would be constrained to mathematicians doing theory, but I now think it is likely that empirical sciences are going to be affected as well. I am both confused but energised to figure out a way forward. The stress of continually having to Bayesian update has made me believe the best strategy is the ‘wake up and adapt to today’ strategy. I just try to work on maximising the expected value of my actions as frequently as I can, for the given moment. I think I have my recent obsession with Age Of Empires II to thank for that one...

Anyways...

Presumably the goal of research is to find fruitful and interesting things. The first set of interesting side effects are a flurry of mixed claims that AI proofs will affect the fruitfulness of research math itself. It is clear that short term wins have been coming fast and hard, like the counterexample of the Jacobian conjecture, the Navier-Stokes resolution, and many other such things. I don’t think anyone can dispute that AI assisted proof has been fruitful in some way. We know more than we did yesterday, we know two more claims are false, and that can’t be a bad thing.

But I, along with most people, am more interested in the long term effects on research, over the next decade or so. And all of these are unclear. Some people seem to think AI is an existential threat and so thinking about the next decade is moot. I don’t know how to feel about that. But as far as math itself goes, some claim that such AI proofs could potentially lead to net detriment in mathematical research in the long run. The mechanics are fuzzy, but here are some claims that are being put out. No one has a crystal ball but these are interesting views.

Terence Tao claims that premature AI assisted proofs may contaminate problems for future inquiry. In this claim Tao suggests that the point of hard problems is the growth of the sub-problems and constructions that come with the attempt to solve it the hard problem. In this paradigm, the result of the problem itself is secondary, the work around it being the main result.

Some historical examples that come to my mind are the whole swathes of modular forms and number theory research that came with the pursuit of solving Fermat’s last theorem. In Tao’s words, if AI prematurely solves something, then contamination means that people will skip this fruitful process of investigation, which was the point in the first place. This investigative act, of asking important questions that might link disparate fields together, finding new questions, or finding the natural perspective for a problem that makes it tractable to solve, is sacred, and skipping it could lead to net detriment to the art of research mathematics as a whole in the long run.

I agree in part with this. In many cases, those novel natural perspectives on a problem are considered research outputs in their own right, and allowing AI proofs would kill that branch of output from research math. Plausible! In a particularly public video on Youtube, Tao used the analogy that AI in proof is like using a helicopter to get to a beautiful waterfall. LLMs might cause mathematicians to miss out on the value of hiking the natural path to that waterfall, missing out the process of more fruitful intermediate research. I am sympathetic to this analogy too, even from a mind- fitness perspective. Imagine if our brains became unfit because we always refused to take the hike, instead always opting for the helicopter.

But, I have mixed feelings about this analogy as a whole. I agree that AI makes it likely that we skip intermediate steps. But objection to this is only really valid if one pursues math for its own sake (which I do). But other people would say that the point of mathematics is to get hard results that we can actually use, and stop at simply just formalising the result, no matter how messy it is. In a world of limited natural resources or state funding, I somewhat understand the view that society can democratically elect to pursue only the results. And I see no issue with going full AI auto-formalisation mode in applied areas of math like cryptography or condensed matter physics. Tangentially, LLMs have shown to string different fields together in unexpected ways. And when I talk to models I also do seem to gain cool new perspectives on things.

Tao’s statements also assume a finiteness about the complexity of the world that I don’t think is true. I take it as an axiom that the universe has an almost infinite level of depth and recursion. And if you think that’s true, then mathematical problems are presumably unbounded in their number and complexity. And so, we should be just racing to solve as many things as possible and make it cleaner later - the problems won’t run out. I don’t think we’ve really given ourself time to probe the areas of math which are impenetrable to AI assisted proof. It might just be the case that we’ve just scratched the surface of everything there is to know, and that Navier Stokes is just the beginning, and none of us have anything to worry about.

However, at the time of writing, I do think that there is a point about AI not being able to find solutions that are beautiful, concise and parsimonious. The examples of proof I have seen so far for research problems appear incredibly terse and dense. They seem to have no respect for what is humanly interpretable. Perhaps the word I’m looking for is that they don’t feel ‘enchanting’, like the work of Dirac, Feynman, Noether and all of the classics.

This is the strongest argument I’ve seen of where AI assisted proofs have a weak point. LLMs so far seem to have no deep concept for what is a beautiful, human interpretable perspective on a problem. This is pure speculation, but maybe its because humans are wired for aesthetics in some weird way that neural networks can’t grok. Maybe there are some deep cultural links that we all have that makes us recognise aesthetics and beauty in a way that avoid the training set of an LLM. But who knows.

On the other hand, I don’t think we understand neural networks enough to rule out the possibility that as they scale, that they just might know what types of interpretations are particularly tasty to humans. In the limit, an LLM might just always be able to give us beautiful and satisfying answers to hard questions. For my sake I do hope we don’t run out of hard questions. But if it does happen, and we don’t have hard questions anymore, then maybe we end up in the equilibrium much like the one competitive chess has reached. We play games, and do maths for leisure, like an insanely cognitively taxing version of paint by numbers. Or, like in competitive chess. Computers can beat chess players without fail. But the games are beautiful precisely because a human has found these strategies. The fact that a human did it is part of the achievement.

I also think that there is a motivational consideration here for the young people in society. If you’re a kid wanting to learn math, that’s presumably a good thing. And if you think that everything out there is to be solved, then you may not want to study math. This is a bad thing. Hell, even if AI hasn’t solved anything, it might push the frontier so far that people don’t have the motivation to get there, and so give up on mathematics as an enterprise outright. I worry about this happening a lot.

To be honest, I don’t know how things are going to shake out on this front. Looking introspectively, I do still love the process of learning math even if its not research level. I spend hours trying to learn things that are presumably well known and don’t really care that I’m spending my time that way. If that means a lifetime of learning how to interpret AI generated solutions for my own understanding, I actually don’t see that as a bad outcome. I also happen to think there are many different ways to look at flowers, and that humans won’t get bored of looking at flowers, and there infinitely many ways to paint and present a flower.

Take a look at the physical sciences. We look at the world around us, we observe reality, and still don’t understand it. Is that so different from trying to comprehend an oracle that rolls out strings of intensely long and complicated logic that solves theoretical problems? I guess it’s quite similar. I consider computers and theory as part of the natural world as well. Feels like a similar game that’s worthwhile.

Anyways, the fuck knows. I’m going to bed and when I wake up things will probably be different in the world. But I do know that I’ll still be chipping a way at that probability example sheet I’ve been working on, I just love the game too much.

Sure, I could just look up Coulomb's law or Maxwell's equations, or ask an LLM, but I'm always amazed that the Greeks managed to learn so much about the world with much less tools. And I kinda want to be able to do the same. One time my friend Cyrus and I we were sitting on the beach in Brighton and then challenged each other to try to compute the radius of the Earth from first principles using the angle of the horizon. I think these types of challenges are both fun and revealing.

There is piece of advice in one of Shankar's texts that stuck with me whilst I was chilling by the pool in Malaysia, from his textbook 'On Fundamental Physics II'. Shankar writes that to get deep understanding of physics, one should think hard about how physical law could actually be tested and measured with real life instrumentation. Lest, we might get lost in 'factors of 2pi' just doing symbolic manipulations like the Cambridge Masters theoretical physics student I was.

I've always had trouble trying to remember something like Coulombs law, so I had a bit of a think about how I could feel it and test it with my own hands. After all, Coulomb's law deals with point charges. And those are abstract ideas, it's not straightforward to just magic up a piece of electric charge. One starting point might be to use something like a pen and rub it against your hair, but

Coulombs law is meant to tell us the force between two charged particles. If we have two charged particles q1 and q2, then observations like two charged balloons tells us that there should be a force between the two charged particles. Coulomb's law quantifies this force.

It states that if the distance between the charged particles is x, then the force between them should be

Ok but let's think critically about this equation to see if there are any new insights to become of it. How could one have come to a reasonable conclusion that this is indeed the law of force between charges? Presumably, the law is a function of distance between the charges, and the charge on both. So we have the force being a function of the following

To help us slim down what this function might be, we might ask what happens when one of the bodies are not charged. If one isn't charged, then intuition says that there should be no forces in between the two things. This means that the charges should enter the equation as multiplicative factors. This would imply then that the force law looks like below, where a and b are some constants

But then by symmetry, we require a and b to be the same. So the force should look like

But it's not at all obvious to me why the exponent a is 1 in nature. I think if I tried to write about a physical rabbit hole is out of scope but I will keep thinking about it.

The next question then is then figuring out the force varies as the distance between the two increases. A logical guess would be that the force law might obey something similar to the inverse square law observed in the intensity of light, or the gravitational constant. For example, Newton's law of gravity reads that the force between two bodies is

And so then the question is - how would you check that Coulomb’s law indeed obeys inverse square law? It's not entirely clear. And in fact, a few scientists in the 16th century actually proposed that the original Coulomb’s law was close to inverse square but not quite. To do this at home, you would probably need to figure out how to charge two electric balls with the same level of charge, hold one fixed, hold the other one by a string, and then measure the difference in angle deflection that the string makes with a vertical line to calculate how much force the ball experiences.

Coulomb did this with a sensitive piece of equipment called a torsion spring, but I’m trying to find easier ways.

Charging an metal ball cleanly and with home materials is proving kind of tricky. Supposedly, one way to make two equal charges is to charge one thing and then put it in contact with the other thing, so that the charge splits by symmetry. But then how would we check that indeed we have two equally charged things?

I thought of maybe trying to make a Faraday cage. But instead, today I tried to make an aluminium foil electroscope. To do this I took some insulated wire from by breadboarding kit, drilled a hole through the top of a jar, made the end of a wire a hook and then cut a thin piece of aluminium foil. I then folded this piece of foil and hung it on the wire. the other side of the wire lies on the outside of the jar where I scrunched up some more foil. And when I charge an object by rubbing it against my hair, putting it on the contact causes the tin foil in the jar to separate because of the repulsion of charge in both sides of the strip!

But right now this is a super messy and non quantitative way to do this. One of the main reasons is because of charge decay, usually because the air is humid and so takes away charge from the object. So I'm trying to think of a more robust way to create a repeatable charge at home to measure inverse square law more accurately as part of a killer experiment.

The first chapter of the book caught my eye. Let me explain. Both the recent technological progress with LLM models, and fragile geopolitical situation in Europe have left me grappling with how to tell what is true. I read something and there is a non-zero probability it is the result of some averaged out mushing of matrix numbers, generated probabilistically or through motivated means of political actors. And so I remain uncertain if this type of averaged response uncovers anything of personal value to me.

And as such, I have been thinking a lot about how to anchor myself closer to reality. But the authors appear to have found a partial answer to my conundrum through the exposition of a conflict between Leonardo Da Vinci and the 15th Century humanists.

The authors illustrate the difference between their ways of studying the world, which seem to be relevant to the level of indirection humans have between them and reality today.

The two different ways are as follows. As a way to obtain knowledge about the world, the 15th Century Humanists preferred to study and defer to the ancients of authority, studying works of Greek mathematics, ethics and classics. If one is unsure of the buoyancy of a shape in fluid, then refer to the works of Archimedes.

But Da Vinci saw a more virtuous pursuit in the direct observation of nature itself. The most virtuous path to studying nature was through experience and through the human senses. As part of the pursuit of understanding, one sees, hears, smells, or measures the natural world, much like Volterra's early discovery of electricity through licking frogs. And once something is experienced, the observer then records that experience in detail. Of course, mathematical rigour was still to be expected, but the root comes from experience and measurement.

Da Vinci also believed this about painting. It was more virtuous to paint what is in front of you, instead of imitating other paintings. The artist should seek to capture reality by observing it directly. The book pushes strongly that Da Vinci believed that knowledge comes from experience. It cites The Literary Works Of Leonardo da Vinci Compiled and Edited From the Original Manuscripts - by Jean Paul Richter. Some attributed quotes to Da Vinci that may or may not have been lost in translation include

• 'All our knowledge has its origins in our perceptions '*

• 'Experience never errs; it is only your judgements that err by promising themslves effects such as are not caused by your experiments'*

Da Vinci was also an observational maximalist and believed in striving for detail when observing something. He also thought that experience through the senses could also be enhanced by instrumentation. He thought that drawing was almost necessary for true observation. When I went to Florence in August I really felt compelled to figure out how I could master the art of scientific drawing.

I can't help but feel something similar when reading about Virginia Woolf's essays on fiction. In 'Modern Fiction', Woolf questions the need for comprehendable structure and narrative in the traditional novel. Why do classical forms of literature like the poem, tragedy or comedy have structure when the human mind is anything but structured? As Woolf writes, 'The mind receives a myriad of impressions' in an ordinary day, without respect to temporal order or reason, and so should writing not be true to observation and paints thoughts as the 'incessant shower of atoms' that they are? In this vein she criticises the materialists, and instead pays homage to writers like James Joyce.

From Woolf's essay on modern fiction:

Write it as it is I guess. In my writing and work I am trying to strive for closeness to reality. Da Vinci would tell me to always just do an experiment where I can, and to use my eyes and my apparatus. But I also am trying to make it as observationally accurate as possible to my readers, recording my thoughts in whatever order they fall, like Woolf's shower of atoms. It is what it is. In that spirit, I cycled along the Thames on my Brompton, down till Wandsworth. I can't help thinking about how beautiful London is on a warm and sunny autumn afternoon.

References

1. Ralph M. Blake, Curt J. Ducasse, and Edward H. Madden (ed.), Theories of Scientific Method: The Renaissance Through the Nineteenth Century (University of Washington Press, 1960).

2. Jean Paul Richter (comp. & ed.), The Literary Works of Leonardo da Vinci, 2 vols. (London: Sampson Low, Marston, Searle & Rivington, 1883).

3. Virginia Woolf, "Modern Fiction" (1925), in The Common Reader (Hogarth Press).

I was trying to follow the procedure in Chopard 1999 - the difference is that I used agar jelly instead of the cross-linked PVA paper that they used in the paper. Otherwise, the concentrations of magnesium chloride and sodium hydroxide were kept the same. (Note - I didn't say the difference between agar and PVA in the last post, and it will be updated accordingly, this is my bad).

In the spirit of transparency, I wanted to show the results of the experiment after 9 days of leaving it in my house in open air. To the best of my knowledge the temperature ranged from around 20C to 25C.

In the images below, you can see the precipitate forming, but it doesn't form clean bands like in the Chopard 1999 paper. The precipitate is concentrated at the top, and seems to get more dispersed towards the bottom - but there is no clear separation of bands. So something is happening, but it's not the effect I want. Also, the density of the precipitate seemed to vary in the two tubes

I'm keeping the third tube undisturbed right now - I'm not even picking it up to take a photo. Will see what happens.

Test tube 1:

Test tube 2:

What went wrong? I don't know.

• Biggest thing is that it could be just using the agar jelly instead of PVA.

  • In the same vein I just used tap water, of which the hardness of the water may have had an effect, maybe because of ions from the minerals.

• One suspicion I have is that I messed up the concentrations because I wasn't looking at the numbers in the paper correctly - I got some help from GPT Sol so it could just be a hallucination. If so this would be a costly mistake and I need to go through it again.

  • I would like to go through the theories behind reaction diffusion systems so I can be more confident that the concentrations should translate with agar jelly.

• Maybe it was because I was handling the tubes after I mixed everything together, causing the liquid to slosh around.

  • Maybe the table that I put it on wasn't stable or something?

• Maybe it was the temperature variation in the room, although this seems less likely.

And so I put off doing any cleaning of the lab space for months. Even when guests came over I would leave all the lab equipment out hoping that no one would notice. It got to a point where I was just dumping stuff that I got onto my lab table when the amazon order arrived.

And that would usually be fine! BUT until a week ago it spiralled into me not being able to do experiments because I didn't have enough space. Also, it would take me much longer than usual to do experiments because I couldn't find things, since there was so much crap lying around. There was one time that I spent an hour trying to find my digital caliper, which is time pissed down the drain. This was the final red line, and so I finally caved in an decided to do some cleaning.

Here are some quotes from family about the state of the lab

'The state of your apartment makes me have a lump in my throat' - sister.

'How do you live like this' - parents.

'We need to get you your own room for your hobbies’ - my gf.

This is what the lab looked like. There is literally no space to put stuff on the table or for me to sit with a chair. The monitor takes up quite a bit of space, the HEPA laminar flow hood also takes up a significant portion of the desk, and thus I have no place to put my microscope. And I use my microscope a lot so it's a shame that it doesn't have a permanent home. Right now its on a shelf on my bookshelf.

Here's what the whole space looks like - ignore my drying laundry

Even the contents of my shelves were messy

Also the 5GBP plastering board that I put everything on looks like it's about to break. You can even see the bending in the middle. And to fix this problem I put two of my bedside tables underneath it with some books to give some structural integrity.

The first step was to get a desk. So I got ordered 2m long sturdy looking one from IKEA. This doesn't arrive till next week, but I still went ahead and started pre-organising stuff.

I have a metal cabinet shelf. I wanted to put a system to label things in these shelved properly. I also wanted to digitise the contents of what I had in the lab so that an LLM would be able to instantly tell me which experiments were possible or not. And so use this opportunity not just to clean but to do also some logging of all the stuff I had. So for your interest, here's a partial tour of what I have so far

I started to collect the easy stuff first, like glassware, and put them all in a single shelf. So I put the following in this shelf

• test tubes

• victorian style sterilisation lamp

• glass petri dishes

• assorted beakers

• glass stirrer

Then I put all of my probes into another shelf

• pressure manometer for biosecurity experiments

• temperature, CO2, and particle concentration monitor for biosecurity experiments

• ammeter / voltmenter / multimeter

• cooking temperature probes

And then I put everything to do with electrical and circuitry in another shelf. Here I keep

• small electronic sensors, like ultrasound sensors

• breadboards

• cables

• transistors, amps, resistors

• power adapters

• other assorted chips like ESP32 dev board, arduino nano, etc

I put the things that can control temperature in another shelf

• magnetic heater and stirrer - very useful for a range of things that I need to do - highly recommend as a piece of equipment

• candles

• matches

• and randomly my jewellers' scale

And then safety stuff like

• nitrile gloves

• safety goggles in another shelf

I am thinking to have another cupboard for live samples, samples and reagants. For example I have chemicals like

• magnesium chloride

• silver nitrate

• dilute hydrogen peroxide

• caustic soda

• agar jelly

• silicone oil

Along with minerals for my curiosity in origins of life

• periodite

• olivine

• obisidan / volcanic glass

Anyways, the lab is a work in progress, I'll keep you guys updated with the full cleanup once my shelves arrive.

But we should allow for the option for science to be done outside of universities. The Independent Science Society believes that this yields high risk-reward discovery, has convincing historical precedent, and increases empirical skills amongst the public. That’s what this whole blog is trying to prove. But don’t take it from me - I’m just a guy messing around at home in my free time. There are already many cool FROs and BBNs doing cool work outside of academia!

And so people outside of academia should be able to at least ask for grant funding.

So that’s why, on behalf of The Independent Science Society, we are undersigning Science Works’ letter on Reforming UKRI Eligibility. The letter is here. It argues that the eligibility rules make it impossible for new orgs to ask for money, and the main ask is as quoted

First, UKRI should remove the de facto ban on supporting new organisations. It should achieve this by offering a forward-looking route through which new organisations can demonstrate research capability and financial viability. Significant financial support from funders that UKRI already trusts should provide such a route. To that end, UKRI should publish a list of trusted funders, including at a minimum those on the existing list of endorsed funders, and should update it regularly.

Second, UKRI should remove the artificial distinction between standard and non-standard eligibility. The requirements for standard eligibility are practically identical to those for the highest band of non-standard eligibility, yet organisations meeting these materially equivalent criteria are treated differently. This distinction blocks organisations with non-standard eligibility from accessing support, even when they have been deemed to have sufficient research capability and appropriate financial governance. If non-standard eligibility must be kept, UKRI’s Executive Committee should mandate all calls to be open by default to organisations with either type of eligibility.

I encourage you to click and check it out. Here is a screenshot of the beginning, and please read it in full.

And on behalf of the Independent Science Society I’ve undersigned it with the cool folks from Renaissance Philanthropy, Amodo Design, the Living Physics Lab, Cultivarium, the London Institute for Mathematical Sciences, and other really cool people!

Maybe one day home scientists like me would be able to ask for funding for UKRI to do cost effective and high risk experiments in our homes. One model would be some pool of cash where we ask trusted home scientists to de-risk weird phenomena that we can easily watch or verify.

A small step for science at home!

The most versatile thing independent scientists can buy are tools that control and measure temperature. Temperature control challenges have appeared in every experimental endeavour I've done, like making a steady temperature gradient for Rayleigh Bernard cells, or keeping the right temperature for biological cultures.

In fact temperature control is probably the most important experimental control to get right regardless of the field of science. But damn, it's such a pain in the ass that even I myself am tempted to bite the bullet and spend a couple grand on incubators so I don't have to go through such a hard time hacking a temperature control system together. I've already installed split condenser AC in my bedroom - maybe I should extend this to the lab space as well... But that would be against the hacking spirit of the Independent Science Society!

Last time I modified a mini fridge as a heat shield from the heatwaves in England.

Now I'm trying to test cheap water baths that you can buy on Amazon for 65 GBP and see if they work. So I bought this one... and trying to check if it worked basically put me down a rabbit hole of finding the potential noise around boiling points and freezing points...

It arrived next day thanks to the wonders of Amazon Prime. I set the temperature to 60C and then tested using two identical kitchen temperature probes. Both showed 62.2C. Excuse the dark image but if you squint you can see the temps in the LCD.

The temperature flickered around a bit on both probes, but despite setting it to 60C, the probes showed the temperature as centered around 62C with a flickering of +- 1C, despite the claimed 60C in the setting. Even after stirring, and moving the temperature probes around in the water this is what I got.

Again after a few minutes of mixing and measuring, to make sure I wasn’t fucking this up with uneven heating, I get 62C, 62.8C

I then was confused... could it be that my temperature probes wrong or was the Chinese water bath wrong? Also, were there mixing effects what I wasn't taking account? Was I measuring in the right place in the water?!

So, inspired by Lord Kelvin, I wanted to test if my temperature probes would work at the boiling point of water. Tap water should boil at 100C - although atmospheric pressure, altitude effects, and mineral effects could push this off. But some rough googling convinced me that such effects weren't going to exceed error 1C off a boiling point of 100C. And so, this was a way to check if the kitchen temperature probes were working correctly.

So I dipped the probes in boiling water to see if they would measure 100C. The first one:

The second one:

And then I tried to see if the probes would match an ice water slurry so I got a bunch of ice, waited a bit for it to melt and tried to see if I could get the probes to show 0C:

Not exactly perfect, and this seems like a fiddlier way to test temperature probes.

But after this exercise I was convinced that the temperature probes were working correctly and that the water bath just had a systemic error of 2C which I could adjust for. That's fine. And then two weeks later I set it again to 60C on the setting and measured it again:

62.8C, 62.5C. So I think it’s fine!

So yeah, it looks like the water bath does what it says, as long as you add +2C and have an error of +- 1C !

Previously I demonstrated Rayleigh Bernard convection cells with Mica powder and oil, where I saw cell-like devisions in liquid when I applied a temperature gradient. This was an example of non-equilibrium , self organising phenomena due to the application of a temperature gradient. I've preciously tried and failed to do other things like the Briggs Rauscher reaction, which is a (safer) example of an oscillating chemical reaction.

With regards to complex phenomena, I am trying to figure out which variables actually matter through both math and physical experiments, which is hard. In the case of convection cells, we have variables like the thickness of the liquid layer, the temperature gradient, the size of the container, amongst other things. And these ideas are something I want to get around to understanding myself in this lab.

Another piece of complex phenomena that caught my eye is Liesegang rings. These are rings that form in a gel according to a spacing that goes like (1 + p)^n, which is a geometric series. You can get them through a bunch of different waysHere is what they look like, images taken from this really cool website on Liesegang ring models.

You can see quite clearly the spacing going in a geometric pattern in this one with magnesium hydroxide.

Why do I find this interesting? When reading books about embryology, like the Triumph of The Embryo, I got interested in how chemical reactions give rise to patterning in some animals. I also find that the theory of patterning in chemical reactions is mathematically rich as well, something which I'm trying to understand more through the lens on non-equilibrium statistical mechanics. The aesthetics of these things are just mesmerising. Even though liesegang rings aren't the mechanism behind animal patterning, you still can't help but marvel at what goes on behind the scenes.

Here's a page out of 'A Field Guide To the Birds of Malaysia'.

And to the best of my knowledge, the mechanisms behind Liesegang rings haven't really been fully resolved yet. Which puts this in prime territory to try and replicate some of this stuff at home.

I had a think about trying to replicate Liesegang rings using Potassium dichromate and silver nitrate, which seems to yield the brightest rings. But when I was shopping for potassium dichromate on sigma aldrich and then realised that it was carcinogenic, with inhalation risk. So not really that appropriate for homelab style stuff...

And then the other example on the Liesegang website was using a gel soak of magnesium hydrochloride with ammonia, but I also found the ammonia quite sketchy since the concentrations looked high.

So then I was looking around with Gpt Sol to try and find some safer versions, along with reagants that were more available. So then I came across a paper by Chopard in 1999 which managed to create Liesgang rings out of agar jelly (safe), magnesium chloride (bath salts) and sodium hydroxide. Sodium hydroxide is called caustic soda and can be bought from stores. It's corrosive but doesn't have fumes and I previously used it trying to make quantum dots at home.

Here are photos of the Liesegang rings from the Chopard 1999 paper

I tried the following recipe to make the rings with NaOH, shown in the image on the right.

The reagents were pretty cheap as well, here is th e complete list with the estimated costs from Claude. Again to stress, most of these available pretty readily out there! I would really like to make chemical network research more accessible to home experimentation,

I got Sol to tell me the concentrations and procedure to replicate the paper.

Here is my first attempt. And spoiler alert, it's a fail and I couldn't get the bands to separate properly for some reason. But I think it's just as important to share failures along with successes in the spirit of being a transparent independent scientist so here goes...

Embarassingly the fiddliest part of all this was trying to get the agar jelly nice and smooth so that the gel wouldn't be cloudy, so that I could see the banding.

I first tried to mix 1.5g of agar powder with 90ml and then put it in my magnetic stirrer and heater, but I only managed to get the agar to a temperature of 60C, which isn't enough to fully dissolve the agar powder - you need to get it to near boiling for it to dissolve properly.

It was much quicker and easier to get the agar to 90C temperature by putting it in a microwave for 40s at 900W. You can get agar from any old food shop or on amazon. I used a basic cooking temperature probe to test that it got to temperature.

Putting it into the microwave for 40s managed to get it up to the right temperature for dissolution - here it's 94C.

I then kept the agar warm on my magnetic stirrer at 60C.

And then after that I prepared 2g of Magnesium Chloride Hexahydrate in 98ml of water and then put it in the agar jelly

Stirring it and getting the bubbles out

And then I put it in some test tubes and let it cool, in tubes of 20g each

I then let the MgCl soaked tubes rest for 90 minutes until it became a gel.

After that I put 1g of NaOH in 50ml of water solution, this is corrosive so be careful

And then i poured the NaOH solution into the gel soak.

And then I did this with 3 test tubes and then left one alone.

I left it for 10 hours and here's what I got. As you can see there is a white precipitate interface, which is promising. But I don't see the band structures that I so desperately want to see!

References

1. B. Chopard, M. Droz, J. Magnin, Z. Rácz, and M. Zrinyi, "Liesegang Patterns: Effect of Dissociation of the Invading Electrolyte," J. Phys. Chem. A 103 (10), 1432–1436 (1999). ACS · preprint arXiv:cond-mat/9809385.

2. Liesegang ring experiments and models, insilico.hu.

3. L. Wolpert, The Triumph of the Embryo (Oxford University Press, 1991).

4. Lim Kim Seng, Lim Kim Chuah, and Yong Ding Li (illus. Dana Gardner), A Field Guide to the Birds of Malaysia, including Sabah and Sarawak (John Beaufoy Publishing). NHBS.

My main method of attack given these new developments in AI has to try and see if there are any conjectures that can be disproven or proven through elementary methods that I am actually able to understand. And then I would go about then parsing the generated results by hand, or with tools like the ones my friend George Smith has made. I am hoping for both results and something of pedagogical value to me. Such records of parsing seem to be what other people are doing, like Terence Tao's recent 'digestions' of AI generated results.

I was slightly emboldened by my progress that I made on a conjecture in random matrices last week (I possibly resolved a conjecture). On that project, I emailed the solution to the authors who then replied saying that the solution looks correct. (More on this later)

The downside of this approach of constructing understandable counterexamples is that my current level and knowledge of math is the limiting factor, and so proofs that I force AIs to generate with methods known to me are likely to be long winded and probably don't have some big insight. Also, it seems less aesthetic than trying to come up with a motivated, constructive theory to resolve something, which is something that I've struggled to get AI to do. If I wanted to solve a problem with AI assistance through theory building, which is how most of current research mathematics seems to be done, then the use of AI doesn't really seem appropriate for someone with my aims. I suspect that I would get lost instantly due to complexity. Also, counterexamples only resolve a conjecture when it's false - there are many conjectures which are likely true and it's unclear how an independent mathematician could contribute a convincing result of something outside of the counter-example type stuff that we see AI doing.

As a companion side project, I am also trying to parse the book on non-equilibrium process by De Groot and Mazur, specifically on chemical reactions. On the experimental side I am still trying to find more non-linear phenomena that you can observe safely at home, like the Briggs Rauscher reaction or Liesegang rings. I failed in my last attempt at Briggs Rauscher which I will write up soon.

Anyways, back to my rough initial thoughts on the paper.

Consider the system of processes that drive our circadian rhythms. They oscillate with a noisy period of twenty-four hours. There seem to be many such biological processes that oscillate (albeit with noise). A biochemical clock is a system in which the concentrations of the chemicals involved oscillate at a near-constant period. Such clocks vary in mechanism. Some involve gene regulation; others require no gene regulation at all and can be assembled purely from biochemicals in a test tube. The paper cites one such protein system [2].

We expect noise in biological environments to affect biochemical oscillators, so it seems reasonable that the oscillations decay in time. The paper uses a measure called the number of coherent oscillations [3] to quantify how long they last. I won't go into too much detail on exactly what this means in this post - the reader can check the references.

The main result of Oberreiter, Seifert and Barato is a conjecture that bounds from below the entropy produced by a biochemical oscillator, where the bound is a function of the number of coherent oscillations. Bounds of these form our cool because it might be able to let us constrain the energetics of some biological processes - an approach that Nick Lane talks about in his book The Vital Question [4]. In the early chapters he also makes a nod to the dissipative structures work by Prigogine.

Here is a screenshot of the conjecture:

To the best of my knowledge, this conjecture remains unproven. Right now I am attempting to get GPT Sol to solve it - it has made a counter example and I am trying to check it rigorously. I am emboldened somewhat by my last submission of a counterexample in random matrix theory, which the original authors said "looks correct" in an email eight days after I sent it to them. (I am not really sure what to do with it, though; it feels like publishing such a thing through formal channels would be a waste of time.)

The preliminary counterexample that Sol came up with is here. GPT Sol first reframes the problem in terms of the eigenvalues of the system and then tries to massage a network to fulfil the inequality without changing the entropy.

This counterexample looks correct at first glance. I'm still trying to digest it by going through the proof manually. On the surface it looks like Sol constructs a bilayer network, one of which is in equilibrium, and one which isn't, such that the slow eigenvalues can be massaged without moving the entropy that much.

Right now, if this example was correct, it would indeed be pretty contrived. It would be cool to find other such counterexamples with the aim of finding a biochemical clock that is below this bound.

In other news, I am finding learning statistical mechanics this way to be a lot more fun than trying to parse textbooks. I have four textbooks right now but I've been struggling to find a mental 'hook' to get this stuff into my brain! We might be able to motivate younger students more by trying to mass-find low hanging conjectures for them to chew on, or to find higher quality digestions of.

Other books I am trying to read

• Kondepudi, D. and Prigogine, I. (2015). Modern Thermodynamics: From Heat Engines to Dissipative Structures, 2nd ed. Wiley. ISBN 978-1-118-37181-7. [Wiley]

• de Groot, S. R. and Mazur, P. (1984). Non-Equilibrium Thermodynamics. Dover (reprint of North-Holland, 1962). ISBN 978-0-486-64741-8. [Dover]

• Livi, R. and Politi, P. (2017). Nonequilibrium Statistical Physics: A Modern Perspective. Cambridge University Press. ISBN 978-1-107-04954-3. [CUP]

References

[1] Oberreiter, L., Seifert, U. and Barato, A. C. (2022). Universal minimal cost of coherent biochemical oscillations. Physical Review E 106, 014106. arXiv:2112.01607. https://arxiv.org/abs/2112.01607

[2] Nakajima, M., Imai, K., Ito, H., Nishiwaki, T., Murayama, Y., Iwasaki, H., Oyama, T. and Kondo, T. (2005). Reconstitution of circadian oscillation of cyanobacterial KaiC phosphorylation in vitro. Science 308, 414–415. https://doi.org/10.1126/science.1108451

[3] Barkai, N. and Leibler, S. (2000). Circadian clocks limited by noise. Nature 403, 267–268. https://doi.org/10.1038/35002258

[4] Lane, N. (2015). The Vital Question: Energy, Evolution, and the Origins of Complex Life. Profile Books / W. W. Norton. ISBN 978-1-78125-036-5.

So I asked GPT Sol Ultra to hunt for some conjectures with resolutions that someone with my background could understand and check myself. Disclosure - I’ve studied theoretical physics up to Master’s level at Cambridge, and the math that I read usually has a statistical physics flavour. I also finished my fourth year with a score of 98/100 (though it was covid and so exams were easier).

One result that it found was a disproof of a conjecture on the limiting behaviour of a matrix model, with a fairly simple proof. The original conjecture is conjecture 2 from the following paper:

Masoud Khalkhali, Nathan Pagliaroli, Andrei Parfeni, and Brayden Smith, “Bootstrapping the critical behavior of multi-matrix models,” Journal of High Energy Physics 02 (2025), 158. DOI · arXiv:2409.07565

The resolution is here, which resolves the conjecture falsely. The full proof is below as well at the bottom of this post. The part which made me feel something was the fact that this conjecture used math that was basic enough for me to grasp it, and I have found the subject matter (field theory, random matrix theory) interesting previously.

I am spending some time to try and check if I got it right. My friend George Smith works on tools for math education and I’m trying to use his generated problems to gain a better intuition of what GPT Sol actually did.

I am well aware of being wrong, so I have emailed the authors of this paper to check to see if it makes sense. Formalising it feels to heavy as a tool right now, so I’ll stick to algebra tools. I will disclose in a later post if I have found that I have made mistakes.

Here are some notes on what I’m looking for when I try to make AI assisted proofs

• Find a problem that I can understand.

  • This feels really important, what’s the point of doing research math if you don’t get the joy of trying to understand something new?

    • If you choose problems that you understand you will be more likely to somewhat be invested in the solution and also be more likely to take it in a useful place.

    • The concepts you learn are more likely to mentally hook to something you care about which might make some cool second order effects.

    • If you choose a problem you understand you will feel good when its solved, which I rate highly.

    • A lot of results in maths aren’t applicable to real life, the search space is huge, just chill.

    • Somehow I feel more drawn to math that has some empiricism in scope, or a model of the world that is not obvious.

• If you understand more math you are more likely to have an expanded universe of problems that feel significant (and can hopefully solve with AI assistance)

  • This means that it is still worth trying to understand math.

  • It feels more likely to me that one part of the future of math is trying to digest results made by AI and trying to see if they have wider significance.

  • I still think people want to understand things, I still find understanding things fun and knowing how things work is fun. I don’t think it matters if something is already known, there are infinitely many presentations of knowledge that can be valuable in different ways.

  • I still think there is scope for a much needed, much better thought out way of communicating and storing such results.

Acknowledgements

Thanks to George Smith for the discussions. All mistakes are mine.

Proof