You're reading the public-facing archive of the Category Theory Zulip server.
To join the server you need an invite. Anybody can get an invite by contacting Matteo Capucci at name dot surname at gmail dot com.
For all things related to this archive refer to the same person.
Magnus (Aug 02 2024 at 10:08):Hello everyone. I was intrigued by recent discussions that suggested that there was a risk of Applied Category Theory being used for great harm. However, I struggle to understand the possible harms here (perhaps because I'm not a theorist).
Is this hyperbole? Or what are the risks, and how can we avoid them?
Nathan Corbyn (Aug 02 2024 at 10:41):I always interpreted the suggestion as a comparison to, e.g., the use of partial differential equations in quantitative finance, and the enormous impact this has had on global economics. That said, it is not clear to me what application domain anyone has in mind when they make this suggestion. It feels unlikely that anyone doing evil is going to do more harm out of a choice to apply category theory over, say, any other mathematical discipline.
Nathan Corbyn (Aug 02 2024 at 10:43):Magnus said:
Is this hyperbole? Or what are the risks, and how can we avoid them?
I’m also interested to hear what proponents of this position believe.
John Baez (Aug 02 2024 at 10:58):I don't think that applied category theory is currently more risky than other forms of applied mathematics. One reason people here talk about its risks a lot is that a community of mathematicians who were used to thinking of their work as pure mathematics is suddenly having to grapple with ethical issues that applied mathematicians have been thinking about for years.
For example, homotopy type theorists in the US have gotten some million- and multimillion-dollar grants from the Defense Department. The Topos Institute is so far largely funded by the US military and a few tech billionaires. The quantum computing company Quantinuum is getting millions of dollars of investments and hiring some category theorists, and recently a venture capitalist put in tens of millions of dollars to start an AI company (Symbolica) that is also hiring category theorists. And a number of category theorists are working on software for modeling in public health.
All this is rather new. So it's natural that category theorists - who traditionally tended to earn their living in academia - are busy discussing these developments, with very mixed attitudes about how to respond.
Cole Comfort (Aug 02 2024 at 11:05):The belief of category theorists that their research is likely to be useful to people outside of academia, or venture-capitalist speculation.... and moreover that this impact can be predicted, in my estimation, seems to be a delusion of grandeur. But maybe I am just being naive.
However, if mathematicians receive funding from an organization, one could make the argument that this gives the organization more legitimacy. This could have concrete impact outside of academia.
Jules Hedges (Aug 02 2024 at 12:02):My current take is that the risk of applied category theory methods being used for evil (whatever that means) is exactly equal to the potential of applied category theory being applied
Jules Hedges (Aug 02 2024 at 12:03):As I put it several years ago: we are in the business of building hammers. Hammers can be used to build houses, or to smash skulls
Cole Comfort (Aug 02 2024 at 12:06):A hammer factory is considerably more concrete than a collection of category theorists. It is almost certain that most hammers that the factory produces will be used by people who have nothing to do with the hammer industry.
The overwhelming majority of category theory research will produce nothing of any concrete value for a very long time.
John Baez (Aug 02 2024 at 12:07):Truly applied category theorists are not merely building hammers: we are using hammers to do specific things in the world, like develop new AI systems, or quantum technologies, or software for epidemiological modeling.
John Baez (Aug 02 2024 at 12:17):Now there could be some 'pure' category theorists who are pretending to be 'applied' because it sounds fashionable. But that's a separate issue. For me, math becomes 'applied' when you use it to do something that impacts the world in ways that affect people who don't care about the math. These people typically don't even know that math is affecting them.
Ryan Wisnesky (Aug 02 2024 at 15:42):delusions of grandeur are pretty much a requirement to get Silicon Valley funding, that part hasn't really changed for decades
Jules Hedges (Aug 02 2024 at 16:35):John Baez said:
Truly applied category theorists are not merely building hammers: we are using hammers to do specific things in the world, like develop new AI systems, or quantum technologies, or software for epidemiological modeling, etc.
Yes, but quite often you do get reusable technology at the application level. For example the machinery of open stock-flow diagrams that you developed for epidemiology can almost have applications in operations research, which is (modulo a bit of historical revisionism) what stock-flow diagrams were originally invented for. My standard go-to example of this is control theory, which is useful for such applications as steering ballistic missiles and steering a centrally planned economy
John Baez (Aug 02 2024 at 17:02):Agreed! Our ModelCollab software can be used for system dynamics models of all sorts of things, like industrial dynamics, and the fact that we're using it for epidemiology doesn't prevent truly horrid alternative uses. Keeping the good uses moving forward faster than the bad ones is one of my main goals , and there's a lot to be said about that.
I'd merely been saying this: in my mind, the category theory I was working on became truly applied when people started using it to create software to carry out specific tasks that will impact non-mathematicians. That's when there was an urgent decision: to join in this work and try to influence it, or stand back.
Eric M Downes (Aug 02 2024 at 18:13):math becomes 'applied' when you use it to do something that impacts the world in ways that affect people who don't care about the math
I really like this definition, and acknowledge this is a summary of what you were communicating in the ACT thread too. I think you can even strengthen that to a "just when". :)
John Baez (Aug 02 2024 at 20:05):Thanks! Yes, I've been tracking work on applied category theory and feel this is a crucial step: when you no longer need to mention the math.
Rémy Tuyéras (Aug 02 2024 at 21:07):To me, successful applications of category theory occur when you have a domain and you try to find the intersection . Once you have , you can use logical deductions and category-theoretic constructions to expand into a superset , potentially recovering different ways to express what is in .
If allows for closer alignment with one of the goals of domain (while the language of could not do so), then I believe this application is on track to be successful.
Rémy Tuyéras (Aug 02 2024 at 21:07):Personally, I have encountered two types of behaviors in my attempt to apply category theory, which I will expand upon to show full narratives:
Scenario 1: There are significant barriers for people from domain to learn and even become interested (due to the psychological challenge of learning something new). This means that cannot be considered a (beginning of) solution for them. Therefore, you either pause and wait for people from domain to find more reasons to learn , or you develop where now addresses one of the goals of . Since nobody will initially want to learn , your only option is to develop as software for people to use. You also need to benchmark it and demonstrate that it performs better than any other software. If you manage to do that, then comes the time where you need to simplify your story significantly to sell .
Scenario 2: Your application contains a nice simple narrative, it has an easy code to understand, and people from domain are receptive to your story. Then, you can find a subset of people from domain that will help you develop .
The potential pitfalls in all this would be when:
Madeleine Birchfield (Aug 04 2024 at 15:20):Most applications of category theory so far involve creating some software on a computer and so by their nature they use fossil fuels via electricity and contribute to the increasing levels of greenhouse gases in the atmosphere. These increased levels of greenhouse gases is changing our climate with bad consequences for our society, so applied category theorists have to ask themselves if i.e. helping to save the world population from a pandemic via their software contributions is worth the additional greenhouse gases in the atmosphere.
Of course, if one finds lowering the greenhouse gas levels to be of utmost importance there is probably no good solution to this except to stop applying category theory to anything software related, and probably stop talking about category theory on this zulip and get off the internet as well.
Ryan Wisnesky (Aug 04 2024 at 15:53):not necessarily: a piece of software may cost X to run, but then automate a process that used to cost 1000*X or more. We even tell our customers: use our static analyzer to check your SQL code before you run it, so that you don't have to run it as many times to debug it, and pocket the cost savings. This is in a context where an overnight run of a data process might cost six figures.
John Baez (Aug 04 2024 at 16:29):I've always wanted to use category theory to help tackle the climate crisis and more generally the Anthropocene: that's why I started doing applied category theory. But it turned out to be essential to have good collaborators to make progress on such complicated projects, and I didn't find collaborators who 1) know how to use category theory in software, 2) want to work with me, and 3) are working on climate change.
Luckily I found collaborators who 1) know how to use category theory in software, 2) want to work with me, and 3) want to develop category-based modeling tools for epidemiology and public health. We're developing those modeling tools now. Once we have those, especially agent-based modeling tools, it will be easier to attract collaborators who want to apply them to climate change - and luckily, some of my current collaborators want to move in that direction. In fact there's a substantial overlap between climate change and public health modeling, so we'll probably start by working in that overlap region.
applied category theorists have to ask themselves if i.e. helping to save the world population from a pandemic via their software contributions is worth the additional greenhouse gases in the atmosphere.
It's true that we have to ask ourselves this, but I think the answer is "yes".
By the way, our software is not mainly aimed at "pandemics". Epidemiologists study many causes of death and disease, including smoking, diabetes, drug abuse, heart disease etc.
I don't actually believe that letting people die prematurely from disease reduces carbon emissions in the long run - even if it were ethical to approach the problem that way.
John Baez (Aug 04 2024 at 16:45):I also don't think "getting off the internet" is an effective way for anyone to reduce their carbon emissions while still helping the world. I've essentially stopped flying to conferences, and that's roughly halved my carbon emissions. I've also installed solar panels. I don't drive to work. Probably the next thing to do would be to completely stop eating meat - so far I've only been able to reduce it. Getting off the internet is not on my list. If you do a few calculations to estimate the carbon emissions of various activities, you'll see why.
Peva Blanchard (Aug 04 2024 at 17:20):A bit tangential to the original topic of the discussion, but climpact is a very nice pedagogical survey that lets you check how accurate your perceptions of the environmental impacts of some usual activities are. The interesting part is that it also shows you how distorted the views of the population of participants are, and how your own answers compare to the population.
ps: it has been developped by people at EPFL in Switzerland; so the questions might be Swiss-specific.
John Baez (Aug 04 2024 at 17:28):I find their claims hard to understand. They claim "Playing tennis for one year releases 15× less CO2 than taking 5-minute showers once a day for a year." But what carbon emissions from playing tennis do they count? Breathing faster? Buying tennis balls? Going to a tennis court? If so, how do you get there? - in the US you might easily have to drive 5 miles to get there. And are the showers hot or cold? Is the water heated by fossil fuels or renewables?
Peva Blanchard (Aug 04 2024 at 19:34):I was not involved in the project so I don't know for sure.
From the page you mention about tennis, they seem to consider the construction, maintenance and disposal of a tennis court. And the functional unit they chose is the number of tennis play that occurs on a tennis court during its lifetime. If that's the approach, then their model excludes indeed the transport of players, and the tennis equipment (balls, shoes, wearings, etc.). In a real LCA report, they would need to justify this exclusion.
The actual flow due to breathing (or eating, drinking, sweating, etc. i.e. all natural bodily flows) is usually not taken into account. Someone explained that to me once, but I can't remember the exact argument. I think it has to do with the fact that these flows are already part of a natural cycle, so they are not charged with any responsibility for environmental damage.
For showers, the page is saying it is 37 degree celsius heated with an oil bowler. Again, I have not checked the details, but usually the energy required will be modeled as a mix of heat service or electricity service, usually conditioned on the country of energy production. And for that, they rely on external database.
Again, it's only me making guesses about how they model stuff based on their info and my prior knowledge of the topic. I've discussed once with the people behind climpact. I can certainly reach out to them if you have a bunch of questions?
ps: by the way, the questions you asked are exactly the kind of questions LCA people ask all the time (scope of the system, functional unit, inclusion/exclusion rules, etc.)
John Baez (Aug 04 2024 at 20:04):Peva Blanchard said:
From the page you mention about tennis, they seem to consider the construction, maintenance and disposal of a tennis court. And the functional unit they chose is the number of tennis play that occurs on a tennis court during its lifetime. If that's the approach, then their model excludes indeed the transport of players, and the tennis equipment (balls, shoes, wearings, etc.).
My only complaint is that I wasn't able to see this sort of information until I answered their questions - or at least I didn't see it - so I couldn't figure out what their questions really meant. Maybe I didn't click on the right thing soon enough.
Kevin Carlson (Aug 04 2024 at 20:59):Yeah, I found it basically impossible to answer the climpact questions. Apparently the emissions of bicycling to work for a year are half as much as the emissions of a single train trip from Zurich to Prague. But this kind of quantity is only meaningful if you make some broad assumptions about how many new bikes need to be manufactured, in what materials, to support some population of people taking some length of commute to work. I have more or less no idea how this kind of information could be useful to me, considering that I already commute to work on a bike that's older than me, which is obviously by far the lowest-emission possibility except possibly for walking.
Kevin Carlson (Aug 04 2024 at 21:00):If I were doing a study like this I wouldn't even try to get people to compare such weirdly ill-defined quantities. Knowing that pork emits much less than beef (and even the factor itself is probably not that important) is the kind of thing that seems actually actionable.
Kevin Carlson (Aug 04 2024 at 21:01):Madeleine Birchfield said:
Most applications of category theory so far involve creating some software on a computer and so by their nature they use fossil fuels via electricity and contribute to the increasing levels of greenhouse gases in the atmosphere. These increased levels of greenhouse gases is changing our climate with bad consequences for our society, so applied category theorists have to ask themselves if i.e. helping to save the world population from a pandemic via their software contributions is worth the additional greenhouse gases in the atmosphere.
I would be really surprised if any applied category theorist has ever considered stopping software work because using computers and the internet consumes electricity.
Kevin Carlson (Aug 04 2024 at 21:03):It's pretty clear to me that online activities are in almost all cases crowding out activities that take far, far more energy, such as sending emails instead of paper letters, reading PDFs instead of paper journals, chatting on Zulip instead of traveling to meet, and building digital models of engineering objects instead of physical models.
Kevin Carlson (Aug 04 2024 at 21:03):You'd have to not only get off the Internet but also stop communicating with anyone not in walking distance to hope that would actually reduce your emissions footprint, it seems to me.
Matteo Capucci (he/him) (Aug 05 2024 at 13:06):CO2 emission estimations (such as LCAs) have always stricken me as dubious (assumptions are never clear) and also potentially a good application of category theory? I imagine one needs to analyze these big and complicated networks of production processes (not unlike a resource theory) composed of hundreds if not thousands of elementary processes, and then 'blame' CO2 on pieces of them. @John Baez have you ever looked into it?
Peva Blanchard (Aug 05 2024 at 13:22):Matteo Capucci (he/him) said:
CO2 emission estimations (such as LCAs) have always stricken me as dubious (assumptions are never clear) and also potentially a good application of category theory? I imagine one needs to analyze these big and complicated networks of production processes (not unlike a resource theory) composed of hundreds if not thousands of elementary processes, and then 'blame' CO2 on pieces of them. John Baez have you ever looked into it?
Indeed ! Actually, I do work with LCA practitioners, and I was involved in a data engineering project for the big networks of processes you are mentioning. They seem to be closely related to Petri nets, and John gave me quite a lot of papers to read (I'm still letting them sink in btw). I will later respond (in another topic) to the points raised above. In the meantime perhaps, just know that LCA practitioners are aware about the importance of implicit assumptions: they actually fight all the time about that :)
Matteo Capucci (he/him) (Aug 05 2024 at 13:48):Great!
Matteo Capucci (he/him) (Aug 05 2024 at 13:49):Have you worked on categorical solutions then? I'd love to hear about it
John Baez (Aug 05 2024 at 14:03):Matteo Capucci (he/him) said:
John Baez have you ever looked into it?
No, but I like the idea a lot. Peva will figure it out, I'm sure.
Owen Lynch (Aug 08 2024 at 18:05):Turning back to the original question of whether applied category theory will end up causing evil, I think one interesting point is that the use of applied category theory is to scale mathematical reasoning beyond individuals, not to necessarily massively enhance the reasoning power of individuals. Or more specifically, certainly applied category theory is a boon for individual reasoning, but mostly because it allows one to better understand what other people are saying in a variety of domains. And it's harder to coordinate a large group of people for evil than it is to coordinate a large group of people for good. So, unlike other mathematical advances (like classical physics for cannonball aiming), it's a tool which is easier to use for good than evil. That is, you can have a single military which figures out how to aim cannonballs better, and then they can use that for evil. Similarly, certainly individual scientific breakthroughs that come from applied category theory can be used for evil. But the overall value proposition of applied category theory (that it makes collaboration easier) is not as easily used for evil as for good.
Owen Lynch (Aug 08 2024 at 18:06):That is, I think applied category theory is somewhat of an asymmetric weapon, in the sense of https://slatestarcodex.com/2017/03/24/guided-by-the-beauty-of-our-weapons/
Kevin Carlson (Aug 08 2024 at 18:24):Can you expand on the claim that it’s easier to coordinate groups of people for good than for evil? Seems like you can at least coordinate groups of people to do evil stuff to a common outgroup, I think?
Noah Chrein (Aug 10 2024 at 16:14):As a slightly different take, I have always felt that CT held the key for AI alignment. So CT is a possible route to saving us from emergent evil.
In more detail, imo, a general enough theory of knowledge representation (GKR) needs CT, Mechanistic Interpretability needs GKR, and AI alignment needs Mech Interp. Scale might be "all you need" for capability, but we definitely need mech interp for control.
Matteo Capucci (he/him) (Aug 12 2024 at 09:58):Kevin Carlson said:
Can you expand on the claim that it’s easier to coordinate groups of people for good than for evil? Seems like you can at least coordinate groups of people to do evil stuff to a common outgroup, I think?
In fact evil is often masked as good, especially when rallying people for the cause. It's unsettling how much harm can be done in good faith. Like Hitler was probably very convinced to be doing good. And there's some less ethically extreme endeavors, like go-engineering, which are very easy to see as good or evil depending on the spin and your opinion.
Owen Lynch (Aug 12 2024 at 14:59):This is true. And yet I think society does end up developing a "memetic immune system" over time, which prevents coordination on at least some classes of evil. On the other hand, society can end up in coordination problems that lead to evil no individual would dream of. So it's not all positive, which is why democracy doesn't beat autocracy on every account. Yet I still have some preference for democracy, and in a similar token, I'd prefer developing "democratic" math than "individual" math.
For instance, applied category theory doesn't help too much with the science of geoengineering, it mostly should help by making geoengineering models legible to many eyeballs. This is not a sufficient condition for a fair, democratic negotiation process, but perhaps it is a necessary condition.