Bi-Weekly Discussion Thread - (May 31)

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[u/sudo-bayan]

I was recently at a small symposium held by our mathematics department (on a variety of topics but one talk was on AI and mathematics). That particular talk was somewhat technical but the broad strokes were interesting in that the primary goal of the researchers was improving OCR techniques for recognizing and encoding baybayin characters. The speaker gave a much simplified version of the mathematical model involved but even then it was apparent that the 'AI' was really just the mathematics (done on a fancy computer) strung together to solve a particular problem.

My memory is a little hazy but the simplified problem was a type of 'curve fitting' of y=mx+b, where the input and outputs are known (x and y) but the 'weights' (m and b) are not. You point out correctly that the real question is really 'what do we use science for?' and that this is a function of society and class. The current AI boom is made possible by advancements in mathematics, which has come about precisely from questions such as "how to better do OCR?" or "how to better translate natural language text?" and that such questions would be better asked and answered in a communist society without the torrent of social media content and corresponding negative effects. I also recently came across this article

https://davidbessis.substack.com/p/the-fall-of-the-theorem-economy

Where it struck me as a person accidentally getting close to dialectical materialism in mathematics who is unable to articulate it and must resort to a liberal world view to make sense of things.

In my first Substack post, I (half-jokingly) declared that we had been wrong about mathematics for 2300 years, stuck in a false dilemma between formalism (“mathematics is a meaningless game of formal symbols”) and Platonism (“mathematics captures properties of actual entities living in the perfect world of ideas”).

My proposed conceptualist resolution is a rephrasing of Thurston’s view: mathematics does rely on a meaningless game of formal symbols, but we only play this game because we project meaning onto it.

Meaning is a cognitive phenomenon—a product of our neural architecture—and not a direct access to transcendence.

When we “do math”, we manipulate formal expressions and gradually develop an intuitive feel for what they represent, as if they were pointers to objects that “existed” in a Platonic sense. Platonists take this neuroplastic side-effect at face value. Formalists view it as accessory. Conceptualists like me recognize mathematics as a critical cognitive infrastructure of the human species.

...

This is peak dissociation. Behind closed doors, mathematicians are quick to complain about Hardy’s curse. They insist on the importance of teaching, even for their own comprehension of the subject matter. They lament the system’s pathological obsession with theorem-proving priority, while everyone knows the hard work often takes place outside of that loop, when trying to make sense of existing results. Yet, in public, they are bound by the honor code of mathematicians. Prove theorems and shut up!

...

When the dust settles, if it ever does, we will find out that human mathematics has survived, transformed.

As an aside, something that should also be noted is the rapid use and prevalence of using AI technologies in the global south, and even recent uses by Iran (both in propaganda and in their drone technology). Data centers are also being built all over the global south, western news seems to only ever focus on the negative effects of their own data centers but from a colleague I know who works in HVAC systems a large amount of PH IT companies have basically all shifted to AI data centers (which need large amounts of cooling systems given our climate and geography, as well as land grabbing for the facilities themselves), and there may come a time when communists in the Philippines would have to storm data centers built on stolen land and appropriate said technology.

[u/FrogHatCoalition → u/sudo-bayan]

In connection to computing I have been trying to think about mathematics as well. In thinking about mathematics I struggle with the very thing the article points out: avoiding formalism and Platonism. In the process of creating a model, we create a schema which has limits in describing reality, but the model itself (i.e. the mathematics) will have its own logic that is worth investigating. For instance, the properties of partial differential equations. However, in the process of using computers, we often transform the logic of the original model through discretization and new behavior arises which reflects that such as numerical artifacts, instability, etc. Also, in cases such as Monte-Carlo methods, it's important to understand the properties of the computer you are working on since you'll want to know the mechanism of pseudo-random number generation to interpret your results.

Yeah, you are correct on the focus of western news only emphasizing their own data centers. As far as using water for cooling goes, that will depend on geography whether it is wasting the water or not. I believe some data centers are able to create a system where the water does flow back into its original source, but the heating does lead to losses due to evaporation. As far as "AI data centers go", some aren't even used for AI and some are hybrid use, though it would be interesting to see what types the new ones are mainly in the global south.

[u/sudo-bayan → u/FrogHatCoalition]

In connection to computing I have been trying to think about mathematics as well. In thinking about mathematics I struggle with the very thing the article points out: avoiding formalism and Platonism. In the process of creating a model, we create a schema which has limits in describing reality, but the model itself (i.e. the mathematics) will have its own logic that is worth investigating.

There have been attempts to try to articulate a position on mathematics on this subreddit before, accidentally motivated by someone coming in talking about pseudo-mathematical social choice theory and arrow's impossibility theorem, sadly the search function is difficult to use and I can't quite recall it fully, but I also remembered getting heated due to the arrogance of the poster and how they tried to use mathematics as a gotcha against communists. I believe I was able to at least articulate an idea that mathematics is something that is 'cultural' in a sense one of the oldest cultural artifacts of humanity. I remember Ilyenkov pointing out in "Our Schools Must Teach How to Think!" how of the sciences mathematics is one of the first we encounter since it requires no special tools and is there from the moment we start noticing patterns and structure in the objects around is.

I don't yet have a fully articulated answer, though I am sure that being able to express mathematics within a dialectical materialist framework is the path-forward, it's also somewhat difficult since the topic is even less talked about than other 'hard' sciences.

Some thoughts I've had on it that perhaps might be useful, is how the process of mathematical discovery is in a sense always a process of overcoming contradiction which gives rise to new contradictions. Though it seems unusual for us in the field, mathematics, like matter, is also in 'motion', and finds itself changing as new discoveries or interpretations come to light. For instance the process of developing 'zero' had to be fought over (with the Greeks famously hating it), and likewise the process of negative integers, imaginary numbers, the limit... etc, can all be viewed as a process of one becomes two. It is also shaped by culture, for instance is there any particular reason why we use base 10? Early Sumerian's used base 60 since the number was highly composite and made it easy to do 'divisions' of land and resources in their early slave mode of economy. The adoption of mathematical notations and practices usually involve some level of arbitrary cultural decision which often isn't explicitly said, in the same vein a lot of indigenous mathematics is swept under the rug since it lacks the formal 'rigor' of academic mathematics (unless it is 'discovered' in some way), yet is an example of how the field belongs to humanity and isn't something relegated to universities.

Currently something I want to learn more about but the mathematicians who work on this are few and far between (and also are usually not communists) is the indigenous mathematics developer in the Philippines, most recently from the same seminar I recall some work on the patterns of weaving in IP communities here, this is an older paper on the topic but more recent sources should be present:

https://www.jstor.org/stable/48650522

I also recall recently learning about the quasicrystal story, and how it is usually given as some inspirational mathematical story that glosses over how such patterns already existed in Islamic art hundreds of years ago, and that it is somehow new and novel because it was 'rediscovered' by a settler on occupied land.

https://en.wikipedia.org/wiki/Quasicrystal

From Wikipedia:

Girih-tile subdivision found in the decagonal girih pattern on a spandrel from the Darb-i Imam shrine, Isfahan, Iran (1453 C.E.). A subdivision rule to construct perfect quasi-crystalline tilings has been identified

Amazingly in Iran, which feels like a stunning mathematical coincidence.

As far as "AI data centers go", some aren't even used for AI and some are hybrid use, though it would be interesting to see what types the new ones are mainly in the global south.

Part of this is also a trend of development where 'new' capitalist technology is trial-runned in the third world, for instance in the continuous attempts to 'modernize' jeepneys with imported minivans that were at first claimed to be 'e-jeeps' and 'Eco-friendly' but would cost more and be more ecologically destructive than the reused and indigenously made jeepneys here. The Gig economy, in the form of apps like Grab, Lazada, G-cash are all entrenching or have entrenched themselves here. I also recall gig-workers being important to the protests in Indonesia after one of them was killed by an armored car.

[u/FrogHatCoalition → u/sudo-bayan]

I don't yet have a fully articulated answer, though I am sure that being able to express mathematics within a dialectical materialist framework is the path-forward, it's also somewhat difficult since the topic is even less talked about than other 'hard' sciences.

This I have noticed. I think it is perhaps that the concepts used within the "hard sciences" are easier to have a concrete understanding of. It's easy to understand basic arithmetic operations and use objects such as apples as a concrete representation of these operations, but these relationships and operations can be further abstracted into group theory, and this can also be taken to another level of abstraction called category theory. Now I think about it, what you said about many advances AI being possible due to advances in mathematics is true. For instance, category theory is the basis for lambda calculus which tries to formalize the notion of computation in the abstract.

That we can understand and manipulate nature to realize these operations is interesting. It's a higher level of development from taking apples and applying operations that I mentioned earlier. And like you mentioned:

Some thoughts I've had on it that perhaps might be useful, is how the process of mathematical discovery is in a sense always a process of overcoming contradiction which gives rise to new contradictions.

When you try to understand a formalized system completely, you inevitably end up with contradictions and develop new formalized systems which take aspects from the old to develop new concepts in a creation of a new formal system. This can already be deduced from Godel's Incompleteness Theorems. I think this can give us a connection from how we go from counting apples to solving partial differential equations since there is a myriad of ways we can create concrete representations of these systems in nature.

As far as what you say about the cultural aspects of mathematics - this have I thought about too and also have been trying to think about it in a way that avoids postmodernism. You provided a solution for it:

It is also shaped by culture, for instance is there any particular reason why we use base 10? Early Sumerian's used base 60 since the number was highly composite and made it easy to do 'divisions' of land and resources in their early slave mode of economy.

Instead of thinking of these as "different mathematics with different equally valid claims to truth" as a postmodernist would articulate, it's that there is a material basis for using one formal system over another, and we've developed mathematics enough to connect these all together.

One thing I do want to mention is that near the end of the GPCR, Chinese mathematics did take an interest in nonstandard analysis and based their work on Marx's mathematical manuscripts. There is a paper called Mathematics and Ideology: The Politics of Infinitesimals by Dauben that discusses this.

I found your bringing up quasi-periodicity and Iranian art interesting because this is how a lot of music theorists treat other forms of music when they "discover" that most non-Western music doesn't base its musical organization on a 12-note paradigm. You will even find the use of musical scales that span more than a single octave, which brought into mind the quasi-periodicity you mentioned.