This essay is a follow-up to an ongoing trend of thoughts that I am unfolding for about a year now. My crude thesis is that topology is going to be the mathematics of the XXI° in the same way that statistics has been the mathematics of the XX°.
Nation spreadsheet
The industrial revolution led to an explosion of things produced. A factory was able to build in one day more goods than the life consumption of all the workers that were inside. Economies of scale were ruling the day. This industrialisation hunted down improvisations. Arts and crafts became a curiosity for tourists, another downstream effect of the industrial revolution. Before you know it, spreadsheets invaded the world: you can’t just rely on memory and shaking hands to handle huge plants. Data became the focus of attention: by inspecting closely the numbers you could spot places in which you could optimize some more, to produce more. This is the administrative world in which the working force is used to push numbers inside the system and extract value from them. The Tables of the law of the modern era.
The advent of new information and communication technologies during the transition from the XX° to the XXI° disrupted the existing norms. Interestingly, the year 2000 problem, which many of us remember, was primarily concerned with databases viewed as extensive tables. The term 'database' was often synonymous with SQL, a method for organizing data using relational algebra. Is there a better way to introduce us to the era of interconnected networks?
The rise of topology
All this is very nice but what does it concretely means that topology is replacing statistics? Let's explore some recent developments that illustrate how this shift is occurring in our daily lives.
The question of identity - who we are - is a complex philosophical inquiry. However, from a practical perspective, the use of passports and state-defined identities (such as social security numbers and names) is a relatively recent development. While humans are more than just numbers, from an administrative standpoint, this wasn't always the case. However, with the advent of the internet, social media, and the rise of pseudonyms, this has changed. Today, who you are connected with is more important than ever before. This is where identity politics come into play. The question of "who are your neighbors?" has become increasingly significant. Analyzing social circles and online tribes is more of a topological question than a statistical one. Knowing which Twitter circles you belong to, for example, is more meaningful than simply knowing your socioeconomic status.
Pagerank: Google became one of the largest corporation on earth using a topological idea. Their ranking algorithm, the one sorting the results of a web search, is based on the idea that “the interest” of a webpage depends on how much it is referenced by other webpages. So if you are looking for “ark of Noah" it will first retrieve all pages containing these words, then it will order them by counting how many pages pointed to each result (actually it is more complicated because you have to assign a weight to the pointing pages etc. but you get the idea).
Shadowban: the recent Twitter files scandal have brought to light what was intuitively felt and presented as a conspiracy theory by many. Nmaely the fact that Twitter had ways to act on the virality of tweets unbeknownst of the users. Puting political lenses aside from a technical point of view the tools and ideas used to regulate the virality of tweets are of a topological flavor.
Distributed systems: the majority of applications used on smartphones are no longer standalone programs but rather components of a distributed system that only function cohesively if multiple programs interact correctly with one another. The system must be viewed as a complete entity, including how the various parts are interconnected, and how they can access and share information with one another.
Social Media Tectonics: The social media landscape is constantly evolving before our very eyes. One recent shift is the introduction of Notes on Substack. This transformation can be compared to what occurred in the press and legacy media industry. For decades, individuals had limited options: they had access to a finite number of TV channels and a stable number of major newspapers. New players in the media business were few and far between. Nothing could be farthest from 2023. The example of Notes is very representative of what is happening. It is very early to know how things are going to unfold but it could go like this:
The point being: it is conceivable that the dynamics of interactions is impacted by those shifts in the social media landscape. The topology of discussions (who react to who, what and how trends are made etc.) is evolving in real time. Compare with what happened in MSM: the geography was not as flexible, the content of the discussion could change but not the infrastructure within which it occurred.
Do you recall the technology that gave the Romans their power? They excelled in civil engineering, and their roads were highly effective in developing the economy, transmitting information, and rapidly deploying troops. However, it would be erroneous to assume that All roads lead to Rome. It would be an error to think that since there are no borders, like Hadrian’s Wall, in the virtual world, the information could go anywhere without friction. It is indeed technically possible, but in reality there is so much information that you can’t retrieve the one you are looking for. A needle in a stayhack. So you have new roads to convey information. Those roads are paved with AIs.
Inside and out
Another theme linked to the evolution of our mental geography is a subtle one: in 1984 like dystopian novel, the idea is that the powers that be see everything. You have no privacy and big brother is recording every move you make. The pinacle of this nightmare was the surveillance capitalism model. This is a prototypical statistician approach. By studying meta data you could optimize your predictions on where the next click would happen. LLMs change that. First they allow the analysis of data (not only of meta data), but more related to the subject of this essay they turn the surveillance model inside-out. By training judiciously the GPTs of the world you can also control what they are going to produce. The most brutal way to do it would be to give it a skewed learning material - think history told by CCP. Now since the access to information will be done through those kind of AIs, you (as a dictator) don’t really care what the population is going to ask to the GPT models, because you know that in every answer you will be depicted as the “Genius of Carpathians” or something like that. It is no longer what you are looking, or listening at, but what is shown or told to you. The control is shifting from trying to get what you do to providing what is allowed. The landscape of political control is changing.
Conclusion
I am still thinking about all that. It is very much “work in progress”. I have the feeling that the frame is correct. More and more activities will be driven by topological considerations rather than statistical considerations. I'll attempt to consider this more coherently, but if I step back and evaluate what I've published on this substack since I began, the trend is evident. It's akin to an imperceptible pattern persisting throughout time."
Also would be interesting to relate the zeitgeist of statistics with the formation of police states. What would change with topological police states? Alphonse Bertillon comes to my mind. Son of of two statisticians and police officer who developed anthropometry for identification (addressability) of individuals via statistics of physical traits.
Very cool