## Theorizing, thought experiments, fake-data simulation

I think of theorizing as like thought experiments or, in statistics, fake-data simulation: A way of exploring the implications of one’s ideas, essentially a form of deductive reasoning. Arguably, much of fiction serves this purpose too, of mapping out the implications of existing postulates, and, conversely, revealing implicit postulates or assumptions that drive our thinking.

1. Daniel H. says:

For me, simulation serves as a good logic check for reasoning. The way my mind works, it’s very easy to miss something important unless I
a) explain it to someone else or
b) build a simulation
(See the link to my website for some more thoughts on the topic, something I wrote a year ago)
Cheers, Daniel

2. Vince2 says:

“I think of theorizing…”

… so you theorize about theorizing.

The term THEORY comes from Greek theōria — “contemplation, speculation; a looking at, or viewing”.

Late 15th Century the term evolved to “principles or methods of a science or art” (rather than its practice).

3. Re-wrote something I have been writing given something Martha and you recently commented https://gelmanstatdev.wpengine.com/2020/08/05/somethings-do-not-seem-to-spread-easily-the-role-of-simulation-in-statistical-practice-and-perhaps-theory/#comment-1411517

If one thinks of simulation more generally than we have so far here [using pseudo-random numbers], as experimenting and critically making sense of abstractions, expressed in diagrams or symbols, taken to be true without question – then mathematics and statistical simulation are just two ways of doing that.

Now, Peirce’s view seemed to be that making sense of abstractions (taken as true without question) by observing them as carefully as one could to fully understand them (as to what to make of them) was mathematics which was more basic that deduction. Here experimenting on diagrams or symbols that represented those abstraction was just to get a better way of observing. Often requiring creative design (theoromatic).

Now fiction is just a set of abstractions (taken as true without question). And like abstract statistical models all are false but some are useful.

Also, some have objected the the fake in the fake-data label. So I wrote this.

As an aside, statisticians Andrew Gelman and Jennifer Hill explained simulation using the expression “fake data” simulation in their 2006 book Data Analysis Using Regression and Multilevel/Hierarchical Models. The fake label emphasized the random samples were not real data but rather came from an abstractly defined possible world producing not real data but fake data. Others use synthetic data. The abstractly defined possible world with known truth also ended up being called a fake world. This was long before Donald Trump made the term fake news well know and the sense of that label may now distract from the positive value of the label fake in data simulation, as here it helps rather than blocks understanding of our actual world. Fake data simulation helps understand what repeatedly happens in possible worlds, where again we have determined the true effect and so we know it exactly. This is done to inform us of what to make of observations in our world when we don’t know the truth.

• Steve says:

Keith:

I don’t think it is quite right to say that Peirce thought that mathematics was more fundamental than deduction. He thought all thought was schematic. So, Frege and Russell’s logicism would not have made any sense to him. In fact, he created a graphical first order logic. I do not believe that he saw a sharp distinction between logic and mathematics and as he rejected both the analytic/synthetic distinction and the possibility of a priori knowledge, no such sharp distinction would have been useful. His pragmaticism already rejected the foundationalism that Tarski and Godel work later established.

• Steve:

First, I don’t think anyone gets Peirce right and his views on mathematics versus deduction may have varied.

The view I related above was from this diagram https://gelmanstatdev.wpengine.com/2017/11/29/expediting-organised-experience-statistics/ and early chapters from CORNELIS DE WAAL: PEIRCE – A GUIDE FOR THE PERPLEXED

In that diagram, mathematics is to the left of logic (which includes deduction) and things are informed by what on their left. See this more involved diagram to see where deduction is placed https://people.uta.fi/~attove/peirce_systems3.PDF. But again, another expert on Peirce may point to something different.

• Steve says:

Keith:

Fair enough and my comment was not meant to nitpick, but just to point out that whatever Peirce means about these relations between branches of knowledge, it is not what a foundationalist would mean. For instance, what is the relationship between science and ethics? In discussing probability, Peirce asks the question why we should care about the long run. I understand his answer to be that there is no reason to care about what is more probable unless you care about humanity and what will happen to future humans. Ethics doesn’t justify induction, but induction depends upon people have some minimal concern for future humans. My point is that many of the lines on the diagrams you share do not represent a justification relation but some other type of dependence. (Thanks for the diagrams.)

• Steve:

Thanks, now I understand you comment more than before.

Peirce did argue that caring about humanity and what will happen to future humans provided a social justification for induction and Ian Hacking once called this the faith, hope and charity justification. However, he also had the justification that induction provided the assurance, that although it might mislead (a false positive) persistence in adequate inquiry would eventually discover the error. That eventually might be for future inquirers but of course no one would ever know they could stop. So again future humans.

But then there was also the regulative assumption that any question we want an answer to, eventually with adequate inquiry there will be an helpful answer. But he indicated there was no justification for it, it was just a hope so that we did not give up on trying to learn. Used an analogy of a soldier surrounded by a formidable enemy shoting himself in the head.

However, I think this is peripheral to conceptualizing mathematics as experimenting on diagrams or symbols. That is primarily just a way of describing the practice of mathematics and a way it can be carried out or understood.

Also, many do not accept foundationalism so I don’t see this as my problem – it is not what a foundationalist would mean.

4. Z says:

It’s interesting, though, that one criterion for what makes “good fiction” is often how well it is obscured that this is what’s going on. If things seem too mechanical or inorganic, i.e. if the simulation settings are too discernible, then it’s deemed cold and inauthentic. I was just criticizing a movie for on these grounds a couple of days ago, but I gave it a pass because the actors were good enough to cover up the obvious plot design and still make it feel real.

5. jonathan says:

I use what I call Storyline to explore ideas. I create a fiction and see how it behaves, so as I develop the story, I’m also developing tracking how that occurs, which I then analyze. It’s equivalent to having a general model, like any rational person has, which I apply to find how that model works and doesnt work. This enables me to fit story pieces together, and then examine them from more angles so they become more nuanced. This can be a realism check, but it can also be a recognition that something else is occurring behind or within the story element. That is how plots work. I do that explicitly.

This is largely separate from my need to identify the fundamental understanding, as opposed to the practical understanding of today. Example: I read a long, beautiful piece about how to dial a phone. Who born in the last 20 years in the US has used a rotary dial phone? You dont need to know how to do that, but that skill embodies a lot of ideas, some technical and some cultural and personal, which get rolled up or inverted imperfectly into the tasks of using a phone today, one that may well present as a piece of flat, sometimes illuminated material. I like to analyze the inversions.

6. jim says:

I often hear writers talk about exploring ideas and outcomes or experimenting with possibilities but I feel like that makes pretty boring fiction.

But I wonder: how did fiction originate? Was it as a form of entertainment, or was it to communicate and/or illustrate ideas (e.g., religion often uses fiction to guide it’s practitioners)? I was going to say it originated as entertainment, but now I think maybe not: maybe it originated as a way to communicate ideas, and somewhere along the line someone realized that it could be used as entertainment as well. Eventually people figured out that it was more fun for entertainment than it was for moralizing or intellectualizing, and that gradually became it’s dominant purpose.

• Martha (Smith) says:

Interesting speculations.

• MaximB says:

Fiction originated as storytelling, which was a way of communicating experience. There is a great essay on the origins and the decline of the true storytelling, by Walter Benjamin (link here: https://arl.human.cornell.edu/linked%20docs/Walter%20Benjamin%20Storyteller.pdf )

Some excerpts:
“Less and less frequently do we encounter people with the ability to tell a tale properly. More and more often there is embarrassment all around when the wish to hear a story is expressed. It is as if something that seemed inalienable to us, the securest among our possessions, were taken from us: the ability to exchange experiences. One reason for this phenomenon is obvious: experience has fallen in value. And it looks as if it is continuing to fall in to bottomlessness. Every glance at a newspaper demonstrates that it has reached a new low, that our picture, not only of the external world but of the moral world as well, overnight has undergone changes which were never thought possible. With the [First] World War a process began to become apparent which has not halted since then. Was it not noticeable at the end of the war that men returned from the battlefield grown silent — not richer, but poorer in communicable experience?

“An orientation toward practical interests is characteristic of many born storytellers”

“Every morning brings us the news of the globe, and yet we are poor in noteworthy stories. This is because no event any longer comes to us without already being shot through with explanation. In other words,by now almost nothing that happens benefits storytelling; almost everything benefits information. Actually, it is half the art of storytelling to keep a story free from explanation as one reproduces it.”

• Martha (Smith) says:

MaximB said,
“With the [First] World War a process began to become apparent which has not halted since then. Was it not noticeable at the end of the war that men returned from the battlefield grown silent — not richer, but poorer in communicable experience?”

I don’t think the process began to be come apparent with WW1. The American Civil war took a large toll in many ways — see, for example, the Wikipedia article at https://en.wikipedia.org/wiki/American_Civil_War#Costs

7. Alex F says:

Ariel Rubinstein has written and talked a lot about how he thinks of models in economic theory as “fables” analogous to fictional stories. (He has a book, which I haven’t read, called Economic Fables.) Here is a talk of his on the subject — the talk starts at 29:50, but relevant section starts at 39:20 — comparing economic models to Chekhov stories:

• jim says:

yeah, that’s the daily market run down: fables! “Boeing was up today on the news that real mean don’t eat quiche, so with quiche prices down, more spinach will be diverted to biofuels, and you know what that means: lower fuel prices and more people flying for vacation, increasing the demand for planes”

just another one of those interactions…

• Alex F says:

32:20, sorry.

• Martha (Smith) says:

Thinking of models in economic theory as “fables” makes a lot of sense to me!