geometric interpretation of the expansion of an epistemology

José Manuel Rodríguez Caballero josephcmac at
Sun Jul 10 17:07:38 EDT 2022

Vaughan Pratt wrote:

> To address my question of what information is contained in disinformation,
> Jos'e Caballero suggests using proof length in a Bayesian framework,

Thanks for the criticism. I developed another version, which is frequentist
in spirit and it is more practical, but the idea is the same: my audience
learns from data using statistical inference. My starting point is the
concept of the Riemann manifold, (M, g), where M is a smooth manifold and g
is a metric. S. L. Lauritzen

Stefan L Lauritzen. “Statistical manifolds”. In: Differential geometry in
statistical inference 10 (1987), pp. 163–

defined a statistical manifold (M, g, C) as a Riemannian manifold (M, g)
equipped with a totally symmetric cubic tensor C. I propose a model of how
disinformation can affect an entity learning about the world through
statistical inference. My model involves constructing a fiber bundle on a
statistical manifold. The points on the base space play the role of
possible worldviews according to a family of statistical models
corresponding to the official narrative. A fiber over a point is the set of
all unconscious biases related to the purely rational worldview that point
represents. My thesis is that disinformation exploits the fact that the
maximum likelihood on the bundle can be projected to a point that is not
the maximum likelihood on the base space. Therefore, in my framework, the
art of disinformation can be formalized as the construction of a fiber
bundle through an alternative narrative that is an extension of the
official one (base space).

This quote expresses the intuition behind the construction of the fiber

Disinformation preys on the cognitive vulnerabilities of its targets by
> taking advantage of pre-existing anxieties or beliefs that predispose them
> to accept false information. This requires the aggressor to have an acute
> understanding of the socio-political dynamics at play and to know exactly
> when and how to penetrate to best exploit these vulnerabilities

Reference: François du Cluzel, innovationhub, June-November 2020

Dennis Hamilton wrote,

> "I find it more interesting that the idea of someone's worldview being
> something having Shannon entropy goes unchallenged."

In my current model of disinformation, the separation between two
worldviews can be measured using the Kullback–Leibler divergence (aka
relative Shannon information):

Kullback, S.; Leibler, R.A. (1951). "On information and sufficiency".
Annals of Mathematical Statistics. 22 (1): 79–86.
doi:10.1214/aoms/1177729694. JSTOR 2236703. MR 0039968.

We may ask: Where is the connection between my model and the foundations of
mathematics? I think that the connection relies on the association between
the data and the statistical model (embedded in the statistical manifold).
The probability Pr( data = d | theta = x ) of getting the data for a
specific value of the parameter theta, which is crucial for statistical
inference, is deeply connected to the proof length of getting the data in a
deductive system (parametrized by theta). That is, the probability of
obtaining a specific dataset may depend upon the complexity of describing
this dataset: the easier is to describe a dataset in a formal system, the
higher the probability to get it in practice.

Of course, one of the limitations of my model is that it assumes that the
audience learns from statistical inference. It is not clear that this is
the biological way in which the human brain learns. Anyway, my model could
be useful for non-human agents, such as neural networks and bayesian
networks, which may also be victims of disinformation. There is nothing
intrinsically human about disinformation, it is just a cryptographic
protocol to affect the way in which the victim processes information to
develop a worldview, i.e., it is hacking on epistemology.

Kind regards,
Jose M.
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