**References for causal sets **
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**
THE ORIGIN OF
CAUSAL SETS
**We can, of course, invent causal sets or generate them artificially
for the purpose of studying them. But in nature, causal sets come from
observation. We learn causal sets by observing nature. Interactions are their
natural source. In Physics, and interaction takes place when two physical
objects, that are different and independent, approach each other and affect
each-other's state. For example, a beam of light impinging on a photosensitive
element that generates a signal is an interaction and gives rise to one causal
pair where the beam is the cause and the signal is the effect. But not the only
cause: the geometry is also a cause. The interaction happens if and only if the
sensor is located in the trajectory of the beam.

Causal sets are very valuable for us, and we treasure them to the point that we are constantly seeking them. A child who asks "why" is asking for a causality. A scientist who studies a disease, a detective who investigates a crime, a viewer who is watching the news, are all seeking causality. Causality is what allows us to predict, and predicting gives us more options and helps us to live better and survive.

Because causal sets are so valuable for us, we save them and preserve them in many different ways: literature, manuals, theories, computer programs, pictures, and many others. The original causal sets can be recovered fro there, at least in some case. One of the most useful sources for recovery are computer programs. A causal set is an algorithm, and so also is a computer program. A computer program is a giant causal set, encoded in some human-readable programming language. Small programs can be converted manually, but specialized language-specific software is needed to make conversion more agile and less error prone. To my knowledge, no such software exists.

But causal sets by themselves have been vastly ignored. There is very little specific literature about them and their properties. Here is what I have found so far.

**
CAUSAL SETS POSING AS QUANTUM GRAVITY
**Most of what has been written so far about causal sets is specific
for quantum gravity. This includes the "A
non-technical introduction to causal sets" by Rafael Sorkin,
Geometry from order: causal sets also by Rafael Sorkin, the
Wikipedia page on causal sets,
the Wikipedia page on
causal structure, the
Wikipedia page on Rafael Sorkin, a
Non-technical introduction to causal sets by Rafael Sorkin, and
Causal sets and quantum
gravity. Causal set theory
and the origin of mass ratio is an article by Carey Carlson where he uses
pure causal reasoning to derive causal models for several fundamental particles
and uses the models to calculate the proton/electron mass ratio. The result is
1836, while the measured value is currently accepted to be 1836.15. This is a
fantastic success for the causal theory.

In the same category, there is also
The scalar curvature of a causal set, by D.M. T. Benincasa and F. Dowker,
arXiv: 1001.2725v4 [gr-qc] 1 Nov 2011. This paper is also about quantum gravity,
but it has a unique feature: it proposes an approximately local ** action
functional for causal sets**.

**
CAUSAL SETS POSING AS PARTIALLY ORDERED SETS
**That is because causal sets are considered as a particular case of
partially ordered sets. Even partially ordered sets came to attention only
recently, and several books have been published about them. But nearly all the
books are concerned mostly with

**
CAUSAL SETS PROPER
**But causal sets are in fact a

Ten simple rules for dynamic causal modeling, by K. E. Stephan, W. D. Penny, R. J. Moran, H. E. M. den Ouden, J. Daunizeau, and K. J. Friston. Neuroimage, 49 (2010) 3099-3109. Many references are included.

Causal sets from simple models of computation, by Tommaso Bolognesi, arXiv:1004.3128, April 19, 2010.

However, none of these authors appears to be aware of my work, specifically
of the following three properties that I have proposed and apply to any causal
set model of a dynamical system:

(1) the causal set is the simplest mathematical object that has a metric;

(2) the simplest metric of causal sets represents action in the dynamical model.

(3) as a physical model, causal sets satisfy Lee Smolin's third rule for
competing hypothesis, also known as Occam's razor.

I also propose that, as a result of the third property, and of the fact that all
physical systems this side of the black holes are causal, the third property
should be reversed as follows: Lee Smolin's third rule and Occam's razor follow
as a consequence of the first and second properties of causal set dynamical
models.

My papers in WASET, Complexity, and JAGI should also be included here. Note that, being unaware of causal sets, I referred to them as canonical matrices, or as partially ordered sets. Now I know I meant causal sets in all cases.