## Hamming-Space Model of Cultural Identity |
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Culture is complex, it is difficult to define, might consist of art, music, laws, tradition, stories, and go well beyond these things. It is a massive job to even contemplate a detailed simulation of human culture, hard to know where to even start. However, in order to even get a foothold in the rock, it is necessary to put together some sort of simplified model, that has at least plausible assumptions and gives results that could be seen as intuitively correct. I propose a binary Hamming space for this purpose.

A binary word is nothing more than a sequence of bits, and we can consider
each bit to be either 0 or 1, in the traditional logical concept these are
*FALSE* and *TRUE* or if we were to ask a suitable question,
the answer to the question might be *NO* or *YES*.

In order to calculate the Hamming distance between two binary words, merely compare every bit in one word against the corresponding bit in the other word, and count the number of bits that are different. If all bits are the same, then the words are identical and the Hamming distance is exactly zero. If only one bit is different then we say the Hamming distance is 1. We can also regard the Hamming space as the set of corners on a hyper-cube, thus if the binary words are 32 bits long (a convenient size for common computing architectures) then the binary Hamming space consists of the corners of a 32 dimensional hyper-cube (that's got 4294967296 corners by the way). From a geometric point of view, the Euclidean distance between corners on the cube is the square root of the Hamming distance but introducing the square root makes things more complex than it needs to be and anyhow, 32 dimensional geometries are difficult to visualize.

The above diagram shows the random spread of distances between a pair of 32 bit numbers, presuming arbitrary bit patterns.

The concept of Hamming Distance was invented by (and named after) Richard Hamming.

Hamming distance is often used in communication engineering and error correction calculations, and significant literature already exists on this subject.

For convenience only, this simulation regards Hamming distance as the
**percentage of bits that are different**, rather than as a "whole number" count.
This is nothing more than a simple proportional scale,
but it remains consistent if the total number of bits in the word might change.
Using this scale, the smallest value is zero (all bits are identical)
and the largest value is one (or 100% if you prefer, implying that all bits are different).

In order to convert a cultural identity into a simple vector of bits,
we consider that suitable questions might be asked, that reliably
yield a *YES / NO* answer, and that the set of answers to these
questions can identify the cultural identity of the person answering those
questions. Note that it is not necessary to actually ask the questions,
nor is it necessary that any particular individual would even decide to
provide honest answers. All that matters is such answers do potentially exist.
Let us presume that the individuals in question are sufficiently of sound
mind that they might at very least be able to be honest with themselves
as to how they would answer such questions.

Since the only valid operation in a Hamming space, is to calculate the distance between two points, we must further presume that people of one culture are able to approximately recognize other individuals who are similar to themselves, vs individuals who are different to themselves. Individuals who are more similar will have a lower Hamming distance, while individuals who are more different will have a larger Hamming distance. Note that in terms of probability, if two samples are taken entirely at random from a large Hamming space, the expected distance is 0.5 (or 50%) and this operation is no different to flipping a big bunch of coins and counting up the percentage of coins that land on heads.

The simulation presented here includes some confusion factors that allow for the situation where individuals may incorrectly judge each other and actually come up with a different distance to the true distance. Maybe this could be put down to poor communication, or perhaps some aspects of cultural identity are difficult to recognize. This is a tunable parameter the effect of which can be investigated.

Without intending to offend anyone, the following table very approximately
represents an outline of several religious responses to a bunch of
moral and cultural questions. All of the answers are restricted to merely
a *YES / NO* response and it is very important to point out that
this is a simplification, and many more nuanced answers are possible.

Question | Strict Muslim |
Moderate Muslim |
Jew | Fundamentalist Christian |
Liberal Christian |
Atheist |
---|---|---|---|---|---|---|

Is it acceptable to eat pork? | NO |
NO |
NO |
YES |
YES |
YES |

Is it acceptable to drink alcohol? | NO |
NO |
YES |
YES |
YES |
YES |

Is it acceptable to smoke marijuana? | NO |
YES |
NO |
NO |
NO |
YES |

Is sex outside marriage acceptable? | NO |
NO |
NO |
NO |
YES |
YES |

Is homosexuality acceptable? | NO |
NO |
NO |
NO |
YES |
YES |

Should an apostate be punished by death? | YES |
NO |
NO |
NO |
NO |
NO |

Is Friday a special day of prayer or holy day? | YES |
YES |
NO |
NO |
NO |
NO |

Is Saturday a special day of prayer or holy day? | NO |
NO |
YES |
NO |
NO |
NO |

Is Sunday a special day of prayer or holy day? | NO |
NO |
NO |
YES |
YES |
NO |

Did one divine being create the universe? | YES |
YES |
YES |
YES |
YES |
NO |

This is **only an example** of how such a concept might be applied,
it is not intended by any means to be a definitive guide to these religions.
The simulation itself just uses raw bit values, without any particular
consideration of what those bit values really mean. Actually, it turns out
that it does not matter, because one way or another, the formation of
cultural identities happens anyway.

To continue the example, here is a tabulation of distances between religions, as a percentage (based on the above 10 questions only, which is far from a complete outline of those religions):

Strict Muslim |
Moderate Muslim |
Jew | Fundamentalist Christian |
Liberal Christian |
Atheist | |
---|---|---|---|---|---|---|

Strict Muslim | 0% | 20% | 40% | 50% | 70% | 80% |

Moderate Muslim | 20% | 0% | 40% | 50% | 70% | 60% |

Jew | 40% | 40% | 0% | 30% | 50% | 60% |

Fundamentalist Christian | 50% | 50% | 30% | 0% | 20% | 50% |

Liberal Christian | 70% | 70% | 50% | 20% | 0% | 30% |

Atheist | 80% | 60% | 60% | 50% | 30% | 0% |

Hopefully, this should serve to illustrate the concept of Hamming distance. Note that it is always symmetric (distance is the same in either direction). I must emphasise that this is an example only, not intended to be a thorough analysis of comparative religion. Some of the answers may even be wrong, or arguable. It just shows that some simple YES/NO questions can efficiently capture a rough indicator of variations between religions in a multi-dimensional world. Actually, this approach could just a easily be applied to political parties or music-video preferences so it is more of a broad cultural identifier than anything specific to religion.

There is a major presumption made in this simulation that individuals will respond in some way to the interactions that they experience. That is, they will learn from what they see.

Most importantly, if an interaction is **successful** (and that is to say,
the individual in question came away from the interaction in a better
position than what they started with, or in other words they made a profit
in some way, or benefited) then the individual will find themselves slightly
impressed with the culture of whoever they were relating to. Thus, there is
a small chance they will change their opinion on some particular issue,
and in the process gradually move closer towards the other individuals
that they might consider "friends".

The contrary position is also in effect: if an interaction is **unsuccessful**
(that is to say, the individual ends up worse off or is harmed in some way)
then they might change their opinion in the opposite direction, and
start to disagree with the other people who have badly treated them.

This simple but effective learning process allows an individual to adapt their behaviour to the behaviour of others, and thus over time, express a preference for some cultures as against others.

- Liane Gabora explores a similar use of Hamming distance

(see Figure 1, Section 4.2, compare with histogram above). - Liane Gabora's Homepage.
- Wikipedia has an article on Hamming distance.
- Some people use the related concept of Hamming weight.
- Sometimes it is called Hamming metric, such as this PlanetMath entry.
- The same concepts appear in statistical clustering algorithms.