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Falkenherz: Thank you all for your replies. From what I have gathered, singuarities seem to be the exception, the cause of which are so complex and varied that they cannot be predicted, while anomalies are kind of a freak law of nature that always applies if certain conditions are met, is that right?

So the floating rocks seem to be caused by a singularity though they themselves might not be a singularity, they have just been "attracted" by it.

What about the fantasy gods? Someone said they are more of an anomaly, but considering that such a god is infinite in its existence and power, wouldn't that be a singularity?

And the collapse of Barad-dûr doesn't seem to be singularity or anomaly either, right?
Lot of different explanations, most of them valid by the way. Initially, a singularity was a scientific term, the point at which a function ceases to operate and returns an extreme or unpredictible variable. An anomaly is an exception. A singularity may be evidenced by anomalies. My way to explain it would be that an anomaly will always be defined by comparison to what the normal situation is. If you take 100 rocks and plunge them in water, the normal ( if not universal ) behaviour of these rocks will be to sink to the bottom. Yet, if your water has a high salt degree, and if the rock has a low density, it may float. Anomaly. A singularity is something unique, that goes beyond any function you may refer to. You plunge the rock into water and it becomes sentient. To take another example : if you observe a heartbeat diagram, it follows a pattern. A disruption in that pattern is an anomaly. The disappearnce of that pattern whereas the observed indivivual still walks and lives normally is a singularity.

The question about god - or gods - being a singularity or singularities is metaphysics. Let's stay with fantasy gods. an existing, established godlike creature would not be an anomaly, and certainly not a singularity, but it may have such disruptive powers that it could create anomalies, or even, in extreme cases, disrupt the pattern so much that it causes a singularity. A singularity would also be a mortal tuning into a god suddenly.

Bard-dûr, now. The dark tower is made of materials. These are normally subject to decay and collapse. It was only the existence of the ring and the power of Sauron that kept those materials together. When the cohesive force disappear, the materials retun to their inert state and the tower collapses. Normal behaviour , thus no anomaly, no singularity. The destruction of the ring is the singularity, since the function that describes the way the power operates suddenly displays an extreme behaviour. The fact the tower was holding together was an anomaly, that is if you don't consider magic to be a normal pattern of MiddleEarth.
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Phc7006: "Here is exactly what you wanted to know."
Thanks a lot. This is basically the scientific, but not too scientific explanation that I was looking for. So basically, if I had a fantasy world where there are disruptive powers that are beyond human understanding, and these powers can cause changes to the world, that defy common laws of nature but seem to be permanent (like a zone of snow in the desert), I would probably call these changes anomalies. The powers that created that change are a part of the world (like an existing, established godlike creature as you said), however the change itself clearly runs contrary to the normal, perceived laws of nature and therefore would probably be viewed as anomalous (speak an anomaly) by the inhabitants of that world.
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Phc7006: "Here is exactly what you wanted to know."
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Falkenherz: Thanks a lot. This is basically the scientific, but not too scientific explanation that I was looking for. So basically, if I had a fantasy world where there are disruptive powers that are beyond human understanding, and these powers can cause changes to the world, that defy common laws of nature but seem to be permanent (like a zone of snow in the desert), I would probably call these changes anomalies. The powers that created that change are a part of the world (like an existing, established godlike creature as you said), however the change itself clearly runs contrary to the normal, perceived laws of nature and therefore would probably be viewed as anomalous (speak an anomaly) by the inhabitants of that world.
Indeed. the "function" that governs the behvioural pattern of these beings is still there and still returns a result that is within the pattern.

A singularity, in that context, would, for instance, be the sudden disappearance of the gods, or some game-changing event making them as weak as the mere mortals, or modifying their powers. A comet in the sky and sudely the one supetnatural being who was travelling with his snowy zone suddenly is surrounded by a permanent thunderstorm, and the one who was allways summoning butterflies and flowers is now summoning ghastly werewolves.
An anomaly is an exception. A singularity is convergence.