Can the dhatu elements (earth, water, wind and fire) be considered as permanent?
No I don't think they ought to be considered as permanent.
Modern physics and chemistry use the word 'element' to refer to the various types of 'atom'.
The word 'dhatu' is translated as 'element' in a different way:
Whatever is characterized:
- by hardness (thaddha-lakkkhana) is the earth or solid-element;
- by cohesion (ābandhana) or fluidity, the water-element;
- by heating (paripācana), the fire or heat-element;
- by strengthening or supporting (vitthambhana), the wind or motion-element.
All four are present in every material object, though in varying degrees of strength. If, for instance, the earth element predominates, the material object is called 'solid', etc. - For the analysis of the 4 elements, s. dhātu-vavatthāna.
Any compound object (for example, a tree) might have some of these characteristics: but the object (e.g. the tree) is impermanent, and (therefore) the characteristics of the object are impermanent.
As far as I can see any thing is impermanent. What is impermanent defies description or conceptualization.
Here is more info on the subject. http://www.buddhanet.net/cbp2_f4.htm
All things arise due to causes and conditions. As causes and conditions are impermanent and will cease one day, all things will also cease correspondingly. When there is rising, there will be falling; when there is existence, there will be extinction. The rising and existence of things has its natural tendency towards cessation and extinction. It is like a wave; it comes and goes. Thus, when one sees the truth of "what this is, that is; this arising, that arises", one should also see the truth of "when this is not, that is not; this ceasing, that ceases". The Law of Dependent Origination pointed out the possibility of ending worldly suffering. It shows the way of liberation that corresponds to the Law of Cause and Effect.
"When one is born, one will die. One who admires high status will fall one day."
This is the natural Law of Cause and Effect. It is also an inner implication of the Law of Dependent Origination. It can be called the Cessation Process of the Law of Dependent Origination.
As soon as one starts discussing permanence, it is already in the field of impermanence. Intellectual understanding may suggest a path. The practice of the path can lead to the unknowable. No one who has been here has ever said anything that could describe it.