[AntonioLao]

In the infinitesimal neighborhood of every infinitesimal vector quantity, there is one and only one opposite infinitesimal vector quantity such that their vector sum is identically zero if they are collinear. If they are not collinear, the resultant is an infinitesimal torque. Nevertheless, the inseparability of these vectors is the duality theorem. This theorem is applicable only in one dimension. In two or higher dimensional analyses, other more powerful theorems (e.g., divergence theorem, Gauss’ theorem, Stoke’s theorem and Green’s theorem) of vector calculus destroy the principle of inseparability. To compensate for the loss of generality, a new vector differential operator is necessary. This is the ‘ta’ operator. When it operates on frequency, the result is velocity. When it operates on force, the result is energy. When it operates on a dimensionless scalar, the result is units of length. When it operates on scalar time, the result is vector time. When it operates on a curvature, the result is a pure direction of tangency. In other words, this ‘ta’ operator creates oriented directional metric property. Furthermore, metric property implies orthogonality.

[Guille]

In which time (scalar, vector, ....) do we live?

[AntonioLao]

Originally Posted by GUILLE In which time (scalar, vector, ....) do we live?

We are all prisoners of the pseudoscalar thermodynamic entropic arrow of unidirectional time.

[Guille]

Originally Posted by AntonioLao We are all prisoners of the pseudoscalar thermodynamic entropic arrow of unidirectional time.

What tells us that?

[AntonioLao]

Originally Posted by GUILLE What tells us that?

Our failure to find the preferred direction of time. Hypothetically, if we do find this direction and can control it, basically, we can choose to stand still in time or move backward or whatever we want. It is the feeling that there is nothing we can do about it just like a prisoner in a jail cell. In other words, no freedom of movement in the time direction or dimension. We are all just going with the flow.