Integration leads to Higher Dimension.

First let us look at the mathematical space. When we integrate we get the higher dimension plus an initially unknown constant.

Integrating a point gives us a line. Integrating a line gives us an plane / area / surface area. Integration again gives us the space / volume of a container (real or imaginary). Integration then leads us to a higher dimension.

Can this be applied to other disciplines / areas of our life?

Now, we come to the hitherto "unknown constant" on integration. Further analysis, application of range of interest, etc., gives us possible value(s) for the constant "c". However, we need not be afraid of this unknown.

Similary, when we try to integrate, then there is that unknown. Should we boldly go where we have not been before? We do take bold steps, repeatedly. Examples: going to a new school, forming new friends, finding your life-partner, taking up new jobs, heading to an unknown land, etc. In each of these situations, we adjust - we find out the values in that new dimension we have entered - and the value of constant is arrived at.

Corrollary: Differentiation gives us the slope of the function, which is a lower dimension. All we find out is "how slippery" the slope is - and usually it is quite definite, without any unknown constants.

Once again, by differentiating this and that, we only are leading ourselves to worry about the slopes... and unless it is a flat horizontal one, there is a downside to it in one way or other! I guess that is why birds of a feather flock together - there is no worry about the slope of differentiation.

First let us look at the mathematical space. When we integrate we get the higher dimension plus an initially unknown constant.

Integrating a point gives us a line. Integrating a line gives us an plane / area / surface area. Integration again gives us the space / volume of a container (real or imaginary). Integration then leads us to a higher dimension.

Can this be applied to other disciplines / areas of our life?

Now, we come to the hitherto "unknown constant" on integration. Further analysis, application of range of interest, etc., gives us possible value(s) for the constant "c". However, we need not be afraid of this unknown.

Similary, when we try to integrate, then there is that unknown. Should we boldly go where we have not been before? We do take bold steps, repeatedly. Examples: going to a new school, forming new friends, finding your life-partner, taking up new jobs, heading to an unknown land, etc. In each of these situations, we adjust - we find out the values in that new dimension we have entered - and the value of constant is arrived at.

Corrollary: Differentiation gives us the slope of the function, which is a lower dimension. All we find out is "how slippery" the slope is - and usually it is quite definite, without any unknown constants.

Once again, by differentiating this and that, we only are leading ourselves to worry about the slopes... and unless it is a flat horizontal one, there is a downside to it in one way or other! I guess that is why birds of a feather flock together - there is no worry about the slope of differentiation.