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The word Dimension merely suggests an attribute, not just a linear measure.
Thus Time is commonly referred to as the 4th dimension, for we can not measure its attributes with only length, height, and width.
But you may want to consider whether mass can be measured by length, height, width and time.
And of course, dimensions are not limited to physics. The beauty of a poem or of a rainbow or a sunrise cannot be described in terms of the first 4 dimensions. Truthfulness; or degree of faith; are similarly outside the physics net.
As is IQ.
And in geometry, one may consider degrees of freedom, which indeed exceed the first four.
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What is after the 4 dimention?
Theoretically the 5th dimension.
Why is adding subtracting and equating quantities possible only if they have the same dimension?
If they are not on the same dimension then you cannot do this. They will be different numbers and will not go together.
Is it possible to be moving from one dimension to another in a physical way?
Nothings impossible.
Is it possible to connect 3 houses to 3 utilities without crossing lines?
this is not possible unless it is in a 3-d dimension
If you are locked in a cube which you can not get out is it then possible to escape by using the fourth dimension?
The fourth dimension has never been reached, may not exist, and frankly nothing is known about it, so while it may be theoretically possible to do this, it has never been done and is likely impossible.
