[Piers]

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So why is it that I cannot conceive of any other dimension? I mean, I can't even get close!

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Try to think in terms of coordinate geometry.
You can uniquely define a point in one-dimensional space by giving one number.
You can uniquely define a point in two-dimensional space by giving two numbers. Latitude and longitude for example.
You can uniquely define a point in three-dimensional space by giving three numbers. Latitude, longitude and height.
You can uniquely define a point in four-dimensional space by giving four numbers. Latitude, longitude. height and time.
You can uniquely define a point in five-dimensional space by giving five numbers.
You can uniquely define a point in 769-dimensional space by giving 769 numbers.
etc…

Do a basic maths course.

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Has any other dimension been proved?

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This question completely misses the point.

The question is not, “Does n-dimensional space exist” for some value of n, but is it useful to model some real world phenomenon using n-dimensional space.

If the answer is yes (which it is), this does not say that the universe is n-dimensional, just that it is useful to model some part of the universe using n-dimensional mathematics.

Or to put it another way, if some current models of the universe require that you have more than four numbers to specify a point of space time then you have in effect more than four dimensions, how you visualise this is a purely personal matter.

It might of course be true that the universe actually is n-dimensional (for some specified n), but of course we will never be able to know that for certain.

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So my question is, why is believing in dimensions any different from believing in God or religion?

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It is different because, with scientific models, you are not making a statement about the real universe, just that it is useful to think about the universe in a certain way to achieve certain ends. Religions typically make firm statements about the universe.

Taking the view that believing in a religion helps you make decisions about your life, and that is why you are religious is fine. The religion can then be judged on how well it attains these ends.

It’s when you start saying that the specifics a particular religion are not a (rather dodgy looking) model, but a firm statement about how the universe really is that the problem occurs.