Surprise! We don’t have to detect other dimensions because we are working with them all the time according to General Schemas Theory (which is theory, but what the heck). S-Prime hypothesis says that there are ten schemas and that every schema is related to at least two dimensions and each dimension is related to at least two schemas, so there is parity between the number of schemas and dimensions. This roughly gives us 9 dimensions stretching up from the negative first dimension to the ninth dimension. And oddly enough String Theory starts right after that in the tenth dimension, and then going on to the Eleventh dimension with M-Theory, and 12th dimension in F-Theory. But these are schematized, in other words we have no conceptual or analogical framework for understanding those higher dimensions than the ninth. We say we can deal with 7+/-2 things in short term memory. But what is little understood is that those things can be independent and thus we can deal with things in a space up to the tenth dimension, in which the minimal solid has nine points. Interestingly enough the ninth dimension is just big enough to contain four dimensions of time and four dimensions of space which I call the Matrix of Spacetime/Timespace.
The scandal of our time is that we do not know what a concept is, or what meaning (Semantics) are. And this is because they are non-representables, that is because they are our insights into higher dimensionalities which when represented two and three dimensionally have to undergo a tremendous flattening dimensionally. We conceptualize designs for instance in higher dimensions and then we realize them on paper or in CAD systems in low dimensions. Understanding things conceptually is to understand them in higher dimensions where representation breaks down. Plato called this the non-representable intelligibles. He said that the men of earth only believe what they can hold in their hands. We have become representationalists and thus men of earth and so we do not understand the invisibles any longer, even though most of what we deal with in science these days are invisibles, like the forces, for instance.