You cannot picture this with your eye or with your visual imagination; but you understand that it is just the same as in three dimensions, but now with one dimension added. It just requires some mathematical imagination or hallucination (or the consumption of drugs…) to that. ‘see’ But mathematically, with our mind, it is just the same, but in one more dimension. And so we can continue, we represent our series of eight numbers as a vector or arrow from the origin to the point with coordinates (112, 115, 112, 106, 120, 105, 111, 109) in a of 8 dimensions’ ‘space and with length SQRT {112² + 115² + 112² + 106² + 120² + 105² + 111² + 109²} We have represented the numbers for height ‘graphically’ as an a direction, pointing out from the origin in a space of 8 dimensions and with length as given above. What if we had another vector, with numbers for another property of the 8 children? Let us say that we have measured also their weight, with the following (transpose) data vector for the weights W’ = 50 51 46 49 54 51 59 55 Now let us enter the 8 numbers for weight in the same 8-dimensional picture used to represent the height numbers. We now see two arrows: one representing height and the other weight. We show how this would look with only the first two coordinates for height and weight. As both vectors or arrows start from the origin (0,0), these two arrows make an angle with one another. We repeat a conclusion from the previous section: if two variables, e.g. height and weight, are associated positively (i.e. taller people tend to weigh more,
You cannot picture this with your eye or with your visual imagination; but you understand that it is just the same as in three dimensions, but now with one dimension added. It just requires some mathematical imagination or hallucination (or the consumption of drugs…) to ‘see’ that. But mathematically, with our mind, it is just the same, but in one more dimension. And so we can continue, we represent our series of eight numbers as a vector or arrow from the origin to the point with coordinates (112, 115, 112, 106, 120, 105, 111, 109) in a ‘space of 8 dimensions’ and with length SQRT {112² + 115² + 112² + 106² + 120² + 105² + 111² + 109²} We have represented the numbers for height ‘graphically’ as an a direction, pointing out from the origin in a space of 8 dimensions and with length as given above. What if we had another vector, with numbers for another property of the 8 children? Let us say that we have measured also their weight, with the following (transpose) data vector for the weights W’ = 50 51 46 49 54 51 59 55 Now let us enter the 8 numbers for weight in the same 8-dimensional picture used to represent the height numbers. We now see two arrows: one representing height and the other weight. We show how this would look with only the first two coordinates for height and weight. As both vectors or arrows start from the origin (0,0), these two arrows make an angle with one another. We repeat a conclusion from the previous section: if two variables, e.g. height and weight, are associated positively (i.e. taller people tend to weigh more,