It is the simple hypotheses of which one must be most wary; because these are the ones that have the most chances of passing unnoticed. - Henri Poincaré

What we call geometry is nothing but the study of formal properties of a certain continuous group; so that we may say, space is a group. The notion of this continuous group exists in our mind prior to all experience; but the assertion is no less true of the notion of many other continuous groups; for example, that which corresponds to the geometry of Lobatchevski.

Each muscle gives rise to a special sensation capable of augmenting or of diminishing, so that the totality of our muscular sensations will depend upon as many variables as we have muscles. From this point of view, motor space would have as many dimensions as we have muscles.

Doubting everything and believing everything are two equally convenient solutions that guard us from having to think.