Despite our natural reluctance to assume that our senses are not sensitive to the majority of the reality around us, there is a very strong arguement from basic principles that the universe (even in our immediate surroundings) could be far more complex than we can imagine.
One has only to compare the amount of man's knowledge obtained (or which could have been obtained) by his unaided senses with the enormous increase provided by the development of such devices as telescopes, microscopes, radio receivers and X-ray machines, to realize how very limited we are. Note that the purpose of each of these is to receive energy which is too weak or of the wrong form to be detected by any of the senses, and to amplify or convert the information in that energy to a form or level which is within the capacity of one of them. Study of a list of such artificial aids shows that they can be separated into two distict categories. Telescopes, microscopes and similar "magnifying" techniques form a continuous and open-ended chain of development. The urge to see farther and smaller has always existed, and is fundamental to the extent of being instinctive. No matter how powerful an instrument is built, there will always be some object of interest which is barely visible, and so an awareness of things still beyond its range and an incentive to improve it. This has encouraged the development of the necessary technology (lenses, etc.).
On the other hand, such developments as radio communication and X-ray examination required the positive discovery of radio waves and X-rays before they could even be contemplated. Only then could the requisite technology be developed so that they could be used to gain further knowledge. One would expect any "extra" dimensions to come into this category, and there could well be other equally fundamental "unknowns." Until an initiating discovery is made, it is extremely difficult to conceive of their existence, speculate on their characteristics or imagine the consequences.
The particular case of radio waves and X-rays are also excellent examples of the limitations of our senses in other ways, since they are two examples of electromagnetic radiation. Such waves have been used or studied with wavelengths extending over a range of 1016 (10,000,000,000,000,000) although our senses respond only to visible light, which covers a range of barely 2:1 in wavelength, and outside this range we must rely entirely on aids. On a dark night, it is possible to see the light from a small torch bulb (radiating about a fiftieth of a watt of energy of visible light) at a range of about half a mile. On the other hand, you could stand within a few feet of an aerial radiating over a million watts of radio-frequency energy and be unaware that the transmitter is switched on.
John Ralphs, Exploring the Fourth Dimension
deoxy » State-Specific Physics