There are four seasons, and four distinct phases of the moon. Perhaps these and other natural occurrences of the number four explain the hold it has over people, including those who find things in fours even when they do not so occur.
Take for example the four alchemical elements - earth, air, fire and water. In more modern terms these are solid, gas, energy and liquid. Today we recognize three of these as states of matter, while energy is distinct from matter in fundamental ways. Part of the problem back then was that the notion of different kinds of observable phenomena had not been fully developed. Thus because wind was regarded as a characteristic of air, and not a form of energy expressed through the motion of air, the fact that wind was more closely related to heat than to gas was not realized until much later when the Four Elements dogma was examined critically and found wanting.
Even that is not the only flaw in the dogma, though. In those days religion still had such a firm hold on people's thinking that the Four Elements were regarded as having, in addition to their physical characteristics, different moral characteristics as well. Earth was seen as least holy because it was lower than all others, and showed no inclination to rise unless pushed from below. Air was most holy because it was above all others, and therefore closer to heaven. Fire was good because it at least had a natural predisposition to rise. But water, which fell, ran downhill, and even seeped into the ground, was the backsliding element.
There was an assumed but never described fifth element in the world of the alchemist against which the moral traits of the other four were judged. As is often the case, the manner in which the world is described tells us more about the describer than the described, and we notice that a five-element conception of the universe was described by referring only to four elements. The number four just seemed better than five for some reason.
Fast-forward to the 20th century, and the definition of time as a fourth dimension. The first three, of course, are measurements of distance in three perpendicular axes to measure space. It's true that thought games do posit spaces containing more than three dimensions, and timestreams having more than one - or at least moving in more than one direction. In fact, we need only go back to religion to find the idea of multidimensional time - an eternal deity predates time and will outlast its ending, and by thus being greater than time must perceive it in ways we cannot. But for our own perceptions, triaxial space and monaxial, unidirectional time are all we get.
The grouping of a temporal dimension with the three spatial dimensions makes perfect sense - until you examine it critically and with an iconoclastic attitude. Yes, both space and time are measurable phenomena - but so are mass and temperature. Why not include these as dimensions? Much of the detailed knowledge we have of our universe is derived from the interaction of mass, temperature, distance and time. Shouldn't they all be taken together as attributes of existence? But if we do this in terms of dimensions we'll get a list longer than the periodic table (where 92 natural elements and a growing number of manmade ones have replaced the four familiar to those who hoped to transform lead into gold).
Okay, so collapse the three dimensions of space into a single concept, with the dimensions relegated to physical characteristics thereof. Add time as a separate concept equally necessary to our perceptions of existence, but clearly not the same thing as space. Throw in matter and energy, the things in which we measure such things as mass and temperature. How many is that? Four again! Well, there are those who already insist on putting a specific Deity into the mix, and others who want to consider an ecumenical Intelligent Design, so perhaps we can hold out the possibility of a fifth - provisionally. For the sake of diversity if nothing else...
There is another Four that has been leading physicists on a merry chase since early in the 20th century - the four Forces that are the subject of the quest for a Unified Field Theory. This quest even left Albert Einstein discouraged and defeated, so don't look to me for an answer. However it does seem interesting to me that one of the proposed effects of defining the UFT would be - among other things - being able to transmute matter. To turn lead into gold. Hoo-boy.
The four Forces are electromagnetism, gravity, the strong force, and the weak force. EM and gravity we all grasp. The strong force is what causes like-charged particles, such as protons, to stick together in atomic nuclei, despite the observed fact that like-charged particles tend to repel one another. The weak force is another subatomic phenomenon, the exact description of which has slipped my mind, but probably has something to do with what keeps electrons in orbit of atomic nuclei, instead of being drawn by opposing charges to join the protons down yonder in the nucleus.
What the UFT would do, its pursuers claim, is show us how to make one force communicate directly with another - to turn energy invested in, say, electricity, into a gravitational field; or manipulate the strong force to produce cold fusion; or deconstruct atoms from a length of pipe and have shiny gold doubloons appear in its place - all without draining half the energy potential of several suns to make it happen.
As things stand now, we can only cause one force to interact with another by translating it through something else. As far as I know, that something else has always been motion. In those particle accelerators you sometimes read about in science magazines, electromagnetism is used to invest kinetic energy in a subatomic particle so that when it hits a nucleus, it neither bounces off nor simply joins the protons and neutrons already there, but actually breaks the nucleus up. You can't do that by applying electromagnetic force directly. You have to translate it through motion.
It may even be that if the UFT is never worked out, it will be because kinetic energy is an overlooked fifth force that is the natural translator for the other four. But since I'm not a trained physicist, no one would listen to me even if I suggested it.
What makes these four Forces most fascinating is what the universe would be like without them. Without the strong and weak forces, all matter would float motionless in a vast fog of loose neutrons. There would be no electrons or protons without electromagnetism, and the absence of gravity would prevent the particles in the fog from clumping together. It sure is a good thing for us that these Forces do exist. However many of them there really are.