The popular theory:
"How a worker communicates the location of a pollen and nectar source to other workers in the hive may be the most incredible and complex form of social behavior existing outside of the human race.
Upon her return to the hive with pollen and nectar, the worker bee performs an elaborate dance on the vertical surface of a comb. If the source is relatively distant from the hive (as it generally is), the dance takes the form of a figure-eight. The forager waggles her body from side to side as she moves forward in a straight line, then circles to the right, back to her starting point, waggles ahead again, and then circles to the left. This dance pattern is repeated a number of times. The angle of the straight run, or 'waggle,' from vertical is equal to the angle from the hive between the sun and the nectar/pollen source. If the flowers are located 45 degrees to the right of the sun, the dance will be oriented 45 degrees to right of vertical. The distance of the straight waggle run is proportional to the distance from the hive to the source. Details of this behavior can be found in many books, including an excellent discussion in Gould and Gould (1988), an easily read and comprehensive reference on the honeybee."
The Honeybee Waggle Dance:
An Active Participation, Role Playing Game
Daniel A. Herms
And the alternative theory:
"The traditional interpretation of the bee dance is destroyed categorically by the observation of one single factor: The human observer observes from above. The bee dances face to face on a lateral plane. What the bee perceives and what the human perceives are two entirely different things. I grant that the dance occurs. I do not grant that it communicates anything at all. It is a sharing of excitement. The knowledge of where the nectar or whatever is is deeper than that. The colony is a manifestation of generations integrated with the patterns of the environment. There is a great mind at play that humans are generally incapable of comprehending."
Principles of Beekeeping Backwards
Bee Culture – July, 2001
Charles Martin Simon