1. The capacity of working memory (WM) for about 7+/-2 ("the magical number") serially organized simple verbal items may represent a fundamental constant of cognition. Indeed, there is the same capacity for sense of familiarity of a number of recently encountered places, observed in radial maze performance both of lab rats and of humans. 2. Moreover, both species show a peculiar capacity for retaining WM of place over delays. The literature also describes paradoxes of extended time duration in certain human verbal recall tasks. Certain bird species have comparable capacity for delayed recall of about 4 to 8 food caches in a laboratory room. 3. In addition to these paradoxes of the time dimension with WM (still sometimes called "short-term" memory) there are another set of paradoxes of dimensionality for human judgment of magnitudes, noted by Miller in his classic 1956 paper on "the magical number." We are able to reliably refer magnitudes to a rating scale of up to about seven divisions. Remarkably, that finding is largely independent of perceptual modality or even of the extent of a linear interval selected within any given modality. 4. These paradoxes suggest that "the magical number 7+/2" depends on fundamental properties of mammalian brains. 5. This paper theorizes that WM numerosity is conserved as a fundamental constant, by means of elasticity of cognitive dimensionality, including the temporal pace of arrival of significant items of cognitive information. 6. A conjectural neural code for WM item-capacity is proposed here, which extends the hypothetical principle of binding-by-synchrony. The hypothesis is that several coactive frequencies of brain electrical rhythms each mark a WM item. 7. If, indeed, WM does involve a brain wave frequency code (perhaps within the gamma frequency range that has often been suggested with the binding hypothesis) mathematical considerations suggest additional relevance of harmonic relationships. That is, if copresent sinusoids bear harmony-like ratios and are confined within a single octave, then they have fast temporal properties, while avoiding spurious difference rhythms. Therefore, if the present hypothesis is valid, it implies a natural limit on parallel processing of separate items in organismic brains. 8. Similar logic of periodic signals may hold for slower ultradian rhythms, including hypothetical ones that contribute to time-tagging and fresh sense of familiarity of a day's event memories. Similar logic may also hold for spatial periodic functions across brain tissue that, hypothetically, represent cognitive information. Thus, harmonic transitions among temporal and spatial periodic functions are a possible vehicle for the cognitive dimensional elasticity that conserves WM capacity. 9. Supporting roles are proposed of (a) basal ganglia, as a high-capacity cache for traces of recent experience temporarily suspended from active task-relevant processing and (b) of hippocampus as a phase and interval comparator for oscillating signals, whose spatiotemporal dynamics are topologically equivalent to a toroidal grid.