# When the search for confirmation becomes a basic logical fallacy

In deductive reasoning we make use of a hypothetical syllogism through the following steps.

• The theory is a true theory.
• Provide the theory with reasonable parameter values.
• To arrive at undeniable consequences of this theory and these parameter values.

A logical fallacy turns this around through the steps

• We observe undeniable ground truth about certain parameter values.
• A theory provided with some of these parameter values provides the others.
• Therefore the theory is true.

Unfortunately for science, the deductive syllogism is of little use, and the logical fallacy appears so reasonable that scientists commit it routinely.

One observation about tides is that they are often exaggerated in bays, inlets and estuaries. A reason often advanced to explain this is that the bay, inlet, or estuary has a natural resonance almost equal to the forcing period of the tides; a diurnal or semidiurnal period. Often the argument for this follows these steps.

• Assume a model of a bay as a rectangular body of water open at one end to the ocean. This body will have normal periods calculable from its depth and length.
• Assume reasonable values for depth and length. A calculation shows the near equivalence between resonant periods and some tidal component.
• Therefore the exaggerated tides result from resonance.

This argument almost verbatim is found in An Introduction to Oceanography by C.A.M. King regarding the exaggerated tides in the Bay of Fundy. This is an old textbook, which actually has an extremely interesting discussion of the tides; but, the same argument appears in modern oceanography texts as well as in magazine articles about tides and tidal bores.

King used 225 feet as the average depth of the bay, and 160 miles as its length. Where did King obtain these figures? There is no clue. But it may be that he worked backward to find plausible values that fit the idea of resonance. The sea-end of The Bay of Fundy has a depth of 200 fathoms; so, an average depth of 225ft is not implausible. The length of the bay from Truro to its sea-end is more than 200 nautical miles, however. Moreover, the bay is not rectangular. It has a gradual opening and deepening from Truro to its sea-end and there is no real justification for the rectangular model at all. Even attempting to assign a length to the bay is problematic. Perhaps it makes a good example of applying a wrong model.

If one were to apply a more correct calculation for tidal response in this instance, the profile of tidal heights from head- to sea-end is a Bessel function and the parameters place it quite far from resonance. The exaggerated tides result from geometry alone, not resonance.