Dichotomies are pervasive, often influencing our perspectives. From early infancy our percepts seem to be based on an inclination to carve the world into objects and backgrounds, figure and ground.

Our concepts often carve the world dichotomously: good and bad, left and right, male and female, this and that. Some of us dichotomize the world into physical and mental substance.

Our approaches are often dictated by our attitude toward the subjective and the objective. Knowledge requires interaction between our percepts, our concepts and our ideas, leading to their modifications and to transformation of our knowledge and means of knowing.

A continuum and a dichotomy are opposites. Dichotomies are easy to grasp, continua, not so much. Even when we learn to use number lines and to think of the number line as continuous, oddly it is a dichotomy that helps us to grasp that continuity.

We imagine an interval on the number line, say from zero to one, and cut it into two parts by choosing a number that divides it. For example, choose the cut at ½. Now we have two pieces: this, from zero to ½, and that, from ½ to 1. We are then told to take one of these pieces and again make a cut. A new two pieces. Again choose a piece. What we mean by the number line being continuous is that we can continue cutting and choosing without end, and we will never reach a grain too fine to be cut.

In the example, after 20 cuts, the size of the segment to receive the next cut will be less than one-millionth. After 40 cuts, less than one-trillionth. Tiny, you say? Yet the notion of a continuum says we can make a thousand such cuts, or a billion such cuts, and there would still be an itty-bitty teeny-weeny segment to which we could apply another billion cuts and not reach an end.

Because with a continuum there is no end. No surprise that thinking with dichotomies is easier.

Thinking in terms of dichotomies may be easier because of the way we are built or the way we develop our concepts and percepts.

Nevertheless we can wonder whether behind all this apparent cleavage into this and that, there is an underlying unity. Many religions teach this. Mind in Zen. Brahman in Advaita Vedanta. Science may get there.

In the case of gender, male and female, we are so captured by this dichotomy that babies born with anatomy that doesn’t fit the dichotomy are often surgically altered to put them in one category or the other. We don’t hear a lot about this messy business because we like to keep things simple: this or that.

It is reminiscent of the Egyptologist who was discovered shaving one of the stones in a pyramid to bring its length into accord with his theory.

In some states, the dichotomy of birth gender and identity gender is now being used politically. Someone’s gender determined anatomically at birth does not always jibe with their own sense of their gender. With restrooms dichotomized for men or women, which room should be used by a person birth-identified as male (BM) but self-identified as female (SF). The threat is supposed to be that men who are BM and SM will feign being BMSF and will enter women’s restrooms and sexually assault them. New laws are passed requiring individuals use the restroom corresponding to their birth gender. But who will check?

At every restroom? Will everyone need a birth gender identity card? Will there be a blossoming business of producing fake identity cards? Will there be false positives with police called about a BFSF who looks too masculine?

And, returning to reality, would any sexual predator choose a women’s restroom for a victim? For the comfortable surfaces? The décor? The fragrance? The guaranteed privacy? So unreal. Such hogwash.

Richard Bogartz is a professor of psychology at the University of Massachusetts Amherst.