When we refer to two things as being "the same" or "equal to one another" we are applying a standard of tolerance. If, for example, we were making standardised cakes for a bakery then we would refer to them as being of the same weight if they did not vary by more than one gram of one another. Beyond a threshold of tolerance, humans interpret a change as qualitative; a change in the kind of thing an object is rather than a change in quantity of one of its properties. Even here though, the change is not exactly sudden, but instead it is underpinned by an ongoing process of gradual change.
The beginning of the correction to this sort of vulgar thought lies in the dialectic approach developed by Hegel. In this system, things no longer had a fixed character but changed according to the context in which they were situated. The principle of motion was introduced for the first time. In the ABC, this is compared to the relationship between a photograph and a piece of film. "Dialectical thinking is related to vulgar thinking in the same way that a motion picture is related to a photograph [...] Dialectics does not deny the syllogism, but teaches us to combine them in such a way as to bring our understanding closer to the eternally changing reality." This, although it was a major step forward, was only an anticipation of the dialectic developed by Marx. As the ABC says "Hegel was operating with ideological shadows as the ultimate reality." Marx corrected this view by rooting his dialectic in the material world; the objective, economic facts of society. "We call our dialectic material, since its roots are neither in heaven nor in the depths of our "free will", but in objective reality, in nature."
The key difference between dialectic and vulgar thinking, according to the ABC, is the movement of unchanging realities to a new level: in dialectics, what is eternal are the laws of motion that govern change rather than the things in themselves as the Aristotelian school held. This is compared with the development of the hard sciences over the past three hundred years to bring out the scientific character of dialectical materialism. To take two examples: in biology, the Linnaean system in which species were seen as fixed and unchanging entities was gradually replaced by the Darwinian perspective in which the gradual changes in organisms progressed slowly until a tolerance threshold was reached and a new species came into being. Likewise in chemistry, the older model in which elements unchangeable gave way to the modern perspective in which elements can (although admittedly at great difficulty) be transformed into other by the addition or removal of proton and electrons. In this way, the scientific character of the dialectic is brought out. "Dialectical logic expresses the laws of motion in contemporary scientific thought", or as is put right at the beginning of the ABC, "The dialectic is neither fiction nor mysticism, but a science of the forms of our thinking."