Capital has two core contradictions, or incompatibilities, with the world it exists within:

• The contradiction with human nature: the class divide which sees some exploited, made to suffer, deprived materially and spiritually of their natural human right to autonomy; others drowning in spoils but experiencing (consciously as guilt, or subconsciously as rage or self-righteousness) the cruelty which their comfort is built upon. Moreover, across all classes, the 24/7 logic of market imperative creates a pervasive feeling of precarity and anxiety. We can call this human pain generated by capitalism, alienation.
• The contradiction with non-human nature: the exponential growth pattern of capital results in a commensurate exponentially growing extraction from nature, or dumping of waste into nature. In either case, an exponentially increasing divergence from our biosphere’s expected condition.

Another way of putting it is that Capital (as a model of reality) has a large “error term” with real reality, and this error term can be decomposed as the combination of the above two terms.

Fundamentally, these errors arise because Capital only can see information about the expenditure of labor-time. It cannot see the alienation caused to people and it cannot see the impact on the biosphere, because neither of these is represented in the input signals (i.e., prices, which correspond to labor-time) processed by Capital.

In capitalism, the capitalist class can never drive these error terms too close to zero. To do so would necessitate the death of Capital as a social process, which means that capitalists would have to go get jobs, which cannot be allowed to happen.

Therefore, they must punt. To this end, they can attempt to shift error back and forth between the terms in order to make sure either one does not get so large as to destabilize the system. It is also important to remember that each of these error terms is not a single number, but a field over the surface of the earth. I.e., we have a differing amount of human alienation at every given location, which we can think of maybe as a function $S^2 \to \mathbb{R}$. The capitalist class can also punt within this error term, and smudge the error around to avoid it getting too concentrated at key points.

Applying this model

A great example of both is what you could call “the imperial mode of living”, after the book of the same name. Inside the imperial core (in the US, Germany, France, Netherlands, etc.), large swathes of the population have enjoyed access to cheap electronics, cars, food, clothing, etc. This consumption serves to compensate for the spiritual emptiness of life under capitalism and adheres to Capital those closest to its levers of power, those theoretically most in a position to act to change the course of things.

This consumption is a reduction in the “alienation” component of the error term at the points within the imperialist core. Because the error term generated by Capital cannot be reduced to zero, if we are able to reduce it at some points, our model predicts it must be increased at other points in the alienation component, or in the error-term with the biosphere.

And indeed this is the case. The cheap consumer goods are only made possible through

• the hyper-exploitation of workers in the imperialized countries (i.e., an increase in alienation at those points)
• the extraction of materials generated by nature (wood, oil, ore deposits) at a rate greater than their regeneration
• the replacement of ecosystems with monocultures and livestock
• the dumping of plastics, CO2, and other waste, at a rate which the biosphere cannot metabolize

The smudging of alienation across humanity can also be done within a polity at a given location, rather than smudging it geographically (which suggests the inadequacy of $S^2 \to \mathbb{R}$ as a model). This is what is accomplished by racial caste systems, such as we have in the United States. The alienation of a certain segment of the population is reduced (or at least, not increased) at the expense of increased alienation for others.

The patriarchal family structure can also be seen in this light. The alienation of the male breadwinner (generated by the class domination of Capital) in the form of insufficient wages and lack of autonomy, is vented by him through domination of his wife: both squeezing domestic labor out of her to compensate for the insufficient wage, and through personal abusive domination, libidinally compensating for the lack of autonomy in his life.

Resolving the core contradictions

Since Capital necessarily generates a certain fairly large level of error, the only way to drive the error term close to zero is to eliminate Capital as a social process and construct new social processes that perform its essential functions (coordination of production of necessary goods, giving people something to do with their time, etc.), but which does not generate large error terms of these types. This is definitionally the project of constructing communism.