Since my last update, I have finished the math based portion of my research, and begun writing the final paper. I focused on Marx’s equation for the rate of profit, and was able to develop a substantial mathematical proof for the conditions under which the rate of profit will fall. I started by using basic calculus to find the change in the rate of profit over time. I found that, for a constant rate of surplus-value (which is often the case), the change in the rate of profit is proportional to the change in the ratio of variable capital (labor) to constant capital (machines and raw materials). While variable capital can only increase alongside constant capital due to the need for tools for workers to work with, constant capital can increase on its own through technological developments and maintenance costs. Due to competition driving capitalists to maximise efficiency, the rate at which variable and constant capital is change is one where the ratio of variable to constant will always decrease, causing the rate of profit to fall as well.

After analyzing the rate of profit through calculus, I modeled a phase space for it to see if there were specific attractors and basins of attraction. I used a 5D phase space with variables for variable capital (v), constant capital (c), rate of surplus-value (s’), and the rate of reinvestment in both variable (a) and constant capital (b). To model the evolution of the system over time, I used turnover cycles to represent how many times the profit from the previous cycle had been reinvested. While modeling this evolution, I found that variable capital evolves similar to a geometric sequence, where the ratio between values is 1+as’. Constant capital evolves similar to an arithmetic sequence, where the difference is bs’v. As the number of turnover cycles approaches infinity, there are two seperate attractors. The rate of profit will tend towards either 0 or s’. The basin of attraction for the rate of profit to approach 0 is primarily defined by the sequence representing variable capital converging to a finite value. This occurs if the rate of reinvestment changes to favor constant capital at a fast enough rate. Due to the tendency for competition and efficiency prioritising constant capital, this will often be the case.

After completing my research, I established a rudimentary outline and began writing the paper. The first section of the paper will cover hyperstitions and the nature of capital as a social construct manifested through processes. The second section will cover the total control of capital over humanity and the impossibility of revolution. The third section will cover Marx’s role in accelerationism and introduce the law of the tendency of the rate of profit to fall. The fourth section will my mathematical analysis of the rate of profit. The fifth section will cover the potential role of AI as a means of achieving communism through morphological change. The last section, although I may move it to earlier in the paper, will cover the concept of heat as the driving force of acceleration. So far I have a draft of the introduction,as well as the first, second and last sections.