|I welcome the author’s constructive comments. The new diagrams allow me to further specify my critique. But let me start with a simple question. Imagine an economy in which GDP ´shrinks every year with a constant rate, until the economy simply vanishes. According to your approach, this economy would still add a certain amount of GDP every year, hence grow in the absolute terms of cumulative GDP. Would you still stick to your argument? In fact, this economy would also consume less and less energy. In my view, this simple argument shows that your addition approach is deeply flawed.|
Let me turn to the diagram showing Lotka’s wheel. This appears confusing to me. The arrows labelled ‘waste’ seem to contribute to the growth of the un-utilized residue. That would violate the Second Law, as ‘waste’ is ultimately entropy production, which by definition cannot be utilized for running the wheel. A correct diagram would show how the wheel contributes to harnessing more energy. Further, the diagram suggests that energy is simply speeding up the wheel. That does not match with Lotka’s original account: What is missing is the key role of natural selection. Natural selection is about competing wheels, such that eventually those surpass others in competition that increase energy throughputs, in relative terms.
Why is this important for assessing the authors’ approach? Lotka considers the evolution of structures. The question is how far cumulative annual GDP reflects this. The authors refer to Bettencourt et al. and indeed, the paradigmatic example for the wheel, in the economic context, is urbanization: cities are Lotka’s wheels. Urban growth is the key driver of GDP growth and wealth creation. But Bettencourt and many others have argued that the cause of this is precisely what is NOT covered in GDP, by definition, namely positive externalities of knowledge production. This is the gist of New Growth Theory modelling, and central to urban and regional economics. Indeed, positive externalities are what Piketty refers to as ‘dark matter’. Knowledge grows, in this sense is a stock, and knowledge guides the designs of technological artefacts that make up Lotka’s wheel.
Now, if by definition positive externalities are not covered by GDP data, how can one argue that GDP, added up through time, reflects the resulting stock of knowledge? The authors must present a convincing causal account for that, which is still missing. For me, this is simply a logical contradiction, given the definition and measurement of GDP. The authors seem to suggest that cumulative GDP directly reflects network growth in figure 2. But what is the causal process that would establish such a connection?
The authors do not need to teach an economics professor about double counting. Cancelling out any double counting is essential for identifying value added. But how does energy consumption causally relate to value added as a measure? I agree that gross production in value terms may also fail to be a good choice, but for that reason I also referred to Material Flow Analysis or other Input-Output frameworks. Every intermediary stage of production is a movement in Lotka’s wheel, isn’t it? Why do you disregard this as irrelevant? Lotka’s wheel is not an accounting scheme which ultimately refers to subjective values, meaning preferences as expressed in demand for products priced on the marketplace and thereby becoming manifest in GDP measures. Lotka’s wheel is a physical structure moving forward.
My flute example is a mere didactic story that illustrates that claiming connection between value added and energy requires a causal account about underlying matterenergy facts. Teaching music could be regarded as extremely valuable, as compared to building fancy cars, in different societies. That would result in very different wheels, wouldn’t you agree?
Science does not need to result in universal consensus. Hence, I do not expect you to give up your approach, but to add a convincing story about the underlying physical mechanisms. Perhaps one argument could be that in the past, society preferred the fancy cars, and not the music, hence creating value added resulted in a high powered wheel, through time. That would explain the correlation?