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Comment by ggm | Hacker News Reader

Charts into the future with an exponential curve. Right.

Look, I could have believed linear at least to some asymptote. And then you plot the exponential to the asymptote after the fact, because curves are nicer.

But at this point, exponential growth into the future that far out is 'busboy giving investment advice' exuberance.

Plot what % of GPP and PPP this represents, and then plot the overhang of debt, and the cycle time to a market correction, and tell me you still think an exponential growth story is going to happen "up and to the right" in this.

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And the headcount charts are “incremental”, i.e. first differences rather than absolute values – hardly like-for-like.

What do you mean by 'overhang of debt'?

Debt and equity are equally valid ways to finance projects. See https://en.wikipedia.org/wiki/Modigliani%E2%80%93Miller_theo... for the spherical cow version, but this holds approximately under real world conditions, too.

In general, I share you skepticism and agree that exponential extrapolation should be done only very carefully at best.

Your link itself says that in presence of taxes and tax deductible interest payments, i.e every single jurisdiction you care about, your firm can be significantly better off with debt. Saying debt and equity are equally valid suggests that you should be fine with a 100% equity financed company, which is completely false.

> Saying debt and equity are equally valid suggests that you should be fine with a 100% equity financed company, which is completely false.

I assume you mean 100% debt financed?

In any case, that's also mostly fine and happens in practice. As soon as that dips above 100%, conceptually your creditors turn into shareholders.

No, I meant equity. If you are not using significant (20%+ of capital at a minimum)debt in your capital structure, you are almost guaranteed to be making a financial mistake.

It depends on your industry and stage of your company and jurisdiction. Many software startups run with 100% equity, and I don't think they are all idiots.

A pet peeve of mine is people complaining about too much leverage, but then not doing anything about the tax systems making debt financing cheaper compared to equity.

P.S. Some companies even have more than 100% equity. In a sense: when their market capitalisation exceeds their enterprise value.

"This time it's different"

I dunno, people really are living in tent cities and Hondas in Canada. The gains were permanent.

Linear growth is nonsensical. Growth is driven ultimately by consumption. Consumption is driven by population. The population either grows or declines in an exponential fashion. That's how this works.

Consumption is not driven by population alone, it’s driven by population with a spending power. And from what I’m seeing, that’s shrinking. The article talks about how tech companies are growing revenues with fewer and fewer employees. An important question to ask there is: is that a good thing?

Then the shrinking is exponential as well. That's the point. Population grows or shrinks according to an exponential curve. If the exponent is one, then things are stable. If it's less than one, then things will experience exponential decline, which is different than linear decline since it never reaches 0. If it's more than one, then things experience exponential growth.

Most problems in life come down to misunderstanding exponents.

Of course linear growth is nonsensical. But if you are plotting into the future its a damn sight less nonsensical than exponential unless you have very strong foundations, and for the 1-2-3 year projection it's pretty much ok. Anyone who thinks they know trends 5+ years out is a loony.

And as I said, thats ignoring market cycles, the debt overhang in the economy, all kinds of problems.

Linear and exponential growth look the same in short term horizons depending on the exponent. However, exponential growth is strictly superior as some things can grow very fast if the exponent is high enough. We saw that with covid. The exponential assumption is correct. For the situations you are discussing, where the exponent is low, the exponential pattern correctly captures that.

Basically true, but there are other potential sources of growth :

- using technology to unlock cheaper energy - using technology to automate boring manual labor - using technology to extend healthy lifespan

Given the demographics collapse and ageing population in most 'developed' countries, we need to look at these other ways of generating economic growth.

Have you looked at the history of the population of various cities, countries or even the globe recently?

It doesn't matter. Even the degrowth due to declining population is exponential in nature. That was the point, population grows exponentially or decreases exponentially. There is no such thing as linear population growth or decline.

Good luck fitting an exponential to the table of population over time in eg https://en.wikipedia.org/wiki/Demographics_of_San_Francisco

Of course, you can do it piecewise, but you can also fit a piecewise linear curve (or even a step function) to any graph.

Or fit an exponential to the graph in https://en.wikipedia.org/wiki/World_population

Just eyeballing the global data from 1950 to 2020 it looks like linear growth would be a much better fit than exponential.

You might also want to look at logistic growth, see eg https://sites.math.duke.edu/education/ccp/materials/diffeq/l...

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