niplav comments on niplav’s Quick takes

[niplav]

Consider the problem of being automated away in a period of human history with explosive growth, and having to subsist on one’s capital. Property rights are respected, but there is no financial assistance by governments or AGI corporations.

How much wealth does one need to have to survive, ideally indefinitely?

Finding: If you lose your job at the start of the singularity, with monthly spending of $1k, you need ~$71k in total of capital. This number doesn’t look very sensitive to losing one’s job slightly later.

At the moment, the world economy is growing at a pace that leads to doublings in GWP every 20 years, steadily since ~1960. Explosive growth might instead be hyperbolic (continuing the trend we’ve seen seen through human history so far), with the economy first doubling in 20, then in 10, then in 5, then 2.5, then 15 months, and so on. I’ll assume that the smallest time for doublings is 1 year.

    initial_doubling_time=20
    final_doubling_time=1
    initial_growth_rate=2^(1/(initial_doubling_time*12))
    final_growth_rate=2^(1/(final_doubling_time*12))

    function generate_growth_rate_array(months::Int)
        growth_rate_array = zeros(Float64, years)
        growth_rate_step = (final_growth_rate - initial_growth_rate) / (years - 1)

        current_growth_rate = initial_growth_rate

        for i in 1:years
            growth_rate_array[i] = current_growth_rate
            current_growth_rate += growth_rate_step
        end

        return growth_rate_array
    end

We can then define the doubling sequence:

    years=12*ceil(Int, 10+5+2.5+1.25+final_doubling_time)
    economic_growth_rate = generate_growth_rate_array(years)
    economic_growth_rate=cat(economic_growth_rate, repeat([final_growth_rate], 60*12-size(economic_growth_rate)[1]), dims=1)

And we can then write a very simple model of monthly spending to figure out how our capital develops.

    capital=collect(1:250000)
    monthly_spending=1000 # if we really tighten our belts

    for growth_rate in economic_growth_rate
            capital=capital.*growth_rate
            capital=capital.-monthly_spending
    end

capital now contains the capital we end up with after 60 years. To find the minimum amount of capital we need to start out with to not lose out we find the index of the number closest to zero:

    julia> findmin(abs.(capital))
    (1.1776066747029436e13, 70789)

So, under these requirements, starting out with more than $71k should be fine.

But maybe we’ll only lose our job somewhat into the singularity already! We can simulate that as losing a job when initial doubling times are 15 years:

    initial_doubling_time=15
    initial_growth_rate=2^(1/(initial_doubling_time*12))
    years=12*ceil(Int, 10+5+2.5+1.25+final_doubling_time)
    economic_growth_rate = generate_growth_rate_array(years)
    economic_growth_rate=cat(economic_growth_rate, repeat([final_growth_rate], 60*12-size(economic_growth_rate)[1]), dims=1)

    capital=collect(1:250000)
    monthly_spending=1000 # if we really tighten our belts

    for growth_rate in economic_growth_rate
            capital=capital.*growth_rate
            capital=capital.-monthly_spending
    end

The amount of initially required capital doesn’t change by that much:

    julia> findmin(abs.(capital))
    (9.75603002635271e13, 68109)