Cold, Locally Linear, and Clumpy

Matt Kornfield
4 min readDec 30, 2024

A refutation of the title of a popular book

Photo by Aaron Burden on Unsplash

Hot, Flat, and Crowded? Nah

The popular title of this book is inaccurate in more than one way, and I thought I’d share why this title, while amusing, is wrong on basically every count.

Cold, but Getting Warmer

The Earth is currently in an ice age. That’s because there is ice on the poles. In Earth’s entire history, very little of its time has been spent in an ice state.

Glaciations, over Earth’s history, from Wikipedia

The little black bar at the end is 542 million years, and basically all multicelular life, but even within that, it’s about half ice age, half not.

The Earth is, as the outside temperature is telling me (it was below freezing in CT), cold.

Even in the hottest summer months, the danger of climate change is not that the Earth will become “hot”, or even “warm”, but that it will, with only a few degrees of heat, become highly more unstable.

The important part of the discussion should not be centered around the Earth being hot or cold and its relevance historically but “are things changing for the worse?” The answer I believe is basically, yes. Not just because the storms are stronger, but because they are more unpredictable.

Either way, the Earth is, historically speaking, pretty cold, not hot. But it is getting warmer.

Locally Linear, but Round

In mathematics there is a concept of “local linearity” that basically means when you zoom in on something round, you get what amounts to a straight line. There are more complicated versions of it (like “locally linear embedding”), but it amounts to something like this:

Example of a tangent line, from wikipedia https://upload.wikimedia.org/wikipedia/commons/thumb/0/0f/Tangent_to_a_curve.svg/1200px-Tangent_to_a_curve.svg.png

The tangent like is a straight like that intersects with the curve. For a sufficiently large curve, the straight line pretty well approximates the curve.

On the Earth’s surface, the curvature is so subtle at our human scale that for all intents and purposes, it appears flat. If you travel a mile in one direction, the planet curves at a rate of about slightly more than half a foot (or 1 km to 8cm as an equivalent of distance to curvature).

That is a ratio of 8cm to 100,000cm, a fraction of a percent grade.

Given any feature like hills, valleys or any other land feature, you won’t be able to distinguish this curvature. But it does affect how far you can see when things are truly flat.

So to the flat Earthers out there: you’re right that the Earth is flat… locally, at a zoomed in, human level. But it isn’t flat everywhere, not by any measurable means we have.

If you go somewhere “completely flat”, you can only see about 3 miles (5km) before the curvature of the Earth starts hiding things from view. But 3 miles is starting to move beyond “local”.

Sparsely Populated, but Dense in Parts

The average human population density of the world excluding the oceans and Antarctica is about 150 per sq km.

This is not at all evenly distributed. This circle is one example:

Found on lmgur https://imgur.com/gallery/CK6aONG

The Indian and Chinese megacities account for an astounding amount of population density and people. Delhi has a whopping 11,000 people per km^2, but the most dense city by population is Manila at 44,000 per km^2.

“Crowded” is relative at that point. Most cities are not nearly that dense. New York City, with the densest population density in the US, is similar to Delhi with 11,000.

There’s more than one reason these cities are so dense, but the simplest answer is: opportunity. Cities have high paying jobs that attract immigrants from within the region, the country, and even from other nations. But housing doesn’t keep pace with the onslaught of people. The “crowded” aspect is a feature, not a bug.

Compare this with the population density of vast regions of the world, like Mongolia, with 2 people per km^2, or Canada, with 4 people per km^2.

The human world is crowded, but only in certain spots. The proper word is probably “clumpy”, though it doesn’t exactly roll off the tongue.

Summary

The world is a clumpy, locally linear, and cold. But human populations and the global temperature are bound to change.

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Matt Kornfield
Matt Kornfield

Written by Matt Kornfield

Today's solutions are tomorrow's debugging adventure.

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