Sankey diagrams are handy ways to visualise material or energy flows through usage and time. They are excellent for displaying energy source and usage, for example the UK government publishes a Sankey diagram of UK energy each year (pdf).

Perhaps the most famous example is Charles Joseph Minard's remarkable visual showing Napoleon's invasion of and retreat from Russia in the Winter of 1812–13. In that chilling example the thickness of the lines represent the remaining size of Napoleon's army.

I learned about Sankey diagrams from Edward Tufte but perhaps people see them most commonly today in Google Analytics showing the different paths visitors take on a website before leaving.

Sankey diagram

Perhaps the most important curve of our times, Charles Keeling’s  curve shows the change in concentration of CO2 in the air with measurements taken every year for over 60 years. Taken at the top of Mauna Loa volcano in Hawaii because of its high altitude and relative isolation in the Pacific, Charles Keeling’s measurements show that the monthly average CO2 concentration in the air has risen from around 310 ppm (parts per million) to around 410 ppm in 2020. As a greenhouse gas this change in CO2 concentration is one of the critical causes of climate change.

The concentration varies seasonally as plants bloom in Spring and Summer reducing the concentration from its high around May as the CO2 has built up over the Norhern Hemisphere Winter.

The Scripps CO2 program is now overseen by Charles’ son Ralph Keeling.

The Keeling curve

I like this simple idea that evidently illustrates that anything that is able to improve, learn, and grow at a faster rate than something else stands a decent chance of making up lost ground pretty quickly. Consider this when you’re hiring, or when you’re worried that some other person or company has got a headstart on knowledge. Position yourself always as the fastest and most persistent ‘improver’ and you’ll stand a chance whatever you’re doing.

Read the full story of Stanford Professor John Ousterhout’s thought for the weekend: a little bit of slope. 

A little bit of slope makes up for a lot of y-intercept.

The value of a telecommunications network is proportional to the square of the number of users of the system.
— Robert Metcalfe

This law explains a little of the remarkable power of a growing network. Each time you add a user, or node, to the network, the number of connections increase in proportion to the square of the number of users. So, in this simple example where every new node gets a connection to each of the existing nodes, you can see that, say, adding a single node to an 11 node network creates 11 new connections.

It’s a simplified example because in most networks the value is not directly proportional to the number of connections as some connections or users may be more valuable than others, and usually adding a new user wouldn’t create a connection to all existing users — say if it was in a different country, or people spoke a different language, or just cared about different things. But nevertheless, you can see how a network quickly becomes valuable as users join.

So, Facebook has about 2 billion users…

Metcalfe was talking about telecommunications networks and the basic proposition has been modified since it was formulated including by Metcalfe himself.

Once again, just because something is called a law doesn’t mean it is one. See Fitt’s Law

Metcalfe’s Law

From the prefix iso meaning equal and khronos meaning time it literally means equal times. And whereas maps are usually put together with lines of equal distance you can either construct maps, or overlay maps as here, with lines of equal time. The overlay view gives you time contours rather than, say, altitude contours. Handy for checking things like commuting distance. I like how you find little islands where there is fast transport in and out like trains or planes.

You can explore time maps of London at mapumental.

Isochrones

Smaller software releases generally means fewer bugs, and bugs that are easier to fix. The number of bugs created typically increases with the complexity of interactions of code, which in turn increases with the size of release. This means that a number of smaller releases can hopefully get you to a large change in a safer way with less bugs, and less problematic bugs, created along the way than a single release with the whole lot. There’s probably a somewhat more general relationship with amount of unexpected problems created and the size of any change.

Bugs and releases

The half-life of caffeine is about 4 hours.

The data vary, but for a medium-sized adult, you can probably expect half of the caffeine from that 3 pm cup of coffee to still be doing half of its thing about 7 pm, 4 hours later. Apparently, smokers deal with caffeine quicker, and caffeine sticks around in children much longer.

You can expect about 10 minutes before it first kicks in, which, I suppose, is why if you’re feeling tired while driving, it’s a decent plan to take a break and drink a coffee, then have a 15-minute nap. See tiredness can kill, take a break. Once it starts to kick in, you might hit peak caffeine any time from 45 minutes to 2 hours later.

Caveat: The chart visualisation is extrapolated from reported data, so the shape is only approximate.

Some references say longer, and some say from 3-9 hours or so. My source, which seemed pretty comprehensive, was:

Bertil B. Fredholm, Karl Bättig, Janet Holmén, Astrid Nehlig and Edwin E. Zvartau, Actions of Caffeine in the Brain with Special Reference to Factors That Contribute to Its Widespread Use, Pharmacological Reviews March 1999, 51 (1) 83-133;

The half-life of caffeine

Translation: The energy efficiency of computers doubles roughly every 18 months.

In a new twist beyond Moore’s Law, which shows signs of reaching it’s limits, there’s Koomey’s Law. In his own words, the idea is:

“…at a fixed computing load, the amount of battery you need will fall by a factor of two every year and a half.”

Why does this matter? It means we can fit more more computing power into smaller and smaller devices. Which is much of the reason the phone in your pocket is probably more powerful than the EDVAC there in the chart.

Koomey’s Law

Very easy to forget the difference between the mean, the median and the mode.

Median: the middle value of a list in ranked order.

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Category: charts