A word spectrum highlights different aspects of a concept from one extreme to another. By arranging words on a spectrum, we can see their subtle differences and nuances.

For example, a word spectrum of happiness might range from "Miserable" on one side to "Ecstatic" on the other, passing through "Gloomy", "Content", and "Happy" along the way.

Or a word spectrum of tiredness might be: Asleep - Drowsy - Groggy - Awake - Alert - Energised

It's not a science, and there's a fair amount of latitude for people to place different words in different positions. Looking at many spectrums, it strikes me that some writers excel at selecting specific and perhaps more intriguing words such as "scrumptious" or "mouth-watering" over the more common "delicious." Roald Dahl often had his characters "guzzle" instead of "eat hungrily," for example.

I became curious about word spectrums when I realised that my understanding of the spectrum of approval was different from that of many of my American friends. In British English, "quite" is often used to mean "a bit less than," but in the U.S., I found it was more commonly used to mean "a lot" or "very."

So, my British English word spectrum of approval would be:

While the word spectrum of approval for many of my U.S. friends might be:

It left me confused several times before I figured it out.

For other variations in interpretation, such as where you might put "awesome", there's an excellent table as a Guide for U.S. students interpreting feedback from faculty trained in the U.K. (and vice versa).

At times, it really matters what someone means with a descriptive word. In the "intelligence" trade "words of estimative probability" relate to specific odds meant by certain terms. For instance, if an attack is "highly likely," just how likely is it? If something is "almost certainly an airfield," how certain is that? Clearly, the choice and interpretation of these terms can be very significant. For a fascinating insight on this, see CIA analyst Sherman Kent's previously classified report Words of Estimative Probability (pdf). Other research has studied individual differences in people's perceptions of probability—and created some fun graphics showing the results.

Estimative probability is also critical in medicine. If exact numbers aren't shared, how frequent is a side effect that occurs "rarely"? Specific guides have been created listing associated probabilities for terms such as "likely", "frequent", "occasional" and "rare".

A reader also shared with me a classic chocolate advert of Fry's five boys, with the face of a boy moving from: desperation, pacification, expectation, acclamation and the realisation "it's Fry's".

More word spectrums, including those illustrated here:

Size: tiny - small - medium - large - huge - gigantic

Frequency: never - rarely - occasionally - sometimes - often - always

Talk volume: whisper - murmur - talk - shout - yell - scream

Intelligence: stupid - dim - average - bright - brilliant - genius

Tastiness: disgusting - bland - tasty - delicious

Word spectrum

It’s pretty hard to get to grips with the scale of the solar system. It's really, really, really big.

To help process the vast distances within our system, astronomers use Astronomical Units where 1 AU is the distance of Earth from the Sun. If you see Venus in the night sky, our closest neighbour just 0.7 AU from the sun, it looks impossibly far away. But the further out you go, the more the distances multiply.

Earth and Venus are practically on top of each other compared to Uranus and Neptune. Neptune is a full 30 times the distance between Earth and the Sun.

Now think about the fact that our little solar system is over 250,000 AUs from our nearest star, which is, in turn, just one of many tucked away in a small corner of the Milky Way, which is only one of many galaxies that make up the known universe.

James O'Donoghue has made some brilliant videos about the solar system that explain this and more.

This sketch, and plenty more in the Starry-eyed Surprises section, features in my book Big Ideas Little Pictures

The original sketch of solar system sizes is on a paper background.

Paper background solar system sizes sketch

Dark sky background solar system sizes sketch

Solar system planets: how big is the solar system?

For almost all mammals, 1.5 billion heartbeats, more or less, is how much you’ve got. From the teeniest, tiniest shrew weighing just a few grams to the largest whale — passing through animals as diverse as robins, monkeys, sea lions, and giraffes — each mammal has broadly in the region of 1.5 billion heartbeats.

Beyond just heart rate, knowing a mammal’s weight can help predict several other fundamental aspects of its life. A tiny mammal will likely have a heart that goes like crazy, live only briefly, and reach maturity quickly. A large animal, in contrast, will have a slow heart rate, a long life, and take its time to adulthood.

The most significant outlier is us, mainly because, in recent years, we’ve significantly extended our lifetime from what would be expected from Nature.

This gem, and many other fascinating insights about size, scale, Nature and physics, from the book Scale by Geoffrey West.

1.5 billion heartbeats in a lifetime

The coastline paradox is the fascinating observation that it’s not straightforward to say how long a coastline is. If you were to measure the coastline of a country by using a ruler on a globe, you would come out with a vastly different number than if you were to pace around the edge. The closer you look, the more wiggles and squiggliness you come across, and instead of converging to a more accurate length, the coastline just keeps getting longer. The smaller your ruler, the longer it gets.

This was originally spotted, incredibly, in the 1950s by an Englishman, Lewis Richardson, when trying to check a theory he had that the likelihood of war between countries depended on the length of their shared borders. Remarkably, he found that the quoted lengths of borders varied significantly. While measuring on maps at different scales, he saw that the smaller scale map he used, or the smaller the width of his callipers he measured with, the length systematically increased. When looking at coastlines, instead of borders, some countries had wigglier coasts, and so the length increased at a faster rate with the scale — for instance, Norway’s coastline, with it’s crinkly fjords, increases faster than Britain’s, which in turn increases faster than South Africa’s, as he zoomed in. The rate of this increase later became known as its fractal dimension.

Long after Richardson’s research, Benoit Mandelbrot published a paper How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension that discussed how the wiggliness of something like a coastline at one scale can be repeated at smaller and smaller scales. The work led to the later term fractals. Many other things exhibit fractal-like behaviour, such as river networks, borders, brains, frequencies, lightning, and even the stock market.

There’s a super section on this in Scale, by Geoffrey West.

The difference between Great Britain, the UK and the British Isles

The coastline paradox

Marchetti's constant is the idea that people throughout history have budgeted, on average, about an hour a day for travelling.

Originally observed by Yacov Zahavi, it came from the observation that even as our means of transport sped up, instead of travelling less each day, we would just travel further.

This leads to the conclusion that the size of our cities increases partly according to how efficiently we can travel in and out—they generally increase to a size that maintains about an hour of round-trip travel time.

Cesare Marchetti observed that Greek villages and ancient walking cities, as marked by ancient city walls, tend to share a radius of about 2.5km. Walking at a typical 5km/hr makes a one-hour round-trip journey. He also pointed out that: “Even people in prison for a life sentence, having nothing to do and nowhere to go, walk around for one hour a day, in the open.”

Unfortunately, if you live in London, the average round-trip seems to be an exception of 1h30.

This is also known as the constant travel time budget hypothesis.

Isochrones. It might be interesting to look at these according to transport method

Our senses are built to take in information at human pace

Image adapted from: Marchetti, C., 1994: Anthropological Invariants in Travel Behavior, Technological Forecasting and Social Change , 47 :75–88, Internal Publication, International Institute for Applied Systems Analysis.

Marchetti’s constant

The Fun Scale categorizes different types of fun experiences into distinct levels. It consists of three main types of fun: Type 1, Type 2, and Type 3. The concept behind the Fun Scale is that not all fun is created equal, and some types may be more rewarding or memorable than others.

My brother, who learned it from a mountain guide, introduced me to the Fun Scale. Before then, I used to think that fun was just fun. But the Fun Scale opened my eyes to the fact that there are levels and types of fun, each with its own characteristics. 

So, what are the three types of fun in the Fun Scale?

Type 1 fun is the most straightforward type of fun. It’s the kind of activity that is fun while you’re doing it, and it stays fun when you think back on it. Picture something like eating ice cream on a hot day, riding a roller coaster, or skiing with lifts to whisk you right back to the top. Type 1 fun is carefree, pleasurable in the moment, and provides uncomplicated enjoyment.

I'm sure you can think of a million more.

Type 2 fun: hurts a bit to do, but fun in retrospect

On the other hand, Type 2 fun is a bit trickier. It's the kind of activity where you may not have a blast while you're doing it—it's probably hard work or even painful. However, once it's over, you look back on it with a sense of achievement, and it becomes fun in retrospect.

This is the sort of enjoyment you get from something like running a marathon or climbing a mountain. At the time, you might question why you're doing it. Brendan Leonard in Ultra-something relates the joke, "You know what I like most about climbing a mountain? It feels so good when I stop."

You'll often think of Type 2 fun as ultimately more fulfilling and often somewhat addictive than Type I fun.

Cycling a mountain stage of the Tour de France

Cold water swimming (or maybe an ice mile)

Type 3 fun: not fun to do, not fun in retrospect, but makes a great story

Type 3 fun is usually type 1 or 2 fun that went wrong. Though it was supposed to be fun, things actually got a little hairy. Perhaps a trip started out like good Type 2 fun, but then you got lost, or it got dark, and it got cold, or things got much more serious than intended. Maybe you had to be rescued.

This kind of fun is not fun while it's happening. It's probably not even fun when thinking back on it. But Type 3 fun sure makes a great story when you make it back, and, well, life is made up of great stories, so perhaps it wasn't so bad after all.

Not practicing your kitchen table survival skills

There are rumours of Type 4 fun and Type 5 fun, but having heard some good stories of Type 3 fun and created a few myself, I can't say I recommend them =)

The Fun Scale, adventure and fulfilment: why we crave Type 2 and Type 3 fun

In our podcast discussing the Fun Scale, Tom, identified Rob and I as Type 2 Fun junkies. There's something intriguingly addictive about setting yourself difficult challenges, pushing through hardship, and emerging out the other side. Rob and I have signed up for a challenging endurance event pretty much every year for the last decade or so. Every single time the event on the day is really hard. And yet, once the immediate memories subside we find ourselves signing up for something similar next year.

Even if it's not you, I'm sure you probably know someone who seems to keep pushing themselves to do things that they don't seem to enjoy. It reminds me of Calvin imitating his dad in Calvin and Hobbes: "Calvin, go do something you hate! Being miserable builds character!"

Type 2 fun and type 3 fun, to some extent, help build character, life experiences and the stories that shape us and are fun to tell others. The sense of accomplishment and unforgettable stories that emerge from these experiences outweigh the discomfort in the long run.

Type 1 fun is fun when you do it and fun to remember.

Type 2 fun is not so fun when you do it, but it is fun in retrospect and is the most fulfilling.

And Type 3 fun is not fun in the moment or when you remember it—but it makes the best stories!

I have seen people write about Type A fun, Type B fun and Type C fun, or Type I fun, Type II fun and Type III fun, but I learned it as 1, 2 and 3.

The Fun Scale is probably my favourite idea that didn't make it into my new book. If you like this one, you'll love the book Big Ideas Little Pictures.

Kaffikok - the distance you can go before needing a coffee

The fun scale: understanding the types of fun

For years, I’ve wondered at how as a kid I found the monkey bars in a playground (often a jungle gym in the US) so much easier to swing on than I do as an adult. And I see our kids swinging around easily on them, while now it’s hard for me just to hang off them. The reason why is partly to do with the square-cube law.

The square-cube law is the deceptively simple observation that as you scale up dimensions — say, as you get taller — then area of the object increases proportional to the square of the length, while volume increases proportional to the cube of length. This fundamental relationship has enormous significance in the sizes and shapes of animals and the limits of how big trees can get and how big we can build our bridges and buildings.

Because the strength of our bones, muscles or wooden beams is proportional to their cross-sectional area, this means that while the strength of a larger object, assuming the same proportions as the smaller one, increases according to the square of a length, the weight (from the volume it takes up) increases according to the cube of a length. So, relative strength decreases as size increases.

Some corollaries are therefore that children’s small size relative to the area of their muscles and bones makes them relatively stronger than adults and so they can more easily support their weight as they swing on the monkey bars. In the same way, press ups are harder for bigger people than they are for smaller. And while an ant has tiny spindly legs, those legs could easily support 50 other ants of its size, whereas for an elephant to support its own weight it needs chunky legs — not spindly ones — and there’s no chance it could get close to carrying 50 other elephants on its back.

It’s also part of the reason short trees can be spindly, but big sequoias have relatively chunkier trunks, and we need increasingly strong materials to build bigger and bigger skyscrapers compared to the shed in your garden.

Galileo discussed this back in 1638, and it still requires some getting your head around today.

For this and other fascinating insights of scaling check out Scale, by Geoffrey West.

The Square-Cube law

The clarity of the night sky. A low number means clear, black and amazing stars. Higher numbers mean gradually more urban environments with increasing light pollution. At 9 you’ll barely spot a star being pretty much in Piccadilly Circus or Times Square.

More detail needed? John Bortle, Light Pollution And Astronomy: The Bortle Dark-Sky Scale, Sky and Telescope, July 18 2006.

Scale sketches