Playwiths: the STEAM book

playwiths cover small (356K)
This book is written for people who, like Schrödinger's other cat, think outside the box.
Mind you, one of my friends who has seen a lot of it says it is designed
to help people who like Schrödinger's other cat to think outside the box.

So whence comes the name?

The first man of science was he who looked into a thing, not to learn whether
it furnished him with food, or shelter, or weapons, or tools, armaments or
playwiths, but who sought to know it for the gratification of knowing…
-- Samuel Taylor Coleridge, (1772-1834), Anima Poetae.


A quick background | Statistics | Chapter headings | Where to get it | A quick taste | Page thumbnails | About the author

STEAM activities for joy, but handy for sanity during the Covid-19 lockdown!
There's a newly revised version in all three versions,with fixed graphics, and there'll be a new (expensive) full-colour print version, one day soon.

More to the point, keep an eye out for Looking at Small Things, now available at Amazon. This, also, is excellent for the home school mob.

Where do you get it?

This link takes you to the hi-res e-book version, nice and clean, not shareable.

Free version from my website with lo-res graphics and a single whiny message asking you to buy the nice one. This freeby is completely shareable at no charge.
Page 2 now has an explicit Creative Commons copyright statement, allowing teachers to use it for non-commercial purposes with attribution.

The print-on-demand ink and paper book from Amazon, now available in Australia. Sadly, it's not in colour, but that keeps the price down. It looks a bit Yuck, so when I have time, I'll set up a colour edition.

Before I do that, I want to add another chapter.

History and why?

About 25 years ago, I started developing the playwiths as a working space to teach teachers. To show how easily web pages could be assembled, I started the first page. I showed my colleagues the things they should do when building pages, courteous and practical stuff like providing a date-created, a date-last-revised, a contact address, and adding a counter. In pre-Google times, I showed them how to get the page up on search engines.

People outside the classroom liked it, and soon the playwiths started spawning more pages, and I had a website. By the late 1990s, the counters had passed 1.5 million when the counter-provider went out of business, so I added new counters and started again, then got on with more serious writing work.

In August 2018, I looked, and the count was back to just under 2.5 million. Two days later, I was on a train to Fairymeadow for a literary lunch with Illawarra kids. Following on from a question by a Year 6 boy, I got to thinking on the train home, and it hit me that, given I had drawn in an audience of more than 4 million people, I really should clean the rough stuff up, and do a "best of" book. In the next two months, I cleaned up the tatty design, ditched a lot of boring stuff, added photos and a great deal of new material, and here it is. Almost, but not as planned.

I have been talking to a publisher for nine months, but they have continually dragged the chain, and I have withdrawn my offer to them. This is because, with schools and such in COVID-19 shutdowns, there are lots of bright students and involuntary home-schooling parents who need this right now. I have no time and no patience with the inactive. I served notice to them on 19 March, and on 26 March, it is up and running.

Publishers take note: in crisis times, THAT's how fast you should work!


82,000 words, 21 chapters, 300 illustrations, about 300 separate activities and explorations on ~270 pages.

About the author

Trained as a biologist, I care about natural history, social history and the stories behind things, and I am now well-regarded as a writer of Australian history. I used to talk on ABC Radio National, I sometimes teach adults how to do extreme research and data handling, and I thoroughly enjoys being the visiting scientist at my local K-6 school. peter rangitoto (66K)

I write blogs, books, magazine articles and occasional radio essays, usually writes about science, or history or both. My hobbies include having temporary obsessions, many of which end up becoming topics to write about; bushwalking swiftly, pausing only to bother plants, insects, venomous animals and other wild things; rocks and volcanoes; science and technology as they existed in the 19th century; chatting to telephone scammers in Latin; reading; creative computing; recreational mathematics; being a grandfather—and writing.

While I write mainly for the general (i.e., adult) market, most of my awards have come from a far more challenging area: writing for children. In the past 20 years, seven of my books have been named as Notable by the CBCA. Once a bureaucrat, I hold all the papers needed to prove I'm retired, but I refuse to stop. For the past ten years, my main publisher has been the National Library of Australia. (For foreigners, that's basically Australia's version of the Library of Congress.)

My main 2019 book for the NLA was Australian Backyard Earth Scientist, or see the author's take here, my 2020 books so far are Survivor Kids or see this link for the author's side, and with Amazon, Mistaken for Granite: Earth Science for Rock Watchers.

Not only but also: I have done a severely strange novel about the mad sheep and their search for the Book of Bells, and a rollicking history of quack medicine.

Do you get the sense that I never get bored?

But wait, there's more... naah, don't go there: they're mainly out of print.

The chapters

Part 1: mainly science and engineering

Introduction: Just a bit about why wonder is a defining characteristic of humans.

1. Science around the house: Kitchen physics, chemistry, fridge magnets, even a lens made of ice. compass (48K)

2. Science for spies: Secret inks, codes and such, including spreadsheet use with codes.

3. Using forces: Pulleys, windvanes, pendula and balances.

4. Sound and hearing: Pitch, frequency, transmission, Doppler, bull roarers and other sound toys.

5. Tricking our eyes: Optical illusions, including the way screens show us pictures. Yes, we could have gone into Cartesian doubt here, but I didn't.

6. Sight and light: Light adaptation, dispersion, refraction. The cylindrical lens on the right is new. 22 055 cylindrical lens (98K)

7. Matter: Diffusion, osmosis and separation, stuff like that.

8. Making things: Möbius strips, atomiser, sundials, cross stave, theodolite, Cartesian diver, stone blades and photometers.

9. Not exactly floating: Surface tension effects and bubbles.

10. Rocks and bits: Messing around with sand and mud, in a number of ways.

11. Living things: Keeping mosquitoes, slugs, snails, pill bugs, leeches and ant lions as well as photographing spiders.

12. Microscopy: Looking at stomates, Lepidopteran scales, fibres, spider web and seeds.

13. Getting artistic: Snow's 'Two Cultures', debating, Piet Hein's superellipses and computer-assisted art, art from broken glass or leaves and drama.

Part 2: mainly maths and computing

14. Some first puzzles: From simple to hard, a series of conundra, curious mathematical oddities, lightning calculation, Fibonacci and puzzles.

15. Some spatial puzzles: The Königsberg bridges and related puzzles, pentominos, soma shapes and the diabolical cube.

16. Numbers, magic, statistics: Magic squares, games, perfect numbers, Köchel numbers, statistics, pi from a spreadsheet, prime numbers and runs of composites, statistics and serious maths around polygonal numbers.

17. Strategy games: Coin puzzles, Nim, Sprouts, numbers in other bases (including 6x9=42, but only in base-13!).

19. Heavy maths: Stuff to get the brain juices flowing.

19. Using technology on numbers: What it says.

20. Can we trust statistics?: Figures don't lie, but liars can figure!

21. Pros and versus: One for the writers among us: clerihews, limericks and a rhyming cookbook.

22. Language and humanity: This is playful linguistics for bright minds. I'm taking no prisoners in this one, which ranges from Klingon to Middle English to loan words, being rude in Latin and comparative linguistics at a gentle level. Already avaiable in tghe free version. coming in a day or two from Amazon.

Postscript: So you want to work in STEM?:

References: Extra reading.


There will be occasional bits like this one, appearing in my blog. As I add more, they will all carry the tag playwiths.

The Möbius strip

This is one of the new ones. Cut a 5 cm strip lengthwise from an old newspaper. Holding the strip out straight, give it a simple Möbius strip (40K) half twist (180º) and glue or tape the two ends together.

Your piece of paper is now a Möbius strip, a shape which is described by a branch of mathematics called topology. When you twisted your strip, the inside and the outside became one continuous surface. And if you cut the strip, it becomes one longer chain but still has only one continuous surface.

Take a pen and carefully draw a line along the centre of the strip. Where do you end up? Is the line drawn on the inside or outside of the paper? Now cut the strip along the line you drew. How many chains do you get? It may help if you use the picture below to make an ant-covered Möbius strip: here is a link to a PDF that you can print. This will give you what you need to print a sheet wth this image front and back.

3 Möbius 2807 (72K) You can use the PDF or blow up the image above on a photocopier, so the chain of ants is 23 cm long then join two copies like the picture on the left, and do back-to-back photocopies. You need to experiment to get the ants on opposite sides of the page going in opposite directions.

4 Möbius 2807 (55K)



Next, take the photocopied sheets and cut two strips, 23 cm x 7 cm, and join them, so all the ants are in columns, and make a Möbius strip which you can cut, either straight down the centre, or off to one side, as shown below.



  5 Möbius (66K) 6 Möbius (64K)

The end results should look like this, and there are some hidden surprises. 7 mobius 1 (24K) 8 mobius 2 (37K) Try the experiment again and give the paper a full twist. Then try one and a half twists, and see what happens. Last of all, see what you can discover about Klein bottles.

Hero was here

b hero 1 (109K) c hero 2 (58K) When I originally learned this one, it was with a paper milk carton. This version uses a 1-litre milk bottle, and it is much better (and messier!).

You need a one-litre milk bottle, a drill and several drill bits, a button, some fine thread and a bucket of water, somewhere safe and outside the house.

Drill out the lid as shown, and attach the string and button through a small hole in the exact centre of the lid.

At the bottom of the bottle, drill a 4 mm hole on the left side of each face. When the water squirts out, Newton's Third Law says that every action has an equal and opposite reaction. Water shoots out the holes, and pushes back on the bottle with equal (but off-centre) force.

d hero 3 (153K) I tried filling the bottle from a tap while blocking the holes, but my holes were too large, so I sank the bottle in a bucket, then got somebody to lift it out, at which point the bottle span like crazy, and she got wet feet. Come summer, I will give this to my grandchildren to play with.

Find out who Hero of Alexandria (also known to us as Heron of Alexandria) was, and work out what this question has to do with a spinning milk bottle. Hint: that's Hero's aeolipile, below.

a hero-turbine (48K) A turbine is formed as the energy of the moving liquid is converted into rotational energy. Hero understood this principle.

Let me just note in passing that my twin 2-year-old grand-daughters think this is the best ever sort of water play and so does their grandfather, and my Year 3 and Year 4 students (I volunteer in a local school) thought this was an excellent end to a full octane class on flower morphology.

Julius Caesar's last breath

Between 44 BCE and now, the air molecules that Julius Caesar breathed out, just before he died, have spread and mixed in the atmosphere. One estimate I have seen suggests that on average, every breath we take contains 1.3 molecules from Caesar's last breath.

There's bread and butter on the shelf, if you want any working you can do it yourself!

A curious series

6, 15, 24, 33, 42, 51, 60…

What is this?

I'm not telling, even if you ask me six or seven times. Keep reading, and you may get it…

Sample pages

sample 016 (148K) sample 019 (135K) sample 041 (123K) sample 050 (121K) sample 056 (114K) sample 085 (133K) sample 113 (135K) sample 125 (122K) sample 138 (117K) sample 150 (108K) sample 168 (123K) sample 182 (112K) sample 194 (127K) sample 209 (115K) sample 240 (140K)
Back to the home page .

Now for the rest, go read the book. If you can't find it, demand it! Trample on a publisher, shout at them.

The author of this page is Peter Macinnis -- This page was first created on October 13, 2018, last updated August 31, 2021.