Math and puzzle fans find magic in Martin Gardner's legacy | Hacker News Reader

Math and puzzle fans find magic in Martin Gardner's legacy

scientificamerican.com

135 pointsColinWright63 comments

> The question is, can you think of a single shape that looks like a triangle from one side, a circle from a second side and a square from the third side?

He goes on to say that it resembles a household item. I can visualise the shape, but I can't think of anything that it looks like. Does anyone know what item it is?

There's a picture here:

https://math.stackexchange.com/questions/1947363/is-there-a-...

Toothpaste tube! https://upload.wikimedia.org/wikipedia/commons/thumb/c/c5/El...

It looks like lipstick to me. Or possibly the end of a screwdriver or chisel.

screwdriver head. perelman's "mathematics can be fun" has that and another couple of fun examples https://archive.org/details/MathematicsCanBeFun-Eng-YakovPer...

i got a copy of that book and gardner's "mathematical magic show" when i was 12 or so, and they both continue to entertain and delight me.

Looks like an interchangable end to a cake frosting spatula.

How bout the rubber tip of a mucilage glue bottle:

https://deepfriedhoodsiecups.wordpress.com/2011/07/04/dfhc-7...

Looks like a duckbill valve. My wife’s breast pump uses them.

Tip of a chisel-headed felt pen.

Marker or soldering iron tip?

Was thinking an axehead

This one was my favorite:

"A carpenter, working with a buzz saw, wishes to cut a wooden cube, three inches on a side, into 27 one-inch cubes. He can do this job easily by making six cuts through the cube, keeping the pieces together in the cube shape. Can he reduce the number of necessary cuts by rearranging the pieces after each cut? Either show how or prove that it’s impossible."

- Martin Gardener

As a woodworker, I wouldn’t say those six cuts would be “easy”, unless you weren’t especially concerned about keeping all of your fingers!

Lbh arrq fvk phgf orpnhfr lbh arrq gb rkcbfr rirel snpr bs gur prageny phor.

Someone downvoted this, but it's a rot13 version of the correct answer. (A very nice a answer, by the way.)

In case rot13 doesn't come naturally:

  alias rot13="tr 'A-Za-z' 'N-ZA-Mn-za-m'"
  echo "Lbh arrq fvk phgf orpnhfr lbh arrq gb rkcbfr rirel snpr bs gur prageny phor." | rot13

I wish I had Mr Gardener's zero-kerf saw blades in my shop!

Saying "Please decode this ..." to Claude worked perfectly.

ChatGPT 4o mini kept getting one of the words wrong, funnily enough

I’m surprised by this - wouldn’t have expected there to be enough rot13 in the training data.

rot13 was commonly used on forums and Usenet to avoid spoilers for a very long time. As forums got the equivalent of spoiler tags or folding or whatever to hide content that changed, and of course Usenet fell out of common use a while back.

rot13.com also works, but this is better.

I really, really wish I could copy comments on mobile. I'm in my doctors office waiting and I want to throw this into rot13 so i can read it

Im really curious, what prevents you from copying comments on mobile?

Perhaps nearly all magazines are in decline (RIP Popular Science, National Geographic etc.), but I still wish that whatever happened to Scientific American hadn't happened to it.

It still exists and has articles. I see it in Mastodon links enough that I have subscribed. What happened to it?

By a former SciAm columnist:

https://michaelshermer.substack.com/p/scientific-american-go...

"It’s great that they’re interested in philosophy. But it is unclear why Scientific American thinks that these people [Shermer, Loeb] are the ones who should be informing their readers about philosophical matters. "

https://dailynous.com/2018/09/13/scientific-american-trustwo...

I don't think he actually ever shows how SciAm has gone off the rails in that post, though. He just asserts that it has, and then does a lot of research showing that allegedly, everything is fine now, and then complains about an article that was rejected because of a specific example he wanted to use.

It would be nice if he, instead, had more numbers about what types of articles Scientific American started running over the past decade, showing a move towards "going woke" as he puts it.

As it is, it just sounds like he's mad that his article was rejected.

Science is woke (global warming is real; LBGT is natural; the variance between groups is swamped by variance within groups whether that be racial or gender; coal is stupid; gun violence is mostly accidents and suicides; etc etc). One of the impressive things SciAm did this year is endorse the reality based candidate, VP Harris.

"Scientific American Didn’t Need to Endorse Anybody"

https://www.theatlantic.com/newsletters/archive/2024/09/scie...

Sure. Ask the woke whether homo sapiens is sexually dimorphic. Or whether individuals who have Y chromosomes and produce male gametes should be competing athletically against those that don't. We will soon have great statistics on how well they do against XX.

Then ask them about the change is murder rates in poor communities that resulted from the police defunding movement.

While the dems may lean slightly more toward science than the GOP on some issues, their science is also a cudgel for cultural issues.

There is nothing quite like it nowadays - not in print, not online. Quanta has a similar vibe, but it's Math-focused.

There is Gathering for Gardner non profit.

for recreational math:

https://www.gathering4gardner.org/

They have conferences and talks and post on youtube:

https://www.youtube.com/c/G4GCelebration

Recreational math and games boosted both computing and science.

Unix was born to play games. And Curses was born for Rogue.

> Unix was born to play games

Please correct me if I am wrong but I thought this was only the reason for the predecessor of it on the PDP-7: Thompson wanted Space Travel to run on the PDP-7 and the necessary boilerplate became a rudimentary OS. But porting this to the PDP-11 was not motivated by Space Travel -- or was it?

I think "games" is one of the most accurate answers to the question "what are computers good for?"

Though games are perhaps a subset of simulation in general (even if their simulation might be of an imaginary world rather than the real one.)

For clarity: the article is written today, but Martin Gardner died in 2010.

Gardeners books and sci-am columns are an amazing resource to get kids and teens interested in math.

In the present time, I find Simon Singh’s parallel.co.uk has been doing interesting work holding weekly math circles for kids - deftly engaging kids with mathematical ideas. I attend a circle with my 9 yo every Sunday.

  > Simon Singh’s parallel.co.uk

Perhaps you mean https://parallel.org.uk/ ?

I'm curious what the age range is? My son is 8.

Yes that’s the one. I’d suggest sit through on of their parallel circles with your son- it’s a free 45 min casual live only session, on Sundays. And the schedule is by age group - listed on their website

Thanks. For my son's age, there's one this Sunday at 9am Pacific Time.

Another fantastic resource is Boris Kordemsky's book The Moscow Puzzles:

https://www.amazon.com/Moscow-Puzzles-Mathematical-Recreatio...

I think it was this book where I first saw the puzzle:

    Does New Year's Day fall more often on a Saturday or a Sunday?

Such a simple puzzle with to (then) me such depth of knowledge to uncover the answer.

I don't see it there: https://archive.org/details/boris-a.-kordemsky-the-moscow-pu...

Do you recall the solution? It seems like a tricky problem. No approach occurs to me aside from a brute force analysis of the 400 year Gregorian calendar cycle, accounting for the complete leap year rules (under which, e.g., 1900 was not a leap year but 2000 was).

It turns out that New Year's Day is a bit more likely to fall on Sunday than Saturday. To confirm, here's a bit of simple JavaScript that checks a complete 400-year cycle. You can run it in your browser's console:

  const counts = Array(7).fill(0);
  for (let year = 2000; year < 2400; year++) {
    counts[new Date(year, 0, 1).getDay()]++;
  }
  console.log(`Number of Saturdays: ${counts[6]}; Number of Sundays: ${counts[0]}`);

Output:

  Number of Saturdays: 56; Number of Sundays: 58

Note: getDay() returns 0 for Sunday and 6 for Saturday (https://developer.mozilla.org/en-US/docs/Web/JavaScript/Refe...).

Unless you're considering a limited date range, it should fall equally often on both in the limit since neither 365 nor 366 (leap year) are multiples of 7.

So you’d think that, and it is approximately true. But the calendar repeats every 400 years (there are 97 leap years in 400, and 497 is a multiple of 7). And 400 isn’t a multiple of 7, so you can’t have it work out exactly.

But if the pair of (date, weekday) repeats every 400*7 years, then it still works out exactly?!

In the Gregorian calendar, January 1 falls on a Saturday in any year that is a multiple of 400. (This follows from any correct day-of-the-week algorithm, such as https://firstsundaydoomsday.blogspot.com/2009/12/quick-start....) Since each 400-year cycle begins on the same day, rather than balancing out, any imbalances would actually accumulate.

To check, see this 5-line brute-force calculation in JavaScript: https://news.ycombinator.com/item?id=42024474

Ah, the number of days in 400 years is 400 * 365 + 97 = (57*7+1) * (52*7+1) + (14*7-1) = 0 mod 7, so indeed it doesn't work out.

Exactly.

Don't forget Raymond Smullyan.

The Lady and the Tiger.

and ian stewart!

All of his Scientific American articles were available as a CD I have. Not sure if they are online yet.

As a youngster they were a source of wonder to me.

https://bookstore.ams.org/view?ProductCode=GARDNER-SET

Cambridge University Press also started on a project to revise and re-release all of it but that stalled out, they published four books.

https://www.cambridge.org/us/universitypress/subjects/mathem...

What is this CD? I like old compilations.

Edit: found it, it's called "Martin Gardner s Mathematical Games: The Entire Collection of His Scientific American Columns"

His annotated Alice in Wonderland is really nice, too.

I agree, although he missed one of the puns. In that day, even young children were taught latin. The speech with "O Mouse" comes from the lesson on conjugation which often used "am" (love): amo, amus, amat, amamus, amatis, amant. Having taken latin I recognized the joke. I always wished I could've written him about it.

The neglected Latin pedant in me can't not comment:

2nd person singular should be "amas". :)

Cunningham's Law strikes again: sorry, but I doubt "O mouse" is a soundalike pun on "Amo, amas". Instead, the English (A mouse, of a mouse, to a mouse, a mouse, O mouse!) is simply the first five declensions in the traditional order: nominative, genitive, dative, accusative, vocative. (Mus, muris, muri, murem, mus.) As seen for example in this Latin schoolbook from 1891:

[1] https://archive.org/details/bellumhelvetiumf00lowe/page/203/

...and Skitt's Law also strikes: sorry, I said "first five declensions" when I meant "first five grammatical cases."

[1] https://en.wikipedia.org/wiki/Muphry%27s_law

Very tardily returning to add that the same Latin textbook, a few pages earlier, gives these English translations for the six cases of the example noun causa, "cause": "A cause — of a cause — to or for a cause — a cause — O cause, or thou cause — with, by, from a cause."

Compare to Alice's "A mouse — of a mouse — to a mouse — a mouse — O mouse!"

[1] https://archive.org/details/bellumhelvetiumf00lowe/page/201

https://archive.is/hyF0u

Peter Winkler's Mathematical Puzzles is an amazing continuation with great teaching.

Reply on news.ycombinator.com