Sunday, March 30, 2025

Counting Critters: Who’s Got the Numbers Game on Lock?



Ever wonder if animals can count? I mean, not like they’re sitting there with a pencil stub and a ledger, tallying up their groceries, but do they get numbers? Turns out, some of them do—and they’re better at it than I am when I’m half-asleep trying to split a restaurant bill. Nature’s got a few math whizzes, and I’ve been digging into which ones stand out. Spoiler: it’s not just the usual suspects.

Take chimpanzees. These furry cousins of ours are basically showing off at this point. I read about studies—fancy ones, like from Kyoto University—where chimps zip through number tasks faster than humans. They can eyeball sets of dots up to 9 and pick the bigger one without breaking a sweat. Imagine them in the wild, sizing up rival groups or eyeballing a fruit haul. Makes me wonder if they’d judge my banana stash—three’s enough, right? Probably not.

Then there’s crows. I’ve always liked their vibe—those sleek, black tricksters perched on telephone wires like they’re plotting something. Turns out, they’re counting too. Scientists say they can handle numbers up to 4 or 5, and some even grok the idea of zero. Zero! I barely got that in grade school. Next time I see one hopping around, I’ll picture it mentally tallying acorns. “Three’s a party, four’s a feast,” it might caw to itself.

Dolphins, though—those sea geniuses—they’ve got a knack for it too. They’ll pick the bigger pile of fishy treats in lab tests, no problem, up to about 5. I can see why: swimming in pods, keeping track of friends or foes, numbers matter. Makes me think of the time I tried counting waves at the beach and lost track at, what, 7? Dolphins would’ve smirked.

And bees! Tiny, buzzing bees! I couldn’t believe this one—research says they count up to 4 and even do basic math. Add one, subtract one, all to find the best flowers. Their waggle dance is like a GPS with a side of algebra. Next time I’m lost in the weeds (literally or otherwise), I’ll wish I had a bee’s brain.

Elephants round out the list. Big, lumbering, and apparently good with headcounts. They can tell 5 rumbles from 10 when listening to calls—handy for spotting trouble or rallying the herd. I once saw an elephant at the zoo, trunk swinging, and now I’m retroactively impressed. It wasn’t just staring at me; it was probably counting my bad hair day.

So who’s the champ? Hard to say. Chimps and crows flex the abstract stuff, bees punch above their weight, and elephants keep it practical. Me, I’m just glad I don’t have to compete. I’d be the guy fumbling with “how many coffee cups is too many?” (Answer: there’s no limit.) Nature’s got its own calculators, and I’m here for it. Which one’s your favorite?

(Post and graphic produced by https://grok.com/chat)

References:

https://www.elephanttrust.org/research (Amboseli project overview; search for cognitive or acoustic studies.)

https://www.science.org/doi/10.1126/sciadv.aav0961 (Direct link to the paper "Numerical ordering of zero in honey bees.")


https://www.ox.ac.uk/news/science-blog/2018/02/crows-can-count-zero (Oxford University news article summarizing the study by Nieder et al.)


Sunday, March 16, 2025

Saint Patrick - Another Prime Day

(Image: By Internet Archive Book Images -  https://archive.org/stream/irelandscrownoft00ryan/irelandscrownoft00ryan#page/n61/mode/1up, No restrictions, https://commons.wikimedia.org/w/index.php?curid=41964622)

A recent post about Julius Caesar introduced the concept of Caesar Primes. Caesar's birthday is the 13th of July (7th month), and 137 is prime. As we celebrate Saint Patrick's Day, March 17, we observe that 317 and 173 are primes. Perhaps this suggests a sequence of primes similar to the Caesar Primes. Other pairs of primes formed by two primes include: {37, 73}, {113, 311}, {313,331},{337,733}, {359,593}...

Wednesday, March 12, 2025

Julius Caesar and Caesar Primes

 

(Image: https://commons.wikimedia.org/wiki/File:Retrato_de_Julio_C%C3%A9sar_(26724093101).jpg)


March 15 is also known as the Ides of March, when Julius Caesar was assassinated in 44 BCE. Caesar was born on July 12 or 13, 100 BCE (records vary on the date of July 12 or July 13). For the purpose of this post, July 13 is consistent with the numbers known as Caesar Primes. One such number is 137 - the concatenation of two primes, 13 and 7 (with Caesar's birthday being the 13th day of the 7th month).

The list of Caesar Primes is found in the On-Line Encyclopedia of Integer Sequences (OEIS) as sequence: https://oeis.org/A133187.

I wrote a Mathematica program to produce this sequence:

lim=2700;plim=Max[FromDigits[Rest[IntegerDigits[lim]]],FromDigits[Drop[IntegerDigits[lim],-1]]];f2p[{p_,q_}]:=FromDigits[Join[IntegerDigits[q],IntegerDigits[p]]];p=Prime[Range[PrimePi[plim]]];p2=Subsets[p,{2}];Union[Select[f2p/@p2,PrimeQ[#]&&#<=lim&]]

The first 46 Caesar Primes are: 53,  73, 113, 137, 173, 193, 197, 233, 293, 313, 317, 373, 433, 593, 613, 617, 673, 677, 733, 797, 977, 1013, 1033, 1093, 1097, 1277, 1373, 1493, 1637, 1733, 1913, 1933, 1973, 1993, 1997, 2113, 2237, 2273, 2293, 2297, 2311, 2333, 2393, 2417, 2633, 2693.

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(Image:  Free 12 singapore icons - Iconfinder ) This past week, more views of this blog were made from Singapore than other country. To ackn...

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