#numerosity

Rowlf had a cameo appearance on Sesame Street during its first season. He made a brief appearance during "Nine Song" or "Song of Nine."

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Unique experiment explores canine ‘numerosity’ — ScienceDaily

Dogs spontaneously process basic numerical quantities, using a distinct part of their brains that corresponds closely to number-responsive neural regions in humans, finds a study at Emory University.

Biology Letters published the results, which suggest that a common neural mechanism has been deeply conserved across mammalian evolution.

“Our work not only shows that dogs use a similar part of…

By Natalie Angier, NY Times, Feb. 5, 2018

Every night during breeding season, the male túngara frog of Central America will stake out a performance patch in the local pond and spend unbroken hours broadcasting his splendor to the world.

The mud-brown frog is barely the size of a shelled pecan, but his call is large and dynamic, a long downward sweep that sounds remarkably like a phaser weapon on “Star Trek,” followed by a brief, twangy, harmonically dense chuck.

Unless, that is, a competing male starts calling nearby, in which case the first frog is likely to add two chucks to the tail of his sweep. And should his rival respond likewise, Male A will tack on three chucks.

Back and forth they go, call and raise, until the frogs hit their respiratory limit at six to seven rapid-fire chucks.

The acoustic one-upfrogship is energetically draining and risks attracting predators like bats. Yet the male frogs have no choice but to keep count of the competition, for the simple reason that female túngaras are doing the same: listening, counting and ultimately mating with the male of maximum chucks.

Behind the frog’s surprisingly sophisticated number sense, scientists have found, are specialized cells located in the amphibian midbrain that tally up sound signals and the intervals between them.

“The neurons are counting the number of appropriate pulses, and they’re highly selective,” said Gary Rose, a biologist at the University of Utah. If the timing between pulses is off by just a fraction of a second, the neurons don’t fire and the counting process breaks down.

The story of the frog’s neuro-abacus is just one example of nature’s vast, ancient and versatile number sense, a talent explored in detail in a recent themed issue of Philosophical Transactions of the Royal Society B, edited by Brian Butterworth, a cognitive neuroscientist at University College London, C. Randy Gallistel of Rutgers University and Giorgio Vallortigara of the University of Trento.

Scientists have found that animals across the spectrum have a keen sense of quantity, able to distinguish not just bigger from smaller or more from less, but two from four, four from ten, forty from sixty.

Orb-weaving spiders, for example, keep a tally of how many silk-wrapped prey items are stashed in the “larder” segment of their web. When scientists experimentally remove the cache, the spiders will spend time searching for the stolen goods in proportion to how many separate items had been taken, rather than how big the total prey mass might have been.

Small fish benefit from living in schools, and the more numerous the group, the statistically better a fish’s odds of escaping predation. As a result, many shoaling fish are excellent appraisers of relative head counts.

Guppies, for example, have a so-called contrast ratio of .8, which means they can distinguish at a glance between four guppies and five, or eight guppies and ten, and if given the chance will swim toward the slightly fishier crowd.

Three-spined sticklebacks are more discriminating still: with a contrast ratio of .86, they’re able to tell six fellow fish from seven, or 18 from 21--a comparative power that many birds, mammals and even humans might find hard to beat.

Despite the prevalence of math phobia, people too are born with a strong innate number sense, and numerosity is deeply embedded in many aspects of our minds and culture.

Researchers have determined that number words for small quantities--less than five--are strikingly similar across virtually every language studied, and the words are among the most stable, unchanging utterances in any lexicon.

They are more conserved through time and across cultures than words for other presumably bedrock concepts like mother, father and most body parts, with a few puzzling exceptions like the words for tongue and eye.

Attitudes about animal numerosity have changed dramatically since the mid-twentieth century when many researchers believed only humans had enough gray matter to think quantitatively.

Chimpanzees are social scorekeepers, episodic warriors and number ninjas. They can be taught to associate groups of objects with corresponding Arabic numerals up to the number 9 and sometimes beyond--three squares on a computer screen with the number 3, five squares with 5, and so on. They can put those numerals in order.

The numeric working memory of young chimpanzees is astonishing: Flash a random scattering of numerals on a screen for just 210 milliseconds--half an eye blink--and then cover the numbers with white squares, and a numerically schooled young chimpanzee will touch the squares sequentially to indicate the ascending order of the numbers hidden beneath.

As a recipient of the Teachers with Apps Certified Badge, Numerosity: Play with Addition is all about making Math fun. Focusing on educating children ages 6 to 8 this app teaches improving numerical skills and reviewing addition concepts in a fun and entertaining way.

Kids will enjoy being able to work at their own pace and not being rushed into learning on someone else’s timeframe. With this app they will be discovering the rules of addition and mastering them on their terms.  Through experimentation they can progress from basic addition to more complex sums. With 20 levels of learning, friends can be challenged by creating a profile, can they beat your scores or will you remain the champion?

Skruff the Streetwise Dog invites you to play and learn with him, and even offers a certificate of achievement that can be printed out and shared with friends and family.