Mathematicians spend a lot of time working on problems in their heads, imagining solutions and proposing theorems. Sometimes an engineer is inspired to flesh out a proposal in real life to prove it’s true. Thus was born the gömböc, pictured above.

In 1995 Russian mathematician Vladimir Arnold described a theoretical object that has just one stable and one unstable point of equilibrium. When it sits on a flat surface it always rights itself like a roly poly toy except the gömböc is not weighted (the toy is).

The gömböc was harder to flesh out than you’d think. Hungarian engineer Gábor Domokos discussed the theory with Arnold in 1995. In 2006 he presented the real life solution. This 5 minute video shows why a gömböc is unique and describes Domokos’ quest.

During the quest, Domokos looked for gömböcs in nature and found tortoises that are shaped this way.

If an Indian star tortoise ends up on his back, he draws into his shell and automatically rights himself because his shape closely resembles a gömböc. (He has to use his limbs sometimes due to less than flat ground conditions and shell imperfections.)

Life imitates math imitates life.

(photos from Wikimedia Commons; click on the captions to see the originals)

20 August 2020:

Today’s Picture of the Day at Wikimedia Commons is an aerial photo of the 154-foot-long geoglyph called the Spider, one of the Nazca Lines of Peru.

The Nazca Lines are hundreds of enormous lines and figures in the Nazca Desert, created about 2,000 years ago when people cleared the reddish pebble surface from the underlying soil. The desert’s stable windless climate has kept the lines visible to this day, helped by the fact that the underlying soil contains lime which hardens when exposed to morning mist.

Many of the Nazca Lines are long straight lines or geometric patterns but more than 70 are animals. The most frequently depicted are birds. Some of the birds are local, some from far away. Naturally the Nazca people depicted an Andean condor though it appears to have a hummingbird’s beak.

If you find it difficult to see the condor click here for an outlined image or compare it to the Andean condor below.

My favorite of the birds, and perhaps theirs too, is the hummingbird whose geoglyph is 305 feet long!

Learn more about the Nazca Lines, see the hummingbird and others from the air in this vintage article: A 2000-year-old Drawing of…

(photos from Wikimedia Commons; click on the captions to see the originals)

Today my husband and I are officially downsizing from a house in Greenfield to a high-rise in Oakland. We’re not moving far, just 1.7 miles as the crow flies.

Moving itself is a pain but I’ll be in a neighborhood I know well, having worked nearby at WQED for 24 years. I’ll miss Greenfield’s nesting robins, cardinals and song sparrows but I’ll gain closeups of my favorite birds: common nighthawks, roosting chimney swifts, the winter crows and peregrine falcons.

Did I say peregrine falcons? Here’s a view from the high-rise roof deck (not from our apartment). When I took this photo I saw two peregrines perched on the Cathedral of Learning, one on the north face, one on the east.

Today we’ll be really busy moving from one side of Schenley Park to the other.

The movers come at 8:45am. Gotta run!

(photo by Kate St. John. Moving Day cartoon from Wikimedia Commons, click on the caption to see the original)

We know that women live longer than men, but why?

In 2017, the average life expectancy of women in the U.S. was 81.1 years but only 76.1 years for men. Longevity differs by country but the sex disparity is true for all humans and for other species as well.

A study at the University of New South Wales, Sydney published in March 2020 examined the life spans of 229 species and discovered it is related to sex chromosomes.

Across the animal kingdom, individuals with identical sex chromosomes — including women with double Xs — live nearly 18% longer than their counterparts with mismatched chromosomes.

— The Secret to a Long Life? Matching Sex Chromosomes, Science Daily

Among mammals, insects, fish and some reptiles, females have matching sex chromosomes [XX] whereas males do not [XY]. In all of these classes females live an average of 20.9% longer and sometimes a lot longer. The study found that female German cockroaches (Blattella germanica) live 77% longer than males. Ewww!

Among birds and butterflies the arrangement is opposite. Male birds have matching sex chromosomes [ZZ] whereas female birds do not [ZW]. In this case the males live longer, but only about 7.1%.

More study is needed to discover why male birds don’t reach the longer life spans that female mammals and insects are able to achieve.

Learn more at “The secret to a long life? Matching sex chromosomes” in Science Magazine.

p.s. Life expectancy in the U.S. has been dropping since 2014.

(photos from Wikimedia Commons; click on the captions to see the originals)

28 June 2020

Coronavirus is surging in many southern and western U.S. states and has increased in Allegheny County at levels far beyond our experience in late April.

The surge in Pittsburgh is ironic. Allegheny County had zero new cases on 17 June. On 27 June we had 90 new cases. At the time it was the highest single-day increase we’d ever seen. In less than two weeks we squandered two months of effort. And it’s gotten even worse! (see Public Source)

What caused it?

• Good news: Black Lives Matter protests did not cause a surge in cases. Here’s the study.
• Bad news: People, especially young people, are getting too close to each other and not wearing masks. Especially in bars. Texas and Florida are closing bars.

After months of study we now know you’re most likely to catch coronavirus through the air, by proximity and time spent near someone (often asymptomatic) who has COVID-19. In other words, not often caught from surfaces. The most likely place to catch it? Bars. (see video).

We know that wearing masks prevents it. Infected people spread the disease before they feel sick so all should wear masks. Your mask protects me, mine protects you.

However, the human brain has a hard time grasping danger it hasn’t experienced yet. We humans don’t learn well from the history of others. And so …

“I think that wherever there’s wood to burn [people to infect], this fire’s going to burn – and right now we have a lot of susceptible people,” said Michael Osterholm, head of the University of Minnesota’s Center for Infectious Disease Research and Policy, on NBC.

“I don’t think we’re going to see one, two and three waves. I think we’re going to just see one very, very difficult forest fire of cases.”

— The Guardian: Half of U.S. states see coronavirus surge… 22 June 2020

UPDATES:

• Ongoing: Allegheny County records new case counts every day. The Public Source graph, above, is updated daily.
• 29 June 2020: Allegheny County bans on-site consumption of alcohol in bars and restaurants. This has been biggest source of the outbreak.
• 1 July 2020: PA mandates masks for everyone who leaves their home.
• 2 July 2020: Coronavirus cases more than double in 1 day: 233. Allegheny County closes bars, restaurants, casinos for one week.
• 10 July 2020: Indoor dining ban extended for 2 weeks.
• 14 July 2020: A one-day spike on 14 July follows a one-day lull due to delayed reporting. New cases on 13 and 14 July average to 200, which is the average daily rate for more than a week. 200 is not good, but it is not growing. Even better, the infection rate went down on 14 July.
• 15 August 2020: August looks better than July so far, but is still not as good as March-May.

(photos from Wikimedia Commons; click on the captions to see the originals)