2018-12-31 (Réveillon)

Today, I learned that:

There are so many beautiful natural scenes around us, if we only take the time to go looking for them. This month, I had the the joy of taking my family on a road trip to the southernmost states in Brazil, Santa Catarina and Rio Grande do Sul.

And it was really worth the while. Our main interest was to know the highlands in those states. In the latter one, we concentrated on “serra gaúcha” with the twin cities Canela and Gramado, and although they now are highly commercialised, they still offer quite some entertainment.

But the highlight of the whole trip was no doubt the highlands of Santa Catarina. In winter, many tourists go their to enjoy (?) snow in São Joaquim, but since that is something I have had way too much of in my life, I prefer the summer that has so much more to offer! Not far away from São Joaquim is one of the most breathtaking views in the world, namely the highway that serpentines Serra do Rio do Rastro down in 284 curves, from an altitude of 1 421 m to 220 m in a distance of a mere 12 km. Of course it is impossible to capture all the excitement in a photo, but I hope that today’s header photo, taken from the belvedere overlooking the abyss, can give you a hint. On a totally clear day, one can even see the Atlantic ocean, 100 km away!

See also references # 1 and 2 below.

Some things to think deeply about

I am sure that more than once in your life, you have been challenged to solve a mathematical puzzle that involves discovering the missing term in a sequence.

One such sequence is called an arithmetic sequence, where the difference between the consecutive terms is constant, e.g. 2, 5, 8, 11, 14, … Anyone promptly says 17 when asked of the upcoming term.

It gets a bit more complicated if I give you a geometric progression, such as 2, 6, 18, 54, … ; or 10, 5, 2,5 , 1,25, …; or even 1, 8, 27, 64, 125, …

But there is also a sequence of numbers that can really trick us, until we discover the underlying fact. Here is one of those, which is the number of the parking space hidden by the car in the following image?

Was that too easy? Try the next one then:

Two cyclists have decided to meet half way between their cities. The distance between the cities is 50 km. Both cycle at a constant speed of 25 km/h. At the very moment they begin their trips, a fly takes off from one of the cyclists and when it reaches the other one, it inverts its trajectory and flies back to the cyclist from where it started. When it arrives there, once more it inverts its trajectory and keeps on repeating the process until it has comes to a stop when the cyclists finally meet. If the fly holds a constant speed of 50 km/h, how far has it flown when the cyclists meet?

The brilliant mathematician John von Neumann, who proposed the computer architecture that now bears his name, was once asked the same question. One of his early skills was to make very complex calculations in his head, so he answered the question in a snap. Can you?

The solution will be published in my next blog post.

I wish you an EXCELLENT YEAR of 2019 !

That’s what I learned in school !


1: Serra do Rio do Rastro live

2: Serra do Rio do Rastro

*: What did you learn in school today ?


2107-08-01 (Mother Nature’s son)

Today, I learned that:

Regardless of what we say and think, we still respond to Her (Mother Nature). Sometimes She shares with us the most amazing scenarios, such as the one in the amazing photo below. It shows a countryside highway with bamboo trees on both sides. And if you can read Portuguese, then you understand that this place is a sanctuary for wild animals. The road sign depicts an ocelot, and furthermore there is an alert that this is a road with a high degree of crashes between cars and animals. The location is close to the city of Assis, state of São Paulo, Brazil, where there is an ecological station.


Highway SP-333 close to the city of Assis, SP, Brazil. This area contains an ecological station with wild animals of various species, the reason why the roadsign alerts for a high degree of collisions between them and cars. The depicted animal is called jaguatirica in Portuguese, ocelot in English, and Leopardis pardalis in Latin. On both sides of the road are planted bamboo, which gives a magical touch to this sacred place. Photo taken on 2017-07-23.

It seems like a perfect coincidence that it is located in Assis, because as you probably remember, in a similarly sounding town in Italy, during the 12th century, there was born a person who later would be known as Saint Francis of Assisi. Among other things, he is known for his friendliness to the birds and in 1979 Pope John Paul II declared him the Patron Saint of Ecology. (The current Pope Francis I also honoured him by adopting his name as his own papal name.) See references #1 and #2 below.

But Mother Nature does not only present us with beauty, She is also very practical. Last Friday, I was reminded twice of that, when Radio Sweden interviewed professionals involved with creating and using practical solutions from Her in favour of humanity.

In the morning, I was told about a new kind of glue, which will permit heart surgeons to glue parts together within a beating heart. The origin of that invention is in the slime produced by a slug, which inspired scientists at Harvard. Hear and read about it in reference #3 below (Swedish), as well as read about in reference #4 (English).


Arion vulgaris, photo by Xauxa Håkan Svensson – Own work, CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=11200581

Then in the evening, another sensational feat. As long as we can remember, the spider has impressed us with its production of ultra-thin, yet extremely strong threads. And now Swedish scientists have discovered a way of recreating such production without using toxic chemistry. Reference #5 contains an audio interview in Swedish with Anna Rising, one of the scientists, and reference #6 is a written interview in English, where she and her fellow colleague Jan Johansson explain more.

Then, over the weekend, I remembered a similar story from exactly 10 years ago. By using practical solutions from a gecko and a mussel, scientists at Northwestern University were able to create a glue that would stick well also under water, see reference #7 below. And in the beginning of 2017, see reference #8, was reported how the very same gecko had inspired researchers at Kiel University to invent a method of immediate grip and release.

But wait, there is more! As a bonus, look also at this article from 2010, reference #9 below, which reports about a combination of mussel glue and nanoparticles to create a proactive cover against corrosion.

To end today’s post, what could be better than listening to the fantastic song writher John Denver, so tragically gone in 1997, to describe his love to Mother Nature! See and here his poem in reference X below.

… That’s what I learned in school !


1: Assis

2: Saint Francis of Assisi

3: Snigelinspirerat lim kan användas vid operationer

4: Slug Slime Inspires Scientists To Invent Sticky Surgical Glue

5: Forskare om att framställa artificiell spindelväv, med början vid 06:20

6: Spinning super strong synthetic spider silk

7: Design by Gecko, Plus Glue by Mussel, Yields a Powerful Adhesive

8: Scientists Can Turn This Gecko-Inspired Gripping Device On or Off With the Flick of a Light

9: Musslornas klister används som rostskydd

X: John Denver – Mother Nature’s son

*: What did you learn in school today ?