Surprising Facts

A collection of facts that I found surprising:

1. Availability of animals for domestication was the reason for deadly animal-human disease transmission and the death of 90% of American indigenous population. And the lack of domestic animals in the Americas was the reason why there was no American plague spreading in Europe.
2. The Wright brothers did not invent flying in the general sense but they invented controlled flying by overcoming adverse yaw during rolling maneuvers.
3. The root cause of the oxygen tank explosion in the Apollo 13 mission was using 60V during ground operations on 28V rated oxygen tank to boil off oxygen in the tank which led to welding of the thermostat and the eventual burning of wire Teflon coating.
4. The Linux Kernel has thousands of goto statements.

Germany-Switzerland Train Tour

This August we embarked on a train tour across Germany and Switzerland, visiting a different city every day. Our route was: Düsseldorf – Köln – Koblenz – Heidelberg – Freiburg – Luzern – Interlaken – Bern – Zürich – Stuttgart – back to Düsseldorf

We chose the cities so that each train journey was around one hour. Every afternoon, we traveled to a new city, rested at the hotel, took an evening walk, ate dinner, then the next morning had breakfast, checked out while leaving our baggage at the hotel, explored the city for a couple of hours, picked up our luggage, and continued on to the next city.

Booking Trains and Hotels

We had secured our train tickets and hotel bookings as early as April. It is not critical for train tickets because you will always find a train with paying around 20% more if you buy on the day of your journey. Buying individual tickets for each route was much cheaper than buying a Eurail Pass. Hotels must be booked in advance, otherwise you won't be able to find a room.

The entire process was digital. To buy train tickeds, we used DB Navigator, bahn.de, Omio for Germany and SBB for Switzerland. You don’t need a physical ticket to board—just show the QR code to the ticket inspector after finding a seat. Seats usually display their reservation status on a small LCD screen next to them. If you don’t have a reservation, simply choose a seat that isn’t reserved.

We used Booking.com for hotel bookings, making sure our hotels were within 15 minutes walking distance of of train stations. We complemented our city explorations with walking routes from the GPSmyCity app (20 USD/year).

Trains

• German ICE trains were fast, comfortable, with free WiFi and quiet 1st class cars.

• Note that sometimes they change the train platform/track number ("Gleis" in German). Pay attention to the screens and announcements. In the photo below, the platform of our train has been changed from 5 to 4:

• Swiss regional trains were slow and more scenic, but 2nd class trains typically lacked WiFi. Even station WiFi required SMS verification—which didn’t accept Turkish numbers. That left us dependent on hotel WiFi unless we wanted to pay roaming fees.

• Trains generally ran within 10 minutes of their scheduled time.

• Seat reservations cost 7 euros per person, but if you travel outside rush hours, they’re unnecessary, there are plenty of empty seats.

One of the trip’s strongest impressions was how deeply rail networks shape daily life in these countries. Every town is linked by trains running at 150 km/h or more. This creates not just convenience for travelers, but also massive employment opportunities for technicians, engineers, and operators who maintain and innovate these networks.

As the saying goes: "A developed country is not a place where the poor have cars. It's where the rich use public transportation." For a deeper dive into this idea, I recommend the YouTube channel Not Just Bikes.

Practical Travel Notes

• We were always able to pay by credit card. Only once did my card not work in a grocery store, and I had to pay in cash. Having 200 euros in cash will be more than enough.

• Breakfast: Hotel breakfasts average 20 euros per person. Since we had modest breakfast needs, we skipped them, preparing our own breakfast, using our own egg cooker. A nice side benefit was that we didn’t have to conform to the hotel’s breakfast hours and each member of our family could sleep as much as they wanted. Grocery chains like REWE, Lidl in Germany and Coop in Switzerland became our go-to spots. Here is our typical breakfast:

• In Switzerland, our egg cooker required a Euro-to-Swiss (Type J) adapter because it had thick pins, while Swiss electrical outlets are designed for thin ones:

• Tap water: Safe and free everywhere.

• Weather: It was a pleasant 25 °C on August 4, but by August 11 a heat wave had reached Germany and Switzerland, with temperatures rising to 35 °C, making walking exhausting. It lasted for a week and subsided just as we returned. Locals said this happens only once a year, and we were a little unlucky to catch it.

Music: Sia - Cheap Trills

The Teenage Attention Crisis

A friend of mine asked me for advice on how to help his 17-year-old son overcome his gaming and video addiction. Short-form social media videos and online games are designed to be addictive. Having been a former StarCraft addict and now the father of a 13-year-old boy, I know firsthand that nothing compares to the thrill of online gaming.

The problem is, these activities don’t just eat up time — they erode attention span. Games and TikTok-style videos constantly reward the brain with quick hits of dopamine. You get instant excitement, instant novelty, instant feedback. Over time, this rewires the brain to expect stimulation every few seconds.

It is not an issue when the child is less than 7 years old and a tablet is a parent's best friend. As the child starts school, it makes it difficult to sit through a class, read a book, or even watch a movie without reaching for a phone. The mind starts craving constant action. Anything slower feels boring, even if it’s meaningful.

This is why expecting teenagers to “just stop” is unrealistic. No matter how fun or beneficial the alternatives may be, those alternatives can’t compete with the rapid-fire dopamine loops of gaming and social media.

And here’s the key point: it’s not about a lack of awareness. Teens know they should be studying, playing sports, or sleeping earlier. The issue is willpower — and when your brain has been trained to chase fast rewards, willpower alone isn’t enough.

So talking them into it rarely works, and even then only for a few days at most. The only reliable way is to restrict access: put the phone away, turn off the computer. Of course, they will get bored. But boredom is valuable because it pushes you to be creative, to explore, to come up with something new. If the phone is always there to fill every empty moment, the brain never learns how to generate its own entertainment or ideas.

For parents, holding the line is hard because kids will push back, they’ll get angry, and they’ll try to negotiate their way around the rules. We use Google Family Link to limit his mobile phone time and app access. During school semester, he’s allowed to use his computer only on weekends, for up to three hours per day. When he breaks the rules by secretly giving himself more time on his mother’s phone or by exceeding the three-hour computer limit, we take away his phone and computer for a couple of days. Before and during exam weeks, he also goes on a digital detox, meaning the phone and computer are completely put away for 2 weeks.

Music: Stromae - Papaoutai

Liselere Giriş Sınavı (LGS) Hazırlığı

Oğlumuz Argun şu an 12.5 yaşında ve 6. sınıfta, LGS’ye hazırlanıyor. Keşke çocuklarımız sınav kaygısı yaşamadan, yetenek ve ilgilerine göre yönlendirilse, eğitim sistemi onları rahat bir yaşama taşıyacak şekilde desteklese. Ancak ortam ne yazık ki şu an buna uygun değil

Lise ve üniversite giriş sınavlarının olmadığı ülkelerin ayırd edici özellikleri:

1. Ekonomi ve sosyal destek güçlü, işsizlik oranı düşük, asgari ücretle geçinmek mümkün
2. Üniversite mezunu olanla olmayan arasındaki iş bulma imkanlarında ve ücretlerde uçurum yok
3. Öğretmen ücretleri yüksek

İlk iki özellik üniversiteye girme baskısını azaltıyor, üçüncüsü de eğitimin ve verilen notların kalitesini arttırıp merkezi sınava ihtiyaç duymadan öğrenci seçmeyi mümkün kılıyor. Bizim içinde bulunduğumuz ortamda bunlar istenen seviyede olmadığından çocuklarımızın sınavlarda başarılı olmasını istemek doğal. Elbette başarıya giden başka seçenekler de var; ancak ne yapılması gerektiğinin en belirgin olduğu yol sınavlardan geçiyor. Diğer seçenekler ise daha fazla çaba ve risk içeriyor. Çocuğunuz kendi başına çalışamıyor ve desteğe ihtiyaç duyuyorsa bu yazıda özetlediğim 5.5 yıllık deneyim işinize yarayabilir.

Eğitim hep özel ilgili alanlarımdan biriydi, ayrıca eşim de fen bilgisi öğretmeni. Argun'un doğmasıyla eğitim hobi olmanın ötesine geçti. Eğitim sisteminin çok sayıda sorunu olduğundan ve çocuğu en iyi velisi tanıyabileceğinden eğitim (terbiye, disiplin) ve öğretimin (matematik, İngilizce) ana sorumluluğu biz velilerde.

Argun'un okulda rahat edebilmesi için anaokulunda bir yıl fazladan kalarak ilkokula geç başlamasını sağladık. "Ya sıkılırsa" sorusuna yanıtımız "geride kalma hissi yaşamasındansa sıkılmasını göze alıyoruz" oldu. 7 yaşındayken (ilkokul 1. sınıf) her gün düzenli olarak Khan Academy ile matematik çalışmaya başladık. Günde 15 dakika ek çalışmayla 4. sınıfın sonuna geldiğimizde 8. sınıf matematik konuları bitmişti. Khan Academy’yi Argun tek başına değil, bizim gözetimimizde kullandı. Her gün düzenli olarak çalışmak çoğu yetişkin için bile zorken çocuğun iradesi yetmiyor. 5. sınıfla birlikte LGS matematik test kitapları çözmeye başladı. Sosyalleşmesi hep birinci önceliğimizdi, ders için sadece bilgisayar oyun zamanından çalıyorduk.

Hedef olmadan sınava hazırlanmak çok zor çünkü ders çalışmaktan daha cazip pek çok şey var. Profesyonel basketbolcu, YouTuber, ya da fizikçi olmak ilk bakışta hedef gibi görülebilir, ancak bu alanlarda konforlu bir hayat sürebilmek için Ankara'nın en iyi basketbolcusu olmak ya da fizik olimpiyat takımına girebilmek gerekir. İstatistik gereği çocuğunuzun böyle bir yeteneğe sahip olma olasılığı milyonda bir. Çocukların bir mesleği hedef haline getirebilmesi için işini severek yapan birilerinden destek alınmalı. Argun hedefi olan bilgisayar mühendisliği için %1'lik dilime girmesi gerektiğini bildiğinden ders çalışmanın sıkıcılığını iradesiyle ve bizim de onu biraz ittirmemizle aşabiliyor.

Hedefi belirledikten sonra çocuğun sınırlı bir kapasitesi olduğundan kapasiteyi idareli kullanmak lazım, yoksa çocuğun canından bezme riski var. Ek çalışmada tüm dersler yerine matematik ve İngilizce'ye odaklanmak en yüksek faydayı sağlıyor. Diğer derslere okulun istediği kadar çalışması yeterli oluyor.

Süreç boyunca sonucun değil gayretin, çözülen soru sayısının ya da harcanan vaktin değil, kapasitesini her seferinde biraz aşmasının gelişim için önemli olduğunu vurguladık.  Örneğin yorgunken 1 soru çözmek bile yeterli olabilir, iyi hissederken 10 soru bile az gelebilir. Kendini kandırmanın ne kadar kolay olabileceğini örnekledik. Argun büyüdükçe bunları daha iyi anlar hale geldi.

Durum değerlendirmesi için okulunun dahil olduğu Sebit SDS (Süreç Değerlendirme Sınavı) sonuçlarına odaklandık. 5. sınıftan başlayarak her dönem üç, yılda toplam 6 sınav yapılıyor, sınavlara farklı okullardan yaklaşık 3000 öğrenci katılıyor. Argun 5. sınıfta pek de iyi olmayan bir başlangıcın ardından inişli çıkışlı bir performansla 6. sınıfı güzel bir yüzdelik dilimde bitirdi:

Sınavlarda Argun'un fire vermesinin sebebi konu eksiğinden ziyade konsantrasyon süresinin kısalığıydı. Son sınav öncesinde kendisinin de rızasıyla bir ay dijital detox uyguladık, kitap okuma süresini arttırdık. İşin ciddiyetinin farkına vardı ve sınava konsantre girdi. Bundan sonrası aynı yöntemi uygulayıp seviyeyi korumak.

Intersection of circle and sine wave

I recently encountered the following question [University of Tor Vergata, Engineering Sciences, PreCalculus self assessment test, Geometry D]: A circle has center at the point A = (1, 1) and has radius r = 2. At how many points does it intersect the function y = sin(x)?

The equation of the circle with center (1, 1) and radius 2 is: (x - 1)² + (y - 1)² = 4

At any intersection point, the coordinates (x, y) must satisfy both equations:

1. (x - 1)² + (y - 1)² = 4

2. y = sin(x)

Let's substitute the second equation into the first: (x - 1)² + (sin(x) - 1)² = 4

This is a transcendental equation and cannot be solved analytically. Luckily, the equations are easy to plot by hand. The circle is trivial and plotting sin(x) only requires you to know that sin(0)=0, sin(pi/2)=1, sin(2*pi)=0. The sine wave amplitude is between -1 and 1. Since the circle has radius 2 and is centered at (1, 1), both the x and y interval for the circle will be [-1, 3]. This results in two intersections. Using Desmos for a cleaner plot:

Note that if we increase the amplitude of the sine wave, we will can have more than 2 intersections. For an amplitude of 3.5, we have 4 intersections:

After amplitude, if we also increase the frequency by 4, we get even more intersections:

It is only reasonable to find the number of intersections by hand drawing if the sine wave is of the simple form sin(x).

If you want to find the numerical values of the intersections (which is not asked for in the question), you have to use numerical root finding methods like Newton-Raphson.

Learning from failures

Failures present valuable opportunities for learning only when there is no blaming or shaming of individuals. What may initially appear to be a foolish oversight often reveals systemic issues. A common cause is placing inexperienced personnel under unrealistic time pressures—neither of which can be resolved in the short term. This can lead decision-makers to treat complex systems as if they were linear or simplistic, ignoring interconnected factors and feedback loops [The Logic Of Failure]. People often focus on immediate outcomes without considering long-term or indirect effects, resulting in burnout, stress, and demotivation [Death March].

If failures were treated as insights that help uncover the mysteries of the physical world, they might even become occasions for celebration—because each failure reveals something new. They could be thoroughly analyzed and shared widely so that everyone benefits. Of course, this requires a reality-based culture of critical thinking, rather than a rush to find someone to blame—whether to feel good about ourselves or crush our rivals—until the next mishap. The road to most engineering catastrophes is paved with cover-ups of smaller mistakes.

The best examples of failure analysis come from the aviation industry, where even seemingly outrageous mistakes [Aeroflot Flight 593, Pakistan Airlines 8303] are traced back to systemic root causes like problematic hiring processes and insufficient training.

Music: Adelita (classical guitar)

Hexagon proofs

Yesterday, I was solving a math problem with my 13 year old son involving a hexagon. The sum of internal angles of an n-sided polygon is calculated by the formula (n-2)*180°. For a hexagon, the number of sides n=6, the sum is (6-2)*180°=720°. I didn't like to use this formula and thought about a proof: Let's draw four triangles inside the hexagon and label the angles:

The 6 interior angles of the hexagon would be:

1. a1+a2+a3+a4
2. b1
3. c1+b2
4. c2+b3
5. c3+b4
6. c4

We know that the internal angles of a triangle, e.g. a1+b1+c1 is 180°. If we sum all the 6 internal angles of the hexagon, we see that they are equal to the sum of the internal angles of our 4 triangles. Therefore, the sum of the internal angles of a hexagon is 4*180°=720°.

Then I wanted to prove that the 6 triangles created by the diagonals of a regular hexagon are equilateral:

We can label the triangle internal angles x, y, z as follows:

 Using parallel lines, we can fill the internal angles of all 6 triangles:

Note that the sum of internal angles of the hexagon are (z+x)+(y+z)+(x+y)+(z+x)+(y+z)+(x+y) = 4*(x+y+z). Since x+y+z=180°, this is another way to prove that the sum of internal angles are 4*180° = 720°. Also note that this proof is only valid for a regular hexagon. For a non regular hexagon, the sides would not be parallel and we would not be able to assert the equality of angles of triangles. The first proof at the top is valid even for a non-regular hexagon.

Since all triangles have the same 3 internal angles (x, y, z), they are similar. Since they also have a side of length "a", they must be congruent. Since the side "a" is opposite to angle x in one triangle and opposite to y and z angles in the others, the angles must be the same, x = y = z, which can only happen if they are all 60°. Therefore, the triangles must be equilateral: