Karthikeyan KC · Mindspace explorer since 9 Aug 2020

I’m an engineer, software developer, and a writer. I created Mindspace to help everyone learn efficiently with crash courses and sparks. Come say hello at Mindspace’s public group. Help me make this better by providing a feedback.



If you have poured tea from a mug you’ll intuitively know what a Coanda effect is. To put it simply, the Coanda effect is the phenomenon where fluids like water tend to follow and stick to a contour of an object.

So what happens here? When the water flows out of the mug, the water molecules encounter the air molecules and try to drag them along due to viscosity. As the air molecules under the mug get dragged off, the pressure at that spot, which is relatively constrained compared to the other side, decreases (Bernoulli’s principle). And as the pressure is higher at the top of the water than on any other side, the water reaches equilibrium by moving towards the low-pressure region, which is what makes it to stick to the surface of the mug.

What’s a timbre of a human voice? Let’s start with the voice! The human voice is created when vocal folds vibrate. It’s this vibration of air molecules when travelling through different cavities like pharynx, sinuses, nose, and mouth, that’s converted to speech. And here is the interesting part that makes them unique to a person.

Like any physical objects, these cavities through which the sound travels have their own properties as well. They have their own distinct natural frequencies because of the geometries of the muscles that are unique to a person and the composition of the air.

And the sound from the vocal folds is made of not just a uniform sine wave with a fundamental frequency, but a composite of other distinct frequencies as well. So when certain frequencies of that sound wave hit the natural frequencies of the cavities, resonance happens, and those parts alone get amplified. The end result of all this is the distinct voice of a person. In other words, the lowest resonant frequency that’s modulated by the rest of the frequencies is what gives that unique tone to your voice. And that’s what we call the ‘timbre’ of the voice.

The voice you hear when you inhale helium, that’s because of the timbre change too. Not the frequency shift!

The longest vertical straw you can drink from is 10.3 metres. Even if you use a vacuum pump it won’t suck the liquid higher than that! Here is why!

Contrary to your intuition, when you drink from a straw you are not actually sucking up the fluid here. Just the air. So, when you do that, inside the straw, the pressure drops lower than that of the atmospheric pressure (101 kPa) outside. So, it’s the outside air pressure that pushes the water into the straw.

As the liquid moves up the straw, it is fighting against the gravity that is pulling it downwards. But it still keeps rising as long as the atmospheric pressure is greater than the pressure inside the straw due to gravity (weight of the liquid column).

The more liquid enters the column, the more it weighs. And at a certain height, there’d be enough water in the straw that’d exert the same pressure as that of the atmospheric pressure. That height, at sea level on earth, for water is 10.3 m.

$$ p_{atm}= 101\;kPa $$

$$p_{straw}= \dfrac{F}{A} \Rightarrow \rho g h$$

$$\rho g h = 101 \times 10^3\;N/m^2$$

$$h = \dfrac{101 \times 10^3\;N/m^2}{10^3\;kg/m^3 \times 9.81\;m/s^2}$$

$$h = 10.3\; m$$

Most of our older memories are partially distorted and has fake details in it. This is a very common occurrence as recalling or ‘remembering’ something is technically a reconstruction of events you learned and encoded into your memory ages ago. Between learning that memory and you recalling it now, you would have learned a lot of new and similar information. And these new encodings in your brain interferes with the old memories and affects the way how you recall them back.

In other words, new memories often interfere with old memories. Remembering is a very complicated process and most of the old stuff what you remember now is likely filled with made-up details. Biased, fabricated, and prone to errors.

You all know what a circadian rhythm is! Biological functions like sleep and wake that are synchronised to the rotation of the earth over a period of approximately 24 hours. And you would also know that there are activities that cycle at a period longer than 24 hours — like menstruation in humans, migration and hibernation in animals. And of course, activities with shorter periods like hunger.

But do you know what these cycles are called? Just learned about the exact terms and they are super cool to say out loud!

Cycles that have a shorter period than the circadian rhythms are called ultradian rhythms. The ones that have a longer period, say like annually, are called infradian rhythms.

In any real-world dataset, the probability of the first digit of a value being 1 is very high compared to the rest of the values, with the digit 9 having the lowest probability. This interesting occurrence is well-known as Benford’s law.

$$ P(d)=\log_{10}(d+1)-\log_{10}(d) $$

The intuition behind this observation is that a value in a real-world dataset spends a long time with its first digit as 1, and then the time shortens for every digit towards the digit 9 where it is the shortest. For example, if a value has to grow from 100 to 200, it needs to double itself. But when it reaches 900, the transition to 1000 is very quick as it’s just a 11% growth compared to 100 to 200, which is a 100% growth.

In other words, growth tends to be slow at the beginning (the first digit being 1) and exponentially faster as it reaches towards 9.

Ever wondered how dolphins, whales, and seals sleep if they require frequent surfacing to breath? Dolphins are known to sleep and stay conscious simultaneously as they lack autonomic breathing. They sleep close to the surface of the water, either by maintaining a steady swim pattern or just floating.

And during their sleep, they keep one eye open. In other words, only one hemisphere is at deep sleep while the other in a state of wakefulness. This keeps them 🐬 aware of their surroundings, alerts the time to surface for air, and maintains other conscious functions. This is known as unihemispheric slow-wave sleep. Fascinating!

Learned helplessness is a psychological phenomenon where an animal, after repeated traumatic experiences, eventually stops making any attempts to act upon it.

Way back, behavioural psychologists experimented on dogs by putting them in a cage where one half of the floor can be shocked. One group of dogs had the option to jump over a small barrier to avoid the shock. Another group of dogs didn’t have that choice. They had to endure the shock as long as it lasted.

Over time, after repeated trials, when the first group of dogs was put in an escapable shock cage again, they escaped by jumping the barrier — just how they were conditioned to. But the second group that had ‘learned’ to endure the shock refused to escape and took the shock passively, even when the escape was as easy as jumping the barrier.

Similarly, when humans are exposed to repeated negative emotions without escape, we eventually learn the ‘helpless’ state and continue to endure it even when we are capable of acting upon it or realising that we have control over the situation.

For the dogs, the learned helplessness was alleviated by training them to take the steps towards the escape. And in humans, just the realisation of the fact that we have control makes a huge difference. This is a widely considered area of research in product design as well.

There’s a constructed language called Esperanto that was invented by Dr Zamenhof around 1887 as a proposed common language that’s much simpler than other languages—with just 16 rules for grammar.

Strongly based on the European languages, It has 28 alphabets and simple rules like nouns end with ‘o’, adjectives with ‘a’, adverbs with ‘e’. And guess what! There’s even a message recorded in Esperanto as part of Voyager 1’s golden record.

Is it practical enough? Nah. Is it cool? Wholesome? Oh yeah! You bet! 😇 Bonan tagon!

Collision cascading in space (Kessler syndrome) is what happens if the density of the space debris in the low earth orbit is high enough that one mishap could start a domino effect and cause more debris, eventually causing the rest of the satellites to collide with each other.

Ultimately, the additional debris from the collisions orbit the earth and render any future space expeditions impossible. Here’s a recent model of the current space debris status.

If you are in space and shine a torch in an arbitrary direction, the photons (although being massless) will impart a thrust on you that will propel you in the opposite direction. This is due to the conservation of momentum as well.

In other words, when photons are ejected out of the torch, they travel outward with a momentum*. And due to this, your momentum changes to conserve the total momentum of your initial state, pushing you in the opposite direction.

* Photons have a relativistic mass and they do have momentum, given by $p = \dfrac{h}{\lambda}$.

Earth’s atmosphere is leaking a few grams of helium this very moment! Yep! As helium and hydrogen are the lightest elements of all, Earth’s gravity has little effect on them in the hydrostatic equilibrium. With higher kinetic energies, hydrogen and helium reach velocities greater than that of Earth’s escape velocity in the thermosphere and they shoot into space.

Most people think that inhaling helium changes the pitch or frequency of the voice. No! That is no what happens. It’s the timbre of the voice that changes.

When you inhale helium, the medium inside the vocal cavities changes from a dense medium, air, to a lighter medium, helium. And we know that in air, any vibrations travel at a speed of 343 m/s. For helium, it’s 1007 m/s. The helium medium now increases the natural frequencies of the cavities. In other words, it changes the responsiveness of the cavities to higher frequencies. This results in the amplification of a higher range of frequencies compared to that of when the air was the medium—causing the squeaky voice!

The key observation here is that the frequency at which the sound is produced by the vocal folds doesn’t change. It’s the resonant frequencies that change, forcing a change in the timbre of the voice.