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The Physics Behind the Nonsense: Kilograms and Instagrams

The Question

On one hand, the kilogram. The SI unit of mass (NOT WEIGHT!). Currently defined as the mass of a certain platinum-iridium cylinder, the kilogram may receive a new definition, or another, soon. For simplicity though, the mass of 1 litre of water is 1 kg.

One of the current proposals for the definition of the kilogram

On the other hand, Instagram. A photo-sharing service, used by millions. Take a photo, apply a filter on it, and share it with the world. Furthermore, an Instagram (note the article an) can denote that said photo sent to the service.

Behold, an Instagram of Instagram!

The question is: how many kilograms are there in an Instagram? In a stricter sense, what is the equivalent mass, in kilograms, of an image sent to Instagram?

How it Works

To answer the question, we need to know what exactly do we mean by equivalent mass. To do so, we need to know how modern computers work.

Instagram – or any electronic service and device for that matter – works on the idea that electrons can be used as a means to store data. Most of the data we currently use is saved either on magnetic hard disks (MHDs) or in solid-state devices (SSDs) such as USB flash disks and SD cards. Instagram is most commonly used with smartphones, which use external or built-in SSDs; hence these storage devices will be the devices of interest  for this

A few examples of solid-state devices.

In essence, an SSD  directly uses electrons to store data in a flash memory (hence the term flash drive). The flash memory has small cells built in it, which store electric charges in the form of excess electrons. These cells are then either  full (1) or empty (0) of electrons. These combinations of 1′s and 0′s, called bits, is what stores the information about the Instagram.

In computing, bits are arranged in groups of 8 to form a larger unit of information called the byte. This term may be more familiar, since this is how electronic file sizes are measured. For instance, a typical Instagram may have a file size of 40 kilobytes, or about 41,000 bytes (1 kilobyte is 1024 bytes). This translates to around 330,000 bits. This means, therefore that the SSD has to use around 330,000 cells in the flash memory to store an Instagram.

The Basic Physics

When a cell in the flash memory is full (1), it contains roughly 40,000 excess electrons. This may seem like a large number, but this number of electrons is nothing to the amount of electrons passing through a light bulb every second (amounts to about \(5 \times 10^{18}\) electrons).

An electronic file like an Instagram normally has about the same number of 0′s and 1′s in it; half of the cells would therefore contain excess electrons. Thus, 330,000 bits will be divided approximately equal numbers of empty cells and full cells.

The mass of the electron at rest is known to be  \(9.11 \times 10^{-31}\) kg.

Now, let’s commence the determination of the equivalent mass of an Instagram.

\(m_I = N \times \frac{8\:bits}{byte} \times \frac{1\:cell}{2\:bits} \times \frac{40,000\:electrons}{cell} \times \frac{9.11 \times 10^{-31} kg}{electron}\)

where

\(m_I = mass\: of\: the\: Instagram\) and \(N = file \:size,\: in \:bytes \)

The fraction \(\frac {1 \: cell}{2 \: bits}\) takes into consideration the approximately equal distribution of bytes between empty and full; that is, 2 bits has the equivalent mass of an empty cell and a full cell together.

\(m_I = 41,000 \: bytes \times \frac{8\:bits}{byte} \times \frac{1\:cell}{2\:bits} \times \frac{40,000\:electrons}{cell} \times \frac{9.11 \times 10^{-31} kg}{electron}\) this, we can find the mass of the electrons comprising an Instagram to be:

\(m_I = 0.00000000000000000000597616 kg= 5.97616 \times 10^{-21} kg\)

This mass is so small, no measuring technique has been developed yet to determine this mass. The smallest mass ever measured is that of a group of xenon atoms, with a mass of a few bilionths of a trillion of a gram, or in the order of \(10^{-15}kg\).  This is similar to the proportionality in the masses between a human and an oil supertanker, or a human and a flea. So the mass of an Instagram is barely there.

So, where do all these additional electrons come from? They all come from a power source, which place the cells in the flash memory in their proper states. This also explains the nature of flash memories, which have no mechanical parts and therefore could last much longer than CDs or MHDs. Electrons are the only things that move about in a flash memory.

Application

This is one instance wherein the application was in place before the question, as flash memories and smartphones have been around far longer than Instagram. However, the ideas behind the answer are what drive current technologies such as the aforementioned smartphones, tablets, USB flash drives, solid-state hard drives, and other file-storage devices. All these devices have enabled us to be more mobile, having to carry a lot less mass than what we would do in the past.

Just 20 years ago, most books were printed on paper and had no electronic equivalent. Music was limited to cassette tapes and CDs which could carry one album from a recording artist. Movies had to be shipped as film to various cinemas, resulting in uneven release dates. Office work that had to be brought from one place to another required huge boxes. Now, one device about 200 g in mass can contain everything mentioned in the list above, and can be accessed easily and instantly. Instagram just happens to be one of the applications of electronics that has dominated our lives over the past few decades.

Final Thoughts

This is going to be the first of a series called The Physics Behind the Nonsense, where we take seemingly weird and whimsical questions and answer them with Physics concepts.

Sources

• http://discovermagazine.com/2007/jun/how-much-does-the-internet-weigh#.UaNCQED040E


• http://wiki.answers.com/Q/How_many_bits_are_in_a_byte


• http://en.wikipedia.org/wiki/Electron_rest_mass


• http://instagram.com/


• http://www.universetoday.com/38394/charge-of-electron/


• http://searchinstagram.com/


• http://en.wikipedia.org/wiki/Flash_memory


• http://science.slashdot.org/story/05/04/01/2323209/scientists-weigh-smallest-mass-ever


• http://asburyandasbury.typepad.com/.a/6a010535893544970c017d3ef41caa970c-800wi


• http://phys.org/news/2011-02-kilogram-approaching-avogadro-constant-enriched.html


• http://en.wikipedia.org/wiki/Kilogram

The Physics Behind the Nonsense: Kilograms and Instagrams

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Adventure Time!

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The Misconception of Mathematics and Women

A pretty common misconception about mathematics is that women and girls are not that good in it. As a teacher, I know this is not true.Here is an infographic about mathematics and women.

 

Makes you ponder, doesn’t it?

The Misconception of Mathematics and Women

Immovable vs. Unstoppable: What's Gonna Happen?

The Question

A few days ago, some students asked what would happen when an unstoppable force meets an immovable object. It was an innocent question, but one that caused the whole class to stop work and ponder on the answer. Since the class was supposed to cover a whole different topic on physics (thermal transfer),  I decided to answer the question, under the condition that we had to finish the topic before going through the physics behind the force and the object.

The Situation

An object is immovable. Something that is unstoppable comes along. What happens when they meet?

This is actually a common metaphor used in the English language, where two large entities collide in an epic showdown. But aside from common usage, this is actually a very common question in introductory Physics courses in university.

So what would happen, theoretically, when this does happen?

The Physics

For simplicity, let’s call the unstoppable force the Ball,and the immovable object the Wall.

The Ball is unstoppable. This means two things. First, it is moving. Second, it cannot stop. In physics terms:

The Ball is always in a state of constant velocity, and will never experience a reduction in its velocity. It will never experience deceleration.

When acceleration is being considered, then force must also be accounted for. Newton’s second law of motion guarantees it.

Let’s take a closer look at this. If the ball has any finite value for its mass, any force can make it accelerate. Hence, anything with a finite mass cannot be the unstoppable ball. This then leads us to the conclusion that the ball has to have an infinite mass.

Now, let’s look at the Wall. Since it does not move, its velocity (relative to us observing it) is always zero. Again, using some physics terms:

The Wall is always in a state of zero velocity, and will never experience an increase in its velocity. It will never experience acceleration.

Let’s analyse the Wall. If it had a finite mass, it would accelerate when a force is applied. It’s almost just like the ball. So we can get to the same conclusion that the Wall has infinite mass.

Many physical laws, especially Special and General Relativity, will have to broken to get infinite mass. However, since we are simplifying everything by ignoring other laws of physics, let’s make the Wall and the Ball collide.

Since the two entities cannot accelerate, nothing should happen when they collide. And by “nothing”, we do mean it. The Ball does not decelerate, so it passes through the Wall. But the Wall does not accelerate in any way (including breaking down), so it must stay whole and unmoving. This means that there should be no interaction between the Wall and the Ball.

Here’s another way of looking at this problem.

A bit anticlimactic, but what can we expect? The whole problem breaks every law of physics that we know.

A Possible Way About This

Since the Wall and the Ball passing right through each other is not too realistic, it’s time to approach this another way.

Immovable is simple enough. The Wall cannot move at all. However, just because the ball is unstoppable does not mean it cannot be deflected. In other words, the problem is not clear as to the Ball has a constant speed or a constant velocity.

If the Ball has a constant speed, then it is still unstoppable, but can still be deflected. The end result now would be that the Wall still does not move, but the Ball is moving one way and then the other.

This time, another law of physics is broken: The law of  conservation of  momentum. Essentially another form of Newton’s third law of motion, this is now the final blow to the scenario.

In Summary

The scenario of an unstoppable force and an immovable object is not only physically impossible, but mathematically nonsense (a paradox). If both exist, nothing else does, and we would not be here to discuss this problem.

I know most of this would be unsatisfying, but don’t worry. You’re not alone, as I am still wondering about the Wall-and-Ball situation even after I have finished writing this article. You have to admit though, that was a good topic to discuss.

Immovable vs. Unstoppable: What's Gonna Happen?

The Beauty of Physics: Waves and Light

When I was taking a break in Bali, I came across a place with a glass tank for a ceiling. The water in the tank was oscillating with the wind, and the sun was in the perfect place its light to shine down from the sky to the floor. It was a marvel by itself, and then I looked at the floor.

Physics is simply beautiful.

The Beauty of Physics: Waves and Light