It's a beautiful May morning. You went out to the seashore to do your favorite thing: blowing bubbles. Lately, you have been blowing bubbles from this cliff every weekend in the morning. It looks beautiful and it's so relaxing. In the morning, the wind blows from the land towards the ocean, and you watch the bubbles swirling around and falling softly in the distance, sometimes on the sand, sometimes in the waves. Sometimes, they get lost somewhere in the sky, or pop on the seagrass nearby.

Last week you noticed that once in a while bubbles split into two smaller bubbles. And today, you realize that it actually happens more often than you expected. If a bubble splits once, it leaves two offspring, right? It's as if that mother bubble still existed, however, it's now flying in two places at once. One might be flying over the beach while the other is over the water, but it's pretty much the same soap. But if a bubble splits and one of its offspring splits again, then the mother bubble will have had a total of three offspring—that one exists in three places.

Now, it's a well-known fact that bubbles don't live forever; once they touch the ground, they pop. Or they might just pop in midair for no apparent reason. But tell me, which one is longer—the time it takes for two bubble to pop, or the time it takes for three bubbles to pop? Well, three bubbles popping implies that at least two bubbles pop, so the time for three bubbles to pop has to be the longest. Therefore, more splitting equals more flying.

In fact, it's the initial size of the bubble that defines whether it's likely to split or not. You now clearly see that a large bubble is much more likely to split than is a small bubble. So in the end, the size of the mother bubble affects how long its soap will be flying around.

I ask you: "What if a mother bubble transmitted its size to its offspring? That is, what if offspring bubbles grew to the size of their mothers?". Well, you laugh at my question, but today you just bought a soap that does exactly that and you were planning to test it yourself! It says on the box that the rays of the sun expand the soap for it to reach precisely the size of a mother bubble! Seems fun. The bubble-blowing industry has surprisingly good chemists.

And it does work! Crazy! No wait, it's not quite as they claim on the box. It's more or less the same size, but the splitted bubbles are not exactly the size of the mother. What were you expecting? It is almost impossible to get it exactly, but on average, it works!

With this new soap, it's even more fun to come to the cliff on weekends. There are so many bubbles in the air. Big bubbles split into big bubbles, which give more big bubbles and so on, and so on. Big bubbles split more often and their offspring outlive the small bubbles, so, there are a lot more big bubbles in the air now than with the previous soap.

Now the funny thing is that if a bubble splits sufficiently fast, there is a chance that it never goes extinct...

But it didn't happen this morning.

But now, while eating a cantaloupe in the heat of midday, you understand that there ought to be a bubble size with an average splitting time that is shorter than its average popping time. Such a bubble would always have an offspring flying around.

This is probably a big bubble that splits a lot!

But can such a bubble size even exist? Maybe not. But you'll have to try.

You sat for hours, and the bubbles always ended up popping. You sat for days. You were the patient spectator of millions of bubbles dancing around, but never they stayed in the air for very long. It's been three months of coming every weekend to that cliff. Suddenly, it's been three years of blowing bubbles. One day, you have seen dolphins, another whales. Seagulls have got used to your presence and don't even bother leaving your spot anymore at your arrival. You don't even remember when it all started.

But today, something crazy happened. Everyone is panicking, running around, the radios and televisions are glaring. And you caused that disaster. As every saturday morning, you went to the cliff, but this time, you witnessed a fascinating phenomenon. One big bubble first flew high up in the air, and there it divided in a few offspring. Some of them were alreadfy quite big, because the inheritance of bubble size can be quite inaccurate sometimes. And as they started falling back down, these gave even bigger bubbles, and these produced some bubbles even bigger that kept dividing. The air around you, especially above the sea where the bubble-mass was drifting, was saturated with bubbles flying everywhere. Bubbles were filling the sky at an alarming rate!

to be continued...