Biological Invaders

I found this old story that I wrote in 2000. Enjoy reading!

 

Biological Invaders

 

 

It was a signal from outer space. After months of studying its statistical properties, we concluded with excitement that it had to origin from an intelligent life form. Nervously, we waited another month for the computer to translate the signal. Finally, the translation was complete, and we gathered in a small room to listen to the conversation.

 

“Observation point reached!” Where were they?

 

“Star S08/15a… there you are.” Short pause.

 

“There, we have nine, no eight planets. But, which…”

 

“Number 3.”

 

“We have the recording of the species’ population over the last 500 thousand orbits of the planet.”

 

“Good. Put the diagrams on screen 5.”

 

“The screen describes the surface of our planet, number 3. On the top, a display shows the number of orbits since the beginning of our recording. The red areas mark the distribution of the potentially aggressive species that we found.”

 

“One red dot appeared and disappeared again.”

 

“200,000 orbits ago, you see that the red slowly expands. 100,000 orbits ago, it was still constraint to a local region only 5% of the planet’s surface.”

 

“Now, it is spreading.” Another pause.

 

“Oh no! It exploded!”

 

"The planet is infected!”

 

“Why is it not all over the place? The red area has a strange pattern. Where are these white areas coming from?”

 

“We checked that. Most of these areas are completely covered in water, 71% of the planet's surface.”

 

“Water? Hmm.”

 

“Which state?”

 

“Mostly liquid.”

 

“The species seems to avoid it, or it cannot survive in an area with too much water.”

 

“We should mark these areas for the presentation.”

 

“Can we have a closer look at the last 2,000 orbits.”

 

“Sure. One moment.” There was silence. Finally, another voice said, “exponential growth! The population more than quadrupled in the last 100 orbits.”

 

“Indeed. This is serious!”

 

“Other species will disappear!”

 

“Right. The number of species declined. The charts are ready…”

 

“We have to restore the ecological balance.”

 

“But how?”

 

“Wait! 20,000 orbits ago, something interesting happened. The red dots disappeared from great parts of the northern hemisphere.”

 

“Hmm. Solid water.”

 

“Right!”

 

“That's it! We freeze the whole planet.”

 

“Stupid!”

 

“No. No. No.”

 

“Impossible! We cannot afford such an impact to the environment. Probably, whole populations of various species might be erased by such a means.”

 

“We need to classify the invader.”

 

“Choose status of planet,” a computer voice said. “One: no life. Two: developing self-reproducing units. Three: intact, no single species is dominating. Four: infected. Five: overturned. Six: Dead.” Some clicks.

 

The computer voice continued, “Choose status of invader. One: isolated. Two: agricultural threat. Three: health threat. Four: tourist.”

 

“What happened to Rusty Rye?”

 

“The planet is dead.”

 

“It was similar to this one. Rusty Rye took over most regions. Exponential growth. Other plants disappeared. The planet looked pretty much red. So, the Delta team planted wild umbrella. This plant can survive among Rusty Rye and takes away the sunshine with its shield.”

 

“Did it work?”

 

“The umbrella overturned the rye. But it got out of control claiming all of the sunshine for itself.”

 

“Hmm.”

 

“Well, besides the dangers of introducing a natural enemy, so far, we don't know enough about this... how the heck is it called?”

 

“The administration is working on the catalogue number.”

 

“Can we have a closer look at these red areas? Is it uniformly distributed?”

 

“No. Have a look! There are a few large spots, many small ones, and a mass of tiny ones.”

 

“In most cases, the large spots grew at a higher rate than the small ones, sometimes swallowing smaller ones. Some of the small dots even disappeared.”

 

“That reminds me of something. Of…”

 

“These species tend to stick to each other.”

 

“Hmm. The accumulation is clearer marked than in the Rusty Rye case. It can't be sexual reproduction alone.”

 

“Water droplets.”

 

“What?”

 

“It is mobile.”

 

“And it secretes a chemical.”

 

“Yeah.”

 

“Prove? I want a prove!”

 

“Look! I traced some single species, and in one case, I got one which jumped all over the planet.”

 

“The planet?”

 

“It could still be a seed hitchhiking around.”

 

“The chemical? We might not be able to figure that one out from the distance.”

 

“We are not allowed to get any closer. Every possible impact to the foreign environment has to be omitted.”

 

“But, before the Delta team is coming…”

 

“Sure, but now our job is to observe and work out an advice for how to cope with the invader.”

 

“I have got one.”

 

“What?”

 

"We build a trap.”

 

“A trap?”

 

“Gold.”

 

“Gold?”

 

“We inject gold onto the surface in high concentration and, then, use the fact that they accumulate.”

 

“It is attracted to gold?”

 

“I've never heard of a species eating such an inert substance. No, that doesn't make any sense.”

 

The transmission stopped for a while. We looked at each other in disbelief. Then, it continued.

 

“What? It left the planet?”

 

“Yes. Encapsulated in an aluminum vessel.”

 

“This is serious!”

 

“So, we should freeze the planet before it is too late.”

 

“Stop that!”

 

“Don't worry. So far, it just diffused into the very near neighborhood of the planet. It is far away from infecting other ecological systems. I think, it cannot survive long enough in these vessels.”

 

“Well, we encountered some…”

 

There was a sound of an explosion. Then, a computer voice said, “Processes received the termination signal.” A loud sigh. The transmission ended.

Space adventure: What happens when you fly inside a black hole?

I take you on a journey into a black hole. Black holes are super-massive objects in our universe that have such a strong gravitational pull that not even light can escape. So, we cannot observe what happens inside from the outside. Get your towel and brace yourself for a ride in a spaceship to experience the inside.

First, we need to pick a suitable black hole for our journey. To experience the inside, we need to pass what is called the event horizon. It is not a physical barrier; it cannot have cracks as depicted in one Star Trek episode; it is the point of no return, an imaginary surface around the black hole at which light can move only along the surface or inside it, but not outside. The closer we approach to the hole the stronger the gravitational pull.  Tidal forces, the difference in gravitational force between front and back of the spaceship, could brake our ship. So, we need to be careful to choose a suitably-sized hole.

Our galaxy, the Milky Way, has a gigantic black hole at its core, Sagittarius A*, with a mass estimated to be about 4 million times larger than our sun. How do we know the mass? In the black hole’s vicinity, we can observe a star, measure its orbital speed and distance, and together with the known gravitational constant (measured on Earth) have all the ingredients to compute the mass pulling at the orbiting star. At the event horizon of this black hole, the gravitational pull is extreme, half a million times stronger than what we experience on Earth. But if we fall at this acceleration together with the spacecraft, we would experience weightlessness like inside the International Space Station - not too bad. The only forces we would experience are the tidal forces. Our black hole, however, is huge: with a radius of the event horizon of about 6 million miles, the tidal forces are minuscule. For smaller black holes, though, they might be deadly.

At this extreme acceleration of our spacecraft, we will approach the event horizon at breathtaking speeds - hardly enough time to enjoy the transition into the black hole. If we want a ride at lower acceleration, we need to pick an even larger hole. The radius of the event horizon scales proportionally to the mass of the black hole. Fortunately, the gravitational acceleration decreases inverse proportionally with the square of the radius. As a result, for every ten-fold increase in mass, we get one tenth of the acceleration at the event horizon. For example, if we pick a black hole the mass of the Milky Way, estimated to be about a trillion times more than our sun’s mass, 250,000 times more than Sagittarius A*, our acceleration would be that of a sports car at peak acceleration - sufficiently low to allow an arbitrarily slow travel speed.

Finally, our journey through the event horizon should be a pleasant ride. Still something unusual happens. Space-time curves as we approach the event horizon. When we stretch out our arm toward the black hole, the blood will take longer to flow back to our heart. When we move the fingers, their motion will appear to be slower than what we commanded them to be. Moreover, the nerve bundles in our arm will return delayed sensations from our fingers. When we look past the fingers to the front of the spaceship, the wall colors appear to have a reddish tint.

We pass the event horizon, but do not notice any difference. Through the rear window, we see the familiar star pattern, a bit distorted on the sides, and through the front window only blackness. As we gaze outside, a crew mate joins us. She says she will get a coffee from the front of the spaceship. We watch her drift away. She appears to move amazingly slow: we are waiting a full hour until she reaches the front. There, her movements are extremely slow, picking up a space coffee pouch in slow motion.

She returns after another hour, but says she was only gone for a few minutes. In disbelief, we compare our watches. Indeed, her watch advanced only three minutes. Strangely, our times passed at different speeds depending on how we moved relative to the black hole. Our crew mate did not experience the slowness herself. In contrast, she observed us wiggling around and moving our hands at unusually fast speed.

Such time phenomena actually also happen on Earth: a person in a valley will experience time passing slower compared to a person on a mountain, but the effect is tiny and barely noticeable (only with super-accurate clocks).  At the event horizon and inside a black hole, however, the effects can be so strong that we notice differences even within a spaceship.

Once our spaceship passes the event horizon, it cannot stop anymore. It will steadily move closer and closer to the center of the black hole. At the slowest possible speed towards the center, even stranger things happen inside the spacecraft.

Anything can move only towards the front of the spaceship or to the sides, but not towards the back. If we stretch out our hand to the front, we cannot see it anymore. In fact, we cannot see anything in front of us, only blackness. Unfortunately, this situation has a catastrophic effect on our brain since communication between large parts of the brain shuts down; communication can happen only on two-dimensional brain slices - likely, insufficient for conscious thought. So, don’t drive the spaceship at the slowest possible speed! Reaching the slowest possible speed is also tough on the engines. The lowest limit of the speed can be reached only by massless particles like light, and the closer we get to the lowest limit, the more force we require - we are fighting the space-time suction of the black hole.

The Myth about Viral Videos

You probably heard about a YouTube video "going viral." Do videos really spread virally? Here, viral implies that a content is so compelling that it spreads between people like an a epidemic, self-propelled, increasingly reaching more and more people.

If one video deserves to be viral, it surely must by Gangnam Style by Psy, the most watched video on YouTube with more than 2.2 Billion views, which recently hit the threshold of 2^31-1; the largest 32-bit integer commonly used in today's computer systems. 32-bit integers range from -2^31 to 2^31-1 since 32 bits (zeros and ones) can represent only 2^32 different numbers. Google used to represent the number of views with a 32bit integer but had to change thanks to Gangnam Style.

YouTube has a function for easy sharing of videos between friends. Let's examine the number of shares for Gangnam Style. The ratio of shares versus views is 0.11%. Are these shares sufficient for viral spread? First, this ratio is only slightly higher than for one of my own videos (0.07%), which I am pretty sure did not spread virally. To illustrate the non-viral nature, the following graph shows the daily views and shares for my video.

Instead of driving more views, the shares seem to be driven by the views. However, small changes in the ratio of shares can have a big impact on viral spread if we get close to a critical threshold. So we need to look closer at this critical number. What ratio of shares do we need for a viral spread?

Your friends and their friends form a network of people, a network with links between people that are friends, ultimately connecting all people on Earth. What is the condition of viral spread in such a network? The average number of facebook friends of U.S. users in 2014 was 350. Let's say 10,000 people noticed a specific video. If 0.11% of them spread the video, 11 will spread them to 350 friends each, reaching 11*350 = 3,850 people (actually, the number will be less since some friends overlap, but for my argument I just need an upper bound). In the next spreading stage, those 3,850 will spread it to 1,482 people. You see the number decays with every stage, which means that the video will not go viral. To go viral, the critical ratio of shares would be 0.29%, well above the value for Gangnam Style and any video I know of.

I like to add the caveat that the YouTube shares do not include all shares of the video and that the number of YouTube friends is likely lower than the number of facebook friends. These numbers might balance out, but I do not know for sure. However, I think that the percentage of our engagement with videos naturally regulates itself to prevent viral spread. Millions of creative people create compelling content every day. If our engagement would be so high to enable viral spread, we would be constantly flooded with shares, and this flood would reduce our enthusiasm to engage. So the level of engagement regulates itself.

Finally, you may ask if that is true, why did Gangnam Style get so many views? Apparently, the creators did not just rely on viral spread. The campaign was well planned. Four days before the main video, a teaser was released on YouTube, which instantly attracted a few hundred thousand views. That shows that Psy was no noname to begin with and the producers probably paid for advertisement. What followed was likely a clever engagement with the media to get the video into the international news. Of course, the video had to be compelling too, but on its own it would not have spread virally.

To conclude, creating compelling content is not enough, traditional marketing matters. You cannot just rely on viral marketing. I am curious about your thoughts and comments.

Just jump to escape to space

The European Rosetta mission achieved the sensational feat of placing a spacecraft in the orbit of a comet and landing a fridge-sized probe onto its surface. The comet is called Churyumov-Gerasimenko, or short 67P. By orbiting around the comet and measuring the changes in the spacecraft's trajectory, we can calculate the comet's mass, who's gravity slightly pulls the spacecraft away from a straight path. 67P's mass was estimated to be about 10^13 kg (a one with 13 zeros). The largest cruise ship in the world, the Oasis of the Seas, weights about 10^8 kg. So the comet weights as much as 100,000 of such cruise ships. Still, this mass is nothing compared to the mass of the Earth, which weights about 6*10^24 kg, 600,000,000,000 times as much as the comet.
    If we would walk on the comet's surface, how strong would be the gravitational pull? Given the known mass and size of 67P in relation to the Earth, we can compare the gravitational forces. This force is proportional to the mass of the space object (Earth or 67P) divided by the square of the distance to the center of the object. (Strictly speaking this relationship is only correct for spherical objects like the Earth, but 67P is shaped like a rubber duck; still it is a reasonably good approximation.) 67P is much lighter than Earth, but we would walk much closer to its center. How much closer? Earth's radius is about 6,400 km (4,000 miles). 67P is maximally 4km long; let's say, we walk 2 km above its center. Then, the gravitational pull would be 3,200*3,200 divided by 600,000,000,000 = 0.002% of the force on Earth. A small force, which makes landing a probe challenging; it could easily bounce off again.
    Imagine how high you could jump on 67P. For each space object, there is a maximum velocity beyond which a spacecraft would escape the object's gravitational pull and never return (it's different for black holes, but I won't discuss them in this post). This velocity is called the escape velocity. For Earth, this velocity is about 11,000 m/s (25,000 mph), which makes it expensive to launch anything into space. The square of this velocity is proportional to the mass of the space object divided by the distance to the center of the object. So for 67P, the escape velocity is the square root of (3,200 / 600,000,000,000) times 11,000 m/s = 80 cm/s (1.8 mph). Compare this value to the average human jump velocity, which is about 3 m/s (6.7 mph). Standing on 67P, you could easily launch into space just by jumping. But you need to walk carefully on the surface to avoid accidentally drifting into space and never returning.

    A manned mission to a comet would be very different from the moon landing. The Apollo mission required a moon lander capable of launching again from the surface. In contrast, a spacecraft circling the comet could eject an astronaut to land on the surface, who then could jump off the surface again to return to the spacecraft.