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As I mentioned on Friday, when I first heard about the Italian Space Agency’s announcement of water on Mars, I was skeptical. Various space agencies have cried wolf on major discoveries before – most famously, with “NASA Confirms Evidence That Liquid Water Flows on Today’s Mars (it’s actually sand) and Discovery of “Arsenic-bug” Expands Definition of Life (it wasn’t, and it doesn’t). This is not a conspiracy — it’s just overexcitement. Scientists work hard to keep themselves free of confirmation bias, but they’re still human, and sometimes they still see what they want to see.

Given this history, how do we know that it really is a wolf this time? I’ve found that it helps to ask the obvious question.

Aside… This is what bothers me most about global warming deniers. They will go on for pages and pages about July temperatures in Paraguay, without even trying to answer the obvious question: why did global temperatures start to increase at exactly the time when we started releasing into the atmosphere a gas that is known to increase temperatures?

In the case of water on Mars, here is the obvious question. We know for sure that there is liquid water on one of the nine planets in the Solar System: here on Earth. The research team claims that there is liquid water under the polar ice caps on Mars. Could the same techniques they used have detected water under Earth’s polar ice caps, where we know there is water?

It’s right there in the second sentence of the paper that published the announcement (Orosei et al. 2018): “Radio echo sounding (RES) is a suitable technique to resolve this dispute, because low-frequency radars have been used extensively and successfully to detect liquid water at the bottom of terrestrial polar ice sheets.”

The technique they used is the IN SPAAAAAAAAAAAACE version of a commonly-used technique called ground-penetrating radar (GPR). GPR involves transmitting radio waves into the ground, then listening for the echoes of those waves reflecting off various underground layers. The strength of the return signals reflected off each layer tells you what the layer is made of, and nothing reflects quite like water. And that water-related pattern is exactly that kind of reflection that the research team saw on Mars.

Obvious question answered, wolf found. We really did it this time!

We found water on Mars!

We found water on Mars!

We found water on Mars!

(“We” = humans)

I’ll admit that when I first heard the news, I was skeptical. Although we try to avoid it, scientists can sometimes fall victim to their own wishful thinking just like anyone else can. But I read the report, and the evidence is solid. We really did it this time.

We’ve known for a while that there is H₂O on Mars, as water vapor in the atmosphere and as layers of dust and ice near the north and south poles. The question was whether we could find liquid water.

The answer came from the European Space Agency’s Mars Express spacecraft. It carries a radar instrument that broadcasts radio waves at the Martian surface and listens for those waves reflecting back from layers under the surface. When the spacecraft flew over a region near Mars’s south pole – shown below – it picked up echoes from a layer buried below the surface.

The radar echo was so strong that it could only be one thing: liquid water.

There’s a lot more to say about this discovery, but first:

WOW!

My colleagues and I are thrilled to announce the latest release of our SciServer online science platform.

SciServer a suite of tools to manage, visualize, and understand large-scale datasets in all areas of science, from astronomy to genomics to soil ecology. SciServer allows anyone to work with Terabytes of data, running server-side analysis and visualization tools in real time, without needed to install anything.

The beating heart of SciServer is SciServer Compute, a browser-based virtual computing environment. Anyone can create a free SciServer account and create analysis scripts in Python, R, or Matlab.

Today’s release is called SciServer Betelgeuse, succeeding the previous system SciServer Altair (#lolSeeWhatWeDidThere). SciServer Betelgeuse adds group functionality for file and data sharing, and also the ability to run asynchronous time- or memory-intensive jobs. We’ve been working on this update for more than two years, and we’re eager to see how everyone can make use of it.

We’re grateful to the generosity of the National Science Foundation (award ACI-1261715) for their generosity in allowing us to create and maintain this resource, forever free to users.

The “we” I keep referring to here is a team of incredibly talented scientists and coders at the Institute for Data-Intensive Engineering and Science (IDIES) at Johns Hopkins University. I’m honored to have been part of this team for the past eighteen years.

And on a personal note, this new release is a major new step in my career. I’ve devoted my entire professional life to finding new ways to bring the real process of science to the world, and this is the realest real way yet.

Think of any natural number (1, 2, 3, 4…). If your number is even, divide by 2. If your number is odd, multiply by 3 and add 1. Repeat with your new number, over and over again.

For any everyday human-scale number, you will eventually end up in an infinite loop of 4, 2, 1, 4, 2, 1… Sometimes you’ll get there quickly, sometimes it will take hundreds of steps.

Here are two examples I tried on the back of a random piece of junk mail: 42 goes into the 4 -> 2 -> 1 loop on the sixth step, while 99 goes on for so long that I ran out of space. Try it yourself with a few numbers to get a feeling for how it works. If you get tired of writing down numbers, this online tool will do the calculations for you.

But of course there are infinitely many numbers… so is that ALWAYS the case, or is there some number that defies the pattern? An exception could either end in a different repeating cycle, or could keep growing forever by multiplying by 3 and adding 1.

This is known as the “3x+1 problem” or the “Collatz Conjecture” (after German mathematician Lothar Collatz). Amazingly enough, this simple problem has never been solved.

Computer calculations show that if there is an exception to the rule, it must be larger than 1,152,921,504,606,846,976. We could keep testing larger and larger numbers on larger and larger supercomputers, and maybe we’d find an exception… but maybe not. Even if we supercompute for ten billion years and still don’t find a counterexample, that’s still not a proof. A proof would require someone to construct a logical argument, starting from things we know to be true, to conclude either that an exception MUST exist or an exception CANNOT exist. (Caveat about this: see below.*) And mathematicians don’t even know where to begin to build that argument (another caveat**).

Probably the world’s top expert on this problem is Jeffrey Lagarias of the University of Michigan, who says: “This is an extraordinarily difficult problem, completely out of reach of present day mathematics.”

Or, put more simply: Math is AWESOME. That is going to be a theme of this blog, I think.

To learn more about the Collatz Conjecture, see this excellent introduction from one of my favorite YouTube channels, Numberphile:

[youtube https://www.youtube.com/watch?v=5mFpVDpKX70&w=560&h=315]

*There is another possibility – it could be “undecidable,” meaning we could prove that the statement could never be proven true or false from the basic assumptions of math. It would be sorta like the statement in simple English, “This statement is a lie.”

**I’m exaggerating a bit, of course, because mumble mumble abstract machine mumble subsemigroup mumble parity sequence mumble mumble matrix something something mumble. But there’s no obvious path forward.