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With technology advancing so rapidly we’re making big discoveries on a daily basis. What fascinating discovery would you like to hear about when you wake up tomorrow morning? Evidence of life on another planet or a moon, signs of bio-signatures on an exo-planet, reception of a signal from an intelligent life or maybe something completely different?
Andrew Rader (SpaceX engineer, MIT PhD, author)

Wow, those would all be good ones! However, in my view, the main point of searching for life on planets and moons in our solar system is to test the hypothesis “are we alone”? (Because we currently have one world with life, Earth, and a 1 out of 1 scientific result is meaningless due to the anthropic principle, but a 2/2 would be a big deal.) Thus, hearing directly from intelligent extraterrestrials would sort of cut to the chase and be an even bigger deal.

Paul Carr (Space Systems engineer at NASA, podcaster, blogger, investigator)

This one got me thinking. Any discovery that would be a real a paradigm breaker would not be one that I could predict, and I doubt even people much cleverer than I would either.

A couple of helpful quotes to keep in mind:
Clarke’s First Law: “When a distinguished but elderly scientist states that something is possible, he is almost certainly right. When he states that something is impossible, he is very probably wrong.”
J.B.S. Haldane: “Now my own suspicion is that the Universe is not only queerer than we suppose, but queerer than we can suppose.”

My own ability to predict future discoveries is probably even more limited than a distinguished but elderly scientist. We will probably need to rework our conceptual toolbox – our vocabulary, if you will – to even be able to recognize what is right in front of us. I am optimistic that this will happen, since it has happened before, such as when we realized that space and time weren’t absolute, or that the Earth was very ancient and not the center of the universe.

However, your question seems to be about discoveries we can predict, and for me the most important would be the confirmed discovery of life in our solar system (possibly even here on Earth) that we unambiguously do not share a common ancestor with. This “second genesis” would effectively nail down the fourth term in the Drake equation – it’s on the order of one, and implies that life is more or less a natural state of warm matter. This may well happen within my lifetime.

Erin Macdonald (Space Science Speaker, Educator, Consultant)

The near-term big discovery I’m looking forward to (now that we’ve got gravitational waves!) is evidence of life (current or past) in our own solar system. With further exploration of Mars (including underwater lakes) as well as future missions to Europa with a warm, seemingly salt-water ocean under the surface, I hope that we find evidence of even past microbial life on other planets. While all the discoveries in the last decade of exoplanets which may be able to support liquid water on their surface, we seem to have collectively made the assumption that there is other life out there, but we have to remember that we still don’t have any evidence of that. Once that discovery is made, I will be literally jumping for joy.

Brian Koberlein (astrophysicist and physics professor at Rochester Institute of Technology, author, podcaster, publisher)

Honestly, I’m really keen to see a black hole directly. If the rumors are true that should happen April 10. My dissertation was on black holes, and at the time we had no way to directly observe one. To finally see that happen would be really cool.

Bob Novella (co-founder and vice-president of New England Skeptical Society, co-host of Skeptics’ Guide to the Universe)

Beyond all other discoveries, I would probably most enjoy waking up one morning to the news of signals from space from an extra-terrestrial civilization. This could minimally be just a “hello world” signal proving to us finally that these technologically advanced creatures are really out there. That would of course be the news of the century but it would also ultimately be quite frustrating since having a conversation given the distances involved would try anyone’s patience. Ideally, this discovery would take the form of what Isaac Asimov and Carl Sagan described as an Encyclopedia Galactica: a cornucopia of detailed information about the aliens and their culture, science and technology, and surely many things that we can’t imagine or even comprehend.

A fascinating variation of this idea that I’ve often thought about involves the discovery of an extra-terrestrial cloaked satellite that has suddenly revealed itself in orbit around earth.
This satellite would have documented in detail the evolution of life on earth for hundreds of millions of years. Imagine having actual documentation of dinosaurs and proto-humans and countless other extinct life forms that we have never found fossils for.