NationStates Jolt Archive

...in our galaxy according to one Edinburgh scientist anyway.



Intelligent civilisations are out there and there could be thousands of them, according to an Edinburgh scientist.

The discovery of more than 330 planets outside our solar system in recent years has helped refine the number of life forms that are likely to exist.

The current research estimates that there are at least 361 intelligent civilisations in our Galaxy and possibly as many as 38,000.

The work is reported in the International Journal of Astrobiology.

Even with the higher of the two estimates, however, it is not very likely that contact could be established with alien worlds.

While researchers often come up with overall estimates of the likelihood of intelligent life in the universe, it is a process fraught with guesswork; recent guesses put the number anywhere between a million and less than one.

"It's a process of quantifying our ignorance," said Duncan Forgan, the University of Edinburgh researcher who carried out the work.

In his new approach, Mr Forgan simulated a galaxy much like our own, allowing it to develop solar systems based on what is now known from the existence of so-called exoplanets in our galactic neighbourhood.

These simulated alien worlds were then subjected to a number of different scenarios.

The first assumed that it is difficult for life to be formed but easy for it to evolve, and suggested there were 361 intelligent civilisations in the galaxy.

A second scenario assumed life was easily formed but struggled to develop intelligence. Under these conditions, 31,513 other forms of life were estimated to exist.

The final scenario examined the possibility that life could be passed from one planet to another during asteroid collisions - a popular theory for how life arose here on Earth.

That approach gave a result of some 37,964 intelligent civilisations in existence.

Form and function

While far-flung planets may reduce uncertainty in how many Earth-like planets there are, some variables in the estimate will remain guesses.

For example, the time from a planet's formation to the first sparks of life, or from there to the first intelligent civilisations, are large variables in the overall estimate.

For those, Mr Forgan says, we will have to continue to assume Earth is an average case.

"It is important to realise that the picture we've built up is still incomplete," said Mr Forgan.

"Even if alien life forms do exist, we may not necessarily be able to make contact with them, and we have no idea what form they would take.

"Life on other planets may be as varied as life on Earth and we cannot predict what intelligent life on other planets would look like or how they might behave."

Source (http://news.bbc.co.uk/1/hi/sci/tech/7870562.stm)

So do you think the way this was simulated is well done, full of flaws, completely inaccurate? Or do you believe that this is spot on and now we just have to figure out why they keep taking our cows?

Discuss!

There's a journal of Astrobiology?

There's a journal of Astrobiology?

Apparently so.

Some days I think that there is more intelligent species of bacteria than there are intelligent members of the human race. Today is one of them.

The current research estimates that there are at least 361 intelligent civilisations in our Galaxy and possibly as many as 38,000.

So basically, they don't have a clue, and only ran with this because they have a bet on to see who can get into the paper first?

I think I will say what everyone is thinking and ask just how many of those can we have sex with?

While researchers often come up with overall estimates of the likelihood of intelligent life in the universe, it is a process fraught with guesswork; recent guesses put the number anywhere between a million and less than one.

:D

While researchers often come up with overall estimates of the likelihood of intelligent life in the universe, it is a process fraught with guesswork; recent guesses put the number anywhere between a million and less than one.


:D

That would be us. ;)

There's a journal of Astrobiology?
I wonder how many articles you can write on "Aliens, do they exist?", "Aliens, If They Exist, Could We Have Sex with Them?", "Aliens, If They Exist and We Could Have Sex with Them, What Is the Likelihood That They'd Put Out for An Astrobiology Nerd Like Me?", "Aliens, Are They Protected Under Existed Laws About Rape and Sexual Assault?", "Spell Check Still Refuses to Acknowledge that Astrobiology is a Real Word. The Prejudice Continues", and "What to Do When People Burst Out Laughing When You Say You're an Astrobiologist."
I guess you could pad it out with reviews of Aliens vs. Predator 2, or still frames of that scene in Aliens where Sigourney Weaver is in her underwear, but even that can only take you so far.

Going off on a slight tangent...

As you know, some objects are tidally locked (such as our moon). Obviously, that would cause one side to be much hotter than a nonlocked world, and the other much colder. So I was actually thinking earlier: is a tidally locked world really lifeless? The dark side of a world hotter than earth may be earthlike; the bright side of a colder world may also be earthlike. If those are possible, then that'd raise the number of habitable planets. Sure, most tidally locked planets would be outside the habitable range, but so would most of the non-locked planets!

Going off on a slight tangent...

As you know, some objects are tidally locked (such as our moon). Obviously, that would cause one side to be much hotter than a nonlocked world, and the other much colder. So I was actually thinking earlier: is a tidally locked world really lifeless? The dark side of a world hotter than earth may be earthlike; the bright side of a colder world may also be earthlike. If those are possible, then that'd raise the number of habitable planets. Sure, most tidally locked planets would be outside the habitable range, but so would most of the non-locked planets!

Surely a tidally-locked moon would need to be built by intelligent aliens in order to seed human life....I compare myself to Rachmaninov.

Well duh. When it became apparent that the universe was almost infinitely massive, it became apparent that humans are not alone.

I wonder how many articles you can write on "Aliens, do they exist?", "Aliens, If They Exist, Could We Have Sex with Them?", "Aliens, If They Exist and We Could Have Sex with Them, What Is the Likelihood That They'd Put Out for An Astrobiology Nerd Like Me?", "Aliens, Are They Protected Under Existed Laws About Rape and Sexual Assault?", "Spell Check Still Refuses to Acknowledge that Astrobiology is a Real Word. The Prejudice Continues", and "What to Do When People Burst Out Laughing When You Say You're an Astrobiologist."
I guess you could pad it out with reviews of Aliens vs. Predator 2, or still frames of that scene in Aliens where Sigourney Weaver is in her underwear, but even that can only take you so far.

Let's not forget: "1001 Low-Fat Recipes Alien Recipes...If they Exist." Afterall, the next most pressing question after "Can we have sex with them?" is, "What do they taste Like?"

Given that irony is the most powerful force in the universe, the more planets they find probably means that depressingly humans are alone.

I, for one, have been looking forward for some time to being recognised as our solar system's first xenoarchaeologist.

My book will be titled "Aliens, If They Exist, What Does the Archaeological Record Say About Their Past Sexual Practices?"

This will be shortly before my well-intentioned but tragically misguided alien excavation leads to the alien plague / lifeform / curse being unleashed on our woefully unprepared civilisation.

I think I will say what everyone is thinking and ask just how many of those can we have sex with?
:D

Someday, a man named Kirk will help us find out.

I, for one, have been looking forward for some time to being recognised as our solar system's first xenoarchaeologist.

My book will be titled "Aliens, If They Exist, What Does the Archaeological Record Say About Their Past Sexual Practices?"

This will be shortly before my well-intentioned but tragically misguided alien excavation leads to the alien plague / lifeform / curse being unleashed on our woefully unprepared civilisation.

I imagine all of #nssport and the WCDT will buy said book.

As for the OP, of course there are other intelligent civs, and they are awfully good at playing hide and seek.

I imagine all of #nssport and the WCDT will buy said book.

As for the OP, of course there are other intelligent civs, and they are awfully good at playing hide and seek.

Space is big, you don't have to try to hide to hide.

While researchers often come up with overall estimates of the likelihood of intelligent life in the universe, it is a process fraught with guesswork; recent guesses put the number anywhere between a million and less than one.

I believe that Douglas Adams provided the maths on this one. There are an infinite number of planets in the universe, but only a finite number of them are inhabited*; any finite number divided by infinity is as close to nothing as makes no difference, therefore the number of inhabited planets in the universe is close to zero.


*And my father, an expert in post-infinite mathematics and nuclear engineering before his retirement, in turn pointed out the fallacy in this argument. If there are an infinite number of planets, there must, by definition, also be an infinite number of inhabited planets. The number of inhabited planets is simply a smaller order of infinity than the total number of planets, even while both nonetheless remain infinite. Clear?

*And my father, an expert in post-infinite mathematics and nuclear engineering before his retirement, in turn pointed out the fallacy in this argument. If there are an infinite number of planets, there must, by definition, also be an infinite number of inhabited planets. The number of inhabited planets is simply a smaller order of infinity than the total number of planets, even while both nonetheless remain infinite. Clear?

Wha?

Space is big, you don't have to try to hide to hide.

Aye, and we're awfully bad at hiding our spot. We have soo many different types of waves coming off the planet that we stick out like Sarah Palin at a gay bar.

Wha?

He seems to be of the impression that the universe is infinitely large instead of roughly 93 billion light years in circumference.

Wha?

Imagine that there's a bus with an infinite number of seats, and carrying an infinite number of passengers. The bus stops to take on new passengers. The existing passengers simply move down one seat to allow the new passengers on to the bus. Therefore while both the number of seats and the number of passengers remain infinite, the number of seats always remains larger than the number of passengers.

Or at least that's how an expert used to explain it to me. Just because I called that expert 'dad' doesn't invalidate his explanation - though it does mean I can't cite it. I do remember a similar explanation appearing in New Scientist or Scientific American in the 80s, though.

Why, I understand it's being seriously tested by the London bus system as a solution to overcrowding on local public transport (that was a joke).

I, for one, have been looking forward for some time to being recognised as our solar system's first xenoarchaeologist.

My book will be titled "Aliens, If They Exist, What Does the Archaeological Record Say About Their Past Sexual Practices?"

This will be shortly before my well-intentioned but tragically misguided alien excavation leads to the alien plague / lifeform / curse being unleashed on our woefully unprepared civilisation.

"we think this had ritualistic purposes..."

He seems to be of the impression that the universe is infinitely large instead of roughly 93 billion light years in circumference.

No, not quite. Douglas Adams, not me, used the mistaken concept that the universe was infinitely large as a means of making a humourous flawed argument on why that meant the number of inhabited planets was close to zero. I then pointed out that even if the universe were infinitely large, there would still be an infinite, albeit smaller, number of inhabited planets due to the nature of post-infinite mathematics.

At no point did I say that I thought the universe was infinite in size.

Some days I think that there is more intelligent species of bacteria than there are intelligent members of the human race. Today is one of them.There are assorted species of bacteria that exhibit teamwork. I presume they do beat the occasional neoliberal...

"we think this had ritualistic purposes..."

Curses!

You know the magic words we use when we can't bring ourselves to say 'I have no idea what this was used for'.

Who gave away our secrets?

You realise I now have to kill you....

No, not quite. Douglas Adams, not me, used the mistaken concept that the universe was infinitely large as a means of making a humourous flawed argument on why that meant the number of inhabited planets was close to zero. I then pointed out that even if the universe were infinitely large, there would still be an infinite, albeit smaller, number of inhabited planets due to the nature of post-infinite mathematics.

At no point did I say that I thought the universe was infinite in size.

I'm fairly certain douglas adams knew the error of the argument :p

At no point did I say that I thought the universe was infinite in size.

Orly?

I believe that Douglas Adams provided the maths on this one. There are an infinite number of planets in the universe, but only a finite number of them are inhabited

Who gave away our secrets?

You did, like two weeks ago, heh

I'm fairly certain douglas adams knew the error of the argument :p

I'm sure he did too - he wrote the preface to a book I contributed to after all - but it's fair to point out I didn't intentionally mean to argue that I thought the universe was infinite.




Orly?

[air of slight exasperation] It's a paraphrase from one of the Hitchhiker's books. Would you prefer for me to go back and provide footnotes and citations?

Only 361? That's nowhere near enough for my vast interspecies orgy.

You could argue that the universe is infinite, but only a finite part of it is nonvacuum -- otherwise some parts would be infinitely distant form the big bang's location, and that would mean that they moved at an infinite amount of speed (which is not possible).

Imagine that there's a bus with an infinite number of seats, and carrying an infinite number of passengers. The bus stops to take on new passengers. The existing passengers simply move down one seat to allow the new passengers on to the bus. Therefore while both the number of seats and the number of passengers remain infinite, the number of seats always remains larger than the number of passengers.

Or at least that's how an expert used to explain it to me. Just because I called that expert 'dad' doesn't invalidate his explanation - though it does mean I can't cite it. I do remember a similar explanation appearing in New Scientist or Scientific American in the 80s, though.

Why, I understand it's being seriously tested by the London bus system as a solution to overcrowding on local public transport (that was a joke).

..and there an infinite number of whole numbers and an infinite number of decimal numbers but the two infinities are of different sizes.

You could argue that the universe is infinite, but only a finite part of it is nonvacuum -- otherwise some parts would be infinitely distant form the big bang's location, and that would mean that they moved at an infinite amount of speed (which is not possible).

Perhaps the Universe isn't infinite then. Maybe it just seems that way because of all the space fuzz.

Afterall, the next most pressing question after "Can we have sex with them?" is, "What do they taste Like?"
Crispy duck.

Isn't this research a bit pointless? Couldn't they just have plugged a range of numbers into the Drake Equation?

Perhaps the Universe isn't infinite then. Maybe it just seems that way because of all the space fuzz.

Well, imagine that you stuck a REALLY BIG sheet of shrink wrap around everything that exists and used a REALLY BIG hairdryer to shrink it (but without moving any of the stuff isnide it). I see the universe as what's inside that shrink wrap. Yes, there's space outside it, but nothing has reached that space yet.

Crispy duck.

Isn't this research a bit pointless? Couldn't they just have plugged a range of numbers into the Drake Equation?

This way got them a bigger budget. ;)

Well, imagine that you stuck a REALLY BIG sheet of shrink wrap around everything that exists and used a REALLY BIG hairdryer to shrink it (but without moving any of the stuff isnide it). I see the universe as what's inside that shrink wrap. Yes, there's space outside it, but nothing has reached that space yet.

So we are vacuum-packed?

So we are vacuum-packed?

You could say that!

We do seem to have a few supervoids (http://en.wikipedia.org/wiki/Supervoid)....

You could say that!

We do seem to have a few supervoids (http://en.wikipedia.org/wiki/Supervoid)....

Room for expansion. I like that. :)

I believe that Douglas Adams provided the maths on this one. There are an infinite number of planets in the universe, but only a finite number of them are inhabited*; any finite number divided by infinity is as close to nothing as makes no difference, therefore the number of inhabited planets in the universe is close to zero.


*And my father, an expert in post-infinite mathematics and nuclear engineering before his retirement, in turn pointed out the fallacy in this argument. If there are an infinite number of planets, there must, by definition, also be an infinite number of inhabited planets. The number of inhabited planets is simply a smaller order of infinity than the total number of planets, even while both nonetheless remain infinite. Clear?

Interestingly, it isn't even a smaller order of infinity. Assume, briefly, that 1 in every 1 million planets in inhabited. As the number of planets is countably infinite, so too is the number of inhabited planets, meaning that we can pair each inhabited planet with an uninhabited planet, despite there being a million times more uninhabited planets.

Wha?

Go look up Hilbert's Hotel (a thought experiment). I shall give a relatively standard version below.

Imagine that there's a bus with an infinite number of seats, and carrying an infinite number of passengers. The bus stops to take on new passengers. The existing passengers simply move down one seat to allow the new passengers on to the bus. Therefore while both the number of seats and the number of passengers remain infinite, the number of seats always remains larger than the number of passengers.

Or at least that's how an expert used to explain it to me. Just because I called that expert 'dad' doesn't invalidate his explanation - though it does mean I can't cite it. I do remember a similar explanation appearing in New Scientist or Scientific American in the 80s, though.

Why, I understand it's being seriously tested by the London bus system as a solution to overcrowding on local public transport (that was a joke).

Not a bad summary, actually. The usual way of presenting it is approximately this:

Think about a hotel with an infinite number of rooms, all of them occupied. The rooms are numbered 1, 2, 3, ... and so on.* Now, another guest arrives, seeking a room for the night. In order to accommodate him, we say to all the guests "Please move to the next room". This leaves room number 1 free for our extra guest (showing that Inf + 1 = Inf).

However, the troubles of the hotel owner are not yet over. A tour bus turns up, also with an infinite number of tourists aboard, all of whom want rooms for the night. Where can we put them? Well, how about saying to all the current guests "Please move to the room with twice your current room number". So the guy in room 1 moves to room 2, room 2 moves to room 4, room 341 moves to room 682. This leaves all the odd numbered rooms free for the extra guests (showing that Inf + Inf = Inf).

This is extremely counter-intuitive, but that is because people's intuitions are not normally designed to cope with infinities.

*For the technically minded, this means there are a countably infinite number of rooms. This is distinct from (and smaller** than) uncountably infinite. An example of something which is uncountably infinite is the set of real numbers.

**Yes, infinity comes in different sizes. Infinitely*** many, in fact. Cantor proved this.

***I just know some smartass is going to ask "What size of infinity?" I think it's countable, but don't know enough about the far reaches of transfinite cardinals to prove this.

Isn't this research a bit pointless? Couldn't they just have plugged a range of numbers into the Drake Equation?

They could have, but that wouldn't nessissarily be as accurate. For example, I think one flaw of the Drake Equation is that it does not take into account the panspermia theory (life spread between worlds by asteroid impacts), which will probably lead to a lower total. The Drake Equation doesn't have to be the be-all and end-all of this field of research.

I find this research to be interesting, but of course rather speculative. Its main immediate practical value, as far as I can see, is in showing that their might be other intelligent life out their and using that to help justify more funds for SETI and NASA, among others.

I do wish people would take this subject more seriously, though. Its all but inevitable that their is alien life, with the three big questions being how common?, how close?, and how intelligent? While its possible that eventually one of them will come here and reveal itself beyond any doubt, or that we'll pick up a clearly alien signal, the only remotely sure bet is to go and look for ourselves. Which we should have been investing a lot more in before we found ourselves in a ressession with record debt.:headbang:

I find the numbers interesting, and if anything I suspect they may be on the low side, especially if we go for "total alien civilisations in our galaxy, including those which have ceased for some reason".

On the other hand, even with the highest number they suggest - 38000 - and rounding it up - 40000 - we still have life as a vanishingly rare phenomenon. Presuming there are roughly 200000000000 (2E11) stars in the Milky Way, we have the percentage of inhabited stars as 0.00002%.

This would gel rather well with the fact that we haven't encountered any sort of reasonable evidence for an alien civilisation yet (and that's presuming we would recognise alien lifeforms when we saw them).

The discovery of more than 330 planets outside our solar system in recent years has helped refine the number of life forms that are likely to exist.


Therefore there are at least 31 more planets that have intelligent life on them? What a pile of shite.

Therefore there are at least 31 more planets that have intelligent life on them? What a pile of shite.

Is not what it means - for a start, none of the planets we have discovered yet are in any way habitable by a form of life we would recognise as such.

What it does do is give us better data to estimate the distribution of extrasolar planets, and from that we can arrive at estimates for the prevalence of life.

Finally, I think you haven't quite realised the scale of the galaxy - there are between 200 and 400 billion stars in the Milky Way. Even if only 0.1% of these have planets and only 0.1% of those can support life, that still leaves a potential 200,000 to 400,000 planets which can support life out there.

Therefore there are at least 31 more planets that have intelligent life on them? What a pile of shite.

What the hell? How do you go from 330 extra-solar planets found so far and 361-38,000 civilizations in Galaxy to "at least 31 more planets that have intelligent life on them"?:confused:

What the hell? How do you go from 330 extra-solar planets found so far and 361-38,000 civilizations in Galaxy to "at least 31 more planets that have intelligent life on them"?:confused:

Because the number of stars searched and the number of them that have planets has led them to revise their statistics of how many stars in the galaxy have planets and therefore, the likelihood of those planets being within the range of habitability...and therefore, how many are likely to support intelligence.

It's nice to know that there might actually be some in this galaxy somewhere. ;)

Because the number of stars searched and the number of them that have planets has led them to revise their statistics of how many stars in the galaxy have planets and therefore, the likelihood of those planets being within the range of habitability...and therefore, how many are likely to support intelligence.

It's nice to know that there might actually be some in this galaxy somewhere. ;)

No, e was ranting about what Adunabar/NNLDI said, not about the work itself. Reread both eir post, the post e quoted, and eir other posts in the thread.

No, e was ranting about what Adunabar/NNLDI said, not about the work itself. Reread both eir post, the post e quoted, and eir other posts in the thread.

Oh. oops. Pardon, Rommy.

Just goes to show, you can use maths to "prove" almost anything!

Shit, now it kind of feels like we're in a really early game of Civilization 3 where I'm frantically sending out as many settlers as I can to claim good land before I encounter another civilization. And then once I do if it's some asshole civ like the Mongols or Zulu I have to produce a ton of spearmen just in case...

Shit, now it kind of feels like we're in a really early game of Civilization 3 where I'm frantically sending out as many settlers as I can to claim good land before I encounter another civilization. And then once I do if it's some asshole civ like the Mongols or Zulu I have to produce a ton of spearmen just in case...

That's basically what we should be doing. Spamming colony ships across our Solar System, harvesting resources, and using them to send out ships to every star we can reach.

I don't know about arming them, though. One, it costs money and fuel to put on more cargo. Two, the chances of the weapons being useful is rather low. Even if we find another civ close by, aren't the odds in favor of it being either so far below us technologically as to make weapons needless, or so far above us technologically as to make them useless?

Edit: However, their are concepts for star ships that involve basically detonating nuclear devices to propel the ship. Perhaps the drive system could double as a weapon?

reasonable speculation is generally preferably to unreasonable speculation.

i didn't see in that statement any suggestion that this was intended to be anything other then a rule of thumb gestimate, other then as also an exercise in developing a methodology for making them.

compared to 'were the only ones there could ever be', which is so blantently a matter of collective ego, almost any such methodology is more USEFUL.

the human uniqueness theory, is like the watch that is right twice a day because its broken. it might be right twice a day, but it sure is a heck of a lot less useful then one that is say five minuets fast or slow.

of course it might at the moment not make TOO MUCH difference, but just on general principals again, i think its a real good idea to get it through our thick heads, that however many others there may or may not be "out there", WE are going to be the 'new kids on the block'!

(and lets hope for our own sake as well as everyone out there else's, there's a very good, effective, and impartial cop on the corner, as i rather suspect there indeed is.)

(i DID kind of miss the bit about how they got from 330 confirmed probability of life supporting capable planets, to 361 almost certain civilizations though. it still doesn't sound like an unreasonable 'guess', but obviously there's more in the actual technical publication, then the dumming down of it for us unwashed pleebs)

(and lets hope for our own sake as well as everyone out there else's, there's a very good, effective, and impartial cop on the corner, as i rather suspect there indeed is.)

Its unlikely that such is the case. While its possible that a more advanced civilization might have reached the point where it will act altruistically and/or out of long-term self-interest to help other species and civilizations, it is unlikely that their is one organization out their that has the power to impose order on all the other civilizations single-handedly.

And if their were, I wouldn't want one faction with that much power unless their were severe checks and balances.

Has anyone pluged in the Drake Equation [N=R*Xf(p)Xn(e)Xf(l)Xf(i)Xf(c)XL] yet?

Its unlikely that such is the case. While its possible that a more advanced civilization might have reached the point where it will act altruistically and/or out of long-term self-interest to help other species and civilizations, it is unlikely that their is one organization out their that has the power to impose order on all the other civilizations single-handedly.

And if their were, I wouldn't want one faction with that much power unless their were severe checks and balances.

HONEST cops, don't work for "one faction" at the expense of others. maybe we haven't had governments here on earth for a long time, if ever, relatively uncorrupted, but an IMPARTIAL peace keeping force is in the interest of everyone who'se peace is kept. those galactic civilization that have survived are likely to have figured this out, as will our own have, once we've grown up enough to join them.

i speculate thus, and believe in doing so, a high probability of some such impartial sort of galactic united nations. i also have reason to believe i may have some modest experience of such things from my previous lives.

Let's not forget: "1001 Low-Fat Recipes Alien Recipes...If they Exist." Afterall, the next most pressing question after "Can we have sex with them?" is, "What do they taste Like?"

To Serve Man:D

HONEST cops, don't work for "one faction" at the expense of others. maybe we haven't had governments here on earth for a long time, if ever, relatively uncorrupted, but an IMPARTIAL peace keeping force is in the interest of everyone who'se peace is kept. those galactic civilization that have survived are likely to have figured this out, as will our own have, once we've grown up enough to join them.

Why the assumption that the typical interstellar civilization is so much more benevolent than ours?

I will however bet that they aren't the trigger happy type, since if that were the case they'd have probably screwed themselves in a nuclear war before they reached that stage (I think that was Carl Sagan's reasoning, anyways;)).

Regardless, though, I'd be wary of any organization wielding such power without sever checks and balances.

i speculate thus, and believe in doing so, a high probability of some such impartial sort of galactic united nations. i also have reason to believe i may have some modest experience of such things from my previous lives.

A United Nations that's anything like ours will only be as impartial as the nations that compose it, and will likely favor those with the greatest influence, or else be impotent when it comes to keeping the peace.

Unless it is significantly different from anything we have.

Why the assumption that the typical interstellar civilization is so much more benevolent than ours?

its called growing up, often learning the hard way through actual experience.

Regardless, though, I'd be wary of any organization wielding such power without sever checks and balances.

such sever checks and balances may be taken as a given.

A United Nations that's anything like ours will only be as impartial as the nations that compose it, and will likely favor those with the greatest influence, or else be impotent when it comes to keeping the peace.

Unless it is significantly different from anything we have.

significantly different indeed. no super power 'security council' imbalance for one thing. one "empire"/"federation", one vote. secretary general is like 'deep thought' from the guide, which operates on consensus forming algorithms. (it is also orders of magnitude more ancient then any current member, and some have been there many times as long as our own solar system)

other details might seem even more alien, but they work.

its called growing up, often learning the hard way through actual experience.

I'm sorry, but smug one-liners do not a rebuttal make.

Again, is their any logical reason to believe that a higher-tech species will nessissarily act in an impartial or altruistic manner? It maybe more likely, given that their are long-term advantages to doing so, and such a species will likely be both secure and good at long-term planning. But its not a given.

such sever checks and balances may be taken as a given.

Unfortunately, no.

significantly different indeed. no super power 'security council' imbalance for one thing. one "empire"/"federation", one vote. secretary general is 'deep thought' from the guide, which operates on consensus forming algorithms.

So a computer tells us how to live our lives? I'm not sure I like that.

Also, why should a civilization with 500 million citizens have the same vote as one with 500 billion? Personally I'd suggest the American solution: a Congress with one house based on population, and one based on an equal vote per member. This is exactly what the UN should have done all along if you ask me.

Again, is their any logical reason to believe that a higher-tech species will necessarily act in an impartial or altruistic manner? It maybe more likely, given that their are long-term advantages to doing so, and such a species will likely be both secure and good at long-term planning. But its not a given. true true. but it isn't a matter of altruism, rather of the congruence of hard learned self interest with the appearance of altruism. though an altruistic perspective is generally a less painful shortcut to getting there.

So a computer tells us how to live our lives? I'm not sure I like that.
it isn't telling anyone how to live their lives, just not to beat each other over the head. they trust it because it has proven, over a longer period of time then species of sentient people remain tangible, more trustworthy then any one or any sovereignty can entirely trust themselves. it isn't exactly just a computer such as we know such things. though it IS just as detached and impartial.

Also, why should a civilization with 500 million citizens have the same vote as one with 500 billion? Personally I'd suggest the American solution: a Congress with one house based on population, and one based on an equal vote per member. This is exactly what the UN should have done all along if you ask me. this would be a very reasonable suggestion if it were about anything that affected the lives of people individually, and perhaps such a formation exists. but it IS more concerned with relationships between each other of world and multi-world governments

Has anyone pluged in the Drake Equation [N=R*Xf(p)Xn(e)Xf(l)Xf(i)Xf(c)XL] yet?

I don't see why one estimate produced in the 60's has to be the be all and end all of the field, especially when we have so little information about most of the terms.

Of course, it's also worth noting that's likely what this team did, but refining the chance of planets forming based on our recent discoveries of extrasolar planets.

Edit: Having just reread the article, that's not what they did. Instead, they did computer simulations of galaxy formation, and used a range of parameters to look at the chances of life developing. I think I prefer their approach.

Edit: Having just reread the article, that's not what they did. Instead, they did computer simulations of galaxy formation, and used a range of parameters to look at the chances of life developing. I think I prefer their approach.

Seems careless that they didn't use the equation, or highly suspect.

Seems careless that they didn't use the equation, or highly suspect.

Why? We have no fucking idea about most of the parameters in the equation. What's f_i? How about f_l? If both are about 1, then the result is four times what we would get if both are closer to 0.5. What if f_l is more like 0.05, as has been suggested? What's the size of L - estimates vary by several orders of magnitude?

The equation is a suggestion for a solution which we can in no way use with any sort of accuracy yet. In order to arrive at an answer from it, we need to make very rough guesses about many of the values. As a result, trying to claim the answer is in any way representative of the likely truth seems far too bold.

Please explain why the Drake equation is the be all and end all of this field, and any work must be done simply by guessing at the parameters and taking the result as gospel truth.

Why? We have no fucking idea about most of the parameters in the equation. What's f_i? How about f_l? If both are about 1, then the result is four times what we would get if both are closer to 0.5. What if f_l is more like 0.05, as has been suggested? What's the size of L - estimates vary by several orders of magnitude?...

*sigh* Drake equation (http://en.wikipedia.org/wiki/Drake_equation)

*sigh* Drake equation (http://en.wikipedia.org/wiki/Drake_equation)

Read it, several times. To quote a few short sections:



Estimated by Drake as 0.5. It is now known from modern planet searches that at least 30% of sun-like stars have planets[4], and the true proportion may be much higher, since only planets considerably larger than Earth can be detected with current technology.[5] Infra-red surveys of dust discs around young stars imply that 20-60% of sun-like stars may form terrestrial planets.[6]

So that's up or down by a factor of three, depending on where we pick our estimate in the range of 20% to 60%.



Estimated by Drake as 1.

In 2002, Charles H. Lineweaver and Tamara M. Davis (at the University of New South Wales and the Australian Centre for Astrobiology) estimated f_l as > 0.13 on planets that have existed for at least one billion years using a statistical argument based on the length of time life took to evolve on Earth.[11]

Okay, so there's only about one order of magnitude between those estimates. Doesn't make much of a difference, really.

Etcetera. Estimates of L, for example, vary from only a few hundred years to effectively infinite, with the corresponding changes in the overall value.

When this much variance is easily reachable, and values differing by so much can be defended, why will whatever answer we pull out of the equation have any meaning? I suppose T.J. Watson's opinion sums mine up:


The Drake equation consists of a large number of probabilities multiplied together. Since each factor is guaranteed to be somewhere between 0 and 1, the result is also guaranteed to be a reasonable-looking number between 0 and 1. Unfortunately, all the probabilities are completely unknown, making the result worse than useless.

Please explain (I ask again) why the Drake equation gives a meaningful answer, and why the values inserted to get said answer are correct.

Well simply (and because I need some sleep) it was meant to give us the best probability of finding intelligent life, and why we haven't found any yet, but it is still based on estimations. So it still gives us "blurry" sums. We now know and have a count of a few extrasolar planets. Scientist, also, recently discovered our galaxy is bigger that previously thought; this again scews Drake's equation. However, the more data we get the better the estimations we get for the equation. What the computer did was simply come up with a number of probable life-giving planets, but not a good guess where to look range wise.

Sorry (once again) I'm tiered, I hope you find this at least somewhat satisfactory.

Well simply (and because I need some sleep) it was meant to give us the best probability of finding intelligent life, and why we haven't found any yet, but it is still based on estimations. So it still gives us "blurry" sums. We now know and have a count of a few extrasolar planets. Scientist, also, recently discovered our galaxy is bigger that previously thought; this again scews Drake's equation. However, the more data we get the better the estimations we get for the equation. What the computer did was simply come up with a number of probable life-giving planets, but not a good guess where to look range wise.

Sorry (once again) I'm tiered, I hope you find this at least somewhat satisfactory.

The point I'm trying to make is that plugging a refined guess for the number of extrasolar planets into Drake's equation won't improve the accuracy of our guesses through it by anything appreciable, as there are still many other factors which are completely invented.

Certainly, the equation includes basically every factor that seems reasonable to include. But we do not have the faintest idea about the values of these factors, and the size of the galaxy makes it almost certain we never will. To answer questions about lifetimes of civilisations, for example, we need to meet them, and I would lay good money on us never meeting an alien civilisation in the entire lifetime of our species*.

I much prefer this computer based work because it explores the problem space in a different way - it says "well, let's generate plausible galaxies, and see what sort of results that gives us." If nothing else, it makes assumptions about particular values in their models easier to justify, and easier to spot.

Tiredness is fine. It's morning in my time zone, so I'm waking up and starting to think now, but I recognise you'll be needing sleep if you're in the USA or similar. Rest well!

*Yes, I know some people claim aliens have visited Earth. I consider those claims to be vanishingly unlikely - the sheer scale of interstellar space makes travel across it practically impossible**. Furthermore, most claims of aliens are far too humanoid to be likely. Our biology and anatomy is a product of our environment, and it is incredibly unlikely that an extraterrestrial species would evolve in a similar enough environment to turn out so similar. Extraterrestrial life is likely so different that we would have trouble recognising it as life, and definitely run into problems recognising it as intelligent.

**There might be some sort of drive that can get us that far. Then there is speed - stars are years, decades, even millenia away while travelling at the speed of light. As far as we know, that's a hard limit, although it is possible we're wrong there. If so, I still think this is unlikely - the scale of space means contact with a specific planet is incredibly unlikely to happen.

You could say that!

We do seem to have a few supervoids (http://en.wikipedia.org/wiki/Supervoid)....

Does anybody else think the map provided was made using MSPaint and the spray paint tool?

*Yes, I know some people claim aliens have visited Earth. I consider those claims to be vanishingly unlikely - the sheer scale of interstellar space makes travel across it practically impossible**. Furthermore, most claims of aliens are far too humanoid to be likely. Our biology and anatomy is a product of our environment, and it is incredibly unlikely that an extraterrestrial species would evolve in a similar enough environment to turn out so similar. Extraterrestrial life is likely so different that we would have trouble recognising it as life, and definitely run into problems recognising it as intelligent.

Well, hypothetically, what's to stop the aliens presenting a human form to us to facilitate communication?

**There might be some sort of drive that can get us that far.

Their are multiple possible options in that area to explore. Light sails, nuclear fusion, and anti-matter top the list. Though anti-matter may well be precluded by cost.

Then there is speed - stars are years, decades, even millenia away while travelling at the speed of light. As far as we know, that's a hard limit, although it is possible we're wrong there. If so, I still think this is unlikely - the scale of space means contact with a specific planet is incredibly unlikely to happen.

Contact might occur after many millennia of gradually spreading outwards. If light speed is indeed a limit, then it may be unlikely a "first wave" ship from Earth will meet aliens face to face, unless they've already expanded to us.

Well the universe is endless....I'm sure there are more alien civilizations that we realize there are. And we probably wouldn't recognize them.

what the hell? How do you go from 330 extra-solar planets found so far and 361-38,000 civilizations in galaxy to "at least 31 more planets that have intelligent life on them"?:confused:

330 + 31 + 361.

330 + 31 + 361.

Error: none of the extrasolar planets we have yet discovered are habitable.

Well, hypothetically, what's to stop the aliens presenting a human form to us to facilitate communication?

Reversal problem - if an alien's form is dissimilar enough that we don't see them as living or intelligent, they will perceive us in the same way. Thus they won't present a human form to communicate with, as they won't see there as being anything to communicate with.


Their are multiple possible options in that area to explore. Light sails, nuclear fusion, and anti-matter top the list. Though anti-matter may well be precluded by cost.

Hehe. None of those will get you going very fast - light is weak in the gulfs between the stars, and any sort of fuel based system will require far too much. As a result, you will take decades or millennia to get anywhere, and that presents other challenges - life support, for a start.


Contact might occur after many millennia of gradually spreading outwards. If light speed is indeed a limit, then it may be unlikely a "first wave" ship from Earth will meet aliens face to face, unless they've already expanded to us.

So unlikely, indeed, as to be near impossible. For all we know, of course, there could be technical issues rendering interstellar travel impossible anyway - power sources and life support present themselves fairly rapidly. But even supposing it is possible, and that we can travel at an average speed of 1% of C, we would take 400 years to get to the next star. To get to the closest planet we know of, 1000 years (Epsilon Eridani). Can you build a system resistant to all possible damage for a thousand years?

I predict that there are extraterrestrials out there, likely many civilisations thereof. But we shall never find them. If we find them we shall not recognise them, and if we recognise them we will be unable to communicate. I also predict that expansion out of the starting system for a species is so technologically challenging as to be impossible, save in a Rendezvous with Rama style, and that this is vanishingly unlikely to ever reach us.

I'm not really happy with the way I expressed this, but I think it makes sense. Do ask for clarification if you find something unclear.

Reversal problem - if an alien's form is dissimilar enough that we don't see them as living or intelligent, they will perceive us in the same way. Thus they won't present a human form to communicate with, as they won't see there as being anything to communicate with.

Baseless speculation. While alien life would probably be very different, assuming that they won't be able to recognize us as life is baseless. We can guess that life, at least, will adhere to certain basic laws.

Hehe. None of those will get you going very fast - light is weak in the gulfs between the stars,

That's why you accelerate while you're still in-system. After that- well, its not like their's a lot of drag in space.

and any sort of fuel based system will require far too much. As a result, you will take decades or millennia to get anywhere, and that presents other challenges - life support, for a start.

Their is the possibility of using a magnetic "scoop" to refuel in-flight. Though their is the potential problem of drag.

So unlikely, indeed, as to be near impossible. For all we know, of course, there could be technical issues rendering interstellar travel impossible anyway - power sources and life support present themselves fairly rapidly. But even supposing it is possible, and that we can travel at an average speed of 1% of C, we would take 400 years to get to the next star. To get to the closest planet we know of, 1000 years (Epsilon Eridani). Can you build a system resistant to all possible damage for a thousand years?

10% C with Fusion, 60% C with anti-matter, theoretically 90%+ C with laser-driven sails. If I'm remembering Entering Space correctly (brilliant book, as always I highly recommend it).

I predict that there are extraterrestrials out there, likely many civilisations thereof. But we shall never find them. If we find them we shall not recognise them, and if we recognise them we will be unable to communicate. I also predict that expansion out of the starting system for a species is so technologically challenging as to be impossible, save in a Rendezvous with Rama style, and that this is vanishingly unlikely to ever reach us.

Its not nessissarily impossible. More likely just very difficult. Of course, one could argue that entire new Solar Systems (and all the resources, knowledge, and security for our species they may entail) are worth it.

I'm not really happy with the way I expressed this, but I think it makes sense. Do ask for clarification if you find something unclear.

I think that their's no way to know for sure yet, but that I will console myself with the knowledge that only one of us can ever be proven wrong.:)

Error: none of the extrasolar planets we have yet discovered are habitable.

Gliese 581 d might be; they don't have a way of estimating its temperature enough to be certain.

Interestingly, it isn't even a smaller order of infinity. Assume, briefly, that 1 in every 1 million planets in inhabited. As the number of planets is countably infinite, so too is the number of inhabited planets, meaning that we can pair each inhabited planet with an uninhabited planet, despite there being a million times more uninhabited planets.
Well, you can point each inhabitable planet to an uninhabited one, but you can't do the reverse...wouldn't that necessitate a smaller infinity? A subset of an infinitely large set can still be infinitely large, just not as infinitely larger as its parent set, right?
Furthermore, most claims of aliens are far too humanoid to be likely. Our biology and anatomy is a product of our environment, and it is incredibly unlikely that an extraterrestrial species would evolve in a similar enough environment to turn out so similar. Extraterrestrial life is likely so different that we would have trouble recognising it as life, and definitely run into problems recognising it as intelligent.

Never been quite sure of this. What are some of the parameters a species is likely to require to attain a level of civilization? Well, they'd need some communicative capacity and social tendencies, this is likely to require some kind of brain equivalent and maintaining proximity to as many sense organs as possible is a sizable increase in efficiency so this makes a head, with an encasing protecting the brain-like-organ, likely. It would need legs of some sort, and some type of hands; however, appendages doubling as both arms and legs seem a bit unlikely due to the potential damage basic transportation would risk to the hand-like-organs so this makes specialized limbs, i.e. arms, likely.

Also, there are limited methods for communication possible. This makes it likely that some kind of ear and sound producing organ would exist. The ear-type-thing would be most efficiently located closer to the brain-type-thing, at this point we have a thing that is recognizable a "head." A sight apparatus seems incredibly necessary, as well and assuming that one of the first steps any evolving life is going to take is to harness solar energy, the evolution of some kind eye-organ isn't too inconceivable. Where would the most efficient location be? Like, in the head-type thing.

So, yea, life is shaped by its environment, however there are certain aspects of the environment that are universal simply due to the physics of our universe. Gravity pulls down, makes it likely waste disposal will be towards the bottom of the body if the creature is vertically aligned, if horizontally, you'd expect it to be not-close to the sensory bundle. Vibrations in matter create sound, it would be beneficial from a competitive and survival standpoint to have an organ for this. Not having sight isn't impossible but due to solar energy being a great resource for primitive life, it seems unlikely some kind of light absorbing creatures and organs would evolve.

There is a valid argument to make that any life-form advanced enough to have civilization and space-travel would be distinctly recognizable as life, though it might not be pretty.

Baseless speculation. While alien life would probably be very different, assuming that they won't be able to recognize us as life is baseless. We can guess that life, at least, will adhere to certain basic laws.

Really? How about this one, which we thought was a basic law: All life on Earth is dependent on the Sun for the original source of its energy. Violated when we discovered life around hot water vents in the depths of the ocean.

Life is virulent and crazy, once it gets into a place, it seems to turn up anywhere. And when circumstances are sufficiently different, the life that develops is unlike anything we have ever seen before. If different environments here on Earth can produce such strange lifeforms, I reckon that other planets could do even more. Hell, they might be silicon and chlorine based or something.


That's why you accelerate while you're still in-system. After that- well, its not like their's a lot of drag in space.

Sure. But you won't have very long to accelerate - a solar system is fairly small in comparison to the interstellar gulfs. You want a system which can accelerate constantly for the first half of the journey, then decelerate constantly for the second half, and that would take an awful lot of power.


Their is the possibility of using a magnetic "scoop" to refuel in-flight. Though their is the potential problem of drag.

And the fact that interstellar space is incredibly empty. It would make a lot more sense to simply carry enough fuel to decelerate on the other end. Indeed, this would be required for fuel sources such as antimatter.


10% C with Fusion, 60% C with anti-matter, theoretically 90%+ C with laser-driven sails. If I'm remembering Entering Space correctly (brilliant book, as always I highly recommend it).

Laser driving sails will run into fairly serious problems over long distances. Consider, for example, what would happen if an unexpected asteroid or similar forced the ship to take evasive action. Or a supernova provided a solid wave of light from a different angle. Once the ship is off it's intended course, it will take years for it to tell the laser base about that, and then more years for the corrected laser beam to reach the ship again.

Antimatter is even more energy expensive to generate and/or contain, I believe, so it would require massive other power sources anyway. And then thermodynamics ensures it's more efficient to just use those directly.

Carrying sufficient fusion fuel for 1000 year flights would present an interesting technical challenge, I think.

And again, I point out the other issues, primarily that of supporting life.


Its not nessissarily impossible. More likely just very difficult. Of course, one could argue that entire new Solar Systems (and all the resources, knowledge, and security for our species they may entail) are worth it.

By the time we were to come out the other end, I'm not sure if it would really be 'our species' any more - thousands of years adapting to a spacecraft environment would make for some fairly reasonable changes. Perhaps most importantly, we would be in no position to treat them as colonisers or agents of Earth - when you're the only outpost of humanity at 10+ light years away, you're in a position to negotiate on basically equal terms.

And I don't think that our government(s) could stand having to do that.


I think that their's no way to know for sure yet, but that I will console myself with the knowledge that only one of us can ever be proven wrong.:)

Of course. I'm just going to add one more statement - if a civilisation does manage to spread between star systems, they will separate into at least two. That is, it is not possible to administrate an empire over interstellar scales.

If I am proven wrong on any of these, I will be extremely impressed, incredibly surprised, and very happy. I expect, however, to remain my cynical unsurprised self.

Gliese 581 d might be; they don't have a way of estimating its temperature enough to be certain.

There's also the second objection. Given how much I've been harping on about alien lifeforms being fundamentally different to our own, there is no guarantee they would find the same temperatures habitable. However, if they are based on water, they would (typing while I'm thinking is always a bad idea).

Well, you can point each inhabitable planet to an uninhabited one, but you can't do the reverse...wouldn't that necessitate a smaller infinity? A subset of an infinitely large set can still be infinitely large, just not as infinitely larger as its parent set, right?

Sure you can. A subset of an infinitely large set can be exactly the same size as its parent set - the natural numbers are a subset of the integers, and there are exactly as many natural numbers as there are integers.

Or we could note that square numbers are a subset of natural numbers, but that there is exactly one natural number for every square number.

1 2 3 4 5 6 ... (naturals)
| | | | | |
1 4 9 16 25 36 ... (squares)

It is evident that continuing this will lead to one natural number for every square number (the square root), and one square number for every natural number (the square), despite an infinitely large set of numbers which are naturals but not squares.

I'm not copying in the full rest of your post, but just to mention one notable difference - there are animals on Earth which don't use ears to hear with. I'll give you a full response in a bit.

My cat also seems to have something to say: mm mmkkkkkkk

Sure you can. A subset of an infinitely large set can be exactly the same size as its parent set - the natural numbers are a subset of the integers, and there are exactly as many natural numbers as there are integers.

Or we could note that square numbers are a subset of natural numbers, but that there is exactly one natural number for every square number.

1 2 3 4 5 6 ... (naturals)
| | | | | |
1 4 9 16 25 36 ... (squares)

It is evident that continuing this will lead to one natural number for every square number (the square root), and one square number for every natural number (the square), despite an infinitely large set of numbers which are naturals but not squares.
Hrm...but in the example of planets the two infinite sets are not of equal size since the habitable planet set is defined as, say, one out of every 200 planets or something. I mean, it seems to me that what you're describing is a...one-to-one onto correlation, when the whole habitable planets in an infinite universe discussion is simply an into correlation...I think, I'm probably not remember my terminology correctly. I.e. say in an infinite universe each solar system, if it has a habitable planet, may only have one; for the sake of the hypothetical we also assume that each solar system only has nine planets; in this scenario each habitable planet could point to 9 uninhabitable planets but those 9 uninhabitable planets only point to a single habitable planet, so the habitable planet set is necessarily smaller, though still infinite, than the planet set.

I like set theory, it's fun. Always wish I had time to take a few classes in it...though without the proof writing component. I had to drop a class because I simply cannot write proofs for even the most easily grasped of concepts.
I'm not copying in the full rest of your post, but just to mention one notable difference - there are animals on Earth which don't use ears to hear with. I'll give you a full response in a bit.

My cat also seems to have something to say: mm mmkkkkkkk

Yes, I realize that there is variance in how animals sense sound...a sizable degree in fact, but my point is that they sense sound and a creature advanced enough to have a space-faring civilization is likely to have evolved towards a certain level of efficiency in their anatomy, while allowing for a "thinking" organ, as well, which could arguably entail all sorts of predictable features.

Hrm...but in the example of planets the two infinite sets are not of equal size since the habitable planet set is defined as, say, one out of every 200 planets or something. I mean, it seems to me that what you're describing is a...one-to-one onto correlation, when the whole habitable planets in an infinite universe discussion is simply an into correlation...I think, I'm probably not remember my terminology correctly. I.e. say in an infinite universe each solar system, if it has a habitable planet, may only have one; for the sake of the hypothetical we also assume that each solar system only has nine planets; in this scenario each habitable planet could point to 9 uninhabitable planets but those 9 uninhabitable planets only point to a single habitable planet, so the habitable planet set is necessarily smaller, though still infinite, than the planet set.

Sounds good. Each habitable planet can point to one uninhabitable planet, and vice versa. For an analagous case, think about the set of multiples of 10 and the set of the naturals. We can construct a one to one mapping between them:

1 - 10
2 - 20
3 - 30
4 - 40
5 - 50

etcetera. Evidently, every natural will have one multiple of 10 associated with it, and every multiple of 10 will have one natural associated with it. The important thing is this doesn't work if you terminate it at any finite point, no matter how large. It only works if you consider the entire infinite sets.

Planets work in the same way. Let's say we number all the planets in the order we discover them, and we number the habitable planets in the order we discover them. Then we have two lists, each infinitely long, and we can simply pair off sequential elements: This is the first planet, this is the first habitable planet, they are a pair. This is the second planet, this is the second habitable planet, they are a pair. Etcetera.

Certainly, if one out of every 200 planets is habitable then the sets will not be the same size if there are a finite number of planets, no matter how large this finite number may be. But when there are an infinite number of numbers (planets), then there are an infinite number of multiples of 200 (habitable planet), and we can pair them off exactly.


I like set theory, it's fun. Always wish I had time to take a few classes in it...though without the proof writing component. I had to drop a class because I simply cannot write proofs for even the most easily grasped of concepts.

Oh yes, it's great fun. But infinite sets are extremely counterintuitive.

And proofs are unfortunately absolutely required in formal mathematics, which set theory is the foundation of.


Yes, I realize that there is variance in how animals sense sound...a sizable degree in fact, but my point is that they sense sound and a creature advanced enough to have a space-faring civilization is likely to have evolved towards a certain level of efficiency in their anatomy, while allowing for a "thinking" organ, as well, which could arguably entail all sorts of predictable features.

Arguably, maybe. But I think that nature is good enough at coming up with all sorts of unusual methods for doing things that we wouldn't necessarily recognise features for what they are.

Sounds good. Each habitable planet can point to one uninhabitable planet, and vice versa. For an analagous case, think about the set of multiples of 10 and the set of the naturals. We can construct a one to one mapping between them:

1 - 10
2 - 20
3 - 30
4 - 40
5 - 50

etcetera. Evidently, every natural will have one multiple of 10 associated with it, and every multiple of 10 will have one natural associated with it. The important thing is this doesn't work if you terminate it at any finite point, no matter how large. It only works if you consider the entire infinite sets.

Planets work in the same way. Let's say we number all the planets in the order we discover them, and we number the habitable planets in the order we discover them. Then we have two lists, each infinitely long, and we can simply pair off sequential elements: This is the first planet, this is the first habitable planet, they are a pair. This is the second planet, this is the second habitable planet, they are a pair. Etcetera.

Certainly, if one out of every 200 planets is habitable then the sets will not be the same size if there are a finite number of planets, no matter how large this finite number may be. But when there are an infinite number of numbers (planets), then there are an infinite number of multiples of 200 (habitable planet), and we can pair them off exactly.



Oh yes, it's great fun. But infinite sets are extremely counterintuitive.

And proofs are unfortunately absolutely required in formal mathematics, which set theory is the foundation of.

What I'm getting caught up on is that for every single habitable planet, there is still 8 other uninhabitable planets. So no matter what, even to infinity, there is always 8 uninhabitable for every inhabitable. Unless the 1 inhabitable points to the entire group of the other uninhabitable, but this seems like something very different than, say, every natural number having a multiple of 10 associated with it because, unlike 1-10, 2-20, 3-30, etc., you have Earth-{Mercury, Venus, Mars, Jupiter, Saturn, Neptune, Uranus, Pluto...why do I feel like I'm forgetting one...and long live Pluto the Planet!}, A-{B, C, D, E, F, G, H, I, J}, etc. Though, I guess your example could be 1-{10, 12-2, 9+1, etc.} but, as you said, that's crazy counter-intuitive if even correct.

And, yea, proofs are why I could never even attempt formal mathematics professionally. I want to say that it's just that and not being unable to conceptually understand what's going, but, if I'm to be honest, the ability to write the proof is as much a component of the concept itself as anything else. I just like set theory because, even if you don't understand the mechanics of it very well, it strikes me as one of those things of which it is importantly to at least be somewhat familiar with, even if just in a vaguely abstract sense. It's good exercise for the mind, to say the least.

What I'm getting caught up on is that for every single habitable planet, there is still 8 other uninhabitable planets. So no matter what, even to infinity, there is always 8 uninhabitable for every inhabitable. Unless the 1 inhabitable points to the entire group of the other uninhabitable, but this seems like something very different than, say, every natural number having a multiple of 10 associated with it because, unlike 1-10, 2-20, 3-30, etc., you have Earth-{Mercury, Venus, Mars, Jupiter, Saturn, Neptune, Uranus, Pluto...why do I feel like I'm forgetting one...and long live Pluto the Planet!}, A-{B, C, D, E, F, G, H, I, J}, etc. Though, I guess your example could be 1-{10, 12-2, 9+1, etc.} but, as you said, that's crazy counter-intuitive if even correct.

Okay, why don't we say (just to simplify the conversation) that there are an infinite number of solar systems. Each has 10 planets, of which the 10th is always habitable. Sound good?

Now let's work out a way of looking at this mathematically. We can number all the solar systems, starting with 1. We will also number all the planets in each solar system, from 1 to 10. Then we can generate a unique number for each planet, by summing 10 times the number of its solar system with the number of its position. That's a really bad sentence, so let's look at an example. What is the number of the third planet in the fifth solar system on our list?

10 * [# of sol system] + [# of planet in sol] = [uniq # of planet]

As it is the 3rd planet in the 5th solar system, we can insert these values,

10 * 5 + 3 = 50 + 3 = 53

So the third planet in the fifth solar system has number 53.

Now I hope how we pair them up should be clearer. Every planet in this system has a unique number, starting from 11 (first planet in the first system). As a result of the way I wrote the rules, every habitable planet has the interesting property of having a number divisible by 10. We can now rank both lists --- a list of all planets, and a list of habitable planets --- by (numerical) size, and then simply pair off the first elements, then the second elements, then the third elements, and so on.

One important thing to note here is that most pairings will be of planets from different systems. So to go back to the way you mentioned it, the Earth might be paired with Mercury, but Venus could then be paired with Fomalhaut B, Mars with Epsilon Eridani A, etcetera. The important thing is that we have a way of listing both sets, and that we can pair them off one to one.

Yes, this is incredibly counter intuitive. After all, in the fictional universe we were working in there, every solar system had nine times more uninhabitable planets than habitable ones. But despite that, we can still list them off, and as both lists are infinitely long, they are the same size. This is extremely crazy, but I guarantee you it is absolutely true (mathematically speaking).

And, yea, proofs are why I could never even attempt formal mathematics professionally. I want to say that it's just that and not being unable to conceptually understand what's going, but, if I'm to be honest, the ability to write the proof is as much a component of the concept itself as anything else. I just like set theory because, even if you don't understand the mechanics of it very well, it strikes me as one of those things of which it is importantly to at least be somewhat familiar with, even if just in a vaguely abstract sense. It's good exercise for the mind, to say the least.

Indeed. While I am not a professional mathematician, I am on my way towards that goal, so I guess I've just got used to the ideas we've been talking about here. Still, it's always fun to find someone to talk with :)