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  #21  
Old 13-12-2011, 09:40 AM
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Joke mode on:

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if it takes an infinite number of monkeys an infinite amount of time to write a shakespearean play, how long would it take half that number?

Really, i think the use of monkeys by mathematicians is extremely distressing...
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  #22  
Old 13-12-2011, 09:42 AM
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It will still take an infinite time.

Here is something for you to contemplate, if you were able to half your set which contains an infinite number of monkeys into a subset, both the original set and subset, contain the same infinite number of monkeys.

Mathematicians refer to both sets as countable infinite sets.

There are uncountable infinite sets which are "larger" than countable infinite sets.

Regards

Steven
i love "infinity".
it reminds me of an episode of "The Tick".
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  #23  
Old 13-12-2011, 10:00 AM
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Yes I understood it was a joke. I can read icons.

Ironically it was this sort of question that completely changed our view of infinity.

The mathematician who came up with the theory was put in a mental asylum, the establishment at the time saw it more than a joke.

Regards

Steven
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  #24  
Old 13-12-2011, 10:03 AM
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Yes I understood it was a joke. I can read icons.
it was the serious answer that tricked me.

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Ironically it was this sort of question that completely changed our view of infinity.

The mathematician who came up with the theory was put in a mental asylum, the establishment at the time saw it more than a joke.
that would make a good chapter in a history book.
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  #25  
Old 13-12-2011, 10:12 AM
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Well .. I was going to let this thread fade away, but a couple of very salient points have arisen, as far as I'm concerned.

It seems that the theoretical proposition of an Infinite Universe, which necessarily leads to the conclusion: "anything which is possible, will happen", (eg: ETs, life, etc), is more or less rendered moot by mainstream Standard Model Cosmology (Big Bang, etc).

This raises a problem however for the Standard Cosmological Model (SCM), as well as for those who use infinity arguments in support of the existence of discoverable ETs. The 'preferred' topological shape of the universe is an infinite flat one … and yet the SCM has roots in the Big Bang phenomenon, which gives us a finite origin in the past.

The best resolution of these problems I can see, is either to go with the concept of a finite universe (which calls for defining what exists beyond the boundary), or move forward acknowledging the flawed Infinite Theory, and seek hard evidence. The latter approach will always be limited by the finite boundary of our observable universe, anyway.

Can this finite volume be searched thoroughly enough to detect ETs (or life)? Theoretically, 'No !". The search must be motivated by faith, alone. To produce meaningful results, the search needs to operate within the limits defined by an attainable result. To build knowledge which can ultimately be used to expand the search volume, incremental steps, beginning locally, is an assured winning strategy.

Other than randomly detecting a fluke intelligent ET radio signal (or a proven ET visitation), I cannot see how a credible exo-life discovery could presently be declared, unless it can be proven to be directly associated with a pre-defined Habitable Zone. The Habitable zone definition itself, will also carry little/no weight as far as the existence of exo-life is concerned, until exo-life is directly discovered in one such zone. The only way to achieve this, is by manned exploration locally.

Cheers
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  #26  
Old 13-12-2011, 10:14 AM
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that would make a good chapter in a history book.
http://en.wikipedia.org/wiki/Georg_Cantor

Regards

Steven
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  #27  
Old 13-12-2011, 12:50 PM
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Well .. I was going to let this thread fade away, but a couple of very salient points have arisen, as far as I'm concerned.
Nah, where's ya spirit of adventure!!!!

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It seems that the theoretical proposition of an Infinite Universe, which necessarily leads to the conclusion: "anything which is possible, will happen", (eg: ETs, life, etc), is more or less rendered moot by mainstream Standard Model Cosmology (Big Bang, etc).

This raises a problem however for the Standard Cosmological Model (SCM), as well as for those who use infinity arguments in support of the existence of discoverable ETs. The 'preferred' topological shape of the universe is an infinite flat one … and yet the SCM has roots in the Big Bang phenomenon, which gives us a finite origin in the past.
No it doesn't. Just because something has a beginning it has no bearing on what that thing becomes, physically or anything else, except that it had a beginning. You were born a tad over 50 years ago....does that make you any less a person than what you are???. No. The age you are has no real bearing on who you are, or how tall you are. Nothing is rendered moot by the SCM.

The preferred topology is an infinite flat one, but the beginning of it all has no bearing on it in so far as it's a starting point (leaving aside all the rest of the physics for the time being). If the Universe is finite, then it is, but that still has no bearing on the possibility of the existence of ET. In actual fact, neither does the possibility that it's infinite. Most of these arguments are based on semantics and probability....they're thought exercises, what if's.


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The best resolution of these problems I can see, is either to go with the concept of a finite universe (which calls for defining what exists beyond the boundary), or move forward acknowledging the flawed Infinite Theory, and seek hard evidence. The latter approach will always be limited by the finite boundary of our observable universe, anyway.
I don't think we're in any position to say anything definitive about this except to make very broad assumptions and hope we get it right. We simply aren't advanced enough (i.e. we don't have the technology), nor are we capable enough of exploring the Universe at a level which would allow us to make a reasonably good attempt at answering the question.

It's really like having three blind men try to identify an elephant based on only what they can sense through touch. One grabs the tail and thinks it's a rope, another grabs the leg and thinks it's a tree, the last one grabs the trunk and thinks it's the arm of an octopus....none are right despite them being thoroughly convinced of their pronouncements. Until the elephant trumpets, none of them know what they've got and if one of them is deaf as well, then he'll never know anyway.


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Can this finite volume be searched thoroughly enough to detect ETs (or life)? Theoretically, 'No !". The search must be motivated by faith, alone. To produce meaningful results, the search needs to operate within the limits defined by an attainable result. To build knowledge which can ultimately be used to expand the search volume, incremental steps, beginning locally, is an assured winning strategy.
You've just contradicted yourself grandly there, Craig. You talk about a thorough search not being able to detect ET's in a finite volume, and say it can't be done, theoretically. Then you give the answer to how you'd do it, which is exactly the way it would be done!!!!. You better watch what you write

Faith has nothing to do with it.

The answer is yes (given enough time and effort, so long as the Universe is finite).


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Originally Posted by CraigS View Post
Other than randomly detecting a fluke intelligent ET radio signal (or a proven ET visitation), I cannot see how a credible exo-life discovery could presently be declared, unless it can be proven to be directly associated with a pre-defined Habitable Zone. The Habitable zone definition itself, will also carry little/no weight as far as the existence of exo-life is concerned, until exo-life is directly discovered in one such zone. The only way to achieve this, is by manned exploration locally.

Cheers
What if they detect a navigation beacon or a distress call, or just random traffic??? Doesn't have to be in a HZ at all...could be in deep space. Just because an intelligent signal (of any sort) is being beamed into space doesn't mean it can't be one because you haven't found it in a HZ. So long as the signal show clear signs of intelligence (extremely narrow band, FM/AM signal characteristics etc etc), it doesn't matter where it's coming from. Be it a planet orbiting a star or from the bridge of a starship out in the middle of nowhere. Many signals, in this case, will be one offs (e.g. the "WOW" signal) and wholly unrepeatable and probably not worth following up (unless you see the same signal again, for some reason). But because they happen only once and aren't repeatable doesn't mean they're not from something of intelligent origin. All you can say with signals like this is that they're unusual, possibly of intelligent origin but ultimately we can't tell. Unless, of course, ET turns up and complains about us eavesdropping in on their private conversations!!! We'd probably be sued and taken to Galactic Federal Court for "wire tapping"!!!
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  #28  
Old 13-12-2011, 04:32 PM
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Originally Posted by renormalised View Post
No it doesn't. Just because something has a beginning it has no bearing on what that thing becomes, physically or anything else, except that it had a beginning.
...
The preferred topology is an infinite flat one, but the beginning of it all has no bearing on it in so far as it's a starting point (leaving aside all the rest of the physics for the time being). If the Universe is finite, then it is, but that still has no bearing on the possibility of the existence of ET. In actual fact, neither does the possibility that it's infinite.
The 'etc' part of what I wrote includes all that goes into the concept of causality .. which is part of the SCM.

I think we also need to make the distinction between the causality boundary and the overall universe, here.
It seems to me, for all intents and purposes, the volume inside the causality boundary is all we'll ever be able to search. Anything beyond it, falls into the realm of (perhaps) the mathematical concept of the Infinite Universe. If the argument for ET's existence relies on arguments from space beyond the causality boundary, then that argument is logically 'moot' and is excluded from verifiability.

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Originally Posted by renormalised
Most of these arguments are based on semantics and probability....they're thought exercises, what if's.
Do you mean … "subject to debate, dispute or uncertainty and typically not admitting of a final decision"?


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Originally Posted by renormalised
You've just contradicted yourself grandly there, Craig. You talk about a thorough search not being able to detect ET's in a finite volume, and say it can't be done, theoretically. Then you give the answer to how you'd do it, which is exactly the way it would be done!!!!. You better watch what you write

Faith has nothing to do with it.
A finite volume still has infinite spaces .. the entirety of a finite volume cannot theoretically be fully searched (and this is regardless of the lack of infinite resources required to do so).
Ok … so who cares ? … the search can still proceed and doesn't doesn't necessarily have to follow the theory. It can be lead by faith, with the sole purpose of then having an attainable goal. But to search without an attainable goal .. is a fundamentally flawed strategy.

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Originally Posted by renormalised
The answer is yes (given enough time and effort, so long as the Universe is finite).
Which we don't have.

Quote:
Originally Posted by renormalised
What if they detect a navigation beacon or a distress call, or just random traffic??? Doesn't have to be in a HZ at all...could be in deep space. Just because an intelligent signal (of any sort) is being beamed into space doesn't mean it can't be one because you haven't found it in a HZ. So long as the signal show clear signs of intelligence (extremely narrow band, FM/AM signal characteristics etc etc), it doesn't matter where it's coming from. Be it a planet orbiting a star or from the bridge of a starship out in the middle of nowhere. Many signals, in this case, will be one offs (e.g. the "WOW" signal) and wholly unrepeatable and probably not worth following up (unless you see the same signal again, for some reason). But because they happen only once and aren't repeatable doesn't mean they're not from something of intelligent origin. All you can say with signals like this is that they're unusual, possibly of intelligent origin but ultimately we can't tell.
Exactly .. ultimately, we can't tell.

Also, your scenario of the 'beacon, distress call, etc' emanating from within space, is covered in the first part of what I said: "Other than randomly detecting a fluke intelligent ET radio signal"

I was referring to the declaration of discovered exo-life on distant, remote exo-planets outside our solar system. If the exo-lifeform detection 'evidence' is not accompanied by hard evidence of a life sustaining HZ, then the discovery carries little scientific meaning, (other than to the faithful). Similarly, for the same reason, the definition of 'HZ' without any accompanying exo-life discovery, carries scientific little meaning as far as exo-life is concerned.

Cheers
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  #29  
Old 13-12-2011, 05:30 PM
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The 'etc' part of what I wrote includes all that goes into the concept of causality .. which is part of the SCM.

I think we also need to make the distinction between the causality boundary and the overall universe, here.
It seems to me, for all intents and purposes, the volume inside the causality boundary is all we'll ever be able to search. Anything beyond it, falls into the realm of (perhaps) the mathematical concept of the Infinite Universe. If the argument for ET's existence relies on arguments from space beyond the causality boundary, then that argument is logically 'moot' and is excluded from verifiability.
I think we also need to realise that most of these "boundaries" are rather arbitrary constructs that depend on ones position relative to where one defines the boundaries (usually via observation and the accompanying theory). Move yourself out 10 billion light years from our position and the boundaries move. It's not like there's a hard and fast barrier beyond which nothing is or can be known. It's a rather artificial construct....move out far enough and our own galaxy would go beyond your horizon. The "barrier" is more of a barrier in time than in space. Space has expanded way beyond that distance, however you cannot see beyond a point in time where the expansion has carried those signals beyond the "causality barrier". In other words, the signals from those far flung galaxies are coming from a long time in the past (due to their distance from us) but the rate of expansion between them and us is such that the light will never reach us from our perspective.

You said it.

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A finite volume still has infinite spaces .. the entirety of a finite volume cannot theoretically be fully searched (and this is regardless of the lack of infinite resources required to do so).
True, but that all depends on how you divvy up that space. It only has an infinite number of spaces if you so desire to partition it up into such or take it to a purely mathematical approach. How far do you want to go...to the quantum level?? With anything like this, you have to make compromises on what you're prepared to do with the resources you have. So, to be practical, a finite volume will be divided up into a number of manageable, finite spaces and searched. If we happen to miss the civilisation hiding behind the cosmic string out by Galaxy X, too bad. Pick them up on the next pass Maybe.

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Ok … so who cares ? … the search can still proceed and doesn't doesn't necessarily have to follow the theory. It can be lead by faith, with the sole purpose of then having an attainable goal. But to search without an attainable goal .. is a fundamentally flawed strategy.
You don't need faith to have an attainable goal. You set your goal and proceed with your search according to good scientific principles and well planned strategy for the search. Belief that something is "out there" doesn't even figure into the equation, except as the possible personal feelings of those conducting the search. But that shouldn't stop them from being completely objective about the way they conduct the search. You can follow theory whether you want to or not....that I agree with. In some case, the prevailing theoretical paradigm can be a major hindrance to those goals you set out to attain, especially if what you're doing is outside those parameters.

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Which we don't have.
How do you know we don't have the time?? No one knows how much time we have. We may become extinct tomorrow, then again we may still be around when you, me and this galaxy have been done, dusted and long forgotten

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Exactly .. ultimately, we can't tell.

Also, your scenario of the 'beacon, distress call, etc' emanating from within space, is covered in the first part of what I said: "Other than randomly detecting a fluke intelligent ET radio signal"
Then we both agree there. But a HZ is hardly mandatory for declaring their existence.


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I was referring to the declaration of discovered exo-life on distant, remote exo-planets outside our solar system. If the exo-lifeform detection 'evidence' is not accompanied by hard evidence of a life sustaining HZ, then the discovery carries little scientific meaning, (other than to the faithful). Similarly, for the same reason, the definition of 'HZ' without any accompanying exo-life discovery, carries scientific little meaning as far as exo-life is concerned.

Cheers
I can agree with you there, for the most part, in principle, but not in the substance of what you wrote. We have no idea what physicality an intelligent form of exo-life might take or where it might reside, except for that which we may know of from extrapolations of an Earth based perspective. It mightn't even need a planet or anything like a HZ to live in. For those that resemble ourselves, then yes we will be looking for similar circumstances (as per your approach), but what would you make of an intelligent cloud that floats around in space outside of solar systems etc. Or even beings of pure energy/thought. Just because we haven't encountered them or can't understand their mode of existence doesn't mean they don't or cannot exist. Only that we don't know...in our ignorance. All possibilities, no matter how outlandish or unseemly they are, need to be taken into account until they can be irrefutably and irrevocably disproved. Or are shown to be nonsensical no matter what theory or level of knowledge is applied.
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Old 13-12-2011, 06:38 PM
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To put into perspective how improbable a finite number of monkeys can reproduce a single work of Shakespeare in a finite period of time consider this.

If we use 10^80 monkeys with typewriters ("roughly" the number of atoms in the Universe) and a typing speed of 1000 keystrokes per second for a period of 10^150 years (the time to the predicted heat death of the Universe), the probability of a single work of say Hamlet being reproduced is a 1 in a 10^183,000 chance.

Not very good odds in a BB universe.

Obviously one cannot draw direct comparisons between monkeys randomly typing on typewriters and the evolutionary chances of ET, except to say the chances for ET's existence seem intuitively far better in an infinite steady state Universe than a finite BB universe.

Regards

Steven
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  #31  
Old 13-12-2011, 07:41 PM
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I think we also need to realise that most of these "boundaries" are rather arbitrary constructs that depend on ones position relative to where one defines the boundaries (usually via observation and the accompanying theory). Move yourself out 10 billion light years from our position and the boundaries move. It's not like there's a hard and fast barrier beyond which nothing is or can be known. It's a rather artificial construct....move out far enough and our own galaxy would go beyond your horizon. The "barrier" is more of a barrier in time than in space. Space has expanded way beyond that distance, however you cannot see beyond a point in time where the expansion has carried those signals beyond the "causality barrier". In other words, the signals from those far flung galaxies are coming from a long time in the past (due to their distance from us) but the rate of expansion between them and us is such that the light will never reach us from our perspective.
Relatively arbitrary constructs ? .. Maybe.
Moving 'out 10 billion light years', is not feasible.
Quote:
Originally Posted by renormalised
You don't need faith to have an attainable goal.
Almost goes without saying ...
Quote:
Originally Posted by renormalised
Then we both agree there. But a HZ is hardly mandatory for declaring their existence.
The HZ is necessary in order to declare an exo-life discovery (beyond an ET 'level' of exo-life). I'm using the term 'exo-life' here in a broader sense to cover other life beyond ETs (eg: bacteria or whatever).
Quote:
Originally Posted by renormalised
Just because we haven't encountered them or can't understand their mode of existence doesn't mean they don't or cannot exist. Only that we don't know...in our ignorance. All possibilities, no matter how outlandish or unseemly they are, need to be taken into account until they can be irrefutably and irrevocably disproved. Or are shown to be nonsensical no matter what theory or level of knowledge is applied.
Agreed.
From my perspective, I'm not attempting to argue whether or not they exist.
My overall point is that our search space is limited by many aspects, which define our universe as effectively finite .. like it or not. Some of these boundaries are theoretically insurmountable without invoking a theoretical Infinite Universe. Even with an Infinite Universe, the flow-on effects, result in inconsistencies once verifiable evidence and accepted cosmology is brought to bear.
Scientific speculation is still subject to falsifiability testing.
Cosmology, verifiable evidence and pure theory, are legitimate tools for falsifying speculation.

Cheers
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  #32  
Old 13-12-2011, 08:38 PM
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Relatively arbitrary constructs ? .. Maybe.
Moving 'out 10 billion light years', is not feasible.
They are. Where is the "brick wall" or physical barrier at the edge??. Certainly don't see one, nor is one detected.

Going out 10 billion light years is not something we can now do, but take it as being able to be done in the context of the discussion.

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The HZ is necessary in order to declare an exo-life discovery (beyond an ET 'level' of exo-life). I'm using the term 'exo-life' here in a broader sense to cover other life beyond ETs (eg: bacteria or whatever).
Agreed. However, I was looking at it from an ET perspective. As far as bacteria and such goes, the only real way to find them is to go to wherever they might be and look for them. Trying to detect them at a distance is a little more than dicey. Detecting photosynthesis on planets is somewhat easier, but still not 100%.

Actually, the crazy thing is it's far easier to find the LGM's (Little Grey Men, btw) than it is to find the more abundant bugs and moss


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From my perspective, I'm not attempting to argue whether or not they exist.
My overall point is that our search space is limited by many aspects, which define our universe as effectively finite .. like it or not. Some of these boundaries are theoretically insurmountable without invoking a theoretical Infinite Universe. Even with an Infinite Universe, the flow-on effects, result in inconsistencies once verifiable evidence and accepted cosmology is brought to bear.
True, agree.

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Scientific speculation is still subject to falsifiability testing.
Cosmology, verifiable evidence and pure theory, are legitimate tools for falsifying speculation.

Cheers
Totally agree with that.
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  #33  
Old 14-12-2011, 08:37 AM
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To put into perspective how improbable a finite number of monkeys can reproduce a single work of Shakespeare in a finite period of time consider this.

If we use 10^80 monkeys with typewriters ("roughly" the number of atoms in the Universe) and a typing speed of 1000 keystrokes per second for a period of 10^150 years (the time to the predicted heat death of the Universe), the probability of a single work of say Hamlet being reproduced is a 1 in a 10^183,000 chance.

Not very good odds in a BB universe.

Obviously one cannot draw direct comparisons between monkeys randomly typing on typewriters and the evolutionary chances of ET, except to say the chances for ET's existence seem intuitively far better in an infinite steady state Universe than a finite BB universe.

Regards

Steven
Chuckle, chuckle .. thanks for that !
Somewhere in the annuls of IIS, Robh got all fired up and performed a similar calculation .. (hope he doesn't mind my quoting a section of that calculation .. it was a work of true commitment, also.
I, fortunately, kept a copy for posterity) ...
Quote:
Originally Posted by Robh
So, lets get one monkey typing 1 character per second for a year.

That increase our chances to 1 in 2.2 x 10^160009 of ending up with Shakespeare's classic.

If you put a trillion (10^12) monkeys on a planet around every star in the Universe (just play the game) and let them type for a billion years, that increases your chances to one in 2.2 x 10^159966.

Even a computer operating at 10^15 calculations per second won't put much of a dent in this figure.

Result ... pretty much impossible. Gone to rest my brain.
… Same order of magnitude .. so its verified !

Cheers

Last edited by CraigS; 14-12-2011 at 09:18 AM. Reason: Spelling
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  #34  
Old 14-12-2011, 11:56 AM
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I need a panadol.
Ditto
Interesting though.....
I wonder if Aristotle, Plato et al did the same thing back in the time....
Cheers
Bartman
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  #35  
Old 14-12-2011, 01:19 PM
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Ditto
Interesting though.....
I wonder if Aristotle, Plato et al did the same thing back in the time....
Cheers
Bartman
Unfortunately these poor wretched individuals had to contend with Archimedes.

http://en.wikipedia.org/wiki/The_Sand_Reckoner

Regards

Steven
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Old 14-12-2011, 02:38 PM
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The monkeys and the typing were just a visual idea of infinitely randomised trials. You would need an infinite number of bananas to feed them. Just too expensive to do.

Matter by doing an infinite number of trials will inevitably lead to life on any planet with constant liquid water and a 'sun'.

The only 'proof' I have is that we are here. All of our biological cellular functions were worked out by trial and error with evolution by primitive bacteria starting about three billion years ago and still doing it today.

We are all assemblies of these cells that somehow cooperate.

Our real delusion is that thinking we are at all unique in having 'intelligence'. We are all polluting space ship Earth to the point where our long term very survival is doubtful.

We are entering a mass species extinction era of our own making.

Paradise lost comes to mind.


Bert
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Old 14-12-2011, 03:18 PM
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Our real delusion is that thinking we are at all unique in having 'intelligence'. We are all polluting space ship Earth to the point where our long term very survival is doubtful.

We are entering a mass species extinction era of our own making.

Paradise lost comes to mind.


Bert
Totally agree, Intelligence and the quest for continual financial growth at all costs = a rather insidious and potent destructuive mix

Just as long as you get to use that OS 8"F3 before it's too late

Mike
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  #38  
Old 14-12-2011, 03:47 PM
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I will try to image the very dim dark dust that are our ancestors or are they others futures?

Bert
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  #39  
Old 14-12-2011, 05:05 PM
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Yep .. I'd say the last few posts contain some individually held, deeply philosophical beliefs ... no point in going there ...

Cheers
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Old 14-12-2011, 07:12 PM
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On the likelihood that life will originate given similar conditions (e.g. Earth-like planet) and due to the sheer number of habitable planets.
The whole thing hinges on whether the inverse of the probability of formation of a living thing is of similar order to the number of life-supporting planets.

The origin of life is both dependent on a supportive environment but due to its random origins dependent on a large amount of time.
Time is a continuous variable and if fragmented into ever smaller units can be compared to a real number line with time as the variable.
The size of a time set is of the same order as that of the size of the set of real numbers, which is uncountably infinite.

For each point in time, a unique set of events can be described in terms of specific atoms, each with a specific location or spatial co-ordinate.
There are of course other factors such as the velocity and direction of atoms and their relationship to each other, which would make the set even larger.
Simplistically, the sequence of events that originated in life on Earth can be designated by a set of atoms + coordinates for each point in time.

As this set is uncountably large, it cannot be matched to the size of the set of habitable planets even if this set is countably infinite.
Therefore, the conclusion that life must originate somewhere else in the universe is not supported in simple probabilistic terms.

However, if the universe has a "predisposition" to create life then the probability that life forms can only be measured in statistical terms by sampling.
At this point in time, there is no statistical evidence for life anywhere other than here on Earth.

Regards, Rob
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