What possible methods
By taking rock and ice core samples and noting any significant changes in atmospheric composition, correlating it with where in the timneline the bluegreen algae appeared, and working out a plausible theory that explains the observations?
Maybe the chemical composition of rocks from that era?
I dunno, I'm just guessing.
Actually, it's pretty obvious that they used the time travel machine found in Area 51.
Well sure you can look for clues about the chemical composition of the environment by drilling for samples in sediment layers, etc etc etc
but you're still guessing. You'll never have a 2.3 billion year old bacterium to toss in a cup of water so that he can demonstrate his amazing ability to disassemble it.
This pretty much reeks of Flying Spaghetti Monster logic, only it's regarding science so it's ok.
It's a scientific theory that explains some observed phenomena. It may be that it never gets proven, or that some prediction can be made using the theory that then fits other observations, or it may be that something will turn up that shows the theory to be false, but it *is* based on observation and appears to explain them, so it's on a lot more solid ground than flying spaghetti monsters. However, it *is* a theory, and noone is claiming it's infallible or the absolute truth.
In science you're free to suggest other answers that explain available data. They're called hypotheses, and that's what this is at this point. A hypothesis. One that's a bit difficult to test at this point, admittedly, but as additional data becomes available, it becomes easier to test.
No amount of data collected, on the other hand, can disprove Flying Spaghetti Monsterism.
To clarify  it's not possible even in theory to disprove Flying Spaghetti Monsterism, even in principle, so it's not science.
In principle, if you did have 2.3 billion year old water withs some 2.3 billion year old algae, you prove one way or another whether this hypothesis makes sense. It may not be realistic, but in principle it could be done.
Apart from trumpets of doom and flights of angels telling us to get in line...
a cynic writes...
August 8th, 2005
In principle you could fly to the edge of the universe, or wherever it is that God lives, and either shake His hand or not, depending upon whether or not He existed.
In most religions, that's not an option. In most religions I've heard of, God does not reside in a realm that is physically accessible.
Not testable.
Er, no you couldn't, that's the problem. For starters, as has been repeated many times, lack of evidence of something is not the same as evidence of the lack of something, so you not finding him is not proof he's not there. Secondly he's not supposed to be a physical being, he's all prevading, so unlike StarTrek V there is no "place where god hangs out". Finally, if you didn't find him it's because you didn't belive hard enough.
Religion by default *requires* faith because it rests on foundations that cannot reasonably be proven or disproven, and any attempt to do so will not convince the believers  it will be your method that is at fault.
19! :)
You can't reasonably prove or disprove this bacteria theory, so I suppose that makes it religion, Mat.
Even as a Christian, I am sometimes suspicious of some of the tenets of Christianity.
I mean, currently we have to take the existence of God on faith. There are no proofs (though there are a few good arguments).
I suppose it would be breaking the rules for God to write "God Loves You" in the clouds every so often, or even repeat that "writing on the wall" thing done in the Bible. Absence of evidence is not evidence of absence  but come on! We're talking about eternal life here, ethical and moral action, faith and belief, a loving God, perhaps a battle between Good and Evil. A complete absence of the miraculous makes it a hard argument to make.
A nice small miracle every so often, something out of the ordinary, done once every hundred years or so, would be so reassuring. Seems that's not the way God works, though.
Instead we Americans seem to be falling for a bunch of charlatans who can wave the Bible, quote verses, and try to get their interpretation of scripture accepted as the ONLY interpretation of scripture. Justifying condemnation, selfrighteousness, and fear in response to a more open society.
Maybe there is nothing more. Maybe all of this religiosity is mere theorizing about what could be, and wishful writing about it. Maybe we are beings of spirit and flesh, inventing a larger mythology to encourage us to live well.
The love of God is all very well, but if the evidence we DO have around us shows that those who claim God and the Bible seem to have very little love, and that God is powerless to enlighten us, and that there is no evidence to support life after death, Christ's sacrifice, or the nature of the unseen  then what good is it all?
Shouldn't there be something?
AllanL5
August 8th, 2005
Who says He has no power to enlighten us? Didn't He do a pretty big demonstration, oh, about 2000 years ago? On a Godly scale, that's probably seconds, or less. It's not His fault if we all have such short attention spans.
You just said that absence of evidence is not evidence of absence, but then you claim that the evidence shows that God is powerless to enlighten us. Maybe He doesn't because it's not His job. It's ours.
Add "science" to the list of things muppet doesn't understand and gets angry at.
ronk!
August 8th, 2005
Right, ronk. You let me know when you have some 2.3 billion year old bacteria to prove or disprove this theory. Science can be quackery just like religion can.
The Babel Fish objection might come in play...
a cynic writes...
August 8th, 2005
Why, thanks muppet. That was kind.
I guess I'm just indulging in some wishful thinking of my own  that this issue of faith would be important enough so that God would provide some periodic reminder to us.
And whenever people do this (ie put some attribute on God they would like him to have), typically they ignore some amazing things that are happening around them everyday. Things like children, or happy marriages, or breathing, or weather, or trees, or even that the Earth is at exactly the right distance from the Sun that all this works.
AllanL5
August 8th, 2005
There is no edge of the universe to fly to, its either infinite or it isn't, if it isn't then we have more serious problems than 2.3 billion year bacteria.
There's nothing too remarkable in finding the bacteria in all of the various stages throughout the sedimentary history along with all of the effects that it had locally to it (which for a bacterium is really quite small and so a very large sample size for testing).
So the hypothesis is testable, though not testable to anything approaching an absolute knowledge, but then so little of what we 'know' is that absolute.
What cataclysmic event happened 2,000 years ago that established an existence of God?
Well Simon that's been the subject of some debate, hasn't it?
I don't think its a matter of debate particularly, there are those that believe it and those that don't. I don't find any documented proof of the Crucifixion, though there are plenty of crucifixions.
Still less is there much about a Resurrection, there's as much about a fake staged crucifixion as there is about an actual Crucifixion and Resurrection.
On the other hand there's an abundance of evidence to sift as to whether bluegreen algae did or didn't have the effects hypothesised and the balance of evidence will accumulate, any other hypotheses will be tested against the same evidence and either found to make more sense or not as the case may be.
Confusing religon and science just debases both.
"You can't reasonably prove or disprove this bacteria theory, so I suppose that makes it religion, Mat."
Can't I? Why not? You don't *need* to actually have 2.3 million year old bacteria to disprove it, and science *never* says "we have perfect understading of [phenomena X] and no additional information will ever come to light that will show the theory to be wrong". Science *embraces* being wrong, and is composed entirely of educated guesses that better and better fit observations and are able to make accurate predictions.
God, on the other hand, always has a getout for any "proof" you may have; belief in god can't be used to make any predictions about the outcome of an experiment, relies on "unexplainable" things to fill in the gaps and allows for supernatural events to occur which means it defies any experimental testing. Results of a "god testing" experiment didn't match the prediction? It's god working in mysterious ways.
"You let me know when you have some 2.3 billion year old bacteria to prove or disprove this theory."
We don't need *proof* in the sense that you seem to be asking for. If, as a model, it allows us to make predictions that we can then verify (such as "if this algae did do suchandsuch, then we should also notice the presence of thingummy in the rock strata") then it's useful, but if the predictions fail or new evidence is found that contradicts the theory then it'll be thrown out or refined. Science doesn't deal in absolutes  "close enough until something better comes along" is a more accurate description  and your insistence that not having the bacteria means the whole thing is just as likely to be true as the spaghetti montser deal shows a great deal of misunderstanding of science on your part.
"Science can be quackery just like religion can."
No, science is science, and quackery is quackery. Some quacks may claim they're doing science, but unless they come up with something that explains observations and can predict new outcomes it's *not* science...
361!
* The only area of "science" that does deal in absolute truths is mathematics.
muppet, you just let me know when the principles of religion let you build a microwave oven, ok?
I mean, not using little things like science.
>> The only area of "science" that does deal in absolute truths is mathematics.
Glad to see the scare quotes, at least.
1) Science != mathematics, nor is it a subset.
2) Say what? What are, a closet platonist, or something? ;) This is a pretty large and highly contentious claim, is it not?
Mongo
August 8th, 2005
Who's trying to compare pure religion to pure science, Aaron? Not me.
I'm saying that believing that 2.3 billion year old algae learned how to eat water and trigger a massive Ice Age (Flash! Bacteria Produces Really Bad Animated Film!!) is pretty similiar to believing that an all powerful being put the world here in the first place. They're both such abstract, evidencelight ideas that neither can ever be proven or disproven to a certainty without divine revelation.
"Science != mathematics, nor is it a subset."
Biology => messy chemistry Chemistry => messy physics Physics => messy maths
Pretty much all of science relies very heavily on maths. In may not be a traditional science, but without it the modern scientific landscape would be a very different, and poorer, place. You may just see it as a tool but I consider it the purest of the sciences  once something is true in maths it is *always* true.
> once something is true in maths it is *always* true ...
... or at least until you change an axiom: e.g. you admit negative numbers, real numbers, imaginary numbers, nonEuclidean geometry, ...
Christopher Wells
August 8th, 2005
"This is a pretty large and highly contentious claim, is it not?"
Rats, forgot that bit.
I don't see it as large OR contentious. It's possible to imagine a universe where, say, the speed of light is 3 feet per year, gravity has a repulsive effect, hydrogen and oxygen mix to make cheese, and the life forms are all made of nylon. It would be a weird universe, but there's nothing special about our universe that means some other fantastical reality couldn't exist. Prime numbers, however, are ALWAYS prime, no matter what.
Prime numbers are always prime because we define prime numbers within our own context of reality.
So what?
>> Pretty much all of science relies very heavily on maths.
But that's my point. "Relies on" is not anything like "is a form of".
>> You may just see it as a tool but I consider it the purest of the sciences  once something is true in maths it is *always* true.
Well, "just" is a little harsh. "Different", though, without a doubt.
You do a lot of empirical mathematical testing to prove mathematical hypotheses?
As to true once, true always ... tell that to Euclid and Lobachevsky.
Mongo
August 8th, 2005
" Prime numbers are always prime because we define prime numbers within our own context of reality."
Again you demonstrate an impressive lack of understanding of the subject. Well done!
Absolutely not, Mat. We are cognizant beings and we understand mathematics to function in a particular way. Who are you to say that there isn't a universe, where, somehow, in some unfathomable way, 2 + 2 = 5? You can't. A prime number will always be a prime number from our frame of reference, as it will also be for any other thinking being within our universe who discovers mathematics, but Math is not necessarily Truth outside of our own existence.
Now, if you want to go worshipping plus signs or something, then go for it.
"As to true once, true always ... tell that to Euclid and Lobachevsky."
But Euclid was just wrong  counterexamples can be found easily, so it was never true in the first place. (Remember, the rigorous form of mathematical proof we use today is a fairly recent innovation, and a couple of hundred years ago empirical "proof" was good enough.)
Wow. We have reached an impasse here. There really is nothing to discuss at this point.
Salad Cream. Nazis. Prime numbers need not be prime.
Thread ends HERE.
I didn't say prime numbers need not be prime in our frame of reference. :)
I said that there could be a frame of reference somewhere where 3 is divisible by banana.
"We have reached an impasse here."
I just don't think I'm explaining myself clearly enough. I know what I mean, but I don't seem to be able to find the right words...
"A prime number will always be a prime number from our frame of reference..."
Quit while you're only slightly behind, there's a good chap.
I understand perfectly the idea you're trying to convey, Mat, I just don't agree that numbers are necessarily absolute truths. You do, and that's fine.
Ok, here's what I mean by "absolute mathematical certainty".
"On a Euclidian plane* the interior angles of a triangle will sum to 180 degrees."
That statement is true, but I don't need to draw every possible triangle, measure the angles, and add them up. I can demonstrate that it is true for every triangle very easily, and noone will be able to come up with a triangle whose interior angles add up to 183 degrees. Given the five postulates, the statement about triangles will never be "refined" in the same way that, say, Newton's Laws were shown to be an approximation at certain scales.
* i.e. a plane where it is assumed the fifth postulate is true. This is where Euclid "went wrong", and as we now know, postulate 5 is variable. The others, however, work everywhere (although the meanings of point, line, etc., vary depending on what you change postulate 5 to).
Mat, the thread ended a while back. He won't attempt to understand you.
>> But Euclid was just wrong  counterexamples can be found easily, so it was never true in the first place.
So, your claim is that people in the past thought they had absolute truth, but they've been proven wrong, so it sucks to be them, fine. But now, we have found a mechanism to show absolute truth (recently innovated rigorous proofs), which _cannot_ ever be disproven, since they're absolutely right.
Seems like I've heard this story before, historically speaking. People have believed this for 2500 years we know of, and have not done terribly well in hindsight.
I'm not sure if you understood the significance of my comment about empirical testing: my point is simply that if it doesn't involve at least theoretically empirically testable results, it's not using the scientific method, ergo it's not science. It's not less than science, it's something else.
Mongo
August 8th, 2005
"What possible methods could there be to deduce the metabolic capabilities of bacteria 2.3 billion years ago?"
That's a lot of talk for someone who hasn't even read the paper. Maybe you should read it and then critic it. Maybe they have rock solid evidence  stuff that cannot be explained any other way (except that "God did it") or maybe it's the swiss cheese of intellectual papers. You're kind of taking it on faith they couldn't possibly have enough evidence. Maybe they have proven, to a reasonable doubt, that it's the most likely occurance.
Almost H. Anonymous
August 8th, 2005
<" Prime numbers are always prime because we define prime numbers within our own context of reality."
Again you demonstrate an impressive lack of understanding of the subject. Well done!>
Depends on the how you understand the statement. There would always be prime numbers. But whether a particular number is prime depends on your factorization methods.
Rick Tang
August 8th, 2005
There's another problem here. Mat is defending that some currently proved claims cannot be disproven, and offers us a good example to try to disprove.
Of course, we may or may not be able to disprove the claim, but the liklihood that current readers of this thread could disprove something like that to Mat's (or other reasonable people's) satisfaction is vanishingly small. He's not offering _easy_ things to disprove, and only those that have not been disproven so far (if they had been, they'd be wrong and so wouldn't count). If not impossible, they at least have not been disproven so far, and there's reason to think they will be any time soon.
It wouldn't matter, anyway, becuase Mat could always just reach into his bag and produce another, more difficult case.
Instead of trying to use concrete examples, and try to knock them down one by one, I'm suggesting an inductive awareness of how many times people have been wrong about absolute proofs in the past should give us pause about such large claims.
The point, again, is that whatever exapmple Mat comes up with, however compelling, is not an absolute guarantee it can never be disproved, it's just an example he can't imagine disproving  it's literally indubitable.
Mongo
August 8th, 2005
"...how many times people have been wrong about absolute proofs in the past should give us pause about such large claims."
for (i = 0; i < 2^128; i++) { claim("X or ~X is an absolute truth"); }
Your claim on number of times of absolute proofs being proven wrong is now irrelevant.
Yup. And all those ALife experiments show (almost) anything is possible.
Rick Tang
August 8th, 2005
> "X or ~X is an absolute truth"
I am a member of the set of somewhat tall people (I'm neither tall nor not tall).
Christopher Wells
August 8th, 2005
Looks like we are all philosophy 101 students ... except AA :)
Rick Tang
August 8th, 2005
"There would always be prime numbers. But whether a particular number is prime depends on your factorization methods"
Sloppy.
If primality makes any sense at all, there would be at least two prime numbers in any number system. But whether a particular number is prime depends on how multiplication is defined.
HeHe ... remember Aaron said 'saving' may be meaningless ...
Rick Tang
August 8th, 2005
I was a Maths student but I have started to read about Artificial Intelligence, hence my "fuzzy logic" statement.
Christopher Wells
August 8th, 2005
for (i = 0; i < 2^256; i++) { claim("X or ~X when using boolean values is an absolute truth"); }
A philosophy minor from over ten years ago is only slightly useful.
Aynway, bored now.
"...is not an absolute guarantee it can never be disproved..."
Er, no. Many mathematical proofs of fact X start "assume fact X is false", then demonstrate that that leads to a contradiction. For example, one simple proof that sqrt(2) is an irrational number starts with assuming that it's *not* irrational:
"Assume that root 2 can be expressed as the fraction p/q, with p and q being relatively prime integers."
sqrt(2) = p/q Multiplying through by q and squaring each side leads to p^2 = 2q^2 Therefore p is of the form 2p' So q^2 = (4p'^2)/2 = 2p'^2 Finally q = 2q' which contradicts that p and q are relatively prime, therefore no values of p and q can be selected such that p/q = sqrt(2)
(The 2p' (two pee prime) can be derived from the fact that the integer p is equal to 2 of some other integer, q^2, so we can replace p with two of this new unknown variable.)
*That* is a mathematical proof. No matter how hard you hunt, you will never be able to express sqrt(2) as a fraction, and those few lines up there save you the bother of ever having to look. It's not that "I don't believe it will be disproved", it *cannot* be disproved. That is the power and the beauty of maths, and what elevates it above the baser sciences. :)
I really like Mat's posts in this thread. Maybe next time I'll let him explain the principle of falsifiability when it comes up. ;)
Snark
August 8th, 2005
"I am a member of the set of somewhat tall people (I'm neither tall nor not tall)."
And I think I am a member of the set of somewhat saved people.
Man, satan's temptation is so strong ...
Rick Tang
August 8th, 2005
Mat, if I may, there's a slight gap in your sqrt(2) proof.
"The 2p' (two pee prime) can be derived from the fact that the integer p is equal to 2 of some other integer, q^2, so we can replace p with two of this new unknown variable."
Rather, p^2 = 2q^2 implies that p^2 is of the form 2n, where n = q^2, and thus p^2 is an even number. Since we know that only even numbers can produce an even result when squared, and that odd numbers will always produce an odd result when squared, we deduce that if p^2 is even then p is even and p can be written as 2p'.
I wonder if it is necessary to prove the squaring of even and odd numbers result before the whole proof is solid?
Ian Boys
August 8th, 2005
Thanks, Pythagoras, er, Mat, but I've told you we're not playing this game by these rules.
>> Er, no. Many mathematical proofs of fact X start "assume fact X is false", then demonstrate that that leads to a contradiction.
So they do, how does this counter my claim? I'm not disputing you have lots of great examples that you or I cannot imagine being disproved. I'm not even saying your example is disprovable. I've already _given_ you that. I'm not at all sure why you think generating a contradiction is more powerful in some way than other forms of proof.
I'm claiming we need to accept that we might, theoretically, some day, be proven wrong about any given case. In the example you give, I can't imagine what that would look like, it may be that no human could. Still, you just have to imagine really, really, hard that it _could_ be wrong. Evil demon, matrix, enlightenment, whatever. However, just pulling out more individual examples is not going to work as a counter to my claims  Aaron's tongue in cheek objection, for example, carries more weight against my actual argument (presuming we could extend the finite list he provides indefinitely, which of course we could)..
Mongo
August 8th, 2005
>> Maybe next time I'll let him explain the principle of falsifiability when it comes up. ;)
Have at it, do. :)
Mongo
August 8th, 2005
Unfortunately, I don't know the Unicode escape sequences for inverted A's and E's or even if there is Unicode for that. Otherwise we could have some real fun with "For All X there exists a Y such that" kind of proofs.
Christopher Wells
August 8th, 2005
Dammit, now I am gonna have to get up off my lazy ass and find my old notes.
Some other time.
Mongo, you've gone off the rails.
If a mathematical proof is correctly derived, it is true for all eternity beyond any possibility of contradiction. There is absolutely no possibility of a counterexample being found under any imagined circumstances whatsoever. No evil demons, no enlightenment, not even God.
If a counterexample to a proven theorem were ever found, it merely demonstrates that the proof was not correctly derived, and that it was not actually a mathematical proof after all.
To summarise: it is possible that a mathematical proof is flawed, and will be shown not to be a proof. But the possibility of a counter example to a correct proof ever being found is precisely and exactly zero.
Ian Boys
August 8th, 2005
"If a mathematical proof is correctly derived, it is true for all eternity beyond any possibility of contradiction. There is absolutely no possibility of a counterexample being found under any imagined circumstances whatsoever."
Actually, that's not quite true...
Godels says there are theorems whose truth or falsity cannot be established even if correctly derived.
There are some theorems which appear to satisfy this  I forget the details[1] but there's some reasoning about the countability or uncountability of some sets of real numbers and you can assume either answer and the entire of the rest of maths works in both cases.
[1] I am not a mathmoid, but I know some of them.
Katie Lucas
August 9th, 2005
