PDA

View Full Version : Question about the anthropic principle


Prodigy54321
05-27-2007, 06:12 PM
This questions may actually just relate to our ability to form conclusions based on hindsight in general actually. (Not about physical laws specifically)

so the general idea behind the antrhopic principle (the weak anthropic principle more specifically) is that the reason that things are the way they are (such that intelligent life could form) because, if it wasn't that way, we wouldn't be around inquiring in such a manner.

this seems obvious when we consider many (or perhaps infinite) "attempts"...for isntance, if there is a never ending cycle of big bangs and big crunches (or even if we just consider the amazing number of possible places chances for life to arise in different areas of the universe), it seems obvious that --to say that we are specially chosen in some way since the chances that we (or any intelligent life) could arise is so low-- is quite weak due to the anthropic principle...for instance, since in another solar system, life can't arise, there is no one to count that instance as a "loss" and coudn't do so if we didn't come into existance because conditions on our planet did not allow it.

and also it seems clear if we consider a scenario..

I have 5 dice...I roll them over and over and over again and if I roll 5 "6s" I tell my friend Bill that I rolled 5 "6s"...If I don't tell Bill how many times I rolled the dice and he can't record the "losses" there is no particular reason to think that this occurrence is extraordinary.

first of all, am I correct about this so far?

my main question is...Does anything chance if we only get one shot at it?

For instance, suppose that after a big bang, the odds that there would be conditions where intelligent life could arise is 1,000,000 to 1 (either because of the chances of physical laws being such that life could arise or whatever).

What if there could only be one big bang? We are living in the one possible shot to "get it right"...does this change anything? Does it still hold that we cannot conclude that it was more than just chance because if things didn't turn out the way they are (or close to the way they are, the 1,000,000 to 1 shot) we wouldn't be here inquiring about it?

If instead of rolling the dice over and over again, I just rolled them once, and if they landed on 5 "6s" I would tell my friend, Bill. And if not, I wouldn't tell him anothing about me rolling the dice. If I came up to bill and told him that I rolled 5 "6s" and only took one shot at it, does that make this occurrence more remarkable? Does it make anotehr possibility other than pure chance more likely?

PairTheBoard
05-27-2007, 06:32 PM
Could you repeat that?

PairTheBoard

soon2bepro
05-27-2007, 07:32 PM
Someone once said:

"When one is dealt a bridge hand of thirteen cards, the probability of being dealt that particular hand is less than one in 635 billion. Yet, it would be absurd for someone to be dealt a hand, examine it carefully, then conclude one can't have been dealt that very hand because it's so improbable."

NotReady
05-28-2007, 02:53 AM
[ QUOTE ]

Does it make anotehr possibility other than pure chance more likely?


[/ QUOTE ]

The less likely something occurs by chance guess what the more likely it didn't occur by chance - i.e., purpose. Suppose 10m rolls, all 6 - someone might suspect loaded dice.

The difference is you can calculate that probablility with dice. You can't with universes and life because the number of "rolls" is unknown. For that matter, we don't know from observing this universe that even one "roll" by chance is possible. After all, that's the question.

Prodigy54321
05-28-2007, 01:30 PM
maybe this will help..

If a random guy comes up to me and says, "Hey, I picked a random person, you, and decided that I would roll 5 dice and if they all landed on 6, I would come over and introduce myself and if they didn't, I wouldn't. I did roll 5 6s so here I am."

What conclusions can we draw here? It is obviously quite unlikely that he would roll 5 6s...but if he hadn't rolled 5 6s, he wouldn't be over here telling us about it and we would never know.

in what respect can we still consider this event "unlikely?"

if we knew that there is at least some possibility that the man is lying (he may have rolled the dice or he may not have, in any case, he may be lying and this unlikely event never took place)...how unlikely this event is (rolling 5 6s) will help us come to our conclusion about how likely it is that he is lying, correct?...if his story is that he rolled 1 die and if he rolled a 6 (yada yada)...would it be more likely that he is telling the truth than if he claimed that he rolled 10 dice and rolled all 6s (yada yada)?

now, if we know of no possible way in which he could be lying (akin to knowing no possbile, nonchance way that the universe could be able to support life), can the odds of this even happening help us to draw conclusions about whether or not the occurrence is actually chance or not? Instead perhaps of an unknown cause? (note that this unknown cause does not imply a god of any kind, just an unknown cause /images/graemlins/wink.gif)

remember that we are not recording the losses here..just the wins, as we are in our universe question.

the "lying" possibility is much like if we knew of another way that life could have arose (a god perhaps?...but this is actually more like a possible, so far unknown possible cause, right?)

actually, this might be even more confusing than the first post /images/graemlins/laugh.gif

Prodigy54321
05-28-2007, 01:48 PM
[ QUOTE ]
Someone once said:

"When one is dealt a bridge hand of thirteen cards, the probability of being dealt that particular hand is less than one in 635 billion. Yet, it would be absurd for someone to be dealt a hand, examine it carefully, then conclude one can't have been dealt that very hand because it's so improbable."

[/ QUOTE ]

true, but in this case, it is entirely possible to record both "wins" and "losses"...if we pick a hand before it is dealt, the it is dealt..we can record each time we are dealt or not dealt that hand...and we can see that there is nothing more than chance involved.

in our case...the problem is that we are forced to look at this in hindsight...like a person in your example would...we cannot record the "losses"...so can we come to any conclusions about whether an event such as this is just chance or something more?

kerowo
05-28-2007, 01:54 PM
[ QUOTE ]
...so can we come to any conclusions about whether an event such as this is just chance or something more?

[/ QUOTE ]

No.

If an event has a non-zero chance of happening you can't make any decisions about why or how it happened after seeing it happen one time. You don't have enough information.

Kaj
05-28-2007, 01:57 PM
[ QUOTE ]
[ QUOTE ]
...so can we come to any conclusions about whether an event such as this is just chance or something more?

[/ QUOTE ]

No.

If an event has a non-zero chance of happening you can't make any decisions about why or how it happened after seeing it happen one time. You don't have enough information.

[/ QUOTE ]

But if you can hypothesize how it happened and perform analysis & experiment to determine if the likelihood (even qualitatively) of that "how" being feasible, then you are on to something! And thus, this is the scientific journey...

kerowo
05-28-2007, 03:11 PM
Meh. Sounds like OP is trying to get from "really, really, rare occurance" to "it must have been caused by something outside of chance." Which is silly.

Silent A
05-28-2007, 03:43 PM
[ QUOTE ]
Meh. Sounds like OP is trying to get from "really, really, rare occurance" to "it must have been caused by something outside of chance." Which is silly.

[/ QUOTE ]

I don't think OP is trying to do this (mostly because it wouldn't be consistent with his post history).

I think he's just trying to get his head around the anthropic principle and the fact that it is often used by both sides of the "does the universe imply a god?" question.

Prodigy54321
05-28-2007, 03:57 PM
[ QUOTE ]
[ QUOTE ]
Meh. Sounds like OP is trying to get from "really, really, rare occurance" to "it must have been caused by something outside of chance." Which is silly.

[/ QUOTE ]

I don't think OP is trying to do this (mostly because it wouldn't be consistent with his post history).

I think he's just trying to get his head around the anthropic principle and the fact that it is often used by both sides of the "does the universe imply a god?" question.

[/ QUOTE ]

word.

I'm not trying to get anywhere...I am genuinely just asking questions that I do not know the answers to.

I made a post a while back in another thread asking about trying to form conclusions based on probability when we can't (or simply don't) record "losses"...no one answered and it's just been on my mind recently.

I can't seem to wrap my head around what the actual consequences of this are...

I decided to relate it to the anthropic principle because I thought people would be more interested in it when it has to do with creation of the universe (and possibly God)...after all, most of the threads in this forum concern belief in a god or lack thereof.

in reality, it's not necessary to talk about a god at all...it is only necessary to talk about currently unknown possible causes.

Silent A
05-28-2007, 04:44 PM
Probability and statistics should only be used when we have at least one of the following:

1) a firm understanding of the underlying mechanisms
2) a significant sized sample of observations

It's best to have (1) because we can use it to analyze what we should expect to see and then compare it with what we actually see. Failing that, if we at least have lots of observations then we can start to formulate some ideas and predictions about future observations.

However, if we have neither then there really isn't much we can say. With most natural phenomena this isn't too bad since we could always do a little research to get more observations. Though in the case of the observed universe itself, we only have one observation. As such, talking about probability w.r.t. the origin of the universe is completely wrongheaded because we don't have the information to justify either analytical or empirical analysis.

soon2bepro
05-28-2007, 04:51 PM
[ QUOTE ]
true, but in this case, it is entirely possible to record both "wins" and "losses"...if we pick a hand before it is dealt, the it is dealt..we can record each time we are dealt or not dealt that hand...and we can see that there is nothing more than chance involved.

in our case...the problem is that we are forced to look at this in hindsight...like a person in your example would...we cannot record the "losses"...

[/ QUOTE ]

Let me put this another way. there is only one hand that has been dealt. You try to find something special about it precisely because you got that hand.

By the way, in my opinion, true randomness probably doesn't exist. Though this doesn't make any difference.

[ QUOTE ]
so can we come to any conclusions about whether an event such as this is just chance or something more?

[/ QUOTE ]

No.

David Sklansky
05-28-2007, 05:24 PM
I think that everybody here is discussing something different from the anthropic principle. That principle, I believe, makes use of the fact that only certain outcomes will result in entities that will understand and discuss probability.

Prodigy54321
05-28-2007, 05:33 PM
[ QUOTE ]
I think that everybody here is discussing something different from the anthropic principle. That principle, I believe, makes use of the fact that only certain outcomes will result in entities that will understand and discuss probability.

[/ QUOTE ]

is this basically the same as being unable to "record losses" in any scenario?

that is what I assumed..perhaps I am mistaken...

If I am not mistaken, can we draw any conclusions from the fact that a "win" has occurred?

for isntance, if it is 1 million to 1 that something would happen that would allow us to exist, people will probably say that it is then very unlikely that it just happened by pure chance...

according to the anthropic principle, this conclusion is bogus, am I correct?

David Sklansky
05-28-2007, 05:38 PM
I think that is what the anthropic principle contends. I'm not sure its correct.

Silent A
05-28-2007, 07:05 PM
[ QUOTE ]
for isntance, if it is 1 million to 1 that something would happen that would allow us to exist, people will probably say that it is then very unlikely that it just happened by pure chance...

according to the anthropic principle, this conclusion is bogus, am I correct?

[/ QUOTE ]

Actually, the anthropic principle says that the event (or, more accurately, series of events) in question had to happen in order for observers to exist. Therefore, we can't really speculate on the improbability of it all because if the universe was differnt, then we wouldn't be here to notice.

If you understand Bayesian statistics, you can think of it as asking the question, "Given the fact that I exist, what is the probability that the universe would have formed in a manner allowing me to exist?"

Obviously, the answer is 100% no matter how unlikely such a universe might otherwise be.

kerowo
05-28-2007, 11:29 PM
So the anthropic priniciple is just a fancy way of saying "If a tree falls and no is around to hear it...?"

A quick look at the wiki page still leaves me a little confused as how it is different from answering a question with "because." It doesn't seem to explain much.

bunny
05-28-2007, 11:35 PM
It's more an answer to people who say "Wow! The universe is exactly tuned to suit our existence. How unlikely is that?" The answer being that every universe containing intelligent speculators is exactly tuned to suit their existence. So it's really not that remarkable that this one is so ideally "tuned".

Prodigy54321
05-29-2007, 12:09 AM
FWIW, I believe the anthropic principle was originally developed to help explain why the universe is the way it is with respect to they properties that allow life to thrive...for instance the physical means (laws included) by which stars can form and create most of the heavier elements (past lithium, If I remember A Brief History of Time correctly)..which are necessary for the life that we see.

since then, there have been several theories that allow for vastly different conditions for the very early universe to translate into the conditions that now allow life to exist..so it doesn't seem as unlikely as it once did..

In any case, that doesn't mean that there is no room for the anthropic principle..just that it may not be necessary in this case.

still can't wrap my head completely around it though...

I get the impression from NotReady's post that he may have some problems with the anthropic principle (at the moment, I think I may as well..maybe the same as him)...perhaps I'm wrong about NotReady, but I would like to hear more about what his take on it is if he indeed has objections.

NotReady
05-29-2007, 03:36 AM
[ QUOTE ]

I get the impression from NotReady's post that he may have some problems with the anthropic principle


[/ QUOTE ]

I found this article by
William Lane Craig (http://www.leaderu.com/offices/billcraig/docs/teleo.html) which I recommend to all as a good discussion of the AP from a theistic standpoint, though he doesn't spend much time on the probability question.

He first defines the WeakAP as:

[ QUOTE ]

If the universe is observed by observers which have evolved within it, then its basic features must be of a type that allows the evolution of observers within it.


[/ QUOTE ]

Not very earth-shattering. As he says, trivial. He then goes on to discuss various positions deduced from the WAP which he calls the Anthropic Philosophy, defined thusly:

[ QUOTE ]

According to the Anthropic Philosophy, an attitude to surprise at the delicately balanced features of the universe essential to life is inappropriate; we should expect the universe to look this way. While this does not explain the origin of those features, it shows that no explanation is necessary. Hence, to posit a divine Designer is gratuitous.


[/ QUOTE ]

Much discussion follows, including a lot about what he calls the World Ensemble, which you can think of as the multiverse theory. I've only quickly read through it but I think his main point is that the WE is more fanciful than theism. I would say there's less evidence since there's none for WE and some for theism.

I tend to think of the AP itself as a modern form of the teleological argument (Craig's article includes teleology in the title) - or Paley's design argument. I've said a few times that it isn't unreasonable to believe that something that looks designed is in fact designed. Oddly enough, Craig found a quote similar to that idea:

[ QUOTE ]

Martin Gardner, quoting physicist Heinz Pagels, says that the Anthropic Principle raises a new mystery:

"How can such a sterile idea," Pagels asks, "reproduce itself so prolifically?" He suspects it may be because scientists are reluctant to make a leap of faith and say: "The reason the universe seems tailor-made for our existence is that it was tailor-made . . . . Faced with questions that do not neatly fit into the framework of science, they are loath to resort to religious explanations; yet their curiosity will not let them leave matters unaddressed. Hence, the anthropic principle. It is the closest that some atheists can get to God."{32}


[/ QUOTE ]

and:

[ QUOTE ]

Similarly physicist Tony Rothman writes,

It's not a big step from the [Anthropic Principle] to the Argument from Design . . . . When confronted with the order and beauty of the universe and the strange coincidences of nature, it's very tempting to take the leap of faith from science into religion. I am sure many physicists want to. I only wish they would admit it.{33}


[/ QUOTE ]

Look, people, you are constantly telling us that there's no evidence for God, that the idea of God is the same as the idea of the FSM or unicorns. But take this verse from Scripture:

"The heavens are telling of the glory of God"

and combine it with the AP - why doesn't the AP tend to show the truth of the verse? Isn't that evidence?

As to the probability question:

I've said you can't apply probability, at least mathematically, to the question of God. I think that applies to attempts to use the AP. I believe it can be used in the sense of psychological probability, which is like, for instance, what a jury uses when determining a verdict. When we examine all we know about the universe the idea that it all happened by chance seems implausible. Of course, this eventually runs into the "God of the gaps" issue, but I believe there will always be an infinite gap between our scientific knowledge of what is and our knowledge of how and why it is. God will always seem the most likely explanation from a psychological standpoint.

The AP is really just a more scientific way of saying "Isn't the universe an amazing place?" But people have always known that. And people have always said:

1. The world has always existed, or
2. The world popped up out of nothing for no reason, or
3. The world was designed by a higher being

No amount of probability calculations will decide the issue, no amount of scientific investigations and no amount of human knowledge will either. I believe the evidence points to Christian theism but humans can't achieve absolute certainty on the basis of merely human methods - faith is still required.

Prodigy54321
05-29-2007, 03:40 AM
thanks NotReady, I'll look over this in the morning.

luckyme
05-29-2007, 03:48 AM
[ QUOTE ]
humans can't achieve absolute certainty on the basis of merely human methods - faith is still required.

[/ QUOTE ]

and faith is - inhuman? unhuman?

I'd go for human but for some reason you've excluded it.

luckyme

NotReady
05-29-2007, 03:57 AM
[ QUOTE ]

and faith is - inhuman? unhuman?


[/ QUOTE ]

I mean human methods of acquiring knowledge - science, logic, etc. Romans 1 says all people know God through what has been made because God makes Himself evident to them - genuine faith is a response to that - so God's activity is necessary for us to know Him truly, i.e., it involves more than the bare intellect.

MidGe
05-29-2007, 05:47 AM
[ QUOTE ]
Romans 1 says all people know God through what has been made because God makes Himself evident to them - genuine faith is a response to that - so God's activity is necessary for us to know Him truly, i.e., it involves more than the bare intellect.

[/ QUOTE ]

And herein lies the obvious proof that Roman 1 is a false doctrine. There is no evidence of a christian type god (benevolent and omnipotent) anywhere manifesting itself to me, in any way shape or form. /images/graemlins/smile.gif

kerowo
05-29-2007, 08:24 AM
The anthropic principle is not falsafiable so it can't be used as proof for anything.

Prodigy54321
05-29-2007, 03:40 PM
WRT to his World Ensemble....this relates to the question that I was first trying to ask...does anything change when we have only one shot, rather than many or an infinte number of them?

for instance...if a woman plays a lottery and picks numbers such that the odds of her winning are 1000 to 1...if she plays every day and on of those days she wins...I doubt anyone would say that there is much cause to suppose an unknown influence here....

but what if she decided that she would only play it once..and she wins it..now is there cause (or at least more than in the first case) to suppose an unknown influence here?

I'm also not sure why he specifically considers various theories such as the multiverse theory as metaphysical...he didn't go into it much other than to quote someone who thought it to be so...and he also used this as justification from introducing his own metaphycial theory..so I'm not sure if he has an objection to it or not...it would seem that he shouldn't /images/graemlins/wink.gif

but in any case, I don't know enough about the current theories to conclude either way.

-----------------------------------------

I don't know how we are getting to a designer in his argument...isn't a rejection of the anthropic principle (as an explanation) and current theories just supporting an unknown cause...I don't see how he gets to a god specifically.

------------------------------------------

again, I'm not sure why we are putting God here...shouldn't we just be lumping God in with all other unknown causes unless we can find evidence for God specifically?

Suppose I reject current scientific theories concerning this matter...and I reject the anthropic principle as an adequate explanation concerning this matter...and I see no evidence for any other hypothesis...

why should I put an infinite intelligent creator in that place, rather than any other unknown cause..

I suppose that you can because you currently believe there is sufficient evidence for this god...but I don't...so wouldn't it be illogical for me to conclude a god over any other unknown cause? For me, I must consider them as one big group.

---------------------------------------------

His firing squad analogy is interesting...

but it doesn't ring apparently true...being surprised that we are alive in this case (such that we conclude that there is likely to be an outside cause) is just like winning the lottery in my first case and concluding the same thing...

and again, I get confused here...because the guy in front of the firing squad only gets one shot here...

if we lined up a few hundred thousand people and one of them was not killed, should that person be surprised? (again to the point that they conclude an outside cause?)

why is this any different than the guy's individual case?

the difference in this case is that, from this guy's point of view, he cannot record the times that he dies and the times that he wins...he is living in a win..pretty much the same situation we are (if our existence is so improbable)

I still don't see how we can conclude that it is more than just chance...of course we also can't conclude that it is ONLY chance...again, because we can't record both wins and losses. (and even then, as I'm sure you would point out, /images/graemlins/wink.gif we can't conclude there was no outside influence.)

what I am trying to figure out though, is how we could conclude that an unknown cause IS responsible or at least likely to some degree.

Prodigy54321
05-29-2007, 03:47 PM
[ QUOTE ]
[ QUOTE ]

and faith is - inhuman? unhuman?


[/ QUOTE ]

I mean human methods of acquiring knowledge - science, logic, etc. Romans 1 says all people know God through what has been made because God makes Himself evident to them - genuine faith is a response to that - so God's activity is necessary for us to know Him truly, i.e., it involves more than the bare intellect.

[/ QUOTE ]

isn't this a circular argument?

if I come to the conclusion that God exists and I claim to "know Him truly"..don't I have to assume that my conclusion is true in order to "know Him truly" in the first place?..since "bare intellect" can't bring me to such a sure conclusion?

Isn't all faith circular anwyay...it can bring you to any conclusion that you have faith in...and if it doesn't..than you didn't really have faith, did you?

NotReady
05-29-2007, 08:12 PM
[ QUOTE ]

isn't this a circular argument?


[/ QUOTE ]

The difficulty with circular arguments has to do with logic. It isn't that circularity is false but that it doesn't say anything - A=A is true but so what? There is a difference when the issue concerns matters of ultimate truth, but that's another ball game.

Faith isn't part of a logical argument so circularity isn't involved. In my example the argument would be that the Bible says God makes Himself known to all through what has been made. If you believe the argument you respond in faith. Not exactly accurate but adapted to illustrate why your objection doesn't apply.

NotReady
05-29-2007, 08:45 PM
[ QUOTE ]

.does anything change when we have only one shot, rather than many or an infinte number of them?


[/ QUOTE ]

Not after the fact. You deal a bridge hand and the odds are it won't be X - but X is dealt. Since you know how the hand came about and the hand you dealt was possible there's nothing unusual. If you deal an infinite number of hands you will get every possible hand an infinite number of times. The reason none of this applies to the universe is we don't know through human knowledge how the universe came about or even that it's possible for it to do so without a designer. It's useless to talk about the probability of an event when we don't know the possibility of the event.

Look at this quote from a probability tutorial on the web:

[ QUOTE ]

Calcuating theoretical proability requires a detailed knowledge of the experiment you are considering.


[/ QUOTE ]

[ QUOTE ]

but what if she decided that she would only play it once..and she wins it..now is there cause (or at least more than in the first case) to suppose an unknown influence here?


[/ QUOTE ]

First, you know the probability. Second, the more improbable (correctly calculated) the more you might suspect something besides an independent trial. Again, none of that applies to the anthropic issue.

[ QUOTE ]

I'm also not sure why he specifically considers various theories such as the multiverse theory as metaphysical


[/ QUOTE ]

I only scanned the article but I believe he refers to the Anthropic Philosophy as metaphysical because there's no scientific evidence for it. It's a speculation, an attempt to give something besides God ultimate explanatory power.

[ QUOTE ]

and he also used this as justification from introducing his own metaphycial theory


[/ QUOTE ]

Craig doesn't need an excuse to talk metaphysics - he's a Christian. /images/graemlins/cool.gif

[ QUOTE ]

again, I'm not sure why we are putting God here...shouldn't we just be lumping God in with all other unknown causes unless we can find evidence for God specifically?


[/ QUOTE ]

But then there's the anthropic principle - Craig says it's either a Designer or the WE, and he asserts God makes more sense. My own approach is to focus more on the consequences of each position - the multiverse can never provide a foundation for human values, etc.

[ QUOTE ]

His firing squad analogy is interesting...


[/ QUOTE ]

I was reminded of that scene in Pulp Fiction - the Sam Jackson character was convinced it was a miracle but Travolta didn't see it that way. I suppose you could calculate the probabilities here, at least approximately - but that's always going to be the case with any miracle.

[ QUOTE ]

what I am trying to figure out though, is how we could conclude that an unknown cause IS responsible or at least likely to some degree.


[/ QUOTE ]

We will never be able to figure that out scientifically. Remember my apple example? You don't know that God's activity isn't necessary even for gravity to work.

Newton had some interesting thoughts on this subject:

[ QUOTE ]

Related to Newton’s notion of the sensorium Dei is his hint in the General Scholium that God is the cause of gravity. Although cautious in this public document, in private he presented his theological speculations on gravity much more openly. For example, he told the Scottish mathematician David Gregory that he believed the ancients understood God to be the cause of gravity


. God’s omnipresence also provided an explanation for the phenomenon of gravity and in private Newton speculated that God was the upholder of universal gravitation. Newton saw the Deity as a God of dominion who ruled creation continuously, intervening with particular providence when necessary. Here Newton’s view of the providence of nature stands in stark contrast to that of Gottfried Leibniz, whose Supramundana used his supreme intelligence and perfect foreknowledge to set the world in motion at creation, obviating the need for intervention.


[/ QUOTE ]

One thing for sure, Newton was no Skanskian.

Metric
05-30-2007, 01:09 PM
This may be slightly beside the point of the main question, but with regard to certain statistical cosmology questions, the anthropic principle doesn't help at all.

Or rather it does help slightly in the sense that the conditional probabilities for getting a universe like ours given our existence are indeed higher than those obtained from the assumption of complete randomness.

However, these conditional probabilities are still so small as to leave exactly the same qualitative problem. The statistical state of the universe is just bizarrely improbable, with or without the probabilities modulated by the anthropic principle.

And btw, getting the probabilities up to something as high as one in a million would be considered a great triumph. They are much more like one in a googolplex!