posted
Many have mentioned it, but there is a fundamental problem with this conversation, that being how muddled the definitions and usages are of these terms.
I agree with what Javert said above about the two. Atheism is defined as lack of belief in a deity. Agnosticism is defined as the view that the existence of a deity is unknowable. Under those definitions I am both an atheist AND an agnostic.
Then there's the point that has been made that it's unscientific to claim anything with 100% certainty. But that's really a technicality since we don't make that distinction in regards to any of our other beliefs, so why harp on it in this situation?
But that's not how those terms are used in practice today. In practice, an atheist is someone who doesn't believe in god. And an agnostic is someone who doesn't know, or who is unsure. It's a soft version of atheism. I tell people I'm an atheist because calling myself an agnostic would give people a false impression of my beliefs.
As for the extraterrestrial life conversation. I'm not sure if this has been specifically mentioned, but it's worth pointing out the distinction between "intelligent" life, and any dorm of life.
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I agree that the muddled definitions are a problem, but my argument is that there's a particular set of defintions that the world would benefit from widespread adoption of.
Strong Atheism (I believe there is no God)
Soft Atheism (There is no God that I know of)
Strong Agnosticism: I believe it is philosophically impossible to know whether God exists or not
Soft Agnosticism: I currently haven't examined all the evidence for or against God, and consequently I still believe there is a reasonable chance of both God's existence and non-existence.
There might be better ways to word the above, but I think the gist is there.
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Russell spoke of the problem, and his solution seems reasonable to me:
quote:Here there comes a practical question which has often troubled me. Whenever I go into a foreign country or a prison or any similar place they always ask me what is my religion.
I never know whether I should say "Agnostic" or whether I should say "Atheist". It is a very difficult question and I daresay that some of you have been troubled by it. As a philosopher, if I were speaking to a purely philosophic audience I should say that I ought to describe myself as an Agnostic, because I do not think that there is a conclusive argument by which one prove that there is not a God.
On the other hand, if I am to convey the right impression to the ordinary man in the street I think I ought to say that I am an Atheist, because when I say that I cannot prove that there is not a God, I ought to add equally that I cannot prove that there are not the Homeric gods.
quote:Originally posted by Raymond Arnold: For a long time that was the way I thought about it to (I called myself Agnostic for a while), but the argument that eventually persuaded me that was kinda silly was the whole unicorn thing. Is there a meaningful distinction between believing that unicorns are not real versus not believing unicorns are real? Is there a meaningful distinction between believing that gravity is real vs not believing that gravity is not real?
Seriously, no. If belief in God was not so ingrained in public consciousness and the word atheist didn't have any stigma attached to it you wouldn't be worrying about it. But the only way for the stigma to end is if people stop shying away from the word.
I'm not sure if it matters that the reason we're making the distinction is that belief in God is so ingrained. Context matters. We cannot escape it. God made or may not exist as a distinct supernatural entity, but he exists in the hearts and minds of people and culture. That is the context against which we define these words and apply the meanings.
I'm not sure where stigma came into the conversation, though. In my experience, both atheist and agnostic carry a stigma, or neither do, depending upon who you ask. The distinction between the two largely matters to those who use the labels.
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It is probably just our lack of understanding, but it is hard to imagine the universe not being infinite.
I mean, what would happen if you got to the "end" of the universe? Would you fall off?
Another theory I have heard (but don't give much credit to) is the whole "worlds within worlds" idea. Our solar system is actually an atom or our galaxy/universe are actually just cells and molecules in some other "bigger" object. Then again, this would have to eventually have a limit as well.
As for life on other planets, I fully believe that there it exists. Just from what we know right now, there are billions upon billions of stars and planets out there. It would be possible that some life forms are in different stages of evolution or progress than we are.
In terms of the progress of the way man understands the universe, in my opinion mankind went through a period of stagnation in the middle ages. There were a few technological discoveries but as a whole we stayed the same for over a thousand years.
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Raymond, for the most part I think your definitions are useful, but I have a problem with your putting strong atheism in the language of belief. And only because I have heard too many arguments from religious folk that go something like, "well, to 'believe there is no god' is to have a belief, and a belief is based on faith, so therefore your atheism is a sort of faith".
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the flaw in their argument is "belief is based on faith." Sometimes it is, sometimes it isn't.
There are strong atheists who really haven't given it enough thought to have rationally come to their conclusions. That's not the same kind of faith as religion usually implies but it's there. There's also people who have done exhaustive research and are justified in saying so with no faith needed. (In this conversation I don't think I need to include the disclaimer "trust that academic papers were completely and peer reviewed honestly is not the same thing as faith").
I think that Dawkins is justified in having Strong Atheism regarding a God who is omnipotent, compassionate and omniscient (I share that opinion with him). I think he's less justified in Strong Atheism regarding other definitions of God, with the degree of not-justified-ness depending on which God we're talking about.
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quote:Originally posted by Alcon: Well, but the cosmos are infinite. So if you run the 1 in 10^18 an infinite number of times doesn't that mean there's a 99.9999...% chance of at least other spawning of life out there somewhere?
A misunderstanding of the meaning of statistics. If there's a 1/6 chance of rolling a 4 with a 6-sided die, does that mean that rolling it 6 times will guarantee a 4?
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quote:Originally posted by Strider: Atheism is defined as lack of belief in a deity.
Denotatively, yes, but it's used as a presence of belief that there is no deity. Which is a very different thing. Someone who simply lacks theistic belief might as well be called an agnostic.
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Lisa, see the definitions listed a few post above, paraphrased from fairly standard definitions used in philosophy. Also see the numerous arguments posted by various people as to why those definitions are more useful.
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What would constitute "evidence" for extraterrestrial life?
The reason I ask is that pretty much the simplest, low tech thing we've done to search for biologically significant compounds in space came back positive for glycine.
Granted, that's not the same as finding a critter, but it's pretty darned tantalizing. I'd call it preliminary evidence pointing toward "yes" rather than "no."
We'll have some interesting things to think about in the next few years as our probes and space-based telescopes seek out new life (if not actually new civilizations). If we find complex compounds in large numbers, how did they get there? Is there a non-cellular mechanism for self-replication? Or, are we going to have to propose that these compounds were "made" inside a living critter of at least the level of complexity of an organelle?
Are prions a model for the kind of "proto-life" that we'd detect passively in space? Maybe all that's required is primordial soup kitchens somewhere.
It's going to be an interesting decade.
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quote:Originally posted by Strider: Atheism is defined as lack of belief in a deity.
Denotatively, yes, but it's used as a presence of belief that there is no deity. Which is a very different thing. Someone who simply lacks theistic belief might as well be called an agnostic.
And agnostic is also used to refer to someone who believes that the question is fundamentally unknowable. It seems more of a stretch, then, to use that term to refer to someone lacking in belief than it does to apply a term that can also mean belief in the lack.
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On the intelligent life and/or statistics note: Rolling a six sided die 6 times does not guarantee a 4. But it is also reasonable to assume that a 4 will probably come up, and even more reasonable to assume that if I were to roll the die 10 or 20 or several billion times that it would come up eventually.
Given the evidence we currently have about how life occurs, it is mathematically likely that there is life out there. Somewhere. Even if that life is just algae. That is far more evidence than we have of God.
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quote:Originally posted by Strider: Atheism is defined as lack of belief in a deity.
Denotatively, yes, but it's used as a presence of belief that there is no deity. Which is a very different thing. Someone who simply lacks theistic belief might as well be called an agnostic.
That is why I try to never say, "I believe there is no God." That can be taken very differently from "I don't believe in God".
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Given the evidence we currently have about how life occurs, it is mathematically likely that there is life out there. Somewhere. Even if that life is just algae. That is far more evidence than we have of God.
I am still sort of in the middle on this one. My issue is that we don't know the math. A lot of things happened to allow life here, the list goes on from the outer gas giants to possibly even having a moon. I keep hearing that if one little detail, out of hundreds, was off there would be no life, let alone intelligent life.
I used 1 in a billion billion arbitrarily. We could very easily be alone based on the same statistics. Say there is a 1 in whatever number of stars there are chance? We don't really know.
Its the main reason I can't stand the Drake equation. You can put in all the numbers you want, but most are just made up.
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quote:Originally posted by Strider: Atheism is defined as lack of belief in a deity.
Denotatively, yes, but it's used as a presence of belief that there is no deity. Which is a very different thing. Someone who simply lacks theistic belief might as well be called an agnostic.
That is why I try to never say, "I believe there is no God." That can be taken very differently from "I don't believe in God".
Why? "I believe there is no god" isn't the same as "I know there is no god," but I don't see how the distinction you're making really matters. "I believe I will live through tomorrow" and "I believe I will not die tomorrow" are pragmatically saying the same thing.
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quote:Originally posted by Strider: Atheism is defined as lack of belief in a deity.
Denotatively, yes, but it's used as a presence of belief that there is no deity. Which is a very different thing. Someone who simply lacks theistic belief might as well be called an agnostic.
That is why I try to never say, "I believe there is no God." That can be taken very differently from "I don't believe in God".
Why? "I believe there is no god" isn't the same as "I know there is no god," but I don't see how the distinction you're making really matters.
It doesn't to me, but some religious people like to latch on to it. Say you believe there is no god, and they will call it a belief, not knowing.
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quote:Originally posted by TomDavidson: I think it's "rational" vs. "irrational."
The rationality card is one I'm reluctant to play. Certainly I agree that it is 'locally irrational' to take the objective evidence for god (such as it is) and conclude that god exists. However, consider the following scenario: Mike was brought up in a devout, church-going family and feels a great sense of well-being practicing his religion. He also greatly values the church-going community and feels a deep sense of satisfaction in the performance of activities within this community. He has the very rational desire that his life go as well for him as possible. If he were to allow himself to be convinced by a wandering atheist of the non-existence of god, his life would be notably worse off: being honest he would feel like a fraud if he mislead his family and community as to his beliefs (or lack thereof); if he reveals his true feelings he would be ostracized. Ergo it is irrational for him to allow himself to be convinced by the atheist.
For myself, I have, a priori, no interest in deconverting believers; I would be content with the acknowledgment that there is a significant subjective component to their beliefs. Hopefully such an acknowledgment would engender restraint (or, better, the cessation) of the enforcement of religion-based limitations on others.
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quote:Originally posted by Stephan: Its the main reason I can't stand the Drake equation. You can put in all the numbers you want, but most are just made up.
A number of them are pretty much made up if we try to plug them in now, but that doesn't make the equation itself faulty.
Personally I've always just viewed it as an attempt to pin down the factors involved. If there are people attempting to actually use it to arrive at an answer, then I agree that the attempt is flawed.
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quote:Originally posted by Stephan: Its the main reason I can't stand the Drake equation. You can put in all the numbers you want, but most are just made up.
quote:Originally posted by Alcon: Well, but the cosmos are infinite. So if you run the 1 in 10^18 an infinite number of times doesn't that mean there's a 99.9999...% chance of at least other spawning of life out there somewhere?
A misunderstanding of the meaning of statistics. If there's a 1/6 chance of rolling a 4 with a 6-sided die, does that mean that rolling it 6 times will guarantee a 4?
Absolutely not. About 33% of the time you will never roll a four. This can be calculated using poisson statistics.
But Alcon isn't totally wrong, Lisa. The likelihood of an null result of a non-zero probability for an infinite number of trials is simply 0.
But we shouldn't be using infinity for our number of trials and one can't spit out a random number (like 1e-18) unless you have some thought behind it.
For one, there are about 10^11 stars in our galaxy. Dealing with other galaxies involves looking into the past too much for my taste.
When calculating these sorts of probabilities properly, scientists do consider the distribution of all possible outcomes and the likelihood of a null result. One in a million for a 100 billion stars? You can calculate the likelihood of 0,1,2,3,4,5,6,7,8,9 ... systems, but the odds of that are low because the mean of that distribution is 100,000.
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quote:Originally posted by Strider: Atheism is defined as lack of belief in a deity.
Denotatively, yes, but it's used as a presence of belief that there is no deity. Which is a very different thing. Someone who simply lacks theistic belief might as well be called an agnostic.
Not even denotatively. Merriam Webster defines atheism as "a disbelief in the existence of deity" or "the doctrine that there is no deity".
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quote:Originally posted by Strider: Atheism is defined as lack of belief in a deity.
Denotatively, yes, but it's used as a presence of belief that there is no deity. Which is a very different thing. Someone who simply lacks theistic belief might as well be called an agnostic.
That is why I try to never say, "I believe there is no God." That can be taken very differently from "I don't believe in God".
Why? "I believe there is no god" isn't the same as "I know there is no god," but I don't see how the distinction you're making really matters.
It doesn't to me, but some religious people like to latch on to it. Say you believe there is no god, and they will call it a belief, not knowing.
but even in your preferred method, you still seem to set up the existence of god as the default truth statement, which you don't believe in. my original definition side steps that issue. Again, acknowledging that for all practical purposes I would never answer a question about whether i think god exists with "i lack a belief in the existence of a deity".
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quote:A misunderstanding of the meaning of statistics. If there's a 1/6 chance of rolling a 4 with a 6-sided die, does that mean that rolling it 6 times will guarantee a 4?
No it's not a misunderstanding of statistics. Infinity is it's own mathematical class of numbers with their own properties.
Rolling it 6 times does not by any means guarantee a 4. In fact, there is a definite probability of achieving a 4 any given number of times when rolling a 6 sided die 6 times.
However, in an infinite number of trials the probability that an event won't occur - no matter how small the probability of that event occurring - drops to zero.
It's like limits in calculus. The value of a broken function at a point might be 5, but the value of the limit of the function as you approach from the right could be 4. As you get infinitely close to the point when out hitting the point, you get infinitely close to 4.
That's partly why the argument falls apart if the universe isn't infinite. Because as soon as it becomes finite, it no longer applies and there's a very definite probability of other life existing in the universe.
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quote:A misunderstanding of the meaning of statistics. If there's a 1/6 chance of rolling a 4 with a 6-sided die, does that mean that rolling it 6 times will guarantee a 4?
No it's not a misunderstanding of statistics. Infinity is it's own mathematical class of numbers with their own properties.
Rolling it 6 times does not by any means guarantee a 4. In fact, there is a definite probability of achieving a 4 any given number of times when rolling a 6 sided die 6 times.
However, in an infinite number of trials the probability that an event won't occur - no matter how small the probability of that event occurring - drops to zero.
It's like limits in calculus. The value of a broken function at a point might be 5, but the value of the limit of the function as you approach from the right could be 4. As you get infinitely close to the point when out hitting the point, you get infinitely close to 4.
That's partly why the argument falls apart if the universe isn't infinite. Because as soon as it becomes finite, it no longer applies and there's a very definite probability of other life existing in the universe.
My understanding of Lisa's point is that the fact that something has probability 1/x of happening does not imply that it necessarily occurs after N>>x experiments (although I'm not sure why she used only 6 rolls instead of, say, 10 000 rolls to make this point).
Anyways, an event having probability one does not mean that it will occur. For example, the probability of randomly selecting an irrational number when picking a number from the interval (0,1) is 1. However, there are quite a few rationals in this interval.
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Heh, this thread is proving a pretty good example of the point Bob posted on the first page. I mean, really, suppose the universe is infinite in reality. How would such a thing ever be proven? In fact how would something ever be measured infinite conclusively?
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You would keep trying to measure or determine it's finiteness to the best of your ability, and continue to conclude that the universe might be infinite.
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quote:Originally posted by natural_mystic: My understanding of Lisa's point is that the fact that something has probability 1/x of happening does not imply that it necessarily occurs after N>>x experiments (although I'm not sure why she used only 6 rolls instead of, say, 10 000 rolls to make this point). [/QB]
It is true that it is always possible for x not to occur. But as N increases, the probability of getting a null result increases to something very very small.
Lisa's example is very bad because the very same formula that tells you that you have a 33% chance of not rolling a 4 after six rolls tells you that you have a 1.5 times 10^(-790) % chance of not rolling a 4 after 10,000 times (yes, I calculated it). Sure, it's still possible, but if you don't call that NEVER, then you are a very silly person. Most sane people will call a number 780 orders of magnitude larger never too. Lisa cherry picked her numbers to make her point work.
This very same formula ALSO gives the result that Alcon suggests.
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quote:You would keep trying to measure or determine it's finiteness to the best of your ability, and continue to conclude that the universe might be infinite.
posted
My understanding is that space may be infinite, and is expanding, but that the actual things in space are finite. Some finite amount of matter/energy was generated at the big bang, and has gradually condensed into other finite things.
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quote:Originally posted by The White Whale: You would keep trying to measure or determine it's finiteness to the best of your ability, and continue to conclude that the universe might be infinite.
You know what? I can can conclude the same thing without having to do any tests or measuring! Posts: 16551 | Registered: Feb 2003
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quote:Originally posted by Strider: Atheism is defined as lack of belief in a deity.
Denotatively, yes, but it's used as a presence of belief that there is no deity. Which is a very different thing. Someone who simply lacks theistic belief might as well be called an agnostic.
Not even denotatively. Merriam Webster defines atheism as "a disbelief in the existence of deity" or "the doctrine that there is no deity".
Hmm. Never thought I'd say this to you, but thanks for the correction.
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quote:Anyways, an event having probability one does not mean that it will occur. For example, the probability of randomly selecting an irrational number when picking a number from the interval (0,1) is 1. However, there are quite a few rationals in this interval.
Hmm, I'm not sure, actually. The probability of choosing an irrational is definitely 1, and the probability of choosing a rational is definitely zero, but I'm not sure how it would work out. After all, the probability zero that something will occur does not mean it will not occur. Take the aforementioned space between 0 and 1 and consider the probability that any given number will be chosen. But I suspect the irrationals so dominate the space that the probability a rational number will be chosen truly is zero (and will never occur).
Alcon is also incorrect, of course. An event with probably > 0 is not guaranteed to occur in an infinite number of trials. For an easy proof, consider this: If we look at the result of the first coin flip (say), of an infinite number (that we did in advance), and it is heads, does this mean the next one must not be heads? (Answer: no). Now, if the N'th one is heads, does this mean the next one must not be heads? (Again, no). Therefore (by induction) it is not necessary for any of an infinite number to not be heads -- that is, they could all be heads.
Now, some infinite things have additional properties which guarantee inclusion. For instance, the infinite digits of pi contain every possible finite subsequence of digits, if I recall correctly. This isn't just because they're infinite, but because they're infinite and have certain other properties.
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quote:Alcon is also incorrect, of course. An event with probably > 0 is not guaranteed to occur in an infinite number of trials. For an easy proof, consider this: If we look at the result of the first coin flip (say), of an infinite number (that we did in advance), and it is heads, does this mean the next one must not be heads? (Answer: no). Now, if the N'th one is heads, does this mean the next one must not be heads? (Again, no). Therefore (by induction) it is not necessary for any of an infinite number to not be heads -- that is, they could all be heads.
Nope. Infinity trumps this.
Besides, it's impossible to have done an infinity of coin flips in advance. Posts: 16551 | Registered: Feb 2003
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quote:Now, some infinite things have additional properties which guarantee inclusion. For instance, the infinite digits of pi contain every possible finite subsequence of digits, if I recall correctly. This isn't just because they're infinite, but because they're infinite and have certain other properties.
quote:Actually, as it turns out there is a theorem which almost guarantees that Sagan's "fiction" about Pi is true. In particular, I have been referred to Theorem 146 in the book "An Introduction to the Theory of Numbers" by Hardy and Wright which proves that the set of numbers that do not contain every arbitrary finite sequence in their decimal expansion has measure zero. (In other words, if you "randomly" pick a number, you can expect its decimal expansion to contain every finite sequence including the Gettysberg Address and the next e-mail message that you will write written out in ASCII.) There is no guarantee that this will be true for the number Pi...but there is also no reason to doubt that it is true.
quote:Originally posted by Strider: Atheism is defined as lack of belief in a deity.
Denotatively, yes, but it's used as a presence of belief that there is no deity. Which is a very different thing. Someone who simply lacks theistic belief might as well be called an agnostic.
Not even denotatively. Merriam Webster defines atheism as "a disbelief in the existence of deity" or "the doctrine that there is no deity".
Yes, but look at their definition for "disbelief":
"to hold not worthy of belief : not believe" or "to withhold or reject belief"
That seems to include a mere lack of belief ("not believe").
Aside form dictionary definitions it seems that atheists largely go with the "don't believe in God" definition while theists largely seem to go with the "believe there's no God" definition. It seems like it's probably best to defer to those who self-identify with the term unless there is substantial disagreement within that group about the correct definition.
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m_p_h: no, it doesn't. Inductive proofs work just fine on infinities.
And, if we can do an infinite number of coin flips (or anything else) at all, we can certainly do it in advance of some later time. Otherwise it would only be the "finite number of things we have done on our way to an infinite number of things".
So, for infinity to "trump" that, you have to grant the possibility of having done an infinite number of things before checking the test
(Not that its actually necessary to have done them in advance; that just makes the language simpler).
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quote:Originally posted by Rakeesh: Heh, this thread is proving a pretty good example of the point Bob posted on the first page. I mean, really, suppose the universe is infinite in reality. How would such a thing ever be proven? In fact how would something ever be measured infinite conclusively?
You can't prove anything conclusively in science. You can make hypotheses and then gather evidence which will allow you to either support that hypothesis or reject it. But you still don't prove it. You just didn't find anything to suggest it's wrong, which means it's okay still okay to use that theory.
It's the reason why many atheists will admit they are agnostic about God's existence, but they don't believe in God. An atheist may not know that there is no God, but he or she operates under the assumption that God does not exist in daily life.
But back to what you said.
Astronomers see the universe as expanding because the redshifts of basically every galaxy besides Andromeda indicate that they are moving away from Earth. Much ::ahem:: smaller models can show that Earth does not need to be at unique place in the universe for this to occur. From any vantage point, everything will appear to recede in an expanding universe.
As for infinite, cosmologists talk about the universe being open closed, or flat. These are tricky to explain, but a closed universe is the one that will stop expanding and turn around and collapse back where it came from once it runs out of whatever kinetic energy is driving that expansion. Flat means that the universe will stop expanding, and open means expansion will not stop.
The way the universe expands is currently defined by something called the Friedman equation. Basically if you know how much stuff, light, curvature and "lambda" there is, then you know what the universe did and is going to do in terms of expansion. One big goal of cosmology is to figure out what those constants are using a whole host of different techniques (one is looking at the Cosmic Microwave Background) . Right now, things are pointing toward flat. But most of this stuff makes my head hurt, so I am not a cosmologist.
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quote:Originally posted by fugu13: m_p_h: no, it doesn't. Inductive proofs work just fine on infinities.
And, if we can do an infinite number of coin flips (or anything else) at all, we can certainly do it in advance of some later time. Otherwise it would only be the "finite number of things we have done on our way to an infinite number of things".
So, for infinity to "trump" that, you have to grant the possibility of having done an infinite number of things before checking the test
(Not that its actually necessary to have done them in advance; that just makes the language simpler).
Right. If you look at the space of all infinite sequences of coin flips, you have probability zero of instantiating that sequence containing only heads. However such a sequence still exists.
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quote:Anyways, an event having probability one does not mean that it will occur. For example, the probability of randomly selecting an irrational number when picking a number from the interval (0,1) is 1. However, there are quite a few rationals in this interval.
Hmm, I'm not sure, actually. The probability of choosing an irrational is definitely 1, and the probability of choosing a rational is definitely zero, but I'm not sure how it would work out. After all, the probability zero that something will occur does not mean it will not occur. Take the aforementioned space between 0 and 1 and consider the probability that any given number will be chosen. But I suspect the irrationals so dominate the space that the probability a rational number will be chosen truly is zero (and will never occur).
I would love to be able to truly randomly sample (0,1) to test this, but I'm pretty sure it's impossible given basic problems with irrational numbers. My point was just that having a set of outcomes having probability one does not preclude the existence of other (very unlikely) outcomes.
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quote:Originally posted by fugu13: [QUOTE] Alcon is also incorrect, of course. An event with probably > 0 is not guaranteed to occur in an infinite number of trials. For an easy proof, consider this: If we look at the result of the first coin flip (say), of an infinite number (that we did in advance), and it is heads, does this mean the next one must not be heads? (Answer: no). Now, if the N'th one is heads, does this mean the next one must not be heads? (Again, no). Therefore (by induction) it is not necessary for any of an infinite number to not be heads -- that is, they could all be heads.
The issue here is that getting N heads in the first place is unlikely and that unlikelihood is calculable. At some point statisticians and scientists draw a line about what is reasonable and what is not.
The point of flipping any coin an ungodly number of times is to see if the coin is fair. 10 heads? Could happen, but still unlikely 1 in 1024 chance. 10000 heads? Someone in Vegas needs to be held for questioning.
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quote:Ergo it is irrational for him to allow himself to be convinced by the atheist.
mystic, it's worth noting that here you're actually discussing a sort of meta-belief: the idea that a person, when choosing to believe something is true, might choose not necessarily the option with the highest personally-demonstrated truth value but rather the option with the highest observable personal benefit. While I personally believe that many people do have this kind of (conscious and subconscious) control over many of their own beliefs, I'm a little surprised that you agree.
Posts: 37449 | Registered: May 1999
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quote:Hmm, I'm not sure, actually. The probability of choosing an irrational is definitely 1, and the probability of choosing a rational is definitely zero, but I'm not sure how it would work out. After all, the probability zero that something will occur does not mean it will not occur.
I think it does, actually. The rationals are a set of measure zero; if you throw a Euclidean point randomly at a circle, what's the probability you'll hit its center? Zero. It just can't be done. This is counterintuitive to brains whose math modules evolved to count bananas, but still true.
However, once we're discussing numbers less than 10^-10, it's easier just to say "never", even though it's not strictly true. To do otherwise is fooling yourself; human brains cannot distinguish that finely, and so we end up calling 1% and 0.0000001% both "A small chance"; worse, we consider 0.0001% about as likely as 0.00001%. The mistake you make by calling all these numbers zero is much smaller than the mistake of trying to plug them into the intuitive machinery that deals with things like "My chance of sleeping with the alpha female". You can fool yourself very badly that way, as witness the profits from casinos and lotteries.
Posts: 10645 | Registered: Jul 2004
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If you had a perfect number spinner (from 0 to 1), what would be the probability of choosing any one number? Yet you can 'spin' it (notionally) and get a number.
If you propose any non-zero infinitesimal to me, I'll just note that then the probabilities sum up to more than 1.
Note: this trick doesn't even require anything beyond the rationals.
Posts: 15770 | Registered: Dec 2001
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posted
Yes, but the numbers from zero to one are not a set of measure zero; the rationals are. You cannot fire one Euclidean point at another and hit; that doesn't stop you hitting a circle with the point.
Posts: 10645 | Registered: Jul 2004
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posted
I think fugu's points is the following. Suppose you spin the wheel and get, say, pi/4. Prior to spinning the wheel, had I told you that you would get pi/4 (or pi/4 union the rational subset of (0,1)) you would have said, no, impossible, this set has measure zero.
Posts: 644 | Registered: Sep 2008
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posted
Well yes, and in fact you will never get pi/4. Spin the wheel as many times as you like. You can come arbitrarily close, but you won't get pi/4 exactly. And I am willing to make the identical prediction for any number you like. And nonetheless you will certainly get some number between 0 and 1, and you will get a number between 0 and 0.1 with 10% probability, and so on. I do not claim that this is intuitive, but it's still true.
Posts: 10645 | Registered: Jul 2004
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