By Will GreenIf we have free will, then we have something that has several unusual attributes.
One feature of free will is that it separates the possibility of something from the probability of it.
We normally think that if something is possible then there's a probability we could give to it happening. For instance, if there's a chance that something will happen at every moment, then eventually it will happen over an infinite length of time. So given an eternity a computer randomly putting letters together will assemble the complete works of Shakespeare, by accident (maybe after 10 to the power of a googolplex years, but eventually...)
Let's apply this thinking to free will and see what happens. Suppose that God made everyone live forever, in comfort and safety, on a planet like Earth.
If we have free will, and have the resources to build a lot of things, then it should be possible for all of us to decide to build a mountain out of books in every year of that eternity.
But does everyone have to build a mountain out of books in an eternity? If we have free will, then you'd have to say no. Because if we have free will, then in each year in that eternity we must be able to reject that idea. So maybe a lot of people won't ever build the book mountain, regardless of how much time passes.
Just because it's possible for everyone to make a book mountain doesn't mean everyone will eventually do so over an eternity, given true free will. So, with free will, a possibility can always exist with zero probability of it happening given the determination never to do it.
Read original post
Recommend
Comments (14)
Even though I agree in principal, this was a strange post. I'm not sure what relevance this has. If there was a more specific application you were writing this in relation to, you should have mentioned it.
In an experiment a couple of decades a group of monkeys did better on the stock market than a group of stockbrokers. In a more recent experiment, a couple of years ago a parrot out did the stockbrokers too. Maybe free will isn't all it's made out to be. :)
I once had a dream. I don't often remember dreams but I woke from this one in a peculiar manner. In the dream I was in an unfamiliar hall with seats and a stage. There was artwork on the wall and I was surrounded by people I didn't know. We were all waiting with great anticipation for someone these people all knew but I didn't know yet to show up on the stage but he didn't show up. About 12 years later I found myself in that very hall with that artwork on the walls, surrounded by those people, waiting for someone to show up. He didn't show up but that happened in a way that I did not imagine from the dream yet now it made perfect sense. It adds a different spin to the idea of free choice. I did choose to go to that hall 12 years after the dream but I had no idea this would be the hall in the dream nor was I thinking about the dream until it dawned on me when I was in the hall. Time and free will can be tricky things.
I'm not sure I follow. I think that if we have no free will, and our decisions are determined entirely at random, then yes, over an eternity, one would eventually have to perform X, where X is any action one is capable of for the entire course of that eternity. Such as building a mountain of books. But I don't believe in true free will or true randomness (or God for that matter), as I think either would violate causality. And causality is the key to understanding this. Our thoughts and actions are as subject to causality as anything else. The intent to perform X is the another of the resources, and just like the physical resources required to perform X might never accumulate, the intent to perform X might never develop. ("Might", as far as any of us know. Though in reality I don't believe there is any "might" about it. It either will or it won't.) In any individual, or in a given individual.
According to my Calc. teacher, the statement that a computer randomly placing letters together will not necessarily ever construct the complete works of Shakespeare.
I'm not entirely sure I agree with the premise of this post. The entire concept of free-will theology is questionable to me. Because many times (though not always) it assumes unlimited free will, however the only thing that I can see from the scriptures point of view is a free-will concerning our aliegiance or rebellion towards God. However, once a side is chosen, the scripture actually teaches limited free will in that you are then restricted in your action.
Romans 7-8, Galatians 3(?), and 1 John (can't remember the chapters) actually teach that those who are of the flesh cannot live righteously while those who are in the Spirit cannot live fleshly.
The only choice we have is whether to accept the Lord which leads to righteousness in Him, or reject him and live in our flesh, which leads away from righteousness (etc).
"If there was a more specific application you
were writing this in relation to, you should have mentioned it."
Yes, the context is that it's part of a series of posts I have been doing exploring the nature of incompatibilist free will. A really interesting kind of free will - one that people unconsciously believe in - implies several 'true contradictions', like the possibility/probability paradox above. I think this is because God hasn't seen fit to allow, or cannot allow, our intellect to understand fully what He has given us. But it's interesting to look at the various paradoxes even though I don't think we can ever get very far in understanding them.
"Because many times (though not always) it
assumes unlimited free will, however the only thing
that I can see from the scriptures point of view is a free-will
concerning our aliegiance or rebellion towards God. However, once a
side is chosen, the scripture actually teaches limited free will in that
you are then restricted in your action."
The Bible certainly teaches that our free will has been greatly damaged out of recognition by whatever the Fall was. So, I think it's something like, in a post-Fallen state we aren't able to choose to live according to moral principles consistently, because selfish reflections form a significant part of our decision making, and selfish reflections, by definition, cannot fit 100% perfectly with following moral principles. But couldn't we have a really amazing free will in a pre-Fallen state or after grace state? And could it be possible in principle?
This post doesn't make a lot of sense to me. (Also, based on previous conversations, I think that @TheSutraDude@xanga will benefit from reading my comment.)
Whenever we're assigning mathematical meaning to words or symbols, it's very important to clearly define that meaning. For instance, you use the words "possible" and "probable" throughout your post, but don't ever say what they mean. I think you are assuming that these words have a well-known mathematical meaning, and I'd like to clear that up here:
PROBABILITY: The probability that an event will occur is a number between 0% and 100%. An event that occurs with 0% probability will never happen. An event that occurs with 100% probability is assured to happen. Generally, an event is called "improbable" or "unlikely" when it has a small (but non-zero) probability of occurring. An event is called "probable" or "likely" if it has a large probability.
POSSIBILITY: Events that have non-zero probability are all possible. Only events that have 0% probability are impossible. Sometimes, though, an event occurs with such a small probability that it will probably not happen within the lifetime of the universe. Such events are said to be "effectively impossible."
In your first example of randomly putting letters together to write a Shakespearean play, I'd say that the probability is so low that this event is effectively impossible. Consider the question, "To be or not to be?" Let's ignore capitalization, punctuation, and spaces for the moment. In this case, there are 13 characters in the sentence. For each character, we have 26 options (letters A-Z). The probability of writing "To be or not to be?" by randomly choosing 13 characters is:
(1/26)^13 = 0.000000000000000004%
If we generate one 13-character string every second, it would take a little less than 80 billion years before we could be certain that we generated the sentence "To be or not to be?" For comparison, the universe has only existed for about 14 billion years. And this ignores spaces, capitalization and punctuation!
Regarding your second example about building mountains of books, this task is clearly impossible. Suppose a mountain has a height of about 1 mile and a diameter of about 5 miles. Then the volume of the mountain is about 27 billion cubic meters. If it is made of books (paper) with a density of about 1 g/cm^3, then the mountain of books will weigh about 27 billion tons. For comparison, there is only about 2 billion tons of "crop biomass."
That is, if the paper is made out of plants (trees), we would need about 10 times the number of plants found on Earth just to make one single mountain of books... The process of building one book mountain each year for eternity clearly has 0 probability.
Probability theory and quantum mechanics have very interesting (and controversial) implications as far as free will, determinism, and predestination are concerned. I'm happy to see this pop up on revelife, but I think you should choose better examples...
As it's written, I'm not even sure what your conclusion is. Are you saying that free will can affect the probability of an event occuring? Because the probability of an event happening is the same whether or not the event actually take place.
I was thinking about the Shakespearean play issue on my bike ride to work this morning, and I realized I made some stupid assumptions. If the computer program doesn't throw out bad guesses (i.e., it really just guess sequences of randomly chosen letters), then the average number of guesses the computer will need to make before guessing the sentence "To be or not to be?" is 26^13 (ignoring spaces, capitals, and punctuation).
A good desktop computer can perform a single operation in about 1 billionth of a second (the speed is referred to as the FLOPS of the processor). Guessing a 13-character string will take about 13 billionths of a second, and so the total amount of time you'd need to wait for the computer to randomly create the string "TOBEORNOTTOBE" would take
1,000 years!
If you include spaces (but continue to ignore capitalization and punctuation), then there are 27 total characters in the alphabet, and 18 characters in the desired string. In this case, the amount of time it would take your computer to randomly create the string "TO BE OR NOT TO BE" would take
33,000,000,000 years!
The time is takes increases exponentially with the number of letters. So, the end result is the same: Randomly guessing a Shakespearean play is effectively impossible. I know you probably don't care *that much* about the real numbers, but I felt compelled to correct myself...
@jim_the_american@xanga - Maybe those examples could be a bit punchier, but I think the underlying point is still valid. When I said 'mountain' I meant a pile of books maybe 3 or 4 metres high, in my mind, I suppose I should have said 'small mountain', because it is meant to be even not too terribly difficult.
@willgreen - It's not that your examples weren't "punchy," they just didn't make sense. (Even if it's a small pile of books, you couldn't do it for eternity because you'd eventually run out of books.)
I'm not sure what your underlying point is. Are you saying that free will can change the probability that something will happen?
If this is your point, then I fundamentally disagree. For instance, the probability that a computer will randomly select 13 characters and come up with the string "TOBEORNOTTOBE" is still 0.000000000000000004% regardless of whether or not such a computer program is actually written.
In fact, you could even say that the probability of an event happening affects how I use my free will. For instance, I will never bother writing a computer program that will randomly guess letters and wait for it to write a Shakespearean play because I know how unlikely it is to be successful.
@jim_the_american@xanga - My point is that with genuine free will something that makes sense as an option can always be possible for you to do. So it's possible, but you may never choose to do it. So if you may never choose to do the thing that makes sense as an option, then it's probability is zero if you keep up saying 'no' to it for an eternity (the small mountain is a one time event, by the way). Because over an actually infinite length of time any non-zero probabilities must happen. But it's still possible. So possibility gets disconnected from probability with free will.
@willgreen - I'm not sure how you are using the words "possible" and "probable" in this context.
There is something in mathematics called conditional probability. (What is the probability that event A occurs given that event B occurs?) The probability that a computer program will randomly write "TOBEORNOTTOBE" is very small, but *given that I never create the program* the probability is zero.
I don't think this is a clash between the concepts of free will and probability; it's merely a statement of the fact that some events have necessary preconditions. For example, the computer program needs to be written, the lotto ticket needs to be purchased, etc., for the statistics to apply.
*If you don't buy a lotto ticket* the probability of winning a cash prize are zero. *If you do buy a lotto ticket* the probability of winning a cash prize is about 20% (depending on the details of the game). But whether or not you purchase the lotto ticket has no bearing on the fact that one in every five has a cash prize.
There are some cool (and controversial) effects of "free will" on probabilities. For instance, there is something called the Quantum Zeno Effect whereby an observer can indefinitely extend the lifetime of an unstable particle just by looking at it over and over again. I'm actually not sure if this fits into the "free will" category, but it's a cool effect that I thought you might be interested in learning about.
@jim_the_american@xanga - Ah, so maybe if I become determined that: "I will never build a small book mountain in an eternity, not even once" then the probability is zero because any probability is conditional on me not refusing to participate in such a choice. So the probability of it happening is zero and, indeed, it will never happen. But even so, even if the probability is zero, it's still possible for me to overturn my determined decision if I have free will, even though I won't in practice. But then have I really determined never to do it? I'm not exactly sure where that leaves this idea...
The Quantum Zeno Effect is interesting, thanks for mentioning it. I might mention also that I think quantum mechanics indicates that free will can exist, because it allows for reality to be essentially 'not fully determined' within a person's neural networks (which are small enough to have quantum mechanics apply to them) until they make a choice, thus allowing free will without contradicting (as is traditionally assumed) the laws of physics.
@willgreen - Yeah, I like where this is going... Probability theory is very good at making statements like the followinf:
"If Bill decides to write a computer program that randomly puts letters together, then the probability of writing the sentence TOBEORNOTTOBE is very small."
But probability theory cannot tell us about the likelihood that Bill will actually write the program, because Bill's decision depends on his use of free will. (I wonder, though, if we had information about all the factors influencing Bill's decision, could we estimate the probability that he would write the program?)
...
Determinism is the belief that, given the current state of things and all the relevant physical laws, we can predict the future state of things. Quantum mechanics is deterministic *until we make a measurement,* This is called the measurement problem, and it is connected with the fact that we don't quite know how to include the "observer" as part of the system.
How does free will manifest in QM? I don't know... Do the electric discharges in our brains determine how we feel, or does how we feel determine the electric discharges?
@jim_the_american@xanga - I believe it can be considered part of the same problem of how consciousness manifests in an otherwise purely physical universe, because you always get consciousness whenever you have any kind of free will. One helpful way of looking at the consciousness problem involves looking at consciousness as a special kind of information: instead of information that purely describes something (like the shape of a rock) one kind of information also has an experiential quality - qualia.
But you can't just say consciousness is a peculiar type of information that's experiential, otherwise you are potentially giving consciousness to rocks, and a consciousness that cannot 'will' anything doesn't fit with our intuitions of what consciousness is. So, probably, consciousness has to go beyond categories of information and becomes its own object, in addition to information. So, from an intuitive point of view, I'd guess that how we feel must partly determine the electric discharges, as consciousness can't be reduced to a certain kind of physical information.