|
On July 18 2013 05:03 Shiori wrote:Show nested quote +On July 18 2013 03:40 corumjhaelen wrote:On July 18 2013 03:36 Shiori wrote:On July 18 2013 03:31 corumjhaelen wrote:On July 18 2013 03:27 Shiori wrote:On July 18 2013 03:20 corumjhaelen wrote:On July 18 2013 03:16 Shiori wrote:On July 18 2013 03:13 Signet wrote:On July 18 2013 02:57 Shiori wrote:On July 18 2013 02:30 Signet wrote:
[quote]
It could be that the universe is ruled by cause and effect (eg laws of physics), but whatever "outside the universe" refers to is not.
Another argument - "cause and effect" itself is a basically a rule or law. If you were actually in a situation where literally nothing existed, then that law would also not exist. Therefore the first event did not need to have a cause. I think that both of these possibilities are basically meaningless. It's absolutely impossible to think of any situation in which causality doesn't exist, because there is no logical structure to such a space that can be hypothesized with any certainty. Agreed. While it's a fascinating concept, there doesn't seem to be much practical use in speculating about what goes on outside of the universe. Like, I mean, if I need to add a "assuming reality isn't fundamentally irrational" caveat to any argument I make regarding first causes or extra-universal properties, I'm totally okay with that. To me, the "maybe causality is an unnecessary feature of logic/reality/whatever" line of reasoning is only marginally better than "maybe the law of non-contradiction isn't true outside our universe" argument. I mean, yes, it's not impossible, but it seems to be largely a sophistical trick rather than possessing any explanatory power. And if I say that causality seems to be a principle of reason (Verstand), and thus only applies to the phenomenological world, and that we have no idea if it applies to the noumenal world, am I being a sophist ? :p No. But then, we have no idea if anything applies to the noumenal world. Thank you Immanuel for saving free will, somehow^^ But I think Nietzsche would have answered yes to that question, so it's not as easy as it seems. Edit : but I'm not sure at all free will exists though, just that something like it might exist. I'm not sure the phrase "free will" has ever really been made coherent. I'm tempted to say you can draw some statements from the Critic of Pure reasons that are coherent about this problematic, but I'm not sure it makes free will itself coherent. Well, Kant is awesome, but even he left us with the antinomy rather than an actual proof ><.
Well he "solves" it in a way, but yeah no proof, but no hope for any proof either if you believe him. Not that bad imo !
|
On July 18 2013 02:02 radscorpion9 wrote:Show nested quote +On July 17 2013 19:18 Rassy wrote:Noooooo Pls come back and make your contribution, the thread needs new input cause it seems to be slowly dying. Maybe because the majority here seems to agree that the mind is indeed all physical and with that there is no real discussion about the original question. We need new and interesting thoughts and someone making an account just to post on this thread gives me hope for just that  lol . If you're referring to skying I discovered that he was banned for advertising. Its so hard to think of an argument against determinism. Maybe the only thing that can be said, is that philosophically, if determinism is true then it leads to a paradox. Because determinism clearly necessitates cause and effect, so in theory that would lead to an infinite chain. But because infinity is too large to exist in nature (and we know a circle wouldn't work as the circle as a whole would need to come from somewhere), then theoretically there must be some alternative to cause and effect, and thus determinism can not be the only mechanism at work. Since this mechanism caused our universe to form, then it must exist at some fundamental level in our universe. Perhaps it just occurred once during the formation (i.e. the big bang), or maybe its ongoing, but we should see some non-deterministic relation that at least can't be explained. Now it may be hard to conceive what this is, much like its difficult to understand what a 4th spatial dimension would be. But scientists now have compelling evidence that there may be more than three spatial dimensions; and so although something is not conceivable, it could still be possible. If there actually is a timeless space that exists outside of our universe, this may be the realm in which this other mechanism exists (it would make sense, as cause and effect would seem to require time, although again perhaps there is another mechanism for this causality to occur besides time?). Its all extremely hypothetical...but maybe the infinity argument is somewhat persuasive. I hope I helped make this thread exciting
Interesting definatly.
Skying banned for advertising? well i guess it was his fate .
Infinity is one of the bigger phylosophical problems for me and there is no way i can get rid of it. No matter how i picture the universe it keeps popping up. The alternative for infinity is having a boundary, but a boundary is far from satisfying either. The only option to avoid both the boundary as well as the infinity is a curved universe, but this in the end leads to infinity again as i will show you.
Lets go on a verry long journey through the universe and all its dimensions,this will take alot of imagination though and probably not everyone will be able to follow it.
In this model the universe starts with a line ( i can make the model more refined by adding particles into this universe wich obey certain rules, particles like + - and 0 (for neutral) but this will make it verry complicated verry fast so i will leave that out for now)
Time in this universe is the 2nd dimension, and we can see this universe going through time as 1 line laid above the other and so on, creating a 2 dimensional space time (though we would see this universe only as a verry short blimpse, since this universe does not travel through our 4th dimensional time)
Now to avoid the infinity of the line, or a boundary by simply cutting it off, we can make the line into a circel.
The next time frame would then be a slightly large circle around the first circle and so on.
We have avoided the infinity of the line but now we have instead the infinity of an ever increasing (as it travels through time) 2 dimensional circular plane.
The highly intelligent beeings living on the line could even find proove for such a universe, they could for example somehow measure the curve of the line, and see that the curve decreases as they travel through time.
To avoid the newly found infinity we have to curve this 2 dimensional timespace into a sphere and the universe suddenly becomes alot more beautifull and understandable, the highly intelligent beeings in this universe come to the conclusion that long long ago the universe started as a very small circle in some event they call the big boom, and at one point in the future, when they see the curviture of their space increase again, they will come to the conclusion that their universe will end in a big crunch.
And there we have it, a finite universe without bounderys but it does not (have to) stop there.
This 2 dimensional sphere can then start moving through a new time dimension, the 3rd one wich could be visualised as a slightly bigger sphere over the first sphere, and so on as the 2 dimensional universe travels through time its newly found freedom, the 3rd dimension.
We get a solid ball stretching out till again infinity (though this universe would only be a blimp in our universe as it still does not travel through our 4 dimensional time) (also notice how the original 1 dimensional circle is still a part of this universe)
Next come the steps wich will require alot of your imagination, and thoose steps are verry difficult to make inside your head, but the analogy of the 1 and 2 dimensional universes should make it a bit easier for thoose who try.
To avoid the newly found infinity we curve this 3 dimensional ball again in the 4th dimension and suddenly we have something that is finite without bounderys again, a finite solid ball traveling through our 4th (time) dimension till ...infinity again.
To avoid this infinity of time the only option is to curve the 4 dimensional universe into the 5th dimension (this requires a huge amount of imagination, so dont feel bad if this does not work for you lol) and the original 1 dimensional circle universe has had manny big bangs and crunches by now. The 5th dimension goes to the 6th, to avoid the infinity of the 5 dimensional time space and then the 6th goes into the 7th, and so on till you have an infinite dimensional universe.
And I have not found anny way to get rid of this last infinity but i am open to sugestions.
This universe can be 100% deterministic in nature as well as stochastic in nature, depending on how you forumlate the rules by wich the particles obey.
|
On July 17 2013 17:53 Reason wrote:Show nested quote +On July 17 2013 13:52 wherebugsgo wrote:+ Show Spoiler +On July 17 2013 13:06 Shiori wrote:Show nested quote +On July 17 2013 11:12 wherebugsgo wrote:On July 17 2013 05:36 positronic_toaster wrote:
Here's a wacky idea, why are we so certain that our mind is a purely 3D construct? Who's to say that there's nothing going on in another dimension that is imperceptible by our senses? Which dimension would that be? You have to provide evidence for this dimension of yours before you assert that anything can exist in it. Or, better yet, that this dimension exists in the first place. The only "fourth" dimension I can conceive of is not a spatial dimension, it's the time dimension. In his defense, he said "who's to say" and "why are we so certain" rather than asserting that any particular dimension really does exist. Show nested quote +On July 16 2013 17:53 Reason wrote:On July 16 2013 10:01 neptunusfisk wrote:On July 16 2013 09:29 wherebugsgo wrote:On July 16 2013 07:34 Reason wrote:On July 16 2013 07:23 neptunusfisk wrote:On July 16 2013 07:15 Reason wrote:On July 16 2013 06:58 neptunusfisk wrote:On July 16 2013 06:44 Reason wrote:How does this : http://en.wikipedia.org/wiki/Almost_surely come into play with what you're saying there? The example given was what is the probability of picking a specific real number between 0 and 1? + Show Spoiler +Similarly, the probability that a random non repeating infinite sequence of integers contains every integer and every finite set of integers is 1 (almost sure). I don't want to go deep into those formal questions, but yes, probability is not always as easy as it seems. I'll leave my probability and set theory books unopened, but just let me say that if you handed me something perfectly random (it doesn't exist) and had some event with zero probability, I would agree to take poison if it happened. But as I said, the main problem is not in how to read the model, it's whether the model is relevant or not that's important here. Throwing a dart For example, imagine throwing a dart at a unit square wherein the dart will impact exactly one point, and imagine that this square is the only thing in the universe besides the dart and the thrower. There is physically nowhere else for the dart to land. Then, the event that "the dart hits the square" is a sure event. No other alternative is imaginable. Next, consider the event that "the dart hits the diagonal of the unit square exactly". The probability that the dart lands on any subregion of the square is proportional to the area of that subregion. But, since the area of the diagonal of the square is zero, the probability that the dart lands exactly on the diagonal is zero. So, the dart will almost never land on the diagonal (i.e. it will almost surely not land on the diagonal). Nonetheless the set of points on the diagonal is not empty and a point on the diagonal is no less possible than any other point, therefore theoretically it is possible that the dart actually hits the diagonal. The same may be said of any point on the square. Any such point P will contain zero area and so will have zero probability of being hit by the dart. However, the dart clearly must hit the square somewhere. Therefore, in this case, it is not only possible or imaginable that an event with zero probability will occur; one must occur. Thus, we would not want to say we were certain that a given event would not occur, but rather almost certain. So.... do you prefer arsenic or cyanide? The thing here is that I won't let you choose "all the points", as the probability for that is 1. If you can decide on one single mathematical point (with P(dart hits that point) = 0), then I'll agree to cyanide and arsenic at the same time. Sorry, I was only covering probability = 0. You do realise I'm just copy pasting all this stuff right lol? Here's P = 1. http://en.wikipedia.org/wiki/Almost_surely#Tossing_a_coin This article does a pretty poor job of covering what it means for a probability to converge to 1. The probability isn't actually necessarily 1, it converges to 1 under certain conditions. e: or 0 or any other probability, for that matter Yeah. And no, why would I take poison for something that is going to happen? That's just absurd. I could agree to the opposite and take that damn poison if you toss either heads or tails infinity times though. This is what you said "just let me say that if you handed me something perfectly random (it doesn't exist) and had some event with zero probability, I would agree to take poison if it happened." Tossing a coin is perfectly random and the dart example is zero probability. Not sure what you old men are grumbling about tbh. Obviously I don't actually want you to kill yourself. Show nested quote +I merely implied this earlier but I'll be more blunt now:
You don't seem to understand the difference between a probability actually being 0 and a probability converging to 0 under certain conditions. The probability actually is zero. It's just that probability being zero doesn't mean "cannot happen." For example, the probability of randomly selecting any particular real number in a trial is actually zero. It doesn't just converge to zero at a limit: it actually is a probability of zero. In fact, even a countably infinite number of trials has a zero probability of selecting any particular real number randomly. Nevertheless, a real number must be selected. The situations are different. I agree that the probability of randomly selecting a particular real number is zero. However, the probability of selecting any number within a range is NOT zero. That's what the meaning of the dart experiment is. No matter how you look at it, you're going to be selecting a range of values. That's why I disagree with the way the article talks about that experiment and the probability. The probability in that case converges to 0. It's not actually 0. On July 17 2013 13:06 Shiori wrote:Show nested quote +(also this doesn't even get into the problems of your thought experiment-in real life there are no things such as points because all measurement is imprecise. The question you're posing itself is meaningless. You need a dart with an infinitisemal point, which by definition doesn't exist-it's zero probability not because the dart will hit the square but not a point but rather that the dart doesn't exist to be thrown in the first place.) That's why it's a thought experiment; it's not supposed to be something one can actually do in real life. But if you think "almost surely" meaning probability of one is a meaningless question, then you're very, very wrong. I'm not sure what measurement has to do with the existence of points; a point is an object defined to have certain properties in a Euclidean space (i.e. zero-dimensional). This is a totally coherent mathematical definition. Sure, if you want to think of a dart with a dimensionless point hitting any given dimensionless point on a 2d plane then the probability of that occurring is 0. Do you see what I mean? It's a question of what does this experiment actually mean. It doesn't mean anything at all, it doesn't tell us anything beyond what we already assumed to be true. That's what I am alluding to when I am saying that this experiment is meaningless. On July 17 2013 13:06 Shiori wrote:Show nested quote +If you haven't made the connection yet that the dart needs an infinitisemal point, then realize that if the dart's point had some area (even a miniscule area) then when it hits the board that area covers a certain subregion. If the point is anywhere within the boundary we can consider the dart to have hit said point. Suppose the dart's point is circular, then you can see where I'm going with that. The board and dart are obviously idealized mathematical objects in a defined Euclidean space. But it doesn't change anything even if the dart actually does have non-zero area, since any particular orientation of that area on the dartboard has probability zero (since we can slice up any interval into arbitrarily smaller sub-intervals). Written in another way, the dart example could go like this: let the board be the Cartesian plane (i.e. 2 dimensions over the reals) and let a dart be a vector of the form (x,y) situated with its tail at the origin. Now choose any point in (a,b) in the space. The probability of a random vector passing through that point is zero. To generally prove the probability thing, just look at it this way: we've got some probability space, and then let's have f(n) be a probability function which outputs probability of getting at least 1 coin flip resulting in heads after n trials where n is a natural number and f(n) is a real number. If you are correct, and probability of a sequence of pure tails is infinitesimally small, but non zero, then you have a contradiction, because f(n) is always a real number, and the only infinitesimal in the real numbers is exactly zero. If a random finite sequence is generated, the probability of that sequence having been generated is zero, because there are an infinite number of finite sequences. This is not the same thing. Does the dart's point have some area or not? If it does, then the probability of the dart's point hitting a particular point on a 2d plane can be interpreted differently, as the chance that said point is contained within a region described by the shape of the dart's point. If the dart's point does not have any area (i.e. it too is also a point) then again, this experiment is pretty meaningless. I suppose you could say that it's nothing more than the pick a number experiment but I don't believe that was what he was suggesting. As to this:
To generally prove the probability thing, just look at it this way: we've got some probability space, and then let's have f(n) be a probability function which outputs probability of getting at least 1 coin flip resulting in heads after n trials where n is a natural number and f(n) is a real number. If you are correct, and probability of a sequence of pure tails is infinitesimally small, but non zero, then you have a contradiction, because f(n) is always a real number, and the only infinitesimal in the real numbers is exactly zero.
If a random finite sequence is generated, the probability of that sequence having been generated is zero, because there are an infinite number of finite sequences.
This makes no sense at all. "if a random finite sequence is generated, the probability of that sequence having been generated is zero" What what?? The probability of it having been generated is ONE. Because it got generated. Since n is finite, if you're talking about a fair coin flip, then the probability you get n - 1 tails and then a heads is just f(n) = 2^-n which is nonzero, just as with any other particular n-length sequence of heads and tails. It's not "infinitisemally" small. It's strictly nonzero. Also, if you mean that you've observed n tails in a row, what is the probability that you now get a heads...and we know for sure that the coin is fair, then the probability of the heads occurring is 1/2. Again, nonzero. You either have failed to communicate what you were trying to communicate or you need to consider remedial high school math. I'm not quite sure why you felt the need to come back and comment so strongly on a discussion that you feel is pointless, especially since from what I can tell a lot of what you're saying is incorrect. "I agree that the probability of randomly selecting a particular real number is zero. However, the probability of selecting any number within a range is NOT zero." The example given previously was pick a real number between 0 and 1. The probability of doing so is 0, just like the probability of picking any integer is 0, as there are infinite integers and infinite real numbers between 0 and 1. Two different questions with the same answer. Did you mean to write what you did? Dart example: + Show Spoiler +Also, with the dart, of course in practice you could not have a dart head small enough to hit only one point on the board because one point on the board has zero area. However if you can accept that the dartboard theoretically has a center point, or as the example mentioned a diagonal line, then you should be able to understand that you could throw a real 3d dart at the board and then take the center point of the dart tip itself, if the center point of the dart tip does not coincide with the center point or diagonal of the board then it could be said that the dart "missed" the target. Such an experiment never need be carried out in practice and is merely a way to explain things for people to understand, much like tossing a coin. There are much better ways of communicating the article's content than coin tossing and dart throwing but it's meant to be easy to understand for the majority. The real number example is fine and can be used to communicate probabilities of both 0 and 1 though neither will be certain events, so you can disregard the impractical dart experiment if you find it flawed. What is the probability of picking a specific real number between 0 and 1? It's 0. Pick a specific real number between 0 and 1. Now pick another at random. What is the probability that they are different? It's 1. I am aware what probability 0 means and probability 1 means if these are sure events. I'm also aware that if probabilities are converging to either 0 or 1 and the sample size is infinite then the probability is represented as a 0 or a 1. If I'm the one who is mistaken here please explain further as these are still relatively new concepts to me.
Perhaps I was unclear, but you took my comment on this:
However, the probability of selecting any number within a range is NOT zero. That's what the meaning of the dart experiment is. No matter how you look at it, you're going to be selecting a range of values.
Out of context.
Basically what I'm saying is that you're taking a range of values in a finite subset of the reals if you throw a dart at a board, assuming the board is of finite size and the dart's point is not dimensionless. The question is then what is the chance that this number you want is in that subset.
So, for example, let's assume the area of the point of the dart is huge for comparison. So large that it's half of the board's area. Then it's roughly equivalent to asking this:
Pick a number in the set [0, 1].
What's the chance that this number is in the set [0, 0.5]. The answer is clearly nonzero (it's 1/2 in this case).
Now, keep reducing the area of the dart, such that the limit of the area of the dart approaches 0 as its limit. You'll see that the probability converges to 0.
Clear enough?
If you want to talk about points coinciding with points then again, I say the experiment is meaningless because it doesn't tell us anything we don't already know (i.e. it's alluding to a property of R) In other words, if your experiment was this:
http://math.stackexchange.com/questions/155156/is-it-generally-accepted-that-if-you-throw-a-dart-at-a-number-line-you-will-neve
Then I agree, though again, I find it meaningless probably because I am inclined toward physics. (some guy astutely pointed out what I was talking about with measurement uncertainty as well)
On July 18 2013 00:12 Shiori wrote:
How exactly is that meaningless? You seem to be equating probability of zero with "cannot happen" when that's not what it actually means. Understood properly, there is absolutely no problem here.
Nah, I think it's an English problem, not a mathematics problem.
There is a difference between impossible and probability 0 in measure theory/some other subsets of mathematics. Outside of that the distinction is meaningless (i.e. applying probability in the real world, not in mathematics).
It's pretty patently true if you think about it for a minute.
That a probability function f(n) which spits out a "probability of successfully having a heads turn up" after n trials is equal to one for (countably, since n is a natural number) infinite trials. This implies that the probability of a sequence of never-ending tails is exactly zero, despite being logically possible since every trial is independent. If you disagree, then you must think that a never-ending sequence of tails has an infinitesimally small, but nonzero, probability, which is impossible since zero is the only infinitesimal over the reals.
2) If you randomly generate a finite sequence of numbers (that's what I forgot to put in, haha!) then the (prior) probability of any particular sequence being the one that ends up getting generated is zero, because there are an infinite number of natural numbers, ergo an infinite number of possible lengths of these sequences. This wasn't meant to have anything to do with the heads-tails things, so I'm sorry for the confusion.
Also, please don't imply I don't know any math. I may not be a PhD mathematician, but mathematics is my field; I'm pretty sure I know it better than a highschooler (what's more: high schoolers rarely deal with set theory involving infinity since they're more focused on applied math like computing integrals and so on).
So you assumed I'm a high schooler? rofl.
You went from a finite number of trials to an infinite number of trials. Thanks for changing the game to make yourself look correct. No point in debating with you when you constantly change the terms of debate.
For proof:
To generally prove the probability thing, just look at it this way: we've got some probability space, and then let's have f(n) be a probability function which outputs probability of getting at least 1 coin flip resulting in heads after n trials where n is a natural number and f(n) is a real number. If you are correct, and probability of a sequence of pure tails is infinitesimally small, but non zero, then you have a contradiction, because f(n) is always a real number, and the only infinitesimal in the real numbers is exactly zero.
You said let n be a natural number...then you say never-ending sequence. Who's got the contradiction here? Certainly isn't me.
There are no problems to be had if we define division of a real by infinity to equal zero (i.e. if infinity is an element of the extended real line). It's a simple definition, so think of it this way: intuitively, division of any real number into infinitely many equal pieces implies that each piece is infinitesimally small. The only infinitesimal element of the real line is zero, ergo all these pieces are zero, and, for the purposes of most "normal" (probability theory or measure theory, basically) zero multiplied with infinity is defined quite cooperatively to be zero.
For a mathematician you seem pretty ready to treat infinity like a number, when I'd expect anyone worth his salt in the field to consider it a concept and not a number. You don't talk about dividing by infinity or operating on infinity in any way like that, because it's not a number.
|
What are you guys talking about?
Finite vs Infinite shouldn't matter for those problems. Uncountable and countable are the only restrictions on such sets. There is no additivity of an uncountable number of sets.
If A and B are disjoint (and measurable), Measure(A) + Measure(B) = Measure(A U B)
You can also do this for many sets. Sum(Measure(An)) = Measure(Union(An)) where n is finite (just stretching the previous statement to multiple sets). So {An} is a finite sequence of disjoint, measurable sets.
You can also do this if n is a countably infinite set, so {An} is a countably infinite sequence of disjoint, measurable sets.
But you can't do that if n is an uncountably infinite set. That doesn't work. You can't pretend that it does, and there are plenty of easy exceptions.
I'm confused because it seems like you should be differentiating between countable and uncountable, rather than finite and infinite. This is measure theory. So just use measure theory.
|
On July 18 2013 07:19 wherebugsgo wrote:Show nested quote +On July 17 2013 17:53 Reason wrote:On July 17 2013 13:52 wherebugsgo wrote:+ Show Spoiler +On July 17 2013 13:06 Shiori wrote:Show nested quote +On July 17 2013 11:12 wherebugsgo wrote:On July 17 2013 05:36 positronic_toaster wrote:
Here's a wacky idea, why are we so certain that our mind is a purely 3D construct? Who's to say that there's nothing going on in another dimension that is imperceptible by our senses? Which dimension would that be? You have to provide evidence for this dimension of yours before you assert that anything can exist in it. Or, better yet, that this dimension exists in the first place. The only "fourth" dimension I can conceive of is not a spatial dimension, it's the time dimension. In his defense, he said "who's to say" and "why are we so certain" rather than asserting that any particular dimension really does exist. Show nested quote +On July 16 2013 17:53 Reason wrote:On July 16 2013 10:01 neptunusfisk wrote:On July 16 2013 09:29 wherebugsgo wrote:On July 16 2013 07:34 Reason wrote:On July 16 2013 07:23 neptunusfisk wrote:On July 16 2013 07:15 Reason wrote:On July 16 2013 06:58 neptunusfisk wrote:On July 16 2013 06:44 Reason wrote:How does this : http://en.wikipedia.org/wiki/Almost_surely come into play with what you're saying there? The example given was what is the probability of picking a specific real number between 0 and 1? + Show Spoiler +Similarly, the probability that a random non repeating infinite sequence of integers contains every integer and every finite set of integers is 1 (almost sure). I don't want to go deep into those formal questions, but yes, probability is not always as easy as it seems. I'll leave my probability and set theory books unopened, but just let me say that if you handed me something perfectly random (it doesn't exist) and had some event with zero probability, I would agree to take poison if it happened. But as I said, the main problem is not in how to read the model, it's whether the model is relevant or not that's important here. Throwing a dart For example, imagine throwing a dart at a unit square wherein the dart will impact exactly one point, and imagine that this square is the only thing in the universe besides the dart and the thrower. There is physically nowhere else for the dart to land. Then, the event that "the dart hits the square" is a sure event. No other alternative is imaginable. Next, consider the event that "the dart hits the diagonal of the unit square exactly". The probability that the dart lands on any subregion of the square is proportional to the area of that subregion. But, since the area of the diagonal of the square is zero, the probability that the dart lands exactly on the diagonal is zero. So, the dart will almost never land on the diagonal (i.e. it will almost surely not land on the diagonal). Nonetheless the set of points on the diagonal is not empty and a point on the diagonal is no less possible than any other point, therefore theoretically it is possible that the dart actually hits the diagonal. The same may be said of any point on the square. Any such point P will contain zero area and so will have zero probability of being hit by the dart. However, the dart clearly must hit the square somewhere. Therefore, in this case, it is not only possible or imaginable that an event with zero probability will occur; one must occur. Thus, we would not want to say we were certain that a given event would not occur, but rather almost certain. So.... do you prefer arsenic or cyanide? The thing here is that I won't let you choose "all the points", as the probability for that is 1. If you can decide on one single mathematical point (with P(dart hits that point) = 0), then I'll agree to cyanide and arsenic at the same time. Sorry, I was only covering probability = 0. You do realise I'm just copy pasting all this stuff right lol? Here's P = 1. http://en.wikipedia.org/wiki/Almost_surely#Tossing_a_coin This article does a pretty poor job of covering what it means for a probability to converge to 1. The probability isn't actually necessarily 1, it converges to 1 under certain conditions. e: or 0 or any other probability, for that matter Yeah. And no, why would I take poison for something that is going to happen? That's just absurd. I could agree to the opposite and take that damn poison if you toss either heads or tails infinity times though. This is what you said "just let me say that if you handed me something perfectly random (it doesn't exist) and had some event with zero probability, I would agree to take poison if it happened." Tossing a coin is perfectly random and the dart example is zero probability. Not sure what you old men are grumbling about tbh. Obviously I don't actually want you to kill yourself. Show nested quote +I merely implied this earlier but I'll be more blunt now:
You don't seem to understand the difference between a probability actually being 0 and a probability converging to 0 under certain conditions. The probability actually is zero. It's just that probability being zero doesn't mean "cannot happen." For example, the probability of randomly selecting any particular real number in a trial is actually zero. It doesn't just converge to zero at a limit: it actually is a probability of zero. In fact, even a countably infinite number of trials has a zero probability of selecting any particular real number randomly. Nevertheless, a real number must be selected. The situations are different. I agree that the probability of randomly selecting a particular real number is zero. However, the probability of selecting any number within a range is NOT zero. That's what the meaning of the dart experiment is. No matter how you look at it, you're going to be selecting a range of values. That's why I disagree with the way the article talks about that experiment and the probability. The probability in that case converges to 0. It's not actually 0. On July 17 2013 13:06 Shiori wrote:Show nested quote +(also this doesn't even get into the problems of your thought experiment-in real life there are no things such as points because all measurement is imprecise. The question you're posing itself is meaningless. You need a dart with an infinitisemal point, which by definition doesn't exist-it's zero probability not because the dart will hit the square but not a point but rather that the dart doesn't exist to be thrown in the first place.) That's why it's a thought experiment; it's not supposed to be something one can actually do in real life. But if you think "almost surely" meaning probability of one is a meaningless question, then you're very, very wrong. I'm not sure what measurement has to do with the existence of points; a point is an object defined to have certain properties in a Euclidean space (i.e. zero-dimensional). This is a totally coherent mathematical definition. Sure, if you want to think of a dart with a dimensionless point hitting any given dimensionless point on a 2d plane then the probability of that occurring is 0. Do you see what I mean? It's a question of what does this experiment actually mean. It doesn't mean anything at all, it doesn't tell us anything beyond what we already assumed to be true. That's what I am alluding to when I am saying that this experiment is meaningless. On July 17 2013 13:06 Shiori wrote:Show nested quote +If you haven't made the connection yet that the dart needs an infinitisemal point, then realize that if the dart's point had some area (even a miniscule area) then when it hits the board that area covers a certain subregion. If the point is anywhere within the boundary we can consider the dart to have hit said point. Suppose the dart's point is circular, then you can see where I'm going with that. The board and dart are obviously idealized mathematical objects in a defined Euclidean space. But it doesn't change anything even if the dart actually does have non-zero area, since any particular orientation of that area on the dartboard has probability zero (since we can slice up any interval into arbitrarily smaller sub-intervals). Written in another way, the dart example could go like this: let the board be the Cartesian plane (i.e. 2 dimensions over the reals) and let a dart be a vector of the form (x,y) situated with its tail at the origin. Now choose any point in (a,b) in the space. The probability of a random vector passing through that point is zero. To generally prove the probability thing, just look at it this way: we've got some probability space, and then let's have f(n) be a probability function which outputs probability of getting at least 1 coin flip resulting in heads after n trials where n is a natural number and f(n) is a real number. If you are correct, and probability of a sequence of pure tails is infinitesimally small, but non zero, then you have a contradiction, because f(n) is always a real number, and the only infinitesimal in the real numbers is exactly zero. If a random finite sequence is generated, the probability of that sequence having been generated is zero, because there are an infinite number of finite sequences. This is not the same thing. Does the dart's point have some area or not? If it does, then the probability of the dart's point hitting a particular point on a 2d plane can be interpreted differently, as the chance that said point is contained within a region described by the shape of the dart's point. If the dart's point does not have any area (i.e. it too is also a point) then again, this experiment is pretty meaningless. I suppose you could say that it's nothing more than the pick a number experiment but I don't believe that was what he was suggesting. As to this:
To generally prove the probability thing, just look at it this way: we've got some probability space, and then let's have f(n) be a probability function which outputs probability of getting at least 1 coin flip resulting in heads after n trials where n is a natural number and f(n) is a real number. If you are correct, and probability of a sequence of pure tails is infinitesimally small, but non zero, then you have a contradiction, because f(n) is always a real number, and the only infinitesimal in the real numbers is exactly zero.
If a random finite sequence is generated, the probability of that sequence having been generated is zero, because there are an infinite number of finite sequences.
This makes no sense at all. "if a random finite sequence is generated, the probability of that sequence having been generated is zero" What what?? The probability of it having been generated is ONE. Because it got generated. Since n is finite, if you're talking about a fair coin flip, then the probability you get n - 1 tails and then a heads is just f(n) = 2^-n which is nonzero, just as with any other particular n-length sequence of heads and tails. It's not "infinitisemally" small. It's strictly nonzero. Also, if you mean that you've observed n tails in a row, what is the probability that you now get a heads...and we know for sure that the coin is fair, then the probability of the heads occurring is 1/2. Again, nonzero. You either have failed to communicate what you were trying to communicate or you need to consider remedial high school math. I'm not quite sure why you felt the need to come back and comment so strongly on a discussion that you feel is pointless, especially since from what I can tell a lot of what you're saying is incorrect. "I agree that the probability of randomly selecting a particular real number is zero. However, the probability of selecting any number within a range is NOT zero." The example given previously was pick a real number between 0 and 1. The probability of doing so is 0, just like the probability of picking any integer is 0, as there are infinite integers and infinite real numbers between 0 and 1. Two different questions with the same answer. Did you mean to write what you did? Dart example: + Show Spoiler +Also, with the dart, of course in practice you could not have a dart head small enough to hit only one point on the board because one point on the board has zero area. However if you can accept that the dartboard theoretically has a center point, or as the example mentioned a diagonal line, then you should be able to understand that you could throw a real 3d dart at the board and then take the center point of the dart tip itself, if the center point of the dart tip does not coincide with the center point or diagonal of the board then it could be said that the dart "missed" the target. Such an experiment never need be carried out in practice and is merely a way to explain things for people to understand, much like tossing a coin. There are much better ways of communicating the article's content than coin tossing and dart throwing but it's meant to be easy to understand for the majority. The real number example is fine and can be used to communicate probabilities of both 0 and 1 though neither will be certain events, so you can disregard the impractical dart experiment if you find it flawed. What is the probability of picking a specific real number between 0 and 1? It's 0. Pick a specific real number between 0 and 1. Now pick another at random. What is the probability that they are different? It's 1. I am aware what probability 0 means and probability 1 means if these are sure events. I'm also aware that if probabilities are converging to either 0 or 1 and the sample size is infinite then the probability is represented as a 0 or a 1. If I'm the one who is mistaken here please explain further as these are still relatively new concepts to me. Perhaps I was unclear, but you took my comment on this: Show nested quote +However, the probability of selecting any number within a range is NOT zero. That's what the meaning of the dart experiment is. No matter how you look at it, you're going to be selecting a range of values. Show nested quote +Out of context. Basically what I'm saying is that you're taking a range of values in a finite subset of the reals if you throw a dart at a board, assuming the board is of finite size and the dart's point is not dimensionless. The question is then what is the chance that this number you want is in that subset. So, for example, let's assume the area of the point of the dart is huge for comparison. So large that it's half of the board's area. Then it's roughly equivalent to asking this: Pick a number in the set [0, 1]. What's the chance that this number is in the set [0, 0.5]. The answer is clearly nonzero (it's 1/2 in this case). Now, keep reducing the area of the dart, such that the limit of the area of the dart approaches 0 as its limit. You'll see that the probability converges to 0. Clear enough? If you want to talk about points coinciding with points then again, I say the experiment is meaningless because it doesn't tell us anything we don't already know (i.e. it's alluding to a property of R) In other words, if your experiment was this: http://math.stackexchange.com/questions/155156/is-it-generally-accepted-that-if-you-throw-a-dart-at-a-number-line-you-will-neveThen I agree, though again, I find it meaningless probably because I am inclined toward physics. (some guy astutely pointed out what I was talking about with measurement uncertainty as well) It's not an actual "experiment." It's a "thought experiment" designed to stop people from equivocating between almost surely and surely so that they don't make theorems that are wrong. Show nested quote +On July 18 2013 00:12 Shiori wrote:
How exactly is that meaningless? You seem to be equating probability of zero with "cannot happen" when that's not what it actually means. Understood properly, there is absolutely no problem here. Nah, I think it's an English problem, not a mathematics problem. There is a difference between impossible and probability 0 in measure theory/some other subsets of mathematics. Outside of that the distinction is meaningless (i.e. applying probability in the real world, not in mathematics).
Uhhh, probability is mathematics. For fuck's sake, they defined the question with respect to a probability space. "Applying probability in the real world" is so broad and vague I don't even know what to say, except that none of our applications would be proved except by exhaustive experiment until we find something that works if we didn't have rigorous, formal proofs which depend on things like probability spaces...
That a probability function f(n) which spits out a "probability of successfully having a heads turn up" after n trials is equal to one for (countably, since n is a natural number) infinite trials. This implies that the probability of a sequence of never-ending tails is exactly zero, despite being logically possible since every trial is independent. If you disagree, then you must think that a never-ending sequence of tails has an infinitesimally small, but nonzero, probability, which is impossible since zero is the only infinitesimal over the reals.
2) If you randomly generate a finite sequence of numbers (that's what I forgot to put in, haha!) then the (prior) probability of any particular sequence being the one that ends up getting generated is zero, because there are an infinite number of natural numbers, ergo an infinite number of possible lengths of these sequences. This wasn't meant to have anything to do with the heads-tails things, so I'm sorry for the confusion.
Also, please don't imply I don't know any math. I may not be a PhD mathematician, but mathematics is my field; I'm pretty sure I know it better than a highschooler (what's more: high schoolers rarely deal with set theory involving infinity since they're more focused on applied math like computing integrals and so on).
So you assumed I'm a high schooler? rofl.[/quote]
In what way did I assume you're a highschooler? Like what?!?!?!
Do you read my posts?!?!?!
Maybe it is an English problem...
You went from a finite number of trials to an infinite number of trials. Thanks for changing the game to make yourself look correct. No point in debating with you when you constantly change the terms of debate. For proof: Show nested quote +To generally prove the probability thing, just look at it this way: we've got some probability space, and then let's have f(n) be a probability function which outputs probability of getting at least 1 coin flip resulting in heads after n trials where n is a natural number and f(n) is a real number. If you are correct, and probability of a sequence of pure tails is infinitesimally small, but non zero, then you have a contradiction, because f(n) is always a real number, and the only infinitesimal in the real numbers is exactly zero. You said let n be a natural number...then you say never-ending sequence. Who's got the contradiction here? Certainly isn't me.
That's because the two posts are different explanations of the same point: that the probability of a sequence of only heads is zero for n-->infinity. The first method does this by looking at one trial and shows f(n)=0 for n-->infinity, whereas the second method goes the other way.
There are no problems to be had if we define division of a real by infinity to equal zero (i.e. if infinity is an element of the extended real line). It's a simple definition, so think of it this way: intuitively, division of any real number into infinitely many equal pieces implies that each piece is infinitesimally small. The only infinitesimal element of the real line is zero, ergo all these pieces are zero, and, for the purposes of most "normal" (probability theory or measure theory, basically) zero multiplied with infinity is defined quite cooperatively to be zero.
For a mathematician you seem pretty ready to treat infinity like a number, when I'd expect anyone worth his salt in the field to consider it a concept and not a number. You don't talk about dividing by infinity or operating on infinity in any way like that, because it's not a number.
Infinity is not a number. It is an element of the extended real line, on which the operation n/infinity is defined to be zero. Probability does not encounter any problems with this definition or with using the extended reals.
|
Let me put it to you this way: both of the examples given in the linked Wiki article have probabilities exactly as stated. The function actually is zero for any particular sequence.
|
It's enlightening to read about distributions (both mathematical and of probabilities). Basically they are generalized functions where the value at some point isn't that important (or doesn't have to exist), but the integrals of this distributions give useful numbers.
|
On July 18 2013 07:42 DoubleReed wrote:
What are you guys talking about?
Finite vs Infinite shouldn't matter for those problems. Uncountable and countable are the only restrictions on such sets. There is no additivity of an uncountable number of sets.
If A and B are disjoint (and measurable), Measure(A) + Measure(B) = Measure(A U B)
You can also do this for many sets. Sum(Measure(An)) = Measure(Union(An)) where n is finite (just stretching the previous statement to multiple sets). So {An} is a finite sequence of disjoint, measurable sets.
You can also do this if n is a countably infinite set, so {An} is a countably infinite sequence of disjoint, measurable sets.
But you can't do that if n is an uncountably infinite set. That doesn't work. You can't pretend that it does, and there are plenty of easy exceptions.
I'm confused because it seems like you should be differentiating between countable and uncountable, rather than finite and infinite. This is measure theory. So just use measure theory.
This'll be my last post on this subject since I regret joining the discussion in the first place. Too much miscommunication going on.
The reason I mentioned infinite vs finite sets is because Shiori said pick n (some natural number) and produce that many trials of a coin being flipped. Then what's the probability you get a heads afterward. So on one hand he's saying take a finite number of trials and on the other hand he's saying take an infinite number of trials.
Clearly the probabilities are going to be different in those two cases. I was addressing the finite case since that was what he first suggested.
|
This math i did ages ago in the early years of highschool, but annyway:
Physics and math have a slightly different vieuw on mathematics, physics is aplied mathematics and math is pure theoretical.
I feel the discussion is mostly a misunderstanding, converging to 0 is seen as the same as 0 and there is only one situation in wich the difference matters, and that is when infinity comes into play. (wich explains all the examples i have seen come by like the dartboard and picking a number between 0 and 1)
Something infinite times converging to 0 is undetermined (can have anny outcome depending on the functions) Or in simple words, something infinitly big times something infinitly small has a not determined outcome,the outcome can be annything depending on the functions wich go to infinity and converge to 0
Something infinite times 0 will always remain 0.
|
On July 18 2013 08:06 wherebugsgo wrote:Show nested quote +On July 18 2013 07:42 DoubleReed wrote:
What are you guys talking about?
Finite vs Infinite shouldn't matter for those problems. Uncountable and countable are the only restrictions on such sets. There is no additivity of an uncountable number of sets.
If A and B are disjoint (and measurable), Measure(A) + Measure(B) = Measure(A U B)
You can also do this for many sets. Sum(Measure(An)) = Measure(Union(An)) where n is finite (just stretching the previous statement to multiple sets). So {An} is a finite sequence of disjoint, measurable sets.
You can also do this if n is a countably infinite set, so {An} is a countably infinite sequence of disjoint, measurable sets.
But you can't do that if n is an uncountably infinite set. That doesn't work. You can't pretend that it does, and there are plenty of easy exceptions.
I'm confused because it seems like you should be differentiating between countable and uncountable, rather than finite and infinite. This is measure theory. So just use measure theory. This'll be my last post on this subject since I regret joining the discussion in the first place. Too much miscommunication going on. The reason I mentioned infinite vs finite sets is because Shiori said pick n (some natural number) and produce that many trials of a coin being flipped. Then what's the probability you get a heads afterward. So on one hand he's saying take a finite number of trials and on the other hand he's saying take an infinite number of trials. Clearly the probabilities are going to be different in those two cases. I was addressing the finite case since that was what he first suggested.
No, that isn't what I said, but I admit I worded it poorly initially. I said you have a probability function f(n) which gives you the probability of there being at least 1 heads for n trials. If n = 1, then f(n) = 1/2. If n=2, then f(n)=1/4. The limit of this function for n--> infinity is zero, which implies that the probability of a random coin flip simulator which runs forever has a zero probability of never getting heads.
The point is that the probability of never getting heads is zero by definition, but it's also logically possible. That's all these examples are meant to show. There's no paradox, because probability zero doesn't mean "can't happen." I'm not sure why you're so resistant to this idea, because all it means is that the mathematical definition of probability zero means a particular thing.
I attempted to explain things by moving over to the extended real line, where x/infinity = 0 for any x, because the extended real line is used in measure theory, and because it might make the example easier to intuitively understand.
At this point, I'm not sure whether you reject that probability zero things do occur, or just that these particular examples are wrong. That's why I brought up the idea of randomly selecting a real number on any interval. The probability of some particular number being generated is exactly zero, and yet obviously some real number would be generated by construction. That's all I've been trying to say. Whether or not you could actually carry out any of these things in practice is largely irrelevant to the definition of the phrase "almost surely," which is the point of exercise.
Also, you randomly deciding to start flaming me certainly didn't help matters, particularly when you took me stating that I'm not a high schooler as an accusation that you're a high schooler. Like what the fuck, man?
|
On July 18 2013 07:42 DoubleReed wrote:
What are you guys talking about?
Finite vs Infinite shouldn't matter for those problems. Uncountable and countable are the only restrictions on such sets. There is no additivity of an uncountable number of sets.
If A and B are disjoint (and measurable), Measure(A) + Measure(B) = Measure(A U B)
You can also do this for many sets. Sum(Measure(An)) = Measure(Union(An)) where n is finite (just stretching the previous statement to multiple sets). So {An} is a finite sequence of disjoint, measurable sets.
You can also do this if n is a countably infinite set, so {An} is a countably infinite sequence of disjoint, measurable sets.
But you can't do that if n is an uncountably infinite set. That doesn't work. You can't pretend that it does, and there are plenty of easy exceptions.
I'm confused because it seems like you should be differentiating between countable and uncountable, rather than finite and infinite. This is measure theory. So just use measure theory.
measurable only in terms of our limited huma knowledge of math and physics
|
On July 18 2013 08:43 yOngKIN wrote:Show nested quote +On July 18 2013 07:42 DoubleReed wrote:
What are you guys talking about?
Finite vs Infinite shouldn't matter for those problems. Uncountable and countable are the only restrictions on such sets. There is no additivity of an uncountable number of sets.
If A and B are disjoint (and measurable), Measure(A) + Measure(B) = Measure(A U B)
You can also do this for many sets. Sum(Measure(An)) = Measure(Union(An)) where n is finite (just stretching the previous statement to multiple sets). So {An} is a finite sequence of disjoint, measurable sets.
You can also do this if n is a countably infinite set, so {An} is a countably infinite sequence of disjoint, measurable sets.
But you can't do that if n is an uncountably infinite set. That doesn't work. You can't pretend that it does, and there are plenty of easy exceptions.
I'm confused because it seems like you should be differentiating between countable and uncountable, rather than finite and infinite. This is measure theory. So just use measure theory. measurable only in terms of our limited huma knowledge of math and physics
Uhh... no. Measurable as in Lebesgue Measure.
|
On July 18 2013 00:12 Shiori wrote:Show nested quote +However I don't agree with Shiori when he said "For example, the probability of randomly selecting any particular real number in a trial is actually zero. It doesn't just converge to zero at a limit: it actually is a probability of zero."
It has been a while since I have done maths involving limits, but it seems to me that the real number selection is an exact example of this, where 1 over infinite approaches 0. There are no problems to be had if we define division of a real by infinity to equal zero (i.e. if infinity is an element of the extended real line). It's a simple definition, so think of it this way: intuitively, division of any real number into infinitely many equal pieces implies that each piece is infinitesimally small. The only infinitesimal element of the real line is zero, ergo all these pieces are zero, and, for the purposes of most "normal" (probability theory or measure theory, basically) zero multiplied with infinity is defined quite cooperatively to be zero.
I thought I made it clear that I understood that we can define one over infinity to be zero the main problem I had was the wording where you said it is actually zero and not a limit approaching zero. I understand that in probability that zero can be defined as one on infinity but in my eyes they are actually different, where one represents something infinitesimally small (yet there is still something) and the other represents nothing.
If you simply meant that within probability theory they are the same thing then I just wanted to clarify that, otherwise I'd like to know what your justification was since my understanding was that in regular mathematics they are different and we just substitute one over infinity for zero for convenience since they are practically the same.
|
On July 18 2013 12:49 Myrddraal wrote:Show nested quote +On July 18 2013 00:12 Shiori wrote:However I don't agree with Shiori when he said "For example, the probability of randomly selecting any particular real number in a trial is actually zero. It doesn't just converge to zero at a limit: it actually is a probability of zero."
It has been a while since I have done maths involving limits, but it seems to me that the real number selection is an exact example of this, where 1 over infinite approaches 0. There are no problems to be had if we define division of a real by infinity to equal zero (i.e. if infinity is an element of the extended real line). It's a simple definition, so think of it this way: intuitively, division of any real number into infinitely many equal pieces implies that each piece is infinitesimally small. The only infinitesimal element of the real line is zero, ergo all these pieces are zero, and, for the purposes of most "normal" (probability theory or measure theory, basically) zero multiplied with infinity is defined quite cooperatively to be zero. I thought I made it clear that I understood that we can define one over infinity to be zero the main problem I had was the wording where you said it is actually zero and not a limit approaching zero. I understand that in probability that zero can be defined as one on infinity but in my eyes they are actually different, where one represents something infinitesimally small (yet there is still something) and the other represents nothing. If you simply meant that within probability theory they are the same thing then I just wanted to clarify that, otherwise I'd like to know what your justification was since my understanding was that in regular mathematics they are different and we just substitute one over infinity for zero for convenience since they are practically the same.
That's the thing, it IS 1 over infinity even in "regular mathematics", since "infantisimally small" numbers aren't allowed when working with real numbers.
http://en.wikipedia.org/wiki/0.999...
|
i can not but equate the believe in determinism with the believe in a god.
faith - 1. Confident belief in the truth, value, or trustworthiness of a person, idea, or thing.
i can not accept deterministic claims because i can not accept the existence of a single god.
there has to be a dualism for evolution/motion/change/vibration to occur and a validation of self, as determinism claims to be, can not exist.
the mind is a stereoscopic like effect, generated by a dualism. certainty vs uncertainty.
if certainty = physicalism then uncertainty = faithism (it exists by means of observation  )
if form is an expression of physicalism and believes an expression of faith, then the stereoscopic effect between form and believe is reality, your reality.
|
On July 18 2013 17:12 xM(Z wrote:i can not but equate the believe in determinism with the believe in a god. faith - 1. Confident belief in the truth, value, or trustworthiness of a person, idea, or thing.i can not accept deterministic claims because i can not accept the existence of a single god. there has to be a dualism for evolution/motion/change/vibration to occur and a validation of self, as determinism claims to be, can not exist. the mind is a stereoscopic like effect, generated by a dualism. certainty vs uncertainty. if certainty = physicalism then uncertainty = faithism (it exists by means of observation ) if form is an expression of physicalism and believes an expression of faith, then the stereoscopic effect between form and believe is reality, your reality.
I don't know why I bother clicking reply on your posts any more, but determinism is nothing like the belief in god.
Everything we know, except some really fringe science where our understanding is limited at best, everything has causes and is dependant on causes. It's perfectly valid a priori knowledge that if everything depends on causes, everything is predetermined. Hell, even if some quantum events are causeless, they are still regular, which leads to determinism as well. We can't tell which atom will decay from a certain amount of radioactive materia, but we know exactly how many atoms will decay within a certain timespan, so it's still deterministic on a macro level.
Non-belief in determinism is far more like the belief in god, since you believe in something supernatural which we have no reason to believe in other than finding it comforting that we are constantly in 100% control.
|
On July 18 2013 02:02 radscorpion9 wrote:Show nested quote +On July 17 2013 19:18 Rassy wrote:Noooooo Pls come back and make your contribution, the thread needs new input cause it seems to be slowly dying. Maybe because the majority here seems to agree that the mind is indeed all physical and with that there is no real discussion about the original question. We need new and interesting thoughts and someone making an account just to post on this thread gives me hope for just that lol . If you're referring to skying I discovered that he was banned for advertising. Its so hard to think of an argument against determinism. Maybe the only thing that can be said, is that philosophically, if determinism is true then it leads to a paradox. Because determinism clearly necessitates cause and effect, so in theory that would lead to an infinite chain. B ut because infinity is too large to exist in nature (and we know a circle wouldn't work as the circle as a whole would need to come from somewhere), then theoretically there must be some alternative to cause and effect, and thus determinism can not be the only mechanism at work. Since this mechanism caused our universe to form, then it must exist at some fundamental level in our universe. Perhaps it just occurred once during the formation (i.e. the big bang), or maybe its ongoing, but we should see some non-deterministic relation that at least can't be explained.
There is no law that says infinity cant exist in nature. For all we know space could be infinite.
|
This thread is like a complete summary of why doctors and psychologists love engineers, but hate mathematicians and physicists.
Arguing over probability confidence intervals, and continuous vs. discrete in nature rather than actually discussing the topic. There are 4 forces, but realistically, the strong force, weak force, and gravity, have negligable effects with anything related to psycology, neurology, electrophysiology, or cellular biophysics. (sourcehysical Chemistry or listen to the feynman lectures)
The holy grail of modeling proteins is to predict their behaviors, rather than have to go through the tedium of measuring every possible protein. We don't know how to predict all the states and transitions, but we can measure the amount of channels in a state at a given condition(voltage, conductance, acidity, etc).(source one of my collaborators:http://www.sci.utah.edu/~macleod/bioen/be6003/notes/W05-Sanguinetti.pdf) The quantum problem modeling proteins and lipids in general are that they are not static. Its very difficult to model the effects of all states a single protein, but the properties of a large group of transmembrane proteins is very specific and a lot of work has been done in this field in IUPHUR and Neuron. . The reality is that the frontal lobe has the ability to inhibit activity with neuroinhibitors, which is a mechanism of free will(the ability to act against instinct, something which lower animals have a slower time adapting to).
I think this rhetoric inferring that people are stupid is just pointless. (which he has done several times in this thread)
Argument over math (discreteness vs continuity, probabiliity intervals, definition of determinism and causality, and context in quantum mechanics, topology) i think should be in another thread.
|
United States9292 Posts
"i write poetry, because, underneath this mean, ugly, calloused exterior... i just want to... be loved?"
|
United States9292 Posts
"Wrong. I write poetry to put my mean, callous, heartless exterior into sharp relief! I'm going to throw you off the ship anyway. Guard!"
|
|
|
|
|
|
EPT
