That said let's consider the system (one roll of a dice) mechanistically. We know from basic physics that given all the information (force, direction, mass, etc.) of the system (one roll of a dice) we can predict the outcome with perfect accuracy. In other words the system (one roll of a dice) is, well, deterministic (certainty assured). — TheMadFool
How do you figure this? Practically speaking, physical science is always subject to some degree of inaccuracy. — Pantagruel
Physics/mechanics???!!! We've put men on the moon. Surely a humble dice is within its reach. — TheMadFool
Physics/mechanics???!!! We've put men on the moon. Surely a humble dice is within its reach. — TheMadFool
What causes an unequivocally deterministic system to exhibit probabilistic behavior? — TheMadFool
1. Is probability an illusion? — TheMadFool
To quote Regis, Is that your final answer? — Pantagruel
It doesn’t take 100% accuracy to put men on the moon. Also modeling gravitation in space is much easier than modeling all frictions on a dice thrown in the air and bouncing on a surface: the dice will bounce differently depending on the hardness of the surface at the precise point where it bounces, and a tiny change in the angle at which the dice bounces will totally change how it bounces and its subsequent motion, so it’s a chaotic system, a tiny difference in initial conditions will change the final state of the dice and in most cases we can’t measure all relevant variables with sufficient accuracy. Also, the guys going to the moon could control their trajectory to some extent during the flight, whereas we don’t have little guys controlling and stabilizing the dice while it flies and bounces :wink: — leo
Exhibit is the keyword here — SophistiCat
Probability is the mathematical study of chance which basically considers events that are uncertain. We can't make definite claims in probability. — TheMadFool
Yes we can. The ‘definite’ claim is probabilistic though. — I like sushi
In my view? You said ‘mathematics’ so I don’t have an opinion on the matter. Certainty, in mathematics, is - for example - 1+1=2. I don’t have an opinion about this.
Mathematical probability isn’t based on observation/experimentation. It is used to interpret experimentation and observation thought aided my measurements.
Don’t conflate the abstract with the concrete when talking about mathematical models and reality. — I like sushi
Yes we can. The ‘definite’ claim is probabilistic though — I like sushi
Actually I think we can calculate "exact" probabilities e.g. in the chance of getting a heads on a single coin-flip is "exactly" 50%. No more, no less. — TheMadFool
Yes, I'm sure about 70% - it's a definite quantity - but are you certain that it'll rain or not? — TheMadFool
Yes. — TheMadFool
Ok. Let's suppose that a normal-sized dice is a "chaotic system" and is actually probabilistic. Just blow-up the dice - increase its size to that of a room or house even. Such a dice, despite its size, would continue to behave in a probabilistic manner despite our ability to predict the outcomes accurately. After all you do accept that rocket trajectories can be predicted and therefore controlled. — TheMadFool
That turned out longer than I expected, hope that helps. — leo
No, you still don't understand. — SophistiCat
Honestly, I’ve no idea what you’re talking about. Sorry :( — I like sushi
It is not probability that is an illusion; it is certainty. — A Seagull
2. We know that the system (person A and the dice) is probabilistic because the experimental probability agrees with the theoretical probability which assumes the system is non-deterministic. — TheMadFool
1. We know that the system (person A and the dice) is deterministic because person B can predict every single outcome.
2. We know that the system (person A and the dice) is probabilistic because the experimental probability agrees with the theoretical probability which assumes the system is non-deterministic.
There is a contradiction is there not? — TheMadFool
This result is in agreement with the theoretical probability calculated (4/6 = 2/3 = 66.66%). In other words the system (person A and the dice) behaves like a probabilistic system as if the system is truly non-determinsitic/probabilistic. — TheMadFool
Set aside the complexity of the issue for the moment and consider that given all initial values of a system the outcome pathway is fully determined. leo said that this isn't possible with 100% accuracy which I disagree to. — TheMadFool
Take the simple example of a space probe. Using rockets in the right locations and fired for the correct durations we can and do predict that the probe lands right side up. — TheMadFool
This is a 100% prediction accuracy and if there are any inaccuracies they are due to unforseen cotingencies like wind or instrument malfunction. — TheMadFool
I hope we can agree now that physical systems at the human scale are deterministic and that includes a fair 6-sided dice which I want to use for this thought experiment. — TheMadFool
1. We know that the system (person A and the dice) is deterministic because person B can predict every single outcome.
2. We know that the system (person A and the dice) is probabilistic because the experimental probability agrees with the theoretical probability which assumes the system is non-deterministic.
There is a contradiction is there not? — TheMadFool
It seems that if your goal is to put a man on the moon and you put a man on the moon, your knowledge was 100% accurate. Now, if you wanted to put a man on a certain area of the moon that is only 50 meters in diameter, then that would be a more difficult stunt to pull off. That would require more specific/relevant knowledge to accomplish.It doesn’t take 100% accuracy to put men on the moon. — leo
It's not just the world, but my own mind. I have reasons for behaving the way I do, or for the conclusions I come to. That is how reasoning works. You use reasons to support your conclusion. Your reasons are usually observations. Reasoning is causal, and can be predictable when you have access to the information in another person's mind - like when you know how they think because you have the experience of having lived with them for 25 years.The world 'appears' deterministic at times at the human scale (e.g billiard balls on a pool table) but this in fact is only an artefact of approximate perception. Is that the origin of the confusion? — Pantagruel
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