Probability and its application

[switz5678]

Something that I haven’t given much thought to, until recently, is probability. This book I have been reading goes into likelihood of certain scenarios, which have already occurred, and makes arguments for/against said scenarios based on probability. This argument(s) started a thought within me that has been banging around, and I hope that freeing it for you to critique will give me some perspective.

I see probability as a mathematical or anticipatory tool for decision making. When were we use it we are determining the likelihood of some hypothetical scenario in the future. I see uncertainty and probability as necessary for each other, or in order for probability to have an application to a situation there must be uncertainty. When we look to the past there is no uncertainty in what happened… Only 1 or 0.. Did or did not. What we recognize as uncertainty is not within the universe itself, but is created due to our intellects inability to recognize the truth with limited access/discoveries. So how can we assign these probabilities, and say these are the likelihood of scenarios of universal beginnings, when there is no uncertainty of the universe in past tense?

Am I going mad? I hope this makes sense because it was hard for me to translate from a mental concept, to written language. I’m willing to expound, and desire some constructive feedback

J

 

[HallsofIvy]

That is the distinction between "mathematical probability" and "applications of probability". In mathematics we assume that we are working with given basic outcomes and compute probabilities of more complex outcomes. The assigning of those "basic" probabilities has to do with the application, not the mathematics.

You say "When we look to the past there is no uncertainty in what happened… Only 1 or 0.. Did or did not." That is true in anyone case but there may be many different cases in the past where all "data" was the same but there were different outcomes. For example, in weather forcasting, we look at cases in the past where all the data (current temperature, wind speed and direction, etc.) were the same as they are now and see how many times it did or did not rain in those cases.

 

[Stephen Tashi]

When were we use it we are determining the likelihood of some hypothetical scenario in the future.

If you make no distinction between the meaning of the terms "likelihood" and "probability", you are asserting that we use "probability" when we use "probability" in a particular way.

People do not apply probability theory only to determine the probability of events in the future. For example when searching for a sunken ship, they may estimate the probability that it sank (past tense) in a particular location.

In the rigorous approach used in higher level mathematics, probability is defined abstractly and within the framework of that definition, there is no discussion of the common notion in applying probability theory that "Some events that potentially can happen actually don't and some actually do". You'll see the reason for this if you attempt to make statements about probability in the way you make statements about deterministic matters. They end up being circular, like your statement above.

As Hallsofivy said, applied probability theory makes deductions of the form : If the probability of this thing is such-and-such then the probability of the other thing is so-and-so. There is not always a restriction about the time of the things happening.

 

[switz5678]

Thanks for the replies!

Couple of quick questions/ideas.

That is true in anyone case but there may be many different cases in the past where all "data" was the same but there were different outcomes. For example, in weather forcasting, we look at cases in the past where all the data (current temperature, wind speed and direction, etc.) were the same as they are now and see how many times it did or did not rain in those cases.

I wonder if all data was exactly the same, or just the data we are/were capable of measuring. IF every input were exactly the same between two events wouldn't that lead to the same result? I realize that this borders on impossible with complex events, but say we were able to rewind time to 'redo' an event... Wouldn't the event play out in the same way? Isn't probability in application just representative of the error we introduce due to not encompassing the infinite inputs.


Stephen Tashi
"People do not apply probability theory only to determine the probability of events in the future. For example when searching for a sunken ship, they may estimate the probability that it sank (past tense) in a particular location."

This just might be pure semantics, but aren't they really using data they have in the present to ascertain where the they will find it in the future?

---
Perhaps I'm just thinking in circles.. I don't know. Hell, I'm inclined to believe that probability/chance wasn't introduced in this universe until life was formed/created. Up to that point what was going to happen was predetermined, whether we have the capability to predict it or not. One could even argue at this point that everything is predetermined if you were just able to realize every input to every part of the conglomerate we call the universe. Maybe this isn't the place for these kinds of philosophical ideas.. I just don't have a lot of people to talk to about these kind of things. This isn't because I feel superior, but people just have different interests that don't result in the obsessive questioning of abstract ideas.

 

[Stephen Tashi]

The math section isn't the place for the discussion of Philosophy. If you have comments or questions that are specific enough to be illustrated with examples of real life or theoretical mathematical problems, they could be discussed in this section.

 

[FactChecker]

I think one aspect of your question is how to distinguish between the unknown result of a past event versus the predicted result of a future event. If you think of probability theory as the theory of guessing, the distinction between past and future is not so important. It is information theory and how to use information to guess a result, be it past or future. If a coin is tossed and you do not see it land, you guess heads or tails exactly as though it has not been tossed yet. That is because your information for guessing is identical in each case. Bayesian statistics then allows you to adjust your guess based on partial information. So I like to think of probability theory as the probabilities of a certain guess being right, not as the probability that something will happen. After all, it may already have happened and we are guess what the result was.

 

[Stephen Tashi]

This just might be pure semantics, but aren't they really using data they have in the present to ascertain where the they will find it in the future?

If we work a probability problem and conclude an event has a probability other than 1 or 0, then, by definition, we don't know with certainty whether the event happened. Perhaps in a particular problem, a person will eventually know whether the event happened, but perhaps not. Problems like "What's the probability of rolling a total of 6 when two fair dice are tossed?" don't refer to a particular person tossing a particular pair of dice at a particular time. In such a "generic" problem, we won't know a specific result at some future time since the problem doesn't refer to specifics.

 

[switz5678]

Thanks.. I guess instead of hoping around the question since I didn't want to bias the results I should just give you the example that bothered me. There is a proposition which is made that God most certainly doesn't exist in a book by Dawkins. He uses probability as the metric... Is using probability in that sense viable? When they make those predictions are they using objective inputs or applying subjective analysis to determine the input value?

Out of nowhere I became compelled to seek answers, but the problem is that most of the things I read makes the assumption that you know the basics. I don't have the ability to test this stuff on my own, and through two years of college into an EE degree I still haven't reached where I want to be. I realized that I know how to do a lot of things, but I truly don't understand the why.

 

[jasonRF]

Out of nowhere I became compelled to seek answers, but the problem is that most of the things I read makes the assumption that you know the basics. I don't have the ability to test this stuff on my own, and through two years of college into an EE degree I still haven't reached where I want to be. I realized that I know how to do a lot of things, but I truly don't understand the why.

I will leave answering your first question to the folks already on the thread. But as an EE I wanted to reply to this. It is normal to not understand all of the why's, especially at first. But I have to say that, at least at the only university I ever attended, in order to really understand all (or most of) the why's requires initiative on the part of the student. Ask yourself the hard questions, work through the derivations of things on your own, and when you get stuck go to office hours. You will learn a lot that way, plus you will get to know your professors more (and the *good* professors like to get real questions that are beyond the "how do you solve problem 3 on the homework..."). In my experience many of the students do not care about the why. The fact that you do means that you have the ingredients to become a good engineer.

jason

 

[Stephen Tashi]

but the problem is that most of the things I read makes the assumption that you know the basics

What kind of things are you reading?

The basics of mathematical probability aren't useful for making proofs that certain events must actually occur or cannot possibly occur. So if someone makes such an argument and you don't understand it, you aren't missing anything from the mathematical point of view. There have been long threads on the forum about questions such as "Is an event with probability 1 a dead certainty?". They wax philosophical because mathematical probability theory does not treat such questions.

 

[FactChecker]

What we recognize as uncertainty is not within the universe itself, but is created due to our intellects inability to recognize the truth with limited access/discoveries.

At the scale of quantum mechanics there are situations that are undetermined, not just unknown. The physics itself has an aspect of uncertainty, independent of human knowledge.

 

[homeomorphic]

I see uncertainty and probability as necessary for each other, or in order for probability to have an application to a situation there must be uncertainty.

Not really. There's a subtle conceptual distinction between probability 1 and complete certainty. However, you could phrase traditional logic as a branch of probability where all the probabilities are 0 or 1, if you wanted. However, if you are just studying logic, there's not much additional benefit to doing so because you are only interested in things that have well-defined truth values in terms of true or false, so there's no need to bring in probability, although you can view it that way. But, for example, in quantum computing, there's this idea that a quantum computer can do anything a classical computer can. How can it do that if quantum mechanics is probabilistic? Answer: you arrange for everything to give you probabilities of 0 or 1, which you can do in theory.

What we recognize as uncertainty is not within the universe itself, but is created due to our intellects inability to recognize the truth with limited access/discoveries. So how can we assign these probabilities, and say these are the likelihood of scenarios of universal beginnings, when there is no uncertainty of the universe in past tense?

I'm not sure there's any more uncertainty "of the universe" in the future than in the past or even if such a concept is well-defined. In fact, relativity teaches us that there isn't really any such thing as "THE future" because such a concept blatantly depends on simultaneity (the idea that everything that happens NOW is simultaneous, everything before that is the past, and everything ahead is in the future). There's my future, or your future (everything in your future light-cone), but no "THE future". Uncertainty, in the applications of probability DOES deal with HUMAN uncertainty, not some hypothetical "uncertainty" of the universe.

 

[switz5678]

Right on, I appreciate the feedback! I got one more question and I don't know if it follows what we are discussing, but oh well...

Say we were to discover a seemingly random string of numbers.. I am using numbers because my mind works that way, but I mean these numbers to be analogous to events, and phenomenon we observe or discover. Quantum Mechanics perhaps..

Say we see something like 2,487,-12,.11224,Green, Jpn

We would say wow... There seems to be no pattern. Random! We could even add another 487 to the mix and say that this shows a probability wave where 487 has the highest amplitude.

One day while trying to understand this string we discover

1+1=
493-6=
Blue + yellow=

At that point was what were observing random, or just seemed random because all we saw was the outputs?

or is random something akin to 1+1=7, where the inputs don't dictate the output. Is it Both?

Aside
Quantum Mechanics is just mind reeling to me.. It seems to fly in the face of everything I've learned, which I'm not implying is therefor wrong. I could be using it in this example incorrectly, and if that's the case I apologize.