I've had the discussion before with Elroch . Seems he thinks in purely mathematical logic. I've suggested abstract thought can never be a "proof" for the possibility of what might have occurred or will occur. He begs to differ. What it often comes down to are a priori beliefs. Citing mathematical probabilities as evidence just doesn't work for me. What ends up happening is any possibility based on the maths results in a prediction of probability. The formula may predict 1 in 100 Gazillion, no matter the possibility exists - therefor it could have happened, becomes a mantra.
Does True Randomness Actually Exist? ( ^&*#^%$&#% )
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Feb 7, 2020
0
#763
If an predicted event did not occur, there was no chance of it happening, regardless of what the maths suggested.
Same for an event that's observed to exist. The maths may suggest it as being a highly unlikely event to have happened. Really? It did happen, the chances were 100%.
The maths may be the best tool man has invented to make sense of it all, but is not as reliable as presumed at probabilities when applied to the real world.
Feb 8, 2020
0
#764
Optimissed wrote:
Elroch wrote:
Review
the concept of randomness is what is used to describe that which is not known, i.e. is uncertain. To quantify this uncertainty, the tool called Probability Theory was designed (and can be shown to be, in quite a strong sense, the only one suited to the job). (It happens that the mathematical theory has (at least) two entirely separate applications, where the same mathematical model is used to model two separate sets of concepts, but as long as you know which is the one being used, all is well).
Example
For example, from your point of view, you might not know if it is going to rain tomorrow. To you tomorrow's weather is random. You might care to quantify your uncertainty, in which case you are using the basic idea of Bayesian probability, where numbers quantify beliefs, according to some very natural axioms. If you have seen the weather forecast or have other information, you quantification may be different. If your information is extremely reliable and definite, the randomness may be almost gone.
Making it general
Some are thinking this notion of a "viewpoint" (which may have partial information) is just a distraction from "real" randomness, which lacks this. But when you go into the details what you find is that "absolute" or "general" randomness really means randomness to the combination of some set of viewpoints, which can be considered a single viewpoint that combines all their knowledge. The best I can do to make the notion of "absolute" or "irreducible" randomness concrete is to note that it describes the combination of all viewpoints that are not in the causal future of some event in space-time.
For example, all viewpoints earlier in time than the roll of a die can be combined and we may still have no idea about what number will come up. (If some special viewpoint knew the die was lopsided, or had very specific information on how it was to be rolled, the probabilities might be different). And if you add a viewpoint after the die has been rolled, the randomness has vanished as surely as the collapsing of a wave function.
Who on Earth wrote that?
I did, in that post.
The problem with it is that the writer is using words like "viewpoint" symbolically for something we are not aware of.
Good point. Definitions are needed when concepts are not clear. A viewpoint is characterised by some set of information, some of which may be used to infer other facts of interest or probabilities for them.
The meaning of "viewpoint" in the context of the passage seems to be described by the combination of all viewpoints that are not in the causal future of the use of the word "viewpoint" in space-time.
I suspect that is a joke. If so, haha.
It's obvious that the writer is immersed in academia and hasn't managed to get his nose out of it in order to get an overview. I'm afraid it doesn't beat discussing what is required of a "pattern".
The writer is in the business of quantifying reality and hasn't been part of academia for a few decades, though he has continued to learn from those who are.
Feb 8, 2020
0
#765
MustangMate wrote:
If an predicted event did not occur, there was no chance of it happening, regardless of what the maths suggested.
Once you have the information that a die has rolled a 6, your belief state that it rolled a 1 should be zero. However, to infer that your belief state that it would roll a 1 should have been so before the die was rolled, when you had less information, is false. You can see how this relates to beliefs (probabilistic view of uncertain events) being dependent on viewpoint in an obvious way.
Same for an event that's observed to exist. The maths may suggest it as being a highly unlikely event to have happened. Really? It did happen, the chances were 100%.
The maths may be the best tool man has invented to make sense of it all, but is not as reliable as presumed at probabilities when applied to the real world.
(Bayesian) probability theory is provably the only consistent way to quantify belief (given pleasantly mild assumptions). See Jaynes - Probability theory: the logic of science.
Fortunately it's simple enough for everyone to understand, like arithmetic is.
its my hair i pull. cuzza ur null and dull skull. its notso full. its moreso a empty hull. its ur attitude we need2cull....cuzza ur bull. so s/o wrap him in wool and send him back to the post office.
Feb 8, 2020
0
#767
Elroch wrote:
MustangMate wrote:
If an predicted event did not occur, there was no chance of it happening, regardless of what the maths suggested.
Once you have the information that a die has rolled a 6, your belief state that it rolled a 1 should be zero. However, to infer that your belief state that it would roll a 1 should have been so before the die was rolled, when you had less information, is false. You can see how this relates to beliefs (probabilistic view of uncertain events) being dependent on viewpoint in an obvious way.
Same for an event that's observed to exist. The maths may suggest it as being a highly unlikely event to have happened. Really? It did happen, the chances were 100%.
The maths may be the best tool man has invented to make sense of it all, but is not as reliable as presumed at probabilities when applied to the real world.
(Bayesian) probability theory is provably the only consistent way to quantify belief (given pleasantly mild assumptions). See Jaynes - Probability theory: the logic of science.
Fortunately it's simple enough for everyone to understand, like arithmetic is.
Your understanding of the maths is unquestionably very high.
I'll only point out, your 1st reaction was to use the rolls of dice as example in support of your thinking, that the maths of probability are can be used to formulate beliefs.
Abstract thought, of any kind, should not be used as such, to formulate beliefs of certainty to things unknown. Mathematics is a tool designed to measure and understand what is being observed. It should not be the foundation of belief.
I'll suggest what is being offered as explanation is in fact - believe something is possible and use the maths as supporting evidence. Abstract thought can not be applied in this manner. You suggest by looking at the maths, which can not be refuted, it offers a logic that becomes a certainty of describing how reality works.
I simply disagree.
Mathematics and probability theory is but one tool to be used. If it becomes the only tool, it's far too simplistic a viewpoint. There are many ways for us to make sense of the world. Maths can not be argued with. The beauty is it can be used to prove itself ! (and should end there)
Feb 8, 2020
0
#768
Maybe this provides an example -
Does Alien life exist?
Maths can be applied to make calculation of it's probability, as the existence of Earth like objects can be measured. A +/- range can be agreed upon. At what point is the line made to conclude possibility is real? What % determines it's likely or not? For some, a 1/M qualifies. Others will think more realistic odds are required before they'll accept the possibility. I'll suggest, it really doesn't matter, what the probability is.
It remains unknown as it's unobserved. Hence, I don't know. Regardless of what the maths say, I believe it's highly unlikely based on my experience and observations. Others might say, a high possibility, but still remains unknown. While still others will believe with certainty that alien life exists and have the maths to prove it ... while others may claim the opposite, that the maths disproves the idea. Same math was used, just a different interpretation and conclusion.
Point being abstract thought can be applied in all shape and manner. To use the maths as foundation of belief is mistaken.
Just as it's quite mistaken to assume maths are evidence of randomness.
Feb 8, 2020
0
#770
MustangMate wrote:
Elroch wrote:
MustangMate wrote:
If an predicted event did not occur, there was no chance of it happening, regardless of what the maths suggested.
Once you have the information that a die has rolled a 6, your belief state that it rolled a 1 should be zero. However, to infer that your belief state that it would roll a 1 should have been so before the die was rolled, when you had less information, is false. You can see how this relates to beliefs (probabilistic view of uncertain events) being dependent on viewpoint in an obvious way.
Same for an event that's observed to exist. The maths may suggest it as being a highly unlikely event to have happened. Really? It did happen, the chances were 100%.
The maths may be the best tool man has invented to make sense of it all, but is not as reliable as presumed at probabilities when applied to the real world.
(Bayesian) probability theory is provably the only consistent way to quantify belief (given pleasantly mild assumptions). See Jaynes - Probability theory: the logic of science.
Fortunately it's simple enough for everyone to understand, like arithmetic is.
Your understanding of the maths is unquestionably very high.
Thank you. Your honest desire to find the truth is clear.
I'll only point out, your 1st reaction was to use the rolls of dice as example in support of your thinking, that the maths of probability are can be used to formulate beliefs.
Abstract thought, of any kind, should not be used as such, to formulate beliefs of certainty to things unknown. Mathematics is a tool designed to measure and understand what is being observed. It should not be the foundation of belief.
[my emboldening]
"Should" indicates advice based on a subjective viewpoint. The problem with these broad generalisations is there are so many examples of what you condemn being hugely successful. For example, based on a very small empirical base (primarily the discovery that the speed of light was constant), Einstein constructed a new model that replaced the flat Universe of Galileo and Newton with a 4-dimensional curved manifold where space and time are not separate things, and a large number of (strong) beliefs arose from the mathematics. Some of these have been tested over the last century, notably the existence of gravitational waves, a massive landmark involving 100 years of theory and several decades of unsuccessful experiments.
I'll suggest what is being offered as explanation is in fact - believe something is possible and use the maths as supporting evidence. Abstract thought can not be applied in this manner.
Large amounts of the (often tested and correct) beliefs of science (which go through phases from idea to hypothesis to tentative result to accepted truth) are based on mathematical reasoning.
There is a special status to abstract reasoning based on probability theory because of its uniqueness. This makes it unlike a mathematical model in physics which can generally be subsumed as an approximation to another more precise and general model.
You suggest by looking at the maths, which can not be refuted, it offers a logic that becomes a certainty of describing how reality works.
Reality is obliged to be consistent with mathematical truth. That is because mathematical truth is universal.
I simply disagree.
Mathematics and probability theory is but one tool to be used. If it becomes the only tool, it's far too simplistic a viewpoint.
It merely confuses the issue to talk about two things at once.
Mathematics is a vast array of tools - basically every technique related to quantifying the behaviour of the Universe. Mathematical models of the world can be (apparently) precise, approximations or wrong.
By contrast, Bayesian probability is a single purpose - quantifying belief - modelled by a single unique mathematical theory - probability theory - which is not subject to being replaced in the same way.
As an analogy, the mathematics of counting is not subject to dispute. It doesn't matter what you are counting, the natural numbers are right for it, and their behaviour is fixed. All sorts of models of the physical world involve counting, and all are obliged to be consistent with the mathematics of counting.
There are many ways for us to make sense of the world. Maths can not be argued with. The beauty is it can be used to prove itself ! (and should end there)
Well, actually that is the thing it can't do (as Goedel discovered) as long as you deal with anything as complicated as the natural numbers. It is necessary to take it as true that the natural numbers is consistent. Most do believe that this is so, and I am one of them.
Feb 8, 2020
0
#771
Your understanding of the maths is unquestionably very high. - MM
Thank you. Your honest desire to find the truth is clear. - Elroch
Feb 8, 2020
0
#772
The only truth in mathematics is that the numbers add up !
Numbers provide truth for unobserved phenomenon ?
That's hilarious !
Feb 8, 2020
0
#773
Trying to explain life with mathematics does not add up. All it is a shield at this point.
Yes.
MustangMate wrote:
I've had the discussion before with Elroch . Seems he thinks in purely mathematical logic. I've suggested abstract thought can never be a "proof" for the possibility of what might have occurred or will occur. He begs to differ. >>>
I think that Elroch would be wrong to differ. Abstract thought still manipulates concepts which we are aware of or at least which are connected with concepts we're aware of partly through observation, so it's still based on an imperfect universal model, as all universal models necessarily are. Ideas are symbolised and manipulated mathematically, resulting in further symbols which are, in part, a function of the original ones and the result then has to be interpreted back into verbal language. I have met some people who don't think this is true but I assume they don't know what they're talking about, in a very literal sense.
It is the interpretative phase that causes the problems. Even the most brilliant mathematician might not be able to interpret the equations back into English. So at the very least, it can NEVER be a proof. All proofs must be backed up by empirical experimentation based on observation. Otherwise we can only take the word of someone who has vested interests.
<<<What it often comes down to are a priori beliefs. Citing mathematical probabilities as evidence just doesn't work for me.>>>
They aren't evidence so far as I can see. Certainly, they are not conclusive evidence. Believe it or not, it's why I can't prove that telepathy exists, because there is always a ridiculously outlandish chance that positive results, which occur all the time when an experiment is set up properly, are just a fluke.
Feb 8, 2020
0
#776
MustangMate wrote:
The only truth in mathematics is that the numbers add up !
Are you saying that? If not, why write such a falsehood? Do you think stating a falsehood is a powerful rhetorical technique?
Numbers provide truth for unobserved phenomenon ?
That's hilarious !
Mathematics is used all the time to confidently reach conclusions about unobserved phenomena. There is not a single part of the hard sciences where this is not important.
If you learned about how Einstein derived his special and general theories of relativity - theories which pushed aside the mathematics that had been used to deal with space and time and replaced it with substantially less intuitive and more complicated mathematics - you would see how much of this is based on mathematics rather than the (quite limited) empirical facts that motivated the need for a new theory.
The fact that there are such striking examples - another is the Higgs boson - should be a hint that this works.
[I pick those two examples especially as they are associated with empirical verification that took a century in one case and half a century in the other].
And unless it produces predictions which are in line with empirical observation, it's completely meaningless. "Mathematics led" doesn't mean "no observation necessary".
88
Feb 8, 2020
0
#779
The only truth in mathematics is that the numbers add up. This is certainly true, if it's understood the suggested meaning. Formula's and equations "add up". Math proofs are developed to verify existing maths.
A single digit number is purely abstract. It has no meaning sitting alone. A number only takes on a meaning in conjunction with other numbers. When used correctly they will "add up".
2>1 . Adds up
1>2 does not add up - improper use of the numbers and symbol.
Simple idea. Too much can be read into the statement, looking for falsehood.
Feb 8, 2020
0
#780
Maths reveals a coin flip to be 50/50. This helps us understand possible outcome using probabilities.
The math make sense, is logical - it adds up.
But here is the gist - It does not prove anything other than itself. It is but an abstract tool. The math is not disputed - hence the math proves itself. And nothing else.
Only by using other math can it be proved the odds are 50/50. Practical attempts of flipping a coin any amount of times will reveal something other than 50/50.
Silver, I think Elroch's attempt was better than that, but for me it was way too technical, as though it had been constructed by an elephant's foot specialist because he was too small to even know it was attached to an elephant.
I agree with you. his definition is very well thought for mathematics. but that's where it should stay. trying to apply it to an everyday use is just funny.