Burden of Proof

[Darth_Yuthura]

'When you get into standard units, this ability is lost.'

 

Bad wording. I meant that inches, feet, yards, and miles are not as easy to work with as meter/centimeters/kilometers. These units of measurement work on factors of ten where standard American lengths are 5280, 1760 (yard), 63360 (inch) Liters and ML as opposed to cups and gallons. These American units are not as easy to convert as metric and although they tend to follow factors of 3 (length) and 4 (Volume), they are not neatly arranged like hexadecimal.

 

I would assume that when working with computers, you have a system of increase that works exponentially. You add a new 50/50 function to a system, you double the possible outcomes that you originally had. If you go 2,4,8,16,32,64,128... this universally makes sense to me.

[Bimmerman]

'When you get into standard units, this ability is lost.'

 

Bad wording. I meant that inches, feet, yards, and miles are not as easy to work with as meter/centimeters/kilometers. These units of measurement work on factors of ten where standard American lengths are 5280, 1760 (yard), 63360 (inch) Liters and ML as opposed to cups and gallons. These American units are not as easy to convert as metric and although they tend to follow factors of 3 (length) and 4 (Volume), they are not neatly arranged like hexadecimal.

 

I would assume that when working with computers, you have a system of increase that works exponentially. You add a new 50/50 function to a system, you double the possible outcomes that you originally had. If you go 2,4,8,16,32,64,128... this universally makes sense to me.

 

 

Ahh, gotcha. The "Imperial" system....sucks. I hate working in it. However, because all old American engineers don't speak metric, and all the new engineers in school are taught metric primarily (but are expected to understand Imperial nontheless), there is a bit of a disconnect. Every engineer I know under 25 or so, when confronted by a problem in English units, immediately converts everything to metric, does the problem, then converts the final values back to English. It sucks, but that's how we do it.

 

Cliffs: Metric is win, Imperial sucks, Americans need to quit being stupid.

 

Back on thread: The exponential system you described is base two, and is binary converted to digits.

 

0 = 0

1 = 2^0 = 1

2 = 2^1 = 10

4 = 2^2 = 100

8 = 2^3 = 1000

 

15 = 2^3 + 2^2 + 2^1 + 2^0 = 1111

 

...and so on. Every number can be described as combinations of powers of two, which is the basis for binary.

[Darth_Yuthura]

Ahh, gotcha. The "Imperial" system....sucks.

 

Back on thread: The exponential system you described is base two, and is binary converted to digits.

 

Yeah, I really need to get my terminology down. I'm good at mathematics, but certainly would be hopeless at teaching it.

 

But in regards to the thread...

 

It can properly be assumed that mathematics is perfect, but any errors that come with it are primarily a result of human error. When a Mars spacecraft was lost as a result of the Imperial units not being converted to metric, the math was perfect; but not properly applied to the situation. The only times when it does fail is when the logic is flawed. Other than that, you will always get the same answer for a given equation and never anything different.

 

I recently spoke with someone about my arguing on this forum and how I go about the subjects. He suggested that before I ever make an argument or counter argument that I go back and brush up on what I know. Then when introduced to something new by other people, go back and read about subjects that I haven't already studied. The whole purpose of this kind of thread isn't so much presenting all the facts you already know, but to allow others to introduce you to new concepts. At that point would you step away and read up on the subject to a broader extent than what you would see on a forum post.

 

'The burden of proof' is what this subject is about. Is there really any argument where one does not ask for another person to present evidence to prove their point? Most who've already made up their minds don't need evidence while others would seek out what evidence leads them to their own conclusion. Therefore I would assume that the art of proving a point isn't so much in the evidence itself, but the manner in which you present it to other people. If you downright disregard or insult the other person, they will not be bloody likely to take all the proof in the world that you can throw at them. Instead it requires more understanding their side of the argument and deciding whether to try and get them to think what you believe, or maybe to consider what they have to say instead. There is no shame in withdrawing from an accusation if you see good reason to do so, but don't make an assumption based on your personal feelings on the matter. All too often people will let their pride get in the way and they make the most absurd justifications in order to keep you from saying 'I told you so.'

[Jae Onasi]

It can properly be assumed that mathematics is perfect,

I would not put that much faith in something created by man. I would not make the mistake of saying it's 'proper' to assume that it's 'perfect'.

Other than that, you will always get the same answer for a given equation and never anything different.

 

'

You can get different answers when working with Non-Euclidean geometry and string theory.

[vanir]

Have to agree with Jae's sentiment although possibly for different reasons. Given a series of assumptions, math is reliable. It would be better to say the actual workings of the physical universe are perfect although I'd suggest placing even that statement within a strict context.

 

Math works fine in non-Euclidean geometry but true enough the math for string theory is largely absent and that for QP is incomplete, lending itself to singularities. These are the reasons for some interest in a unified field theory, Einstein's philosopher stone.

 

Some like myself believe however, like Einstein that it lay in plain view among Relativity and classical physics. This may be supported by recent JPL observations indicating a variant c. based upon gravitational energy distribution. The implications are not yet clear to me, but my academic instincts are way up on this.

[Darth_Yuthura]

In non-Euclidean geometry and string theory, those are incomplete. This doesn't mean mathematics doesn't function in these fields; it simply means that these subjects remain incomplete. If you don't know how to properly apply the mathematics into what you are working with, it goes to human error. In such fields are an assortment of unknowns. It doesn't result in math being imperfect; just incomplete.

 

Logic shows that every cause has an effect and as long as all the causes are the same, the effects will also be the same. If even the slightest distortion is present, you should get the same outcomes within mathematics as you did before. If you are including something such as cloning a person, you will NEVER get the same fingerprints because such traits are completely random. If in the case you calculate something random, then you cannot create a definite effect. That is because something random can't be predicted or projected.

[Jae Onasi]

In non-Euclidean geometry and string theory, those are incomplete. This doesn't mean mathematics doesn't function in these fields; it simply means that these subjects remain incomplete.

If they're incomplete, then how can they be perfect?

[vanir]

You'll have to excuse me, I generally don't like pulling apart posts as often this is simply done in an argumentative way at forums, but there are a couple of specific sentences I'd like to examine.

 

Logic shows that every cause has an effect and as long as all the causes are the same, the effects will also be the same.

This is actually where math makes the departure from mechanics to modelling. Logic also shows that any evolutionary system is so complex that no amount of processing power can replicate predictive results. It's chaos theory and integral to modern views of modelling natural mechanics.

Here's what happens, you put the same data in, exactly the same data, and you use exactly the same equations, you get different results every time with no prediction. Been tried. Evolutionary processes, even such generalised and simplified ones as a proto-solar evolution simply happen anthropically maybe once in a thousand tries, using the same math and same data trying to model the early formation of the solar system. One time you get four planets, another none, the next two planets out near Pluto's position, it seems completely random but is in fact complex evolutionary diversity. It was actually a revolution among mathematicians which created Chaos Theory, because they were expecting at least some degree of rational predictability with a model for the formation of our solar system, since we've pretty comprehensive data for it. It was a completely unexpected result.

 

If you are including something such as cloning a person, you will NEVER get the same fingerprints because such traits are completely random.

Not so much random as complex diversity. There is a formulaic process, but even where concentrating solely on the macro scale the data input and calculations are so complex that results are unpredictable. This is also shown in animal evolution, some species traits have nothing to do with natural selection, however certainly some process is at work.

 

If they're incomplete, then how can they be perfect?

I should think even if they were complete, perfect wouldn't be an accurate description. More like, interesting.

[Darth_Yuthura]

If they're incomplete, then how can they be perfect?

 

Obviously before Newton, there was a means by which to calculate every aspect of calculous he was responsible for; we simply did not know it yet. Newton showed it to us. Evidence shows that Orcemedies may have figured out calculous centuries before, but the knowledge was lost until another person figured out the same things.

 

Don't forget that math is not corporeal. It is not a physical identity, but exists entirely as idea. You can reasonably assume that once you know the right methods, you will always get the right answer. If you don't, you can't.

 

It is like coming across a crime and not knowing what happened and who was responsible, but perfecting a theory in order to determine what happened. Just because you don't know what happened at first doesn't mean you can't eventually figure it out.

 

In regards to the 'evolutionary theory,' that does not work in regards to mathematics. And even if it were; just because something is too complex to figure it out doesn't mean it can't be calculated... just not by us.

 

You can use mathematics to calculate the trajectory you need to position a spacecraft into Mars' orbit, but they can't possibly account for ALL forces that would act on the spacecraft. If their math was wrong, they COULD be able to diagnose the problem and adjust the course of the spacecraft in order to account for those unforeseen forces. If the spacecraft was lost, they could go back and generate an alternate solution that WOULD have worked, had they plugged in an alternate trajectory and velocity. If math weren't perfect, then they might as well just assume it doesn't matter and throw the spacecraft wherever it wants to go and assume the outcome will be different each time.

[vanir]

Obviously before Newton, there was a means by which to calculate every aspect of calculous he was responsible for; we simply did not know it yet. Newton showed it to us. Evidence shows that Orcemedies may have figured out calculous centuries before, but the knowledge was lost until another person figured out the same things.

 

Don't forget that math is not corporeal. It is not a physical identity, but exists entirely as idea. You can reasonably assume that once you know the right methods, you will always get the right answer. If you don't, you can't.

 

It is like coming across a crime and not knowing what happened and who was responsible, but perfecting a theory in order to determine what happened. Just because you don't know what happened at first doesn't mean you can't eventually figure it out.

 

In regards to the 'evolutionary theory,' that does not work in regards to mathematics. And even if it were; just because something is too complex to figure it out doesn't mean it can't be calculated... just not by us.

 

You can use mathematics to calculate the trajectory you need to position a spacecraft into Mars' orbit, but they can't possibly account for ALL forces that would act on the spacecraft. If their math was wrong, they COULD be able to diagnose the problem and adjust the course of the spacecraft in order to account for those unforeseen forces. If the spacecraft was lost, they could go back and generate an alternate solution that WOULD have worked, had they plugged in an alternate trajectory and velocity. If math weren't perfect, then they might as well just assume it doesn't matter and throw the spacecraft wherever it wants to go and assume the outcome will be different each time.

 

Now we're in fascinating territory. Here's where some PhD physicists believe in God. Incredible isn't it? Not really.

 

We don't have any lack of data for the formative solar system for example. You point a telescope, use some field equations, the data is right there. We're not talking about unknown values, we're talking about inherent variables and probability functions. A lightwave, is a probability function. No less real, but you can't describe it in math any other way. Toss in probability, you get a lightwave, get definitive and it disappears, the math no longer works. You have to describe a wavefunction duality or the description just breaks down, probability is an integral part of physical reality, an atom cannot exist without the probability wavefunction, it is an entirely inaccurate description otherwise and simply does not work when applied to engineering.

 

So first you never get the right answer. You get one of many right answers based upon a series of premise or presumption.

 

Secondly algebra was invented by the Tibetans ca.10th century, the name is from the Middle East which is where it came to our hands via the Silk Road. Calculus is not usable for theorum because there is no zero value to it, so it can't postulate. Calculus might be said to be retrospective, algebra predictive.

 

Physical evidence shows clearly calculus was used by the ancient Egyptians, who aligned megalithic structures geometrically and astronomically.

 

The criminal forensic analogy is a very questionable one as forensics is wholly circumstantial evidentiary procedure, it is designed mostly to manipulate juries but otherwise can only suggest avenues of further research as according to the anthropologist ethic "correlation does not infer causation."

Just because you weren't there means precisely you cannot possibly have the slightest idea what actually happened. And all you can attempt to do is suggest reasonable possibilities based upon purely circumstantial and necessarily biased evidentiary procedure. This is how the court systems work, hence it is a matter of reasonable doubt and presumption of innocence among the more democratically benevolent ones. One of the most important steps in criminal procedings is the establishment of criminal intent, because all other evidence is circumstantial and largely open to interpretation. The smoking gun is just a smoking gun, not a slam dunk except for soap opera junkies who hate life and are looking for a Jesus to crucify.

 

For the space probe analogy, geometric probabilities are a lot easier to figure than complex evolutionary diversity since it is not such an evolutionary system until great distances become involved. But certainly a recent problem has been identified by JPL in 2004 termed "a weak anomalous acceleration" which has thrown the entire current cosmological model into doubt.

Little things affect big things, complex evolutionary diversity.

In other words the probes aren't where they should be right now, none of them. Nobody knows why.

 

But certainly Newtonian caluculations were in far greater error. If Relativistic math had not been used by NASA since the very first space launches not a single probe would've ever reached anywhere near its destination, and again, nobody would've known why.

 

I have some homework for you DY. Look up Brownian motion and tell me what you think.

[Darth_Yuthura]

So first you never get the right answer. You get one of many right answers based upon a series of premise or presumption.

 

Secondly algebra was invented by the Tibetans ca.10th century, the name is from the Middle East which is where it came to our hands via the Silk Road. Calculus is not usable for theorum because there is no zero value to it, so it can't postulate. Calculus might be said to be retrospective, algebra predictive.

 

For the space probe analogy, geometric probabilities are a lot easier to figure than complex evolutionary diversity since it is not such an evolutionary system until great distances become involved. But certainly a recent problem has been identified by JPL in 2004 termed "a weak anomalous acceleration" which has thrown the entire current cosmological model into doubt.

 

I have some homework for you DY. Look up Brownian motion and tell me what you think.

 

We're straying off the subject. I want to remind people that I have only breached the surface of calculous. Beyond that, I'm climbing onto a limb.

 

I did examine the Brownian motion theories and I understood not so much the calculations themselves, but why they apply to certain situations. 'Random' doesn't exactly mean you'll get any answer just as easily as another, but it could be like a bell-shaped curve, where a some numbers are simply more likely to come up than others. If you used Brownian motion theory, you could predict a pattern after a few random outcomes with a degree of certainty. But this can only be done for a short-term model and breaks down the further in time you try to predict the pattern.

 

I would think that my opinion isn't worth much if I don't know how the Brownian theory actually functions, but... I would say that I am fascinated by the idea that you could see something seemingly random and be able to discern a pattern to it that you could apply to a problem with a degree of certainty. It would be extremely difficult, if impossible, for me to actually apply this to a real use.

 

You are right that it's easier to launch a spacecraft to a specific destination with the gravity of the sun, moon, earth, jupiter, saturn, and many other bodies light-years away exerting their astronomically-small pull on the craft. That tied with the presence of solar wind, the not-quite-so empty vacuum of space, and margin of safety for human error... you can never account for every force of nature, but because the major forces are the gravitational pull of planets and solar wind, you really just have to account for those.

 

I would continue to say mathematics is perfect, but it's only as perfect as it was created to be. You will ALWAYS determine that the cube route of 329 is 6.903. Of course that is not literally correct if you had to be precise to the 1:10,000 scale, but few people care whether you estimated 328.937 up for a nice, solid number.

 

I think it would be best to assume that you will always get the same results on paper, but that what's on paper won't always be what you took from the real world. The more complex the function, the less reliable your equations will become. Any malfunctions in math are due to either human error, or that something in the real world hadn't been taken into account on paper.

[Ray Jones]

When an equation doesn't work to describe a physical phenomenon the way it's ought to describe it, it doesn't mean the least maths or its laws have failed. The equation is wrong or insufficient, which is a huge difference, actually.

[vanir]

My point with the Brownian motion was simply an interesting observation. There is no such thing as an inert field. For all intents and purposes it is like watching a pool of water in a closed laboratory environment for long enough and getting waves for no reason. Probability function. What's more recent observation dictates these seemingly random probabilities are intensely dramatic, not even the bell curve Einstein supposed.

 

The dramatic way to put this, and what I'm talking here is strict science, get some nothing and somethings spontaneously create themselves. We'll call it virtual particles or information potential for the string theorists. Any field, even a zero point field (ie. classical "nothingness") has motion. We use fluids to study this phenomenon and call it Brownian motion.

 

The point is that according to professional mathematicians and theoretical physicists no matter how complete the data is or comprehensive the math, the best possible result is a likelihood. Math can model natural process, but it cannot ever hope to adequately describe it.

 

When mathematical models for the formation of the solar system were being calculated the seemingly random results were not due to any lack of data or innacurate calculations, they were not due to human error, the math wasn't wrong, incomplete or insufficient.

They were due to an inordinate number of equal likelihoods in the actual formation of the solar system. Given precisely the same circumstances any number of things might've happened.

 

When we say what did happen was a right answer and try to use process of elimination as a scientific process to determine wrong answers we're making a mistake known as anthropic principle.

If you recreated the actual formation of the solar system, done precisely the same way, without changing a thing, something completely different is just as likely to happen as what did happen.

The M-theorists describe this with alternate timelines. We exist simply upon one particular timeline where several were/are possible for every circumstance and situation, all coexisting as alternate realities in separate dimensions. Reality is surprisingly like that.

 

In one alternate dimension our solar system has two planets, another it is just a large gas cloud, another again it is a twin system and all of them resulting from an identical initial formative process. Just all equal likelihoods, nothing to do with the math.

 

In the past what's been done is to try to describe higher likelihoods of probability with bell curves, but recent observations suggest this in error, with extreme variation in equal likelihood to subtle ones at any given instance.

 

Here's an interesting thought-experiment. Get a zero point field, a nothingness and watch it for a while, virtual particles pop into and out of existence and at some point a real particle creates itself. Spacetime immediately folds around the presence of mass-energy, it's a snowball effect, which is a description of spacetime crunch, big bang, inflation...

[Darth_Yuthura]

Okay; way too much effort exerted on that subject. I do comprehend that aspect that you are speaking about, but that doesn't make the statement about math's credibility being in question. Three squared will ALWAYS be nine unless the symbols for three or nine should change before the problem is solved.

 

The thread is meant to emphasize the burden of proof, I believe. The issue is where that burden lays when proof is demanded. Those who make a bold statement should be expected to provide the evidence or proof needed, or their statement doesn't mean all that much. You should not be expected to have your statement taken for granted unless someone disproves you. Because quite frankly, there are an infinite number of statements that you can make which are BS, but can't be disproved. Only when something has been presented and acknowledged as the truth, it holds no water.

 

When a subject hinges upon a vital piece of evidence, then that is when you cannot rely upon a supposition. When you contribute a small element to a larger issue, then it is not so critical to emphasize whether it could be wrong or not.

 

When you shoot down a theory, then I think it should be expected that you provide a better alternate theory. Of course there are some dilemmas that don't have any favorable solutions, so that brings this into question. I have no idea how the US should pull out of Iraq, because I don't see any effective means by which you can do so without the country going to hell.

 

I could go more into detail about this, but that would violate the rules of this thread.

[vanir]

First let me just say DY that I really respect the deep thought you place in things. You're a cool chick. Oh awesome, arctic monkeys just came on the radio, ya gotta listen to them, very cool band, right up your alley.

 

Three squared will ALWAYS be nine unless the symbols for three or nine should change before the problem is solved.

Yes but the point I was trying to make is that when you use 3-squared to describe a physical/natural process you are talking about a mathematical model and not the process itself. The study of the natural universe should not be confused with the natural universe itself.

 

The thread is meant to emphasize the burden of proof, I believe.

Precisely, which is why math cannot be accepted by theoretical physicists to conclude any natural process alone. It must be correlated by reproducible experimentation/observation in nature and then it is forever subject to falsification. Math is great, 100% reliable and does not describe physical reality in all its complexity. It is just a language, with precepts involved.

As physical evidence it is only circumstantial, but can offer one of several reasonable likelihoods for any given problem.

 

The alternative theory I would propose for strict calculus is probability function.