Why is Math so Powerful?

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Yes, they are. Quantum physics makes them play rather oddly, but you're still missing the point - if I throw a dice, I don't know what number I'm going to get, but it isn't infinitely variable. It will be one of a set number of values. Similarly quantum physics is playing with a limited range of choices and isn't completely random - or, if it is, then there are no laws at all.

And no model of reality is faithful. They are models based on limited data. Depending on your needs and resources, an inaccurate model can still be useful. Newtonian physics is still taught in schools despite Einsteinian physics being more accurate, because Newton's equations are simpler. If you're planning on launching a space probe, they won't do, but for most terrestrial problems they are accurate enough.

Computing the odds is NOT predicting a definite outcome.

In the current theory the eigenvalues of the operator describing the observable when squared produce the probability of the outcome associated with that eigenstate. This in no way implies a particular outcome. Run an electron through a Stern Gerlach magnet. What is the spin? 50:50 up:down. Like tossing a coin. You only know the result after it happened and it could have been either.

Not only that the many-worlds interpretation is consistent with the theory (which does not make that interpretation true, mind you, but at least it is possible).

ruveyn

You are forgetting one of your key points you wrote above.

AND



Now, perhaps you simply wrote your statements incorrectly. Given the manner in which you made your statements above, these seem to be your key arguments.

The problem with the bolded elements in your description is that they are both incorrect. A universe does not need to be entirely ordered, in order to produce consistent results. It merely needs some semblance of order in the system. A system that has random elements intermixed with ordered ones can easily produce consistent results regardless of the attributed values. It depends entirely on the context of the system created.

A random element will not throw the whole of existence into doubt. It can certainly make the understanding of it more complicated and difficult.

In fact your previous arguments are wholly inconsistent with your new post. They are opposite of what you originally said:



Namely the bolded part. If something is variable, than it is not ENTIRELY ordered. It has limits. Which means you have one or more mechanics that are ordered, and one or more mechanic that are not ordered. This results in a DYNAMIC system.

An ENTIRELY ORDERED universe means it has one possibility period. In other words, the entire idea of variability is nothing more than illusion. Everything becomes illusory. A STATIC FATE. The dice you rolled would and will always end up the same in reference to the local timeline. As a result, under a system that is as you originally stated, you can in fact read the future once you understand all the basic priniciples. You could figure out what happens for the rest of eternity. No exception.

A universe with order and random elements intermixed, means you can still predict events, get things correct, and understand the mechanics. However, you can never be 100% accurate all the time.

Also to return to a previous post:



Time as a consideration in the universe is in question. Scientists can't even decide if it truly exists. This is why it's often regarded as spacetime (A physical aspect of the effect we describe). If time doesn't exist your point is moot as an effective example.

And again...lastly, prove that the laws of physics are static and not dynamic. What is commonly refered to as the big bang, seems to disagree with your last assertion. The laws we work with start breaking down around 300,000 years from the event. This seems to suggest the laws are dynamic, and that merely it requires tremendous energy to alternate their function.

So while your correct in saying that there may be things which are static, that does not make an entirely STATIC, entirely ORDERED universe. Given what we know about infinite sets and variability it is much more likely there are more random elements, as opposed to more static ones.

Now there's your problem... not knowing whether you are throwing a single die, or several dice.

Maybe you have caught the problem in a nutshell. Quantum mechanics predicts indeterminacy of outcome, but you want that indeterminacy to always collapse to a singular form. I.e. although there could be multiple outcomes, you think that one outcome must be preordained.

Maybe this would help:
http://en.wikipedia.org/wiki/Schrödinger's_Cat_Trilogy

You seem to be under the impression that no random variable can assume infinitely many values. An easy counterexample to that is the standard normal distribution. It is a continuous function centered on zero, with area 1, but can assume any value. It doesn't have a set number of values.

Either you're all thinking very oddly or I'm not explaining properly. The latter seems more likely.

First, I'm not convinced by quantum theory. A lot of it makes no sense. I'm of the opinion that if the theory doesn't make sense but it seems to work regardless, then something is fundamentally wrong with the interpretation of the theory - either that the theory itself is wrong, or that the concept it is applied to is wrong (ie. how we view the universe). I take particular issue with the concept of observing things changing how they work - this is woolly thinking. What is an observer, philosophically speaking?

But this is besides the point. Yes, there's an infinite range of values within a normal distribution. There's an infinite number of positions that a single dice throw can end up in, but they'll end up showing a single number in the range 1-6. An infinity of outcomes, but only six at the same time. We are selective with our data. We could have an enormous range of alternative universes in which everything is identical except for two protons switched round. The outcome would be virtually indistinguishable. Yes, they are different. But only trivially so, and such cases are a rather pointless argument to follow.

The laws of physics are consistent. I'm not aware that they weren't in the first 300,000 years after the big bang (I know that physics goes a bit wibbly in the first few seconds after the big bang) but this is what I'm getting at - the laws apply consistently, but only within set conditions. Outside those conditions they operate differently. But that in itself is consistent - that is, the laws of physics are governed by other laws.

I don't actually believe in randomness. There is chaos in complexity, and that makes things unpredictable, but it's all still deterministic. When you go to the quantum level, you're operating under different rules - but there are still rules. I've heard before that quantum theory is used by devices such as CD players, and I'd say that gives pretty strong evidence that quantum theory is consistent. Even if it's damned weird.

It doesn't have to make sense. It predicts correctly to 12 decimals places. The only thing required of theory is that it make correct predictions. Anything else is optional.

ruveyn

Quantum theory is definitely bizarre. However, the ability of you (or me) to understand something or not doesn't affect whether or not that thing is true.


I'm pretty sure an observation is defined in terms of particles being bounced off of each other and the like, not necessarily involving perception by a human mind.


You seem to be confusing all forms of probability with a six-sided die, but I have no idea why.


Your disbelief in something doesn't make it stop existing or making sense.


That there are rules does not imply that there is no randomness. Also, there are macroscopic effects of quantum physics, so quantum level only sort of makes sense.

Think I'll try one more time, but I feel I'm having to repeat myself.

Your not explaining it properly...but you are also rejecting certain facts to fit your own hypothesis as opposed to the other way around. Hypothesis that don't match the facts are incorrect. You keep saying one thing, than overlooking a key element that contradicts your argument.



Humans prefer things simple and determinable. It's how we work. However, that doesn't make the true system that way. We bend to the universe not the other way around. Truth is truth regardless of whether we can effectively understand and control it or not. In reality, what humans believe really isn't worth anything in the greater scope of things.



As ancalagon said, not all probabilties can be likened to a six sided die. However, to amuse you and hopefully make you understand your continued error. Even if everything could be broken into 6 options at any one time...THAT IS AGAIN A RANDOM ELEMENT!! ! You have a Limit(aka ordered element) that shrinks and confines something non-determinable (Random element). It doesn't matter if there are 6 options or even 2 options...unless you can state exactly which side will appear when your drop it, than you cannot determine the final outcome.

If you do this once...than the universe might not be very different from your prediction about its effect on the universe. Therefore your prediction for the future of the planet will likely be very accurate(because you already have all the other facts).

Do this once for every single event in the entire universe...and even with 1 billion predictions weighing in, you are likely to be wrong. You might get the occasional sub-event prediction right, but that hardly amounts to anything. The reason you would get any of those sub-events right, is because probability was on your side.



First few seconds after the event and the laws of physics as we know them break down entirely...first 300,000 years after the big bang, and they are altered.



Here is your biggest problem with all your statements. You actually do and you just don't realize it. Whether 2 choices, 2 million, or an infinite possible number of choices per scenario...if all events have an equally likely event of happening given the limits of the laws, than You have a random element.

You plugging your ears and claming it isn't random does not change anything. Something with more than 1 outcome, where you cannot predict precisely which of those outcomes will occur makes something non-deterministic. The limit of those outcomes will help you get consistent results, with some semblance of accuracy. However, you will not be able to determine and predict the exact outcome beforehand.

I think we all agree there are laws and limits that govern. They help produce a consistent picture. I have no problem with these statements. However, where you err is in assuming that because of your expectations and experiences, that everything must be 100% entirely ordered and deterministic. This shows an incredible lack of vision and understanding. It also shows a lack of understanding in how ordered limits/laws can work with random elements to produce something that appears relatively consistent for a duration and allows a system to function.



Chaos is the lack of order. You cannot have true chaos in a purely deterministic system. You can merely have the illusion of chaos. Again hence my point of you using terms to fit your ideas and how you see them, as opposed to how they really are and what they really mean.



Having rules is irrelevant. A purely determinstic system requires that all rules correlate to a final predictable outcome. Having even one instance in the entire system where there is a set number of values greater than 1 where you cannot determine the outcome of the flip/dice roll, or whatever else you want to call it, results in a non-deterministic system.

You have already agreed that there are elements which cannot be confined to one outcome, merely a set of possible options in limited venue. Therefore you believe in a non-deterministic system. You claiming otherwise is nothing more than denial. It's the equivalent of arguing that 1 does not equal 1 because you disagree or dislike the idea. The universe really doesn't care what you think, and certainly doesn't bend to your ruling. Learn that truth above all others and maybe everything will come easier to you.

I accept quantum theory works. I have no objection to the equations. It's the... I suppose "narrative" is the best word. It's the narrative I don't accept. The general consensus seems to be that quantum theory says all kinds of weird things, like an electron being a particle and a wave at the same time unless you look at it, and rather than looking at the contradiction and saying "hmmm, maybe that's not right" it's being paraded as a great discovery. The numbers add up, but do they represent the things we think they do?

There are two senses in which "random" is used. The main, and most accurate, is "unpredictable". A random event is still determined, we just don't know what it is. That dice roll of a six was always going to be a six, and if we could take the precise enough measurements and work out the calculations, we could predict it would be a six, but such a task is beyond us. We only think of there being alternative outcomes because we can predict six likely phase spaces, each of which is actually a pretty much infinite range of possibilities.

I quite agree. But a lot of little rules working in a cohesive system is a lot more likely than one big, complicated rule saying "this must be", especially when there is no aim in mind. And no mind to aim.

The other sense of "random" is "non-deterministic" - that something can act without cause. This is, to me, the most bizarre fantasy I can imagine, and doesn't even support its own argument.

The predictions of quantum electrodynamics are good to 12 decimal place experimentally verified.

If the theory is counter-intuitive so what? The answers are right.

Nature is not obliged to make sense to humans who develop their intuition at a gross scale of existence. All that we know of the sub atomic world is by indirect observation We can't see atoms. Atoms are smaller than the shortest wave length our eyes can detect.

ruveyn

Not really. The first sense you seem to be hinting at was really "pseudo-random".

Actually, a cubical die does not only have six outcomes to a throw. Most real dice can also land balanced on any one of their twelve edges or eight vertices - its just a little unlikely (but the probability increases with the stickiness of the casting surface).

The die can also explode, disappear, turn into five chickens, or do a variety of even less likely metamorphoses. Quantum mechanics tells us this.

Your second sense, for "random", is what QM is all about... and is a much better approximation to reality.

PS. Before you leap on me, take it that I've inserted "apparently" in my list of "things a die can do". Conservation of energy/mass is a good working hypothesis. Maybe a die could turn into five very small chickens.

Where's the contradiction?


If an event is pseudorandom and determined by things we don't (and/or can't) know, is there a difference between that and an actually random event from our point of view? Either way, we don't know what the outcome is until we look and see.

I don't see the need for the hypothesis that it's really just pseudorandom under the hood.


"doesn't even support its own argument" doesn't make sense. An argument that is its own support is circular and therefore invalid.

I don't understand the difficulty with the idea of a causeless event happening.

Measurements with particular units and fickle parameters are good to around 12 decimal places. Predictions, taken as different from measurements, are still somewhat poor. Classical Statistical Mechanics makes better predictions than Statistical Quantum Mechanics, though a moderate dividing line between the two is vague, except in the extremes of mandated "renormalization" to eliminate "infinite certainty" where the two somewhat "overlap": http://en.wikipedia.org/wiki/Renormalization

The frequencies of events at very small quantum limits do not obey the laws of probability. The violations of the laws of probability are not observed with the frequency of events on larger scale phenomena (i.e., a die will not turn into five chickens because of Quantum Mechanics).

"Random" has a vague, and controversial, definition in Quantum Mechanics. "Random" has self-contradictory definitions in mathematics, and "Random" has more of an ignorance/religious definitional usage in physics. Some mathematical definitions of "random" numbers and sequences are already established and recognized as self-contradictory:
http://mathoverflow.net/questions/69773 ... dont-exist

Steady-State models of the Universe are better that Big-Bang models. The Universe is infinite in all dimensions and counts, with infinite "repetitions", and all "events" are "predestined".

"God does not [and can't] play dice with the Universe":
http://www.google.com/search?q=Skinner+ ... =bks&tbo=1

Tadzio

The Steady-State theory of the universe is a good theory with one fatal flaw - it's wrong. The Big Bang theory on the other hand has been confirmed empirically many times over, albeit with a few modifications in some cases.

I find the number of particles in the "Big Bang" Universe interesting. Is the number finite, or strangely infinite?

While many people endlessly praise Einstein, some of the same in turn call anyone who still entertains the "Steady-State" of the Universe "crackpots". One of Roger Penrose's latest books, "Cycles of Time" (2010), has the sentences in the preface of: "The scheme that I am now arguing for here is indeed unorthodox, yet it is based on geometrical and physical ideas which are very soundly based. Although something entirely different, this proposal turns out to have strong echoes of the old steady-state model!"

Tadzio