If infinite parallel universes exist ...

[Ginkgo]

Strange....I don't particularly believe in a supreme being, nor am I a rationalist. Maybe some have used either of those things to that end and now you assume I am too?

Yes, I did assume that. Perhaps I was jumping to a conclusion. Pseudo-science has always been my hobby-horse. My apologies.

And actually to go back to what Ginko said too, if you're still following the thread, I understand limits in math, and how it helps with calculations. Notice in the bit you showed me, it shows how to calculate a mathematical idea involving infinity by using limits, but also rather concludes that it's better not to use it. And even in the ones where it is used, it still just remains a concept of something continuing forever.

A famous physicists once said:

"Infinities in physics demonstrates the fact that we just don't know"

I just wish I could remember his name.

[EagerForTruth]

Oh - so we were on the same page...

I try not to have hobby-horses myself, they're too hard to feed for me

But I definately like that quote, I say no matter how much we know - and we should always be learning - there will still be plenty we don't konw.

[uwot]

As for the usage of it in metaphysics, I find that appropriate, because after all, though our knowledge is grounded in physics aren't we trying to go beyond just the physical in this inquiry? Logic, science, reason, these are the the tools and methods we have to explore that which is beyond.

The thing is, as I was saying to Gustav Bjornstrand, you can use logic and reason to explore that which is beyond the physical, to create any number of stories that are consistent with the evidence. All the religions of the world have to accommodate the empirical evidence; they frequently look ridiculous doing so, but they have to be able to account for what is demonstrably so. Likewise, conspiracy nutters will construct a narrative that is based on some ludicrous premise, and any evidence that sane people may think casts doubt on the story, is woven into it with whatever additional clauses are necessary to maintain the original nonsense. Then there is Ginkgo's hobbyhorse, pseudo-science, amongst which I would put astrology and psychoanalysis.
We all, to some degree, have a story or context into which the things we experience make sense. Some people, religious fundamentalists for example, become very emotionally attached to a particular narrative and react with outrage, even violence, if their pet theory is challenged. The more work you have to do to makes the pieces fit, the more likely the story is untrue. Do not multiply entities beyond necessity, said William of Ockham. The simplest explanation isn't necessarily the true one, but it is a good place to start.

[EagerForTruth]

I very much agree....in the bit that you quoted that was my point as well. Logic and reason are the foundation for exploring what lies beyond. I just like to think there are other tools in the toolbox as well, such as empathy, compassion, intuition, etc. I think it's best to use all of these in harmony with each other.

[uwot]

I very much agree....in the bit that you quoted that was my point as well. Logic and reason are the foundation for exploring what lies beyond. I just like to think there are other tools in the toolbox as well, such as empathy, compassion, intuition, etc. I think it's best to use all of these in harmony with each other.

Well, yes, but I think it is probably best to be clear about which tool is suited to what job. I think it is very difficult to build a worthwhile system of ethics without considering empathy and compassion, but I would be very suspicious of any physics that was based on them. Intuition, exploration, guesswork even, are all useful tools in any field. As Richard Feynman said though: "It doesn't matter how beautiful your theory is, it doesn't matter how smart you are. If it doesn't agree with experiment, it's wrong." I think something similar is true of ethics, in that if someone gets hurt needlessly, it's wrong.

[Blaggard]

Strange....I don't particularly believe in a supreme being, nor am I a rationalist. Maybe some have used either of those things to that end and now you assume I am too?

Yes, I did assume that. Perhaps I was jumping to a conclusion. Pseudo-science has always been my hobby-horse. My apologies.

And actually to go back to what Ginko said too, if you're still following the thread, I understand limits in math, and how it helps with calculations. Notice in the bit you showed me, it shows how to calculate a mathematical idea involving infinity by using limits, but also rather concludes that it's better not to use it. And even in the ones where it is used, it still just remains a concept of something continuing forever.

A famous physicists once said:

"Infinities in physics demonstrates the fact that we just don't know"

I just wish I could remember his name.

"how wonderful that we have met with a paradox, now we have some hope of making progress."

Niels Bohr on discovering an infinity.

"God does not play dice with the universe."

Albert Einstein.

"Einstein, stop telling God what to do!"

Niels Bohr.

"We are all agreed that your theory is crazy. The question which divides us is whether it is crazy enough to have a chance of being correct. My own feeling is that it is not crazy enough."

Niels Bohr

"An expert is a man who has made all the mistakes which can be made, in a narrow field."

Niels Bohr

"No,no you are not thinking; you are just being logical!"

Niels Bohr.

"When it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images."

Niels Bohr

As to why infinity is useful as a limit take the equation

x/x+1

Does it converge or not?

1/2, 2/3, 3/4 is a set of fractions defined hence by x/x+1 but not exhaustively, does that set at the limit of infinity equal any real number?

That's why infinity is useful.

At the limit of infinity what does that equation equal if it converges what hence is the value of any x/x+1 in maths, if it does not converge is it in and of itself infinite or not? Express x/x+1 in decimal form, does the decimal form converge if not why not? Which set is greater x/x+1 or x/x+1, if they are equal explain how?
If not explain why x/x+1 ><= than x/x+1 and why?

Which is the larger cardinality of sets the decimals or the fractions, explain why..?

Hence prove why:



Why is hence pi transcendental and irrational and how does that impact on fractions of x/x+1?

is the set of transcendental or irrational numbers larger than the set of real numbers or natural numbers, if it is why and how would you prove it?

See asymptotic functions and assymptote analysis for further proofs.

[uwot]

"When it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images."

Niels Bohr

Maybe, but this is a philosophy forum. Some of us care about ontology. What does maths say matter is made of?

As to why infinity is useful as a limit take the equation

x/x+1

Does it converge or not?

I'm not sure who you are asking, but I don't even understand the question. Could you put it another way?

1/2, 2/3, 3/4 is a set of fractions defined hence by x/x+1 but not exhaustively, does that set at the limit of infinity equal any real number?

That's why infinity is useful.

What would you use it for?

At the limit of infinity what does that equation equal if it converges what hence is the value of any x/x+1 in maths, if it does not converge is it in and of itself infinite or not? Express x/x+1 in decimal form, does the decimal form converge if not why not? Which set is greater x/x+1 or x/x+1, if they are equal explain how?
If not explain why x/x+1 ><= than x/x+1 and why?

Are you sure you've got the right forum?

Which is the larger cardinality of sets the decimals or the fractions, explain why..?

Hence prove why:



Why is hence pi transcendental and irrational and how does that impact on fractions of x/x+1?

is the set of transcendental or irrational numbers larger than the set of real numbers or natural numbers, if it is why and how would you prove it?

See asymptotic functions and assymptote analysis for further proofs.

So, how many parallel universes does that make?

[Bernard]

Yeh never went for the Hilbert hotel hoodwink. You simply can't back away from infinity in order to consider the existence of other infinities.

Ah, but infinity does not behave in the ways you expect! Consider the famous "Hilbert's Hotel" thought experiment, for example. Playing around with infinity quickly yields absurd conclusions.

You only increase chances with reference to infinity if you limit chances in another. If there are infinite variables in the universe, no number of recursive chances increases probability: both are swallowed up in infinity itself.

If you doubt this, take a look at my entry on "Nonsense On Stilts" (the article thread), and you'll get the full explanation.

[Bernard]

Yeh never went for the Hilbert hotel hoodwink. You simply can't back away from infinity in order to consider the existence of other infinities.

Ah, but infinity does not behave in the ways you expect! Consider the famous "Hilbert's Hotel" thought experiment, for example. Playing around with infinity quickly yields absurd conclusions.

You only increase chances with reference to infinity if you limit chances in another. If there are infinite variables in the universe, no number of recursive chances increases probability: both are swallowed up in infinity itself.

If you doubt this, take a look at my entry on "Nonsense On Stilts" (the article thread), and you'll get the full explanation.

[Blaggard]

As to why infinity is useful as a limit take the equation

x/x+1

Does it converge or not?

I'm not sure who you are asking, but I don't even understand the question. Could you put it another way?

1/2, 2/3, 3/4 is a set of fractions defined hence by x/x+1 but not exhaustively, does that set at the limit of infinity equal any real number?

That's why infinity is useful.

What would you use it for?

At the limit of infinity what does that equation equal if it converges what hence is the value of any x/x+1 in maths, if it does not converge is it in and of itself infinite or not? Express x/x+1 in decimal form, does the decimal form converge if not why not? Which set is greater x/x+1 or x/x+1, if they are equal explain how?
If not explain why x/x+1 ><= than x/x+1 and why?

Are you sure you've got the right forum?

Set and number theory are philosophically relevant.

I just showed you how to use it, the set of fractions converges to what?

Does the set of decimals converge to a larger number at the limit of infinity?

write out pi to infinite decimal places.

Cantor proved that the set of fractions is of a lower cardinality than the set of decimals, because you can always add more numbers to a decimal but a fraction is an absolute value. Hence the irrational > set of fractions which together make the set of real numbers which by definition must be larger than the natural numbers which are all positive integers.

http://en.wikipedia.org/wiki/Cantor%27s_theorem

See here for philosophy of maths...

As to how it relates to this thread well that is obvious it is fundamental to all physics both number and set theory rely on axioms then can be further used to define reality in mathematical logical terms or as we call them models.

If for example I say there are infinite universes, what do I define infinite to mean, and believe it or not there are different types of infinity for example the universe is finite and unbounded as far as is known but it is still infinite because as far as is knowable it contains everything to which there is no null set. On the other hand if their were infinite universes then that would also be an infinity but it is important to specify therefore some sort of cardinality to avoid your brain leaking out of your ears. There are also maths terms called hyperreals but they do not concern physics.

Which is the larger cardinality of sets the decimals or the fractions, explain why..?

Hence prove why:



Why is hence pi transcendental and irrational and how does that impact on fractions of x/x+1?

is the set of transcendental or irrational numbers larger than the set of real numbers or natural numbers, if it is why and how would you prove it?

See asymptotic functions and assymptote analysis for further proofs.

So, how many parallel universes does that make?

Twelvty give or take...

"When it comes to atoms, language can be used only as in poetry. The poet, too, is not nearly so concerned with describing facts as with creating images."

Niels Bohr

Maybe, but this is a philosophy forum. Some of us care about ontology. What does maths say matter is made of?

Nothing since maths is an abstract concept.

Physicists say the universe is made of atoms which in turn us made of bosons and mesons/fermions, which are themselves made of quarks.

[Wyman]

... then it is obvious that there is an infinite number
of universes in which a certain event x occurs.

Not only is this not obvious, it is a non sequitur. I can say there are an infinite number of paper cups. It does not follow that there are an infinite number of paper cups with Kool-aide in them.

[Blaggard]

... then it is obvious that there is an infinite number
of universes in which a certain event x occurs.

Not only is this not obvious, it is a non sequitur. I can say there are an infinite number of paper cups. It does not follow that there are an infinite number of paper cups with Kool-aide in them.

Sounds like a classic black swan argument, it does not follow that it is obvious, an a priori assertion is a pretty dubious basis for the following non sequitur, in fact I think that logical fallacy correc t me if I am wrong modus tolens or affirming the consequent .

If there are infinite universes then it only follows that infinite events happen, it does not follow that all events happen in that situation nor that all possible events even will happen or even necessarily they should. After all universes could experience the exact same event with absolutely no difference it also doesn't follow that the chance of anything happening in this universe is 50% because of the above line of reasoning, all that it does in fact say is that something will happen and that is the limit of logic for infinite universes. However there is one caveat obviously in any local real theory where there are infinite universes then then there is always just what happens, the chance of the moon expanding into a balloon, popping and then the resultant noise traversing to the other side of the universe is as exactly likely as it was in one universe. interpretations are pretty much philosophical bias in Science, they really aren't all that coherent any of them as the field stands. They do however allow us to explain what happens if not why it happens, which is not sciences job anyway.

[uwot]

Set and number theory are philosophically relevant.

Depends on the philosophy. Can you give an example?

I just showed you how to use it, the set of fractions converges to what?

Did you? Show me again; I'm still none the wiser.

Does the set of decimals converge to a larger number at the limit of infinity?

I have no idea.

write out pi to infinite decimal places.

3.142 and I forget the rest. I really don't see what you are trying to say. Is there no way you can find to communicate effectively with someone like me? (I shall console myself with Aristotle's assertion that the better you understand something, the better you are able to teach it.)

Cantor proved that the set of fractions is of a lower cardinality than the set of decimals, because you can always add more numbers to a decimal but a fraction is an absolute value. Hence the irrational > set of fractions which together make the set of real numbers which by definition must be larger than the natural numbers which are all positive integers.

Well, I'm no mathematician, so I can't see why you can't do the same with either the denominator or numerator of a fraction. Does any of it say anything about the world we experience; 'reality' for short?

As to how it relates to this thread well that is obvious it is fundamental to all physics both number and set theory rely on axioms then can be further used to define reality in mathematical logical terms or as we call them models.

In philosophy we create metaphysical models. Most of them are complete gibberish, even the good ones are, as you say irrelevant, but they give us a context. Mind you, mathematicians aren't much better at it if String Theory is anything to go by, I think you have already expressed your opinion of String Theory.

If for example I say there are infinite universes, what do I define infinite to mean, and believe it or not there are different types of infinity for example the universe is finite and unbounded as far as is known but it is still infinite because as far as is knowable it contains everything to which there is no null set. On the other hand if their were infinite universes then that would also be an infinity but it is important to specify therefore some sort of cardinality to avoid your brain leaking out of your ears.

Not a danger if you have no idea what you are on about.

There are also maths terms called hyperreals but they do not concern physics.

I won't ask.

Physicists say the universe is made of atoms which in turn us made of bosons and mesons/fermions, which are themselves made of quarks.

Indeed, but what some of us want to know is what are fundamental particles made of? Any ideas?

[Blaggard]

ok did you read the links, because you really are not going to be helped by just my explanations alone, which are intrinsically based on the links.

I am not trying to be obtuse here but you need to click on the links to really understand the concepts of divergence, convergence, cardinality and mapping 1 to 1.

Start with this:

http://en.wikipedia.org/wiki/Limit_%28mathematics%29

Then go back and read the thread again I can assure you it will make way more sense.

Maths is a language like French or German, one needs to have context to understand/translate it this may look like gibberish to the average non maths person but it is perfectly logical:



I will understand if you don't have time though, or the inclination but what I am saying is not meant to be either deliberately misleading or to sound condescending it is just what is logical.

This may also be useful Aymptotic analysis, assymptotic means approaches but never meets:

http://en.wikipedia.org/wiki/Asymptotic_analysis

I really will not judge you if you don't want to read the links, I am just saying this is how it works. It's of course entirely up to you:

http://en.wikipedia.org/wiki/Integral

This may also help. An integral is the area underneath the line of a graph, a differential is the line itself and is often used to describe rate of change such as in s=ut+1/2at^2 the acceleration relation to speed. it's a quadratic equation which you may or may not of learnt about at school. Of course the line of a graph and the area it bounds are intimately related, it is a law of maths which we call the rules of calculus.

Let's take a simple rule of calculus called the chain rule which proves that x^2s derivative is 2x if x=n or any number other than 0 also known as the power rule.

So if x=1 then y =2 if x =2 then y = 4 and so on denoted by x^n=nx^(n-1) in maths gibberish.

any constants derivative is 0 because it results in no change in the value of the graph is another example for example if a=10 and x=n then y=10 always no matter what.

These are basically fundamental rules of maths, that are consistent only if we have rules involving a limit of infinity.

[uwot]

I'm on the case.


Could take a while and/or get me fired.