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Originally Posted By: pokey
"...go down to your nearest metalwork shop...That is 6 inches exactly plus and minus nothing..."

Having metal working experience, all professional mechanical drawings (the old blueprints) I've worked with have a tolerance for length (x,y,z) and angles.

Fwiw


At least someone sees and has experience with the problem of any actual physical construction.

Now as far as we can tell an atom of an element is EXACTLY the same they are completely indistinguishable smile

Pretty neat trick from the universe building system isn't it and it's even trickier when you throw in Heisenberg uncertainty principle. I bet metal workshops would love to know how it does it we could have blueprints with "PAUL EXACT" (tm) measurements on them.

Somehow some forum posters can't see there is a serious issue with how the mathematics as they normally use them for construction is ever going to hold together to do this feat in the real universe. Ignoring all that they then want to ask what infinity means under that ridiculous broken system and half baked ideas.

The answer is you can't use normal real number mathematics and classical construction ideas and that has been known since 1905 but some obviously missed that memo smile

Last edited by Orac; 11/27/14 05:11 PM.

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Quote:
Paul since you are such a genius I would like you to go down to your nearest metalwork shop and ask them to give you a 6inch long bar. That is 6 inches exactly plus and minus nothing because that is what you mean right


and you are calling Bill S a fool ?

is a metal bar a number?

and if I ask for 6 metal bars 6 inches long then they will sell me 6 metal bars the precise length of each bar may not be 6 inches but the ability of a metal shop to cut a precise 6 inch piece of metal has nothing to do with the number 6 unless your a orac or a orac clone.


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If stupid questions were six inches tall, that would be a six-footer!








3/4 inch of dust build up on the moon in 4.527 billion years,LOL and QM is fantasy science.
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Originally Posted By: Orac
Here is a newsflash there is nothing in the world that has an exact measurement and this is part of the problem I am trying to get Bill S to understand. When a layman says 6 inches there is some inaccuracy that is allowed which is obviously dependant on the application. A 6 inch piece of lumber is probably something like a range 5.95 to 6.05 inches which a layman calls 6 inches because that is as close as he needs to know.

Once again that is questionable. It depends on what you are referring to. For instance a 1 by 6 piece of lumber is nominally 1" thick by 6" wide. In fact it is 0.75" by 5.75". That is the finished dimension of a board that was originally cut to be 1X6.

But you are still evading Bill's question. Whether any measurement can be exact has nothing to do with the question of whether infinity is a number. You can have an infinite number of 6" boards that are exactly 6", or you can have an infinite number of 6" boards where the measurement is inexact.

In my opinion, without doing any deep philosophical thinking, infinity is not a number. George Gamow wrote a book titled "One, Two, Three, Infinity". He discussed the matter of primitive tribes having only a limited quantity of counting numbers. To me infinity just means more than I can count, the same as those primitive tribes. And for that there is no reference to the counting system used. In modern mathematics infinity means more than I can count in principle. There may be some numbering systems which are circular and you reach a point where numbers start repeating or decreasing. I don't know if there are any such, but mathematics being what it is I don't want to throw the idea out. Aside from any such systems, in principle, if you name a numbering system and give me a number of any size I can always add one more to that. But if I look at a series and can see that this is possible I just say the series goes to infinity. So infinity is more of a description than it is a number.

At the same time I don't see this as being something that precludes anything, such as the universe, being infinite in size. And being infinite in size just means that there is no way, even in principle, to measure it. That means that we don't say it is infinite just because we don't see a way to measure it, but that we cannot even imagine any way for it to be measured by ignoring physical reality.

And of course I have no idea whether the universe is infinite. It may be or it may not be.

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Originally Posted By: Orac
I think you are being even more obtuse and you are play like the crazy pollack fool you aren't remotely interested in trying to get to the bottom of this.


Orac, you brought Aboriginals into the discussion, not I. If you don’t understand the concept of Alcheringa you should have left them alone. Without it, your argument is rubbish, with it , it is pointless.

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the crazy pollack fool


Define “Pollack”. Is this meant to be an insult?

Quote:
IF YOU DECIDE TO STOP BEING A FOOL AT LEAST LOOK AT THE PRESENTATION


Define “fool”. Could it be someone who doesn’t swallow your line without question?

I enjoyed the presentation; perhaps because it is “in dumb as dog language”, who knows?

BTW, disappointingly, insults from you are beginning to equate with insults from Pre: they are, indirectly, quite complimentary.

You may recall that some time ago I expressed the thought that QM might be “a window on the infinite”. If the presentation has any relevance to the OP, it is to strengthen that thought.


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Originally Posted By: Bill
But you are still evading Bill's question. Whether any measurement can be exact has nothing to do with the question of whether infinity is a number. You can have an infinite number of 6" boards that are exactly 6", or you can have an infinite number of 6" boards where the measurement is inexact.


Thanks Bill, I was beginning to wonder if I was the only one who thought Orac was evading the question.


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I am not evading I am asking Bill S to define the setting so I can answer the question

DON'T TAKE IT FROM ME ASK A MATHEMATICIAN

https://www.math.toronto.edu/mathnet/answers/infinity.html

I need number system, topological space and set construction of what Bill.S thinks the universe looks like to even relate to him.

Bill.S setting and background currently is the stupid crazy layman world at this moment and the question is not answerable and it is as stupid as trying to deal with Marosz. It suffers from the same issues that it's easy to show the view is misguided and wrong yet they want to persist in using it.

If Bill.S does want and answer he needs to deal with the 3 problems which are easily defined under mathematics and physics

1. What "number system" does he propose the universe has
2. What "topological space" does he propose the universe has
3. What "set size" does the he propose the universe has

All the major physics theories that deal with the universe answer those questions and are required to.

So lets write the answers for classic (newtonian) physics

1. Real number system
2. The topological space is convergent
3. The set size is unlimited

Those who are smarter will realize there is already an inconsistency in those answers.

So would any of you care to write the answers for GR?

There are also answers for each of those for QM and String theory if you want to go that far.

So if Bill S wants his answer he needs to deal with the setting smile

Last edited by Orac; 11/28/14 01:22 AM.

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Originally Posted By: Bill
Whether any measurement can be exact has nothing to do with the question of whether infinity is a number. You can have an infinite number of 6" boards that are exactly 6", or you can have an infinite number of 6" boards where the measurement is inexact.

In general your answer is correct and well meaning except the above part which is horribly wrong in a mathematics sense.

This part only makes sense in a philosophical way as under mathematics the operators don't work
Quote:
infinite number of 6" boards where the measurement is inexact.

If you can't measure accurately you can't define your mathematics continuum to allow mathematical operations. No continuum means no mathematics and/or operators will work.

It really easy to show this problem using your above statement lets just simply take your idea to a finite example of inexact board widths.

Question: I have 20 boards how wide is my collection of boards in the real world?
Problem: You can't answer the simple act of addition/multiplication can not be done outside the boards themselves.

Question: I have 10 boards that are 60.78 inches wide I take one away one board how wide is the remaining 9 board stack?
Problem: You can't answer the simple subtraction can not be done outside the boards themselves.

Question: I have 60 inch stack of boards how many boards do I have?
Problem: It's obviously going to be close to 10 but is it 9 or 11 will depend on the exact widths of the board.

You should be able to see what is happening the inaccuracy in the widths makes the boards totally unsuitable to use as any sort of mathematics system to the real world, you are always having to resort to some other unit or measurement in the real world to solve the problem.

You can't even resolve a finite board because the continuum (in your case board width) is uneven. Good luck trying to identify a board to label infinity because it could be +- a number of boards when taken back to real world infinity as an actual number smile

The only concept you can have of an infinity board is actually in the universe outside the board number system itself which is another way of saying the boards are unsuitable to use as a number system and we are talking about the "philosophical infinity".

See the issue mathematics for the real world requires a fixed continuum for the operators to work. Any builder or constructor gets around the problem above by never using the boards as a number system they use proper external measurement and relate it back to boards/bricks size etc.

The heisenberg uncertainty principle makes the universe prone to exactly the same problem.

Last edited by Orac; 11/28/14 02:52 AM.

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Bill S typed: “…unless you can establish that infinity is a number.”

Orac typed:
“…Under the REAL NUMBER SYSTEM no it's not. (http://en.wikipedia.org/wiki/Real_number)
Under COMPLEX NUMBER SYSTEM can be argued either way depending on field of use.
Under QUATERNION NUMBER SYSTEM yes it is.
Under OCTONION NUMBER SYSTEM yes it is.”

It seems to me, Bill S, that when you decide which of the above 4 systems your
definition of a number fits into, you will have Orac’s answer.

It is certainly possible that I’m overlooking something though.

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Nope you have go it exactly Pokey.

The answers come straight from refining the question and the refining actually tells you much much more than the original question.

There are actually hundreds of answers to Bill S question depending on what you accept as the background or basis for the number system, there is no "one number system" which is what Bill S seems to be trying to create it's equivalent to trying to create a zero frame in relativity.

Your metal shop has to work a way to deal with the "inexact" measurements represented on blueprints and in any mathematics they do with them as well as the physical construction. There is no "one way" they would deal with that they have to develop ways and techniques to do it. Whats interesting is how does the universe solve the problem which is the key to the question asked.

The problem isn't the mathematics or infinity it is the basis under the system and it is true of all the physical world and the current state of knowledge.

Last edited by Orac; 11/28/14 04:23 AM.

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Originally Posted By: Orac

It really easy to show this problem using your above statement lets just simply take your idea to a finite example of inexact board widths.

Question: I have 20 boards how wide is my collection of boards in the real world?
Problem: You can't answer the simple act of addition/multiplication can not be done outside the boards themselves.

Question: I have 10 boards that are 60.78 inches wide I take one away one board how wide is the remaining 9 board stack?
Problem: You can't answer the simple subtraction can not be done outside the boards themselves.

Question: I have 60 inch stack of boards how many boards do I have?
Problem: It's obviously going to be close to 10 but is it 9 or 11 will depend on the exact widths of the board.

And you are still evading the question. The question "Is infinity a number". The only mathematical operation used in defining infinity is counting. You are trying to use mathematical operations that aren't needed to do your counting for you. Those mathematical operations are just short cuts to eliminate the need to actually do the count. And for sufficiently accurate production processes using 6 inches (actually 5.75") will provide a correct answer. If I go to the lumber yard and order out a bunch of 1X6 boards I can calculate the width of the stack just fine. If not I take them back and demand a refund because they gave be defective merchandise. Of course the width of the boards doesn't matter if I am just counting boards. In principle I can keep counting them forever. That is because the domain of real numbers is infinite. I have copied what I said about whether infinity is a number, since you completely ignored it in your reply.

Originally Posted By: Bill
In my opinion, without doing any deep philosophical thinking, infinity is not a number. George Gamow wrote a book titled "One, Two, Three, Infinity". He discussed the matter of primitive tribes having only a limited quantity of counting numbers. To me infinity just means more than I can count, the same as those primitive tribes. And for that there is no reference to the counting system used. In modern mathematics infinity means more than I can count in principle. There may be some numbering systems which are circular and you reach a point where numbers start repeating or decreasing. I don't know if there are any such, but mathematics being what it is I don't want to throw the idea out. Aside from any such systems, in principle, if you name a numbering system and give me a number of any size I can always add one more to that. But if I look at a series and can see that this is possible I just say the series goes to infinity. So infinity is more of a description than it is a number.

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Originally Posted By: Bill G
And you are still evading the question. The question "Is infinity a number". The only mathematical operation used in defining infinity is counting.

Ok you have given me a basis I can answer and it becomes really weird in the inexact board example. Note what you have selected is a countable number system you didn't call it by that but that is what you have done you may care to check it out as that is what that definition you have given means and it is one of many not the only one smile

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

The key definition: A set is called "countably infinite" if it has one-to-one correspondence with the natural number set.

So lets use countable number set as basis and see the result

If your world or reference was only the boards and you could see nothing else and the board world is infinite then an infinity for the boards exists that bit is easy.

If you can see and measure to the outside world then the board infinity is problematic depending on the exactness of the boards. The reason is to count you need to create a bound or interval and the interval converges towards infinity (see the mathematical ref again). If the board are exactly the same you can create a straight forward linear relationship between the two worlds and they converge together. However remember part of counting set is "uniqueness" and we have a problem with inexact boards.

In the inexact board example it gets ugly because you end up with some sort of function between the measurement world and the board world. As the relationship is a function all bets are off it comes down like the 60 inch does it contain 9, 10 or 11 boards in the problem above and you can't guarantee the "uniqueness" or one-to-one relationship of the board infinity.

So you now have a very ugly situation of something like a relative infinity depending if you are in the board world or outside it because of the basis definition.

By the way that is one of the real problems physics would face if space wasn't smooth and homogenous.

So there is your answer and it's rather ugly I have to say because of the basis you selected.

If Bill S gives me his basis I can answer his question for him as well without any evasion which was never intended smile

Last edited by Orac; 11/28/14 05:41 AM.

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And what you are counting has nothing to do with its countability. The boards may be 6 inches wide or they may be 4 feet wide (that's the width of a sheet of plywood in the US). But as long as all I am interested in is counting them it doesn't matter.

The question is: IS INFINITY A NUMBER?

All of your digressions have nothing to do with the answer to that question. I have already given my response to that question and you refuse to pay any attention to the it.

The answer is: INFINITY IS NOT A NUMBER!

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Originally Posted By: Bill
And what you are counting has nothing to do with its countability. The boards may be 6 inches wide or they may be 4 feet wide (that's the width of a sheet of plywood in the US). But as long as all I am interested in is counting them it doesn't matter.

Correct I already told you that ... if you can't see anything but the boards or don't consider anything but the boards I gave the same answer ... go back and read smile

Surely you see the problem if there is an outside world here let me write it mathematically for the two situations

Exact board formula:
Real world distance of boards = number of boards x 6 inches

Inexact Board formula:
Real world distance of boards = number of boards x (6 inches +- uncertainty)

The first case holds for each and every value including infinity whether a number or concept. Now try doing it in the second case you can't even do a finite much less infinity.

The problem is there are actually two infinities (one in the world and one in the boards) and regardless of whether you consider infinity to be a concept or a number they are supposed to imply and match the same definition. They don't in the second example so it is hard to work out what to do other than saying it's undefined without more information.

Originally Posted By: Bill
The question is: IS INFINITY A NUMBER?

You set that answer in your selection of basis of countable numbers and that system says infinity as not a number.

Originally Posted By: Bill
The answer is: INFINITY IS NOT A NUMBER!

Your answer is correct but it is merely reflecting back the selection you made in selecting countable numbers.

So your answers are correct to the number basis you selected and I completely agree with you and the logic. The bigger problem is the are hundreds possibly thousands of other number basis you could have used that give very different answers that are equally correct.

So the real question to consider is does your number basis represent a good fit to the physics in the real world because that is what Bill S is trying to work with infinity in the start post?

If you are happy that it is the best fit then your answer makes perfect sense to me and I have listened to you.

Last edited by Orac; 11/28/14 05:03 PM.

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So can you give us a basis where infinity is a number?

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https://www.math.toronto.edu/mathnet/answers/infinity.html

That's a good link, Orac. I shall have to give it some attention, not just for the purpose of finding quotes like this. smile

No "infinity" concept exists in the context of any number system, if by number system one means a collection of concepts that have operations like addition and multiplication the way familiar numbers do, operations which obey the usual properties of arithmetic.


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Originally Posted By: Bill
So can you give us a basis where infinity is a number?

I am not a mathematician but look up extended real line, affinely extended real line which add plus and minus infinity in as concepts and number from memory if I recall correctly. Then there is things like projectively extended reals which I believe does same.

Finally you can completely change concepts of numbers from reals to be complex numbers and you have many many versions over there.

The issue you still haven't dealt with for me was that of the inaccurate boards and the formula

Distance = number of boards * (board width +- inaccuracy)

Which becomes

Infinity = Infinity + (faction of Infinity)

If I am reading you correctly infinity is a concept not a number so that is fine. No judgement here I am not a mathematician just trying to understand it.

Last edited by Orac; 11/29/14 02:01 AM.

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Surely affinely extended real numbers give rise to improper elements that are not real numbers,so this line of argument is not valid in this context.


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In other words you don't know of any system in which infinity is a number.

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In real number systems I am not sure I rarely use them perhaps you are correct.

Infinity is usually a digit number (perhaps always not sure ask a mathematician) in complex number analysis.

I mostly use Extended complex numbers as would many janitors and then quaterions. The extended plane represents the extended complex numbers, that is, the complex numbers plus a value for infinity. As much of my work is with 3D the number set is extended to a 3D spacetime plane.

Link to it's basics
http://mathworld.wolfram.com/ExtendedComplexPlane.html

Quote:
The extended complex plane is the name gives to the complex plane with a point at infinity

Here is the layman wiki entry
http://en.wikipedia.org/wiki/Riemann_sphere

Quote:
It also finds utility in other disciplines that depend on analysis and geometry, such as quantum mechanics and other branches of physics.

I have no doubt your number system is quite natural to you but it is quite foreign to me.

To understand why the use of extended complex numbers is widespread in physics (or at least the areas that I know I won't speak for all) is what I am trying to get you to think about.

Again I am not going to claim we are right or wrong just that we see it different. The use of the two different number systems is what is causing much of the disconnect between us.

Ah but I forgot your claims that apparently there is no number system like that and/or the argument is invalid etc etc. So I guess if anyone did use that system they could only be called a janitor laugh

I understand your logic and view and it's not up to me to convert you to my janitor world, after all who no one is ever going to change your minds smile

I am not sure what to think now because my (and many other physicists) number system doesn't exist now it has had a "Kill Bill" execution laugh

Excuse my jibes but you two have painted yourselves into a very amusing little corner and you were so sure you had me this time. I can catch Bill G every time I just have to say something that science believes but Bill G doesn't know and get him going. Can I suggest the best option now is to go it's all the work of the devil and not god's numbers as the route to dig your way out (Joking lookup Leopold Kronecker). There was perhaps a lesson in this for you which I hope you got.

Seriously the thought you needed was why does physics need complex number mathematics which you both refused to think about. Why is it we can't and don't use your real number systems which even I concede makes sense?

Originally Posted By: Albert Einstein
As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

Last edited by Orac; 11/29/14 09:12 AM.

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Originally Posted By: Orac
Gabble, Gabble, Gabble

In other words you don't have and can't find any source that says that infinity is a number.

Bill Gill


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