Science a GoGo's Home Page Forums General Discussion General Science Discussion Forum Can we lay nothing to rest?

Infinity finds its way into many threads, causes a distraction, then fades away, usually, with no semblance of resolution. Questions about infinity are often linked to questions about time and about nothing.

I propose asking a few questions, in the form of a “poll”, which may help to ameliorate the situation. Each question requires only a yes/no answer, but hopefully these would be accompanied by some thoughts.

1. Is infinity a number?
2. Is eternity a length of time?
3. Is it possible to define Cantor’s “absolute infinity”?
4. If there had ever been (absolutely) nothing, could there be something now?
5. Could there be change without time?

The infinity threads do indeed fade away with no resolution. The problem is that there is no satisfactory answer to the questions. So this thread is headed the same way.

Bill Gill

I'm inclined to agree in general with that; I just thought it would be interesting to have a few opinions on these specific points before closing the book on a lot of circuitous posting.

Define "number" that is a rubbish layman generic term that is poorly defined. Use a proper mathematical definition of what type of number system you are talking about. There is nothing different between infinity, zero, irrational, negative and complex numbers depending on what number system you are using they may or may not exist.

NOTHING SPECIAL ABOUT INFINITY AT ALL

The question can not be answered because it is poorly worded with no clear selection of numbering system.

Ditto to the definitions in rest of questions.

You keep asking the same stupidly worded questions with generic broad layman terms, if you really want an answer how about you try answering some real questions about definitions and refine the questions

1.) What numbering system does the universe use and why?
2.) Is infinity as used above exactly as defined under the choice of the above numbering system.
3.) Is time being defined as a change in observation or are you using it as some other scalar quantity. Even in physics there are multiple definitions of time including Classical, GR and QM to name but a few. What definition of time are you using in the question.
4.) Finally using your definition of time in 3 define eternity it is not in any way a technical or precise term. Even in layman speak someone can wait an eternity meaning they waited something like an hour.

At the moment it appears you don't really want an answer because you refuse to make the questions more precise. The choices of answer to the above questions are actually more interesting than your questions and in particular number 1.

For reference you are taught in school (REAL NUMBER SYSTEM), the second (COMPLEX NUMBER SYSTEM) is known to Calculus students and Engineers and Scientists worldwide, the other two fields (Quaternions and Octonions) are used by Mathematicians and some Physicists.

You could do worse than start with readings about works with octonions (http://en.wikipedia.org/wiki/Octonion). Infinity is really interesting under octonions

BASIC PROBLEM SOLVING THEORY 101

quote: "As such, it makes sense to devote as much attention and dedication to problem definition as possible. What usually happens is that as soon as we have a problem to work on we’re so eager to get to solutions that we neglect spending any time refining it."

quote: "Every problem — no matter how apparently simple it may be — comes with a long list of assumptions attached. Many of these assumptions may be inaccurate and could make your problem statement inadequate or even misguided."

Thanks for that Orac. I don't have time now to give consideration to all the points you raise, but I suspect that working through them will be a learning experience, which is what it is all about for me.

I have to say that my initial impression is that it is a lot of circumlocution of the type that "experts" tend to fall back on when when they don't like to admit that they don't have an answer, but closer inspection could, of course, prove me wrong.

I guess an entirely new language is needed to match the concepts of non-duality in a duality based world.
What is hot without cold and what is cold etc. etc. etc.

Obviously concepts such as infinity or God had some kind of thought behind them, and if no one has learned to explore the concepts as they were presented then its easier to reject them and deny the concept altogether..

Let's scrap all forms of language and start over.

Who wants to take charge?

In the mid 1950s I was building a carrier to use 35mm film in an ancient enlarger. I needed two lengths of curved spring. I went to a clock repair shop to see if I could purchase an old clock spring. I explained what I wanted and the shop owner bombarded me with technical questions that he said needed to be answered before he could know what kind of spring I should have. I left empty handed. In the next shop the man listened to my explanation, rummaged in his throw out box and gave me exactly what I needed. Guess where I went later to buy a clock.

We have a similar situation here.



Perfectly reasonable request, but also the “go-to” response for avoiding saying “don’t know”.


What sort of difference are you referring to? If it makes no difference which number system is used, why do you ask me to specify a number system in order to validate my question?



Have you thought that that is because I keep getting the same evasive, irrelevant responses?



If stupid questions were six inches tall, that would be a six-footer! What degree of presumption does one have to aspire to in order to think he/she can know what the Universe uses? Are you asking what numbering system scientists use when trying to understand the Universe? If so, perhaps you should take your own advice and ask the right question. If not, you should justify your presumption.



This question is meaningless unless one has first answered the question: “Is infinity a number?”



Inherent in this is the assumption that the way in which we choose to define time actually makes a difference to time itself. How would you justify that assumption?



I have not defined time. This point can be addressed only if the question: “Is eternity a length of time?” has been answered.



I would not insult your intelligence by assuming that you really think that has any relevance.



That is judgemental, arrogant and unwarranted.

Just goes to show you that one can easily connect with another in concepts, and then others just get lost in their own minds regarding self constructed details in relevance to the personal isolation of ones self and ones reality.

It then comes down to a choice or willingness to expand beyond the fear of the "personal" being erased by anything that doesn't agree with ones beliefs... or ones experience... or the fear that the personal reality won't be revered by others in the fashion that one desires it to be worshiped, when an argument ensues and the ad hominem becomes the standard when responding to some thing, or some one.

If you can't rule the world, destroy it.

Paraphrase:

"Every problem — no matter how apparently simple it may be — comes with a long list of people who think it’s really a different problem. Many of these other problems may have nothing to do with the original one, and may even be misleading."

Ignore this. I made a post, but then realized that I had a wrong link, so I am taking the whole thing out.

Bill Gill

Seriously Bill S

Let do a simple versions for you to see the problem if your number system only allows positive integers then zero and negative numbers are illegal and not valid. Many what we call primitive cultures have that situation in there numbering systems.

Lets look at a few

Australian Aboriginals have no zero and no negatives and no decimals so if I was an Australian Aboriginal I would have some interesting answers for you.
http://en.wikipedia.org/wiki/Australian_Aboriginal_enumeration

There is no letter for Zero in Roman numerals because they didn't have it either the concept either but they did have fractions. So again if I was a ancient roman I would have some interesting but different answers for you.
http://en.wikipedia.org/wiki/Roman_numerals

Now if we go forward you were taught the REAL NUMBER system at school so you are one up from these primitive cultures. The problem is there is a group of numbers that you can't deal with under that system and some you would have dealt with at school like irrational and repeating numbers. Simple Pi for example can not be written under that system you can only ever approximate it to some number of decimal places or write it in a special symbolic way and you can't use it in that format.

What I am suggesting to you is consider that part of your problem may be you and your primitive number culture and you are giving me interesting answers .

If you go to the highest number system we as human culture in the 20th Century know which is Octonions INFINITY presents no problem you can even do all arithmetic operations with it.



There is nothing evasive about my answer it's very blunt have you consider part of your problem with the questions could be your ignorance in some of your assumptions.


See here again you miss the problem any measurement has an accuracy is it 6 inchs, 6.0001 inchs or 6.00010001.... recurring inches. All scientific measurement is reported with an accuracy look at any scientific paper data .... only layman think 6 inches is actually 6 inches

So your 6 inches to me is 6 inches +- some uncertainty to this janitor and you will never be able to convince me otherwise

Any measurement requires a truncation of the number to some sort of universal grid which in our universe is a Plank distance. Your little REAL NUMBER SYSTEM you were taught at school can not deal with such a cutoff because there is no hint of what precision you need to use.

You have the same issue when you are faced with the common calculator and you want PI what you get is some rounded value that is the best approximation it can do with the decimal point accuracy available. Most calculators are unsuitable for astronomical calculations because they do not have the required precision.

Surely you have thought about this that the whole conservation of energy would be breakable under such a system like the fixed precision accuracy of a calculator. You could engineer situations to exploit the fixed decimal precision roundoff.

We even give it a name "Salami slicing" (http://en.wikipedia.org/wiki/Salami_slicing)


Under Australian Aboriginal numeric no it's not
Under Ancient Roman numeric no it's not
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.

So which numeric system do you propose we use?

You may also please read the warning under Real numbers
QUOTE: "These descriptions of the real numbers are not sufficiently rigorous by the modern standards of pure mathematics. "

If you want it in layman speak the real number system is too primitive to be used for anymore for pure mathematics and I am asking you to consider is it therefore valid to use it for science discussion on the universe.

I will leave the time stuff for now because that gets even trickier with concepts buts lets see if we can work the number system you want to use on the universe and why you make that choice?

This may provide you help thinking about it: https://www.math.toronto.edu/mathnet/answers/infinity.html

I will put this as a seperate post as something you may want to consider.

The Standard Model says that particles that make up an atom, quarks and electrons are point particles they do not take up any "space". What makes an atom take up space is not anything spatial but the indeterminacy of its internal spatial relations because of the uncertainty principle.

Thus the standard model is built around an infinity and renormalization becomes important to it.

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


Given the above you might need to think about the risk to select a number system that does not formally deal with infinity when dealing with the universe

A final presentation which will probably help you

https://dl.dropboxusercontent.com/u/12796267/kapustin-talk.swf

Are you out of your depth here, Orac, or are you being deliberately obtuse? If you want to involve the aboriginal concept of infinity, you need to be looking at Alcheringa in its original form, before it became mistranslated.

Alcheringa has been linked both to infinity and to the work of Itzhak Bars. It would make as much sense to suggest that the Aboriginals were ahead of current thinking about mathematical infinities as to involve their number system in this discussion.

The same charge of irrelevance applies to all your comments about different number systems; unless you can establish that infinity is a number.

FFS orac are you intentionally trying to prove just how ridiculous and dumb your logic is?

the number 6 has no decimal point to consider , there is no decimal point in any whole number.

none !!!

Bill S , clearly specified 6 inches , and an inch is just as much a scientific measurement as a centimeter is.

You should stop trying to bluff your way through a discussion.

your lengthy deposits in this thread may as well have been deposited in the nearest trash bin.

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.

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

https://dl.dropboxusercontent.com/u/12796267/kapustin-talk.swf

It will sort of at least give you a glimpse of the problem and they explain it in dumb as dog language.

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

I really want you to do it and tell me what they say

Then can you pleas send me your bar which is exactly 6.000000000000000000000000000000000000000000000000000000000000000...

Because I want it for the new SI standard

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.

Whatever mathematics system the universe is using has to be able to cope with this problem ... oh but wait you build your own physics system and garbage so it probably isn't like that in your world

The problem is first manifest with ATOMS in that they are EXACTLY the same size for each element and that is sort of tricky to understand given the uncertainty in everything ... oh but wait again your physics is probably different because you can have an exact 6 inch bar

Interesting that the six inches has become so important in the discussion. The intention of the "quote" was threefold:
1. to introduce a trace of humour;
2. to highlight the absurdity of the question;
3. as an homage to "The Navy Lark" q.v.

If the thread is going to descend into personal sniping, I will bow out at this point.

Did you at least watch the presentation to understand why the 6inches becomes a problem?

It's because it has uncertainty the thing you won't even acknowledge and you won't try and understand

They couldn't make it any simpler to understand in the presentation and if you don't get it at that point, then I am sorry but physics is always going to escape you and yes you really need to leave.

"...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

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

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.

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.

Bill Gill

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.



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



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.

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

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

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

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

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.

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.

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.

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.


Bill Gill

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

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

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!

Bill Gill

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

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.


You set that answer in your selection of basis of countable numbers and that system says infinity as 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.

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

Bill Gill

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.

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.

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.

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.

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

Bill Gill

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


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


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

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

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

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?

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

Bill Gill

Orac, in spite of your accusations, I am trying to learn. Some 10 days ago I posted the same OP on TNS.

http://www.thenakedscientists.com/forum/index.php?topic=53002.0

56 posts on, there is very little personal sniping, and quite a lot of material that I am keeping in note form. This is the sort discussion I had hoped to initiate here on SAGG so that my notes could contain a wider range of opinions.

Comments like: “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.” Find no place in my notes. They have no learning value to me.

I would like to suggest that we draw a line under what has gone before, and make a fresh start, perhaps using Orac’s link as our starting point.

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

Let’s consider its opening question: Is there really such a thing as "infinity"?

Any takers?

1. Is infinity a number? No
infinity does not exist , it is a descriptive word that humans use vs other descriptive words such as forever , eternity, when describing the largest amount of time passing...

2. Is eternity a length of time? Yes
but the length of time is unknown like infinity , forever.

3. Is it possible to define Cantor’s “absolute infinity”? No
because a human could not know what absolute infinity could be.

4. If there had ever been (absolutely) nothing, could there be something now? No
something would require something , a spirit is something
even though most humans are not capable of any type of recognition / detection of a spirit through any means.
although most humans do feel spirits they do not recognize them as being spirits.

5. Could there be change without time? No
time is just the measurable part of infinity , forever , eternity , and time passes ...

number 4 might get me into some trouble here on SAGG , but does anybody really care? LOL

I know I don't care ...

You have some good answers there Paul. No. 4 is the one that is really iffy. There may or may not have ever been nothing. but there is not really any way to determine if there ever was or will be nothing.

And I tend agree with your answer to No. 5. Some theoreticians have suggested that there is no such thing as time, but it appears to me that time is an integral part of our 'bookkeeping'. Without time it would be impossible to separate events because they would all occur in one single instant. But I'm not even sure how to say that, because the word 'instant' implies time. Time is deeply imbedded in our understanding of the world.

Bill Gill

If one takes the “dictionary definitions” of infinity and eternity, you are spot on. I’m reluctant to accept everyday definitions as though they were accepted laws of physics. I think accepting them into our more analytical thinking can lead to trouble.

You say infinity is not a number, and justify that statement, yet you say that eternity is a length of time; although you liken it to infinity. Do you not feel there is something of a conflict here?

I have no problem with your answer to 4. Had there ever been nothing, I see no logical explanation for the obvious fact that there is something now. I cannot provide any proof of what the something that has always existed might have been, so I’m not going to try to put down anyone’s thoughts or beliefs on that subject.

In 5; I agree with your “No”, but have reservations about your reasoning. Perhaps we can come back to that.



I think if any of us really cared about what others on SAGG say about us, or call us, we wouldn’t still be posting.

One way to establish that there could have been nothing would be to come up with a self consistent explanation for how something could emerge from nothing.

1. Is infinity a number?
2. Is eternity a length of time?

if you would have asked if infinity was a lenght of time my answer
would have been : Yes

if you would have asked if eternity was a number my answer
would have been : No





there will always be "time" to measure change.

and changes occur as time passes... but there can not be change without "time" passing.

you haven't answered my question about the weather in the UK
in the Climate Change Forum , I would like to have the opinion
of a human and his experiences through the years vs a bunch of measuring instrument's if you don't mind.

"1. Is infinity a number?
I would think concept, not number. Meaning not a real number but I don't understand quaternions and octonions.


2. Is eternity a length of time?
I would think an infinite length of time (if time exists). But I'm troubled that it seems photons don't experience time or distance.


3. Is it possible to define Cantor’s “absolute infinity”?
Haven't looked into that.


4. If there had ever been (absolutely) nothing, could there be something now?
I would not think so. What would anything form from?


5. Could there be change without time?"
Wouldn't think so but there's the time and photon scenario again.

Bill S I am more than happy to discuss things in a civil detailed manner but at the moment you are not actually looking at the matter in a open investigative way and I couldn't help but laugh as you guys dug yourself into a huge hole.

Pokey bought up probably the first point as Layman you guys don't understand why complex number and greater systems exist. So if you really want to get some understanding it is worth taking a few minutes to run thru that. I will have a crack to give the ultra short condensed version as best I know which goes like this.

In the 15th century the imaginary number system was created to deal with square roots of negative numbers. In the 17th century problems to do with engineering often required the use of an imaginary axis(s) along with the normal 3D world to solve problems. A simple example would be the stress inside a 3D beam where you would end up with for every x,y,z a stress value. When you try to solve these problems you find you are dealing with a cubic equation and complex numbers came from the merge of imaginary system and real number systems to solve them.

The number system could have infinity or not depending on use and no one really took any real thought about it because it was not considered to be real. You could use infinity as a number or a concept because the number system was only used for analysis and the relevance of infinity was to the use.

Electromagnetic light waves caused the first problems here we had a waveform which was in 2D in movement (it moves in straight line so 2D not 3D) but contained 2 field strengths for each point on the 2D movement plane. So every point along the 2D space plane required X,Y,E,B as values when doing analysis on the waves. E being the electric field strength and B being the magnetic field strength. If that wasn't bad enough the totally energy between the two fields was linked. This was our first encountering of a real world situation in which 4 degrees of freedom were involved (I avoided using dimension deliberately).

The analysis of the waveforms required the use of complex numbers which was developed in the 18th century by Maxwell. At this stage you can sort of wave your hands and say the complex number mathematics is just a way of doing the mathematics we had not worked out how to do with real numbers.

In 1905 Einstein introduces GR & SR which like electromagnetism involves 4 degrees of freedom linked via equations. In SR and GR the traditional approach was to make time the imaginary component of a complex number co-ordinate of spacetime (it's mostly no longer taught that way but it was and is still valid). So now two of the cornerstones of physics required complex number system to provide solutions.

Finally QM and Heisenberg uncertainty principle create the problem that everything in the universe requires quantum wave description and that can not be done or even written in real number systems. The technical reason is usually expressed as this


In simple layman terms the universe is composed of things that can only be represented by complex numbers.

Once you realize the above fact worrying about the implications and stupidity of what infinity does or doesn't mean in the real number system has about as much relevance to the universe as to whether green aliens exist outside the universe.

Hopefully you might actually use some intelligence and give some more serious thought to the number system because you can't use real numbers to discuss the universe.

Well you can but don't expect me to treat you not like an idiot especially after I told you a number of times

There is no agreed way to handle infinity in complex numbers (largely because of it's history) and there are other similar problems which is why efforts were made to more strictly handle complex mathematics with more formal rules and that is what quaterions and octernions are.

The lesson is (and I told you it) sometimes you need to look carefully at the question and what assumptions underpin it. The problem with the question in the way that you are answering it is that you think real numbers have anything to do with real world physics

You could have saved yourself a lot of grief and embarrassment by a simple google search of "why does physics use complex numbers" when I pointed out that situation

This was one of the funniest threads I have been in for a while and I guess shows the gulf between layman and science dramatically. You just could not see how you could be wrong and I couldn't believe you didn't get the error and problem.

And all of this talk still has nothing to do with whether infinity is a number. Some calculations in both GR and QM wind up with infinities in the answer. In QM this is frequently corrected by renormalization, but it doesn't affect the fact that infinities occur in complex number calculations, just as they do in real number calculations.

Example:
let A = 10 + 10i
let B = 0 + 0i
then:
A/B = infinity, if you ignore the prohibition against dividing by zero.

So all of your blather about complex numbers still doesn't give us an answer as to whether you think infinity is a number.

And Paul's answer to the questions that Bill S. asked at the start of this thread are still pretty good answers.

Bill Gill

Thanks for the interesting history, Orac.



A large part of the problem is that you are reaching that sort of conclusion without any justification. I make no such assumption about the Universe, and if you were able to take my questions and reasoning at face value, instead of trying to force them into a confused and confusing mathematical mould, you would understand that. Interestingly, in this forum you are urging me to study complex numbers in order to solve what you perceive as my "problem"; and in TNS, Pete, who you will remember from his brief sojourn in SAGG, is urging me to study calculus for the same reason.

Possibly the key question from the OP is:

If there had ever been (absolutely) nothing, could there be something now?

Pokey's answer: "I would not think so. What would anything form from?" is concise, reasonable and lacking in extraneous maths. It also anticipates the question that would naturally follow an affirmative answer.

I accept willingly that mathematics is the best language that humans have yet found to probe the mysteries of the cosmos, but I don't necessarily accept that there is some grand mathematical model on which some preexisting intelligence designed the cosmos, and that we cannot even think about the nature of existence unless we discover the mind of some mathematical God.

I have told you the answer a number of times if you bothered to actually read the problem instead or reacting because it's me that said it.

There is no formal way to answer the question in the complex number system. The way you define the complex number system will either allow you to use infinity as a digit in both answer and operator or not. Due to the history of complex numbers and every complex number containing "imaginary" terms the idea of them being or meaning something real is sort of foreign and weird. Perhaps you could argue all complex numbers are concepts because they are all like infinity, but that leads to interesting conclusions about the world

Hopefully you see the problem trying to distinguish any number as being "real" as opposed to "concept" in complex numbers is well interesting by any standard. I would really like to have a mathematician make a comment on it perhaps I am missing something.

Personally there is no selection criteria I could give you as to whether infinity is a "digit representation" or "concept" in complex numbers other than can you use it as a normal "digit" in operations. I really see no other criteria I could use there is nothing special about it compared to any other complex number.

That is why I wanted to talk about operators which you didn't like and instead wanted to make it about "counting". I didn't jibe you about it but had a good chuckle because counting is the operator of "addition" as a heads up.

There is no "authority" that can settle or answer that question you will need to work a basis to make the selection of the answer.

In other words it requires something you refuse to do, which Bill S has sort of come around to which is discuss what is the question really asking and think about it.

Again Bill S there is a huge problem with that question.

1.) You could try to answer that from your experience.

The problem is we live and have experience in one tiny part of a very big universe that may actually be nothing like what we see around us. As humans we once believed the earth was flat, we were the centre of the universe, the sun revolved around the earth by using exactly that sort of reasoning.

Do you really want to go back to the dark ages?


2.) You could try answering the question from the point of view of physics. I know you asked this on a number of science forums and they gave you the same answer I will.

Our current understanding and mathematics of physics does not exclude the possibility that you can create something from nothing, regardless of the fact that probably every scientist hates the idea.

3.) You could try answering the question from what you personally prefer as a cult (although that has really negative context and I don't mean to imply it, my english I can't find a better wording)


This goes down that path and science caress little what Pokey, you me or anybody else "thinks" that is the basis for a cult not science.


Again science does not care what you think. All it cares about is do you have an idea that makes predictions that can be tested and are those answers verified.

Then please give an example of a complex number where infinity is a number and tell us what that number is.

Bill Gill

You are partly correct, but you have it backwards. Addition is a short hand for counting. 5,000 to 6,000 years ago when a farmer brought in his offering to the temple the priests counted how much he brought in and put it in storage. Then when another farmer brought in his they counted that and put it in storage. But inevitably the high priest would want to know how much there was. Then they had to go count it all. But then they invented a short cut, addition. Now all they had to do was to count the income from each farmer and then add it up to figure how much they had. And that was the start of all mathematics, including complex mathematics. All mathematics is a short hand for counting.

Complex math may have a way to handle infinity, but the result of any calculation is unusable it it returns an infinity. So infinity is not a number.

Bill Gill

Dozens of them but a fairly common one related to spacetime is Riemann sphere

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

It's has a lot of uses in physics where you potentially have a real infinity and want to avoid using higher maths schemes.

Ask Dr Maths gives you the background in the best way I could ever express for a layman
http://mathforum.org/library/drmath/view/63359.html


Is that clear enough that infinity is handled exactly the same way as any other complex number under the system and that is why you do it.

As to what number infinity is well perhaps lets write a few complex numbers and you tell me what number they are so I can understand what you mean

3 + 2i = what number to Bill
69 + 3i = what number to Bill
7 + 0i = what number to Bill (you might be able to do)

So can you tell me what those numbers are and I might understand a basis to give you a number for infinity.

Complex numbers calculations return complex numbers

The usability of infinity is a function of the complex number system used as discussed in Reimann Sphere

That was actually my point in many forms of complex number systems, quaternions and octonions you can use operations on infinity. It does not differ from any other number under these schemes because each complex number is nothing like a number in the terms you are thinking of.

So I need you to write me a complex number and tell me what number it represents so I can try and understand you

Here is the general form of a complex number

a + bi
(a is the real number part, b is the imaginary number part)

I want you to explain how any of those numbers so written are different to writing infinity.


Once you get thru that I want you to show me "counting" on a complex number. Oh boy this is going to be a Bill G classic. To give you a heads up you might find a little problem determining which direction to "count" in and I am dying to know how you decide that. Perhaps read Ask Doctor maths answer again because he talks about directions

So when you are ready 23 + 7i what is the next count of that complex number please I am dying to know.

Bill can I suggest the hole is getting deeper stop digging

Ok, let's take a look at that.

let A = 23 + 7i Determine A + 1
let x = 23
let y = 7
let r = length of the vector described by A
let T = the angle of the vector described by A
T = atan(y/x) = 16.927 degrees
r = x/cos(T) = 24.041
let r' = r + 1 = 25.041
x' = r' cos(T) = 23.956
y' = r' sin(T) = 7.291

Then

A' = 23.956 + 7.291i

A has thus been incremented by 1.

Did you forget that complex numbers are basically vectors?

I did take a little longer than it should have to figure that out. I don't work with the trig functions much so I had to do some review.

By the way I didn't see any infinities in that.

Bill Gill

So if I work out the number of "bill counts" from 0 + 0i I guess that must be the bill count number thing you keep asking for and you have no infinity

So lets do it

0 + 0i = 0
0.956 + 0.291i = 1
1.912 + 0.582i = 2
2.868 + 0.873i = 3
....
22.944 + 6.984i = 24

hmmm not quite even so I guess

23 + 7i = 24.058577405857740585774058577406

Are you happy with Bill, I think I have followed your logic correctly?

Anyone else care to comment?

Hints:
Bill count to 23 - 7i, -23 + 7i & -23 - 7i. Those are the obvious easy ones no maths required.
Clever ones will be able to mark all the co-ordinates for a bill count of 24.058577405857740585774058577406 and how many is that
If you haven't got it think circle centred on 0,0


So hopefully you all caught up so Bill says 24.058577405857740585774058577406 bill counts from the complex origin all you have to do is work out which of the infinite points on the circle of radius 24.058577405857740585774058577406 centred on 0,0 he means

In fact for any point you pick you can draw a circle 1 unit in size and those are the infinite number of values 1 bill count away depending on which of the infinite directions you decide to bill count. And you have no idea which way to count until your bill count is given to you as a proper complex number so you can get its direction from 0,0. This is dramatically different from real numbers where any number on has two numbers 1 bill count away.

So every complex number has infinite other complex numbers 1 bill count away and that doesn't even include all the complex numbers because we can see the circle doesn't pass thru every complex number. Good lord there is something therefore bigger than and more tricky than infinity then what shall we call it

Bill can write his bill count number using digits rather than a symbol is about the only difference I can see but I am sure Bill will clear this all up for me.

This should help



Background read the full detail
http://www.clarku.edu/~djoyce/complex/abs.html

And you note


No infinities were harmed in the making of this production of the infinite number of infinities.

I'm glad to see that you can still draw completely erroneous conclusions from my simple demonstrations. In your example that you wanted me to work out you asked me to add 1 to a vector. Since one is not a vector I assumed that you meant me to add the quantity one. That means that you wanted me to add 1 to the length of the vector. So I converted the vector to polar coordinates and added 1, then converted back to XY coordinates. If I had realized you wanted the 1 to be a vector then I would have expressed it as a vector that is, 1 + 0i, and done vector addition. That is a lot simpler than doing the conversions back and forth between XY and polar coordinates. In that case the answer would be 24 + 7i.

As far as an infinite number of directions from the end of the first vector is concerned it is true, but to access those points you have to define a vector that points to the one you want. You did not give me a vector, you gave me a number. So you are once again resorting to obfuscation to hide the fact that:

You still haven't found any place where infinity is a number.

Bill Gill

So you agree there are infinite numbers 1 unit away from any complex number ... excellent we are making progress

Now do you also agree there are complex numbers that are not on that 1 unit circle, say perhaps the ones 2 units away and 3 and so on?

So whats really groovy is the infinite numbers 1 unit away are different numbers to the infinite numbers 2 units away and on and on it goes. Not a single repeat of a number don't you find that slightly strange.

Now give me your definition of infinity as a concept please?

Your current infinity numbers 1 unit away have a lot more different infinite numbers that are not include and I am having a slight infinity issue

So what would they be infinity + 1, infinity + 2, infinity + 3 etc would they. Refer your answer back to your definition of infinity for me please.

Come on Bill think ... what is happening and what is wrong?

Do you need a hint? I am willing to help you if you want but you usually slap me. So all I can do is try to lead you to get the penny to drop. I am not sure you will be able to ask the right question to get yourself out of your current hole because of the very nature of what you have done with complex numbers and I fear you are really stuck in confusion.



The definition you have imposed on "number" is a very slippery slope and actually interesting and hard for me to be certain of anything.

Hey I don't mind being wrong I am always wrong see my byline, but I am just making sure I don't make the mistake again so I need you to explain your logic and my error. I actually accepted I was going to be wrong long ago but that just makes this all the funnier where you end up

Bill.S has gone quiet, you following all this and what do you make of it?

I'm still here. I'm not a mathematician, so the discussion is not one I would attempt to join. I have always maintained that I have no argument with mathematical "infinities"; so it's water under the bridge to me. Anyone who wants to turn his/her mathematical prowess into a display of autopedestalism is welcome to do so.

Ok, Orac. It is obvious that I am too dumb to figure out what your definition of numbers is. So the next step in the discussion requires that you give us your definition of numbers.

Your definition should not involve links to outside sources. Just give us the definition in your words.

Bill Gill

autopedestalism?

Bill Gill

haha I get a pedestal woot.

Ok I will give you what the problem is and it doesn't need references it just needs thinking

The problem is the complex number space is a grid and like all square grids it is m x m.

So the complex number space is infinity x infinity but those cells are nothing more than possible answers. It is what it appears to be a number space for a solution and nothing makes sense in the space until you put in the argument. There is no argument you can put on the space that would pass thru all points or I guess more correctly they would say you are not allowed to frame a question that way. When I was adding multiple abs values I was constructing and adding multiple arguments onto the same solution space which would be invalid because of that last bit.

So you can't turn a complex number x,y cell into a definitive thing called a number until you put the argument in because many of the number cells will disappear as possible solutions as determined by the argument.

The problem exists even for real numbers if I give you the number 23.45, 45.123, Pi etc and then set a question that requires a whole number result those numbers drop off as valid numbers in the set. You can't start counting them because the argument excludes them and the same is true in complex numbers just not as obvious.

So there is nothing strange about complex numbers what is strange is we don't adjust the language to explain some numbers may drop out that is sort of implicit in the system and that was the joke I was having that you didn't get.

The "counting" problem rolled around the fact counting is not a clear argument and it could literally many infinite things on a complex number system hence infinite answer. It's like many things there is no way to decide a preferred frame on the 2D solution space on how to do an argument called "count". Refine the argument of "count" better and you can get a unique solution.

So what was the point?

I was trying to show you the logic that follows that therefore says that all numbers are really a concept relative to an argument there is nothing special about infinity. So this idea there is "numbers" and the infinity as a concept I believe is misguided and your problem above stems out of trying to make things called "numbers". In fact after thinking about it you see I could construct the same argument with real numbers and infinity. I hadn't really thought about it until I tried to answer the question and initially I agreed with your answer.

So what seems to me make infinity special is that under many number systems you can't do operations with it. I can't see any situation that can fail as a definition. Pi is a symbol and a concept and yet you can do operations on it even in the real number system yet infinity you can not.

That to me is the distinguishing feature but it does not appear to be the "accepted answer" which means you can construct some funny arguments which I did.

So I am wrong and happy in my being wrong because I don't won't to be "accepted right" because it gives really weird answers.

Pedestalism: The tendency for members of a group, profession etc to act as though only members of that group possessed valid knowledge, skill etc. I.e. they place that group on a “pedestal”.

Autopedestalism: An individual variant of pedestalism.

Sorry Bill G I forgot if you understood the above you should now get a Reimann sphere which will complete the answer.

What reimann did was say why does the solution space have to be a flat grid (mxm flat earth) why not make it a sphere (like earth). Infinity is now simply the point futherest from you which is the point that is antipodal to where you are now.

It's easy to see the logic if we look at earth if I travel on the surface in a direct line in any direction the point futherest from me is the point antipodal to where I am.

It gives you one correct answer no matter how large or small the sphere. The infinity of the point on earth from where you are now is the point on the opposite side of the earth from where you currently are if you can only travel on the surface. As per earth you must however use some form of polar co-ordinates on the scheme you can't use a square grid of complex numbers.

So there is one complex number system that I believe has a definite number infinity and many shaped solution space would do the same.

The achilles heel is you never proved that such a thing is justified and could or should exist, we just made it so based a familiar background. I growl at Bill S when he does that so I need to be consistent

So I am still happy to say I am not suggesting I am correct, but I can create some good jokes to the "authorities"

Thanks for the clear reply. I don't have time to read and study your response right now. It will take a little while to get it right and I have some other stuff to do. I should get back this afternoon or tomorrow morning.

Bill Gill

In this context what do you mean by argument? I am having a bit of a problem deciding just what you mean and don't want to go off in the wrong direction because I misinterpreted the word.

Bill Gill

http://mathworld.wolfram.com/Argument.html


Sorry I should have made it perhaps a bit more layman friendly and not used that technical term.

Let come back to a real numbers example which might help make it simpler (so my solution space is real numbers) however I decide I want only integer numbers. There are a number of ways I could decide to do that I could make the argument round, truncate, floor, ceil or any of millions of other functions etc

In pseduo code it looks like this

Result = arg (input)

Eg:
Integer result = Round(real number)

So the round function takes a real number argument adjusts the solution space to only integers and maps the real number onto that solution space and returns the result.

So 1.2345 is definitely a "number" to you, but it isn't a valid "integer number". So I am not sure how you want to think of 1.2345 if the answer has to be integer. You could decide it isn't a number, maybe it isn't a valid number, maybe it isn't a possible answer. It doesn't really matter how you want to describe it or what name you want to call it, your solution space excludes that particular number because of the argument solution space is integers.

In complex maths nothing really changes the answer will have a solution space that excludes some answers for the same sorts of reasons. Just because you have a complex number don't imagine it exists as an answer anymore than 1.2345 exists as an answer in the real number example above.

Above we considered only the answer it should be obvious that 1.2345 might not be a valid input. For example can I "count" up from 1.2345. Well if by count we mean the usual integer operation the answer is no because it isn't an integer to start with. Any computer programmer will recognize this as a number type error and count would be defined something like this

int count (x int){
return(x +1);
}

If you tried to count(1.2345) the compiler would say typecast mismatch and refuse it because it wants an integer and you are passing it a real number.

So never assume the full set of numbers in either complex numbers or real numbers is valid to the input or answer to any mathematical problem. All my little examples were trying to get you to see the problem that somehow you have to distinguish between "number" and "valid numbers" for input/output for a maths problem or you get funny answers.

"valid numbers" can only be decided by a concept so in that reguard they are no different to infinity. The difference appears to be what they are allowed to do with the operators.

Ok, I need to clarify something I said up above and which Orac was trying to show was wrong. When I was calculating the addition of 1 to Orac's problem I just added one to the length of the vector and said that was how you did it. Here is the caclulation I made.



I just said that that is how you add a number (any number) to a vector. After Orac's attempt to confuse the issue I started wondering if I was right. So yesterday afternoon I did a little research on the question of adding a number to a vector. I found that there is apparently no definition of that operation. That is: given vector A there is apparently no way to perform the operation A + x. In fact I did a search on the internet and couldn't find any place where that was shown. I even found a couple of places where people had asked that question and been told they couldn't do it. But there are plenty of places that discuss scalar multiplication of vectors. That is: Given vector A you perform the operation A * x. This operation involves determining the magnitude of A designated |A|. The magnitude of A is its length. That was the first thing I calculate in the above example. But there didn't seem to be a way to do the A + x operation. Then I got to thinking, multiplication is a shortcut to addition. For example you can write:

3 * 7 = 21
or you can write:
7 + 7+ 7 = 21

So I started thinking about how I could use multiplication to do addition. Well, it turns out to work quite well. If you want to add a scalar to a vector you just add it to the magnitude of the vector. The vector retains the same direction and changes length.

So Orac's questions about what direction the additional number goes are irrelevant. My answer was entirely correct.

If any body is interested in the details of how I figured this out I will be happy to provide them. Just post your question.

Bill Gill

So what does this have to do with how to do vector math? You choose what kind of output you need, then do your calculations with appropriate adjustments to provide the type of output you need for your application. I do an occasional bit of programming and have run into problems with getting the wrong type of number, but it doesn't change how it works. A while back I was getting an offset in my calculations that drove me crazy until I realized I was converting to an integer at the wrong place. I just corrected the conversion and it started working fine.

Vector calculations use the same functions, basically addition and multiplication with a layer of trigonometry, as any other calculations. Those all work just fine whether you are working with integers or real numbers. The only difference is how you look at it.

As far as counting is concerned I can count by any number I want to. I can count by 1s or 2s or 3.141596s. That last one is Pi and for many application you count angles in terms of Pi.

I haven't had time to look at you other post about spherical coordinates. I will probably get to it later this morning.

Bill Gill

Yep you really don't get it at all and you are off in Bill lala land in another example of "Bill in the box"

No one said you couldn't count by anything you like what I said is SUPPOSE you are REQUIRED to do a whole number count.

REQUIRED is a pretty exact term even for you Bill.

I have no doubt you get errors about type on programming because the language protects itself from idiots because it REQUIRES a certain type in it's function and protects itself from idiots.

All I can say is it is fortunate you only do a little programming and on nothing critical

Unfortunately complex maths problem has no way to protect itself from idiots it will just do the maths regardless of whether it's valid to do so or not and spits the stupid invalid answer.

That is the joke I was playing with you in all the samples but clearly this is way beyond your understanding and as you are happy with the stupid answers you are getting ... be happy my friend

It really isn't worth wasting time on because you aren't trying to actually understand anything, you are doing what you often accuse Paul of going off on tangents because all you care about is being "right" and so you are bending the argument to stupidity. Don't you ever complain about Paul doing that again.

You are "right" Bill whatever that means because you are not worth spending this amount of time on and going thru this crazy garbage which has almost reached Marosz standard crazy.

Well, you did give me an example of a system that works with infinity. The Riemann sphere does have an infinity that can be worked with, and division by zero is possible. However, in the case up above where you were trying to say that adding a number, any number, to a complex number is not defined you are obviously wrong, since I have clearly demonstrated that it is possible under the rules of vector mathematics. If you want to argue with that then you are really just trying to show that you are smarter than any body else. And so I can just ignore all of your ranting, other than trying to point out the facts of life to other people viewing SAGG.

And other than the bit about Riemann spheres you have not shown any place where I am wrong. Just saying I don't understand doesn't demonstrate anything about the facts of the case.

Bill Gill

Would this be like 1.2345 being a whole number in "Bill mathematics", which is sort of looking a lot like "Paul physics" and "Marosz physics"

Sorry Bill I don't know how to do "Bill Mathematics" and I can't get a basis to relate to you in the same way I can't relate to "Paul physics" or "Marosz physics".

I think you are agreeing Reinmann Sphere has a true infinity but I not sure it does under "bill mathematics" because now you have dragged vector maths as being involved and I just don't want to even begin to try and pull this all apart. So I think I am probably wrong under your bill mathematics it's really hard to know and I am going to ignore working it out.

I am ignoring your "bill mathematics" like I ignore the other two because in my world it is simply to stupid to bother. I really never thought I would ever have to argue what what whole number means with anyone and it just keeps getting worse and worse. It reminds me of an argument with Paul where it went down and down to arguing what zero means just so he could be "right".

You really need and want to be "right" all you need to do now is start posting threads continually about your rightness and start countless threads on it.

I think this is a wonderful example of how Orac operates. Even when I agree with him I am wrong. Now for some reason he has decided that I am claiming that real numbers are integers. I have no idea how he ever reached that conclusion. But he doesn't seem to be interested in actually explaining anything he talks about. He makes elliptical statements and then we we try to interpret them he points out how we are wrong. But he can't or won't provide simple point by point explanations of how we are wrong.

I think that it is about time to start ignoring his posts.

Bill Gill

In my world 3.141596 and PI are not integers and can not be inputs or answers to an integer operation. That is why a program compiler will produce and error if you attempt to do that garbage as well. However under "bill maths" there is no problem.

Enough said you either (a) have a different maths system or (b) don't actually read ... pick a or b.

I guess you could try option (c) redefine integer operation but I have had enough of this stupidity.

Please do go ahead and ignore me.