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

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.

About time?...no one could accuse you of a knee-jerk reaction. I take my hat off to you for your perseverence, patience and self-restraint in the face of regular and relentless abuse from SAGG's resident emetic scum.
No, I don't have anything to contribute to the topic - banging one's head against walls is unproductive - and I'd be delighted to have this post removed if all the offensive text posted above goes with it.

What as opposed the SAGG's resident emetic crazies that invent there own systems of physics, maths and anything else and they are always "right". I will go with the scum anyday at least they make sense (so adding the scum to my byline).

Bill eventually realized there was an error but I am not sure mathematics will ever be the same again.

Poor Rede all you can be these days is drinks boy for "Bill in the box" can't event think thru the problem yourself to see an error. Good to see you are here to cheer on his "rightness" that studying is really paying off

All you guys need to do now is start the rabid repeat spam posting an you will be indistinguishable from the rest of the SAGG resident crazies.

Personally I don't care who is "right" all I care about is things that make sense. I have seen so many "rights" that were so wrong they hurt. So next time you are tempted to claim "I am right" perhaps try saying "Can you show the logic to arrive at that answer" instead and take the time to consider the logic.

One more time I just can't resist. When somebody asks you to show the logic you just go off on a side track to keep from having to actually give a coherent reply. That doesn't help us figure out what is actually going on.

Bill Gill