Welcome to
Science a GoGo's
Discussion Forums
Please keep your postings on-topic or they will be moved to a galaxy far, far away.
Your use of this forum indicates your agreement to our terms of use.
So that we remain spam-free, please note that all posts by new users are moderated.


The Forums
General Science Talk        Not-Quite-Science        Climate Change Discussion        Physics Forum        Science Fiction

Who's Online Now
0 members (), 181 guests, and 2 robots.
Key: Admin, Global Mod, Mod
Latest Posts
Top Posters(30 Days)
Previous Thread
Next Thread
Print Thread
Page 1 of 2 1 2
#2274 07/11/05 03:30 AM
A
Anonymous
Unregistered
Anonymous
Unregistered
A
Consider this we you have x amount of a y and it grows over time to become nx then your growth ratio is n ... (nx-x)/x = n
Now if we make x=0 then Maths crashes to infinity... but not the real world.
Why ?
According to Maths anything divided by 0 leads to infinity....therefore it must be called the singularity.
In real world we have profits zooming from 0 to millions... we have a glass getting filled up from bottom to top .. we have no speed to breaking sound barrier... they are infitite no of cases... and as per maths the growth ratio or percentage of that noun was infinite...

.
#2275 07/11/05 07:29 PM
Joined: Oct 2004
Posts: 4,136
D
Megastar
Offline
Megastar
D
Joined: Oct 2004
Posts: 4,136
Lets examine your premise applying logic rather than sleight-of-hand.

1. Consider this we you have x amount of a 'y' and it grows

2. Now if we make x=0

Do you see the problem? You have rephrase statement 1 as "Consider taht you have no 'y'.

No 'y' does not grow ... no 'y' is no 'y'.

When you get some 'y' then, and only then, can it do anything.


DA Morgan
#2276 07/12/05 02:47 AM
A
Anonymous
Unregistered
Anonymous
Unregistered
A
What do you mean by that ?
No is a logical state and is used in Boolean Algebra.
No essentially means Not-Yes. No itself has no meaning. No logical state belongs to group of finite logical gates which can be constructed using Boolean Algebra...
Let me put it more clearly.
Let us assume x=3 then it means no 4 and no 5 and no 6 and no 7 and NO 0 ... Notice that we have applied Negation of 0 in our description... and it is no way trying to suggest that y doesnt exist but just that its quantity doesnt exist...
Similarly when x= zero it means the quanity is not 1 and not 2 and not 3 and not 4 and so on..The quantity is 0....
Application of zero is entirely different in the discussed domains....

#2277 07/15/05 04:34 AM
Joined: Jul 2005
Posts: 17
Y
Junior Member
Offline
Junior Member
Y
Joined: Jul 2005
Posts: 17
Quote:
Originally posted by dkv:
Consider this we you have x amount of a y and it grows over time to become nx then your growth ratio is n ... (nx-x)/x = n
Now if we make x=0 then Maths crashes to infinity... but not the real world.
Why ?
According to Maths anything divided by 0 leads to infinity....therefore it must be called the singularity.
In real world we have profits zooming from 0 to millions... we have a glass getting filled up from bottom to top .. we have no speed to breaking sound barrier... they are infitite no of cases... and as per maths the growth ratio or percentage of that noun was infinite...
I was going to comment on this, but an inteligent remark would blow this entire conversation all to hell. You have mixed so many incompatible and irelevant examples as to be amazing in itself.


People don't care what you have done
People won't remember what you have said
But they will never forget how you made them feel
#2278 07/15/05 05:09 AM
A
Anonymous
Unregistered
Anonymous
Unregistered
A
It is ??!! Then you yourself are a singilarity...
:-))
Btw have you understood 1% of what I am trying to say... I may sound rude but you deserve this.

#2279 07/16/05 06:31 AM
Joined: Oct 2004
Posts: 201
P
Senior Member
Offline
Senior Member
P
Joined: Oct 2004
Posts: 201
OK, dkv, we switched to this thread. Now humor me and state your singularity problem in a logical and comprehensible manner.

dkv:"Consider this we you have x amount of a y and it grows over time to become nx then your growth ratio is n ... (nx-x)/x = n
Now if we make x=0 then Maths crashes to infinity... but not the real world."

You must be kidding me. Have you ever heard of arrays, series and limits? In your case, there is a very nice theorem, called traditionally the "l'Hospital rule", which solves your infinity problem nicley. So math does not always crash at infinity, as you would appear to think.

#2280 07/16/05 06:54 AM
A
Anonymous
Unregistered
Anonymous
Unregistered
A
Ok.
Using l'Hospitals Rule can you come up with a growth ratio value for the follwoing example
intial value = x
final value = z
grwoth = (x-z)/abs(x)
If I apply lHospitals rule I get infinity...because
if x tends to zero then you will still get infinity as x tends to zero the x-z tends to -z.
For simple illustration I had used z =nx

#2281 07/16/05 08:14 AM
Joined: Oct 2004
Posts: 201
P
Senior Member
Offline
Senior Member
P
Joined: Oct 2004
Posts: 201
dkv,we don't seem to understand each other,so I am asking you again. What is the problem that you are trying to solve? State it clearly, as you would read it in a book, if you were to solve it.

You have only given me an initial and a final value, and something you call growth rate. What is growing at this rate and what is the growing law (how does it grow, additively, multiplicatively, exponentially)? I can imagine several problems that I can formulate based on the info you gave.

And you get infinite for what? In the limit of x->0, your growth rate goes to 1 or -1, it that makes any sense of doing.

#2282 07/16/05 09:40 AM
A
Anonymous
Unregistered
Anonymous
Unregistered
A
Boss ...
My problem is very straight forward.
It has two components :
1.A real world concept of growth rate is formulated using Maths ..
Its formula is
(final value - initial value)/ABS(initial value)
Growth Rate is a physical concept and one can easily see its application in almost all the branches..it measures the amplitude of change as a ratio( or percentage)of its own previous value .. just like acceleration measures change of velocity as a ratio of changed velocity and time..
the only difference here is that time and velocity are represented using seperate axis at every instant and in our case the change is measured against a value defined on the same axis..
for e.g my profit this year was 200 and last year it was 100 then i growth rate is (200-100)/100 = 100% growth rate... which means my every penny was doubled ... this also shows how fast the company is growing....(If it is still not clear then consider another mathematical case of gravity where V(r) = -Gm/r )

2.The Formula works absolutely fine for all the values except when the inital value is 0.
I really dont know how you got that 1 and -1 values after applying lHospitals rule...
to put it again simply
growthrate=(z-x)/x = z/x - 1
if x tends to zero and z is a finite quantity then
growthrate = infinity in the limiting case...

So my problem is that a continous domain based experience doesnot break down into infinity whereas the formula breaks down at zero for no apparent reason..
But there is a way to remove this infintiy from zero by shifting the origin to some other finite value.. against this fixed background a new set of number will get formed due to shifting and thus my formula survives at the discussion point...
Consider x = 1 as my new origin .. Origin is just a origin and it can be shifted any where ...
Then the transformed values of x ans z are
x-1 and z-1
so the equation becomes
(z-1-(x-1))/ABS(x-1) = (z-x)/ABS(x-1)
if x= 0
then the growth rate is z and not infinity...
I have used Absolute in the denominator because the growth sign depends on the final and initial value only ...
absolute is valid and real maths function and it has been applied correctly here...
Anyways this how we can survive zero and infact this what we do when we transform a equation...
Do you agree with me till now?
If you do then notice that infinity has shifted to a new position on the transformed axis...
And again it is not a true picture of the growth rate...
The question is not how 0 became 1 but how 1 became 2.

#2283 07/16/05 10:02 AM
A
Anonymous
Unregistered
Anonymous
Unregistered
A
Infact you can get that 1 and -1 ...
It was my mistake .. and i am sorry for that.
But I hope you will appreciate the fact that limiting case of zero is mathematically different from the zero itself...
At zero (without any qualification) you will get that infinity..
And in the case of orthogonal properties where attributes of division are not on the same axis the LHospitals rule does not apply..

#2284 07/16/05 12:18 PM
Joined: Oct 2004
Posts: 201
P
Senior Member
Offline
Senior Member
P
Joined: Oct 2004
Posts: 201
dkv:"It has two components :
1.A real world concept of growth rate is formulated using Maths ..
Its formula is
(final value - initial value)/ABS(initial value)"

OK, you have the "growth rate", fine. But let me tell you something. What you defined is not a growth rate, as growth rate is defined, but a sort of a percentage difference (it is in fact called a relative difference). A growth rate is defined as the variation of a function relative (read divided) to the variation of its argument.

dkv:"Growth Rate is a physical concept and one can easily see its application in almost all the branches..it measures the amplitude of change as a ratio( or percentage)of its own previous value .. just like acceleration measures change of velocity as a ratio of changed velocity and time.. the only difference here is that time and velocity are represented using seperate axis at every instant and in our case the change is measured against a value defined on the same axis.."

Don't stretch it, your "growth rate" has absolutely nothing to do with velocity and acceleration. You are literally confusing de tangent of a curve (say the velocity) with the differential of the logarithm d[ln(x)]=dx/x. So let's stick with the growth rate as you defined it.

dkv:"2.The Formula works absolutely fine for all the values except when the inital value is 0...
So my problem is that a continous domain based experience doesnot break down into infinity whereas the formula breaks down at zero for no apparent reason..."

OK, so your problem can be stated something like this.You have a quantity say Q, qhich is a function of a variable, let's say x, and the variable is defined say in the closed interval [a,b]. You define the growth rate of this quantity as R=[Q(a)-Q(b)]/Q(a), and your problem is that if Q(a)=0, your growth rate becomes infinite.

The only thing that I can deduce from what you wrote is that you don't seem to know what a function is, and that is why you wrote all the, sorry for this, malarkey about growth rate and velocity, acceleration, and so on and so forth. Even if Q(a)=0, the growth rate at a is finite, provided that the slope of the function Q at a is finite.

dkv:"But there is a way to remove this infintiy from zero by shifting the origin to some other finite value.. against this fixed background a new set of number will get formed due to shifting and thus my formula survives at the discussion point..."

Following your reasoning , the formula survives at the discussion point, but you have only shifted the infinity, so to speak, you have not removed it.

dkv:"Consider x = 1 as my new origin .. Origin is just a origin and it can be shifted any where ...
Then the transformed values of x ans z are
x-1 and z-1 so the equation becomes
(z-1-(x-1))/ABS(x-1) = (z-x)/ABS(x-1)
if x= 0 then the growth rate is z and not infinity..."

As I said before, you still have the infinity at x=1.

dkv:"Do you agree with me till now?If you do then notice that infinity has shifted to a new position on the transformed axis...And again it is not a true picture of the growth rate...The question is not how 0 became 1 but how 1 became 2."

I agree that you shifted the infinity. But ost importantly you are in great need to review what a function is.

Infact you can get that 1 and -1 ...

dkv:"But I hope you will appreciate the fact that limiting case of zero is mathematically different from the zero itself..."

Not in this case it isn't. Your function R(a) is in fact a function R[Q{a)], so the value at a depends on how Q approaches a.

dkv:"And in the case of orthogonal properties where attributes of division are not on the same axis the LHospitals rule does not apply..."

Look, in general I appreciate effort more than I appreciate knowledge, as long as the former is in the pursuit of the latter.So let's make a deal. You stick with concepts and words that you know, and we'll discuss this problem. There are no othogonal properties, if you know what orthogonality means, and division is only division, a mathematical operation that involves two numbers. As for the l'Hospital rule, wait first to learn it, and to learn how to apply it.

As for your problem, if you correctly apply the concept of a function, it becomes trivial.

#2285 07/17/05 05:42 AM
A
Anonymous
Unregistered
Anonymous
Unregistered
A
So I have managed to move the infinity to different location...
We all agree .. now I can similary move the infinity to any point of discussion I want ...
The most important fact here is that Physical continuty or comprehensibility can be achieved at the so called infinity by doing transformation... without any application of new rule...
Infact this means that there is no such concept of infinity in reality and it is the limitation of our expression which makes it infinite .. and when we are not able to completely remove it from the system ...then it is the drawback of the tool....
I am computer professional and I know how such cases break the flow of logic... the continuity of a simple mathematical process gets broken down into if and then conditions...
And suddenly the Universe appears to have intelligence ....otherwise how it is able to hide the infinity...
Now I will like generalize the problem for all such cases where we have possible 0 in the denominator...
I know science has been struggling with infinities and if there is any one reason why physics has been able to partially conquer the infinity ,it is because it enforces quantum limits... Infact the uncertainity principle refuses to recognize zero...
Even Vaccum has something in it...
The necessity of something inside nothing is again a logical necessity of the Maths itself and not physics...
Earlier I had discussed why One Unified Theory is a logical necessity of Maths but not reality....(becuase a half truth is still false as per boolean logic)
It is true that I am not very technical in my description but I firmly believe the reality is all about common sense and it should not be confused with the approach used to understand it...
There are many more interesting ideas to share with you but please keep correcting me whenever I go wrong technically...
I hope I am able to make at least some sense ...And my end result is not zero...

As far as functions are concerned the definition has been modified to suit its own limitation ... atleast a function should return the same result on passing the same input..f(x)=y should not give me y1 ,y2 etc...for x1. Incase of limits this rule does not apply ... but we circumvent the problem by saying that limit is a finite value 'just' above(or below) x... But no one dares to ask that no matter how close someone is to the x .. it can not be x...
Maths is self enclosed and I am trying to find something in the real world which will validate it and so far I have not found anything which matches perfectly...almost everything has been reduced to probability and I wonder that one day we may wake up to see that 1+1= 2 is not working because the there was a small probability that it will not work...
I really enjoyed this discussion but have some urgent official work to complete ..
I reply to you on Monday...

#2286 07/17/05 06:43 PM
Joined: Oct 2004
Posts: 201
P
Senior Member
Offline
Senior Member
P
Joined: Oct 2004
Posts: 201
dkv:?So I have managed to move the infinity to different location...
We all agree .. ?

dkv, your infinity is an artifact of improper use of the concept of function. Proper application of the concept of function tells you in fact that if you have a well-behaved function, your infinity does not even exist there.
But it seems you don?t want to use the concept of function. Fine, let?s use the concept of array, and define your array as R(ak)=(ak-b)/ak. Under these circumstances, you are bothered by the fact that in fact you cannot define the array for say a0=0.

dkv: ?Now I can similarly move the infinity to any point of discussion I want ...The most important fact here is that Physical continuity or comprehensibility can be achieved at the so called infinity by doing transformation... without any application of new rule...?

By no means does your ?trick? offer understanding of what happens at the location of the original infinity. The shift that you perform is equivalent to you looking at another point where your array IS defined. You DO NOT look at the point of singularity, but at some other regular point, which does not offer you any fundamental information about the singularity. You have just circumvented the issue of singularity, you have not solved it.

dkv: ?In fact this means that there is no such concept of infinity in reality and it is the limitation of our expression which makes it infinite .. and when we are not able to completely remove it from the system ...then it is the drawback of the tool....?

Nope, your conclusion is invalid. You have just swept your infinity under the rug, but this does not mean that it does not exist anymore. This is not the way to actually remove infinities. You might try another change of variables, like Q(ak)=arctg[R(ak)] on some domain, and this will bring your results in the range [-pi/2, pi/2) with no infinities whatsoever being involved.

dkv: ?I am computer professional and I know how such cases break the flow of logic... the continuity of a simple mathematical process gets broken down into if and then conditions...
And suddenly the Universe appears to have intelligence ....otherwise how it is able to hide the infinity...?

Don?t blame the bloody machine for this, it is just a piece of junk that does what YOU tell it to do, within the limits of what IT can do. Such cases do not brake any flow of logic, because your logic is higher than the machine?s, and before coding a process you can design the process without the limitations imposed by a dumb processor.

As for your conclusion about the intelligence of the Universe, at least in the case of this topic, it is not warranted. Furthermore, if you adopt the previous view that singularities do not actually exist and are just artifacts of the language in which we describe nature, your conclusion in not warranted at all. At the worst, it is based on flawed logic, and at the worst it is a self-serving argument for a, let?s call it mildly, a philosophical agenda.

dkv: ?Now I will like generalize the problem for all such cases where we have possible 0 in the denominator...?

OK, let?s generalize it.

dkv: ?I know science has been struggling with infinities and if there is any one reason why physics has been able to partially conquer the infinity. It is because it enforces quantum limits...?

Well, roughly speaking you are right. However, you don?t know the details of it, so you should be careful when you make such all-encompassing generalizations.
First of all, even at the classical level there are ways to deal with infinities. Some of these ways rely on the fact that the mathematical representation is not appropriate (i.e. by a change of variables as I did above, the singularities vanish, in some cases), others rely on logically introduced bounds (like the infinite-wall interaction potential for the molecules of a gas) which do not require quantum reasoning.
In the quantum case, certain classical singularities vanish, indeed, but other appear and removing them is not a logical step anymore. Introducing so called IR and UV limits/cutoffs is not always natural, and they are mostly introduced by hand and are not emerging from the description. Similarly, renormalization is a rather awkward technicality/principle, which lacks a natural explanation (except for the firm held belief that singularities should not exist!).

dkv: ?In fact the uncertainty principle refuses to recognize zero...?

This is a rather poor interpretation of the uncertainty principle, but so what? This is not a trend in quantum mechanics. Quantum mechanics has no problem in recognizing ?zero?. You have 0-spin states, don?t you? And you also have infinities of your preferred type, i.e. the energy in the Hydrogen atom for n=0, where n is the principal quantum number. In order to remove such an infinity, you have to introduce the assumption that you can offset the energy by an infinite amount and the result is finite, and you actually have no reason to say that (you are back in the renormalization case).


dkv: ?Even Vaccum has something in it...?

You are making the usual confusion between a vacuum state of a system and vacuum. They are slightly different concepts.

dkv: ?The necessity of something inside nothing is again a logical necessity of the Maths itself and not physics...?

No, it is actually a necessity of physics that has to be fulfilled by a mathematical description, and not the other way around. But once again, you are generalizing concepts with no insight in the (already existing) details. Let?s take the vacuum state for a system. You need to have such a state because physically your system may contain no particle. However, this state can be highly unstable, such that the system has a vanishing probability of being in that state. So in reality, a vacuum state exists, but the system almost never uses it. I don?t see how this can be something required by the math and not by the physics. It is physically fundamental for such a state to exist, irrespective of whether the system uses it or not.

dkv: ?Earlier I had discussed why One Unified Theory is a logical necessity of Maths but not reality....(becuase a half truth is still false as per boolean logic)?

Well, in reality the GUT is at this stage nothing more than wishful thinking, based on the argument that in reality nature is highly structured, and the level of complexity is decreasing from classical to quantum (you have fewer distinct processes at the quantum level than at the classical level). So from this viewpoint, GUT are a requirement of the physical reality, as perceived by some. However, there is no actual evidence that such a viewpoint is justified. And since such a GUT has not been implemented yet exactly due to mathematical difficulties, I would say that a GUT is certainly not a requirement of the mathematical description.

Furthermore, there is one more fallacy of your argument. Mathematical description can indeed make predictions, but it never dictates the physical reality. Mathematics is the but a more or less appropriate language in which we express what we learned through observation from nature, and not the other way around.


dkv: ?It is true that I am not very technical in my description but I firmly believe the reality is all about common sense and it should not be confused with the approach used to understand it...?

True, physics should not be confused with math, but believe me when I say that reality is not about common sense. And you should know this, from quantum mechanics. There is no common sense in the uncertainty principle (what do you mean we cannot simultaneously measure any two quantities, when common sense ? i.e. day to day experience - shows the opposite), there is no common sense in saying that Schroedinger cat is half-dead and at the same time half-alive before we check on it, and I could continue. There is a logic of the physical reality, but I am afraid we haven?t learned it yet in totallity.

dkv:?There are many more interesting ideas to share with you but please keep correcting me whenever I go wrong technically...I hope I am able to make at least some sense ...And my end result is not zero...?

Be my guest to share your ideas and discuss them. But I hope to realize that in order to consolidate what you know you will need more than just a conversation on a forum.

dkv: ?As far as functions are concerned the definition has been modified to suit its own limitation ... At least a function should return the same result on passing the same input..f(x)=y should not give me y1 ,y2 etc...for x1.

Well, you only required your function to be a bijection. Which is fine. But beware that there are also functions that are multivalued, i.e, the can return different values for the same argument. They are proper mathematical objects, and they are well-understood.

dkv: ?In case of limits this rule does not apply ... but we circumvent the problem by saying that limit is a finite value 'just' above (or below) x... But no one dares to ask that no matter how close someone is to the x .. it can not be x...?

Of course it applies for limits too. First of all, the limit at a point is the limit at a point, not above the point, and not below. However, when you calculate this limit, you can come from below (limit from below) or from above (limit from above). Both these limits are well defined and have well understood properties.

As for your function, a function of the type f(x)=(x-a)/x is mathematically NOT DEFINED at x=0. You must be very careful about zero and infinity. It does not matter that mathematics includes them, they have a very special statute and cannot be used as the rest of the numbers (for example you cannot divide by zero and infinity IS NOT a number!). So, in attempting to EVALUATE your function at x=0, you disregard the rules for division, and try to extend division in the range where it is not working, where such an operation is not defined. This is not my conclusion, it is the tight logic of the mathematics. Mathematics does not allow you to use undefined operations. Period.
You can however investigate what your function does around that point, by using limits. And in the case of your function f(x) defined above, if you try hard enough you see that as you get closer and closer to x=0, you see that -b is an accumulation point for f (this means that all the values for f are in a smaller and smaller vicinity of ?b as x gets closer and closer to zero). And in this case, you can extend the domain of your function to include x=0 by saying that at x=0 f(0)=-b, and this process is called continuation/extension by continuity. This is your only way in which YOU CAN define a function at a point where its value is ambiguous, or where the function is not defined.

dkv: ?Maths is self enclosed and I am trying to find something in the real world which will validate it and so far I have not found anything which matches perfectly...?

Well, you are looking at the wrong example. Addition of vectors works well in the physical world, within experimental limits, the Fourier transform works well in optics, and I could continue. But exact matches you will never get, because while mathematics is an abstract science, and as such the only exact one, physics is an empirical science, and nature is observed within experimental limits, so perfect matches are principially excluded.

dkv: ?almost everything has been reduced to probability and I wonder that one day we may wake up to see that 1+1= 2 is not working because the there was a small probability that it will not work...?

True, but this may only be a reflection of our poor understanding in very many cases (although there are schools of thought that support the idea that the fundamental level of nature is actually probabilistic). Keep your mind open.

As for your example regarding 1+1=2, let me tell you something (which you should already know, since you work with computers). You can also have 1+1=0, if you use basis 2 or equivalently modulo 2 residual classes. So get use to the fact that things are never what they seem, no matter how much we wish.

#2287 07/17/05 11:11 PM
Joined: Jan 2005
Posts: 375
C
Senior Member
Offline
Senior Member
C
Joined: Jan 2005
Posts: 375
Quote:
Introducing so called IR and UV limits/cutoffs is not always natural, and they are mostly introduced by hand and are not emerging from the description. Similarly, renormalization is a rather awkward technicality/principle, which lacks a natural explanation (except for the firm held belief that singularities should not exist!).
The natural explanation is that the standard model is an effective field theory which describes degrees of freedom of nature below some cutoff momentum.

#2288 07/18/05 04:05 AM
Joined: Oct 2004
Posts: 201
P
Senior Member
Offline
Senior Member
P
Joined: Oct 2004
Posts: 201
Ibliss:"The natural explanation is that the standard model is an effective field theory which describes degrees of freedom of nature below some cutoff momentum."

Yes,true,or below some energy. However, this explanation does not apply to renormalizability. But is such an explanation natural, or is it an a posteriori explanation, a justification of sorts?Is it fact or technique?
Alternatively, think about quantum gravity.Perturbatively it is non-renormalizable, and furthermore, you need to impose cutoffs. But as far as LQG goes, the cutoffs are present in the theory since the area and volume operator are quantized.

#2289 07/18/05 06:07 AM
A
Anonymous
Unregistered
Anonymous
Unregistered
A
First of all I would like to say that I understand Maths and enjoy using it in my day to day life...
However in my opinion there are some limitations attached to it and one major discussion point is the point of origin...or to put it simply the zero....
zero has solved so many problems but has complicated the understanding of reality ...
If a formula gives you something like 1/0 or 0/0 the whole understanding collapses and limits save us within its own limits...I agree that for a well behaved function there limits can remove infinity but consider independent variables...
e.g Energy and radius ....
Let us say we squeeze all the bosons to a radius 0...then it will have something a gravitational pull defined by something like
V(r) -G*Energy/r*c^2 ...(the actual formula may be different but it will help me to illustrate the concept)
at r=0 the energy need not be zero ...and thus the equation goes to infinity...
The trick i used is not at all trick .. it is the real picture...
And I can say with confidence that I have moved the point of discussion to a different location...for e.g if i say that the new formaula(after transformation) collapses at x=1 then it means the x=1 is now as non-understandable as when function was undefined or uncomprehensible at x=0..
Those beautiful equations fail to give the generalized idea of reality .. and this takes away the completeness of the description and we are left with unwanted debated at certain points .. this does not happen in reality...
How universe came into existence is one such point..
In this case the Maths actually dictates the reality in a a very different sense .. and we are forced to believe that there is something special about the origin of Universe or non-existence of existence..
I am happy to hear that no one belives in singularity... but if it exists and is ignored for convinience then its like running away from the logical incosistency of the tool.
As far as spins are concerned it is a vaild concept to consider it as zero or 1 or -1 just as the zero works in most of the cases..
If I choose to call 1 as -1 and -1 as 1 there is absolutely no problem and futher if I choose to call -1 as 0 and 0 as 2 and 1 as 3 there is still no problem if it is a independent variable...because it just changes my understanding of the origin ....for me -1 is the finite everexisting back ground called 0...
If we change every thing which is understood ,to a different scale then we will still have a consistent Physics and Maths but we will end up introducing the infinity at some other location...(and infact if i understood it rightly then this is waht is happening today at quantum level)
Ok thats all I had to say...catch you later..

#2290 07/18/05 08:12 AM
Joined: Oct 2004
Posts: 201
P
Senior Member
Offline
Senior Member
P
Joined: Oct 2004
Posts: 201
dkv: ?However in my opinion there are some limitations attached to it and one major discussion point is the point of origin...or to put it simply the zero....zero has solved so many problems but has complicated the understanding of reality ...If a formula gives you something like 1/0 or 0/0 the whole understanding collapses and limits save us within its own limits...I agree that for a well behaved function there limits can remove infinity??

There are no limitations to mathematics. As I said, it is an abstract science, and as such, there is no limitation to it. If you don?t like this math, you are free to invent your own one, that suits your purposes better (Remember Newton? That is exactly what he did).
But if you decide to use a part of the math that has already been developed, then use it properly, and don?t trey to adapt beyond what it?s good for.
And no, your understanding does not collapse at ratios like 1/0, or 0/0, because if you apply the theorems and postulates of mathematics, such ratios simply DO NOT EXIST. Axiomatically. No more, no less. The only understanding you can gain is by using limits, whenever it is possible.

Dkv: ??but consider independent variables, e.g Energy and radius. Let us say we squeeze all the bosons to a radius 0. Then it will have something a gravitational pull defined by something like V(r) -G*Energy/r*c^2 ...(the actual formula may be different but it will help me to illustrate the concept) at r=0 the energy need not be zero, and thus the equation goes to infinity...?

Once again, you are mixing incompatible things and concepts. First of all, bosons are pure quantum particles, and for this reason the uncertainty principle prevents you from ?squeezing? them in a volume of radius zero (that would mean you can measure exactly their position). This consideration only and it solves your problem.
Second of all, you assume that bosons interact according to classical gravitation at all distances, which for the time being is an unsupported statement. Quantum gravity effects might come into play at such distances.
Third of all, you cannot ignore the nuclear and electromagnetic forces which are much, much stronger than gravitational interaction, and which in fact prevent you once again to squeeze all bosons in a zero volume.

dkv: ?The trick i used is not at all trick .. it is the real picture...?

I have no idea what trick you used, but what you say is far, far away from the real picture.

dkv: ?And I can say with confidence that I have moved the point of discussion to a different location,for e.g if i say that the new formula(after transformation) collapses at x=1 then it means the x=1 is now as non-understandable as when function was undefined or uncomprehensible at x=0.. ?

Your confidence is greatly misplaced. In gravity, if you consider the symmetry invariances, it does not matter where the symmetry is located, it only matters that it exists.

dkv: ?Those beautiful equations fail to give the generalized idea of reality, and this takes away the completeness of the description and we are left with unwanted debated at certain points, this does not happen in reality...?

Those equations you talk about are classical, so by this only fact they only give an accurate picture in the range where classical arguments apply. And they do not apply in the case of your bosons. Nor is it any claim that the classical description should give an overall accurate picture in all instances. Let me put it this way: this is the reason why quantum mechanics was developed, to replace the classical description in the circumstances where the classical description failed.

And what do you mean it does not happen in reality? How do you know what reality is beyond what we have already observed? How can you make claims about something that you don?t have any clue what it looks like? You can only make assumptions and educated guesses (more or less), but these are not a substitute for physical reality.
And for the time being, we have (good enough) theories for the part of reality we have observed.

dkv: ?How universe came into existence is one such point.?

I agree with you that this is a matter of interest, but for the time being there is no fully tested theory that can make any claims about the origins of the universe. There are only theories that have been validated down to the origin of the CMBR, and that?s it. They don?t offer any info about the origin of the universe. Beyond the CMBR range, there are only untested assumptions.


Dkv: ?In this case the Maths actually dictates the reality in a very different sense, and we are forced to believe that there is something special about the origin of Universe or non-existence of existence..?

Pray do tell me how math dictates over the reality. And BTW, since when does math describe reality? It is physics that is concerned with the description of nature, not math.

dkv: ?I am happy to hear that no one believes in singularity, but if it exists and is ignored for convenience then its like running away from the logical inconsistency of the tool.

No one is running away from inconsistencies just for convenience. Not in physics. For the time being, the tools are used until a better understanding of nature is achieved. This has always been the case in physics.

dkv: ?As far as spins are concerned, it is a vaild concept to consider it as zero or 1 or -1 just as the zero works in most of the cases. If I choose to call 1 as -1 and -1 as 1 there is absolutely no problem and further if I choose to call -1 as 0 and 0 as 2 and 1 as 3 there is still no problem if it is a independent variable, because it just changes my understanding of the origin, for me -1 is the finite everexisting back ground called 0.?

Oh, boy. ZERO IS NOT AN ORIGIN! It is only your bias that leads you to this consideration. If you want another definition, consider it as the neutral element of the group/field of real numbers, or integers, or rationals with respect to addition.
Relabeling the quantities you deal with DOES not change any of your understanding, you just changed the language you speak, you haven?t changed what you are actually saying.

dkv:?If we change every thing which is understood,to a different scale then we will still have a consistent Physics and Maths but we will end up introducing the infinity at some other location...(and in fact if I understood it rightly then this is whatt is happening today at quantum level).?

Look, let?s clear up something. Mathematical consistency, even if desired for esthetical reasons, is NOT and has NEVER BEEN the fundamental driving force in physics. It is merely a tool to express our knowledge. No physicist in his right mind in this world will tell you he prefers a mathematically consistent theory instead of observation. This is the reason why at various levels theories can ?live? with singularities. The major issue is not that a mathematical singularity exists in a theory, but the physical meaning of that singularity.

#2291 07/18/05 11:00 AM
A
Anonymous
Unregistered
Anonymous
Unregistered
A
I think you have understood my point of view..
I hope I am not leading you in the wrong or the incorrect direction...
------
There are no limitations to mathematics. As I said, it is an abstract science, and as such, there is no limitation to it. If you don?t like this math, you are free to invent your own one, that suits your purposes better (Remember Newton? That is exactly what he did).
But if you decide to use a part of the math that has already been developed, then use it properly, and don?t trey to adapt beyond what it?s good for.
And no, your understanding does not collapse at ratios like 1/0, or 0/0, because if you apply the theorems and postulates of mathematics, such ratios simply DO NOT EXIST. Axiomatically. No more, no less.

Rep: I agree.But I do not agree that limit to 0 is same as zero.. Zero exists in reality and classicaly atleast there is nothing called tends to zero .. We can achieve perfect 0 ...Maths uses the concept of infinitesimal for its convinience to divide the undividable...
IT has rules to do so...and gives accurate results...My argument is that the process must map to the reality ...the INPUT , the PROCESS and the OUTPUT must map to the reality at every point...This statement has a very DEEP MEANING ..
Limit should not only be consitent with Maths but also with the reality...
(Please understand I am not against any of the existing concepts of Maths or Phsyics but I wish to enrich it if possible.)


------------------
Once again, you are mixing incompatible things and concepts. First of all, bosons are pure quantum particles, and for this reason the uncertainty principle prevents you from ?squeezing? them in a volume of radius zero (that would mean you can measure exactly their position). This consideration only and it solves your problem.
Second of all, you assume that bosons interact according to classical gravitation at all distances, which for the time being is an unsupported statement. Quantum gravity effects might come into play at such distances.
Third of all, you cannot ignore the nuclear and electromagnetic forces which are much, much stronger than gravitational interaction, and which in fact prevent you once again to squeeze all bosons in a zero volume.
REP: Agree this was not a suitable example but my desire was to share the concept with simplicity...
Can a function understood at all points and becomes non-understood at certain points or at exact 0(or any other exact no.)?

-------------------
I have no idea what trick you used, but what you say is far, far away from the real picture.
The trick was to move the reference point to some other place so that we can understand the point of limit without using limit.

--------------------
Your confidence is greatly misplaced. In gravity, if you consider the symmetry invariances, it does not matter where the symmetry is located, it only matters that it exists.
REP: After transformation the position of my so called collapse has changed but it was not removed from the system.If theroy intends to remove it completely then with its current capabilities we can say that it will fail to do so...(after enough digging one will rediscover its new position)
----------------
Those equations you talk about are classical, so by this only fact they only give an accurate picture in the range where classical arguments apply. And they do not apply in the case of your bosons. Nor is it any claim that the classical description should give an overall accurate picture in all instances. Let me put it this way: this is the reason why quantum mechanics was developed, to replace the classical description in the circumstances where the classical description failed.
REP: Give me some time I will find out a real classical case of collapse.
---------------------------

dkv: ?How universe came into existence is one such point.?

I agree with you that this is a matter of interest, but for the time being there is no fully tested theory that can make any claims about the origins of the universe. There are only theories that have been validated down to the origin of the CMBR, and that?s it. They don?t offer any info about the origin of the universe. Beyond the CMBR range, there are only untested assumptions.
REP: Great.

=======================
Pray do tell me how math dictates over the reality. And BTW, since when does math describe reality? It is physics that is concerned with the description of nature, not math.
REP: I also need to revisit this thought..
=========================
No one is running away from inconsistencies just for convenience. Not in physics. For the time being, the tools are used until a better understanding of nature is achieved. This has always been the case in physics.
REP: What if it does not meet to reality in with its full force...Why is it that it allows certain intermediate steps in the derivation to exist independent of reality when it is describing it.. How do you explain Complex no. used extensively in Physics.
---------------
Oh, boy. ZERO IS NOT AN ORIGIN! It is only your bias that leads you to this consideration. If you want another definition, consider it as the neutral element of the group/field of real numbers, or integers, or rationals with respect to addition.
Relabeling the quantities you deal with DOES not change any of your understanding, you just changed the language you speak, you haven?t changed what you are actually saying.
Yes Sir , I undertand that 0 is not origin .. but yes I would like to call it a reference point and there is no need to associate it with existence and non-existence...Boolean algenra is more than enough to handle such concepts...
We are more intersted in classifying the reality relative to a reference.That reference point can ever be absolute or not is a seperate question.
correct me if I am still wrong.
===================
Look, let?s clear up something. Mathematical consistency, even if desired for esthetical reasons, is NOT and has NEVER BEEN the fundamental driving force in physics. It is merely a tool to express our knowledge. No physicist in his right mind in this world will tell you he prefers a mathematically consistent theory instead of observation. This is the reason why at various levels theories can ?live? with singularities. The major issue is not that a mathematical singularity exists in a theory, but the physical meaning of that singularity.
REP:I am afraid that singularity can never be removed.. because there logically it can not be removed from Maths..unless it accepts that INPUT,PROCESS and OUTPUT of a derivation must map to the Reality.
Cheers

#2292 07/19/05 04:46 AM
Joined: Oct 2004
Posts: 201
P
Senior Member
Offline
Senior Member
P
Joined: Oct 2004
Posts: 201
dkv: ?I agree. But I do not agree that limit to 0 is same as zero.?

No, it is not. But in your case, the evaluation of your function in zero is NOT DEFINED, it DOES NOT EXIST, axiomatically speaking.

dkv: ?Zero exists in reality and classically at least, there is nothing called tends to zero. We can achieve perfect 0. Maths uses the concept of infinitesimal for its convenience to divide the undividable.?

Once again, since when does math describe the physical reality? And no, math uses the concept of limit to define also functions like the tangent to a curve, to calculate areas and volumes, and so on and so forth.

dkv: ?IT has rules to do so...and gives accurate results...My argument is that the process must map to the reality, the INPUT, the PROCESS and the OUTPUT must map to the reality at every point?

In within limits. As I said, and I am stressing this again, mathematics is only a tool, and as such it is applied within certain ranges of validity. What matters is only the meaning of the mathematical symbols, and physics assumes its right to use math as it sees fit, and within limits that are not mathematical in nature.

dkv: ? This statement has a very DEEP MEANING. Limit should not only be consistent with Maths but also with the reality. (Please understand I am not against any of the existing concepts of Maths or Physics but I wish to enrich it if possible.).?

It has a meaning only to you, and maybe the Pythagoreic school, but not to any physicist. The concept of infinitesimal is very clear in classical physics, the concept of a limit is also very clear in physics, but no one makes the claim that the mathematical description should be consistent with reality in all the cases. That?s why there is something called classical physics, using one sort of math, quantum physics, using a different math, and so on and so forth.

You cannot enrich mathematics in relation with nature, because while the former is abstract, our knowledge of the latter is empirical, obeyng rules that are not mathematical in essence.

dkv: Agree this was not a suitable example but my desire was to share the concept with simplicity. Can a function be understood at all points and becomes non-understood at certain points or at exact 0(or any other exact no.)?

For the last time now, your function is NOT DEFINED at x=0. As such, it does not exist at that point and mathematical logic tells you that you cannot have any type of knowledge, complete or incomplete, about something that does not exist.

dkv: ?After transformation the position of my so called collapse has changed but it was not removed from the system. If theory intends to remove it completely then with its current capabilities we can say that it will fail to do so...(after enough digging one will rediscover its new position)?

Well, you used the wrong tool. The wrong representation for your function. As I said before, if you take the arctg of your function, you singularity disappears.

dkv: ?Give me some time I will find out a real classical case of collapse.?
Be my guest.

dkv: I also need to revisit this thought..

Once again, be my guest.

dkv: What if it does not meet to reality in with its full force...Why is it that it allows certain intermediate steps in the derivation to exist independent of reality when it is describing it. How do you explain complex numbers used extensively in Physics.

It does not meet reality in full force, as you say it. But this is no problem. Physics only uses what considers necessary and how it considers it necessary. Physics is not dictated by the math, even though math is a very useful tool to ?speak? physics.

In this view, complex numbers are just a convenient way to describe certain issues in physics.

dkv: ?Yes Sir , I understand that 0 is not origin, but yes I would like to call it a reference point and there is no need to associate it with existence and non-existence.?

It is not a reference point either. You cannot allow yourself to be biased in your views either as a mathematician or as a physicist.

Boolean algebra is more than enough to handle such concepts. We are more interested in classifying the reality relative to a reference. That the reference point could ever be absolute or not is a separate question. Correct me if I am still wrong.

I am sorry to say this, but you are wrong. We don?t need to classify reality with respect to a reference, although may think the opposite. The definition of reality itself, even in philosophical terms, transcedes the necessity of a reference.

dkv: ?I am afraid that the singularity can never be removed. Because there logically it can not be removed from Maths. Unless it accepts that INPUT,PROCESS and OUTPUT of a derivation must map to the Reality.?

In your case, of course it can be removed. See above how. And it does not need to map to reality, but to a (very) small fraction of reality, namely the one that can be described by it.

#2293 07/19/05 08:23 AM
A
Anonymous
Unregistered
Anonymous
Unregistered
A
No, it is not. But in your case, the evaluation of your function in zero is NOT DEFINED, it DOES NOT EXIST, axiomatically speaking.
REP:Ok .. so In maths zero does not exist for that function..but the limit to zero exists.
In reality Physics claims that there is nothing called as limit to zero(in general).
And so we have a 'touch-me-not' process in Maths for which there is no equivalent analogy in Reality...But I belive that any intermediate state of the derivation in Maths is as true as the intial state (or the segregated state) and therefore the process must describe the real truth...If it is not so then Maths is not logically true to itself..(atleast to its boolean branch)
This applies to complex number based derivations also...
We need to find the Physical equivalent or else the Maths crashes... ans this is how MATHS SHOULD DICTATE...Infact it has no choice..

========================
Once again, since when does math describe the physical reality? And no, math uses the concept of limit to define also functions like the tangent to a curve, to calculate areas and volumes, and so on and so forth.
REP: Maths does not describe the reality but it conatins logically consistent tools which are found applicable in the Physics.
============================
In within limits. As I said, and I am stressing this again, mathematics is only a tool, and as such it is applied within certain ranges of validity. What matters is only the meaning of the mathematical symbols, and physics assumes its right to use math as it sees fit, and within limits that are not mathematical in nature.
REP: You are free to reduce the physical validity of mathematical concepts which are not applied to PHysics but you can not do that with concepts which are applied..(infact the interpretation extra information can go on to show that how reality can be enriched by Maths..)
=======================
It has a meaning only to you, and maybe the Pythagoreic school, but not to any physicist. The concept of infinitesimal is very clear in classical physics, the concept of a limit is also very clear in physics, but no one makes the claim that the mathematical description should be consistent with reality in all the cases. That?s why there is something called classical physics, using one sort of math, quantum physics, using a different math, and so on and so forth.
REP: Maths must remain consistent with itself if not Physics.
=============================
For the last time now, your function is NOT DEFINED at x=0. As such, it does not exist at that point and mathematical logic tells you that you cannot have any type of knowledge, complete or incomplete, about something that does not exist.
Ok ... fine .
Fucntion is not defined and I can not claim anything more because I am with the Reality.
We can use complex nos. now for convinience but it provides another domain of 'incomprehensibity' in Physics or reality...
Taking a Square root of -1 has survived the cruel neglect of Maths becuase it has many more useful properties than a infinity.
===============================
Well, you used the wrong tool. The wrong representation for your function. As I said before, if you take the arctg of your function, you singularity disappears.
REP:I have droped that function now as I can use my trick to make a complex number real!!!
=============================
dkv: I also need to revisit this thought..
Once again, be my guest.
REP: When ??:-))
I am not getting enough time right now as there are deadlines to meet.But I hope I have been able to communicate the core issue.
===============================
It does not meet reality in full force, as you say it. But this is no problem. Physics only uses what considers necessary and how it considers it necessary. Physics is not dictated by the math, even though math is a very useful tool to ?speak? physics.In this view, complex numbers are just a convenient way to describe certain issues in physics.
REP:Physics does not use what is necessary but the Physicists use what is necessary.. and thats not good.
===================
It is not a reference point either. You cannot allow yourself to be biased in your views either as a mathematician or as a physicist.
REP: I support the truth.
============================
I am sorry to say this, but you are wrong. We don?t need to classify reality with respect to a reference, although may think the opposite. The definition of reality itself, even in philosophical terms, transcedes the necessity of a reference.
REP:It is not a question if I dont need it or not.. but I am afraid that this reality with respect to a reference is as true as reality with respect to 0.(whatever that means)
To me 0 is a ordinary as 1 ,2 or 3.Ofcourse in boolean algebra 0 means the mysterious NOT.
(NOT EVERYTHING is not equal to NOTHING becuase even Nothing belongs to everything)
=========================
In your case, of course it can be removed. See above how. And it does not need to map to reality, but to a (very) small fraction of reality, namely the one that can be described by it.
REP: It was removed by introducing a new concept which remains unexplained physically .. or rather no has dared to explain it physically..
Who knows what does that concept stands for in reality.. even reality is not completely known.

In a nutshell I hope one day we will be able to map (rather understand)the INPUT, PROCESS and OUTPUT as written in physics and not in Maths.
Once Maths is applied to reality .. its every step should express the reality only (no maths there)...The derivation of TRUTH can not oscillate between Physics and Maths and may be it does not.

Page 1 of 2 1 2

Link Copied to Clipboard
Newest Members
debbieevans, bkhj, jackk, Johnmattison, RacerGT
865 Registered Users
Sponsor

Science a GoGo's Home Page | Terms of Use | Privacy Policy | Contact UsokÂþ»­¾W
Features | News | Books | Physics | Space | Climate Change | Health | Technology | Natural World

Copyright © 1998 - 2016 Science a GoGo and its licensors. All rights reserved.

Powered by UBB.threads™ PHP Forum Software 7.7.5