What is wrong is Russell's and Einstein's paradoxes?
V.Gopal
then it makes no sense - it leads to an endless regress on one side
and an endless progress on the other side. The term 'set of sets' is
like the terms 'the truth about a truth','knowledge about knowledge',
'facts about facts', 'method of justifying a method of creating
knowledge', 'constituents of a constituent', number of numbers' etc.
In all these cases if one of the terms is the primary object the other
is 'knowledge' about that primery. When we have to develop knowledge
about the primary object of sense then the same object has to be the
source of all knowledge that we (are going to) apply to it. In this
situation IF we do not want to simply describe the primery object it
self (the self evident facts) instead, if we want to CREATE knowledge
about it, then the only reliable method is 'statistical - empirical'.
Here 'creation' of knowledge requires either prediction of future of
that primery object or retrodiction of its past. In physics the
physicists attempt to solve a similar problem - the are trying to find
the 'constituents of a constituent' or the ultimate internal
constituents of 'matter'. Russell's paradox leads to the conclusion
that it is futile to try to find the ultimate internal constituents of
matter if we begin with the simplifying assumption that 'matter is the
ultimate constituents of matter'. Similarly acceleration is 'speed of
increase in speed'. It is impossible to have an expression for 'speed
of increase in speed'.
'Speed of increase or decrease in speed' must be an exponential
function of which 'speed' itself is the base (like half-life time in
case of natural radioactive decay). Acceleration = s^t (where s is a
time-like quality).
The idea of 'number of numbers' also leads to problems that are
impossible to solve. We all accept that N*1/N=1. Here, if N is always
a number less than 1, then, 1/N is always more than 1. When N=0, 1/N
must be infinite and when N=1, 1/N also must be equal to 1. The
problem is, if N*1/N=1 then there must be one to one relation between
N and 1/N, that is. the number of numbers between 1 and 0 must be
equal the number of numbers between 1 and infinity if N*1/N=1.
In XY=1, if X is not equal to Y then for each value of X (<1)number of
values of Y (corresponding to that single value of X), is infinite!
What Russell's paradox reveals is the limitations of the positive
communicable language (verbal or numerical) when it is used as the
carrier of knowledge.
Charles R. Bond
> <snip pseudo-scientific babble>
> In XY=1, if X is not equal to Y then for each value of X (<1)number of
> values of Y (corresponding to that single value of X), is infinite!
It should be easy to enlighten the rest of us with this profound
observation. Let X = 1/2. Since you claim there are an infinite number of
values of 'Y' which satisfy XY=1, perhaps you could give us just eight or
ten of them...
--
There are two things you must never attempt to prove: the unprovable --
and the obvious.
http://www.crbond.com
Thomas Worthington
> There is no such thing as 'set of sets'.
You've never worked in a shop, have you? I have opened boxes containing
boxes on many occasions. If you think that can't be represented in set
theory then you need to do back to school.
TWW
V.Gopal
> V.Gopal wrote:
>
> > <snip pseudo-scientific babble>
>
> > In XY=1, if X is not equal to Y then for each value of X (<1)number of
> > values of Y (corresponding to that single value of X), is infinite!
>
> It should be easy to enlighten the rest of us with this profound
> observation. Let X = 1/2. Since you claim there are an infinite number of
> values of 'Y' which satisfy XY=1, perhaps you could give us just eight or
> ten of them...
You must note the conditions and my statement: The following is the
condition: XY=1, X is not equal to Y and X<1. My statement is: 'The
number of values of Y is infinite'. It means the relation between X
and Y is not obvious, rational
or communicable. In "XY=1 and X not equal to Y", we can always imagine
X to be a continuous variable and once we have imagined X to be a
continuous variable we have to accept that Y also is a continuous
variable; it would be wrong to say that Y is not a continuous
variable. This is the reason we show hyperbola by a continuous line.
But a hyperbola that is asymptotic to both the axes of coordinates is
symmetrical about Y/X=1. The scale used to mark X coordinate and Y
coordinate is same. Therefore the condition that makes hyperbola
symmetrical
about Y/X=1 is that thoughout the length of the curve WE DRAW
Y/X=-1.What it means is we draw a hyperbola by assuming two
conditions: XY=1 and Y/X=-1.
We may call this as 'mathematical deadlock', because X and Y cannot
have any value other than one or [1] in this condition. We may be able
to imagine that the value of X is increasing continuously from 0 to 1
but we can never imagine how the corresponding values of Y or 1/X is
changing. WHEN X REACHES 1/2 FROM 0, Y REACHES 2 FROM INFINITY AND NOT
FROM 1 (please not this fact.) Out of these infinite number of numbers
or values of Y between infinity and 2 how many of them actually
correspond to X=1/2 we cannot know. This is the reasion why we cannot
have an expression for angular acceleration (T=infinity and 1/T=0 or
state of rest becomes T=1and 1/T=1 or 1 cycle per unit time) within
finite time.
By assigning values and calculating values (if X=1/2, Y=2) we should
not forget
the direction of change. In geometry sense of direction is always
lost.
In XY=1, even when we assume X to be a rational number Y cannot be a
rational number. The truth, that is not obvious, cannot be proved or
disproved by logic. And the obvious requires no proof. It means we are
never required to think!
Charles R. Bond
> "Charles R. Bond" <cb...@ix.netcom.com> wrote in message news:<3D7529DC...@ix.netcom.com>...
> > V.Gopal wrote:
> >
> > > <snip pseudo-scientific babble>
> >
> > > In XY=1, if X is not equal to Y then for each value of X (<1)number of
> > > values of Y (corresponding to that single value of X), is infinite!
> >
> > It should be easy to enlighten the rest of us with this profound
> > observation. Let X = 1/2. Since you claim there are an infinite number of
> > values of 'Y' which satisfy XY=1, perhaps you could give us just eight or
> > ten of them...
>
> You must note the conditions and my statement: The following is the
> condition: XY=1, X is not equal to Y and X<1. My statement is: 'The
> number of values of Y is infinite'.
I *did* note them. In fact, I quoted them directly from your previous post. Your statement *was*:"In
XY=1, if X is not equal to Y then for each value of X (<1)number of
values of Y (corresponding to that single value of X), is infinite!"
My request was that you enlighten us by citing eight or ten of these values taken from the infinity
of those you claim are available for the specific case XY=1, X = 1/2 so that (X < 1) and X is not
equal to Y. I come up with X = 2. What are some of the other values?
<snip more babble>
Gib Bogle
I don't think school would help.
V.Gopal
Number of primery objects within a set is always in terms of units or
whole numbers or integers. If we accept this fact then Russell's
paradox does not exist because then we accept that we cannot
arbitrarily assign any value (N) to the number of sets within the
mother set (which is the set of all sets) independent of total number
of primery objects within the mother set. If there are N primery
objects within mother set, we cannot have more than N/2 sets within
the mother set, if we want to have minimum of two primery objects
within each set. There is no paradox here. If we talk of 'set of sets'
independent of number of primery objects within the mother set then we
reach a stage when we have to know 'number of numbers' within unit or
within 'one'. We cannot know number of numbers within ONE because
number of numbers within ONE must be equal to that between infinity
and ONE because T*1/T=1.
We can never prove that set theory is wrong by using Russell's
paradox. Set theory is perfectly logical. But we can use Russell's
paradox to prove that we cannot have any expression for angular
acceleration or increase in frequency per cycle or rate of increase in
number of CYCLES PER CYCLE. If a flywheel, initially at rest (period
per cycle=infinity and frequency=1), reaches a frequency of one in one
second then what is its angular acceleration? Note that increase in
frequency (in whole numbers?) has to be continuous within cycle (or
within 1)! This is a paradox and if we use any expression to convey
the rate of change of frequency it would engender the same paradoxes
that Einstein created in his Special Relativity Theory.
I believe that our idea of paradox and illusion are born out of our
inability to understand continuous change.
V.Gopal
There is a typing mistake in my previous posting ; when period per
cycle is infinity frequency should be zero and not one, by mistake I
have typed one.
I am sorry for the error.
Charles R. Bond
> <snip babble>
> I believe that our idea of paradox and illusion are born out of our
> inability to understand continuous change.
Speak for yourself (and possibly Zeno).
Charles R. Bond
> <ssnip>
> I *did* note them. In fact, I quoted them directly from your previous post. Your statement *was*:
> "In XY=1, if X is not equal to Y then for each value of X (<1)number of
> values of Y (corresponding to that single value of X), is infinite!"
>
> My request was that you enlighten us by citing eight or ten of these values taken from the infinity
> of those you claim are available for the specific case XY=1, X = 1/2 so that (X < 1) and X is not
> equal to Y. I come up with X = 2. What are some of the other values?
>
> <snip more babble>
>
I've been waiting for an intelligent reponse to the above question, but I now realize that such a
response is impossible.
Why?
Because, before you are able to derive and post a complete reponse, you must first have completed 1/2 of
the total response. But before you compose 1/2 the total response, you must compose 1/2 of the 1/2
response (1/4 of the total). Before you compose this, you must have first composed 1/2 of it, ad
infinitum. Therefore, there are an infinite number of steps required before you even type the first
letter of your post. It follows that a response is impossible.
It also follows that that your original argument was never derived or presented and that your original
post was never completed.
V.Gopal
> V.Gopal wrote:
>
> > <snip babble>
> > I believe that our idea of paradox and illusion are born out of our
> > inability to understand continuous change.
>
> Speak for yourself (and possibly Zeno).
believe
that the unprovable must always be false and the truth must always be
provable.
Every incommunicable truth is unprovable. I can at least give one
example of
unprovable or incommunicable truth. The state of change is
incommunicable and
therefore existence of state of change is unprovable. No scientist
seems to be convinced that 'state of change' is a reality. This is the
reason why scientists replace the state of change by a series of
equilibrium states. The belief that there is one value of the
reciprocal of 1/2, and it is 2, cannot be proved wrong if we are not
able to visualise - feel - the state of change.
Deceleration represents a state of change in the following example:
A fly wheel is initially rotating at 1 RPM. This is a state of
equilibrium. An external force (say brake) brings it to 0 RPM. A clock
shows the duration of deceleration. Numerically it means: Initially T
(or period per cycle)=1 and also 1/T (frequency)=1. At the end of a
finite duration, T=infinity and 1/T=0.
The state of change or deceleration makes the number(s) representing
1/T(or frequency) to decrease continuously from 1 to 0 and the
number(s) representing T
(or the period per cycle) to increase from 1 to infinity. Here all
numbers between 0 and 1 and also 1 to infinity are continuous. If you
say that 1 becomes 1/2 and also 2 at the same time then does it mean
that within the next 1/2 (half) 2 becomes infinity?
What is the mathematical relation between T and 1/T? It is like the
relation between mass and number atoms within that mass.
The natural radioactive gives the continuous relation between a number
and its reciprocal. In the process of natural radioactive decay mass
at any instant of time is like period per cycle (T) and the number of
decaying atoms is like frequency (1/T).
When mass (T) becomes 1/2 what is the corresponding number of atoms
(1/T) at that time? Is it 2? If number of numbers between 0 and 1 is
N, then is the number of numbers between any two consicutive integers
same as that between 0 and 1? (Here set theory is used, numbers are
not continuous and T*1/T=1 is not true beacuse each set contains only
numbers between 0 and 1) If T*1/T is true
then the number of numbers betwen 0 and 1 must be equal to that
between 1 and
infinity (like in the case of RPM decreasing from 1 to 0). In this
case the relation between number of values T and 1/T is one many.
One can only create (explain?) a situation in which the unprovable is
proved by the situation itself, but one cannot do anything further to
make one to understand the situation itself. Those who do not
understand the situation in which the unprovable is true should not
conclude that the unprovable is always false.
Nick Maclaren
In article <38af3945.02090...@posting.google.com>,
vgop...@rediffmail.com (V.Gopal) writes:
|>
|> Dear brother, we seem to differ at the fundamental level: You seem to
|> believe that the unprovable must always be false and the truth must
Given that incompatibility, do you think that we could drop this
thread? It has little or nothing to do with numerical analysis.
Regards,
Nick Maclaren,
University of Cambridge Computing Service,
New Museums Site, Pembroke Street, Cambridge CB2 3QH, England.
Email: nm...@cam.ac.uk
Tel.: +44 1223 334761 Fax: +44 1223 334679
Charles R. Bond
> "Charles R. Bond" <cb...@ix.netcom.com> wrote in message news:<3D7765A5...@ix.netcom.com>...
> > V.Gopal wrote:
> >
> > > <snip babble>
> > > I believe that our idea of paradox and illusion are born out of our
> > > inability to understand continuous change.
> >
> > Speak for yourself (and possibly Zeno).
> Dear brother, we seem to differ at the fundamental level: You seem to
> believe
> that the unprovable must always be false and the truth must always be
> provable.
<snip babble>
I doubt anyone has any interest in your interpretation of my beliefs -- I certainly don't. (Besides
which you are not even close!)
Stick to the topic of this thread, if you have anything to offer. Give us some of the values for Y
from the infinite set associated with the value of X=1/2.
V.Gopal
I had stated: if T*1/T=1. and, if T decreases continuously from 1 and,
if and only if we accept that 1/T also increases CONTINUOUSLY from 1,
then for each value of T, 1/T has in an finite number of values. I
accept that my statement is unprovable, but at the same time I KNOW
THAT MY STATEMENT IS TRUE.
The integral of units of time (T) is again time T (total). But 1/T or
frequency has no unit, it is the level of activity like temperature
(1/T is not additive), therefore integral of 1/T (or angular
acceleration) is given by the Log(T) and this logarithmic scale has to
begin from T=1 (Log 1=0) AND NOT FROM ANY OTHER VALUE OF T. Moreover
we cannot arbitrarily asign any balue to the base of this lagarithmic
table. 1/T as the continuous function of T is incommunicable there I
cannot give 'values' of 1/T corresponding to any value of T. I am
sorry.
Gib Bogle
Oh no! I'm getting a Zenophobia attack!
Evan Arsenault
"Thomas Worthington" <t...@theBitBeforeTheAtSignAgain.cx> wrote in message
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