What makes a trivial operator trivial ?
Huang
mathematics has no trivial operators. I think that this is a flaw. A
FLAW.
Zero apples can be regarded as the trivial apple.
Zero oranges can be regarded as the trivial oranges.
We know that the trivial apple and the trivial orange are
indistinguishable, because we are talking about nothingness. The
trivial apple is an apple trivially, and the trivial orange is an
orange trivially.
So what about the trivial operator ?
If the trivial apple and the trivial orange are indistinguishable,
then SO TOO you have that trivial addition and trivial multiplication
would likewise be indistinguishable in the same exact way and for the
same exact reasons.
A trivial operator could behave as addition, and it could behave as
multiplication. This is no different than saying that nothingness may
be regarded as zero apples, alternatively nothingness may be regarded
as being zero oranges. These situations are precisely analogous to
each other.
The fact that contemporary mathematics has no trivial operator is not
my problem - it's yours. Your weakness, not mine.
Mathematics embraces the number zero, but to contemplate a trivial
operator is perhaps too difficult an abstraction for the modern mind.
An operator which is "indeterminately either addition or
multiplication" would be an extremely useful thing in many instances,
notably QM and I would also predict importance in Astrophysics as
well. If you cannot understand the simplistic analogy between the
"trivial apple/orange" and the "trivial multiplication/addition"
examples I provided, then my conclusion would be that your cognitive
skills are severly lacking.
William Elliot
> Trivial things are interesting in their own right, but contemporary
> mathematics has no trivial operators. I think that this is a flaw.
>
> So what about the trivial operator ?
>
It's a do nothing.
Huang
Bending space is not interesting ?
Understanding phyisical conservation as an operator is not
interesting ?
Answering the question of whether the universe is deterministic or
not ....... a do nothing ?
Hmmmm.....lets see.
Zero can be regarded as "the trivial magnitude". It is very useful in
orthodox math. We can agree on this.
A trivial operator is a kind of quasi-existent thing, it may be
regarded as being existent, or nonexistent. If we regard it as being
existent, then it must have some utility to the orthodox mathematician
just the same way that zero does. At this time I do not understand
exactly what that would be, but it would be a highly abstracted
contemplation on what operators are in the first place, there is no
mathematics developed yet which understands operators this way...not
even modern algebra.
I have to disagree that it's a do nothing. I think that there may be a
potential utilitization of such a thing in orthodox mathematics. My
interest in this is how it relates to Conjectural Modelling, but I
think it actually does have a place in standard Math.
Huang
"what might be". This is really the diffirence between determinacy and
indeterminacy. The difference between truth and conjecture.
Amazingly, whether you model things using either math or conjecture
the numerical results will match exactly.
Whether you begin by assuming "what is", or if you model things based
on "what might be", both will produce identical results if done
properly.
You know something, in physics you take a measurement. Lets say it is
5 centimeters. So we have the number 5 and at some point we have to
make the leap of faith that the value 5 is a given. We then can
perform all kinds of mathematics and it all makes sense.
But we have no way to prove that our 5 is really a 5. We accept this
as truth, and this allows math to work properly. You can allow
probabilistic error terms if you want, that's fine, but you are still
making the assumption of "what is".
Using conjeture makes the opposite assumption. It does not say that 5
is a given, it says that "5 might be a given".
The difference is very subtle, but I dont think that this can really
be characterized as a non-starter. If both modelling schemes produce
identical output it seems to me that there's something to it.
William Elliot
> On Feb 25, 1:46�am, William Elliot <ma...@rdrop.remove.com> wrote:
>> On Wed, 24 Feb 2010, Huang wrote:
>>> Trivial things are interesting in their own right, but contemporary
>>> mathematics has no trivial operators. I think that this is a flaw.
>>
>>> So what about the trivial operator ?
>> It's a do nothing.
>
> Bending space is not interesting ?
>
That's not a trivial operator.
> A trivial operator is a kind of quasi-existent thing, it may be
> regarded as being existent, or nonexistent. If we regard it as being
> existent, then it must have some utility to the orthodox mathematician
> just the same way that zero does. At this time I do not understand
> exactly what that would be, but it would be a highly abstracted
> contemplation on what operators are in the first place, there is no
> mathematics developed yet which understands operators this way...not
> even modern algebra.
You have changed the topic from mathematics to philosophy.
> I have to disagree that it's a do nothing. I think that there may be a
> potential utilitization of such a thing in orthodox mathematics. My
> interest in this is how it relates to Conjectural Modelling, but I
> think it actually does have a place in standard Math.
Trivial groups, trivial sets, trivial sums and products, trivial
etc., all need to be checked for inclusion or exclusion from a
theorem or a definition.
Philosophy is elaborate trivial thinking, the trivial thought operator.
Huang
> On Thu, 25 Feb 2010, Huang wrote:
> > On Feb 25, 1:46 am, William Elliot <ma...@rdrop.remove.com> wrote:
> >> On Wed, 24 Feb 2010, Huang wrote:
> >>> Trivial things are interesting in their own right, but contemporary
> >>> mathematics has no trivial operators. I think that this is a flaw.
>
> >>> So what about the trivial operator ?
> >> It's a do nothing.
>
> > Bending space is not interesting ?
>
> That's not a trivial operator.
Well, simplified space bending is a result of this approach, mentioned
only to demonstrate the utility of even considering such silly things
in the first place.
> > A trivial operator is a kind of quasi-existent thing, it may be
> > regarded as being existent, or nonexistent. If we regard it as being
> > existent, then it must have some utility to the orthodox mathematician
> > just the same way that zero does. At this time I do not understand
> > exactly what that would be, but it would be a highly abstracted
> > contemplation on what operators are in the first place, there is no
> > mathematics developed yet which understands operators this way...not
> > even modern algebra.
>
> You have changed the topic from mathematics to philosophy.
Some would say that math is philosophy, even though it does not like
to admit it.
I think that it could be regarded as "the philosophy of things which
exist", and provability and logic and all of the other structural
things are things are all resulting from the initial assumption that
these things exist.
If we modify this fundamental assumption and consider instead "things
which might exist", then you have something which might exist and it
might not. If it exists then it is the same as mathematics, and if it
does not then it is singular and nonsensical nonexistent. But being in
a permanent state of existential indeterminacy means that it is
neither one or the other.
It may be philosophy, but mathematics itself must be seen as a
philosophy which starts with a fundamental assumption that things
either exist or not, and there is no middle ground. That is the
philosophy of math.
The philosophy of conjecture takes a different approach than math by
assuming that existence is indeterminate. The overall structure of
conjectural modelling would look identical to mathematics on paper,
and conjectural modelling as a whole would neccesarily be equal in
size to all of mathematics. But the fundamental assumptions are
different.
Mathematical and conjectural models may have identical syntax, but
would have very different explanations.
> > I have to disagree that it's a do nothing. I think that there may be a
> > potential utilitization of such a thing in orthodox mathematics. My
> > interest in this is how it relates to Conjectural Modelling, but I
> > think it actually does have a place in standard Math.
>
> Trivial groups, trivial sets, trivial sums and products, trivial
> etc., all need to be checked for inclusion or exclusion from a
> theorem or a definition.
>
> Philosophy is elaborate trivial thinking, the trivial thought operator.
It may be a complete waste of time to think of such things, but that's
no excuse for failing to make things as elegant as possible IMO.
Ostap S. B. M. Bender Jr.
> Trivial things are interesting in their own right, but contemporary
> mathematics has no trivial operators. I think that this is a flaw. A
> FLAW.
>
> Zero apples can be regarded as the trivial apple.
> Zero oranges can be regarded as the trivial oranges.
>
> We know that the trivial apple and the trivial orange are
> indistinguishable, because we are talking about nothingness. The
> trivial apple is an apple trivially, and the trivial orange is an
> orange trivially.
>
> So what about the trivial operator ?
>
> If the trivial apple and the trivial orange are indistinguishable,
> then SO TOO you have that trivial addition and trivial multiplication
> would likewise be indistinguishable in the same exact way and for the
> same exact reasons.
>
> A trivial operator could behave as addition, and it could behave as
> multiplication. This is no different than saying that nothingness may
> be regarded as zero apples, alternatively nothingness may be regarded
> as being zero oranges. These situations are precisely analogous to
> each other.
>
> The fact that contemporary mathematics has no trivial operator is not
> my problem - it's yours. Your weakness, not mine.
>
> Mathematics embraces the number zero, but to contemplate a trivial
> operator is perhaps too difficult an abstraction for the modern mind.
>
Not to every modern mind. There are still several geniuses living
among us: JSH, Inverse Cone of 19, and you. The brilliant men who have
selflessly devoted their lives to triviality.
Huang
lol -
I try to elicit some vehement rebuttals because I really want to dig
into this question I have. I would be much more satisfied having a
really vulgar swearing match, slugging it out and hurling concepts
around very violently .......
...... but it seems that mathematicians are too polite to put me in my
place. Too polite to tell me to fuck off, or that I am a damn idiot.
It's really very disappointing.
I dont really want anyone to agree with me at all. I would be much
more happy if everyone disagreed with me, and would at the very least
explain why they disagree. That would be much more satisfying.
But no reasons are presented.
You can put me in a class with JSH and I may very well belong there,
but I would like to know why. If conjectural models can do the same
thing that mathematical models do, and the numbers crunch the same,
then I think that I'd like to see the reason why I should neccesarily
adopt the Law of the Excluded Middle instead of other views which
produce equivalent results.
Even one reason would suffice.
Ostap S. B. M. Bender Jr.
Here is one reason: your thoughts are trivial. You sound like an 8
year old child who is beginning to learn arithmetic but expects
serious mathematicians to pay attention to his "great ideas".
William Elliot
>> That's not a trivial operator.
>
> Well, simplified space bending is a result of this approach, mentioned
> only to demonstrate the utility of even considering such silly things in
> the first place.
>
Twisted. 2 + 2 = 4. Ya wanta make of it?
----
William Elliot
>>>> So what about the trivial operator ?
>>> Not to every modern mind. There are still several geniuses living
>>> among us: JSH, Inverse Cone of 19, and you. The brilliant men who have
>>> selflessly devoted their lives to triviality.
>>
>> lol -
>>
>> I try to elicit some vehement rebuttals because I really want to dig
>> into this question I have. I would be much more satisfied having a
>> really vulgar swearing match, slugging it out and hurling concepts
>> around very violently .......
>>
> Here is one reason: your thoughts are trivial. You sound like an 8
> year old child who is beginning to learn arithmetic but expects
> serious mathematicians to pay attention to his "great ideas".
>
You've fallen for that trivial operator's
bait to get into a swearing match.
Huang
>
> - Show quoted text -
I dont care if it's a great idea or not. An idea is an idea, and Im
surely not the first person to think about it. The fact that it makes
sense to me is interesting and so I have a view that others may or may
not share. So what.
Here's the deal. You flip a coin. You cannot possibly hope to ever
prove that it is really random or not. You can model it with random
variables just fine. But you can also model it with standard mechanics
and sensitive dependence on initiail conditions and you will get teh
same "random looking" behaviour under the assumption that the whole
thing is actually deterministic.
So what, you may say.
Well, in my opinion the whole damn universe is just the same as this,
and it's just that simple.
I may argue like an 8 year old, but at least there is a point to it.
There is a conclusion to be drawn from all of this. It is not eactly
the kind of thing that 8 year olds argue about.
You can model the whole universe using mathematics just fine. You can
also model it using conjectural models and the results will be the
same. You will have no way to know if determinism or indeterminacy
reigns supreme, they are equivalent. They are not the same, but they
are equivalent.
And this usage of equivalence is basically the same as similar
applications of equivalence for example in Relativity Theory. And
speaking of which, how exactly does anyone ever intend to unify QM
with the rest of physics anyway ? If we persist to insist that
determinacy and indeterminacy are immiscible like oil and water - how
can they possibly connect up ? Seems quite dubious to me given the
assumptions of incompatibility of determinacy and indeterminacy.
I do have a very different view, I will admit that. But I am not yet
ready to concede defeat, even if I do behave like an 8 year old - lol.
So where's my milk and cookies ?
glird
> On Feb 26, 7:55 pm, Huang <huangxienc...@yahoo.com> wrote:
> > On Feb 26, 8:45 pm, "Ostap S. B. M. Bender Jr."
> > <ostap_bender_1...@hotmail.com> wrote:
> > > On Feb 24, 7:30 pm, Huang <huangxienc...@yahoo.com> wrote:
>
> <<< Mathematics embraces the number zero, but to contemplate a trivial
operator is perhaps too difficult an abstraction for the modern mind.
I would be much
more happy if everyone disagreed with me, and would at the very least
explain why they disagree. That would be much more satisfying.
But no reasons are presented.>
Though trivial, here is a valid reason: Zero is NOT a number. It is
a cipher.
glird
Huang
I want to take an "existent 5" and compose it with a "nonexistent 5".
Standard addition will not work for this. You must have a trivial
operator. I dont really have a symbol for this thing, but lets just
invent one. Lets write it this way [@]
This thing has some wierd properties. It can behave like addition, and
it can also behave like multiplication. It is indeterminate whether it
is addition or multiplication unless you destroy the indeterminacy by
doing things such as asking "which way".
Trivial operator is trivial, and as such it is existentially
indeterminate. It may or may not be there. In other words, models
which incorporate the trivial operator may be rewritten in different
forms which cause it to disappear completely. In fact, trivial
operator does not appear anywhere through the entirety of known
mathematics, nor can it. It can only make sense in conjectural
modelling, that is where it lives.
Back to the example of composing 5 [@] ~5. You have an existent 5, and
a nonexistent 5 which we write as ~5. Let 5 and ~5 both represent
length.
5 + 5 = 10
and
5 * 5 = 25
So, one would naturally expect that 5 * ~5 yields a 5x5 tile, an area.
But I dont think that's how it works. Trivial operator combines
behaviours of additive and multiplicative identities into a single
thing.
So, even though you are multiplying 5 * ~5, I dont think that you
interpret this as an area. I think that the proper interpretation is
as a 1 dimensional segment.
If 5 [@] ~5 is taken as addition,
5 + ~5 has a conjectured magnitude of 10, an expected magnitude of 5.
It looks like this:
existent part nonexistent part
[-----------------------------] + { ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ ~ }
If 5 [@] ~5 is taken as multiplication,
5 * ~5 looks like this :
[...................................................................]
and each point has a given probability of existing.
So you have a discrete case and a continuous case, and they are
equivalent.
By insisting on _conservation_ of the nonexistent part, this should be
convertible into a probabilistic problem from standard mathematics
using random variables and trivial operator disappears.
I can dig up a better explanation of how to crunch actual numbers,
here's a older thread on that topic:
http://groups.google.com/group/sci.physics/browse_thread/thread/a9d11a37a08d34cf/4c8ec33435791ddb?hl=en#4c8ec33435791ddb
Huang
http://groups.google.com/group/sci.physics/
browse_thread/thread/a9d11a37a08d34cf/
4c8ec33435791ddb?hl=en#4c8ec33435791ddb
If you can grasp the basic idea described in the link above, you will
have some new ideas regarding length. It is just a very small step to
extend the application of those concepts to time.
If you can visualize this model of time, then go over here and look at
this experiment :