The Physics of Paradox: A Theory of Everything

[Mentat]

Originally posted by wuliheron
LOLOLOLOLOLOL... is that a fact?

Yes. Facts are things that are observably, demonstrably, and conclusively true. They are not brought into question. If they turn out to be wrong, then they weren't a fact to begin with.

 

[wuliheron]

Yes. Facts are things that are observably, demonstrably, and conclusively true. They are not brought into question. If they turn out to be wrong, then they weren't a fact to begin with.

Yes, the Earth is flat. I have seen it with my own eyes and know the facts. Of course facts such as the Earth being flat are observably, demonstrably, and conclusively true, I've seen this with my own eyes as well. What rubbish and, of course, that's a fact.

The map is not the territory. Instead of insisting we know the facts or even have a clear idea of what the word means we can let nature speak for herself and just take it in as it comes.

 

[Mentat]

Originally posted by wuliheron
Yes, the Earth is flat. I have seen it with my own eyes and know the facts. Of course facts such as the Earth being flat are observably, demonstrably, and conclusively true, I've seen this with my own eyes as well. What rubbish and, of course, that's a fact.

The map is not the territory. Instead of insisting we know the facts or even have a clear idea of what the word means we can let nature speak for herself and just take it in as it comes.

Wu Li, think! Astronauts have observed that the Earth is not flat. If you could make precise measurements of the Earth, you would also observe that it is curved.

 

[drag]

Greetings !

No offense, but that exchange between wuli and
Mentat is really funny !

Anyway, I was reading the first two messages
of this thread 'cause I had'em saved on my
PC (before the other posts appeared ).
I thought they were very impressive.

What I wanted to ask wuli is the following :
Your approach towards QM, to me personally, appears
to constitute a "partial" belief. I mean it's like
religous people waiting for a messiah and thinking
he's about to come any moment now. Your references
on the subject say it's an almost clear indication
that here we are - really coming close to the PoE
and all. But in fact, we have no way of knowing
how close we are to the end of scientific discovery,
by whatever means we use, in fact I find it quite
likely there will never be an end to it (although
it may very well turn totally theoretical at some
relativly close point). Do you agree that your
perspective as you expressed it leans too much
in this direction to the point that it "slightly"
turns into a belief (maybe it's just part of your
attempt to tie philosophy to reality in order to
convince people who have a hard time accepting it,
but if it is - I'm not certain it's a good idea).
Anyway, remembering your "teachings" it just tastes
a bit "off" to me, wouldn't you agree ?

Live long and prosper.

 

[wuliheron]

Originally posted by drag
What I wanted to ask wuli is the following :
Your approach towards QM, to me personally, appears
to constitute a "partial" belief. ...Do you agree that your
perspective as you expressed it leans too much
in this direction to the point that it "slightly"
turns into a belief (maybe it's just part of your
attempt to tie philosophy to reality in order to
convince people who have a hard time accepting it,
but if it is - I'm not certain it's a good idea).
Anyway, remembering your "teachings" it just tastes
a bit "off" to me, wouldn't you agree ?

Live long and prosper. [/B]

Nah, I don't believe in the paradox of existence. That's an oxymoron. I suppose you could argue that I must have some tiny little bit of faith in the idea, but then you could say the same thing for anything. Absolute objectivity may just be impossible. I know I sound a bit strident at times when people decide to take everything I say out of context, split hairs, and attack my integrity... but I'm only human. ;0)

The idea of my philosophy is not to describe the paradox itself, but why it appears to be paradoxical and how we can work around this enigma which has proven so impenetrable. If anyone ever proves a rational explanation to the paradox of existence, hey, that's great. That's actually part of the beauty of such philosophies, you can toss them into the trash can any time you want. I've actually done this several times already, but I keep coming back to it because it provides answers nothing else I've found can.

As for the end of science, I don't think that's possible. We might find a theory of everything and science may eventually slow down its rapid pace of discovery sometime in the next few hundred years, but end? If existence really is a paradox the discoveries can never end.

 

[drag]

Greetings !

Originally posted by wuliheron
As for the end of science, I don't think that's
possible. We might find a theory of everything
and science may eventually slow down its rapid
pace of discovery sometime in the next few
hundred years, but end? If existence really
is a paradox the discoveries can never end.

Well, I'm not so certain about that - it could
go either way. Basicly, as I see it, it is likely
we will reach the end of observation possibilities
and once no verification is possible science as
we view it today will cease to exist.

Live long and prosper.

 

[wuliheron]

Originally posted by drag
Greetings !

Well, I'm not so certain about that - it could
go either way. Basicly, as I see it, it is likely
we will reach the end of observation possibilities
and once no verification is possible science as
we view it today will cease to exist.

Live long and prosper.

Science as we view it today has little resemblance to what it did a hundred years ago, so why should we not expect it to change. The biggest change that I see coming in the near future is the equivalent of what the blues is to jazz. An entirely new affect that will emerge from the old stuffy objectivity and prove its worth through shear creativity and applicability. Like the blues, its also likely imo to emerge from the ghettos of science today.

 

[Royce]

If you two would stop arqueing semantics for a minutes I'd like to say something or better put in my two cents worth.
my good buddy mentat and of course many other say or imply that paradoxes do not really exist; that it is just that we do not yet know enough to explain them. That there are underlying yet undiscovered logical explanations fro paradoxes. I disagee, while not in anyway claiming that we already know everything, it is my opinion that paradoxes are real and necessary for existence and that the uncertainty principle is equally real and necessary.
Our physicists have reached the point in their probing that the universe has become gainy at the Planck level and at the other extreme the time, matter, enery, mass and gravity become al but indistinguishable from on another.
Uncertainty is necessary for existence at the Planck level, I believe, because if it were possible to know the exact position and momentum of an electron or photon the it would be logically possible to know the exact position and momentum of everything and thus the cosmos would be deterministic. What would be the point of creation if everything were already known or could be known. Uncertainty can only exist at the Planck level or all of our physical laws would break down and the universe wouldn't work and nothing could exist as it is.
Paradox exist and is necessary because our logic has yet to catch up with reality, not necessarily in what is known or unknown but in how we think and perceive reality. Our logic is still in the classical stage where our physics has entered the modern era. An analogy is trying to do and prove Euclidean geometry on the surface of a sphere.
It is our thinking that creates the paradox not nature. Nature just keeps on doing its thing as it has always been doing it and it works fine thankyou.

 

[Mentat]

Originally posted by wuliheron
Nah, I don't believe in the paradox of existence. That's an oxymoron. I suppose you could argue that I must have some tiny little bit of faith in the idea, but then you could say the same thing for anything. Absolute objectivity may just be impossible. I know I sound a bit strident at times when people decide to take everything I say out of context, split hairs, and attack my integrity... but I'm only human. ;0)

Of course, someone like you has probably already noticed the self-contradictory nature of saying that you don't believe in anything, including not believing in anything.

 

[Mentat]

Originally posted by Royce
If you two would stop arqueing semantics for a minutes I'd like to say something or better put in my two cents worth.
my good buddy mentat and of course many other say or imply that paradoxes do not really exist; that it is just that we do not yet know enough to explain them. That there are underlying yet undiscovered logical explanations fro paradoxes. I disagee, while not in anyway claiming that we already know everything, it is my opinion that paradoxes are real and necessary for existence and that the uncertainty principle is equally real and necessary.
Our physicists have reached the point in their probing that the universe has become gainy at the Planck level and at the other extreme the time, matter, enery, mass and gravity become al but indistinguishable from on another.
Uncertainty is necessary for existence at the Planck level, I believe, because if it were possible to know the exact position and momentum of an electron or photon the it would be logically possible to know the exact position and momentum of everything and thus the cosmos would be deterministic. What would be the point of creation if everything were already known or could be known. Uncertainty can only exist at the Planck level or all of our physical laws would break down and the universe wouldn't work and nothing could exist as it is.
Paradox exist and is necessary because our logic has yet to catch up with reality, not necessarily in what is known or unknown but in how we think and perceive reality. Our logic is still in the classical stage where our physics has entered the modern era. An analogy is trying to do and prove Euclidean geometry on the surface of a sphere.
It is our thinking that creates the paradox not nature. Nature just keeps on doing its thing as it has always been doing it and it works fine thankyou.

Actually, Royce, I don't believe that there are no paradoxes on the conceptual level. I just don't think that there are any physically manifest paradoxes. I don't think the universe allows for it. If someone could show me a physical phenomenon that was in fact self-contradictory, then I would believe in it, but I haven't seen one yet.

The issue of Quantum Uncertainty (and whether it is paradoxical or not) was covered rather well, in the thread, "Quantum Mechanics: Paradoxical?".

 

[Royce]

I haven't had a chance to read that one yet.
I'm also thinking as I write which is not always a good idea.
I think that what I'm trying to say is that paradoxes exist through out nature and since that is so they cannot be paradoxes. It must be then our logic that is paradoxal or creates the paradox. As Spock said "If your logic is correct and the only possible conclusion is impossible then you premis must be wrong." or something to that effect. I think that our logic needs to be brought up to date to include Relativity and Quantum Mechanics and possibly "Fuzzy Logic is the first step in doing so.

 

[wuliheron]

Originally posted by Mentat
Of course, someone like you has probably already noticed the self-contradictory nature of saying that you don't believe in anything, including not believing in anything.

Belief is a colorful hope or fear,
The beginning of folly.
The sage goes by harmony, not by hope;
She dwells in the fruit, not the flower;
She accepts substance,
And does not put abstractions on a pedestal.

Originally posted by Royce
...while not in anyway claiming that we already know everything, it is my opinion that paradoxes are real and necessary for existence and that the uncertainty principle is equally real and necessary.
...Uncertainty can only exist at the Planck level or all of our physical laws would break down and the universe wouldn't work and nothing could exist as it is.

Sorry, but uncertainty demonstrably exists at all extremes, not just size. The Big Bang, for example, is as magical and bizarre a phenomenon as any Quantum event. Likewise, when attempting to describe "uncertainty" we come up against those same semantic difficulties you complained about precisely because, again, we are taking conceptual reasoning to an extreme. Like up and down, left and right, uncertainty has no meaning outside of the context of certainty because they are really describing one and the same thing.

Paradox exist and is necessary because our logic has yet to catch up with reality, not necessarily in what is known or unknown but in how we think and perceive reality. Our logic is still in the classical stage where our physics has entered the modern era. An analogy is trying to do and prove Euclidean geometry on the surface of a sphere.
It is our thinking that creates the paradox not nature. Nature just keeps on doing its thing as it has always been doing it and it works fine thankyou.

This is one of two approaches to the subject currently receiving a great deal of attention in the west. One proposes we just need to develop more complex logistics while the other says the issue is one of semantics. The logicians are attempting to create the foundations for a TOE while the semantists like Mentat are attempting to disprove the existence of genuine paradoxes. My approach to the subject is more along the lines of Asian thought which stresses attitude over reason.

These two western approaches are arguably both founded upon rejection, denial. The asian approach is founded upon acceptance. Acceptance that our perceptions of existence and the languages we use to describe existence ultimately have no meaning whatsoever outside of the personal context. You can argue with someone over the meaning of 9-11 or the word "uncertainty" until you are blue in the face, but until they actually accept something in your arguments nothing will change from their point view.

Is paradox real, for that matter, is reality real? Who cares! What conceivable difference could it make in my life. Each approach to the problem possesses unique value, that is what matters.

 

[Mentat]

Originally posted by wuliheron
Belief is a colorful hope or fear,
The beginning of folly.
The sage goes by harmony, not by hope;
She dwells in the fruit, not the flower;
She accepts substance,
And does not put abstractions on a pedestal.

And your point is...? You obviously believe that whoever wrote this is correct, and thus contradict it's teaching (of course, you're only contradicting it because your agreeing with it...paradox alert!).

 

[wuliheron]

Originally posted by Mentat
And your point is...? You obviously believe that whoever wrote this is correct, and thus contradict it's teaching (of course, you're only contradicting it because your agreeing with it...paradox alert!).

I believe whoever wrote this, supposidly Lao Tzu, was describing the paradox of existence from a personal cognitive viewpoint. My point was, of course, that you were quite correct when you wrote:

Originally posted by Mentat
Of course, someone like you has probably already noticed the self-contradictory nature of saying that you don't believe in anything, including not believing in anything.

 

[drag]

Greetings !

Originally posted by Mentat
I just don't think that there are any
physically manifest paradoxes. I don't
think the universe allows for it.

That is a belief. The relevant religion is
what I call "old" materialism.

Originally posted by Mentat
If someone could show me a physical phenomenon
that was in fact self-contradictory, then
I would believe in it, but I haven't seen
one yet.

Wave-particles are self-contradictory according
to "normal" logic. So's lack of individuality for
example. QM and GR together are also
self-contradictory. You could call them all
paradoxes, the reason you prefer not to is
because you BELIEVE they can be solved and
so you think they're temporary misunderstandings -
observation without an appropriate reason
pattern deduced from it.

In a similar way the PoE can not be proven
absolutely (nothing can), but it is a lot
more likely to be a real paradox by comparisson.
So why won't you believe(NOT totally accept) in it ?

Live long and prosper.

 

[Mentat]

But, wuliheron, I posted that because I wanted to know why you hold to a belief that requires that you hold to no belief. Isn't it impossible to do that anyway?

 

[Mentat]

Originally posted by drag
Greetings !

That is a belief. The relevant religion is
what I call "old" materialism.

I don't understand this. Yes, it is a belief. It's as valid as any other, until someone can prove otherwise.

Wave-particles are self-contradictory according
to "normal" logic. So's lack of individuality for
example.

Wrong. These do not contradict normal logic. They contradict normal reasoning. I pointed out this difference in "Quantum Mechanics: Paradoxical?".

QM and GR together are also
self-contradictory. You could call them all
paradoxes, the reason you prefer not to is
because you BELIEVE they can be solved and
so you think they're temporary misunderstandings -
observation without an appropriate reason
pattern deduced from it.

Wrong again, I don't think they are resolvable, because I don't think that they need resolution. There is no paradox, if you just stop taking "one thing cannot exist in two, different, states at the same time" as a premise.

In a similar way the PoE can not be proven
absolutely (nothing can), but it is a lot
more likely to be a real paradox by comparisson.
So why won't you believe(NOT totally accept) in it ?

Well, I don't even really know what the PoE is (how can you, when all you have to go on is Wuliheron's philosophical applications of that which he already accepts?). However, if you are asking why I don't just accept that existence is paradoxical, my answer is "because you haven't given me any reason to believe that in the first place".
Live long and prosper.

 

[wuliheron]

Originally posted by Mentat
But, wuliheron, I posted that because I wanted to know why you hold to a belief that requires that you hold to no belief. Isn't it impossible to do that anyway?

Its not impossible at all. Wisdom is not so much the accumulation of knowledge, as it is the process of dumping a lot of garbage. For example, a bigot might choose to consciously dump their beliefs about other races. This might take years of effort, but eventually the process itself becomes a self-extinguishing pursuit. Once we loose such negative beliefs, there is nothing left for us to continuing believing we need to get rid of.

Taken to its extreme, we can consciously focus on ridding ourselves of even the belief we need to get rid of certain beliefs. Many accomplish this through meditation. At some point, our cognitive processes lead us inevitably to a personal practice like meditation. Some former slavers, for example, became abolitionists. From one point of view, they were paying for their sins, but from another, they were healing.

 

[Mentat]

Originally posted by wuliheron
Its not impossible at all. Wisdom is not so much the accumulation of knowledge, as it is the process of dumping a lot of garbage. For example, a bigot might choose to consciously dump their beliefs about other races. This might take years of effort, but eventually the process itself becomes a self-extinguishing pursuit. Once we loose such negative beliefs, there is nothing left for us to continuing believing we need to get rid of.

Taken to its extreme, we can consciously focus on ridding ourselves of even the belief we need to get rid of certain beliefs. Many accomplish this through meditation. At some point, our cognitive processes lead us inevitably to a personal practice like meditation. Some former slavers, for example, became abolitionists. From one point of view, they were paying for their sins, but from another, they were healing.

Are you honestly missing the contradiction, or are you ignoring it?

Seriously, why would one rid oneself of the belief that one needs to rid oneself of beliefs, unless that one believed that one needs to rid onself of beliefs? This contradicts itself, and is thus impossible. Just like being limitless.

 

[drag]

Greetings !

Originally posted by Mentat
I don't understand this. Yes, it is a belief.
It's as valid as any other, until someone
can prove otherwise.

How about not having a belief - remaining
open to possibilities. Beliefs are required
to make use of them - to verify them, thus
they are useful, otherwise they're not.

Then again, the difference between a belief and
what you consider real is just what you consider
more probable. Thus, if the lack of a PoE seems
more likely to you then so be it. I just
find it difficult to understand such a perspective
because it seems to me like the most certain
of all things(although not absolute).

Originally posted by Mentat
Well, I don't even really know what the PoE
is (how can you, when all you have to go
on is Wuliheron's philosophical applications
of that which he already accepts?). However,
if you are asking why I don't just accept
that existence is paradoxical, my answer
is "because you haven't given me any
reason to believe that in the first place".

Does the inability of any reasoning (so far)
to solve the mystery of existence not provide
sufficient proof ? Notice that I speak of
total inability, NOT partial success or simply
lack of reasoning effort. The limmits are well
defined for any reasoning currently known and
that you'd care to use. What is it that prevents
you hence from accepting the PoE as a probable
assumption ? Is it the lack of such formulated
limmits (the many "faces" of the PoE) ? I've
repeatedly mentioned a lot of these.

What is the mystery of existence (the PoE) ?
How can I answer that if there's no apparent
solution to this ? All I can do is define
the limmits of this paradox.

Live long and prosper.

 

[wuliheron]

Originally posted by Mentat
Are you honestly missing the contradiction, or are you ignoring it?

Seriously, why would one rid oneself of the belief that one needs to rid oneself of beliefs, unless that one believed that one needs to rid onself of beliefs? This contradicts itself, and is thus impossible. Just like being limitless.

No, I'm not missing the contradiction, its a difficult concept to express well to westerners. Beliefs from my point of view are better described as habits. By making it a habit to rid oneself of bad habits what are left are good habits. Getting rid of habits altogether is, paradoxically, as easy and difficult as anything.

A child suddenly dancing spontaneously, a musician becoming lost in their music, etc. are all examples of people spontaneously choosing in the moment to drop their habits and go with something else. For young children, such an act usually comes easy while for adults who have acquired a tremendous number of habits it can be incredibly difficult. However, there are simple ways to cultivate this ability.

Taoists like to say, "Eat when you are hungry, drink when you are thirsty, and sleep when you are tired." By focusing on paying attention to your own body and feelings you can rid yourself of a number of habits and, eventually, go with your own spontaneous inclinations while shrugging off whatever habits might remain.

Unlike the concept of infinity, this may present an apparent paradox but is something easily observed and varified.

 

[drag]

wuli, if I'm gon'na end up meditating
after reading these ideas you express,
I want you to know I'm gon'na blame you
for it...

 

[wuliheron]

Originally posted by drag
wuli, if I'm gon'na end up meditating
after reading these ideas you express,
I want you to know I'm gon'na blame you
for it...

If necessary, I'll just push the blame on the AMA, they recommend meditation. Guilt is a terrible thing to waste, so no matter what I won't dwell on it.

 

[pelastration]

Laugher

Wu Li,

can you tell us more about the relationship between Paradox and laugher. It seems to me that both have a similar 'growth' of tension in the mind. With laugher it can 'come out'.

I like this active approach: http://www.laughteryoga.org/biodata.htm

 

[wuliheron]

Taoist writings are particularly paradoxical, and can be interpreted in several distinct ways. It's really up to the individual to interpret them. In the case of the Tao Te Ching, for example, it is particularly written in such a way as to encourage argumentative people to argue with the text. However, because it is so paradoxical, it is also written so it can interpreted as just so much pretty prose or as a subtle sense of humor-that-is-not-humor.

The more paradoxical something is, the more it allows us to choose as individuals how we wish to interpret the text. Rather than asserting itself, the writing makes itself available to our personal assertions by incorporating an accepting attitude and a more descriptive than prescriptive prose. The Chinese are inordinately fond of paradoxes and often hang them on their walls the way we do mirrors, but these are mirrors for the mind. Rather than telling us what to think, they allow us to see reflections of how we ourselves think and feel at the moment.

The writings of Chuang Tzu are particularly humorous as paradoxical writings go, and achieve this in the classic chinese style of telling outrageous stories. As is common in shamanism, the proverbial fool plays a central role. Two good modern day examples of shamanistic or Taoistic fools commonly sited are Jackie Chan and Whinnie the Pooh. Their characters tend to be unassuming and affable, yet socially inept and backwards, immature even. They will bumble through one outrageous situation after another, sometimes unwittingly risking life and limb, yet everything always works out in the end.

Such humor is self-effacing, humble, and modest rather than sarcastic or whatever. Here is one of my favorite examples:

A Zen master and Indian Guru were waiting by the pier for the fairy boat to take them across the bay. The Guru looked at the master and said, "I've spent the last ten years learning how to walk on water, why don't we just forget the fairy and walk to the other side of the bay?" To which the Zen master replied in astonishment, "You spent ten years learning how to walk on water? Why? The fairy is only a dime!"

 

[Mentat]

Originally posted by drag
I just find it difficult to understand such a perspective
because it seems to me like the most certain
of all things(although not absolute).

If you are most certain about something that doesn't allow you to be certain about anything, where do you find room for rationalization?

Does the inability of any reasoning (so far)
to solve the mystery of existence not provide
sufficient proof ? Notice that I speak of
total inability, NOT partial success or simply
lack of reasoning effort.

This is the difference between you and me. You take the pessimistic view-point, that things are unexplainable, while I (realistically, or - perhaps - opptimistically) allow for them to simply be unexplained.

What is it that prevents you hence from accepting the PoE as a probable assumption?

The same thing that doesn't allow you to accpet my view, probably just stubornness.

What is the mystery of existence (the PoE) ?
How can I answer that if there's no apparent
solution to this ? All I can do is define
the limmits of this paradox.

You can only define the limits of something after assuming it's existence.

 

[drag]

Greetings !

Originally posted by Mentat
If you are most certain about something
that doesn't allow you to be certain about
anything, where do you find room for
rationalization?

An excellent point !
I think that rationalization of any kind
can only be drown from and connected to
our data input (perception/knowledge/sense) -
sum of all our observation.

I believe many ancient philosophers saw it the
same way, however, they knew far less in terms
of science to learn how misleading and complex
it can be and thus some of them preferred to
see the observed as absolute, which I think is
certainly a mistake.

Another point is what we call abstract thought.
Apparently another type of data within the
total input data. Abstract thought, however,
does not show signs of any uniqueness, it seems
to be just a consequence of observation without
any specific difference.

Even more basicly, the above approach can not be
drown from anything. It appears to be like
the simplest approach, a default if you like.
Most current physical laws, for example, are
the result of seeking the shortest possible
explanation - optimizing the observed into
the ultimate pattern. In much the same way I think
the most basic approach is to accept the
data you observe without ANY application
of prior reasoning. If new data replaces it -
so be it and it must not be stopped by rationale
drown from the previous data(even if it seemed
so simple and basic earlier).

As you can see, such an approach can not support
any absolutes because it recognizes the possibility
(the most basic and simple one I think) that
new observation may refute them. As such, this
system can't also absolutely support itself because
it can't prove absolutes and thus can't show
it's really the most basic, simple, productive
or usefull approach. On the other hand, it
doesn't seem to be able to allow a refutal of
itself. In short, it's doubt.
It teaches you to accept all views and never
dismiss any. And what's wrong with that ?

Originally posted by Mentat
This is the difference between you and me.
You take the pessimistic view-point, that
things are unexplainable, while I
(realistically, or - perhaps - opptimistically)
allow for them to simply be unexplained.

Well, notice I did not say the PoE's lack of
solution is absolute. I just said it's most unlikely.
I prefer not to have any bias but rather
view the situation as it is. This may not
always work , but I think it does here.
The PoE presents many unanswerable questions
of the most basic type, hence it's solution
seems most unlikely.

Of course, often the most extrordinary questions
lead to the most extrordinary and yet very simple
and basic answers that due to that simplicity
also often prove to be very usefull (like
relativity for example), and that's what I
believe this thread enitially referred to.

Originally posted by Mentat
The same thing that doesn't allow you to
accept my view, probably just stubornness.

Stuborness is a result of some effort,
an intellectual effort in this case,
and that is ussualy a positive thing
so it's not too bad either way - it's
the usefullness part again.
btw, I do ACCEPT your view as any other,
I simply do not agree with it for now.

Originally posted by Mentat
You can only define the limits of something
after assuming it's existence.

Hmm... Existence of existence...
Existence IS absolute, but there's no
way of defining it I think (and again,
that is already a claim of some sort and
hence not absolute , aren't you tired
of hearing it again and again ? believe me
it's even greater trouble of reminding
it all the time in every message ).

Live long and prosper.