Is there a common misunderstanding of inertia?

[johann1301]

According to wikipedia, «inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion.»
To explain what i think the common misunderstanding of inertia is, one finds it helpfull to talk about matter without inertia.

Mass with- and without inertia:
If I were to talk about matter without the property of inertia, I would be talking about an unobserved object. In other words; Matter without inertia does not really exist(or very unknown). Yet it is important to stress that a hypothetical object without inertia, would also keep its original state of motion when not-forced-upon, just as an object with inertia would. At least hypothetically.
The difference lies in the amount of force needed to move the objects. An object without inertia - no matter how big or small it is - would need a force of zero Newton(no force) to change its state of motion. In the case where the object has inertia(wich is the realistic case), the amount of force would vary proporsional with the objects mass. (this is a known fact). If the mass is bigger, the inertia is bigger. (and vica versa)
If this hypothetical presumtion is true, it would imply that inertia (not matter) is the reason why a force is needed to move an object.
For example: You get shot by a pistol. If the bullet has no inertia, you would not feel the bullet hitting you.
To explain even further; the period where an object goes from beeing in one state of motion A to another state of motion B, is the timeframe where inertia plays its role. This is the period were one observes resistance. In the case were inertia does not exist, there would be no resistance in this period. In any other time then between A and B, no-inertia and inertia would be the same thing.

These postulates about inertia are therefore misleading:

1. An object at rest tends to stay at rest.
2. An object in motion tends to stay in motion.
Source: http://www.qrg.northwestern.edu/projects/vss/docs/Propulsion/2-what-is-inertia.html

These are well known statements about inertia, but they do not mention anything about resistance.(at least not directly) These statements imply that objects stay in motion and rest becouse of inertia. As described earlier, this shouldn't be the true. They stay at rest and in-motion becouse nothing is acting on it. This leeds to another question...

What makes objects move?
In the example where the non-inertial bullet hits you without you feeling it, the bullet also stops!
Inertia shouldent stop objects, in fact it is known to resist any change of motion. There is no logic then, in that a non-inertial bullet should act any different. Inertia has therefore nothing to do with why objects change their state of motion or change shape. That must be explained by something else.
There are probably many explenations why an object can change its shape or state of motion. The Pauli exclusion principle is perhaps one of the explenations or our general idea of friction.

anyway...

Are there other people who agree with me?
Is saying «An object at rest tends to stay at rest» the same as saying that «An object tends to resist any change in its motion»?

i think not...

 

[Freye]

I'm really not quite sure what you're trying to get at here, but to answer your last question "Is saying <an object at rest tends to stay at rest> the same as saying that <an object tends to resist any change in its motion>?", the former statement does not imply the latter, it is merely a specific application of it, whereas the latter (which is essentially Newton's first law) implies the former. Hopefully this at least partially answers what you're asking.

 

[Andrew Mason]

These statements imply that objects stay in motion and rest because of inertia. As described earlier, this shouldn't be the true. They stay at rest and in-motion because nothing is acting on it. This leads to another question...

What makes objects move?
In the example where the non-inertial bullet hits you without you feeling it, the bullet also stops!
Inertia shouldn't stop objects, in fact it is known to resist any change of motion. There is no logic then, in that a non-inertial bullet should act any different. Inertia has therefore nothing to do with why objects change their state of motion or change shape. That must be explained by something else.

You have put some thought into the nature of inertia. It is one of the real mysteries of the physical world. Good luck in trying to figure it out.

You are right that inertia alone does not explain why objects speed up or slow down when they interact with other objects.

For example, neutrons, which have significant inertia, will go through matter quite easily without slowing down (unless they hit an atomic nucleus). So if you could make a bullet out of neutrons, the bullet could go through you without leaving a hole and without slowing down (much). That has nothing to do with inertia. It has to do with its ability of neutrons to interact with the molecules in your body. (Since you can't make a bullet out of neutrons for other reasons, we don't observe this).

Neutrinos are particles that have inertia. They are emitted during nuclear reactions such as occur in the sun. Huge numbers pass through the sun and through the Earth every second without slowing down at all. Very few get stopped. Again, it has nothing to do with inertial. It has to do with the ability to interact with other matter.The reason a normal matter bullet slows down when it strikes something has to do with the electromagnetic forces between atoms. A bullet slows down because there is an interaction - a mutually repulsive force - between the atoms in the bullet and the atoms in the target. These are electromagnetic forces.

When, however, two particles do interact, inertia does matter. It determines how the particles will behave in the interaction and what the momentum will be after the interaction.

So, you are right. Inertia does not explain why particles are subject to forces. But inertia does determine how two bodies will move if they are subject to forces.

AM

 

[256bits]

According to wikipedia, «inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion.»
To explain what i think the common misunderstanding of inertia is, one finds it helpfull to talk about matter without inertia.

Just consider what the situation was before the concept of inertia and that was that it was incorectly believed that a body in motion needed a continious force to keep it in motion.

There is also the debate of whether or not gravitational mass is the same as inertial mass. So far the two seem to be equal and the question then is why? No one has come up with a complete explantion to explain the equality if I am not mistaken.

 

[johann1301]

There is also the debate of whether or not gravitational mass is the same as inertial mass.

What is the difference between gravitational mass and inertial mass?

 

[johann1301]

When, however, two particles do interact, inertia does matter. It determines how the particles will behave in the interaction and what the momentum will be after the interaction.AM

I guess you are talking about velocity here??(after the interaction)

I didn't think of that, of course inertia plays a role after! But i guess i was thinking of the acceleration, not the velocity when i said:

In any other time then between A and B, no-inertia and inertia would be the same thing.

If i could re-express myself:
In any other time then between A and B, no-inertia and inertia would give the same acceleration. 0 m/s2 to be accurate.

I totally agree that both velocity, position(at a specific time) AND acceleration would be influenced by inertia IN the interaction, but after; the acceleration has nothing to do with inertia.

right?

 

[Samshorn]

... a hypothetical object without inertia, would keep its original state of motion when not-forced-upon... An object without inertia would need a force of zero Newton (no force) to change its state of motion...

Aren't those two statements mutually contradictory? Or do you claim "no force" is different from "not-forced-upon"?

It's questionable whether postulating attributes for non-existent things (e.g., objects without inertia) has any rational content, but postulating mutually contradictory attributes surely has none.

 

[Dickfore]

For me, the principle of inertia simply follows from the Lagrangian formulation of Mechanics. Namely, for a free point particle, the Lagrangian can not depend on position and time due to homogeneity of space and time, and it cannot depend on the direction of its velocity due to isotropy of space. Therefore, it can only depend on the square of the magnitude of velocity:
$$L = L(v^{2})$$
But, when we try to insert the derivatives:
$$\frac{\partial L}{\partial \mathbf{v}} = 2 \mathbf{v} L'(v^{2})$$
and
$$\frac{\partial L}{\partial \mathbf{r}} = 0$$
into the Euler-Lagrange equations of motion:
$$\frac{d}{d t} \frac{\partial L}{\partial \mathbf{v}} - \frac{\partial L}{\partial \mathbf{r}} = 0$$
we get:
$$L'(v^{2}) \mathbf{v} = \mathbf{\mathrm{const.}}$$
This vector equation implies that:
$$\mathbf{v} = \mathbf{\mathrm{const.}}$$
which is a mathematical expression of the principle of inertia: That a free point particle tends to move with a constant velocity, i.e. uniformly along a straight line.

 

[Dickfore]

Notice, however, that this only applies to a point particle. A free rigid body, for example, can continue to rotate along a any of its principal axes of inertia with a uniform angular velocity.

 

[johann1301]

Aren't those two statements mutually contradictory? Or do you claim "no force" is different from "not-forced-upon"?

Yes it is contradictory, sorry about that! usually when an object changes momentum there has been some force involved. that's why i wrote "not-FORCED-upon".

An object without inertia would also keep its original state of motion when not-being in contact with any other object.(just as an object with inertia).

This shouldn't be a problem; because inertia does not explain why particles are subject to forces. (as concluded earlier).

 

[johann1301]

It's questionable whether postulating attributes for non-existent things (e.g., objects without inertia) has any rational content, but postulating mutually contradictory attributes surely has none.

true.

 

[chrisbaird]

The word "inertia" can be misleading because it historically can refer to two different things. So you always need to be clear with you mean. It can mean "the amount of resistance an object has to a change in velocity" which is the same thing as inertial mass, or it can mean "the amount of powerful movement contained in a moving body" which is the same thing as momentum. These are different concepts. When you speak of a speeding bullet having more inertia because it is harder to stop than, say, a large shopping cart, you mean momentum. In the sense of accelerating from 0 to 60 mph, the bullet actually has less inertia (less mass). Some of the confusion in the OP may lie with these two meanings.

If you mean inertia in the sense of mass, than to speculate about an object that has mass but no inertia is meaningless. It is like talking about an orange carrot that is colorless.

 

[Andrew Mason]

I guess you are talking about velocity here??(after the interaction)

I didn't think of that, of course inertia plays a role after! But i guess i was thinking of the acceleration, not the velocity when i said:



If i could re-express myself:
In any other time then between A and B, no-inertia and inertia would give the same acceleration. 0 m/s2 to be accurate.

I totally agree that both velocity, position(at a specific time) AND acceleration would be influenced by inertia IN the interaction, but after; the acceleration has nothing to do with inertia.

right?

Inertia and force determines the accelerations resulting from an interaction. a = f/m

After the interaction, there is no force and no acceleration.

AM

 

[johann1301]

When Newton says in his first law of motion:
The velocity of a body remains constant unless the body is acted upon by an external force.
-http://en.wikipedia.org/wiki/Newton's_laws_of_motionHe could just have said:
The acceleration of a body remains zero unless the body is acted upon by an external force.

This is becouse the derivative of a constant always have a value of zero.(ofcourse)

If the accelleration remains zero, inertia plays no crucial role. This is what i believe we have established erliar.

In other words Newtons first law has nothng to do with inertia. Or; Newtons first law is valid with- and without the existence of inertia?

(i know this is stretching it far) When people use Newtons first law as an illustration of inertia, i believe that it is wrong to do so. This is what i believe is the common misunderstanding of inertia.

Feel free to disagree, honestly;)

 

[Dickfore]

Newton's First Law holds only in Refrence Frames that are called 'inertial'. It should be treated as a criterion of whether or not a particular frame is inertial and not as a consequence of Second Newton's Law:
$$\mathbf{F} = \mathbf{0} \Rightarrow \mathbf{a} = \mathbf{0} \Rightarrow \mathbf{v} = \mathbf{\mathrm{const.}}$$
This is not the essence of it, because it is supposed to be a logically independent statement from the other two Laws. And, in the context that I mentioned, it is. Newton's Laws strictly hold only in Inertial Reference Frames.

 

[Ken G]

One way to look at all this is to imagine we have a series of questions that first deal with understanding our reference frame, and later with understanding the forces present. We might define an inertial reference frame as one that exhibits the symmetries that Dickfore mentioned, and invoke the dynamical laws to then assert, as he showed, that in such a frame, velocity will stay constant. We are then not using the constant velocity as our definition of an inertial frame, we are using the fact that we will observe the laws to hold good in that frame. In that program, Newton's first law is indeed contained in the second law-- the law that must hold good is the second law, if we are in a frame with those symmetries. We call that an inertial frame.

Seen this way, the point of culling out the first law for special attention, even though it is contained in the second, is expressly because the first law does not make reference to inertia. There is no requirement to have a concept of inertia to have the first law, we only need a concept of an inertial frame (an unfortunate overlap in terms). So I think the issue raised in the OP is a valid one-- the term "inertia" really does get used in two quite different ways, one around the lines of "what will not happen when there are no forces on a body" (which relates only to the issue of what the observer is doing, i.e., whether the observer frame exhibits symmetry in space, time, and orientation), and the other around the lines of "how much will happen when there are forces" (which relates to the concept of mass, often used as a synonym for inertia).

 

[Andrew Mason]

When Newton says in his first law of motion:
The velocity of a body remains constant unless the body is acted upon by an external force.
-http://en.wikipedia.org/wiki/Newton's_laws_of_motionHe could just have said:
The acceleration of a body remains zero unless the body is acted upon by an external force.

This is becouse the derivative of a constant always have a value of zero.(ofcourse)

If the accelleration remains zero, inertia plays no crucial role. This is what i believe we have established erliar.

In other words Newtons first law has nothng to do with inertia. Or; Newtons first law is valid with- and without the existence of inertia?

(i know this is stretching it far) When people use Newtons first law as an illustration of inertia, i believe that it is wrong to do so. This is what i believe is the common misunderstanding of inertia.

Feel free to disagree, honestly;)

To determine whether Newton's first law is valid with or without inertia, you would have to find a physical entity that has no inertia and see if Newtons' first law applies. (There are such particles eg. a photon).

Newton's first law:
Every body persists in its state of being at rest or of moving uniformly straight forward, except insofar as it is compelled to change its state by force impressed.

It can be shown by experiment that a photon will impart momentum to an atom when an atom emits or absorbs the photon. So the photon carries momentum ($p = h/\lambda$). In this respect, it behaves like a matter particle. But does it follow the first law? In these interactions with atoms, does its state of motion change? No. It doesn't. It always travels at c.

So I would say that Newton's first law does not apply to bodies that have no inertia. You are quite right that it is not about inertia (the second law is about inertia). But it certainly has something to do with inertia. It describes the motion of inertial objects that are not subjected to forces.

AM

 

[zoobyshoe]

These are well known statements about inertia, but they do not mention anything about resistance.(at least not directly)

To the contrary. Newton, very directly, defined inertia as a resistance:

"Definition III.

The vis insita, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, endeavors to persevere in its present state, whether it be of rest, or of moving forward in a right line.

This force is ever proportional to the body whose force it is; and differs nothing from the inactivity of the mass, but in our manner of conceiving it. A body, from the inactivity of matter, is not without difficulty put out of its state of rest or motion. Upon which account, this vis insita may, by a most significant name, be called vis inertiae, or force of inactivity. But a body exerts this force only, when another force, impressed upon it, endeavors to change its condition; and the exercise of this force may be considered both as resistance and impulse; it is resistance, in so far as the body, for maintaining its present state, withstands the force impressed; it is impulse, in so far as the body, by not easily giving way to the impressed force of another, endeavors to change the state of that other. Resistance is usually ascribed to bodies at rest, and impulse to those in motion; but motion and rest, as commonly conceived, are only relatively distinguished; nor are those bodies always truly at rest, which are commonly taken to be so."

-Newton
Principia Mathematica

Newton's three Laws are much clearer if you make the effort to penetrate the somewhat archaic language and read the definitions that preceed them in Principia Mathematica:

http://www.archive.org/stream/Newtonspmathema00newtrich#page/n77/mode/2up

A body without inertia would, by definition, offer no resistance to being moved. And, since it offers no resistance, it would deliver no impulse to the body that moved it, effecting no change in the state of rest or motion of that other body. Matter like this would be useless, undetectable, ignorable.

 

[Ken G]

If we imagine a sequence of objects with less and less inertia, it would be odd to expect something different to happen to a zero-inertia object than happens in the limit as the inertia goes to zero. Therefore, if Newton's first law applies throughout that sequence, as is the claim in that law, then it would also apply to a zero-inertia object. Ergo, the first law does not refer to inertia in any way. In other words, a law that does not care what the inertia is, does not refer to inertia.

 

[johann1301]

If we imagine a sequence of objects with less and less inertia, it would be odd to expect something different to happen to a zero-inertia object than happens in the limit as the inertia goes to zero. Therefore, if Newton's first law applies throughout that sequence, as is the claim in that law, then it would also apply to a zero-inertia object. Ergo, the first law does not refer to inertia in any way. In other words, a law that does not care what the inertia is, does not refer to inertia.

Someone finally sees my point!

 

[Drakkith]

From wikipedia:

Physics and mathematics appear to be less inclined to use the original concept of inertia as "a tendency to maintain momentum" and instead favor the mathematically useful definition of inertia as the measure of a body's resistance to changes in momentum or simply a body's inertial mass.

I would say that an object tends to stay in motion or at rest because it does resist changes in its momentum. With no force applied the resistance to change keeps the object from just randomly shifting it's momentum up or down.

 

[Andrew Mason]

If we imagine a sequence of objects with less and less inertia, it would be odd to expect something different to happen to a zero-inertia object than happens in the limit as the inertia goes to zero. Therefore, if Newton's first law applies throughout that sequence, as is the claim in that law, then it would also apply to a zero-inertia object. Ergo, the first law does not refer to inertia in any way. In other words, a law that does not care what the inertia is, does not refer to inertia.

There is a significant material difference between a body having small inertia and a body having no inertia. This is not an abstract calculus problem. It is physical reality. A body either has a finite inertia or it has no inertia. It cannot have an infinitessimal inertia. No inertia means that it has no mass. It means that a collection of Avogadro's number of such bodies, or Avogadro's number to the exponent Avogadro's number of such bodies would have 0 mass.

Newton did not say that his first law applied to light. He never says so. His use of the term "body" suggests he was not talking about light which does not seem to have the attributes of a "body". Whether it actually applies to light has to be determined by experiment. From what I can tell, one cannot impress a force on a photon and one cannot change its speed. So how does the first law apply to a zero-inertia particle such as the photon?

AM

 

[zoobyshoe]

But does it follow the first law? In these interactions with atoms, does its state of motion change? No. It doesn't. It always travels at c.

"Acceleration" includes changes of direction.

 

[Ken G]

There is a significant material difference between a body having small inertia and a body having no inertia.

I see nothing about m=0 that does not emerge simply from the limit m->0.

A body either has a finite inertia or it has no inertia. It cannot have an infinitessimal inertia.

How would we know? Do we know about any bodies that have zero inertia?
(Don't think "photon", we have no idea if photons in vacuum really have zero inertia.)

Newton did not say that his first law applied to light.

It doesn't make any difference if his law applies to light, it's just a law. No one knows when laws work and when they don't, and Newton was no different. The issue is what the law says, not when it is true.

So how does the first law apply to a zero-inertia particle such as the photon?

The first law is just a law, it doesn't say when it applies. And how do you know the photon is a zero inertia particle anyway?

 

[Andrew Mason]

I see nothing about m=0 that does not emerge simply from the limit m->0.

Being arbitrarily close to 0 is something that one can do in mathematics but in real life quantities are finite.

How would we know? Do we know about any bodies that have zero inertia?
(Don't think "photon", we have no idea if photons in vacuum really have zero inertia.)
It doesn't make any difference if his law applies to light, it's just a law. No one knows when laws work and when they don't, and Newton was no different. The issue is what the law says, not when it is true.
The first law is just a law, it doesn't say when it applies. And how do you know the photon is a zero inertia particle anyway?

I thought you were serious about this subject.

AM

 

[Andrew Mason]

"Acceleration" includes changes of direction.

Ok. But is it the same photon?

AM

 

[zoobyshoe]

Ok. But is it the same photon?

AM

I was thinking of GR.

 

[Ken G]

Being arbitrarily close to 0 is something that one can do in mathematics but in real life quantities are finite.

You don't understand what I'm saying. I'm saying that we all know that a photon could have a very tiny inertial mass, and none of modern physics would be the least bit different. It is simply something that we don't know. But why doesn't that bother us? It doesn't bother us because none of our laws of physics act any differently on zero rest mass than they on, say, 10^-100 g of rest mass. Can you say what predicted behavior would be different in those situations, in either Newton's laws or any other? All physical laws are idealizations, and none of the idealizations give a different answer for m=0 than they give in the limit m->0. If that weren't true, physics just wouldn't work. Seriously.

 

[D H]

It can be shown by experiment that a photon will impart momentum to an atom when an atom emits or absorbs the photon. So the photon carries momentum ($p = h/\lambda$). In this respect, it behaves like a matter particle. But does it follow the first law? In these interactions with atoms, does its state of motion change? No. It doesn't. It always travels at c.

Not a good example, Andrew. You are talking about a regime where Newton's laws are known to fail. Newtonian mechanics break down at relativistic velocities. In Newtonian mechanics, the only speed that all observers agree is the same is an infinite one. We live in a non-Newtonian universe, where that maximum attainable speed is finite.

Suppose we did live in a Newtonian universe, where the maximum attainable speed is unbounded. Just as massless particles must travel at c in our real, relativistic universe, massless particles would have to travel at an infinite velocity in this hypothetical Newtonian universe. Just all observers agree on the speed of a massless particle in our relativistic universe, all observers would agree on the speed of a massless particle in this hypothetical Newtonian universe.

 

[Ken G]

Suppose we did live in a Newtonian universe, where the maximum attainable speed is unbounded. Just as massless particles must travel at c in our real, relativistic universe, massless particles would have to travel at an infinite velocity in this hypothetical Newtonian universe.

Or, alternatively, they'd have to be built to be unaffected by any forces-- no "charge" at all. Yet such particles could be treated in the limit as mass->0, simply by assuming a constant ratio of "charge"/mass. Indeed, this is just how Newton's laws were used to predict how gravity would bend light. The idea is simply to imagine that the photon has a very tiny mass, and assume the laws will work the same whether the mass is 10^-100 g or 0 g. The problem with the Newtonian version of light bending by gravity was not that it couldn't be done, it was that it comes out wrong by a factor of 2.

 

[Andrew Mason]

Not a good example, Andrew. You are talking about a regime where Newton's laws are known to fail. Newtonian mechanics break down at relativistic velocities. In Newtonian mechanics, the only speed that all observers agree is the same is an infinite one. We live in a non-Newtonian universe, where that maximum attainable speed is finite.

There are no examples of Newton's first law applying to objects with zero mass! I used the only one available. Of course, it does not work with photons.

AM

 

[Ken G]

There are no examples of Newton's first law applying to objects with zero mass!

Again, that is not correct. Light does not change motion when moving through a vacuum, that's Newton's first law. But it doesn't make any difference when the law applies, it's just a law, and it says what it says. Newton had no idea if it would apply to massless particles or not. Also, Newton's second law is easily applied to light, in the manner I mentioned above-- and it only gets the answer wrong by a factor of 2 because Newton's second law isn't right (in F=ma form rather than F = dp/dt form) when you are not in the rest frame of the object-- something he also didn't know and something that is not included in the laws.

 

[zoobyshoe]

Therefore, if Newton's first law applies throughout that sequence, as is the claim in that law, then it would also apply to a zero-inertia object. Ergo, the first law does not refer to inertia in any way. In other words, a law that does not care what the inertia is, does not refer to inertia.

Your logic is that, since the law allows for a fiction to be treated, it must be false when applied to realities?

 

[Ken G]

Your logic is that, since the law allows for a fiction to be treated, it must be false when applied to realities?

No, I said what is true: laws are just assertions, they are never responsible for when they are true. It can be part of a law to make such an assertion, in which case that is explicitly part of the law. Do you see any such thing in Newton's first law? Then it is irrelevant when the law is true, if you are simply trying to understand what the law asserts. Besides, as I said, Newton's first law works fine for particles with arbitrarily small inertia, including zero inertia, so in this particular case there is no fiction required. Of course, the law becomes questionable in quantum field applications-- again that is completely irrelevant to the issue of what the law asserts.

 

[zoobyshoe]

No, I said what is true: laws are just assertions, they are never responsible for when they are true. It can be part of a law to make such an assertion, in which case that is explicitly part of the law. Do you see any such thing in Newton's first law? Then it is irrelevant when the law is true, if you are simply trying to understand what the law asserts. Besides, as I said, Newton's first law works fine for particles with arbitrarily small inertia, including zero inertia, so in this particular case there is no fiction required. Of course, the law becomes questionable in quantum field applications-- again that is completely irrelevant to the issue of what the law asserts.

I have no idea what you're saying or where you're going with this.

Newton presented his three laws as "Laws or Axioms". Wiki defines axiom:

"In traditional logic, an axiom or postulate is a proposition that is not proven or demonstrated but considered to be either self-evident, or subject to necessary decision. In other words, an axiom is a logical statement that is assumed to be true. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths."

http://en.wikipedia.org/wiki/Axiom

which is probably close enough to what Newton meant when he used the term to be of service here. The "law or axiom" is asserted as truth in the interest of getting traction on a problem. It provides a basis for a train of logic in analyzing something. Einstein characterized physics as the attempt to get our minds in line with what is really happening in nature. I subscribe to that, and I think Newton and Andrew Mason would as well. The Laws or Axioms are not, therefore, "just" assertions. There's a good faith assumption that the proposer of any law or axiom believes it will lead to an understanding of reality and is not just proposing trains of logic which, however logical, have no bearing on reality. Your observation "laws are just assertions, they are never responsible for when they are true," strikes me as the expression of a peculiar attitude. I can't, at this point, even characterize it to myself.