## HSW2 – How I see Newton’s mechanics

This continues my discussion of how science works, a topic that I introduced in a recent post.  The “HSW” in the title of this post is intended to indicate that.  My plan, for this post, is to describe how I look at Newton’s laws.  I won’t be discussing his law of gravity here, mostly to keep this post reasonably short.  I might post on that at a future time.

## A note on history

I am not an historian.  My primary concern is with how the science works, rather than with how it was discovered.  If you think that I have said something about history, then you have misunderstood.  Some of what I am discussing here might actually be due to Galileo or to other scientists.

## Newton’s mathematics

I’ll start with a brief mention of Newton’s mathematics.  Newton was one of the inventors of The Calculus, which played an important role in Newton’s science.  In particular, his differential calculus made it possible to define velocity as $v=ds/dt$ (or the rate of change of position), and to define acceleration as $a=dv/dt$ (or the rate of change of velocity).  This provides a concept of instantaneous velocity and instantaneous acceleration (or, velocity at an instant and acceleration at an instant), instead of having only an average velocity or an average acceleration.  And because position can be seen as a vector quantity (having direction and size), velocity and acceleration can likewise be seen as vector quantities.

## Laws of motion

For a statement of Newton’s laws of motion, see the Wikipedia entry.  Incidentally, that Wikipedia entry does provide some historical background.  I shall refer to the laws as stated there, and presume that future editing of Wikipedia won’t change those statements too much.

Newton’s first law asserts that the natural tendency is for moving things to keep moving in a straight line, and to only vary from that straight path if some force is applied.  I see this as a methodological principle.

The tradition from philosophy of science seems to be to assert that the first law was discovered by induction.  It is very difficult to see how this could have been a matter of induction.  If I drop a rock, it falls down to the ground.  It starts at zero velocity when I release it, and then speeds up.  There is no evidence of any force being applied.  The Aristotelian view appears to be that falling was just the nature of things.  It was Galileo who questioned that traditional view, suggesting that a force was involved.  Note, however, that the view from Einstein’s relativity is that there is no force involved.  The relativist might possibly say that the rock is not really falling to the ground – rather, the ground is accelerating upward toward the rock.  For most of us, consistent with Galileo’s view and with Newton’s first law, we usually think of gravity as exerting a downward force.

It is my assumption that the traditional notion of force was not precise enough for us to be able to see that there were forces involved in changes of velocity.  And this is why it seems impossible for the first law to have arisen by induction, based on traditional concepts.

Newton’s second law quantifies the first.  That is to say, it precisely defines force in terms of the acceleration of the object.  This is an example of where Newton’s work on the calculus was important.  Because it is a definition, it is not arrived at inductively.  That it is a definition makes it a necessary truth, assuming that we accept the definition.  And that would make the second law an analytic statement.

I also see Newton’s third law as a methodological principle.  If I push against something (i.e. apply force), what I can feel is the force experienced by my hand.  We need Newton’s third law to be able to assert that the force applied to the object is identical to the force experienced by my hand.  And the same applies to any measuring device that we might use to measure force.  Patently, the measuring device measures the force on the device.  It is Newton’s third law that allows us to conclude that the force being measured is identical to the force applied to the device.

## Newton’s theory of moments

While perhaps less well known than Newton’s laws of motion, his theory of moments is also of great importance.  It deals with rotational motion.  We often find the mass of an object using a beam balance.  We place the object on one pan, and balance it with standard weights on the other.  We need Newton’s theory of moments to connect the forces on the one pan with those on the other, in order to explain the operation of the beam balance.

Once again, I see this as a methodological principle, rather than something that could be found inductively.

## Newton and time

Newton’s definition of velocity and acceleration both depend on time.  If we assume Newton’s laws, then the earth should be rotating at a near constant speed because there appear to be few external forces acting on it which are large enough to significantly alter that speed.  Astronomers were already using sidereal time, which measured time in terms of the earth’s rotation relative to the fixed (or distant) stars.  If we use sidereal time as our basis for measurment, then the earth is rotating at a constant speed.  If we instead use solar time (based on 24 hours from noon till the next noon), then the rotation speed of the earth is not constant.  It speeds up and slows down.  The Newtonian concept of time was based on sidereal time rescaled so that, on the average, a solar day would be 24 hours.  This was referred to a mean solar time.

Some philosophers of science have seemed troubled that data often seems to be theory laden.  For that would appear to contradict the common assumption that scientific theories arise by induction.  Indeed, the theory ladenness of data was one of the reasons that Popper objected to induction.

When we look at Newtonian science, as I have understood it, we can see why data is theory laden.  For Newton’s science consists primarily of methodological principles and definitions that define the kind of data to be used.

For sure, one cannot just pull methodological principle out of one’s hat and expect them to be useful.  There is a lot of testing and experience involved in deciding what will make for useful methodological principles.  Saying that the science consists of principles, and that the data is theory laden, in now way denies the importance of experience, both ordinary life experience and laboratory experience.  However, the relation between theory and experience is not a simple as inductionists would claim.

## How Newton’s science works

The traditional view seems to be that science works by discovery of patterns in nature, and that those patterns are discovered by induction.  I am unable to find any basis for that view.

My alternative view is that Newton’s science worked, and worked very well, because it vastly expanded the amount of information (data) available.  Based on his laws of motion, we could now talk about friction being a force and we could now measure that force.  We could now talk about air resistance as being a force, and we could now measure that force.  Later scientists could use this idea to define the unit of  static electrical charge based on the force of attraction/repulsion (as Newton had defined force).

Newton gave us a highly extensible way of gaining new information, and I see the productivity of Newtonian science as mainly due to the vast increase in the amount of information that we are able to acquire and use.

Newton’s approach to this was very systematic.  I see the mathematical structure of Newtonian science as arising from the systematicity of Newton’s methods.  If we were still using Aristotelian science, we would not be able to discover Newton’s laws as patterns in the data available to Aristotelians.