Question: In Newtons *Principia* he wrote:

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> Absolute, true and mathematical time, of itself, and from its own nature flows equably without regard to anything external, and by another name is called duration.
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Hence, Newton distinguishes *three* forms of time - absolute, true and mathematical - and then identifies them.

Whereas for Aristotle, time was an aspect of change, and of which one aspect is physical motion; Newton reverses this conception, in a sense.

Thus, Newtonian time flows everywhere in space at the same rate; so for a man positioned somewhere in space he can 'see' in a sense (as in McTaggarts 'tensed' time) the future coming forward becoming the present and then going behind to the past; or in Heracleitian imagery time is like a river.

But it's the relative motion here that counts.

So, one might equally say that time rather than flowing like a river, stands still, like a lake it's surface is unruffled; until one puts a particle on it, which then moves ahead of its own volition.

This in fact is the usual way that one describes the classical trajectory of a cannonball in a space and time diagram; an exercise that one might do at school, say on graphed paper with the horizontal axis for time and the vertical one for displacement.

So, here - time does not *flow*; the cannon-ball *moves* in time.

The difference between the two pictures, Newtons original conception and the standard one taught is not usually remarked on. 

Philosophically, or ontologically, though, is there a difference between saying that time flows or not? 

Even when the physical picture, the expressed by calculations in Newtonian Physics, give the same result?

Answer: 
Newton has only one form of time, Absolute Time, but with three atributes: absolute, true (whatever that means) and mathematical. He then identifies it with idealized form of subjective "duration" as well. The particle does not move "of its own volition" though, Absolute Time drags it along in synchrony with everything else. And synchronous motion of multiple disjoint particles is exactly the mathematical picture of ideal fluid flow. So Absolute Time flows, it is just a uniformized, depersonalized, mechanized, really really boring kind of flow. 

But it is a flow, Newton specifically rejects relativity of motion, so contra Galileo uniform motion is not the same to him as rest, perception alone is not enough. The lake standing still with frozen present, past and future is metaphysically different. In [Newton: A Very Short Introduction Iliffe writes:](https://books.google.com/books/about/Newton.html?id=BfaAds6XKosC)

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> "*Newton remarked that ‘ordinary people who fail to abstract thought from sensible appearances always speak of relative quantities so much so that it would be absurd for wise men or even Prophets to speak to them otherwise’. Without the reference to theology, this significant view made its way into the Principia, where the vulgar were said to consider quantities only as they related to ‘perceptible objects’. However, Newton went on, ‘in philosophical discussions, we ought to step back from our senses, and consider things themselves, distinct from what are only perceptible measures of them’*". See 
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I think this has more to do with the idea of *fluxion* and the cohesiveness that surface tension gives to fluids, not of relative motion.

To think of the thing that allows for motion as moving seems like a logical trap that can only lead to paradoxes.

We segment the metaphor of fluidity into at least three aspects. Time 'flows' in that it maintains continuity (as in the way hair or robes flow, even if they don't move) not in that it arrives at a given rate (the way bullets might flow out of a machine gun) or that gets from one place to another (the way traffic flows).