Re: Reconsidering Halton Arp

>>>And it occured to me today to wonder which he was referring to.  Was much 
>>>of a distinction made in Aristotle's day between velocity and 
>>>acceleration?
>>
>>Of course not! The concept of acceleration would have been quite outside
>>of the mindset of that time. In particular, you could only consider
>>ratios of like things, eg. lengths and lengths, times and times.
>>Doing even a velocity (ratio of length and time) was stretching
>>things. Usually for 'constant velocity' they said something about
>>the ratio of the lengths traveled and the ratio of the times taken
>>being equal.
>>
>>It wasn't really until Oresme in the 14th century that even constant
>>acceleration was thought about. And Oresme was way ahead of his time.

>Looking back from the 21st century, that seems strange.  Clearly states of 
>motion change.  That must be one of those paradigm things.  They could 
>determine how far something goes, and how much time it took, and the thing 
>that gets there first went faster.


And they were aware of that, of course. But they had no mathematical
way of thinking about it. Remember that ratios were *not fractions* for 
these people. They could talk about equal ratios, but did not consider
ratios to be numbers. Furthermore, the ratio of say, an area to a
length was just not allowed, let alone a ratio of a length to a time.
It really was a major advance to be able to think about velocity
as a separate thing and as a ratio.

--Dan Grubb