Re: Reconsidering Halton Arp

In article <[EMAIL PROTECTED]>,
Daniel Grubb <[EMAIL PROTECTED]> wrote:
>
>>>>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.

I never really thought about fractions as such a conceptual advance.  And 
if the Greeks had thought about fractions, one of them would have been 
sure to have worried about a ratio of distance to time that can't be given 
as a ratio of integers, and drawn conclusions about the validity of the 
method or the nature of motion from that.


-- 
"You're not as dumb as you look.  Or sound.  Or our best testing
indicates."  -- Monty Burns to Homer Simpson