Re: [Phys-L] irrationals

[brian whatcott <betwys1@sbcglobal.net>]

Perhaps it would be helpful to creep up on a structure of irrational  
lengths - say a square of area 2. It is easy to specify rectangles of 
rational length that enclose slightly  different areas:  7/5 and 
10/7;    141/100 and 200/141; 1414 /1000 and 2000/1414 ;  14142136 
/10000000 and 2000000/14142136 and so on.
Which reminds me that mathematicians may insist that a recurring 
fraction of this form: 1.9999... is identical to 2 see 
https://arxiv.org/abs/0811.0164

Brian W


On 9/11/2017 1:49 PM, Bob Sciamanda via Phys-l wrote:
> Alex wrote:
> " .. . I  do not think I can really solve your (real) problem, but I 
> can say that
> one will  have a difficulty finding an actual real example of an 
> irrational
> number. . . . "
> Yes - my problem is not with the behavior of external reality. It is 
> with the impossibility of forming the very CONCEPT of an irrational 
> number - With QM weirdities it is  just the opposite..
> Thanks for the response, Alex.
>
> Bob Sciamanda
> Physics, Edinboro Univ of PA (Em)
> treborsciamanda@gmail.com
> www.sciamanda.com
>
>
> -----Original Message----- From: Alex. F. Burr via Phys-l
> Sent: Monday, September 11, 2017 2:38 PM
> To: Phys-L@Phys-L.org
> Cc: Aburr@aol.com
> Subject: Re: [Phys-L] irrationals
>
>
> IRRATIONAL NUMBERS
> Interesting. But why do you want a rational explanation of an irrational
> concept?
> -
> I  do not think I can really solve your (real) problem, but I can say 
> that
> one will  have a difficulty finding an actual real example of an 
> irrational
> number. There  is, of course, no real pair of lines with an irrational
> ratio. Every real line  will have an integer for its length. The 
> length unit
> cannot be made as small as  you wish because quantum mechanics will 
> rear its
> ugly head when the unit gets  small enough.
> What  about the square root of 2? It has no “reality”. It is a concept. A
> useful  concept, true; but you cannot write it down in any number system.
> (You can  define a symbol to represent the concept.) You CAN write down a
> number which  when multiplied by itself comes as close to 2 as you 
> wish, but it
> will never be  exactly 2.
>
>
> In a message dated 9/11/2017 11:46:19 A.M. Mountain Daylight Time,
> phys-l@mail.phys-l.org writes:
>
> I have  recently been pondering the concept of the irrational number.  
> This
> is a  number which cannot be expressed as the ratio of two integers.  The
> Pythagoreans rejected this concept and, according to legend, executed a
> member  who asserted (and proved) its existence.  An example is the 
> square root
> of 2 - the diagonal / side ratio of any square.  A little thought 
> leads  to
> the following  logical implication of the irrational number concept
> (quoting a Wikipedia author):
>
> " When the ratio of lengths of two line  segments is an irrational 
> number,
> the line segments are also described as  being incommensurable, 
> meaning that
> they share no "measure" in common, that  is, there is no length ("the
> measure"), no matter how short, that could be  used to express the 
> lengths of
> both of the two given segments as integer  multiples of itself."
>
> To me, this is a weirdity that rivals (perhaps  exceeds) the 
> weirdities of
> Quantum Mechanics.  Quantum weirdities are  concerned with the weird
> behavior of material objects.  The irrational  number is a weirdity of 
> CONCEPT -
> apart from any problems of measurement,  construction or material 
> existence.
> I simply cannot form a valid and  self consistent CONCEPT of such a 
> quantity.
>
> Somebody please straighten  me out!
>
> Bob Sciamanda
> Physics, Edinboro Univ of PA  (Em)
> treborsciamanda@gmail.com
> www.sciamanda.com