This question initially arose while translating a technical document from German. The original text was 'physikalische Heizzonenummer', literally 'physical heating-zone-number'.

My immediate reaction was to think of heating zones which are numbered 1 to n but which can be addressed in other 'logical' ways. However, the German does seem to mean that the number itself is 'physical'. For me, a number is a concept and cannot be physical (except for those digits you can screw on to your front door). You can have a group of physical apples or heating zones but a number allocated to each one is surely in itself not physical itself.

Am I wrong here? Perhaps the original German is a bit clumsy and imprecise but it just set me wondering about the concept of numbers. I would be interested to hear other opinions :-)

  • Is the Heating Zone 'physical'? – Autoresponder Sep 7 '11 at 6:32
  • @user11761 - there are physical heating elements in the machine arranged in zones. So I guess the zones are physical. To be honest I don't know how they might be logically organised. Perhaps they can be grouped (e.g. as pairs) and then addressed logically rather than physically – paul Sep 7 '11 at 6:38
  • Can you first elaborate on what exactly is heating-zone-number? I'm in no way an expert in German and can't understand the meaning from just literal translation of one short phrase. – Philoto Sep 7 '11 at 6:41
  • Is the heating zone physically labeled with the number? (That would be similar to those digits for your front door). – D Krueger Sep 7 '11 at 6:44
  • @Philoto - that's really my point. See the second paragraph. I would say that you can enumerate physical and logical objects but a physical number itself makes no sense – paul Sep 7 '11 at 6:45

Can we? Probably not. A number is an abstract object, not a real thing, and we can't give an abstract idea/object the description of a physical object. A number, as defined by Wikipedia is:

A number is a mathematical object used to count and measure. A notational symbol that represents a number is called a numeral but in common use, the word number can mean the abstract object, the symbol, or the word for the number

A mathematical object is an abstract object.

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