تناهي ابعاد، مساله‌اي هندسي يا طبيعي؟

Is the Problem of the Finitude of Dimensions Related to Geometry or Physics?

حكيمان مساله تناهي ابعاد را در مبحث «سماع طبيعي» از علم طبيعيات بررسي كرده‌‌اند. اما از آنجا كه تناهي و عدم آن از عوارض ذاتي مقدار است كه موضوع علم هندسه است، ظاهراً مساله تناهي ابعاد بايد از مسايل علم هندسه باشد. با توجه به آنكه حكيمان در كتاب‌هاي «سماع طبيعي» از اين بحث با عنوان تناهي اجسام نام مي‌برند و لفظ جسم ميان دو معناي جسم طبيعي و تعليمي مشترك است، مي‌توان گفت كه در علم طبيعي از تناهي جسم طبيعي و در علم هندسه از تناهي جسم تعليمي بحث مي‌شود، به تعبير ديگر در علم هندسه از تناهي ابعاد به طور مطلق و در علم طبيعي از تناهي ابعاد عارض بر ماده بحث مي‌شود و براهين تناهي ابعاد از علم عام هندسه به علم خاص طبيعيات نقل شده است.

The problem of the finitude of dimensions has been discussed by Islamic philosophers in “Physics”. However, since the finitude and infinitude are among the essential occurrings of magnitude, which itself is the subject matter of geometry, it seems that the problem should be classified among the geometrical problems instead of physical ones. In their works Islamic philosophers have discussed this problem as the problem of the “finitude of bodies”, and if we recall that “body” has two meanings in Islamic philosophy, the natural or physical body and the mathematical one, we can dissolve this problem by stating that what has been discussed in physics is the finitude or infinitude of the body in the first meaning and what has been discussed in geometry is the finitude or infinitude of body in the second meaning. In other words, the finitude of dimensions has been discussed in geometry in an absolute way, while physics has discussed the finitude of the dimensions as far as they relate to matter, and then the proofs of the finitude of dimensions in the general science of geometry have been transferred to the special science of physics.