Tuesday, July 25, 2017

sci.physics.research Mathematics of physical units and dimensional analysis

Mathematics of physical units and dimensional analysis

Interesting clarifications, Jan.

Regarding agreed upon dimensions, typed algebras, decisions and
adoptions of conventions, and standardization in units in terms of of T
(or 1/T), doesn't all of this also expose why or how, people got/get the
idea that '~consciousness' and/or observation is ~necessary/related in
sorting out quantum mechanical ~results? ...That is, the ~mental-related
qualities or aspects are already (sub-consciously) inserted in an
earlier, previously adopted set of conventions and thus are already
'nested' in the activity/experience.

In the storyline I advocate and express, 'reality is nested
structured~duality' which means pick a structure and pick a duality
(that is, had I had a better math education, aka, in your terms: 'typed
algebras'). But, with this more unified (NSD) perspective, what we also
have is nested fields within nested fields, rather than just an
idealized or assumed L^3 (length-cubed) container containing other
collections which somehow, inexplicably pop in and out of
particle-anti-particle existence.

One can sort of conceptualize 1/T vibrational features in a nested
fields within nested fields system, perhaps as sub-divided tetrahedra
within tetrahedra, whereas it seems a bit more difficult to grasp 1/T
everywhere starting with the initial condition of an un-nested L^3,
cubic model.


Best regards,
Ralph Frost

Reality is nested structured~duality.

On Sunday, July 23, 2017 at 9:41:36 PM UTC-4, J. J. Lodder wrote:
> Tom Roberts wrote:
>> On 7/21/17 7/21/17   7:29 PM, rockbrentwood@... wrote:
>>> Physical quantities form a TYPED ALGEBRA.
>>> The system of types form an Abelian group with the identity 1
>>> standing for the type of dimensionless quantities
>>> A type judgement e: T means quantity e has type T, which in dimensional
>>> analysis means [e] = T.
>>> Addition and subtraction are subject to type-restriction: e + f and
>>> e - f are only defined if e:T and f:T, in which case (e +/- f): T.
>> OK, except there is also the concept of compatible types: cm and inches
>> (in) are not equal (same type), but are compatible:
>>       1cm + 1in = 3.54cm
>>       1in - 1cm = .606in
>>       1in / 1cm = 2.54
>>       2 * 1cm = 2cm
>>       1cm / 2 = 0.5cm
>>       convert(1in,cm) = 2.54cm
>>       convert(1cm,in) = 0.394in
>>       ... etc.
> That is just saying 'have the same dimension' in other words.
> And that has just the same problem:
> what is, or isn't deemed to be 'compatible'
> depends on your choice of units and dimensions.
> For example, is a centimeter compatible with a nanosecond?
> No, of course not, well indoctrinated kiddies will tell you
> with the wisdom of 1793.
> However, these days the nanosecond equals 29.9792458 cm (exactly)
> This is what your little GPS unit is doing for you:
> it counts, adds, and multiplies with all those nanoseconds,
> and presents the results of it all in meters or miles.
> (and of course also seconds, for it solves four equations,
> with four equivalent unknowns, to tell you when and where you are)
> In a very real sense the metric system came too early.
> (before the relevant physics was well enough understood)
> If we could start all over again
> there wouldn't be a separate length unit at all.
> (and E and B would have the same dimension)
> If we ever meet those fabled intelligent LGM in their UFOs
> we may discover that they find our having both meters and seconds
> a very quint idea indeed.
> (just like sane humans find it quaint that those Americans
> have both inches and miles)
> Jan

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