Re: The Fifth Dimension

From: Bilge (dubious_at_radioactivex.lebesque-al.net)
Date: 07/05/04 

Date: Mon, 05 Jul 2004 17:48:30 -0000

 Leonard Pardin:
>"Cozmo Man" <cozmologist@scientist.com> wrote in message news:

>> Assuming what you say is true, I wonder if you know just how those
>> mathematical symbols are to "relate to reality." For instance, taking
>> a very simple case, can you explain just how the mathematical symbol
>> "i", meaning the square root of minus one, relates to reality?
>
>
> "i" is the symbol of a mathematical operation--

  By the same token, so is the number `1' or \pi. Do you think a
better understanding of a circle will clarify what \pi ``really means?''

> but I understand
>your point. There may be times when an symbol in an equation stands
>for some physical thing we don't fully understand and can't describe
>in literal terms,

   Why do you conflate what _you_ ``don't fully understand'', with what
``we don't fully understand''? Isn't that a bit presumptuous, given that
those whom you are addressing have probably spent at least a decade longer
than you have studying how all of these mathematical symbols relate to
the physical ``things'' to which you refer?

>like Maxwell's "permitivity" or "magnetic flux." But that's also a sign
>of the limitations of mathematics.
 
  Have you considered the possibility that the limitations reside with
person _using_ the mathematics? Do you think it's reasonable to expect
someone to condense 8-10+ years spent learning something into a few
usenet posts containing everything you need to have a comparable
understanding of the subject?

> Mathematics tells us what "things" do and helps us to predict what
>they will do next, not necessarily what they are or why they do it.

   If I have 1 apple and I am given 1 more apple, it's a fairly safe bet
that I can deduce how many apples I really have by adding 1 and 1 to get 2
and infer that the number 2 is more than just a hypothetical abstraction
having nothing to do with real apples. The number `i' doesn't come up much
with apples, because an apple doesn't have a phase angle. Some things do
have phase angles, however, in which case, the number `i' happens to be
just the right mathematical symbol for the job.

>Newton's laws tells us what gravity does, not what it is or what
>causes it.

  Which was a major part of einstein's motivation to develop general
relativity.

>Planck's constant gives us a number to insert that makes an
>equation work, even though no one is sure why.
 
  That isn't really true either. By digging a little deeper, one
will come to realize that numbers like `6.626 x 10^-34 J-s' are
artifacts of units invented by people, which is made more obvious
by how inconveniently small it is in units based on meters, kg and
seconds. By digging still deeper, one will discover that angular
momentum comes in discrete units, so the natural way to denote
planck's constant is starting from the bottom as 1 unit of angular
momentum and going up, rather than from the top going down.

> Mathematics most certainly is essential to physics, because just
>describing what something is may be useless in learning what it will
>do next.

  It's only useless if you also think the only valid description of a
bolt has to be in terms of some combination of machines that bolts hold
together. I personally think defining a bolt in terms of a things like
thread pitch and bore diameter will give me a better idea how bolts
hold machines together even if those abstractions don't make any sense
when trying to describe a tractor.
 
>But discovering what something really is, what is behind the action,
>can be important in knowing where to look next, where to search next,
>and where not to go.

  What's wrong with accepting what the equations say something is, given
that you aren't going to describe a pion in terms of familiar items like
gears and pullies? Have you considered the possibility that an equation
that really predicts the behaviour of a pion contains the only things
which make a pion a pion? How about the possibility that concepts like
``cue ball'' and ``rack of balls'' aren't ever going to be a realistic
description of particle collisions?

>It seems, at least to me, that every attempt should be made to clearly
>describe the mathematical conclusions in our common language.

  Which elements of our ``common language'' would you suggest we use to
describe something which behaves in a way which differs from anything
upon which our ``common language'' is based? Why isn't that a fallacy?
The ``common language'' to which you refer is only common because
because people pointed to common things like apples and said ``apple''.
Not very many people point to angular momentum and say ``angular momentum'',
and I presume that particular mathematical abstraction wasn't a major
issue or else you would have to reject newtonian mechanics. Why is it
that kids accept the fact that they can learn new things like ``angular
momentum'' but adults can't accept the fact that they don't have all
of the knowledge necessary to understand something given a 5 second
explanation in terms of what they know?

> Remember, mathematics is not the only means of communication that
>uses symbols. The written and spoken language also uses symbols--and
>once the meaning of those spoken and written symbols have been
>decided, they should not be changed at random.
 
  Could you please spell the word ``unique'' without using the
symbol `q' and just use the ``common symbols?'' I've been wondering
if that word really exists since I can't spell it correctly without
having to resort to using the symbol `q' and `q' just isn't very
common compared to the symbol `n'.

>If mathematical formulae require that established definitions be
>abondoned--straight lines, Euclidian geometry, objective time,
>empty space--such that these accepted common concepts no longer
>have any meaning, then someone should question the mathematics.

  Then, I guess it's a good thing that mathematics has been developed to
make the meanings of those things much more precise than ever before.
 
>If some mathematician says we can no longer imagine a perfect Euclidian
>straight line but can only imagine curved lines instead, someone should
>challenge such an illogical and absurd statement.

  Please define a ``straight line'' in a way that isn' circular and
skips all of the superfluous professorial knuckleraps. Give me a physical
example of something that represents a ``straight line'' (again, without
being circular or falling victim to the lure of recreating in mathematical
compexity).

>If someone asserts that nothingness has corners, we have to reject such
>a statement or redefine "nothing" or "corners."
 
  Or, you might try defining both of those things in a way that leaves
no doubt about what you mean in the first place. Then, the obvious
thing to do is invent a new word which is also well-defined rather
than redfine an existing word. You'll have a harder time defining those
things precisely than you think you will. If the word ``nothing'' has
no precise common meaning which is suitable for use in physics, why
do you object to physicists giving a precise meaning for use in talking
to other physicists?

> So even though we nonmathematicians may be at a disadvantage in
>the physics world, we still have rightful place. We can challenge
>theories that offend our senses and garble our language. We have as
>much right as anyone else.
 
  No, you don't. No one writes journal articles based upon the assumption
that anyone other than physicists in the same field could expect to
fully understand them. Other might understand them, but ``understanding''
is a burdon placed on the reader. The author's only burdon is to explain
something another expert can understand, namely the referee whose job
is to be convinced the author has a plausible case for publishing the
article in the journal to which the article is submitted.

  You have the same right to burdon yourself with the responsibilty of
understanding an article you read. You have the right to send in your
criticism and try to make whatever point you want to make. You don't
have the right to insist you are exempt from having your criticism
rejected or ignored based upon not knowing what you are talking about.

  Would you trust a surgeon if the medical establishment caved in to
some irrational idea that physicians have acheived true understanding
when they can completely convey what they know using common language
like ``leg bone'' instead of ``femur'' or ``funny bent-over-forward
sort of posture'' rather than ``ankylosing spondylolisthesis'' just
because you think you have a right to criticize surgical technique
once some surgeon eliminates the fine points that would take too much
of your time to fully appreciate?

  Personally, I'd prefer physicians who differentiates between a femur, a
fibula and a tibia and between ankylosing spondylitis and ankylosing
spondylolisthesis and ankylosing spondylolysis, even if those aren't part
of the ``common language''.

  You might think that spending 4 years in medical school or 5+ years in
graduate school mainly involves going to lots of parties and holding
spelling bees over technical jargon on days that no one has a hangover and
bad weather prevents everyone from going to the beach. In reality, we had
to spend at least 1 hour a month reading a textbook and we had to bring a
note from a neighbor who promised, in writing, that we really spent an
hour holding the book right side up as proof we understood some of the
technical jargon used in the spelling bees. [Students also had to promise
that their neighbor's neutrality wouldn't be affected if the student
was sleeping with his/her neigbors, to safeguard the school's academic
integrity.]

  Of course, some schools might not demand any proof or allow for one's
dog or cat to substitute for a neighbor to vouch for the monthly 1 hour
marathon reading session, but that mainly happens only at third tier
institutions like the University of Antarctica, where your only neighbors
are one or two other students who might help each other cheat if an
impartial pet wasn't permitted to substitute for a neutral neighbor.

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