Learning first-grade Mathematics. But not knowing something has never stopped you from talking about it. In fact, the less you know, the more you blabber.
primitive axiom terms. > In mathematics these are terms that we agree upon to > use, but which > have no further explanation, such as a point is > without length width > or depth. Or a line has length only. Equality and > equivalence are also > primitive terms. > > In physics, when we have the Maxwell Equations with > the facts of > Chemistry as the axioms, there are primitive axiom > terms involved, > such as duality, rest-mass, electricity, magnetism, > energy, time, > space, momentum, charge, spin. > > I need to spend a little bit of time
Getting yourself to know what you're talking about.
discussing the > primitive term > equality and equivalence of mathematics and its > misuse and > understanding in mathematics and then its horrible > flagrant misuse in > physics. > > In mathematics, equality is sameness. So to say that > 2 = 2 means one > is the same as the other. But what about 2 = 1 + 1? > Well, in > mathematics, since math is abstraction and not > physical objects, that > 2 = 1 + 1, is just as acceptable as 2 = 2. So what > about equivalence? > In math, equivalence is something like 1/2 equivalent > to 3/6. Now in > physics, if we have a pie cut in 2 parts and a pie > cut in 6 parts, > that 1 part of the one pie is the 3 parts of the > other pie. Which is > not exactly sameness of math but similarity of math, > but for physics, > equality and equivalence are used when there is no > equality nor > equivalence. > > Now I am not here to straighten out math and physics > as concerns > equality and equivalence. I am here to draw attention > to this thorny > troubling problem that is in both mathematics and > physics. There is no > clear way of dismissing as to what is equal and what > is equivalent, > because 1/2 = 3/6 and > 1/2 equivalent to 3/6. > > But major problems do occur in physics when we think > that equality is > everywhere in physics. The equality or equivalence in > E = mc^2. It is > not really equality at all, nor is it equivalence. > > In physics, often the concept of "proportional" is > used. Now let us > try that on mathematics. Is it better to say 1/2 is > proportional to > 3/6, rather than say it is equal or equivalent. It is > safe to say that > 2 = 2, because equality is identity. But in physics > is it safe to say > the Coulomb force is a equality? Or is there equality > in the Maxwell > Equations? > > When physicists use "proportional" they still have > some linear factor > to include before they can put in a equal sign. So > that in Faraday law > emf is proportional to -dB/dt. Once we include the N > windings do we > have equality, emf = -N dB/dt. > > But do we really have equality in physics as in > mathematics? I would > say no, because mathematics is not physical objects > and physical > structure but rather abstraction divorced of physical > objects and > structure, whereas physics is all about objects and > structure. An > electron at point A in space is different from > electron at point B in > space, simply because they are at different > locations. The share the > same charge of -1 and other attributes but they are > not the same and > identical. > > So that in physics we just borrow the concept of > equality from > mathematics to allow us to make deductions. > > So I guess I can help a little bit, by saying there > are terms better > suited than equality or equivalence for physics. > Terms such as > "transforms" or "proportional" or "becomes" or > "changes" or "dual". > > So that in the formula E = mc^2 we can say energy > changes to mc^2 or > the neutron in this formula: > > Neutron = proton + electron + neutrino > we can say Neutron tranforms into proton + electron + > neutrino > > In the formula E = mc^2, perhaps the best term for > that is that Energy > is the dual of mc^2. So if we symbolize duality with > a O symbol and a > arrow in that O such as the arrow in -->, that the > equation looks like > this E Q mc^2, (sorry the keyboard cannot do the > symbol, but the > letter Q imagine that slash bar as a arrow in the > circle), meaning > that energy is the dual of mass * c^2. > > And so the four Maxwell Equations have no equal sign > but a sign of > duality. > > I do not want to spend much time on this because > someone can devote > their entire life on just this topic with no > guarantee of success or > improvement. > > I do want to point out the gray and prickly area of > logic of > "primitive axiom terms". > > And it should be obvious to all who master physics > that although we > should not use equality symbol in physics, we do so > anyway, since it > is the most practical means of going forward. So as > long as we keep it > back in our minds that equality is a symbol for > mathematics, but not > really for physics. > > -- > > Google's archives are top-heavy in hate-spew from > search-engine- > bombing. Only Drexel's Math Forum has done a > excellent, simple and > fair archiving of AP posts for the past 15 years as > seen here: > > http://mathforum.org/kb/profile.jspa?userID=499986 > > Archimedes Plutonium > http://www.iw.net/~a_plutonium > whole entire Universe is just one big atom > where dots of the electron-dot-cloud are galaxies