6: Combination Rule/Regraduation Function- transforms speeds into quantities that
	are additive in the same way that slopes are not additive, but angles are.
	-Should satisfy: identity (0), annihilator (c), assosciativity,
		4) d(u@v)/du and d(u@v)/dv exist and cnt in u and v
		5) d(u@v)/du>0 and d(u@v)/dv>0 provided u,v!=0,c
8: If you assume that the combination rule must be symmetrical and linear,
	it must be of the form:
	 l+m(u+v+w)+n(vw+wu+uv)+puvw=0  (u,v=input speeds k=resultant speed, w=-k)
	-When u,v=0, w must be 0 too, so l=0
	-More generally, if v=0, then w=-u so l+n(-u^2)=0
		therfore, since l=0, it follows that n=0
		We now have: m(u+v+w)+puvw=0
	-From the universal property if v=c, w=-c so: 
		mu-puc^2=0 => m=pc^2
		We now have:    pc^2(u+v+w)+puvw=0
				c^2(u+v+w)+uvw=0
				w(c^2+uv)+(c^2)u+(c^2)v=0
				k(c^2+uv)=c^2(u+v)
				k=c^2(u+v)/(c^2+uv)
				k=u+v/(1+uv/c^2)
9: This is similar to the hyperbloic tangent function:
	tanh(u+v)=tanh(u)+tanh(v)/(1+tanh(u)tanh(v))
	So this suggests regraduating using: u=c*tanh(phi)
	Which makes phi=arctanh(u/c)
	Then cosh(phi)=1/sqrt(1-v^2/c^2)=gamma (originally Beta by Einstein)
12: Hyperbolic trig functions differ from ordinary trig functions only in their
	exponents differing by a factor of i.
---------End of Chapter 1--------- 
51: F=dP/dt  -equivalent way of expressing force, more compatible with QM
76: Twins Paradox- It seems like there is a paradox because both see the other
	going through time slower than themselves, but the spaceship twin leaves
	out a big period of time in the middle that corresponds to him turning
	around to come back to earth, which is the result of shifted lines of
	simultaneity. The earth twin has an uninterrupted view, so his calculations
	are correct and the spaceship twin ages less.
192: It is often said that the Special Theory implies that mass increases by the 
	proportion of gamma, but this is only one of the two equivalent ways of 
	interpreting it. Einstein didn't use this one, he used the convention that
	mass stays constant.
208: Orientable- doesn't allow continuous transformation of left-handed figures into
	right-handed figures.
214: Handed-ness has a fundamental asymmetry in some processes(favorative of one hand)
	but it appears that this is just the manifestation of a higher order symmetry
	(three factors combined are conserved, handedness alone isn't)
236: Einstein asked: Why is the inertial mass of a body the same as its gravitational 
	mass?
xxx: Covariant- varying together so as to preserve mathematical relations
248: Bradwardine- Galileo studied his formulation that acceleration is the derivative
	of velocity with respect to time rather than with respect to distance.
285: Huyghen's Principle- in 3D space, the wavefront remains sharp so that a sharply
	localized initial state is observed later as an effect that is equally 
	sharply delimited. -Uses example of ripples in the surface of a pond to 
	show that it doesn't work for 2D, but this is questionable because it seems
	like the only reason multiple ripples occur is because of the extra dimension
	of freedom that height allows for. It then claims that different scientists
	proved that different dimensions also didn't work until eventually only 3
	was left.
293: Arago Spot- used initially to falsify the wave theory of light because it 
	wasn't found, until Arago went looking for it and found it, hence
	falsifying the falsification
293: After metioning Rutherford's foil experiment: "Equally unexpected was the
	inversion of the tip-top." Then later: "The tip-top phenomenon, on the other
	hand, turned out to be deducible from classical mechanics." -I could not find
	further information on this!