SCIENCE

a - independently measured variable

b - independently measured variable

c - independently measured variable

Functions of a scientific theory

a(a,b) - theorized function

b(a,c) - theorized function

c(a,b) - theorized function

Scientific discoveries:

All variables: a, b, and c.

All functions: a(b,c), b(a,c), and c(a,b).

x - independently measured variable

y - independently measured variable

z - independently measured variable

r - calculated variable

Functions of a scientific theory

r(x,y) - theorized function

z(r(x,y)) - theorized function

Scientific discoveries:

Most variables: x, y, and z.

One function: z(r(x,y)).

Conclusion:

The scientific theory can help us predict the value of an independently measurable variable as long as we know the value of other variable(s).

PSEUDOSCIENCE

a - independently measured variable

b - independently measured variable

c - calculated variable

Functions of a pseudoscientific "theory"

c(a,b) - theorized function

b(a,c) - theorized function

a(b,c) - theorized function

Scientific discoveries:

The variables a and b.

Conclusion:

The pseudoscientific theory was not needed.

APPLICIATION IN COSMOLOGY:

Independently measurable

- spectrum

- spectral pattern

- redshift

- photon count

- exposure length

- angle between approaching photons at surface of imaging

- angular width of an image

- angular change of position in the sky

Calculated

- angular width of the object which was imaged

- brightness of an object at its surface

- comoving distance

- light travel time distance

- luminosity distance

- angular diameter distance

- radius of a galaxy

- radius of the universe

- age of a photon from the Cosmic Background Radiation

- age of the universe

- mass of a galaxy

- mass of a cluster of galaxies

- 4D velocity of a galaxy

RULE OF SCIENCE: Each of your calculated variables must be used to predict variables outside its definition. For example r may be derived from x and y, which then may be used to calculate z, which can be formulated in terms of x and y alone. Discontinue use of those calculated variables which do not serve any purpose in determining independently measurable variables outside its definition. A theory whose aim is to show these calculated variables to be the case cannot be a scientific theory. Calculated variables must serve simply as tools of math to get from one set of independently measurable variable(s) to another - in correspondence with observations.