Dear Barry, As promised, I've pinpointed some mathematical errors in your book. And they are significant. I have said in my first email that it is "not a minor issue". The errors in the mathematical formulas are a serious threat to your theories, and they undermine the wording of ideas that might have been worthwhile otherwise. But despite of all this, there are still aspects in your work that I find trustworthy. Sorry I have to inform you in this way, but that's the way science works and the way it is demanded by just being honest. I would say: keep breathing. Thanks for your data too. My personal bias is that the universe in reality is much smaller and much younger and maybe those data might help to find some "I did it my way" confirmation. Best wishes, HanIt would be impolite to disclose the answer given by Setterfield here, because it's part of private communication. But my own answer to it is not subject to such a restriction. So here comes.
Allright, I see that you've adopted a different strategy. Let's try to summarize it.
It is supposed by you that the redshift is explained by the PPP, simply as:
$$
1+z = \frac{1+T}{\sqrt{1-T^2}} = \frac{1}{A-N}
$$
Then indeed it follows that:
$$
A-N = \frac{\sqrt{1-T^2}}{1+T} \\
T = \frac{1-(A-N)^2}{1+(A-N)^2}
$$
The derivative as derived by you is correct:
$$
\frac{dN}{dT} = \frac{1}{(1+T)\sqrt{1-T^2}}
$$
And upon substitution of $T$ we find, indeed:
$$
\frac{dN}{dT} = \frac{\left[1+(A-N)\right]^2}{4(A-N)} =
\frac{1}{4(A-N)}+\frac{1}{2}(A-N)+\frac{1}{4}(A-N)^3
$$
Now the only problem is to bring this, term by term, in agreement with the PPP equation:
$$
\frac{dN}{dT} = q - r\,N^2
$$
And yes, of course that is going to succeed if you assume that $q$ and $r$ are not constants
but vary with $N$.
Since I'm playing the role of a pure mathematician here, I cannot judge
if such is correct or not, so I'll give you the avantage of the doubt.
The mathematics could
have been done in a more concise way, but this time I've found no errors in it. Well done!
Kind regards,
Han