Dear Aidan,

My wife is not a JW. She told me that in her Protestant Sunday School they were told to pick a Bible verse at random and memorise it for homework. It didn't matter what it was. In that method it was taken out of context and not discussed. It is not unique to Protestantism or to Christianity. Some Jewish schools have their students learn the Jewish Bible by rote. Madrassas have their student memorise the Koran. Scripture can be studied in a methodical purposeful way, but that is usually the way it is done. When it is studied in a methodical purposeful way students may become aware that is basically nonsense and leave the faith.

Virgin birth, trinity, Nirvana, dietary laws, supernatural beings etc. are all nonsense which do not stand up to logical analysis.

Nothing prevents me from dissenting. I find the history and beliefs of religion fascinating but recognise it is basically superstition. Many thoughtful people simply abandon it. It don't think it will ever disappear as it fulfills a need for the gullible and a sense of community for those who would otherwise be rootless.

Dear Craig,

I have no Erdos number. My dinner with Erdos was when I was a student at Syracuse University.

My mathematical work has been all in applied math. Computer design, computer algorithms, Fourier transform development, linear and dynamic programming, computer displays, medical applications. I am 89 retired 27 years ago and have not kept up with the field.

When the article you referred to mentioned the difficulty of a computer simulation the implicit meaning was that it referred to a digital computer. The pipe itself through which one sends the fluid can be regarded as an analog computer. A transparent pipe and photographs of the birth and death of the puffs should provide the data for computation of the Reynolds number.

You're quite right, David, that is the gist of Hof's work, but it's also true that defining the transition point has been an elusive problem for a very long time.

In undergrad fluid mech laminar flow is defined very vaguely as being below Re 2000, with the transitional range as high as Re 5000 in some texts. Hof, by narrowing it down to ~2040 and redefining turbulence effectively in terms of propagation of "puffs", has done something very important, that I suspect will have very significant implications for flux generally, not just fluid velocity fields, in the same way as Stokes' work did.