Tag Archives: Isaac Newton

A book worth buying for the preface alone (or how to review a book you haven’t read)’

Everyone in grade school writes a book report on something they haven’t completely read (or read at all). Well, I’m long past, but here’s a book worth buying for the preface alone — Visual Differential Geometry and Forms by Tristan Needham.

His earlier book Visual Complex Analysis (another book I haven’t read completely) is a masterpiece (those parts I’ve managed to read) with all sorts of complex formulas and algebraicism explained visually.  It’s best to be patient, as Needham doesn’t even get to complex differentiation until Chapter 4 (p. 188) The Amplitwist concept.

On page xviii of the preface, Needham describes the third type of calculus Newton invented, and the one he used in the great Principia Mathematica of 1687.

The first one of 1665 was basically the manipulation of power series (which I’ve never heard of.  Have you?)

The second was one we all study in school, dx dy and all that.

Newton called the third method of calculus “the synthetic method of fluxions.”

Bishop Berkeley had a field day with them.  “And what are these fluxions? The velocities of evanescent increments? And what are these same evanescent increments? They are neither finite quantities, nor quantities infinitely small, nor yet nothing. May we not call them ghosts of departed quantities?”

Laugh not at the good Bishop;   Berkeley California is named for him (as long as the woke don’t find out).

Needham gives a completely nontrivial example of the method.  He shows geometrically how the derivative of tan(theta) is 1 + [ tan(theta)]^2,.

The diagram will not be reproduced here but suffice it to say you’ll have to remember a lot of your geometry, e.g. two lines separated by a very small angle are essentially parallel, the radius of a circle is perpendicular to the tangent, what a similar triangle is.

The best thing about it is you can actually visualize the limit process taking place as a triangle shrinks and shrinks and eventually becomes ‘almost’ similar to another.  No deltas and epsilons for Newton (or Needham).  There is some algebra involving the ratios of the sides of similar triangles, but it’s trivial.

Buy the book and enjoy.   You’ll never think of differentiation the same way.  Your life will be better, and you might even meet a better class of people.

Goodbye to the blind watchmaker — take I

The Michelson and Morley experiment destroyed the ether paradigm in 1887, but its replacement didn’t occur until Einstein’s special relativity in 1905.  One can disagree with a paradigm without being required to come up with something to replace it. Unfortunately, we tend to think in dichotomies, so disagreeing with the blind watchmaker hypothesis for life itself tends to place you in the life was created by some sort of conscious entity.  “Hypotheses non fingo”  (Latin for “I feign no hypotheses”) which is what  Newton famously said  when discussing action at a distance which his theory of gravity entailed (which he thought was pretty crazy).

Here are  summaries of four previous posts (with links) showing why I have problems accepting the blind watchmaker hypothesis.  These are not arguments from faith which nowhere appears, but deduction from experimental facts about the structures and processes which make life possible. Be warned.  This is hard core chemistry, biochemistry and molecular biology.

First the 20,000 or so proteins which make us up, a nearly vanishing fraction of the possible proteins.  For how vanishing see — https://luysii.wordpress.com/2009/12/20/how-many-proteins-can-be-made-using-the-entire-earth-mass-to-do-so/.  Just start with 20 amino acids, 400 dipeptides, 8000 tripeptides.  Make one molecule of each and see how long a protein you wind up with making all possibilities along the way.  The answer will surprise you.

Next the improbability of a protein having a single shape (or a few shapes) for some chemical arguments about this — see https://luysii.wordpress.com/2010/08/04/why-should-a-protein-have-just-one-shape-or-any-shape-for-that-matter/

After that — have a look at https://luysii.wordpress.com/2010/10/24/the-essential-strangeness-of-the-proteins-that-make-us-up/.

The following quote is from an old book on LISP programming (Let’s Talk LISP) by Laurent Siklossy.“Remember, if you don’t understand it right away, don’t worry. You never learn anything, you only get used to it.”   Basically I think biochemists got used to thinking of proteins have ‘a’ shape or a few shapes because that’s what they found when they studied them.

If you think of amino acids as letters, then proteins are paragraphs of them, but to have biochemical utility they must have ‘meaning’ e.g. a constant shape.

Obviously the ones making us do have shapes, but how common is this in the large universe of possible proteins.  Here is an experiment which might show us (or not)– https://luysii.wordpress.com/2010/08/08/a-chemical-gedanken-experiment/.

From a philosophical point of view, the experiment is quite specific.  From a practical point of view quite possible to start, but impossible to carry to completion.

Well this is a lot of reading to do (assuming anyone does it) and I’ll stop now (although there is more to come).

Why do this at all?  Because I’ve been around long enough to see authoritative statements (by very authoritative figures) crash and burn.  Most of them I didn’t believe at the time — here are a few

l. The club of Rome’s predictions

2. The population bomb of Ehrlich

3. Junk DNA

4. We are 98% Chimpanzee because our proteins are that similar.

5. Gunther Stent, very distinguished molecular biologist, writing that we were close to the end of our understanding of genetic biology.  This in 1969.

The links elaborate several reasons why I find the Blind Watchmaker hypothesis difficult to accept.  There is more to come.

“Hypotheses non fingo”