Leonard A. Smith > Quotes

“الواقع هو الذي عندما نتوقف عن الإيمان به لا يتلاشى”
― Leonard A. Smith, Chaos: A Very Short Introduction

“تقريبًا كلّ" بالنسبة للرياضي: عبارة رياضية معروفة تنطوي على تحذير من أنه على الرغم من أن شيئًا قد يكون صحيحًا 100% فثمّة حالات يصبح الشيء فيها خاطئًا.
"تقريبًا كلّ" بالنسبة للفيزيائي: تقريبًا كلّ.”
― Leonard A. Smith

“Taking least squares is no longer optimal, and the very idea of ‘accuracy’ has to be rethought. This simple fact is as important as it is neglected. This problem is easily illustrated in the Logistic Map: given the correct mathematical formula and all the details of the noise model – random numbers with a bell-shaped distribution – using least squares to estimate α leads to systematic errors. This is not a question of too few data or insufficient computer power, it is the method that fails. We can compute the optimal least squares solution: its value for α is too small at all noise levels. This principled approach just does not apply to nonlinear models because the theorems behind the principle of least squares repeatedly assume bell-shaped distributions.”
― Leonard A. Smith, Chaos: A Very Short Introduction

“Embedded in the mud, glistening green and gold and black,
was a butterfly, very beautiful and very dead.
It fell to the floor, an exquisite thing, a small thing
that could upset balances and knock down a line of
small dominoes and then big dominoes and then
gigantic dominoes, all down the years across Time. Ray Bradbury (1952)”
― Leonard A. Smith, Chaos: A Very Short Introduction

“Throughout this Introduction we will see that confusing our mathematical models with the reality they aim to describe muddles the discussion of both.”
― Leonard A. Smith, Chaos: A Very Short Introduction