CHASING DRAGONS BETWEEN DIMENSIONS: 

An Exploration of Fractals: Mathematics, Philosophy, and Reality (Mathematical Mischief: Unraveling the Secrets of the Numberverse) 

Is our vision patterned or we set up a patterned vision?  Perceptibility moves on certain liminal tropes and fault lines of imperceptibility. The blindspot too owes its due. Euclidean geometry streaks across higher realms of metaphysics with the makeover of fractals projecting much of a muchness.

This book starts on the nebulous note of transmigration of soul. A seasoned mathematics teacher does so while ‘chasing dragon curves’ albeit between fractal dimensions to ‘navigate the world around us’. Matthew Weinberg finds self similarity of perception, ‘a framework’ to be ordained as fractals. ‘Self similarity’ devours itself to beget forth and in turn they all get devoured. A cyclical symphony unfolds of what he calls, 'intuition and imagination'. The geometry of shapes has pervading realms of prescience into it. It is not a revelation. Matthew dwells on this interplay of perception and absolutism with geometrical lore. He hewns philosophy out of shapes and goes on patterning to construct and deconstruct philosophies. 

The book is non-technical and readers with a scientific bent of mind can relish its novel orientation. The narration of mathematical concepts is lucid for all and sundry. He poses numerous paradoxes such as Koch curve with infinite length but finite area and Koch anti-snowflake has a finite perimeter with infinite area. To comprehend the abstruse infinity, Matthew explicates the Cantor set in a riveting manner. Sierpinski shapes, Mendelbrot and Julia sets likewise find a vivacious account in the book. Again it is not just the shape but the profound implications of space and dimension, such as in Hilbert curve. There’s rare beauty to behold all this amidst ‘astounding complexity’. There’s a chapter literally going ad infinitum that stands out a brilliant exposition to read. Matthew uses the tesseract metaphor to comprehend time vis-à-vis the universe. Believe it, quantum entanglement falls in line with this fractal tesseract aka fractal universe. And then the nature of consciousness spills out to establish ‘the very nature of reality’. Some readers may find it a whiff of far-fetched supposition. Matthew has his robust line of arguments too.

The book brings together esoteric aspects and semblances in entire creation and in relating the varied facets of existence and non-existence too. Hyperdimensions tweak one’s intuition into astonishing complexity yet remaining imbued with the beauty of it. And then there is the fractional dimension that Matthew calls, ‘hallmark of the mathematical richness’. He goes on to lend several hands-on approach to fractals, not constrained to theory alone. Matthew analyses the software called Mendelbrot Viewer that is used to gauge the infinite universe and again he discusses the utiliy of Fractal Lab, Fragmentarium etc.     

Fractal pattern of dendrites and axons of neurons enable optimizing nervous communication. Our lungs and circulatory system too portray fractal geometry. Matthew vouches for ‘maximum efficiency in a compact space’ under the aegis of fractals. From Plato’s dialogues to machine learning, there’s an undertone to imply upon population patterns, analyze financial markets and devise modeling of biological processes.

Is the cosmos patterned or we set a pattern to the cosmos? The lightening snaps with fractal tag and so do galaxies roam with fractal flair to set the ‘fractal cosmos’. Matthew is infatuated with the fractal paradox ‘where the finite harbors the infinite’.

It’s natural for readers to doubt the claim of Matthew over the ambit of patterning everything like peas in a pod. So the credibility of the pervasiveness of fractals set a delimiting notion to cut everything from the same cloth thereby falling oblivious to the vastness and the freedom of creation. Verily, a question arises over the self replication of fractals attaining what Matthew calls ‘self similarity’. Is the all encompassing fractals some visual design or a property or even a phenomenon too? The author loosens out the paradigm of fractal that can be physical or just a property. Then the aura of ‘self similarity’ being cast in the same mould may deprecate with such a broad definition. Nonetheless, Matthew bolsters his claims with hard mathematics.

Even in the case of chaos, Matthew sees an undertone of fractals that ‘embody a delicate balance between chaos and order’. However to see a pattern in chaos may initially fall antagonistic upon readers. A pattern has an orientation and chaos runs berserk sans any order. The consonance of pattern and chaos as vouched by the author may be jarring to readers. Clouds that are symptomatic of randomness, they too pay heed to ‘self-similarity’.

Nonetheless Matthew Weinberg evokes a maverick trajectory to perceive not just shapes and linear progressions but to conjecture their ‘interconnected patterns and recursive processes’ kowtowing their implicit purpose of creation and existence. Such fathomless domain has ‘Many more fractals to be discovered; fractals that haven’t been imagined yet’. Singularity and multiplicity of creation play hide and seek.

If readers get dreary with ‘similarity’ swirling all around, then ‘Fractals are ever changing mathematical chameleons’ to provide them Bitcoins by prophesying blockchain trends. Fractals are serenading machine learning models to spot diseases in medical images.

What is set in order to square up? The leitmotif fractals have intrigued one and all down the ages and now Matthew Emmanuel Weinberg embarks on seminal dimensions to ‘measure, perceive and interact with our surroundings’. The ‘dragon curve’ calls our ecclectic perception to order!

Print Length: 282 pages