Please don't let me miss Autumn this year

 

Beech avenue, Manor Kilbride

Last year I apparently missed it. So even though it was overcast (contrary to the weather forecast) I ventured out with the intent of making it to the Sally Gap and the two Bray Loughs (far left in map below). Alas I ran out of time and was cold anyway so took my photos and hurried home. To lamb chops and apple pie (not together) courtesy of my beloved daughter (one of them).  Here's a link to more photos.

33 miles, elevation gain 720m

The end is nigh

 Moore's Law is the empirical observation that the number of transistors in a dense integrated circuit doubles about every two year and it has approximately held true since it was proposed in 1965.

It is driven by the economics of the insatiable demand for ever increasing electronics complexity and the steady reduction in feature size in the fabrication of silicon chips (integrated circuits).

In 2013 Robert Calwell vowed the end would come in 2022, maybe even 2020, with the herald of 7nm and even 5nm feature size.

And today the BBC has announced that Apple's new flagship iPhone 12 will incorporate the "A14" processor with 5nm feature size - the chip's transistors have been shrunk down - the tiny on-off switches are now only about 25 atoms wide - allowing billions more to be packed in.

These electronic chips use "solid state" technology, i.e. they have no moving parts which makes it sound like they can never wear out, will last forever short of physical damage. Alas, such is a dream. I am well used to using Flash and other types of non-volatile solid state memory (chips) in my work and I am all too aware that the specification documents mention a lifetime of sometimes as little as 100,000 re-write cycles. When software is running at GHz speeds this many can clock up quite fast!

Chips are made by first growing a very pure silicon crystal, slicing it into wafers, and then diffusing into it a photographic pattern of known amounts of certain impurities that give the silicon its required special electrical properties. Diffusion (the intermingling of substances by the natural random movement of their particles) is both the essential mechanism and Achilles' heel of solid state chips.

Back in college days I was told that the lifetime of a solid state circuit was limited by diffusion - what can be diffused in to make it work can, by the same token, diffuse out and self destroy it. OK, it is diffused in at high temperature where the particles are in much stronger random movement, so what may take seconds to diffuse in might take many years to diffuse out at room temperature. But the smaller the feature size, the more likely that diffusion defects can occur - the particles have less distance to move.

The aging problem is discussed in this paper - so I am not just imagining it!  Many people regard their cell-phone as a consumable item, with expectation that it be replaced after a year or so. Those people may have limitless bottoms to their purses but I, for one, am happy enough with my Pixel 2 and have no desire to shell out to upgrade it. So I'm hoping that all those billions of transistors inside will not diffuse into randomness too soon. All are of the dust, and all turn to dust again.

Sorrel Hill

My track 22.5 miles part cycle part hike

OpenTopo map

Sunday afternoon again, and mild at 12'C and the mountains were calling again. Or "hills" if you insist. The last time I climbed (hiked) up Sorrel Hill was many years ago and with my daughter S. It was one of those father-daughter times. Our route back then was different from mine today.

So I started by deciding to cycle around the Lake Drive, but stopped at Lacken to inspect the tourist map they have erected and which informed me that just a few yards to the left I would find access to the "MASSPATH", and so I did and, oh my - I have to apologise for maligning Ireland's lack of well maintained footpaths! This end in particular but the whole trail was well maintained. I could not resist such a temptation so I rested my bike against a handy post, removed shoes and helmet and set off. I met perhaps a dozen other people - I think Covid has encouraged folk to get outdoor exercise. There were the usual comments on my lack of shoes, but all very friendly.

If you look closely you might notice the hang-gliders, even a powered one, and a bi-plane

 

Elegance

Elegance - the beauty of an idea characterised by minimalism and intuitiveness while preserving exactness and precision.

Complex - not simple, easy or straightforward. A Complex system is one that has multiple paths to multiple answers.

So now I've learnt how to make Julia sets.  Using the same colour palette as for my Mandelbrots here are a couple of my home made images. Of course there are far better ones on the internet, but I'm pretty pleased that I have even got this far. 

The Julia and Mandelbrot sets are mathematically very similar, so my program can generate either. The maths is so very simple - elegant indeed. But the resulting fractal images are complex, anything but simple. And there's the rub - the conjunction, the juxtaposition, the synergy of elegance and complexity. We see it again and again - the human body for one - such complexity from relative simplicity of DNA. The 90 or so naturally occurring chemical elements that are each made up of so few elementary particles (the periodic table and all that) giving rise to such diversity of materials and, indeed, life. How such a vast assortment of vividly coloured flowers are created from dirt, water and sunlight. Water gushing over a precipice: any student can calculate its maximum rise in temperature as it falls, but how to predict its impact as you swim beneath its fall?. And of course the much maligned "butterfly effect".

For those interested but too idle to google for themselves, the Mandelbrot set is the set of points c on the complex plane (aka Argand diagram) for which the iteration formula is bounded (z does not fly off to infinity), starting with z = 0.  There is a Julia set for every point c in the Mandelbrot set and it is the set of points z on the complex plane for which the same iteration formula is bounded, starting with z = that point. It can be proved (so I am told) that if, during the iteration, the modulus of  z exceeds 2, then z is bound to be unbounded: we need iterate no further. For cases that never or are slow to reach that stage, the iteration ought to go on ad infinitum - in practice such a requirement is onerous, and instead one sets an arbitrary limit of the number of iterations, for example 500.

Here's two of my favourite Mandelbrot zooms:

A trip to infinity - 2 hours 

The deepest hard zoom at 100,000,000 iterations - zoom depth 10^2126

The guys who create such videos (God bless them) have access to better software than mine but even so take perhaps a month or more of computer time to do the job. Not for the faint hearted or those of us with other more pressing calls on our time!

My brain still has problems understanding how so much complexity is bound up in so simple an equation.

This, my interest in Mandelbrot et al, started when reading an article about deep learning. Deep learning is AI (artificial intelligence) on steroids. The mechanics is based on a neural network (i.e. that tries to mimic how the human brain works). Faced with a complex task, for example recognising a particular face in a picture of a crowd, rather than trying to figure out software code that analyses the face you "simply" show the deep-learning-thing (DLT) zillions of pictures of the face in question from many angles and in many circumstances and with varying expressions.  Then when faced with the picture to be analysed, the DLT does a sort of mathematical correlation with all the pictures it has been shown and comes up with a score, a likelihood of each face in the picture being the one. Etc. A very different way of approaching software and clearly akin to what goes on in the brain (for those of use lucky enough to have one). Deep learning is the in-thing at the moment.  If you are young and mentally supple enough to get a grasp of all this, I'd imagine that designing these DLT's is the way to go. Or if interested in investing your fortunes, investing in DLT's might prove profitable. 

Deeping learning, complex systems, AI, chaotic systems, fractals (e.g. the Koch snowflake which has infinite perimeter and yet a finite area.  Plenty here to keep me amused for many a let's-avoid-Covid evening.