About me (Robert Walker)
I'm a mathematician and a music software developer, author of Bounce Metronome and Tune Smithy. I have an MSc in Maths (first class), and MHum (a second undergraduate degree in philosophy done as a postgraduate course).
I studied for postgraduate at Oxford University but I didn't complete my doctorate. However that gave me the background in checking sources and how to read academic papers which has been very useful for my science blogging.
Nowadays I spend most of my time helping people who are scared of asteroids, climate change, cosmic disasters, and this has lead me to write many science blog posts on climate change, asteroids and various other topics, applying the same rigour and attention to detail that I learnt for my mathematics research. I have been following many of these topics since my childhood in the 1960s.
I also write science blog articles and kindle books with a strong focus on planetary protection, and careful and responsible space exploration respecting Earth as our "pale blue dot", a place to cherish, and the only place in our solar system where humans can live without protection from a vacuum or a hazardous atmosphere. My Touch Mars? Europa? Enceladus? Or a Tale of Missteps on Kindle seens to be the first book written for the general public on planetary protection, it also goes into "galaxy protection" and is over 2,000 pages.
I have also written a kindle book for musicians "Vanishing Metronome Clicks, for Timing Sensitivity" (also available to read online for free) coming out of my research for my software Bounce Metronome, and a book of 163 of my recorder tunes as "Recorder Tunes from the Heart".
Also as a part time job now, perhaps 15 hours a week, I work on my software business, selling my programs: Bounce Metronome,Tune Smithy, Lissajous 3D and Virtual Flower over the internet.
I'm a mathematician, from the UK, currently living on the Isle of Mull in Scotland where I work from home as a software developer selling my own software over the internet. I studied at York university, got a good first class degree, and went on to do a second undergraduate degree in philosophy - then did postgraduate research at Oxford for some years. Neil Armstrong and Buzz Aldrin landed on the Moon when I was 14, soon to turn 15, so I'm an Apollo era kid. I've had a long term interest in science, and astronomy (armchair amateur astronomer). I grew up with Patrick Moore explaining astronomy on TV. I write a blog at Science20. I have a special interest in planetary protection and my article "Ten Reasons Not to Live on Mars, Great Place to Explore" lead to an invitation as the guest for David Livingston's "The Space Show" podcast and radio broadcast on the US east coast (an hour and a half program). I've had three return visits to his show. I also write answers on Quora, on space exploration, astronomy, science, mathematics, music, and many other topics, and have been top contributor there for the last two years. I've had articles published in Forbes Magazine, The Huffington Post, Slate, Newsweek, and Business Insider. The most recent is my article for Forbes "Is There A Fortune To Be Made On Mars?"
I was also guest speaker for a conference on the search for extra terrestrial life in the subsurface oceans of Enceladus and Europa in Oxford in 2015, I was invited on the basis of my quora answers on planetary protection and on the scientific interest for the search for extra terrestrial life in our solar system.
As software developer, my top selling products are two music programs Bounce Metronome which helps musicians to play complex rhythms and work on precision and sensitivity of timing, and Tune Smithy which is used for algo comp, and for microtonal music.
I joined Amazon in order to put some of my writings onto Kindle for those who prefer to read them in book format. Most of the books here are also available to read for free as Science20 articles or as books on my website. My amazon bookshelf is here.
Some of the books on my bookshelf:
These ones are a bit out of date now:
I've also been answering many questions from the general public about hoax and fake Doomsday stories, which get them really scared. I'm astonished how many people are really worried that we might have a second sun or even an entire second solar system due to hit Earth in the next week or month. They are often so worried they even feel suicidal. Sometimes it feels like emptying the sea with a bucket trying to do something about it ,but though there are huge numbers of people scared like this, they are also individual people and every one you can help is a real person who was upset and scared and now is relieved and relaxed. I wrote my Doomsday Debunked book as well as the Imaginary Bullshit Nibiru to help these people. Though these also are a couple of years out of date now and I'd add a lot to them if doing them now.
My debunkes to help scared people are here:
My science blog at science20 is here
My lecture on super positive outcomes for the search for life in the moons of Europa and Enceladus is here
My four appearances on David Livingston's "The Space Show" are here
This is my blog annotating mistakes in Wikipedia as I find them:
Annotating serious mistakes and omissions in Wikipedia
These wikis are developed from Wikipedia pages originally:
See also, my science blog post here:
My published quora answers on other sites include:
Forbes magazine:
Huffington post:
News week:
Slate
My quora answers are here:
I trained as a mathematician originally. Went on to study philosophy then to do post graduate research into set theory and foundations of mathematics.
Then I tried my hand at inventing board games. One of them was accepted for publication by Gibson's Games, a large UK games company, but they were unable to publish it because of technical difficulties. Though they were really keen on the game, they were unable to make the pieces at a suitable price, which was a major disappointment for them as for me.
I then got involved in programming music after I invented a particular type of fractal tune based on self similar sloth canon sequences. It's related to the Danish composer Per Nørgård's "infinity sequence" though not identical. Through these tunes I got involved in music software programming, first in order to hear what the tunes sounded like myself - but then added more capabilities and began to sell the software commercially.
I added microtonal capabilities, originally just as a way to explore more tunes, but then got a lot of interest from microtonal composers. As it turned out, my program gave them an easy way to compose and play microtonal music on many synthesizers and computers (through creative use of midi pitch bends), something which was hard to do at the time. Now there are many programs with that capability but I still have keen users of my program.
At present my main focus is on Bounce Metronome, another music program valued by musicians for its ability to play complex polyrhythms, rhythm cycles etc., and for its visual "bounce" effect inspired by the motion of a conductor's baton.
I have had a long term special interest in astronomy, and space science since the 1970s. I have also researched into cellular automata, recreational mathematics, and non periodic tilings, amongst other things, in my own time, since the 1990s. I found some interesting results but that was two decades ago now. I haven't tried to publish it as I got caught up with the software programming as well as the game inventing. (Probably others have proved most of the results by now). I think perhaps some of the inspiration from those mathematical ideas found their way indirectly into my music programming. Also the experience in identifying reliable sources and how to do academic research has stood me in good stead.
This page is sort of in historical order so starts with the mathematical logic, then the tilings research, then the games, and finally the software and the booklets, which is what I work on all the time nowadays. So if you are mainly interested in the software, skip forward towards the end of this page. As you'll see for one reason and another I have not yet brought any of this to publication except the software and booklets, but I do have it in mind to return to some of it later when I am less caught up in other things.
I'm a mathematician originally by training.. I did research on a style of mathematics in which everything is finite, in which exceedingly large numbers take the place of the infinities that come up so often in mathematics. The idea is that mathematical infinity arises through attempting to reach exceedingly large numbers with insufficient resources, where the numbers are more than astronomically large, quite unimaginably large. But just very very very large numbers, not truly infinite.
The idea isn't to downplay infinity particularly, rather the idea is that in maths we may think we have some grasp of infinity because we can put it into our equations etc - but that the real infinity is far vaster than anything we can imagine. So in some ways it is more realistic to treat the infinities of maths as just exceedingly large numbers. The idea is, if you make truly large numbers large enough then they are indistinguishable to us from true infinities as far as maths and practical purposes are concerned.
For more about this see the page on Infinity and very large numbers.
After that I did some research into cellular automata, trying to find one with simpler rules than Conway's Game of Life that could simulate the workings of a computer and so lead to similar results to the ones Conway found for his cellular automaton. This was unsuccessful, I found some interesting patterns, promising enough to keep me at it for a number of years - but not the logic gate type interactions between the gliders I was looking for - but it got me involved in programming again after a lapse of many years since my early days learning programming on big mainframe computers with paper tape and punched cards. This was for cellular automata on a square tiling mainly though I think I also explored hexagonal tilings briefly.
Then I got involved in research into non periodic sets of tiles - tiles that can tile the plane as far as you like right out to infinity - but there is no way to put them together without gaps to make a tiling that repeats exactly. I found some new non periodic sets of tiles in 2D and 3D, but never published the results.
I tried once but realised that though my proofs were sound as far as I could tell, it needed more work to put it into a form appropriate for publication, so I got a bit discouraged at that point (I was very poor at explaining my ideas to other mathematicians, especially in print, in those days). This was clear from the reviewers' comments - I simply hadn't explained the proof in the paper as intended, as they didn't even comment on the proof but focused only on inadequacies in other sections of the paper which were only intended as a summary of current knowledge as background for the proof. Then concluded (naturally enough) that there was insufficient new material for it to be of interest to publish it. It all makes perfect sense with hindsight. But I didn't understand then, and I was too tired at that point after a run of failures to try again or attempt to take it any further, so I gave up.
I plan to return to the research if I can at some point, and if no-one else has proved the non periodicity of the tiles yet. I did bounce the ideas of the first proof off Roger Penrose (originator of the two tile non periodic Penrose Tiles), (that would be some time around 1990 or so, not sure of the exact year), as I was doing post grad research in the Oxford maths dept at the time, and he was interested enough in my non periodicity proof to hear me out, and didn't spot any obvious flaws in it when I explained it to him.
This was another area of interest, I found tilings which had a "taxicab geometry" that in the limit got arbitrary close to ordinary euclidean geometry. I also proved that any such tiling has to be non periodic. This maybe is the first paper I'll try to publish if I get time to work on it again (and if it hasn't yet been published by anyone else) - it is the last thing I worked on before I got involved in full time software programming and is also reasonably self contained and could be not too long if written with care. I tried at an early stage, to publish it as a question in a recreational maths magazine (before I had the main theorem or the results), and got some encouraging comments about it though it wasn't actually published at that stage. I think it has a reasonable chance of being accepted for publication if I try again.
Again I found some new results in peg solitaire, particularly in higher dimensions and large boards, again not published, sorry. This could be of interest to those keen on recreational maths.
I got involved in inventing several games, board game type games I mean, some with associated software you could use to play the games on a computer (Win 3.1 programs, as this was some time ago now) - but all playable using a board and pieces. I don't want to say too much as some I may still perhaps publish them at some point, and would rather do it all in one go rather than give hints about how they work first. One was nearly published, was accepted by Gibson's Games (a fairly large games company in the UK), but unfortunately ran into production issues, and was never published. A rival game by another company in New Zealand was similar enough at least in appearance to probably hit sales - and got published world wide including in the UK soon after that, so that the prospects for my game seemed remote after that. But I still have some hopes to revive it at some point possibly.
Then I got involved in writing music software, originally to explore an idea I had for a fractal tune built up from a simple seed. This was far more successful than I expected, the results were very musical, at least many users of my programs seem to think so as I do myself too - you can judge for yourself by listening to the music that comes with the fractal player in Tune Smithy. So I tried selling the program and was encouraged further by the enthusiastic feedback from users. This is what later became Fractal Tune Smithy.
Later I added in scales from the SCALA archive with permission from Manual Op de Coul. This lead to microtonal fractal tunes. It turned out then that my program was useful for microtonal composers to retune their keyboards and pieces composed in notation software. So I developed that side of it further. I also got involved in composing small chamber type pieces of microtonal music myself which I greatly enjoyed, got encouraging positive feedback from other composers about them, and they were useful also as I could include them in the program as examples of various things you could do with the program.
It also turned out to be useful for music therapy in connection with Barbara Hero's Lambdoma keyboard - I adapted Tune Smithy so that it could be used to play the notes for her keyboard. Other spin off additions to the program include the chord progression player, the polyrhythm metronome, and the audio pitch tracer used to transcribe bird song.
Tune Smithy is my top selling program. But I also wrote some other software as well. Lissajous 3D was written in order to make Lissajous Patterns in 3D - originally for use with Tune Smithy for the music therapy connection, an implementation of ideas by Barbara Hero, and a suggestion to develop them in 3D by the composer Charles Lucy.
Virtual Flower originated in a discovery that it was possible to make very compact fractal trees in VRML - a few KB instead of the usual several MB that would be required for such complex 3D shapes. It also developed as a way to make geometrical shapes, polyhedra and animated star spheres.
Other programs I've written include the Activity Timer which is used to track time spent on projects on the computer, and Text Field Echo a text tool with a few special features - including a wild word search and replace, and search and replace all the files in a folder.
I've been programming on and off since the days of punched cards :-). My first experience of programming was with a machine like this:
(not me in the photo!)
That's just the machine for punching the cards. The computer itself occupied a large room about the size of the ground floor of a house, and was probably less powerful than the first ever home PCs.
Here is one of the patterns I explored as a mathematician (I didn't invent this particular pattern indeed all of them I found had already been invented by someone else, but I had new results about the patterns):
I'd love to share this program, but it isn't suitable for public release in its present form as it was written for Windows 3.1 and hasn't yet been updated. It would run okay as a 16 bit program but I need to make some changes before it could be released, and the easiest way ahead is to update it to 32 bit first, which is a bit of an undertaking. (See Porting 16-Bit Windows-Based Applications to Win32) You can see more pictures of the tiles here: Robert.
I also wrote some programs to play some board games and puzzles that I invented, and to draw and print out the pieces for the games. I still have hopes to publish these in print however rather than software (or with the software as a companion to the published game) - and the software again is all for Windows 3.1 and not updated, so for both reasons, none of my board games programs are yet in a state suitable for a public release as software.
I wrote other programs too, earlier on - the most complex of my early programs was a cellular automaton simulator for the cellular automaton research, optimised to run especially quickly by using bitwise operations (particularly fast on a 64 bit machine) so that you can quickly fast forward through the generations to see what happens. These programs are for Linux (the X-Windows system) and haven't been updated or even tested for many years now, and aren't available for download.
More about how I developed the programs.
Developed out of an idea for a fractal tune I had that would continue endlessly. The first version was very basic and just played a single melodic line of notes all the same length, and then I elaborated it to a kind of fractal polyphony. Long after I discovered that the composer Danish composer Per Nørgård developed a similar idea (not identical) which he caleld the "Infnity sequence".
See: Music And Mathematics Of Fractal-Like Sloth Canon Number Sequences
However fairly early on I began to explore some of the tunings in the huge Scala scales archive in Fractal Tune Smithy. I was delighted when Manual Op de Coul gave me permission to use those scales in FTS, and then found out that FTS was doing things that few other programs could do, so it was quite in demand with some microtonal composers. I also got more and more interested in microtonal music so it developed like that.
Later I heard through Denny Genovese (who was a keen supporter of FTS) that Barbara Hero was looking for someone to do the software retuning for her Lambdoma keyboard, so through that eventually I wrote the music therapy section of the program for users of her keyboard, which then became usable also by mouse and PC keyboard. Also indirectly that lead to Lissajous 3D.
Developed from Barbara Hero's work with Lissajous patterns corresponding to musical chords. You often have chords of three or more notes in music so it was natural to extend the idea to three or more frequencies played simultaneously, but I hadn't noticed the connection that made with 3D shapes until the composer Charles Lucy pointed it out, which then lead to the idea of Lissajous 3D. Just to make it clear - the idea of a 3D Lissajous pattern isn't a new idea actually, as later on I found out that Lissajous knots figure in the mathematical discipline of knot theory, but it was new to me when I wrote the program.
Developed originally to keep track of the time I spent on projects myself - as with many software developers I was very prone to overwork, often late at night when everyone else is asleep - and have a great tendency to forget how long I was on the computer, so needed a software reminder to take short eye breaks from time to time, and to stop work for a longer break. Hopefully it is helpful for others in the same situation, and also for those who need or want to find the total times they spend on their various computer related activities.
Developed to explore certain programming possibilities to see how they could be done, vis. echoing and directly editing text fields in other programs - and then it was a natural to develop it further to do certain text editing tasks I needed to do such as a flexible way to do a search and replace of multiple search terms simultaneously in all the files in a folder, and to do page redirects for all the web pages in a web site in one go. So - though there are many programs that work with text, this one does have its special points. It goes back to before Windows XP.
My reason for sharing it was that I thought TFE might be useful for occasional fairly techy users who may have similar requirements to myself. The text font transforming and text enlarging properties of TFE can be fun for less techy users, and it could also be used to directly read or edit text in tiny scrollable regions of web pages, but changes in the way that Windows and browsers work made this no longer functional.
Apart from that, the main point of interest is perhaps the wild words search. Perhaps the search and replace of all the files in a folder can be useful, particularly the capability to search and replace several words or phrases simultaneously, or even to use a list of as many replacements as you like from a file, and carry them all out simultaneously on all the files in a folder and (optionally) all its sub-folders. TFE can also be used as a text magnifier for partially sighted users, which I may develop at some point. But it isn't that great for that - as it can't echo most documents. Generally - I'm not sure where TFE is going and what will be developed out of it later on.
I have temporarily withdrawn TFE so it is no longer available for download - hardly anyone was using it. There is a hard to locate but significant bug I have to fix then I can make it available again, but it is at present low priority due to the lack of interest in this program. It is a non reproducible bug that happens occasionally while editing once or twice a month if you use it as your only text editor, and it changes the text you edit.