This little image is a closeup of the top of one of the
regions occurring at frequencies that are
specifically, the one that appears on the
iterated circle map. There are many more pictures in my
Rant about the difficulty of using Linux
What more can I say? I fell in love with Linux many decades ago, because
it was fair, fun, and it worked really really well. Now, it just gets
a little harder to use, a little more unpleasnt every year.
Open Letter to Debian and Ubuntu Developers.
The Home Page of Linas VEPSTAS
Welcome to my home page! There's a lot of stuff here, some quite good,
and some that's so bad I'm ashamed of it. Yet I've been too busy to
find it, figure out if it really is that bad, and remove it. So its a
grab bag. Some of it's funny but mostly it's not. A lot of stuff here is
hopelessly dated. I tend to spend most of my on-line social time on
the opencog blog, freenode.net/gimp.net irc, maling lists, wikipedia,
and google+, rather than in polishing this web site. Basically, this
page is a snapshot frozen in time: its what a blog looked like in the
1990's, before blogs were invented.
Who am I?
At various times in my life, I've been a scientist, technologist
and entrepreneur. I have broad interests in mathematics, physics,
and computer technology.
My current technical interests focus on
natural language processing and
artificial general intelligence.
I've held jobs working in the above areas; unfortunately, I now
pursue these only as a hobby. The NLP directory
has pre/re-prints of some of the academic publications that have
come out of this work.
My primary research platform is the
open-source OpenCog project. For me,
OpenCog provides a general technical setting where I can experiment
with different machine learning theories and algorithms, with both
connectionist and symbolic processing flavors. I've compiled a messy
list of related open-source AGI projects here.
I've spent many years at
IBM; most recently
working on the
Linux kernel for
Linux on the PowerPC
wiki is a good place to find out more about IBM Linux mainframes and systems.
I've been active in the Linux community; I was a founder of the
Gnome Foundation; and was the lead developer for
GnuCash for over 7
years. I've founded three dot-com startups, all of which failed to
enrich me financially. I was a founding member of the
OpenGL Architecture Review Board;
and spent 8 years learning about and designing
3D graphics hardware and software. I have a PhD in
theoretical physics from
SUNY at Stony Brook. Currently, I am
utterly infatuated with
mathematics, and have made large contributions to
over 400 math articles in Wikipedia. BTW, y'all,
global warming is for real. Do something about it.
Vytautas O. Virkau Memorial Archive
- Vytautas O. Virkau Memorial Archive.
Linas' Mathematical Art Gallery
- A colorful exploration of some well-known, but under-examined
equations. I think some of this is high Art, and much of the
rest of it should be an eye-opener for even jaded fractal
The Art Gallery has been running for fifteen or twenty years
while being silent about the underlying math. I suppose its
high time to make amends. The core idea of the dissertation
is that the shapes of fractals are describable through Farey
Fractions, which appear naturally through continued fractions,
which have the symmetry of the Modular Group SL(2,Z), which
is inter-twined with the Riemann Zeta and the structure of the
set of rational numbers. Besides the four basic operations
on the real numbers (addition, subtraction, multiplication,
division), there is a fifth basic operation which is rarely
taught in primary school and under-appreciated at higher
levels, namely, "Farey Addition" or, expressed correctly,
group multiplication in SL(2,Z). The modular group doesn't
just lead to Pellian equations and algebraic numbers, it
in fact intertwines all rational numbers (and their extensions
to reals and p-adics) in crazy, fractal ways. This is why,
for example, one sees Farey Fractions in the Mandelbrot Set.
In number theory, the structure of the Modular Group
provides a unifying theme for understanding the nature of
factorization and primality. This is why, for example,
power series and Dirichlet series (such as the Riemann Zeta)
exhibit such crazy fractal Cantor-Set type patterns. Despite
this connection being seen by Weierstrass as early as 1872,
its more-or-less entirely ignored in standard textbooks on
Analysis and Number Theory. A series
of articles tries to provide some of the underpinnings
for the above breathless assertions. Some highlights include:
- Distributions of
Rationals on the Unit Interval (or, How to (mis)-Count
Rationals) is a high-giggle-factor review of
some so-called "facts" about fractions that you learned
as a child, and which every math teacher ever since has
repeated, but which are simply not true. I used to think
Number Theory was boring until I saw this.
- The Bernoulli Map,
the Gauss-Kuzmin-Wirsing Operator and the Riemann Zeta
reviews the basics of using the Frobenius-Perron Operator
as a tool for studying fractals, and then applies it to
to Bernoulli Map and the Gauss Map. Along the way, we discover
that the eigenfunctions of the Bernoulli Operator are the
given by the Hurwitz Zeta, and show the connection between
them and the traditional fractal eigenfunctions. The details
of the connection between the Riemann Zeta and the
Gauss-Kuzmin-Wirsing (GKW) Operator are presented. A couple of
exactly-solvable toy models of the GKW are presented as well.
About half of this is a pedagogical introduction; the other
half is a presentation of all-new results.
- A series representation for
the Riemann Zeta derived from the Gauss-Kuzmin-Wirsing
Operator is a less rambling, more tightly focused extract
of the above, meant for publication.
Minkowski Question Mark and the Modular Group SL(2,Z)
shows that the distribution of Farey Fractions transforms
under the dyadic representation of the Modular Group.
It constructs the Minkowski Question Mark Function as a
set-theoretic representation of (a subset of) the Modular
Group. Reviews the hyperbolic rotations of binary trees.
This paper provides the core background material for the
structure of the Modular Group that is used in the other
papers of this series.
- Symmetries of
identifies the Modular Group
SL(2,Z) as the basic symmetry group of a large class of
fractals. Although this relationship is obvious, it never
ceases to amaze me that books on modular forms never mention
fractals, and that books on fractals never mention modular
forms, despite the obviousness of self-similarity of
the Modular Group. Even Mandelbrot's most recent book,
published in 2004, doesn't breath a word of this.
This paper develops the Takagi or Blancmange Curve as
a fractal curve that transforms under the three-dimensional
representation of the Modular Group. It then shows how to
build higher-dimensional representations out of the Bernoulli
- Continued Fractions
and Gaps provides a very curious function that is
discontinuous on the rationals and whose discontinuities
seem to be perfectly randomly distributed. I find this
to be a rather dramatic result, possibly because I've never
heard of such a thing before. I've stared at a lot of fractals
and space-filling curves, but nothing like this.
to Abramowitz & Stegun
includes a set of annotations to the classic Handbook of
Mathematical Functions, including new integrals over
Bessel functions, and some sums over the Riemann Zeta function.
Theory develops some basic relationships between continued
fractions, fractals and Farey Numbers.
- My Wikipedia
User:Linas web page. I've written or revised some two
hundred-plus articles on assorted mathematical topics.
- Political, Economic and Social Screeds
- Some short essays on emerging economic and political forces.
Most of these are just sly, corrsive expressions of anger and
hostility, a lashing out at events beyond my control. Kind of
like those ugly tv/radio talk shows, just not from the wacko
right-wing nut-job perspective.
Unreality, 2008. Yes, politicians are from outer
space, and they arrived in a flying saucer called "journalism".
How can you tell? They focus on everything except what is
Why did Bush promote warrant-less wiretapping? Why is Obama
continuing these Bush policies? I can guess why, and I really
don't like it. Stop Illegal
Wikipedia needs new leadership! I used
various essays about the structural and cultural
problems in Wikipedia, and the things that could be done to
solve them. These were posted on my
user page. Unfortunately, the malicious and stupid
leadership there found these so offensive that they deleted
the essays. Boo-yah! So now my profile is just soo
very squeky-clean and totally inoffensive. To anyone,
that is, except me. You might never guess that I'd been
raped by the admins there. Woo hoo! Go Wikipedia!
This is Your Brain on Drugs
explores drug use in America today, and the political
forces wrestling with this social problem.
Labour of Love - The Volunteer Economy
Free-market economists, thinkers and pundits (correctly)
champion the power of free markets to create a better world.
Yet if one opens a history book, it is hard to find
a historical figure that was motivated by greed.
Both prominent and emerging social and economic institutions
are marked by excellence due volunteer, freely donated
efforts, rather than wealth accumulation. When will
we recognize the economic benefits of channelling
this powerful force with social, political and governmental
Free Software ~ Free Trade?
An examination of the powerful economic forces driving the
acceptance of Free Software/Open Source in corporations
and businesses. When we realize that Free Software is
not just a (political) philosophy, or a social or anthropological
movement, but an economic force akin to the removal of
trade barriers, we can finally understand why its adoption
by corporations promises to be a sea-change in the
way that software is used. Reviews a business case study
of a very large, failed technology project. If you thought
the Internet was big ... this is bigger.
DeCSS: Consumer Politics in the 21st Century
A moral/sociological/legal diatribe about the immorality
and evil ethics of the Digital Millennium Copyright Act
(DMCA) and the corporations that wish to squish human
endeavor in the name of the protection of intellectual
Open Source and Code Quality
The relationship between the software worker and the software
means of production leads to fundamentally new economic forces
that will change the very nature of the software industry.
A collection of outlaw computer technology, harvested from the
net. Why would I mirror such dangerous and subversive material?
In order to protect my personal freedoms -- and yours. Seems that
greed and lust for power -- happily wrapped in the flags of "free
enterprise" and "democracy", continue to lie at the root of many
political and social evils and ills.
Linux Enterprise Computing
- (Old, out of date) References, resources and a guide to prominent
Free Software systems and technologies, from the corporate
computing perspective. This is a snapshot of what Linux tech was
like back in the late 1990's. Topics include:
- My Free Software Projects
- I've worked on many free software projects.
Below are some of my favorites, with a more complete list
provides details and statistics for some of my more recent,
- Technical Ruminations
- Miscellaneous technical articles and notes.
A Better Way to do SETI
makes the argument that if extra-terrestrials are trying to
send us a radio message, then they will be using broadband
spread-spectrum (pseudo-random noise) modulation techniques.
Finding such a signal is much, much harder, but when found,
it provides a much, much clearer communications channel
than any other modulation technique. The ET's know this,
and they know that we know this, and will thus use this
technique preferentially. Essentially all of the current
SETI searches, while being important so as to rule out
other methods, are all really looking for the wrong thing.
is a commentary on the basic ideas behind Napster as viewed
through the eyes of David Gelertner. David chooses not to
dirty his prognostications with the names of present-day
technologies. I do. They are E-Rights, distributed.net, and
Eternity Service, all mashed into one.
A Digression on Artificial Life and Cellular Automata
This web page is a very long diary of a set of experiments that
were run in the early 90's with a collection of cellular automata.
The automata were designed to have a 'genetic code' that was
shared between cooperating individuals. By cooperating (or not)
individual cells could (and did) self-organize into 'symbiotic'
plant-like structures. Lots of interesting stuff was seen.
Never attempted to write this up for publication; I should have.
- Philosophical Ruminations
- Sophomoric, half-baked, incoherent, nutty ideas, most of which
have probably already been better-expressed in some top-ten
selling book. These include, but are not limited to:
The Origins of Quantum Mechanics
An attempt to re-derive QM (and GR+QFT) from first principles.
I like to think of the present as a wave-front where the liquid
future freezes into a solid past. Mathematically, the past is
a sheaf or a topos, the future is a pre-sheaf, not yet glued
together, and the gluing axioms happen at the surface of
light-cones. QM is that fluid thing that lives near the present,
where space-time itself is being glued together; the
indeterminacy of QM is the not-yet-glued-ness. Or something
like that. This and many other ideas and possiblities are
The Origin of Time, Quantum Mechanics, and Free Will
A nutty digression that asserts that quantum mechanics is
a side-effect of Planck-scale physics, rather than something
In the Beginning was the Word
An unfinished defense of the Platonic Interpretation of
Mathematics. Mathematics does not exist solely in the
heads of humans, but in and of itself. Indeed, even the
almighty God does not have the power to change the value
of Pi (which, I believe, is a statement about God, and not
A Digression on the Non-Computability of Thought
Something about incoherent, irrational clocks powering
parallel Turing machines.
- Free Will and Determinism
An very weak (and ultimately failed) attempt to disentangle free will
and consciousness from physical (Newtonian) determinism.
- Heidegger's Fundamental
Question, some sophomoric notes.
Ties together some of the essays above.
- My Weblog
- This is the output of my new experimental note-taking and
publishing and general-diary tool,
We'll see how easy, scalable, effective this tool really is.
Or, how dis-interested I am in using it ...
The good stuff is in the form of letters:
- Employment History, Schooling
- References pertaining to the various jobs I've held,
and what I did while I worked there. In reverse chronological
order. My sort-of current resume is here.
An Airline Flight Reservation System
I founded Teleport Travel, and was bought out by Intransco,
where I served as Chief Technology Officer.
More work, for less money, at an Internet startup.
Developed the prototype entirely by myself.
Teleport Travel was the very first on the
'net (Spring/Summer 1995) with an actual functioning
airline reservation system, never mind that it worked
better, and had a nicer user interface than many/most travel
res systems today. An unhappy experience in the end, as
this was a dot-com that dot-bombed. I shoulda been a
billionaire by now, but it turns out (duhh) that superior
technology has no correlation to success. Its all
about the management, the CEO, the board of directors.
I was unable to control the company, and was bitter about
it for a long time -- my baby was taken away from me.
Anyway, the actual technology does live on at
and some good friends still work there.
Pioneer 10/11 Silver Anniversary Commemorative Site
Dr. John Simpson hired me to work on Pioneer 10/11 Charged
Particle Instrument data analysis programs for my first paying
computer programming job, twenty years ago. These are now
the farthest spacecraft from our solar system.
Goodbye Pioneer 10/11!
Morgan Park Academy
Class of `76.
Web Site Mirrors and
More Web Site Mirrors
- A random assortment of mirrored web sites. I mirrored these
because at some point in time I thought their content was
interesting, and they seemed to be at risk of disappearing
forever... and some of them have ... This is my attempt to
archive some of these, for some distant future rainy day.
Vintage Netscape Navigator
- Some vintage copies of Netscape Navigator, v1.0n, v1.1 beta 1 and v2.0,
for Linux/x86. These are circa 1994-1995. The binaries still run on
A really great photo of me at the 2009 Pumpkinhead 5K head race
(7:45AM 31 October 2009). Peter Hoffmann in stroke, we're enroute
to the starting line. During the race, we ran the boat aground
(into a pollution control barrier), got completely hung up,
lost a few minutes trying to get underway again, and still
managed to win the race!
Training video, with coach's chase-boat in pursuit.
- May 5, 2011, calm day,
- April 2011, double w/
Peter Hoffman; strong headwind & big waves.
- April 2011, double w/
Peter Hoffman; strong tailwind, calm water.
- May 12, 2011, quad w/
Sue Carter, Connie, Sommers, row by pairs.
- Stick figure
body prep by Flip Luisi.
- Taip, aš kalbu Lietuviškai. Parašykite!
- Taip, tevas iš Panevežio.
- Dabarmėtiniais laikais gyvena apie 6000-12000 kalbėtoju kalbos
'Veps', ant Rusijos-Finlandijos sieno, Karelijoje. Man šove į galvą,
ar gali būti, kad, sakykime, prieš 5-10 generacijiu, gal koks žmogus,
o gal visa šeima ar giminyste, atvažiavo iš Karelijos, ir apsigyveno
Lietuvoje? Nu, Karelija ne taip jau toli nuo Lietuvos. Jeigu taip
tikrai iškylo ta keista pavarde 'Vepštas', tai tas primas 'Veps'
negalėjo atkeliauti ilgiau negu prieš 10 generaciju (200 metu),
nes Vepštai nepaplite po visa Lietuva; bet irgi ne greičiau
negu 5 generacijas, nes yra šimtai Vepštu. Tai ... ar galėtu būti?
Finlandijoi randama pavarde 'Vepsalainen'. Dagiau apie
- My Goddess
- Please buy some of this beautiful jewelry!
If you like this work, send bitcoin!
Started in 1995, last updated October 2010
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