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Archive for the ‘musings’ Category

The edges of existence.

Everything is an edge – an edge of an edge – an edge of an edge of an edge. Existence is an infinite regress of edges encoding, decoding and recoding other infinite regressing edge networks. The explanations for the unexplained, even in their simplicity, are infinite regresses.

A dictionary is a book of words defining words. Where does a definition end?

Human language is a loose collection of rules to be excepted and exceptions to be ruled by effect. If a communication communicates it’s acceptable?

Sensory perceptions and the instruments of perception cannot be fully perceived. Are we to believe our eyes about our eyes?

Mathematics and its objects and relations are designed to perfectly articulate all that is the case and yet hiding with infinity are infinities and transcendentals that cannot be defined, systematically discovered, nor hardly described. (http://vihart.com/transcendental-darts/)

Our science modernized from the mystics (Kepler) and numerologists (Newton) and the faithful (Leibniz) strikes out, pathetically, against leaps of faith. This science likely has led to the heating of the planet via industry which now can only be reversed by more science?

Turing conceived computers to mirror the way humans thought – conceived when our collective knowledge of brains was rather small. Ironically, within a few lines of code computers (theoretical and physical) become nearly inscrutable in terms of what they might do. Are more inscrutable machines required to create and understand more inscrutable machines?

Currency is abstracted not just from physical objects but from any tangible value other than a sustained believe that this $ will be understood and honored by some anonymous entity beyond oneself. The beliefs sustained by what most label as “the dismal science” (economics) and its backer, the state.

The desired progress of all of the above can be summarized as “prediction”. If something is predictable it is controllable is the underlying point of most modern obsessions with science, technology and information. Even though our most precise and abstracted efforts have shown prediction, by in large, is impossible. Not just for complex systems of the natural world but the very simple mathematical objects we create. https://www.youtube.com/watch?v=sHYFJByddl8

Despite all the empirical evidence over hundreds of thousands of years and the theoretical proofs of the 20th century as a whole, our culture – primarily in the US but spreading elsewhere – simply refuses to give up control through prediction. It persists, likely, because we are limited beings in energy and time and need whatever perceived advantage we can get. Right? Seeming identification of a pattern reinforces that identification when paired with the perception of reward or advantage. That is learning itself is an edge of an edge of an edge and fully infinitely regressive to its own contradiction.

Prediction and learning and control are all about probability. For a prediction to be useful it must tell us something about the probability of conditions coming to be. For us to do something based on a prediction we must believe that prediction to be as accurate at least as much as the probability of events it predicts. That is, our beliefs should only be as strong as the probability predicted. Or so logic would suggest. However, probability itself turns out, with no surprise here, to be an infinite regress. Probability is really a statement about lack of information. (Sure some people argue that chance/randomness is implicit to existence while others say it’s an artifact of our limited perceptions. In either case our ability to say anything about the existence of things comes down to ignorance and the infinite regress of existence.)

This information remains forever out of reach. It is both at the heart of everything and is the edge of everything. We cannot know. We can only play with these edges, find more of the edges, recode edges into edges. Our struggles philosophically, scientifically, spiritually and educationally come down to this straightforward non-fact. Should we continue our answer and prediction seeking efforts in spite of their impossible hope? That is a personal question that each will have to answer over and over for themselves. For me, I will, not so I can be right or in control, but because I enjoy the edge want to live outside of control. I paint to paint, not because the painting says something about reality. “The good life” is proportional to the number of edges explored, clanged to, jumped from, thrown away, revisited, and combined.

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Certain activities are fundamental to the human endeavor.

The list:
Acquisition of food, shelter and water
Mate attraction and selection
Procreation
Acquisition or forage of information regarding the first three
Acquisition of goods and services that may make it more efficient to get the first three
Exchange of above three

Only software that deals directly with these activities flourishes into profitable, long term businesses.

I define software here as computer programs running on severs and personal computers and devices.

The race to the bottom in the pricing of information and software and hardware that runs that software ensures that only software businesses that scale beyond all competition can last. Scale means massive and efficient data centers, massive support functions and a steady stream of people talent to keep it all together. And the only activities in the human world that scale enough are those things that are fundamental activities to us all.

Sure there’s a place for boutique and specialist software but typically firms like that are swallowed by the more fundamental firms who bake the function directly into their ecosystem and then they give it away. And this is also why the boutique struggles long term. Those fundamental software builders are always driving the cost down. So even if a boutique is doing ok now it is not sustainable if it is at all relevant. It will be swallowed.

Open source software only reinforces this. In fact it takes this idea to the extreme. The really successful open source projects are always fundamental software (os, browser, web server, data processing) and further drive the price of software to zero.

Scale is the only way to survive in software.

This goes for websites, phone apps, etc. All the sites and apps that focus on niche interests that don’t deal with the fundamental activities above directly either get assimilated into larger apps and sites with broad function or they whiter and die unable to be sustained by a developer.

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There is truth.   Truth exists.  There is a truth to this existence, this universe.   We might lack the language or the pictorial tools or the right theory and models, but there is truth.

What is this truth?  what is truth?

Things exist, we exist, there is a speed of light, the square root of two is irrational, the halting problem is undecidable, there are abstract and real relations between abstract and real things.

The truth is a something that, yes, has a correspondence to the facts.  That is not the end of it though (despite the pragmatic claims of some!).   The truth has a correspondence to the facts because it is true!   The facts HAVE to line up against a truth.   The truth exists outside of specific events or objects.   A number has an existence, if even only as an idea, and it has relations to other things.  And the description of that number and those relations ARE truth.  A computer program has its truth whether you run the program or not.  If you were to run it it would halt or not halt, that potential is in the computer program from the beginning, it doesn’t arise from it’s execution.

On Proof and not Proof but Use

We can prove these truths and many more.  We can prove through English words or through mathematical symbolism or computer programs.   Our proofs, put into these formats, can and are often wrong and set to be revised over and over until there are no holes.   No matter how fragile a proof and the act of providing proof the truth is still not diminished.  It is still there, whether we know it or not and whether we can account for it or not.  And the truth begs proof.  It begs to be known in its fullness and to be trusted as truth to build up to other truths.

BUT!

Proof isn’t always possible – in fact we’ve learned from issues in computability and incompleteness – that complete provability of all truth is impossible.   This beautiful truth itself further ensures that the truth will always beckon us and will never be extinguished through an endless assault.  There is always more to learn.

The unprovable truths we can still know and use.  We can use them without knowing they are true.  We do this all the time, all day long.   How many of us know the truth of how physics works? or how are computers do what they do?   and does that prevent their use – the implementation of that truth towards more truth?

Why?

Why defend truth?  Why publish an essay exalting truth and championing the search for truth? Does the truth need such a defense?

Being creatures with intelligence – that is, senses and a nervous system capable of advanced pattern recognition – our ultimate survival depends on figuring out what’s true and what isn’t.   If too many vessels (people!) for the gene code chase falsehoods the gene code isn’t likely to survive too many generations.   Life, and existence itself, depends on the conflict between entropy and shape, chaos and order, stillness and motion, signal and noise.  The truth is the abstract idea that arises from this conflict and life is the real, tangible thing born from that truth.  We learn truths – which processing of this thing into that thing that keep us alive, we live to learn these things. In a completely entropic existence there is nothing.   Without motion there is nothing.   In total chaos there is nothing.   It is the slightest change towards shape, order and signal that we find the seeds of truth and the whole truth itself.  The shaping of entropy is the truth.   Life is embodiment of truth forming.

So I can’t avoid defending the truth.  I’m defending life.  My life.  In defending it, I’m living it.  And you, in whatever ways you live, are defending the truth and your relation to other things.  If I’m alive I must seek and promote truth.   While death isn’t false, chasing falsehood leads to death or rather non existence.   Could there ever be truth to a statement like “I live falsely” or “I sought the false.”   There’s nothing to seek.  Falsehood is easy, it’s everywhere.  It’s everything that isn’t the truth.  To seek it is to exert no effort (to never grow) and to never gain – falsity has no value.  Living means growing, growing requires effort, only the truth, learning of the truth demands effort.

How do we best express and ask about truth?

There’s a great deal of literature on the unreasonable effectiveness of mathematics to describe the world.  There’s also a great deal of literature, and growing by the day, suggesting that mathematics isn’t the language of the way the universe works.   Both views I find to be rather limited.   Mathematics and doing math is about certain rigor in describing things and their relations.   It’s about forming and reforming ways to observe and question ideas, objectives, motion, features…. It’s about drawing a complete picture and all the reasons it should and shouldn’t be so.   Being this way, this wonderful thing we call mathematics, there is no way mathematics couldn’t be effective at truth expression.   Ok, for those that want to nit pick, I put “computation” in with mathematics.  Describing (writing) computer programs and talking about their features and functions and observing their behavior is doing math, it is mathematics.

Art has very similar qualities.   Art doesn’t reduce beyond what should be reduced.   It is the thing itself.  It asks questions by shifting perspectives and patterns.  It produces struggle.  Math and art are extremely hard to separate when done to their fullest.  Both completely ask the question and refuse to leave it at that.   Both have aspects of immediate impression but also have a very subtle slow reveal.  Both require both the artist and the audience, the mathematician and the student – there is a tangible, necessary part of the truth that comes directly from the interaction between the parties, not simply the artifacts or results themselves.

Other ways of expressing and thinking are valuable and interesting.  That is, biology and sociology and political science, and so on….. these are all extremely practical implementations or executions of sub aspects of the truth and truth expression.  They are NOT the most fundamental nor the most fruitful overall.   Practiced poorly and they lead to falsehoods or at best mild distractions from the truth.  Practiced well and they very much improve the mathematics and art we do.

What does any of this get us?  What value is there in this essay?

This I cannot claim anything more about than what I have above.   For example, I don’t know how to specifically tell someone that the truth of square root of 2 is irrational has x,y,z value to them.  It certainly led to a fruitful exploration and exposition of a great deal of logic and mathematical thinking that led to computation and and and.   But that doesn’t even come close to explaining value or what talking about its value today, in this essay, matters.

My only claim would be that truth matters and if there is any truth in this essay then this essay matters.  How that matter comes to fruition I don’t know.   That it comes to any more fruition than my pounding out this essay after synthesizing many a conversation and many books on the subject and writing some computer programs and doing math is probably just a very nice consequence.

The truth’s purpose is itself, that it is true.

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Apparently a lot of people want to live forever.

Last week I read an article about cryonics company, Alcor, and their founder.  Apparently he passed away. A couple of years ago I read the book “Frozen”.   (Alcor has been fighting that book for some time.)   I’ve also read / watched stuff from Aubrey De Grey and all the stuff from Ray Kurzweil.   I’ve had conversations face to face with “singularists”.   And, of course, the efforts to get humans to mars I watch with extreme curiosity.

All of these are modern equivalents of the search for the fountain of youth, religious salvation and belief in the afterlife.

Do you, dear reader, want to live forever?  Do you want to preserve some specific way of life, your way of life, humanity?   It’s maddening to me that a large number of humans want to make some basic version of this existence go on forever.   It seems insane to me to want to promote this specific way of life considering how little we actually know and how frequently we kill each other and the planet.

Personally I’d find it miserable to live forever or to be reanimated in the future with my current form.   One lifetime, as a human, is enough.   A couple of years ago I read this book, Forever, by Pete Hamill.  It depressed me a great deal.   The main character lives forever.  He watches many generations and friends live, suffer and die.   All the joy and up moments were dwarfed by knowing it was an endless cycle – living forever wasn’t all there was!  It was a similar lesson I pulled from Man from Earth and Moon.  Maybe I need to read and watch more hopeful views of living forever.

Chasing immortality strikes me more as fear than some aspirational ideal.  If not the fear of death or regret over something not done in the life time, it must be some ridiculous belief that one or humanity SHOULD live forever and promote this particular formation of life.   Whether it’s fear or some anthropocentric imperative the pursuit of immortality seems like a big fat cop out.

People die.  Species go extinct.  We have limited time and resources at our disposal.  We should stop looking for infinite sources of energy and life and start learning to live better (in whatever way you take that) with less.   Stop damaging other things in pursuit of a cop out.  It’s a waste.  In fact, it appears to me to be a HORRIBLE strategy for ultimate survival of whatever it is we’re trying to protect.

But is the pull of survival of genes, the body, the species so great we can’t help ourselves but to spread the human and our own gospel?  I don’t think so.  Thousands of other species of life execute a variety of other strategies that don’t seem so damn selfish and fated.   Insects, fish and the dinosaurs have about 100x+ the longevity as humanity and as far as history suggests, none of the creatures in those phylums chased immortality.

Could “intelligence” be at the root of this?  Hard to give a truthful argument for this idea.   I conjecture that it’s actually a horrible side effect of “intelligence” in the same vein as the illusion of free will.   Intelligence conjures these things up by accident and they seem to fit conveniently into a world view that keeps the intelligent being going – being fruitful and multiplying.   It might also be the case that this is an evolutionary mutation where a strategy extinguishes itself.

We’ll never know… or maybe some will find a path to immortality and they will come to know.  or maybe we’re actually creating these immortal versions of ourselves in all these Web based things we keep inventing.  If any of that comes to pass I hope whatever carries on has a far better grasp of reality and what’s worth carrying on.

And please oh please don’t let immortality be born out of freezing our heads and reanimating them in some weird duct taped, half baked future.  It’s just creepy.

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I’m obsessed with big questions.  What is life?   Why are we here? How did we get here?  Why do we experience time the way we do?  Why haven’t we seen another planet teeming with life?  What is mathematics?  What is currency?   Why does learning work the way it does?   How do we come to understand each other or anything at all?  Is there free will? How should we live? If not democracy, then what? and so on!

We all start our intellectual life focused on the big questions.  As children we’re unconditioned to censor our questioning of how and why things work.   We are also natural experimenters of theories and are able to quickly absorb new views/ideas.

We’re such good learners as kids that it doesn’t take too many years before the process of turning kids into responsible adults destroys most of our original questioning and critical thinking ability.     Instead of taking advantage of the amazing sponge like years, we teach our children not to think, not to question, not to risk.  We teach them to follow rules, not think and write their own rules.  Our culture is so adept at squashing original, inquisitive thinking that many of us then need 4 years+ in higher education to “learn how to think.”

It happens moment by moment.  From TV, movies, books, our schools, our homes, our politics, the things we say, the way we are.  (Ever caught yourself telling your child, “That’s just the way it is.   You ask why a lot.” …

It happens because we get tired. and having dogma and previously used answers keeps it simple and saves energy, in the short term.

Big Questions take energy.  Lots of energy.  And kids have a lot of that.  Adults don’t, in general.   Adult life seeks order.  Keep the disturbance to a minimum.

If you stop asking the big questions your actions become small, orderly, understandable.   but!   the engine of progress is mutation.  Exploring strange intellectual places.  and, I believe, those strange places can only be reached in ones lifetime by never ceasing to ask and attempt to answer the big questions through thought and deeds.

Kids make big strides quickly for many many reasons, and I believe fearlessly asking big questions and not looking for intellectual order is one of the bigger reasons.

 

 

 

 

 

 

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place poem: Andover, OH

State routes cutting through fields of home grown generations

lives lived in desolate desperations

 

pull up to a driveway, to a home, brimming with life

completely contained within this acreage

the woods, a garden with a full year of food, a pond

100 years of fond memories of raising kids, corn, horses, birds, bees

trees grown and felled and turned into a barn and house and fire

 

and a town square, usually empty, but on thursday nights and some saturdays

the homes release their owners into the restaurants and community fare

sharing stories and catching up on those no longer there

gone off to school or war or a career

likely one day to return to repair

broken hearts and spirits

as only a self reliant existence can

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Mathematical Inspiration from Mathematicians: An Outer View of the Inner World, Mariana Cook, Princeton University Press, 2009

“In the past, mathematicians always tried to solve problems exactly. Now we realize that most problems will never have an exact solution. Nonetheless, we can hope to understand the general shape of a solution, and topology gives a language for talking about these shapes. Topology gives a new point of view on all kinds of physical phenomena: the collapse of a bridge that vibrates too much, the tangling of strands of DNA, and so on. But I have to admit that my own interest is based on the joy of understanding shapes rather than on any particular applications.”

– Burt Totaro, page 64 (a professor I had in college, FWIW)

 

“As a grad student I had become interested in the annulus conjecture. Saunders Mac Lane advised me that it was a bit hard for a thesis problem (it was), but I thought about it whenever I had an idea. In 1968, while looking after my four-month-old son, an idea occurred to me, now called the “torus trick.” It only took a few days to realize that I had reduced the annulus conjecture to a problem about PL homotopy tori, and in a different direction had proved the local contractibility of the space of homeomorphisms of n-space.”

– Robion Kirby, page 62

 

“The imprint of the world in our minds is not photographic; all the brain knows of the outside world is a chaotic sequence of electric impulses and out of these it creates a structural entity: our perception of what we see and hear. Most of the time, an adult’s brain talks to itself and creates more and more refined structures within itself. The word “structure” means a mathematical structure, something which becomes more and more abstract and better and better logically organized in the course of this self-conversation….

We are all fascinated with structural patterns: periodicity of a music tune, a symmetry of an ornament, self-similarity of computer images of fractals. And the structures already prepared within ourselves are the most fascinating of all. Alas, most of them are hidden from ourselves…. Brains are our masters, with only 2 percent of our body weight, they take 20 percent of the oxygen resources of our bodies; you cannot cannot resist their commands. You become a mathematician, a slave of this insatiable hunger of your brain, of everybody’s brain, for making structures of everything that goes into it.”

– Mikhael Leonidovich Gromov, page 34

 

“I often think of cats. I think of trees. I think of dogs occasionally but I don’t think of them all that much because dogs are agreeable. They do what you want them to do to some extent. Some people believe that mathematics is what we think it is and it’s created by our thoughts. I don’t. I’m a Platonist at heart, although I know there are a very great difficulties with that view.”

– John Horton Conway, page 18

 

“At the moment, one of the things I’m working on understanding is the total wavelength of a surface like a sphere or something of greater complexity, such as the surface of a bagel or a pretzel. What is the total wavelength? … I first became interested in the total wavelength as a model related to a question which can be roughly stated as, can one hear the shape of the universe?”

– Kate Abedola Okikiolu, page 98

 

“For example, the “Ode to Joy” would be 334554321123322 for the right hand, and 332112345543344 for the left, with corresponding digits always adding up to 6. Soon music became a passion itself, on a par with my passion for numbers, though on its own terms.”

– Noam K Elkies, page 158

 

“In mathematics, there are not only theorems. There are, what we call, “philosophies” or “yogas,” which remain vague. Sometimes we can guess the flavor of what should be true but cannot make a precise statement. When I want to understand a problem, I first need to have a panorama of what is around it. A philosophy creates a panorama where you can put the things in place and understand that if you can do something here, you can make progress somewhere else. This is how things begin to fit together.”

– Viscount Pierre Deligne, page 156

 

” I prefer to close my eyes when I think about mathematics. The best work is done by night, in half sleep. Sometimes I go to bed thinking, “Ah, I have a nice lemma to prove–or disprove.” (Should I explain what a lemma is? A mountain climber needs holds to get from one level to the next one. Lemmas are the the holds of a mathematician.)”

– Jean-Pierre Serre, page 144

 

“How to define the roughness of rusted iron, of broken stone, metal, or glass? What shape is a mountain, a coastline, a river, or a dividing line between two watersheds? That is, can geometry deliver what the word seems to promise, namely, truthful measurements of untamed Earth? How fast does the wind blow during a storm? what shape is a cloud, a flame, or a welding? What is the density of galaxies in the universe? What is the volatility of the prices quoted on financial markets? How to compare and hopefully even measure different writers’ vocabularies?”

– Benoit Mandlebrot, page 94

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