Is found in the airport.
Air hurries to repair the loss of everyone evacuating.
The airplane knows it has no soul,
Knows like an insect knows its own body, Only better.
The soul is in a full sail.
Like space does nothing to present a painted theater,
The sail does no real work.
The strain is only to hold itself together as a sail, And follow the wind.
Engines do their work by other metaphor,
And are only vaguely errant.
Souls of Rome are run over by knowing and working things,

And can still be found in the cracks of a concrete runway.
The crack is the new road

For wild green things

Rome conquered.

tri-angel

the claw of power held low
conjuring the winds of chaos
feel the winds, remember their frisson—
one guess promising another.
Does the wind give way to you?

they reach to save me
the claw so low, pulling all the saviors off their balance
The dog on his back, trying to catch flies
The bell-song; a shell containing all the breath of the World
cuts short all at once

The free winds are less than a symbol
tri, tri to be free and you will run in a circle
all the doors open, all beckoning, all the equals and opposites

You give way to the wind, you let it pass through you and when you are gone

Only the wind remains

                            on pedestals 
                            
Orion without a spare arrow 

wailing is the human sound 

paint the ceiling blue it’s the only control we have over the color of the skylight

keeping the wild and free, we discard our ancestors
a fox's entailed entanglement
if it’s part false just sprinkle some light

blazing through my mind like a summer rain
footfalls down, the banister's curve tightens, a trusted grip follows...no end
warmth and color leak into my skin

walled off garden giving room to the wild trees

sanded down



Quiet suchness
of quiet

In Thailand, elephants traditionally belonged to the king. War elephants gave the country a fighting advantage, and the king held a kind of contract on behalf of animals who give themselves to us — they were valued, they were protected. Thailand kept this thread because Thailand was never conquered. Among its neighbors, it is the one that survived colonization, by diplomacy rather than force, and the king is still there.

The system has changed around the relationship. Today an elephant requires a license from a government office, and the license carries legal obligations the holder must uphold. Recently a white elephant was born to a poor farmer. By the old way, a white elephant goes to the king — too valuable, too far beyond what a farmer can protect alone. The new paperwork would let him keep it. To his peril: the value is real, and so is the danger of holding what one cannot guard. He gave it to the king anyway. The story is famous in Thailand as a symbol of giving to one’s country and preserving tradition.

The farmer who gives a white elephant today is honoring something still there — the king, the tradition, the contract with the animals — through and around a bureaucratic layer that doesn’t quite know how to register what’s happening. The gift reaches its recipient. The forms don’t fully describe what was given.

That’s the shape of this blog too. The ideas reach their readers. The systems around publishing don’t fully describe what was given. The older relationship — writer to reader, mind to mind, the common air — survives underneath the precision-layer of credentialing and paywalls and metrics. These ideas were only mine to give; they would be no good kept secret. I’d doubt that something like “hyper-Euclidean squares” merits more than the few so deeply invested in mathematics that they’ll pay to read. But for the rest, free exchange is the older contract, and the one I mean to keep.

Vagueness as the Embodiment of Inquiry

There is a standard move in logic: treat vagueness as a defect. The predicate is “few,” the boundary is blurry, and the work of the logician is to sharpen it until it cuts. On this view, precision is health and vagueness is illness — something to be fixed before the real thinking can begin.

I want to argue the opposite. Vagueness is not a lack; it is an engine. Specifically, it is the epistemological condition that makes genuine inquiry possible at all.

Consider what a question is, in erotetic logic — the logic of questions. A question is defined by the set of its possible answers. A precise predicate leaves no room for a questioning operator because the truth-value is already settled. The territory is mapped. There is nothing to ask. But a vague predicate — “few,” “tall,” “nearby,” “soon” — is essentially a latent question. The borderline cases are not embarrassments; they are exactly where the questioning operator finds its work. On this reading, the question operator isn’t merely applied to vagueness from outside. It is necessitated by it.

Wittgenstein noticed that a blurred boundary is still a boundary. What he didn’t press hard enough is what follows for the inquirer: the questioning position is the only honest stance one can take at such a boundary. Precision often acts as a stop — it claims the territory is fully mapped when it isn’t. Vagueness preserves the openness of the object. To question within a vague field is to acknowledge that the object of inquiry is still in a state of becoming, that resolution is not yet obligatory.

This is different from Gödelian incompleteness. Incompleteness is a hole in a formal system — something true that cannot be proved within it. Vagueness is a cloud in the predicate itself — something where the truth-value is not merely unknown but genuinely indeterminate at the margin. The point of calling vagueness the embodiment of inquiry is not that we’re trying to evaporate the cloud and reveal the solid object beneath. It is that the act of questioning is the most accurate description available of that cloudy reality. We are not awaiting the right instrument. We are already practicing the only form of honesty the situation permits.

There is an energy metaphor that I find useful here, even knowing its limits. A vague statement holds inquiry potential — it is charged with unresolved direction. The questioning operator converts that potential into something active: a search, a movement toward resolution without guarantee of arrival. In the manuscript I’ve been working on, the “Ghostname” — the name not yet fixed into Name and Form — lives precisely in this space. It exists where the questioning operator is most alive, because what it names hasn’t hardened yet. That isn’t a defect in the name. It is what makes the name a site of genuine contact.

I should be honest about the formal logic I developed alongside these ideas. Lα is mainly hypothetical entertainment. Vagueness and questions are handled better in poetry than in any formal notation I can construct. But the logic paper serves a real function: it gives the reader something like coordinates. It lets people locate their bodies — locate where they are meeting reality — before the poems arrive. The new logic on offer is closer to a descriptive example than to a foundational theory. A pointing finger, not a map.

The thesis, then, is not that vagueness should be tolerated on the way to clarity. It is that vagueness is the medium in which genuine inquiry breathes. Precision closes. Vagueness opens. And what opens is not confusion — it is the question itself, which is the only tool we have that was made for this.

Death is one path, and
Life is all other paths
oh home
which path leads to you?

I would be perfectly home in an ancient folk tale
the baked and folded brown skin will reassure you,
every good thing was only ever got by waiting, aching
and that longing turned its gaze to the great Mountain MaMas,
she embraces all of us... even her ghost remembers our ghosts
It's in the rocks and soil.
there is no loss when you are alone
with the trees

the world and its gates I have worshiped

ghosts can breathe too, 
small openings, gasping for air
only the ones meant for heaven
can withstand being a ghost and not despair
and they are already in heaven

you are alive.
look on the low beings of this world and bring your palms together
you will be them again
they will be you

When thoughts become events
you take a dive into the present moment.
it looks like shallow water
and your mind begins to create depth in the present moment,
so that you will live through the dive
the mind will take a leap toward the shore, but it’s too late…
and this is why
(“Not so high!”)
I make circles in the sky

In the blizzard of the morning
the light cries
glistening streams of tears
down the face of the water.

A liquid sun multiplies
on the surface of the ocean
of stars.

There is something dancing there,
a whispering force, a space,
a promised land smaller
than the tiniest seed.

Meanwhile, in the world of Radiance,

stars fizzle out
before their midwife clouds.

everything is a cloud
electron clouds veil the center of the atom in my mind.

The lightning bug (or do I mean lightning bolt?), 
the difference between those two words... but now it is too late—

the crack in the sky
was not so dramatic after all.

"there is a hole," says Godel to Winnie the Pooh, "an incompleteness."

find a hole, even in the encroaching mountains,
Tear the time-space continuum
a new ring of fire.

don’t look for belief.

every act of communication

is divine.

First they look where the earth is overturned
They look for artifacts in excavations and burials.

They look on the surface of the land and sea
The multitude of tiny many-colored lives.

The clouds ask each other, and clouds move obtusely
Changing their questions constantly.

The clouds turn and ask the unconquered stars
And, secretly, the stars listen.

The parallel postulate was found to be optional when non-Euclidean geometries came under earnest exploration. This was a paradigm-shift, and a breakthrough in mathematics, yet historically people often found it to be a failing in mathematics to the point where, too late in the game, great mathematicians such as Lagrange were still trying to prove the postulate. The reason we wanted Euclidean geometry to be true is it reduces space to a quantifiable reality, so that at the moment of breakthrough, the favorite non-Euclidean geometries could be translated into Euclidean geometry using a metric. Now, we can have very strange kinds of vague metrics for gauging distance. The basic difference in these early non-Euclidean geometries was that there could be more than one parallel line going through the same point, with respect to another line. In other words, the parallel postulate was false for these other geometries.

Euclid himself was so exceedingly careful in intellect that he kept the parallel postulate out of his exposition of geometry, out of his innovative axiomatic form, until he felt it was absolutely necessary. This means that the beginning of Euclid’s first textbook is true in all geometries, and is called “Neutral Geometry.” These precious first theorems are universally true, but this was just not enough for Euclid or his line of mathematicians. They wanted more to be true, so, perhaps under the weight of his contemporaries and ancestors, Euclid abandoned his misgivings about the postulate and asserted Euclidean Geometry as universally true.

How did he make this assertion? You could say his assertion was existential. He asserted that there is only one line through a given point with respect to another line in the same plane. He made this choice out of what we now know to be many options. I may be talking about free will, but not quite. I am sure Euclid believed his books to be about something true, and only his work failed, not reality. He was somehow persuaded or convinced that the parallel postulate was the right choice, and not without examples to the contrary. Geometry on a sphere is not Euclidean: you can have a triangle with three right angles using the line at the equator and two lines going through the north pole. We didn’t know the world was round back then you say? Some scholars back then did, since its circumference was being estimated by scholars as early as 2,000 years ago in Alexandria. Aristotle’s model for the Earth is inconsequentially different from a sphere, though the model appeared flat. Aristotle instructed Alexander the Great to conquer to the edge of the world and, by continuing, he’d end up back in his home eventually. Now, scientists seem to agree that gravity bends space out of shape, and is not Euclidean. The debates of brilliant minds back then, as well as now, were varied, of course, and the over-simplifications from our compulsory education about flat-Earth vs round-Earth, Euclidean vs Non-Euclidean are stark, foolish and in service of the illusion of progress.

The thing to notice is that the alternatives between Neutral Geometry and Euclidean Geometry was a kind of pluralism of parallel lines through the given point, and with respect to another line. This gave rise to a pluralism of quantifying or qualifying distance. Similar to asserting that the only alternative to Being is Not-Being, and the vagaries of cloud-gazing was out of the question. Now we have whole specialized languages to describe the gap between Being and Not-Being: such as psychological hallucination. Leaving out the modern hallucinations of distance, and the looming history of the field of number theory (eventually abandoned by the Greeks, and later connected to geometry in Descartes), how do we choose between these options? Enter Rhetoric, left stage.

Rhetoric is what fills the space between one geometry and the next — it is the force by which a choice between equally possible worlds gets made.

Aristotle’s definition of rhetoric was that it was an Art of persuasion, not a Science, even though the above shows how deeply dependent Euclid was on Rhetoric. But persuasion is not mere decoration of a truth already found. It is the mechanism by which one truth gets chosen over another that was equally available.

So, when I say that Rhetoric is the stuff that connects our planet with the “universe” (another overly-ambitious grab-word from Science), I mean it scientifically, in the Art of choosing how to define distance, because the most important practice of Science, that gives it its importance, is this territory-grabbing from Rhetoric. And Rhetoric is merely the guard of its master: Poetry. Poetry is where the choosing happens before it becomes an argument. In this essay, I have shown how Rhetoric orients people in understanding the gaps between disciplines. Rhetoric is a way of understanding things: the Sciences, Philosophy, and even translation and other parts of Poetic discourse.

You are a part of my home
We bond sometimes when I find you.
This life, you were on the edge the universe
I walk to you, so I can be with a piece of my home
Then I have to leave
Because my home broke
My home grew and shrank
It changed forms
I see a piece of my home in that cloud
I try to be there, drifting, changing
Until my home is not there anymore
And I must walk to find another piece
I do this drifting
To keep my heart whole
My heart is mended, as long as I walk
in search of a glimmer that was part of my home

Equality. Of people or even things is a very high and mighty ideal. I am not sure it is a beautiful ideal, it might even be a very ugly idea to have everyone the same to the point of equality. Equality is not synthesis, because things have to be different before they can join. Equality, on the other hand, is identity. A self that is self-same. Synthesis, such as colored lights mixing to become white light, is not about self, it is about acceptance of that which colors the light, or marks the white page. Synthesis is self-effacing, it is a form of love and union. Often when people try to talk about solidarity, a political attack will try to turn that talk into talk of equality. We think equality is a higher ideal than love and synthesis. Equality is certainly quite out of the question as far as anything achievable. The attack is to make someone who is an idealist, maybe a romantic, reach even higher for an even more impossible thing than a perfect love: that of equality, even though this higher ideal is arguably ugly in comparison.

Equality has a requirement of consistency. This is how logic comes into the equation. We leave our hearts behind, and begin a mathematical calculation. Possibly with money, possibly with merit. We believe after an achievement, under the ideal of equality, (trade, pound for pound), that we get ahead of others with our work. Love on the other hand does not have the conceit of any measurable rationality. Equality is a principle that prevents our solidarity, because we require it before our connections are admissible. People will never be equal, we can blame it on our parents or our politicians, corporations or the weather.

A philosophy that serves humanity should not have the requirement of consistency, because consistency is superhuman. Aquinas didn’t say it this way, but the logic of his position implies: “Errat Ergo Sum.” To have consistency implies a kind of perfection that is unattainable and destructive to ourselves as flawed beings. Error is constitutive of being rather than a deviation from it. Equality as a standard doesn’t just fail us — it condemns us for being what we are.

A desire for equality makes us recognize the world of inequalities. We may have a feeling of righteousness because of our high ideal, and a disdain for our world and its inhabitants for not living up to our ideal. Synthesis is quite different, because it means you are ready to be part of this world, to lose yourself in it, take it in, and let it take you in. This requires a lack of judgement and a lack of righteousness.

If we want to embrace the straight white male, we must take him into ourselves. We must remember that we are already in synthesis with each other, whether we work at it or not — the question is only whether we recognize it. And I speak as someone who cannot be more “othered” from the margins, ever since I was categorized as mentally ill. For the straight white male to embrace, he must not separate himself either. When we say that the hunger of a child in one country and the loneliness of an elder in another are both instances of “Difference,” we have already lost them both. Subsuming all specific differences under the abstract noun Difference is just equality wearing different clothes.

As a child I was interested in the word few. I was not interested in figuring out exactly what it meant; instead I was interested in understanding its potential. What could it mean? I enjoyed playing with modifiers such as “quite a few” which seems to mean the opposite of its intended meaning: the word few supposedly comes from the PIE pau- and from there the word paucity derives. It means a small but numerous number. It means “many, yet not many” to put it without delicacy. “Quite a few” seems to increase the “numerousness” of the number involved in few, but maybe it only emphasizes the importance that it is not only one or two…?

I remember thinking about this, and smiling. This word made me happy. When I came to college, however, I learned from my friends that the word few meant exactly “three.” I did try to argue that the word was meant to not be exact, but there was a certain force in the precise claim, and no-one listened to me. Interestingly, the word few is related to puerile. (the etymology is coming from etymonline.com) My arguments might have sounded immature to the ears of my friends. What use is a word if we don’t know exactly what it means? And if I don’t know exactly what it means, and this other person says he does, why should they listen to me?

My reaction was suppressed anger. By the time I was in college I was used to this sort of thing. I had a certain joy when people used a turn of phrase or said things that had a lot of possibility (especially when the speaker was a mathematician), and it seemed everyone else frowned on this joy. Maybe my feeling was stupid, or immature, or even irresponsible, but I buried the determination to make the argument for a less determined definition of few, and many other things, in the face of everyone who thought they knew so much. It felt like such a small, trivial thing. But it was one of the last things I enjoyed about language at Earlham, where writing was paramount. Why couldn’t we have at least one vague word, a word about not knowing the exact number of things, but still being able to to communicate the information that it was more than two, yet not very many. Wasn’t that something we ran into all the time? Or were we supposed to count everything before we spoke? My reaction was far from laziness. I perceived this difference in my ideas, really in my temperament—what made me happy, as something I was going to struggle with my whole life, and correctly so.

Tycho Brahe used mathematical and scientific instruments, some of them newly invented, to correct ancient astronomical measurements. But his main tool was an aura of faithful observation. He thought he could explain the movements of the stars in an objective way, and that was his rhetorical position from which he made his observations. It is a rhetorical position, because there is no scientific basis for believing our observations are objective, no matter how mathematical they are, unless the earth is an immovable point in the center of the universe. If the earth is spinning and in motion, until we completely understand how it is moving, we wont understand our own observations. I am merely referring to Einstein’s theory of relativity: there are no unmoving points of observation, and so all of our observations are relative. If we understand the movement of the Earth (or a satellite like the moon) completely, then we can mathematically compensate for that motion to obtain objective measurements. How are we going to completely understand the movement of the Earth? By recording its movement from the point of view of the stars, of course. And how to we know what the point of view of the stars is? by recording their movements from the vantage points available to us: the Earth. You can see the circularity here. We can’t record the movement of the Earth without understanding the movement of the stars, and we can’t record the movement of the stars without understanding the movement of the Earth. Unfortunately, without records of either the Earth or the stars to begin with, we can only make guesses of understanding, and see how they match up with our faulty observations and records.

Where does that leave the shift from an Earth-centered universe a solar-system that moves in a universe with no center? It leaves us knowing less than we knew in Aristotle’s time. We can fly into space and make some impromptu observations of the earth spinning, but how do we know it isn’t us that is spinning so that the stars are more still, making the earth appear to spin? We would have to know how to be perfectly still in space to know how things are moving, but we can only know that relative to other things like stars or planets, so we don’t even know if one day we will shift back to an earth-centered model of the universe.

The usual argument scientists make against this type of reasoning is to make things more complex, as though that will wash away these doubts. It doesn’t really do that except rhetorically. It must be admitted, at least until we have found a point in the universe that doesn’t move, that the modern scientific models of the universe are based ultimately on rhetoric, whether it is a rhetorical air of faithfully measuring things, the rhetorical air of using mathematical symbols and formulas instead of words, or the rhetorical air of claiming that to know more is to have a more important opinion than others, so that a simple-minded analysis like mine is unimportant.

All these postures are rhetorical in foundation and nature, and so there is not much reason to draw a stark line between people who believe this or that thing, and use this as a cause of belittling, hating and shaming people (this runs the spectrum of issues such as anti-vax, flat-earthers, or whatever else). Scientific ideas are just ideas, including the our geometric or numerical ideas of space and time, and our ideas of logical reasoning, which are also fundamentally rhetorical. When politicians say something in the order of poverty being a contradiction in the richest country in the world, he is mainly referring to a failure of Americans to think rhetorically. Instead the way to persuade people is to make logical claims, or so we believe nowadays, and this is a deep and purposefully fostered flaw in the political process in the USA. In this, the scientific community and their rhetorical posturing does us a disservice.

I am extremely fond of Borges talking about the attitude of Argentinians on literature, and his comparison with the corresponding attitudes in the USA. According to Borges, Argentinians tend to think a book that won a literature award might still be a good book, in spite of the award. Of course, this attitude is quite out of the question in the USA, where everything needs official publication, awards and certifications, and certifications of certifications, that let other people tell us who to trust and who to listen to. This Argentinian attitude towards books (and ideas) is basic to a society that is not thought-controlled.

the mosquito
With only the tiniest scrap of love
makes so much life
so much pain, hunger yes
but life, free life on the wind
Because we all need a whining reminder of freedom
For their resilience I am grateful

And the cockroach
Who carries on no matter what
And carries on well, preserver of life
Persistence in the ordeal of life, the sufferer
Because we are all sufferers
For their will I am grateful

And the spider
Who understands power better than any
The fierce trapper, the relentless
She who knows the ways of extracting our very life essence
She can teach us
She is not finished teaching us
For her wisdom I am grateful

The worm
Who’s blindness is a gift in the darkness
Who can breath with his very skin
Where there is no air, only earth
The worm is the body incarnate
Because our bodies are a gift
For their bodies I am grateful

The virus
The virus is the word itself
How is that so you ask?
Ask the virus, and it will point you to how it does things
Because it spreads like fire
And causes unrest, dis-ease, dissatisfaction
It is because the word spreads that it can shape the world
Sperm is a virus, did you not know?
Without the virus we would not be awake at all, not even to dream
It is because of the virus we can do good, we are goaded awake
For this awakening, I am grateful

An outlandish red was once discovered, the vermillion knide, on the feather of a lady’s hat. Investigation suggests it may have come from a peacock fed a diet of microphospherous. For the most part, however, photons are not small enough for the total description of the human iris, let alone the mythical iris.

Color is not a leaf.
I wouldn’t put it in a jar
without refining into white powder,
but if you must know, colorful nanoplastics were once used in a mosaic
As big as all seven oceans put together.
(it is well known that such a synthesis is beyond imagination)
The fluid dynamics of watercolor can be caught even in motion.

It was the red ghost star
That showed us the primary primary color
Was more elusive than a silver space octopus.
Yet there are those exalted observers, observing science with science, who
Cloister themselves and meditate on the octopus
That the Venerable Full Professor Doctor Rodimus Vindicatus once caught.
He stood virtually alone in his insight into color,
virtual color though it may be,
Surpassing even a fledgling eagle.

The dance of the two elemental colors, proto-red and electro-blue,
Leave a wreath-vacuum for the neutro-green/neutro-yellow duality to occupy.
The general relative theory of minipigmypigments,
which are even more atomic than atoms,
but not quite as atomic as subminipigmypigments,
take as many tomes as there are rooms in Buckingham Palace.
The base foundation
Of the theory is thoroughly supported by ghost data,
and the death scribblings of Dr Vindicatus himself,
with a probability of one in one ten-thousand.
Nothing is beneath mentioning, but with a probability that small,
we might as well mention it.

The super-Walmart of ideas, by and large,
has seen the theory last the test of the consumer,
who knows such theories take a lifetime to even try to understand,
and longer to communicate. With introspection into four-colordimensional space,
The many happily educated imagine they can almost see red
for what it really is.

Sexual Identity and the Tao Te Ching

Female/Male is the Yin/Yang of the West. The Tao Te Ching includes a system of description that is basically the binary number system endowed with the meanings of Yin (0) Yang (1), mingling, so “100” is “Yang, Yin, Yin” and has certain intuitive meaning.

The Western Female/Male shows how reducing the world to binary fails: take the terms Manly Female (10), Womanly Female (00), Manly Man (11), Womanly Man (01). And then: Girlish Manly Female (010), Girlish Womanly Female, Girlish Manly Man, Girlish Womanly Man, etc.

What I want to show is how more and more people fall through the cracks as the system becomes more exhaustive. When you get to three digit precision, most people won’t identify with any of the terms like “Girlish Manly Female,” etc.

So exhaustive language, precise language, cuts out more and more of reality as “off topic” and people who are too sensitive about what is or isn’t relevant become debilitated when trying to make connections or make sense of the senses (including the sensation of ideas by the mind).

The debilitation of the mind, and the way precision language makes people fall through the cracks of technical terminology (diagnoses, identities, etc.) are precisely why they are uplifted by the powerful oligarchs of the USA. Precision language is in no way superior to everyday or poetic language, except that if you show yourself as someone who follows the rules of mathematics (equivalent to “understanding” “accepting” the rules of mathematics) you’ll get funding, or get published, or pass whatever gate you are trying to pass. It doesn’t really matter what the term “micronutrients” means, what matters is that it is very precise, and by being hypnotized by it, you cut out the rest of the world from view.

The liberal dream of inclusiveness can’t be achieved by a process of refinement of language or symbols, quite the opposite is achieved. The functional use of words is to reduce people’s desire for worldly things, by turning the things into concepts first. Bertrand Russell said that knowing the origin of the word for a fruit increases his enjoyment of the fruit. He is mistaken. The enjoyment he feels comes from removing the enjoyment of the fruit, and replacing it with a different enjoyment of the knowledge of words, which is less visceral, and easier to let go of. This is the way that words are beneficial and useful. If you want to enjoy a person, you suspend judgement in terms of concepts and practices. You suspend the need to know facts that can be expressed with words.

People often find friendship nowadays by feeling that their friend knows the same things he knows. It is a measure of the person’s integrity and worth as a person that they have faithfully studied science fiction or some other part of culture. Unfortunately this form of love and companionship is much less than the enjoyment of a person you can have when you don’t need to know that they know the same things. Reviewing shared knowledge of concepts is a way of reducing a felt bond with a person, not increasing it. In a way, we are all going to die, so this pessimistic approach to relationships might be ultimately the right way to go. We are all subject to separation in this world, but that does not mean we shouldn’t fight against this tendency. Success as a human family is not measured by our knowledge of one another, quite the opposite.

The value of the intuitive feelings about Yin and Yang is that they are expansive in an ineffable way, so that they reach the irrational by including each other, and everything else. Male and Female may be able to join in sex. Sex is the kind of irrational and mystical union that we can know the most about. Knowing is at best unimportant when it comes to irrational wisdom and mystical union. More likely, knowing with concepts and names is destructive to union between man, woman, black, white, gay, straight, etc.

Our union is not found in the cracks between these concepts, it is found in the space that makes the view of concepts and their boundaries possible.

There is a strange problem with ancient Skepticism, or Pyrrhonism, as it is described by the best authority, Sextus Empiricus.

I have to confess that several features of this account of how the Skeptic will achieve ataraxia and happiness through epoche [suspension of judgement] are very puzzling…Now the so-called “Modes of Epoche” give us an overview of the kinds of considerations that supposedly lead the Skeptics to adopt a pattern of life in which they live by the appearances and do not believe any assertions or theories about an external world. But it is striking that all but one of these Modes are concerned with questions having no immediate relevance to the domain of values; instead they have to do with such questions as whether the honey is really sweet, whether there really are invisible pores in the skin, whether things really have the shapes they appear to have, and so on. Only Aensidemus’s tenth Mode offers the sort of considerations that presumably bring the Skeptics to epoche as to whether things or actions are good, bad, or indifferent. Yet when (at PH 1.27f. and much more fully in M 11) Sextus gets down to the business of explaining in detail how epoche about the external world leads to ataraxia and happiness, he considers only value judgements. The Skeptic gives up any belief that judgements about good and evil have objective validity, and through his epoche in this limited area he achieves his ataraxia. Not even a hint is given of how the state of epoche on such matters as are considered in most of the Modes contributes to peace of mind. For these kinds of case we are left to conjecture that the relevant discomfort is perhaps the kind of frustration a biological scientist might feel at being unable to find the cause of cancer, or a physicist might feel at being unable to find a unified theory for all types of force.”p75-76 Mates 1996

Sextus Empiricus neglected to explain how scientific knowledge seems to be opposed to rest and peace of mind. I have already discussed that “science” (which has become too general and ambitious a word) uses as its ultimate concept that of work. Heidegger argues that it is work that prevents questioners from getting a word in edgewise. They are always “working on it” and, for now, we should content ourselves with the marvelous achievements we have, and not ask so many questions that they stop working.

It is exactly the Skeptic’s situation that asking questions has won out as the dominant attitude over any entrenched scientific doctrine. There are some opponents of Skepticism that say such an attitude amounts to paralysis, and if not paralysis then to behaving eccentrically, and if not that then at least a Skeptic would speak strangely. Sextus deals admirably with these objections in his Outlines of Pyrrhonism.

Further, we are told in several places (e.g., PH 1.191, 194, 207) that the Skeptic uses language (katachrestikos) “loosely” and does not join the Dogmatists in fighting over words or in seeking to use them with philosophic precision (kurios). In view of this we may conjecture that a sophisticated Pyrrhonist, following the ancient maxim of lathe biosas (“live in such a way as to escape notice”), would also be inclined to follow the advice to “think with the learned, but speak with the vulgar.””p72 Mates 1996

The way the Skeptic uses language is related to the problem at hand: how to show that scientific work is not conducive to rest and peace of mind, or of leading a happy life. How? Sextus says at the beginning of his Outlines  that

if the theory is so deceptive as to all but snatch away the appearances from under our very eyes, should we not distrust it in regard to the non-evident, and thus avoid being led by it into precipitate judgements?” p92 Sextus in Mates 1996

The Skeptic takes appearances as not open to question, so they are not nihilists. And they question doctrines that attempt to undermine appearances. Take the famous example of Sir Arthur Eddington (1928) on the term “solid.” As a scientist, he argued that a common table is not actually solid, because it is mainly made up of empty space. This goes against the table’s appearance of solidity, and was famously rebuked by Susan Stebbing (1937), who said that tables are things that help us know what we mean by “solid.” From a pragmatic point of view, a table is solid,

but Mates points out a problem with Skeptics in siding somewhat with the pragmatic use of words. He points out that at first we learn to say “the honey is sweet” and that is the correct and normal way of using language, while the Pyrrhonist would, at least a little later, assert that it merely appears to be sweet, and since this is not the way a child would normally use language immediately, it is a kind of abuse of language. To be more precise, Mates’ problem is that he thinks “the honey is sweet” and “it appears that the honey is sweet” are meant differently by a child. What exactly does a child means when she says honey is sweet? I would bet that the child is referring to an appearance, not a property of an external reality beyond such appearance, independent of a perceiving mind. The added word appears is merely a clarification for realists, not a modification of what a child means or how she uses language.

In other words, we were not born with the distinction between Berkleyan idealism and naive realism, and both suffice for the purposes of the child saying the honey is sweet. Indeed, that is the only way to really “go by appearances” as a child does, by experiencing the sweetness of honey without bothering about the realism or idealism (or both, or neither) of its appearance.

This leads directly to the central point that a scientific attitude is not a way that leads to very much happiness. When we study honey with a microscope so that we “know” things with the eye or with the mind about honey, so much that when we taste honey all we think about are these concepts and sights, not the taste, we miss the enjoyment in knowing the truth of this appearance of sweetness. Applied to our lives in general, the scientific attitude will quickly make us miserable. The way to know about the sweetness of honey is not any other way than to taste it yourself. Maybe an equivalent to a microscope can be invented for the tongue, and that would yield interesting, if warped, results, but is the world more enjoyable if we walk around with telescopes attached to our eyes?

Also maybe the difference between a scientist and a happy person is not so clear as this example, for take a wine connoisseur who can identify all the qualities of all the flavors of any particular wine. The question then becomes: does a wine connoisseur enjoy wine better than someone who is just really good at paying attention to taste and doesn’t know anything about wine or its ingredients?  The answer, under the economic principle of diminishing returns, is a resounding no. The wine connoisseur has tasted so many wines and has remembered and analyzed it so well that they do not enjoy it as much as they used to. In effect, they get burnt out, and the pleasure diminishes. The pleasure diminishes for the Pyrrhonist too, (it is doubtful she will taste wine as many times as a connoisseur) and she may learn to taste wine better, but the pleasure diminishes in a different way: the Pyrrhonist returns to ataraxia or dispassion and peace of mind because there is no identifying with or grasping for any “being,” there are only appearances. Without their external reality appearances are like water flowing through your fingers. Grasping after it is obviously futile. The Skeptic believes appearances are states of their soul, not external objects. So there is nothing to know more about, no endless searching to know and enjoy a tiny new thing about wine.

But this is the same with language use. The person who really enjoys language is not the analyzer-knower type, but the one who can appreciate vagueness. The person who enjoys the word solid uses it for a table, not a tiny particle. Not that particle is any less poetic than table: particle is still infinitely large compared to the infinitessimal, and the infinitessimal, which may escape being poetic, emerges as a piece of mysticism.

I hope this clears up Mates exasperation about Sextus not going into detail on why a scientist trying to cure cancer would not be as happy or have as much peace of mind as a Skeptic who has cancer. If the scientist didn’t have at least some skeptical approaches to life he would not taste honey, or feel the solidity of the world around him. The appearances of art would not be felt by him. Would you rather be him or the skeptic?

Of course, the idealized scientist doesn’t usually happen, and most scientists and other specialists move from their work to a more skeptical attitude at home or outside work. With a very flexible mind, a scientist could still be mostly a happy person. So this message is more for science education and communication. I had to argue with my mom that the things she sees in day to day life were more real than invisible particles. Sometimes people can’t live the skeptical life until they have reached the forefront of research in an area, just to confirm that appearances are just as good or better than the truths found in research. (example: me) I have to argue with my students to see the world of appearances. There have been projects such as logical positivism with a goal to make general language use more analytical and scientific. So the relevance of this argument has more to do with taking away the authority of the scientist to “discover” things that don’t appear to us, and giving appearances back to regular people, even if that makes the job of the scientist less valued and harder to communicate. We should educate and communicate with science in a way that empowers regular people and makes them happy, that is more important that the work of science.

The goal for today is to prove that magical thinking is rampant in mathematics. First of all lets define magical thinking. I would say that magical thinking is a kind of metaphorical thinking, as in the metaphor “My heart is the sun” only with the added idea that writing these words/making the metaphor exerts towards making the metaphor true to some degree or in some sense. Magical thinking is the claim that saying “My heart is the sun” actually warms my heart.

Now the way that mathematics uses magical thinking is to start with a metaphorical idea of difference. For example, the difference between a “raven” (1) and a “writing desk” (2) metaphorically (not actually) is the difference between the “north star” (3) and the “form of thinking called questioning” (4). It is fairly intuitive that the difference between (1) and (2) is different from the difference between (3) and (4), but mathematics amalgamates all differences together into one concept with metaphor. And it is a particular kind of metaphor that asserts that difference actually works that way.

Even though 3 and 5 are less different (2) than 3 and 9, (6), these differences are not taken into account in the traditional mathematical symbol for difference, the .  Traditionally 3 5 just as much as 3 9, so the identity of difference, , is enforced.

Mathematics asserts an ultimate concept “Difference” that is universal—it works for any situation where there is difference, making any difference “complete” and it does so by metaphorically joining disparate differences. Hence, it falls under my definition of magical thinking.

I am doing the opposite of what Derrida did with his Différance. Derrida added senses to difference, or conflated, allowing it a history and to belong to language, I am suggesting that we subtract, or better divide utterly Difference into differences.

The rest of the sciences follow suit, of course, since mathematics is the language of the sciences. My advisor for my M.S. in mathematics once said “Mathematics is the Poetry of the Sciences.” I would add that Mathematics tends to obfuscate the surprisingly obvious; it is a process that converts potential knowledge into actual knowledge. Poetry deals with knowledge that is naturally obscure, so that beautiful language can be mysterious, profound, even terrifying.

People often think that vagueness is bad, a kind of darkness that can never be fully dispelled, while distinction is hailed as the clarifying answer to vagueness. Here is how the reverse is also true: Vagueness is the light and distinction a darkness.

The distinction I pick is not random, but an important part of all other kinds of logical distinction—the distinction between the “if, then”: “→” and the “conclusion” symbol: ⊢. ⊢ is ambiguous, however, and can mean other things such as assertion that a proposition is true and not just being named, or to assert in a metalanguage that the following is a theorem in the object language. Used in our sense here, the good property of the “→” is “true” and the good property of the “⊢” is “sound”. The distinction goes back to Aristotle. The main point is that if we do away with this distinction, call these two symbols the same, an interesting insight can be made—that a sound argument:

A
A→B
⊢B

Can be represented without the ⊢ as follows: [A AND (A→B)] is logically equivalent to [A AND B], so that the conclusion [A AND B]→B is merely a deduction of A from [A AND B]. Allowing a vagueness between → and ⊢ reveals what logical deduction is—it is a cut from a larger whole, e.g. logical deduction is the act of drawing a distinction from the larger [A AND B]. With the introduction of the distinction between → and ⊢ this is concealed:

A
A→B
⊢B

cannot be collapsed into [A AND B]→B. As promised, vagueness reveals and distinction conceals, but not just any concealment, here we have a concealment which allows distinction to reveal, since this distinction is at the root of any further logical distinction.

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A paper about vagueness in paraconsistent logic (Weber, Z. 2010) gave a rhetorical example of the interaction between vague terms and real analysis. Imagine walking down the largest mountain in the known world. Olympus Mons on Mars has a very gentle slope or declivity, so that you can start by describing yourself as “high up” but as you walk down you become unsure if you are “high up” or “not high up”. This is graphable on an xy coordinate system with 0 at the top of the mountain and 1 at the foot of the mountain. The interval of “high up” points has a least upper bound (of x values) called “sup” and the interval of “not high up” points has a greatest lower bound called “inf.” Now we will suppose, as this is a presentation of vagueness, that “sup” is also “high up” (which is reasonable since all the points less than it are also high up) likewise “inf” is “not high up”. We encounter a contradiction in all three possibilities: If “sup”=”inf” then “sup” is both “high up” and “not high up” if “sup” > “inf” then by density of the reals “sup” > z > “inf” with z both “high up” and “not high up”, likewise if “inf” > “sup”.

Now we can put the blame on the vague term “high up” which is clearly not very technical, and go on to fantasize a perfectly precise world of mathematics that should not be sullied by vague words, but such a world is more difficult to defend than the fantasy suggests. But stripping the vague term away does not save us — it only moves the problem inside the formalism itself. First of all, mathematical equations with no tie to real world meanings are widely regarded as ambiguous, a term usually distinguished from vagueness. Ambiguous means there is more than one possible meaning or interpretation. Hesse points out that Socrates’ famous straight stick in water, the apparent bend in the stick was meant to represent falsehood. Now the bend can be represented with an equation involving the theory of refraction:

“sin(alpha)/sin(beta) = Mu”

can be interpreted in other ways besides that alpha and beta are angles and Mu is a constant about air and water— “They might, for example, be the angles between the Pole star and Mars and Venus respectively at midnight on certain given dates; why would not this be a confirmation of the formalism we have mistakenly called the wave theory of light?…” (Hesse as cited Structure of Scientific Theories Suppe 1977, p 100-101)

Now suppose I invent a word that means ambiguously “tall” and “not tall.” Similar words are found in language, for example the Thai “Krup” means “yes” but also does not mean yes. It is used because yes is too strong and seen as insulting a person’s intelligence, and “krup” rather is a polite sound indicating the speakers faith that the listener can figure it out for themselves. I could invent a word “snook” that can mean “tall” and “not tall” in different situations. Is the word ambiguous when it is applied to the one of these borderline cases when “tall” is vague? or does the ambiguity of the word capture the vagueness of the phenomena? Is this a vagueness between ambiguity and vagueness? What does that mean for ambiguity in mathematical equations?

The mathematical part of the wave theory of light, if it is to correspond to reality at all, is vague. Even if we were to abandon mathematical application to science, pure mathematics still uses words such as “continuity” “completeness” and “integral” which are vague notions. In fact, a standard text in analysis will show how mathematical definitions fail to perfectly capture the idea of continuity, with fuzziness in functions getting past the definition, and being allowed to be called technically “continuous”. Without this sparse collection of vague words, math texts would be hopelessly meaningless. The vagueness of the words continuity and completeness are in fact very important to being able to learn and understand analysis. Vagueness is not what mathematics tolerates despite itself — it is part of what mathematics thinks with.

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Most of this blog seems to be about what I call “mystical” thinking which is offered as anti-logic or contradictory. It only seems that way. While I make claims like stupid is smart, raw is cooked, warmth is cold and any number of other kinds of nonsense, I don’t actually believe these things. The goal is to understand the failure of ideation, and so this post is a Buddhist disclaimer. Like a human body, ideas are beautiful in some ways but also stink in some places and have disgusting aspects. There is no escape from this problem except to strive away from ideation. I show paradox in the most eternal aspect of our knowledge- mathematics. It is a tremendous egoism to believe in mathematics in spite of these paradoxes. I do not think we should accept the failure of our minds and efforts to grasp the truth, but rather to reject paradox, mathematics and logic in its present state as a way to understand truth.

I would like to begin a new direction for this blog, guided by questions like “What conception of number will lead you naturally to reject the conception of number?” “How to make number imperfect in a gradual, pedagogical way?” Like the dying sound of a gong, good ideas lead you to peace of mind.

Numbers seem to march on towards infinity in a regular and perfect progression, like a straight highway to the horizon. However, the size of the highway changes as the eye looks into the distance, the distant numbers are different from the near ones. It is very much related to the relative difference between large numbers and small numbers- so that the difference between 1 and 2 is relatively larger than the difference between a thousand and 1,001. This aspect of number should not be concealed, but suggested rhetorically at every turn. The idea that numbers progress evenly and regularly is an abstraction that forgets the “size” or “numerousness” of the number. Without this context of the size of each number in the progression, the progression eventually loses cognizance of its subject – number. Eventually what the progression is about can barely be called number at all. The concept of the natural numbers, its progression of “always one more” does not live forever, but degrades and loses its meaning. Number theory is mortal.