#meaning
Beyond the Enlightenment Rationalists:
From imaginary to probable numbers - I
Imaginary numbers arose in the history of mathematics as a result of misunderstanding the dimensional character of numbers. There was a failure to acknowledge that numbers exist in a context of dimension. This has earlier been addressed at length.[1] Simply put, numbers exist always in a particular dimensional context. Square numbers pertain to a context of two dimensions and therefore to a plane, not a line. Square roots then ought justly reference a two-dimensional geometrical context rather than the linear one mathematics has maintained ever since mathematicians of the Age of Enlightenment decreed it so. Square roots contrary to the way mathematics would have it can neither exist in nor be found in any single line segment, because they do not originate in the number line but in the two-dimensional square.
Algebra, not geometry, provided the breeding ground for imaginary numbers. They were given a geometric interpretation as an afterthought only, long after the fact of their invention. Rationalist algebraists, feeling compelled to give meaning to equations of the form b2 = -4 came up with the fantastic notion of imaginary numbers. Only indirectly did these grow out of nature, by way of minds of men obsessed with reason.[2]
Descartes knew of the recently introduced square roots of negative numbers. He thought them preposterous and was first to refer to the new numbers by the mocking name imaginary, a label which stuck and which continues to inform posterity of the exact manner in which he viewed the oddities. It is one of the ironies of history that when at last a geometrical interpretation of square root of negative numbers was offered it involved swallowing up Descartes’ own y-axis. Poetic justice? Or ultimate folly?
Had the essential dimensional nature of numbers been recognized there would have been no need to inquire what the square root of -1 was. It would have been clear that there was no square root of -1 nor any need for such as +1 also has no square root. As linear numbers, neither -1 nor +1 can legitimately be said to have a square root. Both, though, have two-dimensional analogues and these do have square roots, not recognized as such unfortunately by the mathematics hegemony.[3]
In the next post we will look at a comparison between imaginary numbers, which were formulated in accordance with this misconstrual about how numbers relate to dimensions, and probable numbers which grow organically out of a consideration of how numbers and dimensions actually relate to one another in nature.[4] The first of these approaches can be thought of as rational planning by a central authority; the second, as the holistic manner in which nature attends to everything, all at once, and without rational forethought.
(continuedhere)
Image: A drawing of the first four dimensions. On the left is zero dimensions (a point) and on the right is four dimensions (A tesseract). There is an axis and labels on the right and which level of dimensions it is on the bottom. The arrows alongside the shapes indicate the direction of extrusion. By NerdBoy1392 (Own work) [CC BY-SA 3.0orGFDL],via Wikimedia Commons
Notes
[1] See the series of about nine posts that begins here.
[2] The Rationalists missed here a golden opportunity to relate number and dimension by defining square root much too narrowly. They seem to have been so mesmerized by their algebraic equations that they failed to pursue the search into deeper significance pertaining to essential linkages between dimension and number that intuition and imagination might have bestowed.
[3] As Shakespeare correctly pointed out, a rose by any name would smell as sweet. Plus one times plus one certainly equals plus one but that has nothing to do with actual square root really, just with algebraic linear multiplication. Note has often been made in these pages of the difference between mathematical truth and scientific truth. Whereas mathematics demands only adherence to its axioms and consistency, science requires empirical proof. Mathematics defined square root in a certain manner centuries ago, and has since been devoutly consistent in its adherence to that definition. In so doing it has preserved a cherished doctrine of mathematical truth, as though in formaldehyde. It has also for many centuries contrived to be consistently scientifically incorrect. The problem lies in the fact it has converted physicists and near everyone else to its own insular worldview.
[4] For an early discussion of the probable plane, potential dimensions, and probable numbers see here.
© 2016 Martin Hauser
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-Page 306-
meaningless; sometimes charming, like the feeling of ordering Chinese food from the sky • sinnlos und meist charmant, als würde man chinesisches Essen vom Himmel bestellen - December 2018 - #toomanyhashtags #dontcare #xmas #2018 #german #deutsch #candid #chinese #chinesefood #diy #shadow #fish #surreal #idk #photography #moment #meaning #rochesterny #tuesday #mittwoch #rochester #lakeontario #normal #flashback #throwback #picoftheday #reallife (at Lake Chinese Food To Take Out)
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Kolmogorov Complexity and Our Search for Meaning - Issue 63: Horizons - Nautilus
We abhor randomness and love patterns. We are biologically programmed to find some patterns that explain what they see. But we can never be certain that the pattern we’ve identified is the right one. Even if we could somehow be assured that we haven’t made a mistake, and we are exhibiting a computer-like perfection, there may always still be a deeper truth to unearth. This tension helps drive our love of literature, theater, and the cinema. When we read a novel, or watch a play, the author or director is presenting us with a sequence of events that has a common theme, pattern, or moral. Literature, plays, and the cinema offer us a delightful escape from the usual unintelligible, meaningless chaos that we find in the real world around us. Really good literature goes further, and leaves us with the possibility of many interpretations. We come face to face with the incomputability of the Kolmogorov complexity.
This tension also defines how we engage with our own lives. While we travel through the seemingly random events in our life, we are searching for patterns, and structure. Life is full of “ups and downs.” There are the joys of falling in love, giggling with your child, and feeling a sense of great accomplishment when a hard job is completed. There is also the pain of a crumbling relationship, or the agony of failing at a task after great effort, or the tragedy of the death of a loved one. We try to make sense of all this. We abhor the feeling of total randomness and the idea that we are just following chaotic, habitual laws of physics. We want to know that there is some meaning, purpose, and significance in the world around us.We want a magical story of a life, so we tell ourselves stories.
Sometimes the stories are simply false. Sometimes we lie to ourselves and those around us. And sometimes the patterns we identify are correct. But even if the story is correct, it is not necessarily the best one. We can never know if there is a deeper story that is more exact. As we age and suffer from ennui, we gain certain insights about the universe that we did not see before. We find better patterns. Maybe we get to see things more clearly. Or maybe not. We will never know. But we do know that the search is guaranteed to never end.
(1) Untitled Album | via Facebook on We Heart It. http://weheartit.com/entry/55508790/via/Alice_Coppen
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Why so Serious? | via Tumblr on We Heart It. http://weheartit.com/entry/65894643/via/RockMeIan
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four horsemen stormed in i tried to warn em
false gods aint reform this the new corinth
adorned in course leather forged in moria
hide of moloch took no pleasure killed the sorcerer
crusader no better than the forfeiter
still searching for the source code to glory
still searching for the meaning of my story
found motivation love and connection
pride still got me 2nd 3rd guessing
wonder if theres real estate right outside the pearly gates
trying get my story straight fore i put my life at stake
floating thru a dreamstate surfin on the astral plane
never felt more lucid than on acid and forgot my name
this the kind of passion making pancakes of the fallen man
pavarotti weeping from the beauty singing sonograms
take command make a stand
How to Use the Feynman Technique to Identify Pseudoscience
Earlier this year, a study made headlines worldwide by bluntly demonstrating the human capacity to be misled by “pseudo-profound bullshit” from the likes of Deepak Chopra, infamous for making profound sounding yet entirely meaningless statements by abusing scientific language.
This is all well and good, but how are we supposed to know that we are being misled when we read a quote about quantum theory from someone like Chopra, if we don’t know the first thing about quantum mechanics?
In a lecture given by Richard Feynman in 1966, the influential theoretical physicist told a story about the difference between knowing the name for something and truly understanding it:
“This boy said to me, ‘See that bird standing on the stump there? What’s the name of it?’ I said, ‘I haven’t got the slightest idea.’ He said, ‘It’s a brown-throated thrush. Your father doesn’t teach you much about science.’
I smiled to myself, because my father had already taught me that [the name] doesn’t tell me anything about the bird. He taught me ‘See that bird? It’s a brown-throated thrush, but in Germany it’s called a halsenflugel, and in Chinese they call it a chung ling and even if you know all those names for it, you still know nothing about the bird — you only know something about people; what they call that bird. Now that thrush sings, and teaches its young to fly, and flies so many miles away during the summer across the country, and nobody knows how it finds its way,’ and so forth. There is a difference between the name of the thing and what goes on.
The result of this is that I cannot remember anybody’s name, and when people discuss physics with me they often are exasperated when they say, 'the Fitz-Cronin effect,’ and I ask, 'What is the effect?’ and I can’t remember the name.
There is a first grade science book which, in the first lesson of the first grade, begins in an unfortunate manner to teach science, because it starts off on the wrong idea of what science is. There is a picture of a dog — a windable toy dog — and a hand comes to the winder, and then the dog is able to move. Under the last picture, it says, 'What makes it move?’ Later on, there is a picture of a real dog and the question, 'What makes it move?’ Then there is a picture of a motorbike and the question, 'What makes it move?’ and so on.
I thought at first they were getting ready to tell what science was going to be about — physics, biology, chemistry — but that wasn’t it. The answer was in the teacher’s edition of the book: The answer I was trying to learn is that 'energy makes it move.’
Now, energy is a very subtle concept. It is very, very difficult to get right. What I meant is that it is not easy to understand energy well enough to use it right, so that you can deduce something correctly using the energy idea — it is beyond the first grade. It would be equally well to say that 'God makes it move,’ or, 'Spirit makes it move,’ or, 'Movability makes it move.’ (In fact, one could equally well say, 'Energy makes it stop.’)
Look at it this way: That’s only the definition of energy; it should be reversed. We might say when something can move that it has energy in it, but not what makes it move is energy. This is a very subtle difference. It’s the same with this inertia proposition.
Perhaps I can make the difference a little clearer this way: If you ask a child what makes the toy dog move, you should think about what an ordinary human being would answer. The answer is that you wound up the spring; it tries to unwind and pushes the gear around.
What a good way to begin a science course! Take apart the toy; see how it works. See the cleverness of the gears; see the ratchets. Learn something about the toy, the way the toy is put together, the ingenuity of people devising the ratchets and other things. That’s good. The question is fine. The answer is a little unfortunate, because what they were trying to do is teach a definition of what is energy. But nothing whatever is learned.
Suppose a student would say, 'I don’t think energy makes it move.’ Where does the discussion go from there?
I finally figured out a way to test whether you have taught an idea or you have only taught a definition. Test it this way: You say, 'Without using the new word which you have just learned, try to rephrase what you have just learned in your own language. Without using the word “energy,” tell me what you know now about the dog’s motion.’ You cannot. So you learned nothing about science. That may be all right. You may not want to learn something about science right away. You have to learn definitions. But for the very first lesson, is that not possibly destructive?
I think for lesson number one, to learn a mystic formula for answering questions is very bad. The book has some others: 'gravity makes it fall;’ 'the soles of your shoes wear out because of friction.’ Shoe leather wears out because it rubs against the sidewalk and the little notches and bumps on the sidewalk grab pieces and pull them off. To simply say it is because of friction, is sad, because it’s not science.”
Feynman’s parable about the meaning of science is a valuable way of testing ourselves on whether we have really learned something, or whether we just think we have learned something, but it is equally useful for testing the claims of others. If someone cannot explain something in plain English, then we should question whether they really do themselves understand what they profess. If the person in question is communicating ostensibly to a non-specialist audience using specialist terms out of context, the first question on our lips should be: “Why?” In the words of Feyman, “It is possible to follow form and call it science, but that is pseudoscience.”
Source:BigThink|
Video:Richard Feynman on What It Means | Blank On Blank @pbsdigitalstudios
SUNNY SIDE UP
beginning of pre-omelette stage series
[BETTER WAYS TO HIDE EGGS INCLUDE 1966 TIGER CAMOUFLAGE]
#eggs
#omelette
#omelettestage
#jaqueslacan
#semiotics
#kajasilverman
#jeanfrancoislyotard
#libidinaleconomy
#postmodernism
#postmodernart
#contemporaryart
#contemporarypainting
#contemporarydesign
#contemporaryphilosophy
#contentandform
#meaning
#waysofseeing
#dramaliamesabains
#ephemerality
#stagesofdevelopment
#postdevelopmentalinventory
#complexposttraumaticstressdisorder
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SUNNY SIDE UP
beginning of pre-omelette stage series
[BETTER WAYS TO HIDE EGGS INCLUDE 1966 TIGER CAMOUFLAGE]
#eggs
#omelette
#omelettestage
#jaqueslacan
#semiotics
#kajasilverman
#jeanfrancoislyotard
#libidinaleconomy
#postmodernism
#postmodernart
#contemporaryart
#contemporarypainting
#contemporarydesign
#contemporaryphilosophy
#contentandform
#meaning
#waysofseeing
#dramaliamesabains
#ephemerality
#stagesofdevelopment
#postdevelopmentalinventory
https://www.instagram.com/p/Cchtk1hrxd1/?igshid=NGJjMDIxMWI=
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I tell you, even a half-dead man hates to be alive and not be able to see any sense to it.
The Sirens of Titan
Kurt Vonnegut
I tell you, even a half-dead man hates to be alive and not be able to see any sense to it.
The Sirens of Titan
Kurt Vonnegut
Words that should exist
A more concrete word for the subjective ‘line’ that exists in people’s minds. The whole 'you’ve crossed the line now’. Usually it refers to when something goes from being ok to being unacceptable. Varies depending on the person.
There is a sunflower field
in Dixon. I’ve never been,
but I used to own a dress
the color of red plums and milk.
I tore it dancing in the orchard
that October forgot to map.
This is about lines, but mostly about what humans
say about sunflowers, about being golden inside
& we keep singing light & we keep saying no & seek.
& there is this bit about freedom
& the edge of the world being not edged
but centered close
& sometimes even in the poems we are strayed.
I should have kept the torn
dress for the daughter I will have,
but I can’t stop thinking about florets
& if they are rust
or luster or maybe like that skin
between my knees that keeps shedding—
Space any space begs, move
slower, bite softer, kiss
less of me.
I thought love was like this
& flesh was a word you learn
in girlhood. I thought I want familiar
& wild & blue-eyed & here, I am dreamscape —
my feet are healed
& I am turning in a fog film
of flowers. I get to kiss every boy
I’ve ever lust if just for a sap minute,
only soon they are tearing my dress
off & there is plum juice
on my shoulder blades & the law of gravity
is the law of wanting; there is this center
of pollen & it keeps pulling us,
bending earth to grain.
& its not about reflection or maybe it is
but backwards; the sky is warm rust orange
& moonbeams green & all these boys
are in the stars & I am left with one
I barely know but want to turn to comet dust.
His name changes when he touches me,
& this fog is rain we’ve danced with before
& we are drinking on a cloud—a glass
atrium filled with glass bottles blue
like hope & light is seeping
& pollen is longing & I say
earth dream earth, and his refrain is flesh flesh flesh
meaning whole meaning, this is our home &
our bath tub is oil & stem, meaning
kiss more of me. Blow me to powder,
pulp me to sun-milk, leave me lineless.
