• Random numbers
    Are there any truly random phenomena in the universe?Agent Smith

    The outcome of measuring spin up or down is random. It is actually the device measuring the electron spin that should be used in casinos. "I have put all my money on spin up". "That's stupid! Spin up has fallen 7 times already". "I have put my last money on upupupup!"

    The true challenge lies in the search of random choice. Can we randomly choose? Totally unpredictable?
    If we mentally envision a device measuring spin up or down, and mentally watch the outcome...
    Best is to memorize the ups and downs in a real experiment, though even there it remains to be seen if the superposition is really 50-50. And maybe God intervenes.
  • WTF is Max Tegmark talking about?
    That's to say, mathematics only brings high levels of exactitude to what's actually a nonmathematical idea/theory/hypothesisAgent Smith

    An exactitude that that can only be reached in a very limited practice though. An approximation is not exact, for there is no real thing corresponding to an approximation. What is the real form of that approximated? There is no exact form. Is the mathematical approximation of the electron orbitals in an iron atom the real thing? Or an approximation of them when together a zillion-fold?
  • WTF is Max Tegmark talking about?


    I knew if! Peoqle who bon'f see fhe qitterrence detmeen q, t, f, p, q, and p, are zecrefely fruing fo tree thewselwez trow fhe consfraints ot vriffen synpolz! What a great quality! :smile:
  • What do you call this? Architecture that transforms and is being transformed?


    Indeed. The architectures of totalitarian regimes look alike. Vast squares surrounded by homogeneous creations, a big front building from where the führer, duce, commandante, pope, tsar, king, or general speaks from a high balcony. Height, centrality, so everyone can see it. Like those damned corporate-elect buildings, with mouthpieces in government, directing the mass, by education and other propaganda, to think and behave as longed for. A depressing realization.
  • The Diagonal or Staircase Paradox


    This paradox shows that intervals dx are not the same as x. All dx tògether have length 2, because you lay them together mutually orthogonal. Points can't be laid aside mutually orthogonal. The continuum can't be constructed from points x. But it can from dx's.
  • James Webb Telescope
    Did they actually practiced the telemetric operations at 40 K?
  • Need help wondering if this makes sense
    The interpretation is just a way to simply the math behind it. It's one of the large problems of quantum physics to be honest, to even understand what is meant requires a lot of high level mathTerraHalcyon

    The measurement problem exists in QFT all the same. QM is a cross section, for free fields, of QFT. However complicated you make the math, the problem of collapse is not solved. You merely use the so-called authority of math to strengthen your case. But the interpretation is not about math. It's about what math describe (a unitary evolution operator can't be applied to collapse. In QFT, the creation and destruction operators, create states in Fock space, but the states of real particles still evolve and there is a collapse if the actually are observed. If you apply the probabilistic interpretation of QM. The only objective way out are hidden variables. So the guy is just right. Because you don't understand the problem and secretely project an objective collapse on nature.
  • What do you call this? Architecture that transforms and is being transformed?
    I had a dream I was in a place with nothing but Hundertwasser building. Somehow I didn't feel at easeCaldwell

    The dream reflects the unconscious longing for being in his paradise. Your not feeling at ease in his paradise reflects your attachment to the enormity of the architecture you are used to. It's a conflict between the place you want to be and the place you're born into. The tension expresses itself in the nightmare you had. You're afraid to break free but the longing is there.

    Or you just don't like his buildings. They look if they can fall down because of a gentle push.
  • What do you call this? Architecture that transforms and is being transformed?
    Architecture was and is considered of great importance to express state power and give people a sense of being submitted to the system. In modern-day cities, the dominance of global corporations and economy is expressed by huge towers baring the names of companies. They are usually created by architects without an milligram of fantasy, and mainly impress by size and a basic mathematical structure as the expression of an overwhelming power and mathematical efficiency, giving the individual a sense of utter unimportance.
  • What do you call this? Architecture that transforms and is being transformed?
    Hundertwasser. There should be more buildings like his.
  • What do you call this? Architecture that transforms and is being transformed?
    In some cases, this effect is extreme, such as indigenous populations being introduced into Western ways of livingWarren

    What about western populations being introduced in indigenous ways of living? Florinda Donner wrote an excellent book about her experiences inside an Indian community in the Amazon area. She observed from a distance at first (being an antropologist) but little by little she gets drawn into the reality of the Indians.

    Although her writings are controversial, she gave an vivid impression how life for an anthropologist could be in an indigenous community in the South American rainforrest.
  • Global warming and chaos
    It's since the Enlightenment, when the ancient Greek ideas were reinvented, that a part of mankind started to live in a way that inevitably leads to the fall of civilization, dragging along nature. Before the enlightenment mankind lived peacefully in balance with nature over 100 000 years.The irony or paradox is that despite of science claiming to have knowledge about nature, mankind is farther removed from it than ever. Science poses man vis a vis with nature. Nature is restructured to fit knowledge claims. The biologist is disappointed when a species disappears, because then the species can't be studied anymore...
  • Global warming and chaos
    Hydrogen cars would be great. You can even drink water from the exhaust pipe.
  • Need help wondering if this makes sense


    It's not the math telling you that. That's the easy part. It's the interpretation that's the hard part.
  • Need help wondering if this makes sense
    Sorry but if you don't have a degree on the stuff you don't really have business calling the guys who actually do the math right or wrong, tTerraHalcyon

    How do you know I haven't got a degree? What is so important about a degree? I actually studied physics if you put so much value in that. Quantum field theory was my last year's choice subject. And let me tell you, your opponent is right. All people claiming an actual collapse is occurring in a measuring device, or in any interaction, are fooling themselves. And you also. That's the whole point of interest of the interpretation of QM. The Copenhagen rules are clear. Had they decided back then to stick to hidden variables, the problems wouldn't have arisen and Hugh Everett wouldn't have eaten, drunk, and smoked himself to death. And his daughter wouldn't have killed himself. His many worlds interpretation was invented exactly to account for the non-unitary behavior of collapse, and he thought he continued living in a parallel world, like his daughter thought she would meet him there if she killed herself...

    So the lesson to be learned: everyone claiming that collapse is an objective event hasn't understood QM. It's hard to believe. That's why I think hidden variables are real and actually constituting space.
  • James Webb Telescope


    Dunno if that's a good idea. "We"?

    The original plan contained no cameras, as these were too big then. They stuck to the original plan, so no cameras on board. I'm sure for Roman they use cameras. A problem might be time delay. "A bolt on the loose...!" "Grab him!" "Oops, 10 seconds too late..."
  • WTF is Max Tegmark talking about?
    If the magical thinker uses quantum physics to piggy bag on quantum mechanics or quantum fields he is fully justified in doing so. The expert Brian Cox advocates the idea that when QM is used in the magical realm and the person uttering the language used in QM, one only has to ask if the person in question knows about the mathematics involved, a typical attitude covering up a misunderstanding of what quantum field theory actually stands for. Nobody knows the true nature of quantum fields because only their outside appearance is described by mathematics without even a speck of inside understanding. No physicist in the world understands the nature of the charges and the particles these are contained in. The concept of a point particle is problematic, and the way they interact, by virtual or real fields of intermediaries, can be perfectly described by the mathematical language, but any question about what's really going on is countered with a vague reply hiding a basic ignorance using math to justify ignorance. For whatever math is used, the ingredients described by the math remain a magical mystery, which forms the foundation of consciousness and will. The dualism is not between reality and the mind, with the mind never being able to make direct contact with reality. The true dualism is the dualism between the outside description and the inside ingredients. Every outside description of a material creates a direct knowledge of and a direct contact with the material studied. There is no gap. But the inside nature of the material (not the Ding an Sich, as this doesn't exist), will remain unknown. Only by eating it material reveals its inside nature.
  • Proof of Free Will
    The quark model (and it is just a model) is based on empiricism, not beliefKenosha Kid

    I see what you mean. I think though, that the scientific approach, the empirical approach involving setting up experiments, watch what's going on, report the fidings, and theorize about it is a belief an Sich. If I don't believe in this approach (I do though), then one can say whatever they want about quarks and leptons, they existing whatever I think about them, but if I don't belief in the approach, or if I don't value it, the quarks will be non-existing for me.

    About absorption and emission. Isn't the emitted photon different from the absorbed? A creation and destruction operator are applied in asymptotically free perturbative approach, and can't be applied to a bound system like an atom. The photon absorbed is a different one than the emitted one. Only in Compton scattering they can be interchanged, so it looks. Do you agree with this?
  • WTF is Max Tegmark talking about?
    But I’ve always been bothered when people say that music is mathematical -javra

    Consider me on your side mate! Many physicists, mathematicians, and computer scientists, are fan of Bach. Because of the beauty of the mathematical structure. Well, I dunno. If that's the reason you like it, you seem to miss the point of music somehow. However much structure it may contain, however difficult is to play, somehow I feel they like it to pat their ability of abstract mathematical thought on the back.
    I have a friend who can't distinguish between p and q. He got mad after I told him the q and p were mixed up on a shopping list. I tried to imagine what's it like. Of course I can't. Maybe it's me who perceives wrongly! Do p and q , or b, look the same to you? Are the three the same? Is ppp the same as pqq or qpq? Just curious. I'm raised in a society that stimulates curiosity...
  • James Webb Telescope
    JDEM, ,together with SNAP, AdEPT, INTEGRAL, ALGILE, and FERMI, powerful instruments to unravel the dark energy behavior of the early universe. Finally, the secret will be uncovered in the near future. A quest started when the Black Monolith suddenly appeared and made the monkeys use bones to bash in each others head or to throw to the Moon and investigate. Along with science morality was born.
  • James Webb Telescope
    Their sensors are more informative than the "engine" light on our old VW's dashboard which could mean anything from "the engine will explode in 10 seconds to a sensor is sending a meaningless warning, or maybe both. You can interpret it however you like."Bitter Crank

    Seeing that widgets are joint out of balance, when the telemetry system provides exact information would be handy. Building on basis of telemetry and computer aid seems a shaky base. If some widget is accidentally directed in the wrong direction, can the on-board robot correct?
  • James Webb Telescope


    It seems the problem is that a small camera disturbs the equipment, because maybe a wire emitting IR radiation can produce false images. Still... For the installation phase the newly invented sand grain sized cameras could have been sent along, or a small accompanying guiding satellite could have been send along shining light and registering the process. Would have provided the public with a contextual, though interesting construction story. You can generate a visual computer narrative, but the real thing would be great to see. Once the starting conditions are set, bye bye camera. Off you go.

    Nancy Grace Roman will join James Webb in a few years.
  • WTF is Max Tegmark talking about?


    I think Plato's idea of the metaphysical domain of mathematical objects was a domain of unchanging objects, indeed as you described. The 5 Platonic bodies, like the cube or the isocahedron. There was an over 100 year physical model discovered in a university basement. A paper mache partial model of a special function, I can't remember which one. Beautiful, a true piece of art, made without computers. Would fit in Plato's realm. But what are these structures made off? Plato said we can't know them an Sich. Every math formula or physical realization, say a cube, is an approximation, even an exact formula. They are the shadows on the walls of a cave. They are lit by light, and the shadows can be investigated, with a model or a formula. Aristotle said the cube is just the construction of clay, and the formula an abstraction without real existence. Now who is right? Plato says the real cube exists, and can never be known, only approximated, while Aristotle says the dirty cube is the real cube and the mathematical cube a unreachable abstraction. Somehow, Tegmark is sandwiched between the both. The cube, or any other form, is real, and all forms are mathematical. So, the formula of the cube refers to a shape present in the world. At least, potentially, because nobody has seen a perfect cube. Like in general, no perfect mathematical forms can be found. Particular cases can be found though. The archetypal example being the hydrogen atom. The wavefunction has an exact 3D shape and the electron conforms to this. It depends on your view of particles what the shape actually is. A shape without substance is, well, an empty shape. There has to be something that is in shape. Tegmark conjectures tha the shape is devoid of substance. People too are complicated mathematical shapes, and contrary to Platonic objects they can shape-shift. He misses an essential part of reality. My reality, that is.
  • Mathematics of the tractatus logico philosophicus
    yes I think that is the correct term. But then what is a function of a functional - a functionalal?Robert Durkacz

    Haha! Well, the integral, for example, is a functional. It's a function of a function. Every function returns a value (considering bound, continuous functions only). The area between the function and the domain axis, say x (say there is an x domain only). How would the integral of the integral look like? You calculate the area first. Of an arbitrary function (well, bounded, continuous, and one variable). Say you calculate the integral of f=x. So F(f(x))= int(f(x), say between 0 and 2. So the integral is 1/2x^2+c, put in the values 2 and 0, and subtract. So, you get two. Now what about F(F(f(x))? Is it 1/6x^3+cx+b? The integral of the function returns a number, the area. If you apply the integration to this number, what do you get? If you integrate f(x)=x between 0 and 2, how is the integral of this integral defined?
    Note that differentiation is not the inverse of integration. If you see differentiation as an operator, the operator is applied not to the whole function, but only pointwise to the range points and the domain points (df(x)/dx). The function can be seen as an operator on the. If the operator is to multiply by one, then f(x)=x and f(f(x))=x also. The integral operator takes the whole function as argument. All points of a function are involved, the domain as well as the range, like in the integration (dx and f(x)). Differentiation is no functional. The process of finding a primitive function is the inverse of finding the derivative function though.
  • Global warming and chaos
    No God can save the planet, only humans can stop the destruction. It is about morals and morals mean knowing the laws of nature and good manners. Those two things would resolve many problems.Athena

    Moral means knowing the laws of Nature? Isn't knowing these laws the cause of the chaos we increasingly observe in Nature?
    I know what you mean, but if we don't want to find out how Nature behaves at all levels, in every direction, and at every height and depth, wouldn't that be better for Nature? We are taught from small age that acquiring knowledge is of uttermost importance. The children are treated as ignorant to be filled with a kind of knowledge only possessed by the ruling power, which makes the claim of possessing objective knowledge to be obtained by strict methods. The methods as well as the value judgement of the importance of the subject matter is subjective though, but in modern society it's made the so-called objective norm, while this so-called objectivity is just a label to cover the subjective essence, thereby lending it a justified power position, like God was once used to justify claims on power.
  • Global warming and chaos
    No God can save the planet,Athena

    Dunno. Only by a strict following of His Final, Undubitable and Infallible Word, humanity can be saved from eternal damnation and premature extermination.

    Ah yes, The One Eternal, that Fortuitous Indolent Inert Being, praise His Name until the Day of Doom, who created the Sacred Universe by a Holy Ejaculation of The Word. Logos, He spoke.

    We can only find True Joy in life by listening with our full religious being to His Wondrous and Wide Word. And spreading it into every earthly soul, thereby acknowledging the submissive and bowing part we have to play in His Glorious Creation, that Magnificent Manor, in which we can receive a holy washing from our inborn sins only by conversion from the cursed ways to the Path of True Heavenly Enlightenment.

    Genuine Joy can only be felt by receiving His True Ejaculate and accepting it voluntarily. If not voluntarily accepted, the wrath of the Truly Righteous Beloved will be legitimate, righteous, and justified, and directed towards those who refuse to conform to the wisely revised edition of His Blissful Word, flowing from His Crystal Sparkling Spring.

    A stoning will descend from the celestial sphere, thereby cleansing the Earth from the disturbing wicked elements that stubbornly resist to comply and be recipient to the Golden Ejaculation emanating from His Infinite Erectedness like a brightly colored fountain. The idle, sanctimonious, and pharisaic erections, and the false ejaculates spat out off it, can only be acted against by the incandescent Ejaculate of the immense Erected, and it will strike the ephemeral with unprecedented force to restore the eudomoniatic state of Divine Dedication and Total Obedience.

    Only by strictly attending to the confines of the Honest and Pure Trail of the Word spoken by the Incendiary Erect Being, one can hope to avoid the amnesiac beating of His Stern Stick.

    So brothers and sisters, let's pray, and show the Greatest and Most Appreciated that we are a faithful image of the Holy Erection that only speak out the True Logos of the Pure Ejaculate. Let's turn our sinful heads away from the raped ramifications tentatively lurking in the dark, luring us invitingly to step in the nefarious and ill traps of non-belief, causing the nasty and mucky ways of our pitiful fellow men, who can only be true fellow men if the Holy Ejaculate from the Heavenly Erected is injected by fierce force and severe determination.

    Let's pray that the megalomanic erections our fellow men show in their ruthless plays for merciless domination, will be righteously unearthed and sent to eternal oblivion. Let's send the heavenly armies to those who erect blindly, let's show them no remorse.

    The earthly erections should be subjugated to the Gigantic and Sublime Erection of the Grand Erected. Only by receiving the Holy Ejaculate salvation can be expected.

    Let's pray, brothers and sisters. Let's pray that the bombastic and pompous ejaculations of the crooked deviant will be counteracted by Consecrated Ejaculate. Only by acknowledging (the) Great Erect, (the) Great Ejaculate can be received and turn the deviant into compliant. Only by complying to the One and True Erect and by receiving the Undubitable and Immaculate Ejaculate, salvation can be expected.

    So, brothers and sisters in the Proper Ejaculate, children of the Proper Erection, what is the proper reason for our prayers, orisons, and invocations? The proper reason petitioning the Undeniable Anointed lies in amoral self-righteous erect used by fellow men to spawn amoral sinful ejaculate. The Essential and Eternal Erect and the Eponymous Ejaculate can't be turned against though!!! If the Eternal Erect and Ejaculate are challenged, ignored, ridiculed, or suppressed, the deviant elements should not be surprised if proper action followed their diversion from the Proper Erect and Proper Ejaculate. If the ignorant deviant will not comply voluntarily to the Untouchable, Mercurial Erect and Ejaculate, no merci should be expected when their false erects and wickedly ejected ejaculates are methodologically cut out, including all abject roots.

    The ignorant deviant should be educated properly and restructured. The True Errect and Ejaculate should be imposed gently, whilst force should be applied if being gentle doesn't suffice. Praying might help to eradicate the roots. It establishes a community, which might be able to get rid of unwanted ejaculations or erections. The words transpire to our Beloved Lord and the Shining Beacon of Humanity will forcefully push down the erects of the deviant and reduce ignorant and contemptuous ejaculate.

    Let's pray, brothers and sisters. Let's ask the Miraculous, Statuous,. and Astute Director to redirect the deviant who lost track of the Great and Pure Erect. Let's ask the Firm Founder to redirect the deviant who falsely ejaculates from a deviant erect, opposing the Essence of the Pinciple of Ejaculation.

    If we do not comply to the Great Mysterious Pristine and continue to erect and ejaculate inflationary, the Great Admired Regulator will aim His Divine Ejaculation towards Earth and the sky will be filled with lightning and thunder, the Great Diluve will flood our damned erections, and our dirty ejaculates will be whiped away consistently and efficiently. Then it will be silent and on the remnants of the corrupted ejaculate the Eternal Erect and Immaculate Ejaculate will install themselves again, never to be taken down again.

    To be read firmly, strictly, eloquently. Self-assured and exalted, implying moral superiority. Charismatic like our friend JC.
  • James Webb Telescope
    No, light cannot be cast, because it operates in the dark.Wayfarer

    It operates in the dark because no light is cast. Wouldn't it be handy, only to get the teĺescope started, to see what they are doing? So they can manually control the installation? Or can't you intervene when something goes wrong because of the time delay? I mean, if some widget is wrongly directed and flies into space, you will see it a few seconds later, and that could already be too late. How do they know the tennis court shield is in order? They can't see it.
  • A different style of interpretation: Conceptual Reconstructionism


    The recontruction of a painting then needs context too. I referred to the other thread because also there a context is eliminated. The same kind of context you refer to. It focuses on knowledge, like you focus on a piece of art. There is no piece of art, knowledge, or any kind of material, existing in a vacuum. The duck and the rabbit
    can be narrated like a duck, a rabbit, both dubbit or a rabbuck, or just a curvy black line. Or as a collection of particles on a white underground. Any narrative will do when both viewers agree on the narrative. What's the real view? Is the creator of the work important? Is it important what they wanted to say? What if it's an image of gods or a mathematical expression? Or an image trying to convey the meaning of freedom or suffering? What if we look at the Quernica picture by Picasso? Should we take the war or his family into consideration, or just the painting "as it is"?
  • James Webb Telescope
    the reason there’s no camera on board being that JW operates in pitch darkness (and at -440 degrees c)Wayfarer

    Can't some light be cast? With a lantern? Would be nice to see an actual image of the telescope. You could see what's going on. I think you mean -440 Fahrenheit.
  • James Webb Telescope
    Are other galaxies more violent than ours?The Opposite

    Once upon a time, in a galaxy far, far away...
  • A Physical Explanation for Consciousness
    Why s that more correctly?
    — Raymond
    Because, in the subject of consciousness, it is better and more exact to speak about "non-physical" than "non-substance", which can mean anything, physical and non-physical.
    Alkis Piskas

    The content of the physical can be non-physical? Who knows what the substance of charge is made of? You can describe the outer manifestations, but the inside can't be described in the same language. You can label it "charge", like you can label a brain or body structure "pain", but that doesn't explain what's inside.
  • Mathematics of the tractatus logico philosophicus
    Isn't the function of the function a functional?
  • Need help wondering if this makes sense
    Actually to claim anything existing in superposition (which again isn't how you use the term) would nullify solipsism because it's acknowledging something else existing (or at the very least knowing) apart from you. So in a sense he can't have solipsism AND superposition in his argument.TerraHalcyon

    But the something existing apart from you can be said to be still in a superposition. Which means you are a kind of solipsist, denying the collapse you or I see.
  • Need help wondering if this makes sense
    Except that isn't true. Trust me when I say I have asked people who do this for a living and they say consciousness has nothing to do with itTerraHalcyon

    Of course they tell you that. I have thought about it a lot. I thought the same as you. Precisely because I don't do it for a living, I know that people who say that a measuring device measures or collapses independently of us are wrong. That's because, again, the basic interpretation says that an observer (so not a measuring device) is needed to collapse the wavefunction. Bell, in his quest for hidden variables, said he couldn't imagine that only an observer with knowledge of QM could collapse the wavefunction retroactively (in the past). Which is indeed hard to imagine, but if you stick to the rules, the measuring device stays in superposition untill measured by an observer. That's the fucked up feature of QM, and anyone claiming that the world collapses independently of us hasn't understood QM. Of course, when you work in the field, you want your collapses to exist independently of yourself. But then you silently presume hidden variables causing objective collapse (Bell's experiment allowed for the non-local hidden variables).
  • WTF is Max Tegmark talking about?
    Both idealists and realists can agree with the Ontic-Structural Realism of Tegmark. For example, British idealism's doctrine of internal relations is in logical agreement with OSR, without jumping the shark to conclude that only unthinkable and unperceivable mathematical structure exists in a way that is divorced from the Lockean secondary qualities of perceptionsime

    This sounds like nuking the fridge.

    or, in this case, the universe as we know it.javra

    The fire that breathes life in the physìcal theory describing the fundamental physical/mathematical structure ĺies in the content of what they describe. The structure of the two basic fields in nature, interacting on an evolving background of spacetime, can be described mathematically exactly only in a very limited area of nature. If we apply that theory to the atom, the theory is non-applicable, as it describes only free fields that interact shortly (asymptotically free is a misnomer, as the fields are free all of the time, except for a short interaction, which can be described by an infinity of ďiagrams, all happening simultaneously, so the story goes. Do all these diagrams to describe the interaction exist there in spacetime? Is spacetime itself a mathematical structure? Who knows. The wavefunction to describe the hydrogen atom is a harmonic function. It seems to exist truly and it can be depicted. It can't be describe by quantum field theory though. Do mathematical structures exist which are not exact and which can be described by an approximation only? And what about the mathematical structure of the human face and its connection to emotion, the face laughing or talking?
    The fire left out of the mathematical structures is that what is inside of them, so I think wholeheartedly. It could be the concept of charge, be it electrical or color and the mass describing the evolution of particle fields. Nobody knows exactly what a particle is. Only on the inside of the particle (the field of all its simultaneous paths or the bath of hidden variables it finds itself in, which could form space itself) the fire can be known. It's called charge. Maybe all charges interacting give holistically rise to new charges, leading to structures with forrest fires, or exploding fires, inside of them. I can feel this fire within. It's hot.
    I think Hawking referred to the fire of charge. Near the big bang, massless charges were waiting for the moment to get real and form massive structures, to interact with each other, form bodies and run through the forrest of trees and plants (silently charged structures, just wanting to wave their leaves in the wind). Are they mathematical structures? Dunno. I Tegmark thinks so, it's a reality for him. I wonder if he could find a mathematical structure of people. If there isn't a mathematical structure to be found of an isolated iron atom (there exist approximations only), I doubt it. There is no exact mathematical structure if we can't find it. If there exists an approximation only, then what's the real, exact structure?
  • James Webb Telescope


    Is there a camera on board (apart from making pictures of the stars)? They should see what they do, or not? Is it all automated?
  • The Diagonal or Staircase Paradox
    the paradox is due to intuitions that aren't compatible with the definition of the classical Euclidean topology.sime

    Why? Can't we imagine small pieces of lines put together non parallel? Even orthogonal? The pieces are no points, however small you choose them. If you tried to construct the diagonal with points, laid side by side, you always need more points which can be fit in between. A line can be cut in pieces but not in points.
  • The Diagonal or Staircase Paradox

    This is the thread that doesn't end.
    It just goes on and on my friend.
    Some people started writing it, not knowing what it was.
    Now they'll continue writing it forever just because,
    This is the thread that doesn't end [repeat]
    T Clark

    Sounds an awful lot like life. Except for the repeat maybe.
  • The Diagonal or Staircase Paradox
    The paradox: 2=sqrt2, while 1/2=1/2.
  • Proof of Free Will
    By that logic, it's equally sensible that something that diffracts and interferes isn't a way, which is linguistically incoherent.Kenosha Kid

    I'm not sure I understand. Something isn't a way? And why is it a bad thing that something is linguistically incoherent? I can say that I see, interact, with quarks, make triplets and duals of them collide and still say they are not real, however incoherent that might be. The incoherency stems from your concept of reality. If you base that on being able to grab it, then it's incoherent, if not, then it's coherent.