PLato said,"Look to the perfection of the heavens for truth," while Aristotle said "look around you at what is, if you would know the truth" To Remember: Eskesthai
"The adventure of our science of physics is a perpetual attempt to recognize that the different aspects of nature are really different aspects of the same thing" -- Richard Feynman
Source:Amazon.com Richard Feynman: Cover of The Feynman Lectures on Physics See also: The Feynman Lectures on Physics
Commerce is of trivial import; love, faith, truth of character, the aspiration of man, these are sacred.Ralph Waldo Emerson
Illustration from Tacuina sanitatis, Fourteenth centuryReverse chronology — narrating a story, or parts of one, backwards in time — is a venerable technique in literature, going back at least as far as Virgil’s Aeneid. Much more interesting is a story with incompatible arrows of time: some characters live “backwards” while others experience life normally.
Steve Paulson:I know neither of you believes in paranormal experiences like telepathy or clairvoyant dreams or contact with the dead. But hypothetically, suppose even one of these experiences were proven beyond a doubt to be real. Would the materialist position on the mind-brain question collapse in a single stroke?
PINKER: Yeah.
GOLDSTEIN: Yeah, if there was no other explanation. We'd need to have such clear evidence. I have to tell you, I've had some uncanny experiences. Once, in fact, I had a very strange experience where I seemed to be getting information from a dead person. I racked my brain trying to figure out how this could be happening. I did come up with an explanation for how I could reason this away. But it was a very powerful experience. If it could truly be demonstrated that there was more to a human being than the physical body, this would have tremendous implications.
"Death, so called, is but older matter dressed
In some new form. And in a varied vest,
From tenement to tenement though tossed,
The soul is still the same, the figure only lost."Poem on Pythagoras, Dryden's Ovid.
Imagination in a man, or reasonable creature, is supposed to participate of reason, and when that governs, as it does in the belief of fiction, reason is not destroyed, but misled, or blinded: that can prescribe tot he reason, during the time of the representation, somewhat like a weak belief of what it sees and hears; and reason suffers itself to be so hoodwinked, that it may better enjoy the pleasures of the fiction: but it is never so wholly made a captive as to be drawn headlong into a persuasion of those things which are most remote from probability: 'tis in that case a free-born subject, not a slave; it will contribute willingly its assent, as far as it sees convenient, but will not be forced....Fancy and reason go hand in hand; the first cannot leave the last behind; and though fancy, when it sees the wide gulf, would venture over, as the nimbler; yet it is withheld by reason, which will refuse to take the leap, when the distance over it appears too large
He turned the lens of mathematics on itself and hit upon his famous "incompleteness theorem" — driving a stake through the heart of formalism By DOUGLAS HOFSTADTER
Source:ALFRED EISENSTAEDT/TIME LIFE PICTURES-Kurt Godel at the Institute of Advanced Study See: The Time 100-Scientists and ThinkersThe upshot of all this is that the cherished goal of formalization is revealed as chimerical. All formal systems — at least ones that are powerful enough to be of interest — turn out to be incomplete because they are able to express statements that say of themselves that they are unprovable. And that, in a nutshell, is what is meant when it is said that Gödel in 1931 demonstrated the "incompleteness of mathematics." It's not really math itself that is incomplete, but any formal system that attempts to capture all the truths of mathematics in its finite set of axioms and rules. To you that may not come as a shock, but to mathematicians in the 1930s, it upended their entire world view, and math has never been the same since.
Gödel's 1931 article did something else: it invented the theory of recursive functions, which today is the basis of a powerful theory of computing. Indeed, at the heart of Gödel's article lies what can be seen as an elaborate computer program for producing M.P. numbers, and this "program" is written in a formalism that strongly resembles the programming language Lisp, which wasn't invented until nearly 30 years later.
In the late 1940s, Gödel demonstrated the existence of paradoxical solutions to Albert Einstein's field equations in general relativity. These "rotating universes" would allow time travel and caused Einstein to have doubts about his own theory. His solutions are known as the Gödel metric.
Because of the homogeneity of the spacetime and the mutual twisting of our family of timelike geodesics, it is more or less inevitable that the Gödel spacetime should have closed timelike curves (CTC's). Indeed, there are CTCs through every event in the Gödel spacetime. This causal anomaly seems to have been secretly regarded as the whole point of the model by Gödel himself, who allegedly spent the last two decades of his life searching for a proof that death could be cheated, and apparently felt that this solution provided the desired proof. This strange conviction came to light decades after his death, when his personal papers were examined by a startled astronomer.[citation needed].
A more rational interpretation of Gödel's motives is that he was striving to (and arguably succeeded in) proving that Einstein's equations of spacetime are not consistent with what we intuitively understand time to be (i.e. that it passes and the past no longer exists), much as he, conversely, succeeded with his Incompleteness Theorems in showing that intuitive mathematical concepts could not be completely described by formal mathematical systems of proof. See the book A World Without Time (ISBN 0465092942).
CTCs have an unnerving habit of appearing in locally unobjectionable exact solutions to the Einstein field equation of general relativity, including some of the most important solutions. These include:
* the Kerr vacuum (which models a rotating uncharged black hole)
* the van Stockum dust (which models a cylindrically symmetric configuration of dust),
* the Gödel lambdadust (which models a dust with a carefully chosen cosmological constant term).
* J. Richard Gott has proposed a mechanism for creating CTCs using cosmic strings.
Some of these examples are, like the Tipler cylinder, rather artificial, but the exterior part of the Kerr solution is thought to be in some sense generic, so it is rather unnerving to learn that its interior contains CTCs. Most physicists feel that CTCs in such solutions are artifacts.
No closed timelike curve (CTC) on a Lorentzian manifold can be continuously deformed as a CTC to a point, because Lorentzian manifolds are locally causally well-behaved. Every CTC must pass through some topological feature which prevents it from being deformed to a point. A test particle free falling along a closed timelike geodesic transits this feature; in the test particle's frame, the feature propagates toward the test particle. This features resembles a glider in Conway's Game of Life, but in a continuous spatial automaton rather than a (discrete) cellular automaton.
It is an important open question whether pseudo-photons can be created in an Einstein vacuum space-time, in the same way that a glider gun in Conway's Game of Life fires off a series of gliders. If so, it is argued that pseudo-photons can be created and destroyed only in multiples of two, as a result of energy-momentum conservation.
How can a speck of a universe be physically identical to the great expanse we view in the heavens above? (Greene, The Elegant Universe, pages 248-249)
As Alice learned, it's not always clear what's a looking glass, and what's a window to another world. Mirrors and windows are often interchangeable: we look out into the world, and see ourselves reflected back. We look at a reflection, and believe it's showing us a world beyond. We internalize the mirror image and project the one inside. Objects, actions and ideas can become so confused with their reflections that it's impossible to untangle them. What's phantom and what's real? Is there even a relevant difference?
"The worst disease afflicting human kind is hardening of the categories." - Artist Bob Miller.
Miracles StudiosThrone PlatesTo activate Thorne plates, the distance between each plate must be less than the width of an atom. The resulting wormhole will be equally small, so getting in and out might be difficult. To widen the portal, some scientists suggest using a laser to inject immense amounts of negative energy. In addition, Thorne believes that radiation effects created by gravitons, or particles of gravity, might fry you as you enter the wormhole. According to string theory, however, this probably won't happen, so it's scant reason to cancel your trip.
Miracles StudiosGott LoopTo take you back one year, the string must weigh about half as much as the Milky Way galaxy. You'll need a mighty big spaceship to make that rectangle.
Many scientists believe the big bang that created the universe left behind cosmic strings - thin, infinitely long filaments of compressed matter. In 1991, Princeton physicist J. Richard Gott discovered that two of these structures, arranged in parallel and moving in opposite directions, would warp space-time to allow travel to the past. He later reworked the idea to involve a single cosmic-string loop. A Gott loop can take you back in time but not forward. The guide to building your own:
Miracles StudiosGott ShellThis is a relatively slow method of time travel, and life inside the shell could become tedious.
In essence, a Gott shell is a huge concentration of mass. The shell's sheer density creates a gravitational field that slows down the clock for anyone enclosed within it. Outside, time rolls along at its familiar pace, but inside, it creeps. Thus the Gott shell is useful for travel into the future only. If you're planning a jaunt to the past using a Gott loop, you might want to bring along a Gott shell for the return trip. What to do, step by step:
Miracles StudiosVan Stokum CylinderThe cylinder must be infinitely long, which could add slightly to its cost.
Mass and energy act on space-time like a rock thrown into a pond: the bigger the rock, the bigger the ripples. Physicist W. J. van Stockum realized in 1937 that an immense cylinder spinning at near-light speed will stir space-time as though it were molasses, pulling it along as the cylinder turns. Although Van Stockum himself didn't recognize it, anyone orbiting such a cylinder in the direction of the spin will be caught in the current and, from the perspective of a distant observer, exceed the speed of light. The result: Time flows backward. Circle the cylinder in the other direction with just the right trajectory, and this machine can take you into the future as well. How it works:
Kerr RingThe Kerr ring is a one-way ticket. The black hole's gravity is so great that, once you step through it, you won't be able to return.See:A User's Guide to Time Travel-Superpower Issue
When Karl Schwarzschild solved Einstein's equations in 1917, he found that stars can collapse into infinitesimally small points in space - what we now call black holes. Four decades later, physicist Roy Kerr discovered that some stars are saved from total collapse and become rotating rings. Kerr didn't regard these rings as time machines. However, because their intense gravity distorts space-time, and because they permit large objects to enter on one side and exit on the other in one piece, Kerr-type black holes can serve as portals to the past or the future. If finding one with the proper dimensions is too much trouble, you can always build one yourself:
Welcome to the mirror world, in which every particle in the known universe could have a counterpart. This cosmos would hold mirror planets, mirror stars, and even mirror life.
Crucifixion (Corpus Hypercubus) (1954)-Salvador Domingo Felipe Jacinto Dalí i Domènech, 1st Marquis of Púbol (May 11, 1904 – January 23, 1989), was a Spanish surrealist painter born in Figueres, Catalonia, Spain.
Image Source: The Universe in a Nutshell, by Stephen Hawking, page 198
A tesserack or hypercube is a four dimensional analogue of a cube. See the figure on the left for a 2-D representation of this 4-D object. More information about these can be seen and found. Many people have difficulty believing such can exist which is why such books as Flatland (Abbott, 1884), Sphereland (Burgers, 1983), and Flatterland (Stewart, 2001) were written.
The Navier-Stokes equations are also of great interest in a purely mathematical sense. Somewhat surprisingly, given their wide range of practical uses, mathematicians have yet to prove that in three dimensions solutions always exist (existence), or that if they do exist they do not contain any infinities, singularities or discontinuities (smoothness). These are called the Navier-Stokes existence and smoothness problems. The Clay Mathematics Institute has called this one of the seven most important open problems in mathematics, and offered a $1,000,000 prize for a solution or a counter-example.
SETH LLOYD — HOW FAST, HOW SMALL, AND HOW POWERFUL?: MOORE'S LAW AND THE ULTIMATE LAPTOPHis stunning conclusion?Bold emphasis added by me.
"The amount of information that can be stored by the ultimate laptop, 10 to the 31st bits, is much higher than the 10 to the 10th bits stored on current laptops. This is because conventional laptops use many degrees of freedom to store a bit whereas the ultimate laptop uses just one. There are considerable advantages to using many degrees of freedom to store information, stability and controllability being perhaps the most important. Indeed, as the above calculation indicates, to take full advantage of the memory space available, the ultimate laptop must turn all its matter into energy. A typical state of the ultimate laptop's memory looks like a plasma at a billion degrees Kelvin — like a thermonuclear explosion or a little piece of the Big Bang! Clearly, packaging issues alone make it unlikely that this limit can be obtained, even setting aside the difficulties of stability and control."
Ask Lloyd why he is interested in building quantum computers and you will get a two part answer. The first, and obvious one, he says, is "because we can, and because it's a cool thing to do." The second concerns some interesting scientific implications. "First," he says, "there are implications in pure mathematics, which are really quite surprising, that is that you can use quantum mechanics to solve problems in pure math that are simply intractable on ordinary computers." The second scientific implication is a use for quantum computers was first suggested by Richard Feynman in 1982, that one quantum system could simulate another quantum system. Lloyd points out that "if you've ever tried to calculate Feynman diagrams and do quantum dynamics, simulating quantum systems is hard. It's hard for a good reason, which is that classical computers aren't good at simulating quantum systems."
Hey I got one for you. You remember mission impossible. Well in this case, your only able to use the ipod once, then it turns into a super liquid.
Michio Kaku:I like to compare it to wandering in the desert, and stumbling over a tiny pebble. When we push away the sand, we find that this "pebble" is actually the tip of a gargantuan pyramid. After years of excavation, we find wondrous hieroglyphics, strange tunnels and secret passageways. Every time we think we are at the bottom stage, we find a stage below it. Finally, we think we are at the very bottom, and can see the doorway.
One day, some bright, enterprising physicist, perhaps inspired by this article, will complete the theory, open the doorway, and use the power of pure thought to determine if string theory is a theory of everything, anything, or nothing.
Only time will tell if Einstein was correct when he said, "But the creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed."
Tscan ("Trivial Scanner") is an event display, traditionally called a scanner, which I developed. It is a program that shows events graphically on the computer screen.See:Trivial Scanner
It was designed to be simple ("trivial") internally, and to have a simple user interface. A lot of importance was given to giving the user a large choice of options to display events in many different ways.
Tscan proved to be a very useful tool for the development of fitters. A particularly useful feature is the ability to show custom data for every photpmultiplier tube (PMT). Instead of the usual time and charge, it can show expected charge, scattered light, likelihood, chi-squared difference, patches, and any other data that can be prepared in a text format.
Credit: Super-Kamiokande/Tomasz Barszczak Three (or more?) Cerenkov ringsMultiple rings of Cerenkov light brighten up this display of an event found in the Super-Kamiokande - neutrino detector in Japan. The pattern of rings - produced when electrically charged particles travel faster through the water in the detector than light does - is similar to the result if a proton had decayed into a positron and a neutral pion. The pion would decay immediately to two gamma-ray photons that would produce fuzzy rings, while the positron would shoot off in the opposite direction to produce a clearer ring. Such kinds of decay have been predicted by "grand unified theories" that link three of nature's fundamental forces - the strong, weak and electromagnetic forces. However, there is so far no evidence for such decays; this event, for example, did not stand up to closer scrutiny.See:Picture of the Week
General objectives:To collect precision cosmic ray data at high energies, including 10^10 protons; to discover or rule out certain particles as explanations for dark matter; to study cosmic ray propagation in the galaxy; to search for exotic particles or spectral features among cosmic raysSee:AMS experiment mission overview
AMS is a particle detector for the International Space Station. A group of high-energy physicists are taking their experimental expertise - acquired in thirty years of experience at particle accelerators - into orbit. Space is full of high-energy particles of many types (collectively called "cosmic rays"), many of them originating in supernova explosions in distant galaxies. AMS detects them using a huge superconducting magnet and six highly specialized, ultra-precise detectors. It will sit on the ISS main truss - far above the obscuring atmosphere, and making full use of the ISS's irreplaceable support systems - and gather data for three years.
Beyond the experiment itself, the standoff represents a clash between two of the more strong-willed and brilliant leaders of Big Science in America: Dr. Ting of the Massachusetts Institute of Technology, who is known for his autocratic management style and obsession with detail, and Michael D. Griffin, the NASA administrator, who has shown himself willing to make tough calls in reshaping the space program away from the shuttle and toward the Moon and Mars.
Photographs by The AMS Collaboration "I’m a Platonist — a follower of Plato — who believes that one didn’t invent these sorts of things, that one discovers them. In a sense, all these mathematical facts are right there waiting to be discovered."Donald (H. S. M.) Coxeter
Source:Numerical Relativity Code and Machine Timeline
NASA scientists have reached a breakthrough in computer modeling that allows them to simulate what gravitational waves from merging black holes look like. The three-dimensional simulations, the largest astrophysical calculations ever performed on a NASA supercomputer, provide the foundation to explore the universe in an entirely new way.Scientists are watching two supermassive black holes spiral towards each other near the center of a galaxy cluster named Abell 400. Shown in this X-ray/radio composite image are the multi-million degree radio jets emanating from the black holes. Click on image to view large resolution. Credit: X-ray: NASA/CXC/AIfA/D.Hudson & T.Reiprich et al.; Radio: NRAO/VLA/NRL
According to Einstein's math, when two massive black holes merge, all of space jiggles like a bowl of Jell-O as gravitational waves race out from the collision at light speed.
Previous simulations had been plagued by computer crashes. The necessary equations, based on Einstein's theory of general relativity, were far too complex. But scientists at NASA's Goddard Space Flight Center in Greenbelt, Md., have found a method to translate Einstein's math in a way that computers can understand.
See: Dealing with a 5D World
There are two reasons that having mapped E8 is so important. The practical one is that E8 has major applications: mathematical analysis of the most recent versions of string theory and supergravity theories all keep revealing structure based on E8. E8 seems to be part of the structure of our universe.Most people think of "seeing" and "observing" directly with their senses. But for physicists, these words refer to much more indirect measurements involving a train of theoretical logic by which we can interpret what is "seen."- Lisa Randall
See:Computer Graphics In Mathematical Research
Whereas Stephen W. Hawking (having lost a previous bet on this subject by not demanding genericity) still firmly believes that naked singularities are an anathema and should be prohibited by the laws of classical physics,
And whereas John Preskill and Kip Thorne (having won the previous bet) still regard naked singularities as quantum gravitational objects that might exist, unclothed by horizons, for all the Universe to see,
Therefore Hawking offers, and Preskill/Thorne accept, a wager that
When any form of classical matter or field that is incapable of becoming singular in flat spacetime is coupled to general relativity via the classical Einstein equations, then
A dynamical evolution from generic initial conditions (i.e., from an open
set of initial data) can never produce a naked singularity
(a past-incomplete null geodesic from scri-plus).
The loser will reward the winner with clothing to cover the winner's nakedness. The clothing is to be embroidered with a suitable, truly concessionary message.
Stephen W. Hawking, John P. Preskill, Kip S. Thorne
Pasadena, California, 5 February 1997
In general relativity, the cosmic censorship hypothesis (CCH) is a conjecture about the nature of singularities in spacetime.
Singularities that arise in the solutions of Einstein's equations are typically hidden within event horizons, and therefore cannot be seen from the rest of spacetime. Singularities which are not so hidden are called naked. The weak cosmic censorship hypothesis conjectures that no naked singularities other than the Big Bang singularity exist in the universe. The hypothesis was conceived by Roger Penrose in 1969.
What good is a universe without somebody around to look at it?
Robert Dicke
John Archibald Wheeler (born July 9, 1911) is an eminent American theoretical physicist. One of the later collaborators of Albert Einstein, he tried to achieve Einstein's vision of a unified field theory. He is also known as the coiner of the popular name of the well known space phenomenon, the black hole.COSMIC SEARCH: How did you come up with the name "black hole"?
John Archibald Wheeler:It was an act of desperation, to force people to believe in it. It was in 1968, at the time of the discussion of whether pulsars were related to neutron stars or to these completely collapsed objects. I wanted a way of emphasizing that these objects were real. Thus, the name "black hole".
The Russians used the term frozen star—their point of attention was how it looked from the outside, where the material moves much more slowly until it comes to a horizon.* (*Or critical distance. From inside this distance there is no escape.) But, from the point of view of someone who's on the material itself, falling in, there's nothing special about the horizon. He keeps on going in. There's nothing frozen about what happens to him. So, I felt that that aspect of it needed more emphasis.
“Roger Penrose and I worked together on the large scale structure of space and time, including singularities and black holes. We pretty much agree on the classical theory of theory of relativity but disagreements began to emerge when we got into quantum gravity. We now have different approaches to the world, physical and mental. Basically, he is a Platonist believing that’s there’s a unique world of ideas that describes a unique physical reality. I on the other hand, am a positivist who believes that physical theories are just mathematical models we construct, and it is meaningless to ask if they correspond to reality; just whether they predict observations.”See: Phil Warnell's comment.
( Chapter Six-The Large, the Small and the Human Mind-Roger Penrose-Cambridge University Press-1997)
Whereas Stephen Hawking and Kip Thorne firmly believe that information swallowed by a black hole is forever hidden from the outside universe, and can never be revealed even as the black hole evaporates and completely disappears,
And whereas John Preskill firmly believes that a mechanism for the information to be released by the evaporating black hole must and will be found in the correct theory of quantum gravity,
Therefore Preskill offers, and Hawking/Thorne accept, a wager that:
When an initial pure quantum state undergoes gravitational collapse to form a black hole, the final state at the end of black hole evaporation will always be a pure quantum state.
The loser(s) will reward the winner(s) with an encyclopedia of the winner's choice, from which information can be recovered at will.
Stephen W. Hawking, Kip S. Thorne, John P. Preskill
Pasadena, California, 6 February 1997
Drawing Credit: XMM-Newton, ESA, NASA-Image sourced from: Pictured above is an artist's illustration of a black hole surrounded by an accretion disk.The black hole Information Paradox results from the combination of quantum mechanics and general relativity. It suggests that physical information could "disappear" in a black hole. It is a contentious subject since it violates a commonly assumed tenet of science—that information cannot be destroyed. If it is true, then cause and effect become unrelated, and nothing science knows, not even our memories, can be trusted.
Professor Sir Roger Penrose, OM, FRS (born 8 August 1931) Before the Big Bang Three Different Views of Quantum Weirdness
(and What It Means)
A: According to the orthodox view of quantum mechanics, called the Copenhagen interpretation, a system (represented here by a child’s block) does not occupy a definite state or location until it is measured. Before then it is just a blur of overlapping possibilities.
B: The many worlds interpretation insists that the system occupies all its possible states but that every one of them exists in its own alternate universe. Each universe sees one state only, which is why we never observe the block in two states at once.
C: In Penrose’s interpretation, gravity holds our reality together. In each potential state, the block generates a separate gravitational field. Over time, the energy required to maintain these multiple fields causes the block to settle into one state only—the one that we observe.
See:If an Electron Can Be in Two Places at Once, Why Can't You-by Tim Folger, Photograph by David Berry, Illustrations by Don Foley?
See:Quantum State reduction as a real phenomenon by Roger Penrose (Oxford)2 Sep 1999“Some people have difficulty with accepting Plato’s mathematical world as being in any sense ‘real’, and would gain no comfort from a view that physical reality itself is constructed from abstract notions. My own position on this matter is that we should take Plato’s world as providing a kind of ‘reality’ as mathematical notions (and as I’ve tried to argue for forcefully for in the case S1.3) but I might baulk at actually attempting to physically identify physical reality within the abstract reality of Plato’s world. I think that Fig. 34.1 best expresses my position on this question, where each of three worlds, Platonic-mathematical, physical and mental-has it’s own kind of reality, and where each is (deeply and mysteriously) found in one that precedes it ( the worlds take cyclicly). I like to think that, in a sense the Platonic world may be the most primitive of the three, since mathematics is a kind of necessity, virtually conjuring its very existence through logic alone. Be that as it may, there is a further mystery, or paradox, of the cyclic aspect of these worlds , where each seems to be able to encompass the succeeding one in its entirety, while itself seeming to depend only upon a small part of its predecessor.”
(Page 1028-The Road to Reality- Roger Penrose- Borzoi Book, Alfred A. Knoff- 2004)
"It was a matter of putting things together and ‘seeing’ the answer!" Roger Penrose- Shadows of the mind
"To answer ‘by intuition’, is hardly satisfactory."Paul Benacerraf and Hillary Putnam
According to Plato, knowledge is a subset of that which is both true and believedEpistemology or theory of knowledge is a branch of philosophy concerned with the nature and scope of knowledge. The term was introduced into English by the Scottish philosopher James Frederick Ferrier (1808-1864).[2]
Much of the debate in this field has focused on analyzing the nature of knowledge and how it relates to similar notions such as truth, belief, and justification. It also deals with the means of production of knowledge, as well as skepticism about different knowledge claims. In other words, epistemology primarily addresses the following questions: "What is knowledge?", "How is knowledge acquired?", and "What do people know?"
The terms "a priori" and "a posteriori" are used in philosophy to distinguish between deductive and inductive reasoning, respectively. Attempts to define clearly or explain a priori and a posteriori knowledge are part of a central thread in epistemology, the study of knowledge. Since the definitions and usage of the terms have been corrupted over time and therefore vary between fields, it is difficult to provide universal definitions of them. One rough and oversimplified explanation is that a priori knowledge is independent of experience, while a posteriori knowledge is dependent on experience. In other words, statements that are a priori true are tautologies.
Innatism is a philosophical doctrine that holds that the mind is born with ideas/knowledge, and that therefore the mind is not a 'blank slate' at birth, as early empiricists such as John Locke claimed. It asserts therefore that not all knowledge is obtained from experience and the senses.
