Notes on "The Book of Nothing" by JD Barrow.Pg.15: Base ten comes from fingers. Some advanced cultures in history have had base 20 - fingers and toes (three score years and ten, quatre-vignts, quatre-vingt-dix etc.) - some less so 2 or 5.
One noticable one was base 8 an American Indian counting system depending on the gaps between the fingers rather than the fingers themselves.
A Turkish system for remembering differences in month length also counts the gaps and the knuckles of two clenched fists on top of each other - the knuckles being 31 days the gaps less than 31. July/August skip across from the last knuckle of one fist to the first knuckle of the other.
Also relics such as time - base sixty - and angles, degrees - 360. A gross, a dozen eggs.
Pg. 20: Counting system of early Sumer had base ten, but also base 60 as a secondary - from this comes our tradition of time-keeping.
Pg.19: Egyptian counting symbols do not carry numerical information related to position - ie: a particular number's symbol in position X, relative to other symbols, equals exactly the same even should that number's symbol be switched to position Y.
Without "position related numerical information", a blank entry in a composite number need never be marked, and thus a zero never be needed. ie: 11=two cf: 11= eleven --> 1_ = 1 = one cf: 1_ = 10 = ten.
cf: pictographic languages - they do not need blanks between 'words' to convey meaning because each pictograph's meaning is isolate of any other, and individual letters and spelling are not integral concepts.
Pg.25: Positional/placevalue system (a natural progression in efficiency - fewer characters required to write the same number) first appeared in Babylonia in about 2500bc (cuneiform notation - additive base 60).
Pg.27: For Babylonians - the Zero was really simply a 'spacer', they [as far as is known] attached no other deeper philosophic meaning to the concept of 'nothing'. Also it was never used as a 'result' ie: 1-1=0, such a thing was always explained in words.
Pg.39: AD200-458: The Indians (decimal counting system) take the idea of a zero spacer (a dot, rather than the modern 'O') and develop it into a more philosophic signifier of 'nothingness'. They also develop arithmatic - subtraction, multiplication and division and through division by zero, infinity.
"sunya" or "shunya" indian word for "void".
Pg.42: Indian culture, posessing as it did/does an array of conceptualization of nothingness/emptiness were ready to accept the true zero without major realignments of philosophy.
Hebrew traditions view the concept of 'void' with utter repugnance - to them void signified a state of being separate from God, removed from his favours.
Greek philosophies, and their high respect for logic led to an aversion toward the zero as a paradox - 'something' pertaining to be 'nothing' - or simply treating 'nothing' as if it were 'something'.
ie: Assholes.
Pg.49: 900AD - Indian zero - sunya - adopted by Arabic world - translates to 'as-sifr' meaning "empty" or "absence of anything". Passes into English as "cipher"meaning originally 'nothing' or as an insult "nonentity".
Pg.51: "theca"meaning "little circle" referred to the circular zero symbol branded into the cheeks and foreheads of criminals in the middle ages.
Pg.56: Infinity: Most scientists believe infinities are never physically manifest - if they appear in a calculation they simply imply that the theory involved has run up against the limits of its validity (the range of values it can be usefully used to describe cf. Newton with Relativity with Quantum) and that a new theory must be found to replace the mathematical infinity with a finite measurable quantity.
Pg.166: The empty set. How all numbers can be defined using absolutely nothing:
Define zero as the empty set: Ø because it holds no members.
Then define "1" as the set which holds one member - the empty set - {0} ie. {Ø}and "2" as the set which holds {0,1} ie: {Ø,{Ø}} and "3" as the set which holds {0,1,2} ie: {Ø,{Ø},{Ø,{Ø}}}
... ad infinitum.
The null set can define all the rest. Nothing becomes something - Think of nothing. Think of thinking about nothing. Think about thinking about thinking about nothing... The 'nothing' becomes a definable object. A foundation.
Pg.59 God: European christianity tried to wed the two conflicting ideas of divine creation - Greek "god as architect moulding the world from pre-existant materials" with the Jewish "creation from nothing".
Pg.60: "horror vacui" a morbid aversion to nothingness. Seems to be a human trait, all cultures elaborately decorate empty spaces.
Pg.63: Empedocles - water catcher experiment - early vaccuum discovery. 2000 years later Torricelli gives correct explanation. (first made the mercury tube manometer)
Pg.71: Moslem art shows appreciation of the concept of infinity - repeated patterns - no blank space could be left empty - all 'voids' were filled.
Pg.74: Augustine proposes God created time as well along with the world - sidestepping any 'beginning' or 'before' problems with scripture.
Pg.99: AD1643 Mercury is used in barometers because it is the densest liquid (14x more than H2O) - reducing the length of the tube. Torricelli. There is a limit (dependent on density of medium) on the height a liquid can be raised by a vaccuum pump. Air pressure bearing down on the mercury at sea-level = 76mm of Hg.
Pg.142: Disproving the concept of 'ether'. (An invisible medium through which all light, heat and electromagnetic waves propagate. Pronounced "eether" with the "th" as in the word "thought," ether was postulated from the 1600s to the 1800s. Newton/Newtonian physics)
1881 Michelson's experiment (beams of light at 90 degrees - if out of sync at return -> interference bands) shows no evidence of stationary ether.
Pg.145: FitzGerald-Lorentz shrinkage (things contract lengthwise related to their speed eg. 500km/hr = contraction of 0.000000000001%) ie small but effective at very high speeds. It was discovered that this contraction would mask the effect of 'ether' slowing one of the beams of light - so stationary ether was back online as a possibility.
Pg.147: Einstein 1905 - Relativity. All motion is relative:
*The laws of motion and electromagnetism must be found to be the same by all experimenters moving at constant velocities relative to one another.
*The velocity of light in empty space must be measured to be the same by all observers regardless of their motion.
The concept of ether becomes unecessary to explain properties of light and electricity. Einstein took Michelson's experiment as his inspiration.
Pg.155: Geometry. Euclid's plane geometry is a good example of localization - ie. in a small enough area the natural curvature of the earth is negligible, and so Euclid's [and at the time supposedly the only logically consistant ie: Absolute truth] geometric laws adequately describe/predict reality. However, expand the area involved and the curvature does become a factor, and so non-euclidean geometries are required.**
People were so impressed by this 'axiomatic method' (definition>axiom>theorem>proof) that even some philosophers - for example Spinoza - laid out their propositions in the same way. Gimic.
**But Carl F Guass (1777 - 1855) discovered that it was perfectly possible to construct other non-euclidean self-consistant geometries, that worked just as well, except for non-planar surfaces.
Working rules of thumb relating points and lines on curved surfaces were also worked out waaaaaay before the mathematicians got their grubby little paws involved, by potters guilds, for illustrating pottery accurately. Which is funny.
Pg. 180: Gravity - gravity acts on all forms of mass and energy. Gravity itself gravitates - Waves of gravity spread - rippling the curvature of space - carrying energy that in turn acts as a source for its own gravity field. Gravity interacts with itself in a way that light does not.
Pg.182: visualizing the universe. Imagine a stack of holographic cards. Any particular card represents the state of the universe at any instant of time. Now simply weld those cards into one. Et voila.
Pg.205: Lambda. Introduced by Einstein as a new "cosmological" constant. Representing a force opposite to that of gravity (an [attractive] force between two masses which decreases with distance - following Newton's inverse square law) lambda being a [repulsive] force that increased in proportion to the distance between two masses. Balancing out gravity and providing a 'static' universal model - one neither collapsing of expanding eternally. [see pg.273.]
Friedmann finds other solutions saying that a static model is inherrently unstable unless spacetime is absolutely smooth with regard to density. The final expanding universe model becomes standard. 1929 confirmed by observation. (All distant galaxies show a red shift proportional to their distance from the earth as a result of the general expansion of space-time )
Pg.207: Quantum physics 101:
* Energy is quantised: in atoms it doesn't take on all possible values but hikes itself up and down a ladder of specific multiples of h - planck's constant () -
because values of energy between divisions of h do not allow for a whole number of wavelengths to fit within an orbit.
** All particles act as if they were a wave with a wavelength inversely proportional to their mass and velocity. As objects increase in mass, their quantum wavelengths 'shrink' to ranges contained within the boundaries of their physical size, masking any wave-like properties. If the mass of a "particle" is low enough that the quantum wavelength exceeds the boundaries of the particle's physical size, then these intrinsic wavelike properties become dominant - producing novel behaviour.
Get small enough and you cannot measure both mass and velocity with any meaningful accuracy. But probability math gets around this, kinda. Identity holds, we just can't meaningfully examine it.
Pg.209: Erwin Schrödinger and Max Born - Schrödinger's equation describes the probability we will obtain result X from quantum experiment Y. Wave function. The equation preserves determinism at the quantum level - but not at the level of appearances - by providing accurate predictions over time of a pattern of outcomes, some more probable than others.
Pg.210: Planck constant constrictions on energy levels preserve the uniformity of matter - if all energy levels were universally permitted - then each atom, each molecule would be - being effected, on however miniscule a level, by their histories - subtly different, allowing no predictable interaction,
and no life.
Pg.216: No system is ever completely devoid of energy, no vaccuum ever absolute. Thus the definition of vaccuum changes to "the emptiest possible state, the lowest possible energy - the state from which no more energy can be removed". This then becomes the ground state, or vaccuum state. But it is never zero. This is in concordence with the uncertainty principle. ie. if we knew the location of a particle oscillator exactly (as we would, if we removed all its energy and made it still, or at least as still as possible), its energy will still be uncertain - varying by ½hf (one quantum of energy) or zero point motion.
Pg. 273: A non-zero value for Lamda (the lowest state of energy in a vaccuum) results in "vaccuum energy" - inferred from supernovae observations as 10 to the -120th power. [Can be demonstrated by Casimir plates - so close that there are more zero-point fluctuations outside them than in, providing a (very small) inward pushing force].
Pg.222/3: Sonoluminescence. Bombard water with soundwaves - air bubbles form which very quickly contract then disappear in a flash of light. Contracting bubble-walls act like mini-casimir plates..?
Ships at sea, rolling on swells [the wavelengths of which are much longer than the distance between the two ships], side by side in time - the rocking motion of the ships caused by their hulls' absorbance and re-transmission of wave energy can create out of sync wave patterns between them, which cancel each other out - producing an 'energy vaccuum' in the gap as each hull radiates wave energy effectively outward, but not inward - effectively thrusting them together. For example two 700 ton Clippers would have an attractive force of about 2000 kg generated between them.
Pg.226: Solidity and superpositions. How, if an object is mainly empty space with an very small amount of actual matter flying around within it, be solid..? ie. every inquisitive prod being met by resistance at the boundary of a certain volume.
Probabilities. The boundary of a 'solid' object forms naturally at the point where the probability of a resistance generating particle/force being met reaches levels of near certainty. Think of a piece of string being whirled so fast it blurs into a disc. It's still only ocupiying a fraction of the volume, but spin it fast enough and it would deflect anything trying to penetrate the area of its arc.
Pg.227-229: Quantum particles and 4 forces.
Graviton: A massless [therefore having infinite range] particle carrying the gravitic force in exchange. Acts on every particle, even itself.
Photon: A massless [therefore having infinite range] particle carrying the electromagnetic force in exchange. Acts on any particle possessing an electric charge.
W+, W-, and Z° intermediate vector bosons [massive - 90 times heavier than a proton - and the force they mediate has a finite range 100 times less than the radius of an atomic nucleus]: they carry weak interaction forces that act on Leptons (Greek - "light ones") - electrons, muons, tauons and associated neutrinos.
Gluons: Mediate in exchange the strong force (binds atoms into distinct objects) which has a range of about the size of the radius of the largest atomic nuclei. Acts on Quarks (three of which constituate a proton) possessing three 'colours' of an electric charge analogue. The strong force or colour force acts on every particle that carries a 'colour' charge. They are 90 times less massy than bosons.
At least for now, leptons and quarks seem to be the elementary particles - possessing no apparant internal structure.
Note: Dark Matter (the 'missing' matter from the universe) is thought to be carried by 'sterile neutrinos:
Scientists have discovered that neutrinos have mass through neutrino oscillation experiments. This led to the postulation that "sterile" neutrinos exist - also known as right-handed neutrinos. They do not participate in weak interactions directly, but do interact through their mixing with ordinary neutrinos. The total number of sterile neutrinos in the universe is unclear. If a sterile neutrino only has a mass of a few kiloelectronvolts (1 keV is a millionth of the mass of a hydrogen atom), that would explain the huge, missing mass in the universe, sometimes called "dark matter". Astrophysical observations support the view that dark matter is likely to consist of these sterile neutrinos.
Pg.233-6. Virtual pairs. (unobservable)
Quantum vaccuums are never empty - they are a sea of elemetary particles and their antiparticles constatly appearing and anihilating each other quicker than anything can detect them.
For example - a positron and electron appear - tot. mass 2m - 'borrowing' (e=mc²) 2mc² from available vaccuum energy resevoir to manifest themselves - and anihilate - returning 2mc² again. If there time of existance is so small as to not obey the uncertainty principle - (Energy time)
- their existance will be unobservable - hence the term 'virtual pairs'.However, they still have effect. Possessing charges, they are attracted to, and surround real particles of the opposite charge, acting like padding. (Vaccuum polarisation).
During low energy collisions between real particles, deflections are shallow and slight, because the two point charges never come close, the padding of each gently pushes each away from the other. But in high energy collisions, deflections are shaper, more intense, because the padding has little effect, and the two bare point charges interact. ie: in a high energy enviroment effective electromagnetic interactions become stronger and stronger - it is not a linear progression.
Same principle effects quarks and colour charges - save that the strong force becomes effectively weaker at higher energies.
Pg.237: Asymptotic freedom. The above means that at very high temperatures - 10 to the 27th degrees Kelvin - all the forces become equal in strength. A grand unification.
In the beginning everything was simpler, then as the universe cooled, the forces separated and everything got complex.
Pg.240: Evaporating black holes. Virtual pairs materializing near enough the event horizon of a black hole to have one of the pairs sucked in prior to mutual anihilation, and one of the pair to 'escape' and persist long enough to become 'real' means that the so-called black holes are not black bodies, but radiative bodies.
It also means, because the energy 'borrowed' by the virtual pairs from the local surroundings - in this case the gravitic well of the black hole - is not returned, that the black hole will gradually evaporate away, its energy spent on the creation of new elememtary particles.
Pg.247: Symmetry breaking and critical thresholds. Laws of nature are unerringly symmetrical - they must appear the same to any and all observers in the universe. However, this does not mean that the outcomes of these laws cannot be asymmetrical. Magnetization for example - at high temperature, a metal bar can maintain a stable minima (lowest energy state possible given external conditions) without a polarization/direction. However, below a critical temperature, two stable minima arise - N/S or S/N - only one of which any particular metal bar can adopt.
Cf. Phenotypic canalization.
Pg.249-52: Scalar Fields and universal expansion rates. (hypothetical aid to visualisation) These are fields which have only one atribute. Imagined en toto as a pendulum having two energy components - kinetic, from motion and potential, from location.
Anyway, not too important in detail, the thing to remember is stable states of vaccuum energy with respect to background temperature. ie: an (oscillating) scalar field in a high temperature universe inhabits a single stable 'valley' vaccuum minima. But subsequent lower temperatures means that a scalar field swings up and over the dividing 'rises' between its old stable minima valley, into an adjoining, lower one. And again, and again, with periods of prolonged stability in between.
If the transition between minima is slow - imagine a ball rolling gently, but inevitably, down a rounded-stepped pyramid - this produces an 'anti-gravitic' effect, pushing matter apart, which drives universal expansion at a [vastly] accelerated rate.
Pg.253: Uniformity in the visible universe. Why scalar-field/vaccuum minima-accellerated expansion is absolutely critical to life.
(Visible space - we cannot see further than a distance of about 15 billion light years - ie the distance light has travelled since the beginning of the expansion of 'our' part of the universe.)
(Wherever we look into visible space its temperature and intensity is the same to a tolerance of 1/100,000. However, as it stands presently, the universe is too large to have been traversed by light - so how did this standardization come about..?)
A period of accelerated expansion, beginning very early on in the general expansion of the universe, means that small areas of that infant universe, small enough such that their properties could have been 'standarized' by the transmission of light, could expand to areas of greater magnitiude than visible space at the present time.
These inflations of limited area also serve to iron-out irregularities in space-time, producing a near uniform flatness. However, remaining quantum uncertainty fluctuations (teeny-tiny origionally but expanded out into macroscopic scales during inflation) in the vaccuum so produced act like seed crystals, causing matter to acrete around them. ie: planets, suns and life.
Our universe appears to be expanding at a rate very, very close to the dividing line between a state of eternal expansion and an eventual contraction. The chances of this situation occuring are astronomically small btw.
(note - explained by anthropic principle).
Pg.274. Residual Lambda force (energy level above zero in vaccuum) is equal to 10 to the power -120. This is an extremely low number, but one absolutely critical to the formation of planets/life. A case of no more or no less will suffice.
Doom..? We may not have reached the lowest minima for Lambda. Perhaps we are on the edge of another shelf. If the value for L changes, we are completely fucked. Completely, totally and irrevocably. Fucked.
Pg.278-86: Summary of String theory. (Too long for here).
Pg.296: Theology - schisms of "creation from nothing" and "creation from existing materials".
Pg.304. Roger Penrose's argument for a temporal starting point, and an infinitely dense big-bang, assuming a strict Einsteinian universe.
Pg.308..311: New theory - Bouncing, ever larger universes.
Lambda - turns (too short-lived for life) bouncing universes of a size large enough for its anti-gravitic properties to produce eternal expansion into universes that can support life. Also however, this expansion guarrentees that universe's eventual lifeless uniform entropic state.
Eternal expansion also eventually means isolation and difficulty of information exchange. At the point where everything is moving away from everything else [effectively] at the speed of light no information transmission can be undertaken. The bubble of communication shrinks and shrinks.
Black Swan saviour. In an infinitely long time, anything not absolutely impossible will come to pass.
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