User:Dan Gluck

I am a physicist and an algorithm developer (machine vision and machine learning). I've done my PhD in theoretical physics (or is it mathematics?) - string theory, and did post-doc in cell biology. Also have studied math and philosophy.

And if anyone is still reading - please stop killing animals just because they taste good.

Work to do

 * Merge Luxon and Bradyon into Mass in special relativity if no objections are raised.
 * String theory: Rewrite overview, replace first image, add AdS-CFT images.
 * Write String theory: a technical review.
 * Add general w=p/u into Thermodynamics of the universe, which covers also Cosmic inflation and Big rip cases.
 * Supersymmetry breaking.
 * Gravitational instanton, instanton, Gravitational singularity (general - add massless fields, conical - blow up of orbifold)
 * Angular momentum: commutation relations of J with any vector operator are like those of J with itself.
 * Commutator, Commutativity: add a part about significance and use in Quantum mechanics.
 * Expand Particle physics in cosmology.
 * Expand Lattice QCD some day.
 * Lagrange multipliers - add intuition (show 2d case).
 * Prove Snell's law using Fermat's principle and Lagrange multipliers (+ add link in the latter to this as an example), and using Maxwell's equations.
 * Expand Biblical criticism.
 * Add Socrates's debate over whether evil is ignorance in Unsolved problems in philosophy and Problem of evil?
 * Mass–energy equivalence: add a section about the difference between E=MC2 and E=(1/2)Mv2.
 * Expand the Meat article and add pictures of the production process.
 * Mention this in Global warming.

Major contributions
(pages I've started or was significantly involved in their writing):
 * String theory
 * Nuclear magnetic moment
 * Shell model
 * Woods Saxon potential
 * Fermion
 * Boson
 * Measure (physics)
 * Particle physics in cosmology
 * E6 (mathematics)
 * E7 (mathematics)
 * E8 (mathematics)
 * Gravitino
 * Thermodynamics of the universe
 * Proof sketch for Gödel's first incompleteness theorem
 * Lattice QCD
 * Unitarity (physics)
 * Gravitational singularity
 * Entropy (arrow of time)
 * Arrow of time
 * Relationship between string theory and quantum field theory
 * Particle statistics
 * Picture (string theory)
 * Ramond sector
 * Neveu-Schwarz sector
 * Conformal symmetry
 * Friedmann-Lemaître-Robertson-Walker metric
 * Euler number (topology)
 * Sphaleron
 * Beta trefoil fold
 * Two Tracts on Government
 * Illustrative model of greenhouse effect on climate change

sections

 * Deuterium
 * Quantum number
 * SO(10) (physics)
 * Split supersymmetry
 * Physical cosmology
 * Tachyon
 * Evolution as theory and fact
 * Lindemann–Weierstrass theorem
 * Baryogenesis
 * Liénard–Wiechert potential#Derivation#Lorenz Gauge, Electric and Magnetic Fields
 * Net (mathematics) (first proof: equivalence of continuity definitions)
 * Seafloor spreading (may be moved to Mid-ocean ridge in the future).
 * Von Neumann bicommutant theorem (major revision)
 * Cochran's theorem
 * Riemann integral (rewrote proof which was wrong)
 * Conway's Game of Life
 * Factor_V
 * Factor_VIII
 * Factor_XIII
 * Endothelial_protein_C_receptor
 * Protein_S
 * Decay-accelerating_factor
 * Arithmetical_hierarchy
 * Post%27s_theorem
 * Primitive_recursive_function
 * Computable_function
 * Machine_that_always_halts
 * Tidal_acceleration
 * Dynamo_theory (revised and added two subsection)
 * Gamow_factor
 * Stellar_nucleosynthesis
 * Mass–luminosity_relation
 * Mass–luminosity_relation
 * Radiation zone
 * Radiation zone
 * State of the Teutonic Order
 * Separation of powers
 * Hilbert–Bernays provability conditions
 * Deduction theorem
 * Spin (physics)
 * Normal force
 * Angular momentum (except for the "general considerations" part)
 * Second law of thermodynamics
 * Big Bang
 * Chronology of the universe
 * Ozone–oxygen cycle

very short stubs which I may want to expand

 * Dimensional reduction
 * Superghost
 * Worldsheet
 * Secrets of the Baby Whisperer
 * Multiplet
 * Dilatino
 * Adaptin
 * Reclinomonas

A proof sketch that $$2^{\sqrt{2}}$$ is irrational
We first consider the following matrix: $$M_{ij} = (s_i + t_i\sqrt{2})^{u_j}2^{(s_i + t_i\sqrt{2})v_j}$$

where i runs over all (2S-1)2 pairs (si, ti) with -S < si, ti < S, and j runs over all (L0+1)(L1+1) pairs (uj, vj) with 0 &le; uj &le; L0, 0 &le; vj &le; L1.

S is an arbitrarily large integer, L0 = S [Log(S)], L1 = [S /Log(S)]. (here [x] denotes the integer value closest to x from below).

Mij is a (2S-1)2 by L matrix, and since (2S-1)2 > L for large enough S, we may look at any determinant of an LXL sub-matrix of M, which we denote &Delta;.


 * &Delta;| can be shown to satisfy an upper bound, |&Delta;|&le;x-L 2/2 for some x>1, as we later discuss.

Now let us assume that $$2^{\sqrt{2}}$$ is rational. Then for some integers a, b with b>1, $$2^{\sqrt{2}} = a/b$$. Therefore:

$$M_{ij} = (s_i + t_i\sqrt{2})^{u_j}2^{s_i}a^{t_i v_j}b^{-t_i v_j}$$,

and hence:

$$\Delta = (A+\sqrt{2}B)p a^{t_i v_j}b^{-t_i v_j} $$, for some integers A, B, p.

Then one uses Liouville theorem on diophantine approximation to show that |&Delta;| satisfies a lower bound, |&Delta;| &ge; bSL1L.

For every x,b>1 there exists an S large enough such that: bSL1L< x-L 2/2. We thus arrive at a contradiction, and therefore $$2^{\sqrt{2}}$$ must be irrational.

We turn now to the upper bound of &Delta;. As S (and hence L) grow larger, the determinant &Delta; contains multiplication of more factors (which tend to increase its size), but it also contains more lines and columns which become closer and closer to being linearly dependent (which tend to reduce its size), and the second effect is shown to be more prominent.

To show this, we see that every entry in the matrix M satisfies: $$M_{ij} = W^{u_j} 2^{W v_j} f_j(z_i)$$, with $$f_j (x) = x^{u_j}2^{W v_j (x-1)}$$, $$z_i = (s_i + t_i \sqrt{2})/W$$ and some $$ W > S(1+\sqrt{2})$$. Note that $$|z_i|, |f_j(z_i)|<1$$ for all i, j. Therefore:

$$\Delta = L! W^{L\sum_j u_j} 2^{W L \sum_j v_j} \Delta_1 L! W^{L\sum_j u_j} 2^{W L \sum_j v_j} \Delta_1$$ where $$\Delta_1 $$ is the determinant of the LXL sub-matrice fj(zi) (instead of Mij).

An example for a Gödel number in Peano arithmetic
Let's try to write a concrete example for the Godel number required here, with Peano arithmetics and the decimal system. We will have to use abbrevations for lengthy expressions.

A k-ary relation
(under work)

A list of words similar in Hebrew and Greek
α-           alpha privativum, expressing want or absence. αγείρω  (root ΑΓΕΡ-)   to bring together, gather, assemble δωμα     a house, a chief room, a hall, αδρός     strong, great. Of persons: large, fine, well-grown. αγαπάω  to treat with affection, love, be fond of      έχω         to have or to hold    (Ionic imperative:  εχεσκον) Iliad: to grip αυριον   dawn, aurora,     ουρανός    the sky [perhaps source of light?], ελλος      a young deer, fawn ελλοψ     Hesiod = mute (for fish) ύλη         a wood, forest, woodland. Homerus and Herodotus: forest trees. άνθρωπος        man, or woman. (latin: homo, not vir) a human being οπτάω    to cook  by means of fire or dry heat. όφις        a serpent, snake αράχνη   a spider,  a spider’s web αρά         I.  a prayer. Especially a prayer for evil, a curse, imprecation. II. The effect of the curse, bane. δόλιχος    long έρα           ground ερώ          say, speak αίθω         (1) to light up, kindle. (2) intransitive: to burn or blaze. αιθάλη      soot. Αιθίοψ =  Ethiopian = פני אש. αίθος = fire αστράπτω hurl lightnings (of Zeus)  αστραπή = lightning,  αστήρ =star σοφός       skilledin any handicraft or art, cunning in his craft. Clever, wise. βαίνω (ΒΑ-)     to walk, to step, to go, to come, to arrive, to depart, etc.       φρέαρ                  Iliad etc,: a well βάραθρον           a pit, (at Athens a left behing the Acropoliw, into which                                                   criminals were thrown

φαείνω   Skt. *bha-  to shine, give light           בהר, בהק βύσσος    a fine flax and the linen made from it     (a later borrowing?) βωμός     any raised platform, or stand, araised place for sacrificing, altar. πυρός      wheat flee, flight Skt. palay-                   ברח      (Gothic: pliuhan, etc.) πέσσω     I : of the sun: to ripen. II. By the action of fire: to cook, bake. όχθη                                                      גדה γίγας      mostly plural: Γίγαντες = Giants, a savage race destroyed by the Gods κυλίω     to roll,         גל    (see,  γογγύλος – עגול) γλάφω    to scrape up (the ground). γλαφυρος =  polished, finished. γλυπ-, γλυφ-  (akin to γλάφω)  to carve, cut out with a knife γοάω, γόος      to wail, groan, weep Αίγυπτος        Egypt                      (αια-γυπ)     ארץ גושן γεφυρόω        to bridge over, make passable by a bridge,   γέφυρα = a bridge τιτθός        a teat, nipple γύρος          a ring, circle δύη            a woe, misery, anguish, pain. θολός       mud, dirt, the dark juice of the cuttle-fish. θολόω  to make turbid τρέχω        to run, move quickly έρχομαι (fut. ελθω)    to come, to go         ολολύζω,  αλαλάζω     (= crying aloud to the gods in prayer or thanksgiving) όρος         a mountain, a hill (Cf. C.D. Buck, A Dictionary of Selected Synonyms in the Prinicipal Indo- European  Languages:  “Gr. όρος ..…  from  IE *er-  ‘move, raise, rise’     seen in Skt. ŗ-, G r. όρνυμι , Lat. oriri.”.    Heb.  רם= high, also connected?      αράω (old verb: to harm)                         σφάζω     to slay, slaughter, properly by cutting the throat.    σφαγή   slaughter,       σεύω (έσσευσα)   to put in quick motion.  σείω  to move to and fro.                                                                                                   σεισμός = earthquake      σκώληξ          a worm.      μέλος  (for the  σ  see μικρ-, σμικρ)   a song, tune      [ζέω ( =  to boil)                                      זעם  (= anger)]      ρέω (ροή)    to flow, stream, gush                     σπείρω    ( Lat. sero)    to sow seed                     Akk. zāru      זרע κόπτω      to strike, smite, knock down, cut off chop down χωμα      earth thrown up, a bank, a mound,   a dike Lat. forare,                Akk. harāru    חרר      ( hole, Old Eng.: hol,   חור ) άλσος      a glade or grove            (see ύλη,  אלה, etc.) γάλα  (root: ΓΛΑΚ-, ΓΛΑΓ-)   milk                                                  חלב connected to γλαύκος, γλυκύς, glow, etc. ? and to λευκός,     --   לבן  ? χαλάω              Iliad:  to slacken, loosen γάμος, γαμέω)     a wedding, wedding-feast, marriage, wedlock.            ξένος    In Homer: a guest friend, i.e. any citizen of a foreign state, with whom one                                     has a treaty of hospitality for self and heirs,  a refugee.              σκεπάω         to cover, shelter.       σκάπ-τω        to dig        σκότος          darkness, gloom                                                 χήρα (-ος)     a widow, bereaved               Akk. Һarābu        חרב                       and κάρφω  to dry, destroy      ορρωδέω       to fear, dread, shrink from. (formed so as to express the shuddering of fear)           χαράττω (ΧΑΡΑΚ-)     to cut into, to sharpen, whet,   scratch.   (χαράσσω)       αρόω         to plow              δείδω   (epic aor. έδδεισα)   to fear, dread   ω                                                               εδνόω   to betroth, to marry       σφαγ- σφακ-      slaughter (see above:  טבח (זבח) δρόσος =  dew,    υδωρ = water,   θάλασσα = sea, τέλμα = standing water, marsh, pool, pond. τρέφω (έθρεψα)      to rear, feed. τροφή  food, nourishment μογέω, μόγος      to toil, to suffer *δάω (anc. root =learn, perf.: to know)     Skt. vid- = to know    Akk. idu    ידע οίδα (perf. of to see= know) οίνος       wine οιωνός   = a bird of omen, and also omen. Aesch. οιωνός γόος,  but the only bird that makes a wailing sound – γόος --  is the dove! Ιάπετος      one of the Titans (sons of Uranus and Gaea), father of Atlas, Prometheus, etc. According to a tradition – rather late—he formed the body of the first man with earth and water (perhaps his own                              tears) into which Athena breathed soul and life. לא במקרה,הסופר בחר שם זה לאבא של פינוקיו! :Japetto ύπνος        sleep, slumber ιασπις                               Akk. (j)ašpu  ישפה  (but not a basic, primitive word…) ιθύς          straight, direct    ιθύνω:  make straight, guide in a straight line καίω         to light kindle, Passive: to get burned,   καύμα : burning heat. κικυς  (in Homer)    strength, vigour. (h)όλος   whole,  entire,              Akk. kullatu   כל κλείω   to shut, close, bar, to confine. σκύλαξ (OE hwelp) a young dog, puppy, a whelp, generally: a dog --  Κέρβερος κλωβός     a bird cage      (El Amarna:  kilubi) κάμνω (root: KAM-)    Iliad: to work, of smith’s work. κύπελλον   a big-bellied drinking vessel, a beaker, goblet, cup κυφός  (r.: ΚΥΠ-)     bent forward, bent, stooping κριός       a ram χράω    (1) to be eager to do  (2) to furnish what is needed. χρη = must, need κείρω   (I) to cut the hair    (II) to cut, to hew  out (of wood), destroy γρύψ, Eng. Griffin κρόκος, IE crocus            Akk. kurkanu        כרכם χιτών (κιθών)   the garment worn next the skin, in early times: a man’s frock. Later worn by women as well. νάσσω, νάττω     to press, squeeze,  ναστός: a well kneaded cake λανθάνω (root: ΛΗΘ- ΛΑΘ)       to escape notice, be unseen, etc. λέων       a lion                           Akk. nesu               ליש μανθάνω (r.: ΜΑΘ-)   Iliad: to learn, to know, to understand. λέγω       to say, to speak                          larynx =  לע       ( whence Arab.                λάρυγξ  = לע + ρύζω(=to growl) ?           λωβάομαι    to treat despitefully, to outrage,    λώβη    an outrage, dishonour                                                                                               λείχω           to lick up         γλω̃σσα       the tongue, the organ of speech.  Homerus:  language         μω̃̃̃μος          a blame, riducule, disgrace.     μωμεύω (Hom.) to find fault.         μίσγω         to mix one thing with another, join together, to mingle.         μυελός =  marrow, μύχιος = inward, inmost,  μυχός = the innermost place.                                      Connected to μυέω, μυστήρια?    סתר – מוסתר?) Lat. amarus   French:  amer, = bitter μετρέω    to measure πίμπλημι (r.:ΠΛΕ- or ΠΛΑ-)   to fill full of a thing. Passive: to be filled. μέγαρον      Homer:  a large room or chamber, a hall. βασιλεύς     a king, chief μάσσω        to handle, touch εγγύς = near, near at hand ναίω, ναιετάω = dwell νέω                 to go,         νέομαι      to go or come έχις, έχιδνα     an adder, viper   (Skt.  ahi) πίπτω       to fall δάκνω (root: ΔΑΚ-)  to bite δίδωμι (root: ΔΟ-)      to give, to grant σηκός, σακός        a pen for lambs)          σής               a moth (which eats woolen stuff)           αγαπάω        to treat with affection, to caress, love, be fond of..           γογγύλος      round                                                       γερανός         a crane          κόραξ            a raven, crow           αιξ                a goat          αετός             an eagle          αχλύς             a mist, a mist over the eyes of one dying          άναξ               a lord, master, being applied to the gods, esp. Apollo and Zeus.                                                                            A title given to all men of rank and note.

άγχω        to strangle, throttle,       αγχόνη       a throttling, strangling, hanging ενίπ-τω    to reprove, upbraid          ( connected to όνειδος ) ασκέω      to work, to form by art, to fashion, to practice and art. ίδη           in plural:  a timber tree,  in singular: a wood ακίς                                                      עקצ, עֺקץ σκορπίος                       Akk. aqrabu עקרב Έρεβος                         Akk. erebu          ערב εγείρω                              Akk. êru               ער  (root: ,עור  Aram. עיר ) IE *ger-  Skt. jagr-, Av. gar- είς                                     Akk. iśten         עשתי-  (found only in composites) [Καφτωρ                       Akk. Ištar          עשתרת    Was the island named in honour of the goddess   (as Athens for Athena) and later renamed Crete under the           influence of Ugarit (as St. Petersburg –Leningrad)? πεδίον                        Akk. šadu                פדן     [a different form of שדה ?] πω̃; όποι, etc. Lat. qu-                          פה πέρδομαι,     Skt. pŗd-   Akk. balātu     פלט     (fart, peter, etc.) πέλας, πελάζω                                        פלש πατέω                                                     פסע      (and in the Bible: [פשע      βοάω, βοή,                                            פעה          πόρτις                         Akk. parru        פר, פרה      flight,     Skt. palay-                   ברח  ,פרח                                                                                                                                                                                                                                                      οπώρα, fruit   Skt. phala-                            פרי     (connected to root פרה = grow)                   Lat.flos,  IE *bhle-, bhel-   Akk.pirhu   פרח             πείθω                                                פתה, פֽתה    (later borrowing?)      Πύθων                               Akk. bašmu  פתן            σχελίς                                Akk. şelu      צלע σκοπέω                             Akk. šafu       צפה       (and ; שקפ    (Latιn: aspicere)                             κάπρος = wild boar        Lat. caper                        Akk. şapir       צפיר   ]       Lat. strictus                                          צרר   [ = bound together, whence narrow: Skt : avi-stīrņa- and avistŗa           צר           (It. stretto,  Fr : etroit ; etc )   καλέω     to call, to summon, to call by name, to name,                                                                                   κλαίω    to weep, lament, wail, cry.    κράζω, κραυγή, cry out,     καίνω  ( = kill, in Iliad)                                קין  (the name)   ( Hitt.: kwen-)   εύ-κολος    easy   δύσ-κολος  difficult   κέλυφος     a sheath, case, pod, shell     καλύπτω  (r. KΑΛΥΒ-)   to cover with a thing   κάννα    a reed   κρύος      icy cold, chill, frost   κυρέω, κύρω         meet with, light upon, fall in with,   κέρας      the horn of an animal, horn as a material, anything made of horn

οράω  (and  λάω)      to see, look at, behold οργή     Ι. natural impulse, temperament,  ΙΙ. passion, anger, wrath οργίζω      to provoke anger ορμάω          to set in motion, spur on, push on, ορμή         a violent movement onwards, onset, an attack έρπω            to creep, crawl, to move slowly ρύπος           dirt, filth, dirtiness ορχέομαι      to dance in a row, and generally:  to dance εθέλω or θέλω  (Doric δήλομαι)   to wish, will, purpose θήρ, φήρ      awild beast, a beast of prey θηράω = to hunt or chase wild beasts        θήραμα = the hunted animal ταυ̃ρος         a bull σκηνή     a covered place, a tent, a tented cover στέλλω     I.  to set in order, equip, furnish with   II. to dispatch, send. In Medium: to  to send  for one. συλάω     to strip off, esp. to strip off the arms of a slain enemy, to pillage, plunder, rob. λεηλατω̃ to drive away cattle as booty, to make booty, plunder, despoil λεία    booty, plunder. ληστής     robber, plundered. πλήρης    full of a thing, complete. οδούς (gen. oδόντος)  a tooth σινέομαι, σίνομαι       to do one harm or mischief, πνίγω        to choke, throttle, strangle θεάομαι     to look on, gaze, behold. θύω           to rush on or along, of a rushing wind. To storm, rage. θύελλα      a furious storm, hurricane. θύρα         a door. In Homer mostly of double doors πύλη         one wing of a pair of double gates. In plural (in Iliad): the gates of a city έθειρα       hair. In Homer in plural: either a horse;s mane, or horsehair crest on                     helmets. Εθειράζω = to have long hair. πηγάζω       gush forth with water. πηγή = mostly in plural: running waters, streams σακίον, σάκκος      a sack, bag. Akk. šaqqu      שׂק έρπω          to creep, crawl ρίζα           a root                        (Lesb.: βρίσδα ) πορφύρα    the purple-fish, purple dye, purple ίστημι (r.  ΣΤΑ-)   to stand. To make to stand. To set up. To raise, rouse, stir up. τίθημι   (r. ΘΕ-)  to set up, put, place πίνω      (ρ.  ΠΟ-)  to drink. πόσις = a drinking, a drink, beverage. θαυμάζω     to wonder, to marvel, be astonished. θαυ̃μα         whatever one regards with wonder, a wonder, a marvel τρέπω      to turn or direct towards a thing. θώς          (Iliad) the jackal