User:Dan Gluck

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I am an Israeli algorithm designer, working on image analysis. I've done my PhD in physics, in string theory (or is it mathematics?), and did post-doc in biology.[1] Also have studied math and philosophy.

So please don't argue with me about physics unless you're a physicist yourself.

(Sorry for the arrogance but you may understand the need after reading this)
‏משתמש זה דובר עברית כשפת אם.‏
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Work to do[edit]

My contributions[edit]

Major contributions[edit]

(pages I've started or was significantly involved in their writing):


very short stubs which I may want to expand[edit]

A proof sketch that 2^{\sqrt{2}} is irrational[edit]

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 ≤ uj ≤ L0, 0 ≤ vj ≤ 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 Δ.

|Δ| can be shown to satisfy an upper bound, |Δ|≤x-L2/2 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 |Δ| satisfies a lower bound, |Δ| ≥ bSL1L.

For every x,b>1 there exists an S large enough such that: bSL1L< x-L2/2. We thus arrive at a contradiction, and therefore 2^{\sqrt{2}} must be irrational.

We turn now to the upper bound of Δ. As S (and hence L) grow larger, the determinant Δ 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[edit]

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[edit]

(under work)

A list of words similar in Hebrew and Greek[edit]

     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