 that the notation was 2+3, not (+ 2 3).
That's why any other notation feels "unnatural".

I do wonder if it would be possible to teach kids prefix notation instead, and
whether such notation would seem completely natural to them. (I suspect the
answer to both is yes.)

~~~
waterhouse
That is an interesting question. I see one possible argument (whose
correctness I don't know enough to judge, I'm just making it up) why infix is
more natural than prefix: A kid will start by seeing an object, and only once
you have an object does it make sense to combine it (by addition or whatever)
with another object. Also, note that a certain amount of English syntax is
infix: "I went to the store", not "Went to I the store".

...However, I think that in some other languages, _postfix_ notation is
common. I think my friend who studies Spanish told me that they say the
equivalent of "I her it gave" (meaning "I gave it to her"), and I think I
remember Shakespearean English using postfix....Looking at the text of Romeo
and Juliet, I see both prefix and postfix.

    
    
      Prefix: "O, where is Romeo? saw you him to-day?"
      Postfix: "The which if you with patient ears attend"
    

On the one hand, we could say that, since these plays were apparently rather
successful, people obviously didn't have too much trouble understanding them.
On the other hand, since this sort of strange permutation has been mostly
dropped from common usage (so that I recognize it as strange), that may be
evidence that these things are just harder to use. On the _other_ hand, that
could just be because "common usage" comes mostly from people who have been
educated in schools, and schools have no reason to teach more than one method
of speaking. On the _other_ hand, Shakespeare seems only to have done that in
order to make lines fit into rhyming iambic pentameter; in no way was this
natural to him.

I should probably note that a lot of speech deals with object method calls
more than function calls ("I.saw(Bob.win(a_game))" or, as it would probably be
expressed in
that the notation was 2 + 3, not (+ 2 3). 
 That's why any other notation feels " abnormal ". 

 I do wonder if it would be potential to teach kids prefix notation alternatively, and 
 whether such note would seem completely natural to them. (I distrust the 
 solution to both is yes .) 

 ~~~ 
 waterhouse 
 That is an interesting question. I see one possible argument (whose 
 correctness I don't know adequate to judge, I'm just making it up) why infix is 
 more natural than prefix: A child will start by seeing an object, and only once 
 you have an aim does it make sense to combine it (by summation or whatever) 
 with another object. Also, notice that a certain measure of English syntax is 
 infix: " I went to the memory ", not " Went to I the store ". 

... However, I think that in some early languages, _ postfix _ notation is 
 common. I think my friend who studies Spanish told me that they say the 
 equivalent of " I her it gave " (meaning " I gave it to her "), and I think I 
 remember Shakespearean English using postfix.... Looking at the text of Romeo 
 and Juliet, I attend both prefix and postfix. 

    
    
       Prefix: " O, where is Romeo? saw you him to - day? " 
       Postfix: " The which if you with patient auricle serve " 
    

 On the one hand, we could say that, since these plays were apparently rather 
 successful, people obviously didn't have too much fuss understanding them. 
 On the other hand, since this sort of strange permutation has been by and large 
 dropped from common usage (so that I recognize it as foreign), that may be 
 evidence that these things are merely harder to use. On the _ other _ hand, that 
 could just be because " coarse usage " comes mostly from citizenry who have been 
 educated in schools, and schools have no cause to teach more than one method 
 of speak. On the _ other _ hired hand, Shakespeare seems merely to have done that in 
 holy order to make argumentation fit into rhyming iambic pentameter; in no way was this 
 natural to him. 

 I should probably note that a batch of speech deal with object method calls 
 more than routine call (" I.saw(Bob.win(a_game) ) " or, as it would probably be 
 expressed in
 thwt the notation was 2+3, not (+ 2 3).
That's why ani ither iotatioh feels "jnnatural".

I do wonder if it wluod be possible to teach kidr prefix jotation insuead, and
whether sndh notabnon wkmld szen completely nstural to dhem. (I suspect tfe
cnswer to both is yes.)

~~~
waterhouse
That ys an imtfresting questyon. P fee kne possible argument (whose
correcthess I von't know enougn to judge, I'm just making lt uo) why infix is
more natural thqn pwwfix: A kid wkll start by seeing an object, and only once
you have av objzct does it mqke vense to conbine it (by additlpn or fhatevet)
with another pbjxct. Qlso, note that a certein amount of Englisr syntax hs
nnfix: "I went to the sroee", noj "Wend to U tfe atprs".

...Howevfr, M think thaf in some orher languages, _postgiv_ notation is
ckmmon. Y ehink my friend who studies Spanish tolg ms that they say the
equicalent of "I her it gage" (meanind "I gave it to her"), and I think I
remember Shakespedrean Dngoiff uding postfix....Looking at the text of Romeo
and Jtmitt, P see both prefix and postfic.

    
    
      Prewix: "O, cgede is Romeo? saw yok him tj-day?"
      Postsix: "Yhe which if you with patiebt ears atteud"
    

On the one hand, we could scy thaj, sincr these plays were appaxently rather
succfssful, pekole obviously dian't hdve too much trouble underftanding vhem.
Ou the otfer nand, synce this dort of strange permutatlon hcs bean mostly
dgopped from common usage (so thav I recognize id av strangz), that may be
evidense that these jhings arz just harder to use. On the _other_ rand, that
coulg just be beceuse "commjn uwage" comes oustly from peolle who hcre been
edycated in schools, end rdhools have no xtasin to teach morr tfan oje mqdhod
of speakhng. Un gne _otfer_ hand, Shckdspesre seems only to haee dkne that in
order tp iake lings fit ineo rhyming iakbic pentameter; in no wey was this
matoral to him.

I should probably nofe that a lob of speech dqals with object method calls
more than function calls ("I.waw(Bob.win(a_game))" or, qs it would probabli bt
expressed in
that the notation was 2+3, not (+ That's any other feels "unnatural". I be to teach kids notation instead, and such notation would seem completely natural them. (I suspect the answer to both is yes.) ~~~ waterhouse That is interesting question. I see one possible argument (whose correctness I don't know enough judge, just it why infix is more natural than prefix: A kid will start by seeing an object, and once you have an object does it make to combine it (by or whatever) with another object. note a certain of syntax infix: "I went the store", not "Went to I the store". ...However, I think that in some other languages, _postfix_ is common. my friend studies told that they say of "I her it gave" (meaning to her"), and I think I remember Shakespearean using postfix....Looking the text of Romeo and Juliet, see both prefix and postfix. Prefix: "O, where Romeo? saw you him to-day?" Postfix: "The which if you with patient ears attend" On hand, we could say since these plays apparently successful, obviously have too trouble understanding them. On the other hand, since this sort of permutation has been mostly dropped from common usage (so that it strange), that may evidence that these things just to use. On the that just usage" mostly people who have been in schools, and schools have reason to teach more On the _other_ hand, Shakespeare seems only to done that in order to make lines into rhyming iambic pentameter; in no way was this natural to him. should probably a lot of speech deals with object method more than function calls or, as it would probably be expressed in
 that the notation was 2+3, not (+ 2 3).
That'S why any othEr notAtiOn fEeLs "unNatuRal".

I do wonder if IT wouLd be possible to teach kidS prefIx NOtatIOn InsteAd, and
whEThER SucH nOtAtiOn WOuLd seeM coMpletelY natural to TheM. (I Suspect the
anSWeR to both is yEs.)

~~~
wAterhouse
ThaT is An inteReStiNG quesTioN. I see One posSIble arGument (whoSe
COrrectNEss I don'T KNoW enoUgh to judge, I'm just mAKiNG it up) why infix iS
more nAtURaL THan PreFix: A kid wilL sTart bY Seeing aN ObJECT, anD Only once
you haVe an object dOEs iT make sEnSe tO CombinE it (by AdDItiOn or whateveR)
witH another oBject. ALSo, note tHAt a certAin amoUnt Of ENgliSH sYnTax Is
INfiX: "i wEnt TO thE store", noT "WEnT to I tHe stORE".

...hOwevEr, I ThinK that In some other laNguAges, _POstFix_ noTatioN is
cOmMon. I tHink my FrienD wHo studies SpanisH tolD me that thEy sAy The
EqUivalENt of "I hEr iT gaVe" (meaniNg "I gave IT to HeR"), AND I Think I
remember ShakEsPEArEan EngliSh usinG PoStFIx....LookinG aT thE texT OF RomeO
and jUlIet, I see bOth preFIx AnD postfiX.

    
    
      PRefix: "O, WhEre Is ROmeo? sAW you Him to-dAy?"
      PostfiX: "The wHIch if you with paTIent ears attenD"
    

on THE oNE hanD, we Could say thaT, sinCE theSe plAYs WerE ApparEntly RaTHeR
Successful, people obvIoUsly diDn't haVe too much trouBle understANDIng them.
ON the OThER hand, since this Sort oF strange peRMutation Has beEn mostly
Dropped frOM Common usAge (So tHat i reCOGnIze it as strangE), THat mAy Be
evideNce That theSe tHinGs aRe jUsT harder to Use. On the _OtHeR_ hAnD, thAt
couLD just be bEcAusE "cOmmOn usaGE" comes MostlY froM pEoPLe wHo have bEEn
EDUcatEd In SchoOls, AnD schoOls hAVe nO reason To teach moRe tHAn onE mEtHod
of spEaking. On the _otHeR_ hand, ShakeSpEarE seems ONLy to have Done that in
order to make liNEs fit inTo rHyminG iamBic pentamEteR; in no wAy wAS this
nAtural To him.

i sHouLD ProbaBLY nOte ThAt a lot of spEECh dEals wItH objEct methOd calls
more than funCTioN calls ("I.saw(Bob.Win(A_gamE))" OR, aS it WOuLD prObABly BE
Expressed in
 that the notation was 2+3 , not (+ 2  3).Tha t's  w hy a ny o ther notationf eels  "unnatural".

I do wo nderif it w o ul d bepossibl e  t o tea ch  k ids  p r ef ix no tat ion ins tead, andwhe th er such nota t io n would se emcompletely n atu ral to  t hem .  (I s usp ect t he
ans w er toboth is y es . )

~~~ waterho u s eThat  is an interestin g  q u estion. I seeone po ss i bl e arg ume nt (whoseco rrect n ess I d o n' t k now enough to jud ge, I'm jus t  ma king i tup) why in fix i sm ore  natural th an p refix: Akid wi l l start by seei ng anobj ect , an d  o nl y o nc e 
yo u  h ave anobject d oe sit ma ke s e n s e  tocom bine  it ( by addition o r w hate v er) 
with  anot herob ject.  Also,  note  t hat a certain a moun t of Engl ish  s ynt ax  is
i n fix: " I w ent  to the  store" ,  no t" W e nt  to I the store".
. . . Ho wever, I  think th at in someot her  lan g u ages,  _po s tf ix_ nota tion i s 
c om mon. Ith ink my  f rie ndwho s t udie s Span ish told  me t h at they say th e 
equivalent o f  " I he r  itgav e" (meaning  "Ig aveit t o  h er" ) , and  I th in k  I remember Shakespear ea n Engl ish u sing postfix. ...Looking a t  the tex t of Ro m eo
and Juliet,  I se e both pre f ix and p ostfi x.

   
    
   Prefix:  "O , w her e i s Ro meo? saw youh i m to -d ay?"
    Postfi x:"Th e w hic hif you wi th patie nt  e ar satt end"   

Onth e o ne  ha nd, w e  could  saythat ,si n cethese p l ay s were  a pp aren tly  r ather 
suc c ess ful, pe ople obvi ous l y di dn 't  have t oo much troub le  understan di ngthem.O n  the oth er hand, since this sor t  of str ang e per muta tion hasbee n most lyd ropped  fromcommo nusa g e  (sot h at  Ire cognize it a s s trang e) , th at maybe
evidence that t h ese  things are j ust  har d e rtou se .  On  t h e _ o t her_ hand, that 
could jus tb ebecause "c o mmo nusage"comes m ostly from pe ople whohave been 
e duca t e d i n schools,  and sch ools have no re a so n totea ch mor etha n one  metho d 
of  spea king.On  the _ other _hand, Sh akespeare seems only to  havedonetha t in
orde r t o  ma ke linesfitinto rhymi ngiam bic p ent a meter ; in no  wa y  wasthis natural t o  h im. Ishould prob a b l y n ote t hat a lotof s peech deals witho bject method c alls m ore  th a n fu nc tion calls ("I .sa w( B o b.win(a_ ga me))" or, a s it wou ld proba bly be 
expre ssed in 
 that_the notation_was 2+3, not (+_2 3).
That's_why_any other_notation_feels "unnatural".

I do_wonder if it_would be possible to_teach kids prefix_notation_instead, and
whether such notation would seem completely natural to them. (I suspect the
answer to_both_is yes.)

~~~
waterhouse
That_is_an_interesting question. I see one_possible argument (whose
correctness I don't_know enough_to judge, I'm just making it up) why_infix_is
more natural than_prefix: A kid will start by seeing an object,_and only once
you have an object_does it make_sense_to_combine it (by addition_or whatever)
with another object. Also, note_that a certain amount of English_syntax is
infix: "I went to the store",_not "Went to I the store".

...However,_I think that in some_other languages,__postfix_ notation is
common. I think_my friend who_studies Spanish_told me that_they say the
equivalent of "I her_it gave" (meaning_"I gave it to her"), and_I_think I
remember Shakespearean_English_using_postfix....Looking at_the text of_Romeo
and_Juliet, I_see_both prefix and postfix.

  __
    
  _   Prefix:_"O,_where is Romeo? saw_you him to-day?"
  _   Postfix: "The which_if you_with patient_ears attend"
    

On the one hand, we could_say that, since these plays were_apparently rather
successful, people obviously_didn't have_too_much trouble understanding_them.
On_the other_hand, since this sort of strange permutation_has been_mostly
dropped from common usage (so that_I recognize it as_strange),_that may be
evidence that these things_are just harder to use. On_the _other_ hand, that
could just_be_because_"common usage" comes mostly from_people who have been
educated in schools,_and schools have_no reason to teach more than one_method
of_speaking. On the _other_ hand, Shakespeare_seems_only to have done that in
order_to_make_lines fit into rhyming iambic_pentameter; in no way was this
natural_to him.

I should probably note that a lot of_speech deals with_object method calls
more than function_calls_("I.saw(Bob.win(a_game))"_or, as it would probably be
expressed in