Re: Ada Lovelace: others & forerunners
"David Deutsch david.deutsch-LR/[email protected] [Fabric-of-Reality]" <[email protected]> Sat, 10 Oct 2015 23:02:12 +0100
| Newsgroups | gmane.science.physics.fabric-of-reality |
|---|---|
| Message-ID | <[email protected]> |
--Apple-Mail=_9D0FCF84-0EDD-46FA-AD22-A64546D08D58 Content-Transfer-Encoding: quoted-printable Content-Type: text/plain; charset="UTF-8" On 9 Oct 2015, at 12:20, Bruno Marchal [email protected] [Fabric-of-Reality= ] <[email protected]> wrote: > > On 08 Oct 2015, at 23:21,= David Deutsch david.deutsch-LR/[email protected] <mailto:david.deutsch-LR/[email protected]> [Fa= bric-of-Reality] wrote: > >> The documentary says (and gives what I consid= er very strong arguments and evidence for, including Babbage's own letters = to Lovelace) that Babbage totally 'got' computational universality in the a= rithmetical sense, > > > In the arithmetical sense already? I guess you = mean in the sense of computing all arithmetical computable function (all co= mputable function from N to N), Yes. > and not as meaning: being able to = be emulated by arithmetic Yes. > (the later discovery made partially by G= =C3=B6del and clearly by davis and Kleene that a tiny part arithmetic (Robi= nson arithmetic) is Turing universal. > Today we know that just diophantine= polynomials are already Turing universal, even with the polynomial degree = limited to 4. > >> and was the first person ever to do so, and to recognis= e its importance. > > Interesting! That's new evidence for me. It confirm= s Lafitte analysis, which was informal, as Lafitte did not yet know about C= hurch-Turing thesis. > >> But he didn't even conceive of using the registe= rs of the Analytical Engine as symbols for anything but numbers -- until he= read it in Lovelace's commentary. And even then, he thought it an interest= ing but incidental property, not the fundamental and much more significant = one. > > I will think about this, and look further. Thanks. > > Bruno Mar= chal -- David Deutsch --Apple-Mail=_9D0FCF84-0EDD-46FA-AD22-A64546D08D58 Content-Type: text/html; charset=UTF-8 Content-Transfer-Encoding: quoted-printable <!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01//EN" "http://www.w3.org/TR/htm= l4/strict.dtd"> <html> <head> </head> =20 <body style=3D"background-color: #fff;"> <span style=3D"display:none"> </span> <!--~-|**|PrettyHtmlStartT|**|-~--> <div id=3D"ygrp-mlmsg" style=3D"position:relative;"> <div id=3D"ygrp-msg" style=3D"z-index: 1;"> <!--~-|**|PrettyHtmlEndT|**|-~--> <div id=3D"ygrp-text" > =20=20=20=20=20=20 =20=20=20=20=20=20 <p>On 9 Oct 2015, at 12:20, Bruno Marchal <a href=3D"mailto:marchal@u= lb.ac.be" class>[email protected]</a> [Fabric-of-Reality] <<a href=3D"ma= ilto:[email protected]" class>Fabric-of-Reality@yahoogroups= .com</a>> wrote:<br class><div><blockquote type=3D"cite" class><br class= =3D"Apple-interchange-newline"><div class>On 08 Oct 2015, at 23:21, David D= eutsch <a href=3D"mailto:david.deutsch-LR/[email protected]" class>david.deutsch@= qubit.org</a> [Fabric-of-Reality] wrote:<br class><div style=3D"font-f= amily: Monaco;font-size: 14px;font-style: normal;font-variant: normal;font-= weight: normal;letter-spacing: normal;text-align: start;text-indent: 0px;te= xt-transform: none;white-space: normal;" class><br class=3D"Apple-interchan= ge-newline"><blockquote type=3D"cite" class><div style=3D"background-color:= rgb(255, 255, 255);" class><div id=3D"ygrp-text" class><div class>The docu= mentary says (and gives what I consider very strong arguments and evidence = for, including Babbage's own letters to Lovelace) that Babbage totally 'got= ' computational universality in the arithmetical sense, </div></div></= div></blockquote></div><div style=3D"font-family: Monaco;font-size: 14px;fo= nt-style: normal;font-variant: normal;font-weight: normal;letter-spacing: n= ormal;text-align: start;text-indent: 0px;text-transform: none;white-space: = normal;" class><br class></div><div style=3D"font-family: Monaco;font-size:= 14px;font-style: normal;font-variant: normal;font-weight: normal;letter-sp= acing: normal;text-align: start;text-indent: 0px;text-transform: none;white= -space: normal;" class>In the arithmetical sense already? I guess you mean = in the sense of computing all arithmetical computable function (all computa= ble function from N to N), </div></div></blockquote><div><br class></div>Ye= s.</div><div><br class><blockquote type=3D"cite" class><div class><div styl= e=3D"font-family: Monaco;font-size: 14px;font-style: normal;font-variant: n= ormal;font-weight: normal;letter-spacing: normal;text-align: start;text-ind= ent: 0px;text-transform: none;white-space: normal;" class>and not as meanin= g: being able to be emulated by arithmetic </div></div></blockquote><div><b= r class></div>Yes.</div><div><br class><blockquote type=3D"cite" class><div= class><div style=3D"font-family: Monaco;font-size: 14px;font-style: normal= ;font-variant: normal;font-weight: normal;letter-spacing: normal;text-align= : start;text-indent: 0px;text-transform: none;white-space: normal;" class>(= the later discovery made partially by G=C3=B6del and clearly by davis and K= leene that a tiny part arithmetic (Robinson arithmetic) is Turing universal= .</div><div style=3D"font-family: Monaco;font-size: 14px;font-style: normal= ;font-variant: normal;font-weight: normal;letter-spacing: normal;text-align= : start;text-indent: 0px;text-transform: none;white-space: normal;" class>T= oday we know that just diophantine polynomials are already Turing universal= , even with the polynomial degree limited to 4.</div><div style=3D"font-fam= ily: Monaco;font-size: 14px;font-style: normal;font-variant: normal;font-we= ight: normal;letter-spacing: normal;text-align: start;text-indent: 0px;text= -transform: none;white-space: normal;" class><br class></div><blockquote ty= pe=3D"cite" style=3D"font-family: Monaco;font-size: 14px;font-style: normal= ;font-variant: normal;font-weight: normal;letter-spacing: normal;text-align= : start;text-indent: 0px;text-transform: none;white-space: normal;" class><= div style=3D"background-color: rgb(255, 255, 255);" class><div id=3D"ygrp-m= lmsg" class><div id=3D"ygrp-msg" class><div id=3D"ygrp-text" class><div id= =3D"ygrps-yiv-985293242" class><div class>and was the first person ever to = do so, and to recognise its importance.<span class=3D"Apple-converted-space= "> </span></div></div></div></div></div></div></blockquote><div style= =3D"font-family: Monaco;font-size: 14px;font-style: normal;font-variant: no= rmal;font-weight: normal;letter-spacing: normal;text-align: start;text-inde= nt: 0px;text-transform: none;white-space: normal;" class><br class></div><d= iv style=3D"font-family: Monaco;font-size: 14px;font-style: normal;font-var= iant: normal;font-weight: normal;letter-spacing: normal;text-align: start;t= ext-indent: 0px;text-transform: none;white-space: normal;" class>Interestin= g! That's new evidence for me. It confirms Lafitte analysis, which was info= rmal, as Lafitte did not yet know about Church-Turing thesis.</div><div sty= le=3D"font-family: Monaco;font-size: 14px;font-style: normal;font-variant: = normal;font-weight: normal;letter-spacing: normal;text-align: start;text-in= dent: 0px;text-transform: none;white-space: normal;" class><br class></div>= <blockquote type=3D"cite" style=3D"font-family: Monaco;font-size: 14px;font= -style: normal;font-variant: normal;font-weight: normal;letter-spacing: nor= mal;text-align: start;text-indent: 0px;text-transform: none;white-space: no= rmal;" class><div style=3D"background-color: rgb(255, 255, 255);" class><di= v id=3D"ygrp-mlmsg" class><div id=3D"ygrp-msg" class><div id=3D"ygrp-text" = class><div id=3D"ygrps-yiv-985293242" class><div class>But he didn't even c= onceive of using the registers of the Analytical Engine as symbols for anyt= hing but numbers -- until he read it in Lovelace's commentary. And even the= n, he thought it an interesting but incidental property, not the fundamenta= l and much more significant one.</div></div></div></div></div></div></block= quote><div style=3D"font-family: Monaco;font-size: 14px;font-style: normal;= font-variant: normal;font-weight: normal;letter-spacing: normal;text-align:= start;text-indent: 0px;text-transform: none;white-space: normal;" class><b= r class></div><div style=3D"font-family: Monaco;font-size: 14px;font-style:= normal;font-variant: normal;font-weight: normal;letter-spacing: normal;tex= t-align: start;text-indent: 0px;text-transform: none;white-space: normal;" = class>I will think about this, and look further. Thanks.</div><div style=3D= "font-family: Monaco;font-size: 14px;font-style: normal;font-variant: norma= l;font-weight: normal;letter-spacing: normal;text-align: start;text-indent:= 0px;text-transform: none;white-space: normal;" class><br class></div><div = style=3D"font-family: Monaco;font-size: 14px;font-style: normal;font-varian= t: normal;font-weight: normal;letter-spacing: normal;text-align: start;text= -indent: 0px;text-transform: none;white-space: normal;" class>Bruno Marchal= </div></div></blockquote><br class></div><div>-- David Deutsch</div><br cla= ss></p> </div> =20=20=20=20=20 <!--~-|**|PrettyHtmlStart|**|-~--> <div style=3D"color: #fff; height: 0;">__._,_.___</div> =20=20=20=20=20=20=20=20=20=20 =20=20 =20 =20=20=20=20 <div style=3D"clear:both"> </div> <div id=3D"fromDMARC" style=3D"margin-top: 10px;"> <hr style=3D"height:2px ; border-width:0; color:#E3E3E3; background= -color:#E3E3E3;"> Posted by: David Deutsch <david.deutsch-LR/[email protected]> <hr= style=3D"height:2px ; border-width:0; color:#E3E3E3; background-color:#E3E= 3E3;"> </div> <div style=3D"clear:both"> </div> <table cellspacing=3D4px style=3D"margin-top: 10px; margin-bottom: 10px= ; color: #2D50FD;"> <tbody> <tr> <td style=3D"font-size: 12px; font-family: arial; font-weight: bo= ld; padding: 7px 5px 5px;" > <a style=3D"text-decoration: none; color: #2D50FD= " href=3D"https://groups.yahoo.com/neo/groups/Fabric-of-Reality/conversatio= ns/messages/25705;_ylc=3DX3oDMTJxMW9uMDRiBF9TAzk3MzU5NzE0BGdycElkAzE4ODg2MD= AEZ3Jwc3BJZAMxNzA1MDIwNTg1BG1zZ0lkAzI1NzA1BHNlYwNmdHIEc2xrA3JwbHkEc3RpbWUDM= TQ0NDUxNDU4Mw--?act=3Dreply&messageNum=3D25705">Reply via web post</a> </td> <td>•</td> <td style=3D"font-size: 12px; font-family: arial; padding: 7px 5p= x 5px;" > <a href=3D"mailto:david.deutsch-LR/[email protected]?subject=3DRe%3A%20Ada= %20Lovelace%3A%20others%20%26%20forerunners" style=3D"text-decoration: none= ; color: #2D50FD;"> Reply to sender </a> </td> <td>•</td> <td style=3D"font-size: 12px; font-family: arial; padding: 7px 5p= x 5px;"> <a href=3D"mailto:[email protected]?subject=3DR= e%3A%20Ada%20Lovelace%3A%20others%20%26%20forerunners" style=3D"text-decora= tion: none; color: #2D50FD"> Reply to group </a> </td> <td>•</td> <td style=3D"font-size: 12px; font-family: arial; padding: 7px 5p= x 5px;" > <a href=3D"https://groups.yahoo.com/neo/groups/Fabric-of-Realit= y/conversations/newtopic;_ylc=3DX3oDMTJlNXBkMzRwBF9TAzk3MzU5NzE0BGdycElkAzE= 4ODg2MDAEZ3Jwc3BJZAMxNzA1MDIwNTg1BHNlYwNmdHIEc2xrA250cGMEc3RpbWUDMTQ0NDUxND= U4Mw--" style=3D"text-decoration: none; color: #2D50FD">Start a New Topic</= a> </td> <td>•</td> <td style=3D"font-size: 12px; font-family: arial; padding: 7px 5p= x 5px;color: #2D50FD;" > <a href=3D"https://groups.yahoo.com/neo/groups/= Fabric-of-Reality/conversations/topics/25699;_ylc=3DX3oDMTM2M25yN2VnBF9TAzk= 3MzU5NzE0BGdycElkAzE4ODg2MDAEZ3Jwc3BJZAMxNzA1MDIwNTg1BG1zZ0lkAzI1NzA1BHNlYw= NmdHIEc2xrA3Z0cGMEc3RpbWUDMTQ0NDUxNDU4MwR0cGNJZAMyNTY5OQ--" style=3D"text-d= ecoration: none; color: #2D50FD;">Messages in this topic</a> (7) </td> </tr> </tbody> </table> =20=20=20=20=20=20=20=20 <!------- Start Nav Bar ------> =20 <!-- |**|begin egp html banner|**| --> <div id=3D"ygrp-vital" style=3D"background-color: #f2f2f2; font-family: Ver= dana; font-size: 10px; margin-bottom: 10px; padding: 10px;"> <span id=3D"vithd" style=3D"font-weight: bold; color: #333; text-transf= orm: uppercase; "><a href=3D"https://groups.yahoo.com/neo/groups/Fabric-of-= Reality/info;_ylc=3DX3oDMTJlaWl1cDk2BF9TAzk3MzU5NzE0BGdycElkAzE4ODg2MDAEZ3J= wc3BJZAMxNzA1MDIwNTg1BHNlYwN2dGwEc2xrA3ZnaHAEc3RpbWUDMTQ0NDUxNDU4Mw--" styl= e=3D"text-decoration: none;">Visit Your Group</a></span> <ul style=3D"list-style-type: none; margin: 0; padding: 0; display: in= line;"> </ul> </div> <div id=3D"ft" style=3D"font-family: Arial; font-size: 11px; margin-top: 5p= x; padding: 0 2px 0 0; clear: both;"> <a href=3D"https://groups.yahoo.com/neo;_ylc=3DX3oDMTJkY2g0MDN1BF9TAzk3ND= c2NTkwBGdycElkAzE4ODg2MDAEZ3Jwc3BJZAMxNzA1MDIwNTg1BHNlYwNmdHIEc2xrA2dmcARzd= GltZQMxNDQ0NTE0NTgz" style=3D"float: left;"><img src=3D"http://l.yimg.com/r= u/static/images/yg/img/email/new_logo/logo-groups-137x15.png" height=3D"15"= width=3D"137" alt=3D"Yahoo! 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