Re: A useless machine

Path	csiph.com!eternal-september.org!feeder.eternal-september.org!nntp.eternal-september.org!.POSTED!not-for-mail
From	Tim Rentsch <tr.17687@z991.linuxsc.com>
Newsgroups	comp.arch
Subject	Re: A useless machine
Date	Thu, 12 Mar 2026 21:14:43 -0700
Organization	A noiseless patient Spider
Lines	29
Message-ID	<86h5qk74cs.fsf@linuxsc.com> (permalink)
References	<10mpgtp$32h0n$1@dont-email.me> <10ms1rm$3s9f4$1@dont-email.me> <10msdau$3vgrg$2@dont-email.me> <10msqc3$4011$1@dont-email.me> <20260218182251.00004e44@yahoo.com> <10n61l5$36tk6$1@dont-email.me> <jwvwm08a3e4.fsf-monnier+comp.arch@gnu.org> <10ng813$2im23$1@dont-email.me> <10nhci9$2t9mc$1@dont-email.me> <10ninsn$3e0da$1@dont-email.me> <10njhce$3l6lq$1@dont-email.me>
MIME-Version	1.0
Content-Type	text/plain; charset=us-ascii
Injection-Date	Fri, 13 Mar 2026 04:14:47 +0000 (UTC)
Injection-Info	dont-email.me; posting-host="cb1c5db134e2203ca5fd5b23b9ffc3a7"; logging-data="2855307"; mail-complaints-to="abuse@eternal-september.org"; posting-account="U2FsdGVkX1+3g5qi1EEcNWUGTTvpDa2UMMPkEFNoFpI="
User-Agent	Gnus/5.11 (Gnus v5.11) Emacs/22.4 (gnu/linux)
Cancel-Lock	sha1:DTH4xd7SCaQ227p+0vdv0qxUbwY= sha1:VGgg8mKTyJCSPFz0/ex8z2v34yY=
Xref	csiph.com comp.arch:115311

Show key headers only | View raw

Thomas Koenig <tkoenig@netcologne.de> writes:

> BGB <cr88192@gmail.com> schrieb:
>
>> My own looking into this led me to realize that the number-space is
>> modulo (relative to a cone with a spiral that repeats with every
>> power-of-2), and that all the odd steps only ever increment the phase
>> angle by 1, or fall down to a lower level (whenever the phase angle is
>> not incremented).
>>
>> In effect, each odd step jumps to the opposite side of the cone, but
>> slightly increments the angle.  Since the phase-angle path can never move
>> backwards, it can't touch any previous paths, thus, no loops can happen
>> this way.
>>
>>
>> The only way a cycle could exist is if (somehow) there were an
>> impassable wall where pretty much *no* value could descend unless it
>> hits the power-of-2 descent path, and then somehow miss this path as well.
>>
>> But, since "3*n+1" results in the minimum forward step, this means that
>> one of the sides *has* to hit the power-of-2 descent cases at some point.
>
> The same argument would hold for the 3n-1 problem, where there is
> more than one cycle.

3*n-1 = -(3*(-n)+1)

So 3n-1 is just the same as 3n+1 on negative numbers.

Thread

A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-14 09:57 +0000
  Re: A useless machine MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-14 18:48 +0000
    Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-14 20:18 +0100
      Re: A useless machine MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-14 21:22 +0000
        Re: A useless machine Stephen Fuld <sfuld@alumni.cmu.edu.invalid> - 2026-02-14 13:30 -0800
        Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-15 12:50 +0100
          Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-21 13:48 -0600
            Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-21 21:40 +0100
              Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-21 15:17 -0600
                Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-22 04:50 -0600
              Re: A useless machine Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-03-12 21:01 -0700
            Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-22 14:43 +0100
              Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-22 12:38 -0600
                Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-23 10:51 +0100
                Re: A useless machine MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-26 01:27 +0000
                Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-26 09:21 +0100
                Re: A useless machine Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-03-12 21:11 -0700
      Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-15 14:58 +0100
      Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-21 12:27 -0600
        Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-22 15:14 +0100
      Re: A useless machine Stefan Monnier <monnier@iro.umontreal.ca> - 2026-02-22 11:41 -0500
        Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-23 10:53 +0100
          Re: A useless machine Stefan Monnier <monnier@iro.umontreal.ca> - 2026-02-23 10:52 -0500
  Re: A useless machine Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-02-14 21:19 -0800
  Re: A useless machine Robert Finch <robfi680@gmail.com> - 2026-02-15 03:58 -0500
    Re: A useless machine David Brown <david.brown@hesbynett.no> - 2026-02-15 13:14 +0100
      Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-15 15:46 +0000
      Re: A useless machine Robert Finch <robfi680@gmail.com> - 2026-02-15 10:56 -0500
        Re: A useless machine MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-02-15 19:16 +0000
          Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-15 22:40 +0100
            Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-26 19:31 +0000
        Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-18 18:22 +0200
          Re: A useless machine Robert Finch <robfi680@gmail.com> - 2026-02-18 22:56 -0500
            Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-19 12:10 +0200
              Re: A useless machine Robert Finch <robfi680@gmail.com> - 2026-02-21 01:56 -0500
                Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-21 19:23 +0200
                Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-21 20:36 +0200
                Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-22 10:46 +0200
                Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-22 12:45 +0100
                Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-22 16:35 +0200
                Re: A useless machine Robert Finch <robfi680@gmail.com> - 2026-02-22 19:12 -0500
                Re: A useless machine Robert Finch <robfi680@gmail.com> - 2026-02-22 19:47 -0500
                Re: A useless machine EricP <ThatWouldBeTelling@thevillage.com> - 2026-02-21 15:39 -0500
                Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-22 03:16 +0200
                Re: A useless machine EricP <ThatWouldBeTelling@thevillage.com> - 2026-02-22 14:48 -0500
                Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-22 23:25 +0200
            Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-19 11:51 +0100
              Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-19 23:12 +0200
                Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-20 15:11 +0100
            Re: A useless machine Stefan Monnier <monnier@iro.umontreal.ca> - 2026-02-19 15:27 -0500
              Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-20 11:41 +0200
              Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-22 18:41 -0600
                Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-23 11:10 +0000
                Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-23 17:24 -0600
                Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-24 06:44 +0000
                Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-24 01:38 -0600
                Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-24 03:16 -0600
                Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-24 04:52 -0600
                Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-24 11:16 +0000
                Re: A useless machine BGB <cr88192@gmail.com> - 2026-02-24 13:19 -0600
                Re: A useless machine Tim Rentsch <tr.17687@z991.linuxsc.com> - 2026-03-12 21:14 -0700
          Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-20 08:01 +0000
    Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-15 15:35 +0200
      Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-15 18:33 +0200
        Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-15 19:19 +0000
          Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-16 12:31 +0200
            Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-17 15:41 +0200
              Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-17 18:17 +0200
    Re: A useless machine anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-02-15 22:41 +0000
  Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-15 14:52 +0100
    Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-15 16:45 +0000
      Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-15 18:01 +0100
        Re: A useless machine Thomas Koenig <tkoenig@netcologne.de> - 2026-02-15 19:42 +0000
          Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-15 22:59 +0100
            Re: A useless machine Robert Finch <robfi680@gmail.com> - 2026-02-15 21:53 -0500
              Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-16 12:40 +0200
                Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-16 20:34 +0200
              Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-16 16:08 +0100
  Re: A useless machine Stephen Fuld <sfuld@alumni.cmu.edu.invalid> - 2026-02-16 07:50 -0800
    Re: A useless machine Michael S <already5chosen@yahoo.com> - 2026-02-16 18:31 +0200
    Re: A useless machine Terje Mathisen <terje.mathisen@tmsw.no> - 2026-02-18 21:56 +0100

csiph-web