tag:blogger.com,1999:blog-11295132.post1013073177509119669..comments2019-07-19T01:35:14.385-07:00Comments on A Neighborhood of Infinity: Self-referential logic via self-referential circuitssigfpehttp://www.blogger.com/profile/08096190433222340957noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-11295132.post-67845237104515158392017-07-17T21:41:54.331-07:002017-07-17T21:41:54.331-07:00@patchworkZombie You're absolutely right. I...@patchworkZombie You're absolutely right. I'll have to delete that paragraph :-(Dan Piponihttps://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-51467112887861746882017-07-17T20:53:18.782-07:002017-07-17T20:53:18.782-07:00You say that tit-for-tat permanently defects if it...You say that tit-for-tat permanently defects if it is ever defected on. My understanding was that tit-for-tat was a NON-latching delay circuit, so that it is perfectly willing to cooperate again if the opponent ever retried cooperation.<br /><br />(and boy google is getting intrusive, they require cookies to post a comment)patchworkZombiehttps://www.blogger.com/profile/18279408952877283952noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-59372648865641692252017-07-17T06:32:56.644-07:002017-07-17T06:32:56.644-07:00Yes, I've built some BEAM robots and I was tem...Yes, I've built some BEAM robots and I was tempted to mention that. Also, I believe there is an "analogue" synthesizer that has digital components at its core and this gives it a unique sound. But I've forgotten its name and couldn't find it again.<br /><br />And another twist: I've built an inverter from a transistor or two and connected the feedback via a wire a few metres long. Due to the delay the result was an RF oscillator and the wire also acts as an antenna. Wave your hand around near the wire and the frequency changes. You can use this as the basis for a (not very reliable) theremin.Dan Piponihttps://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-14562939540624367052017-07-17T01:59:37.024-07:002017-07-17T01:59:37.024-07:00I'm a little rusty... but IIRC, your initial &...I'm a little rusty... but IIRC, your initial "paradoxical circuit" is perfectly sane in an analog world. It will produce a nice stable voltage at half the supply, where the NMOS & PMOS bias currents are equal.<br /><br />You can read more about it here: https://electronics.stackexchange.com/questions/130413/cmos-inverter-with-feedbackbeambothttps://www.blogger.com/profile/06066673853768524678noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-57726563802197682242017-07-15T21:19:08.604-07:002017-07-15T21:19:08.604-07:00Seems obvious that you can deduce p from □p. And t...Seems obvious that you can deduce p from □p. And that's what we do in practice - we assume things are true once we prove them. But we can't prove it from the usual axioms of mathematics! It's more sort of an empirical truth.<br /><br />Suppose we have □p→p. Then we'd have □⊥→⊥, which is the claim that ⊥ is unprovable. That's the same as saying PA is consistent. But Gödel's theorem says that if it is consistent, we can't prove it.Dan Piponihttps://www.blogger.com/profile/08096190433222340957noreply@blogger.comtag:blogger.com,1999:blog-11295132.post-40165183749093632132017-07-15T18:51:40.074-07:002017-07-15T18:51:40.074-07:00"as well as a rule that allows us to deduce b..."as well as a rule that allows us to deduce box-p from p."<br /><br />Should that be the other way around?Joshua Ballhttps://www.blogger.com/profile/06420272596782781072noreply@blogger.com