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BB(3, 4) > Ack(14)

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Re: BB(3, 4) > Ack(14)

#31

Post by vlovich123 »

lisper wrote: post #15
immibis wrote: post #9

Discord links! As citations for major results in foundational computer science!

Why not? The idea that the only valid way to publish a scientific result is in a (so-called) peer-reviewed journal is a relic from 200 years ago when the scientific community was small enough to fit within the monkeysphere [1]. It is being clung to only because it is profitable for a small group of powerful academics and publishing houses, not because it has any actual merit in terms of the advancement of science. In…

To be fair, the responsibility for the replication crises is much trickier. It’s based on human motivations and poor science:

1. Outright fraud

2. Lack of independent verification of results before building up a body of work resulting in a bunch of garbage. Contributes to making #1 “easy”.

3. Financial pressures to publish or perish contributing to 1 & 2. If peer review didn’t exist you’d still something similar about producing “recognized” results. This is also probably why we haven’t done any major breakthroughs in particle physics which now has a much longer term thinking phase to come up with anything.

The biggest problem with peer review is actually the establishment of an orthodoxy which discourages itself being upended by controlling the career success of anyone who dare challenge it - you have to support the orthodoxy to get career success and you fail to get recognition if your idea challenges the peer reviewers ideas and careers. That being said, such pressures existed before, but at least you could try to build your own following and it was competing orthodoxies instead of a single one winning out.

Re: BB(3, 4) > Ack(14)

#32

Post by nilstycho »

tromp wrote: post #10

The new BB(3,4) record holder is 0 1 2 3 A 1RB 3LB 1RZ 2RA B 2LC 3RB 1LC 2RA C 3RB 1LB 3LC 2RC with the triple (t',d, s') in row s column t specifying the transition from state s with symbol t under the tape head. the machine overwrites symbol t with t', moves the tape Left/Right according to direction d, and changes state from s to s', halting if s'==Z. This is 3*4*log2(4*2*log2(4+1)) or about 64 bits of information…

Can you help me understand the log2(4+1) term?

I calculate 3*4*log2(4*2*log2(4+1)) ≈ 51.

I (a layperson) would have thought the calculation would be 3*4*log2(4*2*4) = 60.

Is it perhaps 3*4*log2(4*2*log2(3*3*4-1)) ≈ 64?

Re: BB(3, 4) > Ack(14)

#33

Post by TeMPOraL »

pollyturples wrote: post #26
TeMPOraL wrote: post #22

Earlier quoted context omitted.

Because Discord is a proprietary glorified IRC SaaS; its contents are, by nature, ephemeral and under control of the vendor. I'd expect such links to rot very quickly. Collaborating on Discord is fine. Important results, including citations backing them, should really be published or at least replicated in more durable medium that's less susceptible to link rot, and easier to archive. Today, that's PDFs in paper repo…

MySpace: 16 years (2003–2019) Friendster: 12 years (2002–2013) Google+: 8 years (2011–2019) Vine: 4 years (2013–2017) Orkut: 10 years (2004–2014) Path: 8 years (2010–2018) Yik Yak: 4 years (2013–2017) Meerkat: 2 years (2015–2017) Windows Live Messenger (MSN Messenger): 15 years (1999–2014) AIM (AOL Instant Messenger): 20 years (1997–2017) ICQ: Ongoing (since 1996) but significantly declined after the early 2000s Yaho…

Even with services that lived over a decade, it's not clear whether messages were accessible for all that time. E.g. Google Talk/Meet/Whatever seemingly lost all messages before ~2013. Links to Facebook posts tend to die quickly, as both users and Meta itself seem to constantly play with privacy features. Etc.

Re: BB(3, 4) > Ack(14)

#34

Post by mikewarot »

This all sounds like extreme Code Golf to me.

Here's a tangent to explore:

A BitGrid[1] (my personal hobby horse) only has 4 bits of state per cell, so a 4x4 grid of cells can't count more than 2^64, no matter what. Finding the highest it could count would be interesting. For small grids, the edge connections would dominate the outcome.

[1] https://esolangs.org/wiki/Bitgrid

[2] https://github.com/mikewarot/Bitgrid

Re: BB(3, 4) > Ack(14)

#35

Post by LegionMammal978 »

nickdrozd wrote: post #29

It is sometimes thought that extremely long-running Turing machine programs must be deeply complicated, or "spaghetti code". This new reigning champion program is a counterexample. All things considered, it is relatively simple. There are three states: A, B, C. (States are just like goto targets in C.) State B passes control to A and C, but states A and C don't "know about" each other; they only pass control back to…

There is some debate in the bbchallenge project regarding the current long-running champions: do their properties reflect those of the actual longest-running machine of that size, or are their properties just the easiest to automatically search for and prove things about, as a kind of streetlamp effect? There's no way to know, until the entire search space has been ruled out, either definitely or heuristically. (Every size past BB(5, 2) contains chaotic, pseudorandom machines that are expected to run forever, but can't be proven to do so without big advances in number theory.)

Though I suspect that no long-running machine can be utterly chaotic, at least when you look at the patterns it produces on the tape. To run for a long time, a machine must simulate some sort of higher-level rule: if it were dumping symbols on the tape at random, then it would very soon reach a halting configuration, a cyclical configuration, or some other simplified pattern. Still, one can have long-running machines that do simulate something chaotic on a higher level, spending an inordinate amount of time between each high-level step until it halts.

Re: BB(3, 4) > Ack(14)

#36

Post by Almondsetat »

wizzwizz4 wrote: post #20
Analemma_ wrote: post #11

Earlier quoted context omitted.

I understand the complaint here, but a lot of recent impressive progress in mathematics has been by rapid collaboration + iteration (e.g. the project to improve Zhang's prime gap bound), and it may be the case that different communication tools are not easily fungible with Discord in this regard. You have to go where the people actually are.

But Discord isn't citable . Somebody needs to archive the Discord and make that available through the proper channels (e.g. a website, a book, the Internet Archive).

But papers aren't citable. Somebody needs to archive the paper and make it available through the proper channels (e.g. a website, library, journal, the Internet Archive).

Re: BB(3, 4) > Ack(14)

#37

Post by lisper »

vlovich123 wrote: post #31
lisper wrote: post #15

Earlier quoted context omitted.

Why not? The idea that the only valid way to publish a scientific result is in a (so-called) peer-reviewed journal is a relic from 200 years ago when the scientific community was small enough to fit within the monkeysphere [1]. It is being clung to only because it is profitable for a small group of powerful academics and publishing houses, not because it has any actual merit in terms of the advancement of science. In…

To be fair, the responsibility for the replication crises is much trickier. It’s based on human motivations and poor science: 1. Outright fraud 2. Lack of independent verification of results before building up a body of work resulting in a bunch of garbage. Contributes to making #1 “easy”. 3. Financial pressures to publish or perish contributing to 1 & 2. If peer review didn’t exist you’d still something similar abou…

> Financial pressures to publish or perish

But those only exist because of the current peer-review model. There is a huge non-linearity built in to the publication process that provides disproportionate rewards for conning a small number of people, fewer than half a dozen. That, combined with a presumption of trustworthiness, produces a perverse incentive for attempting such cons because they are very easy to pull off, much easier than actually doing good science.

Re: BB(3, 4) > Ack(14)

#38

Post by vlovich123 »

lisper wrote: post #37
vlovich123 wrote: post #31

Earlier quoted context omitted.

To be fair, the responsibility for the replication crises is much trickier. It’s based on human motivations and poor science: 1. Outright fraud 2. Lack of independent verification of results before building up a body of work resulting in a bunch of garbage. Contributes to making #1 “easy”. 3. Financial pressures to publish or perish contributing to 1 & 2. If peer review didn’t exist you’d still something similar abou…

> Financial pressures to publish or perish But those only exist because of the current peer-review model. There is a huge non-linearity built in to the publication process that provides disproportionate rewards for conning a small number of people, fewer than half a dozen. That, combined with a presumption of trustworthiness, produces a perverse incentive for attempting such cons because they are very easy to pull of…

The rewards come from the grant model which I forgot to mention and also has similar problems to peer review. The stipulation to publish is a secondary effect. If peer review didn’t exist there would still be pressure to show that you somehow convinced the leading experts in the field.

Re: BB(3, 4) > Ack(14)

#39

Post by JadeNB »

lisper wrote: post #28
TeMPOraL wrote: post #22

Earlier quoted context omitted.

Because Discord is a proprietary glorified IRC SaaS; its contents are, by nature, ephemeral and under control of the vendor. I'd expect such links to rot very quickly. Collaborating on Discord is fine. Important results, including citations backing them, should really be published or at least replicated in more durable medium that's less susceptible to link rot, and easier to archive. Today, that's PDFs in paper repo…

I don't see any reason why the original publication venue has to end up being the canonical reference. That's not even true for traditional peer-reviewed papers. Have you ever seen an original physical copy of, say, Einstein's annus mirabilis papers? I haven't. I suspect that these are extremely rare and valuable collectors items and only trained archivists are even allowed to handle them. The right way to reference…

> Have you ever seen an original physical copy of, say, Einstein's annus mirabilis papers? I haven't. I suspect that these are extremely rare and valuable collectors items and only trained archivists are even allowed to handle them.

I'm not sure that they're collector's items, but they're probably not in that many university libraries. For example, the University of Michigan library has a physical copy in its special collection, but my university's considerably smaller library does not. But that's just because of age: this is a 119-year-old paper; were it a little younger, say, about 70 years, it would be in my university's holdings. I think that's a considerably different order of magnitude of its lifetime from a Discord link that I'd be absolutely astounded to see last a decade, and that in practice will probably last much less time than that.

Re: BB(3, 4) > Ack(14)

#40

Post by kevinventullo »

LegionMammal978 wrote: post #35
nickdrozd wrote: post #29

It is sometimes thought that extremely long-running Turing machine programs must be deeply complicated, or "spaghetti code". This new reigning champion program is a counterexample. All things considered, it is relatively simple. There are three states: A, B, C. (States are just like goto targets in C.) State B passes control to A and C, but states A and C don't "know about" each other; they only pass control back to…

There is some debate in the bbchallenge project regarding the current long-running champions: do their properties reflect those of the actual longest-running machine of that size, or are their properties just the easiest to automatically search for and prove things about, as a kind of streetlamp effect? There's no way to know, until the entire search space has been ruled out, either definitely or heuristically. (Ever…

At a high level, wouldn’t you expect Champions to be chaotic in the limit? As in, the halting problem tells us that any increasing sequence of Champions is not computable.
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