On ordinal and cardinal numbers...

(Dedicated to Jeff and Joel :) I didn't want to partecipate to the "indexing" thread... but I couldn't resist pointing out my point of view. I promise I'll keep this message as short as possible; I'll send a personal mail with all the reasoning for the following to anyone that really wants to read such a thing. :-) - Ordinal numbers and Cardinal numbers are different things. I see everyone here seems to confuse the two concepts. The set of cardinal (i.e. natural) number is {0, 1, 2, 3, ...} and is defined by the axioms presented by Joel. The set of ordinal numbers has nothing to do with the above, and is {1st, 2nd, 3rd, ...}. Jeff, please notice that the set of ordinal numbers does not contain the symbol 0th or zeroeth. This monster exists for other reasons, which I think I can explain if you want. - The two sets above CAN be put in 1-1 relationship. The common 1-1 relationship between the two is {(0, 1st), (1, 2nd), (2, 3rd), ...} which says that 0 is the first natural number, 1 is the second natural number, and so on. Please notice that REBOL perfectly agrees with this:

>> N: [0 1 2 3 4 5 6 7 8 9 10 11 12] ; and so on... imagine this being infinite

>> first N

>> second N

>> third N

> I didn't want to partecipate to the "indexing" > thread... but I couldn't resist pointing out my point of > view.

Hi, Gabriele, Excellent summary! Gabriele Santilli wrote:

> the set of ordinal numbers can be represented by a subset of > the set of natural numbers (i.e. N - {0}); unfortunately this > seemed to create a certain confusion amongst REBOL users. >

Hello Joel! On 06-Lug-01, you wrote: JN> (Not confusion, IMHO, just a plea that there really are some JN> legitimate roles for the poor orphan.) (I was surely not referring to you about confusion. :) This seems to be 2.3 times slower than pick: ofs-pick: func [series offset] [pick skip series offset 1] The following is only a bit faster, but has a hole in -1 which is way worse that the hole in 0 of pick: ofs-pick: func [series offset] [pick series offset + 1] If you put the code of the first ofs-pick inline, it is only 1.6 times slower (with the + 1 we go down to 1.3); provided the cases in which such code is needed are few, I think the overhead is not that great. Do you think this is worth adding new natives? (I'm really asking!) Regards, Gabriele. -- Gabriele Santilli <[giesse--writeme--com]> - Amigan - REBOL programmer Amiga Group Italia sez. L'Aquila -- http://www.amyresource.it/AGI/

Hi, Gabriele, Gabriele Santilli wrote:

> This seems to be 2.3 times slower than pick: > > ofs-pick: func [series offset] [pick skip series offset 1] >

> If you put the code of the first ofs-pick inline, it is only > 1.6 times slower ... provided the cases in which such code > is needed are few, I think the overhead is not that great. > Do you think this is worth adding new natives? (I'm > really asking!) >

First, let me say that as a programmer I do not like one-based math. I've felt that way for more than 20 years. Second, let me ask what is the first paragraph of this email? It is paragraph 1. That's how most of the world sees it. So, there's the rub. Some of you are searching for mathematical purity because you think REBOL is a programming language. REBOL is a language for communication. There are plenty of programming languages out there. Use APL if you want math purity. Use Scheme if you want functional purity, or Prolog if you want logic purity. In REBOL, first = 1 That's the way it is. Sorry if you do not like that. I did not like it. I resisted it for years. I fully understand the singularity it creates in some types of math. That has not been a problem for *most* of the code I write. If you really feel that you need a native or two to deal with it, send me an email with what you want. (If you post it to the list I probably won't see it.) Be sure to provide a good name, since that takes more time than coding. -Carl The guy responsible.

RE: [REBOL] Re: On ordinal and cardinal numbers... Hi Larry, Joel, interesting solutions :) [larry--ecotope--com] wrote:

> Hi Joel > > Nice variation on the theme! > doubt there are many cases where one is interested in a very large skip on a > small series. Still.. see below.

> >> b: make block! 10000 > == [] > takes one cycle for the iterative version because LOOP falls through (i.e., > the code block does not execute).

On Fri, 6 Jul 2001, Carl Sassenrath wrote:

> In REBOL, first = 1 That's the way it is. Sorry if you do not like > that. I did not like it. I resisted it for years.

Hi all, Oops, my bad. There was a stupid (and critical) typo in the recursive version, in the function body it called the iterative version RING-SKIP instead of itself, RING-SKIP2.

> The second uses recursion: > ring-skip2: func [s [series!] n [integer!]] [ > ] > ]

>> t: now/time/precise loop 100 [ring-skip b 1514] now/time/precise - t

>> t: now/time/precise loop 100 [ring-skip2 b 1514] now/time/precise - t

Since I'm relatively new at programming, can you explain what is meant by recursion and iteration? I just want to learn ;) Paul Tretter

Hi Paul,

>Since I'm relatively new at programming, can you explain what is meant by >recursion and iteration? I just want to learn ;)

Ken Anthony wrote:

> So you would agree that the moment of midnight belongs to the day that > follows as 12am above suggests? > reasonable to vote? I don't think so, but hey I don't want to be different! > Oops! Too late... ;-))

Dave, Thank you for the geographic analogy. I thought it was very good. So your voting for the third scenario, neither. Any of the five scenarios could have there proponents. So how do we come to an agreement? When a day starts is one of those things that is subject to a committee decision which makes it an artificial thing IMHO. Which is to say, it's not something to go to the mat over. However, it is one of those things that barring a political action we can agree on if we choose to. Your saying days are discontinuous at midnight? Doesn't sound good when I put it that way. ;-) Is it only the moment of midnight or any moment that's "too brief to belong to anything?" In other words, would July 9th 12:01am belong to July 9th, but July 9th 12:00am not? Respectfully, Ken.

Paul Tretter wrote:

> Since I'm relatively new at programming, can you explain what is meant by > recursion and iteration? I just want to learn ;) > > Paul Tretter >

BTW, Dave, Did you note that you started your measurement of Acres at zero rather than one? ;-) Just an observation. Ken.

Hi, Paul, Paul Tretter wrote:

> Since I'm relatively new at programming, can you explain what > is meant by recursion and iteration? I just want to learn ;) >

>> nums: [90 1 45 52 42 19]

>> sum-o-nums nums

>> pp [2 [3 5 7 [9]] 11 13]

>> tr-sum nums

>> ti-sum nums

Ken Anthony wrote:

> Dave, > > Thank you for the geographic analogy... >

> Your saying days are discontinuous at midnight? ... > > In other words, would July 9th 12:01am belong to July 9th, > but July 9th 12:00am not? >

> > ... be like having Canada and the US argue over who owns > > the land under the 49th Parallel. > > In total there's 0.00 acres there to worry about just like > > there's 0.00... seconds to worry about at the `moment of > > midnight'. >

Aw Joel, ya took away my thunder. Great job though... From: "Joel Neely" <[joel--neely--fedex--com]>

> 11:58 11:59 12:00 12:01 12:02 > ...: : : : :... > an hour (as a duration, not a boundary) is labeled 00. > -jn-

RE: [REBOL] Re: On ordinal and cardinal numbers... Hi Joel, its the proto for the Zine i hope? Great! -Volker [joel--neely--fedex--com] wrote:

> Hi, Paul, > Paul Tretter wrote: > indirectly. (The standard joke, from the Jargon File, is > recursion n. See recursion. See also tail recursion.

Hi all, is there a chance that Carl gets something more people can agree upon? My idea is to have something like these: 1) SKP function, a zero-based linear skip. The word "linear" means, that it would behave like SKIP, if skipping into the series, which means, that (skp block n) shall produce the same result as (skip block n) for 0<= n <(length? block). For greater offsets it should produce different results. E.g. (skp tail block 1) should produce the same result as (append block 1 result: skip tail block remove back tail block result). Similarly, for negative offsets, if skipping into the block, the result should be the same as the result of SKIP. For lower offsets it should behave differently than SKIP, see below. 2) SKP? function, that will be a counterpart of SKP, i.e. for any block BLOCK the following identity would hold: ((skp? head block) = 0) and for any integer I the following identity would hold: ((skp? skp head block i) = i). 3) a PEK function, that should work (in essence) as follows: pek: function [ [catch] block offset [integer!] /default handler [block!] ] [err] [ if error? err: try [ return first skp :block offset ] [ either default [ return do handler ] [ throw err ] ] ] 4) a POK function, that should work (in essence) as follows: pok: function [ [catch] block offset [integer!] value [any-type!] /default handler [block!] ] [err pos] [ if error? err: try [ pos: skp :block offset return change pos get/any 'value ] [ either default [ return do handler ] [ throw err ] ] ] Regards Ladislav

Hello Joel! On 06-Lug-01, you wrote: JN> 1) The issue of whether "the cases in which such code is JN> needed are few" is highly dependent on the application. Yes... it's just that I didn't need that more that a couple times until now. ;-) JN> 2) Having to repeat JN> pick skip foo glarp 1 JN> throughout the code sounds like a great opportunity for JN> typos and other such bugs to creep in. Of course! But you'll need to optimize only that 10%... :) JN> Thanks again for your thought -ful and -provoking comments! The same is valid for me too! Regards, Gabriele. -- Gabriele Santilli <[giesse--writeme--com]> - Amigan - REBOL programmer Amiga Group Italia sez. L'Aquila -- http://www.amyresource.it/AGI/

Hi, Ladislav, and all, Ladislav Mecir wrote:

> is there a chance that Carl gets something more people can > agree upon? My idea is to have something like these: >

> ----- Original Message ----- > From: Carl Sassenrath <[carl--rebol--com]> >

> > > > Be sure to provide a good name, since that takes more time > > than coding. > >

Hi, 1) I don't know, whether the ATZ and SKIPZ function should differ from each other? 2) If I use one of Joel's naming conventions, I would prefer, that: a) for any block (same? block atz block 0) yields true, it should never yield and error instead b) INDEXZ? shall never yield an error c) for any block and any integer - even for integers greater than the length of the block (equal? i indexz? atz head block i) shall yield TRUE d) PICKZ should behave as follows: pickz: function [ [catch] block offset [integer!] /default handler [block!] ] [err] [ if error? err: try [ return first atz :block offset ] [ either default [ return do handler ] [ throw err ] ] ] d) the POKEZ function, that should work (in essence) as follows: pokez: function [ [catch] block offset [integer!] value [any-type!] /default handler [block!] ] [err pos] [ if error? err: try [ pos: atz :block offset return change pos get/any 'value ] [ either default [ return do handler ] [ throw err ] ] ] 3) The LENGTHZ?, function could be implemented as follows: lengthz?: func [ block ] [ (indexz? tail block) - (indexz? block) ] Regards Ladislav

Jeff Kreis wrote:

> > I think that having 0-based analogs of the following words > > would be *quite* sufficient: INDEX? SKIP AT PICK POKE > > LENGTH? >

> foo/0 ? >

> How does SKIP change? >

> I think that having 0-based analogs of the following words > would be *quite* sufficient: INDEX? SKIP AT PICK POKE

RE: [REBOL] Re: On ordinal and cardinal numbers... reading Joel he really complains two things: a) stuff is not zero-base b) Joel would be pretty like modulo-arithmetik. i suggest a ring! make ring! 5 could be .. 0 1 2 3 4 5 6 7 8 9 .. or .. -4 -3 -2 -1 0 1 2 3 4 5 .. that means with modulo we could say zeroth: :last while usual c-programming works: while[index < length? block][..] will never touch last! since joel found explaining modulo with a clock works great, how about context clockwise[pick: .. skip: .. ..] ticktack: does bind-to clockwise[ forever[ probe first tick tick: next tick ] ] ? a more complete (complex?) version could really have ring! datatype, which could be a special reference. a: [1 2 3 4] b: make ring! a skip b 24 would work a: make ring! 4 would give us a clock-type counter with no buffer-memory. maybe even a: make clock! [24 60 60 decimal!] there are some uses.. :) Drawback: Joels char-counter would not throw exception on overflow. modulo with subrange just for 0? hm, or 7 as Joel noted. [lmecir--mbox--vol--cz] wrote:

> Hi all, > > is there a chance that Carl gets something more people can agree upon? My > idea is to have something like these: >

Carl / Jeff / Anybody at RT inc. Why not simply have system/options/index-base: Which would be set to 1 if in REBOL 1 = first. But could be set to any number ordinal or cardinal thus allowing whatever base number indexing suits you. I know this would require 'pick etc to be redefined but so perhaps this is less likely to introduced than say a well named base-indexing function(s). Cheers, Mark Dickson In a message dated Fri, 6 Jul 2001 8:27:58 PM Eastern Daylight Time, Carl Sassenrath <[carl--rebol--com]> writes: << First, let me say that as a programmer I do not like one-based math. I've felt that way for more than 20 years. Second, let me ask what is the first paragraph of this email? It is paragraph 1. That's how most of the world sees it. So, there's the rub. Some of you are searching for mathematical purity because you think REBOL is a programming language. REBOL is a language for communication. There are plenty of programming languages out there. Use APL if you want math purity. Use Scheme if you want functional purity, or Prolog if you want logic purity. In REBOL, first = 1 That's the way it is. Sorry if you do not like that. I did not like it. I resisted it for years. I fully understand the singularity it creates in some types of math. That has not been a problem for *most* of the code I write. If you really feel that you need a native or two to deal with it, send me an email with what you want. (If you post it to the list I probably won't see it.) Be sure to provide a good name, since that takes more time than coding. -Carl The guy responsible.

> > LENGTH? > > > just as there are ten numbers in each of the sets {1 > ... 10} and {0 ... 9}

> I assumed that the other option that had been raised > (having some sort of global flag that would switch all > existing words between 1- and 0-origin behavior) was not > acceptable/feasible.

Jeff Kreis wrote:

> Okay, but the important caveat for everyone to remember is > that with 1-based indexing, LENGTH? blk corresponds to the > range of positions that can be picked from, changed, etc. > However, with zero-based indexing, LENGTH? blk refers to 1+ > the range of values pickable, changable. >

> So, for example, the following code behaves > differently depending on the base: > > x: [1 2 3] > change at x length? x 0 > > 1-based == [1 2 0] > 0-based == [1 2 3 0] >

> This leads to a change of REPEAT as part of a very common > REBOL idiom: > > repeat i length? block [ print [i pick block i ] ] > > Works for 1-based, but without changing both REPEAT and > LENGTH? will break for 0-based (skips the zeroth element and > prints NONE on the final iteration). >

Hello all, A guiding principle for me is simplicity. Mark's suggestion of a switch is simple but introduces mode which IMHO should almost always be avoided. Of the suggestions put forth by Joel, Ryan and others I would with respect say the following: I emphatically do not like the idea of adding new words that are variations on existing words but the /zero refinement seems most in the spirit of Rebol. Having said that, and even though I think it is a huge mistake for the reasons I will outline (not reiterating the technical points which have been very well represented in this discussion but a touch more on philosophy) I would think it best to remain with the 1-based indexing until such time that Carl changes his mind on the matter. I do a lot of maintenance coding. As a result, although I produce a lot of new code I amazingly find myself reducing the amount of code in a project on any given day. Hardly ever have I seen code, whether I produced it or someone else, that with a little more thought could be made less complicated, cleaner, more elegant, easier to understand, efficient, or... well, you get the idea. There are times when you stop and look at what you've done and you see the very rightness of it. It's a thrill and nobody can take it away from you. Then there's the satifaction of working with some great programmers. When some ask me to review their code I might note that they know there's something not quite right. On those occasions where I can offer a simpler solution I may be giving something that will be carried to others. This isn't always something you can prove or disprove (especially when the very rules of proof are not agreed upon.) But you can sense the rightness. There's a lot of Hype surrounding Rebol which is not unusual when promoting a language, but I want to think about the phrase I've heard that Rebol can take us to the stars. This implies that the language is somewhere on the path that began with stone knives. It also implies that Rebol will not someday be realized to be a dead end as so many others before it have been. For better or worse the design decisions made today guide the very thoughts of the people that will use and produce Rebol code in the future. So is there a rightness about the Rebol language? Obviously so, or there would not be the fuel to ignite the hype. However, there is a dichotomy. What is real and what is artificial? I am of the camp that believes that rigorous proof (as found in mathmatics) is real. I believe that how people feel about doing something because they've always done it that way is artificial. Today, we do not do what we've always done. If we look back at examples, they are embarrassing and silly. Look back 100 to 200 years and they are even more so. Go back a 1000 and things that every child knows today would be incomprehensible to the most educated person. We know the difference between ordinal and cardinal numbers. That has not always been the case. This is a maturing understanding. Most of the numbers we deal with are cardinal and what people think of when we talk about numbers. The ordinal numbers first, second and so on came about as a mapping of position in a series to the quantity to that point. Offsets obviously start from zero (here is always zero away from here - argue against that point at the risk of being revealed...) However, there is no rule anywhere that says what number applies to the position in a series. It is only convention (and simplicity of algorithms) that makes us start with a low positive integer (zero or one) and proceed to assign the next higher integer to the next position. So that leaves us in the uncomfortable position that if we choose zero as the first integer assigned to a position, we've just equated (first = zero.) It's very understandable that some people would be repelled by that. Give it time, in 100 (or 1000) years it will seem natural to you. I have no more to say at this time on this subject. It's been interesting, Ken.

> The above fragment of code would still work. Anyone who > knew (or had learned) enough to write the 0-origin versions > could also write it as > > repeat i length? block [print [i - 1 pickz block i - 1]] > > Unless, of course, you're joining with me to extend the > list of suggested new words to include REPEATZ

> .. so that one could write it as > > repeatz i length? block [print [i pickz block i]]

> The only rule is "Be consistent." Don't mix origins unless > you know what you're doing.

> On second thought, replicating all the series actions is > sounding much more preferable. . . .

Joel Neely wrote:

> This really is familiar to anyone who's used 0-origin. The > 60 minutes in an hour range from 0 to 59. The 24 hours in > a standard 24-hour clock range from 0 to 23.

Hi Dave, Good thing we're talking about clocks and not ordinals because I've already had my last word on that subject for now ;-)) ----- Original Message ----- From: "David Ness" <[DNess--Home--Com]>

> Joel Neely wrote: > > This really is familiar to anyone who's used 0-origin. The > used [6,...,29] for a `standard day'. again for `communications' > reasons.

Hello, again, Jeff, Jeff Kreis wrote:

> > I assumed that the other option that had been raised > > (having some sort of global flag that would switch all > code twice for each base that your REBOL might be running > under.

> On second thought, replicating all the series actions is > sounding much more preferable... >

Hi, Ken, Admirable (and thought-provoking) summary! Thanks! Ken Anthony wrote:

> I believe that how people feel about doing something because > they've always done it that way is artificial. Today, we do > every child knows today would be incomprehensible to the > most educated person.

> It's very understandable that some people would be repelled > by that. Give it time, in 100 (or 1000) years it will seem > natural to you. >

Jeff Kreis wrote:

> > .. so that one could write it as > > > > repeatz i length? block [print [i pickz block i]] > > .. prints NONE on the last iteration I guess. >

> You sure you don't want LENGTHZ? too? >

Quoting Carl,

> If you really feel that you need a native or two to deal with it, send > me an email with what you want. (If you post it to the list I probably > won't see it.) > Be sure to provide a good name, since that takes more time than coding.

[agem--crosswinds--net] wrote:

> reading Joel he really complains two things: >

> i suggest a ring! >

>> nursery-rhyme: make ring [] >> nursery-rhyme/data ["eenie" "meenie" "mienie" "moe"]

>> loop 5 [prin [nursery-rhyme/next " "]] print ""

>> loop 5 [prin [nursery-rhyme/prev " "]] print ""

>> nursery-rhyme/curr

>> nursery-rhyme/at?

>> nursery-rhyme/skip 7

>> nursery-rhyme/at 38

>> nursery-rhyme/at?

>> nursery-rhyme/skip -5

> ;-) Volker > --zero is the highest number >

RE: [REBOL] Re: On ordinal and cardinal numbers... [joel--neely--fedex--com] wrote:

> [agem--crosswinds--net] wrote: > > > > reading Joel he really complains two things: > > > > Me??? Complain??? 8-O >

> > > > i suggest a ring! > LENGTH? _DATA cached instead of being re-evaluated all over > the place.

>> loop 15[random "Hello Jeff"]

> > > > ;-) Volker > > --zero is the highest number > > > > ROFL!!! >

Hello Jeff! On 07-Lug-01, you wrote: JK> Okay, but the important caveat for everyone to remember is JK> that with 1-based indexing, LENGTH? blk corresponds to the [...] Ahem... Jeff... what should then LENGTHZ? [] return? Puzzled, ;-) Gabriele. -- Gabriele Santilli <[giesse--writeme--com]> - Amigan - REBOL programmer Amiga Group Italia sez. L'Aquila -- http://www.amyresource.it/AGI/

> Ahem... Jeff... what should then LENGTHZ? [] return? > > Puzzled, ;-)

Hi Joel, Volker Here is a different approach to circular addressing of a REBOL series. The heart of the matter is to be able to skip forward or backward by an arbitray number of steps. Here are two functions which serve that purpose. Rather than copying the the list being operated on, they create and return a series reference with the current index pointing to the desired position. No new series are created, just references. The original series is untouched. Neither of the functions does ANY numeric indexing into the original series. If you want to operate on a copy of the original series just do s: ring-skip n copy b which creates a new series and returns the desired reference. The first function uses iteratation: ring-skip: func [s [series!] n [integer!]] [ either positive? n [ loop n [if tail? s: next s [s: head s]] ][ loop abs n [s: back either head? s [tail s][s]] ] s ] The second uses recursion: ring-skip2: func [s [series!] n [integer!]] [ if n = 0 [return s] either positive? n [ if tail? s: next s [s: head s] ring-skip s n - 1 ][ s: back either head? s [tail s][s] ring-skip s n + 1 ] ] Examples:

>> b: "abcde"

>> ring-skip b 24

>> ring-skip b -1

>> s: ring-skip b -1

>> ring-skip s -1

>> ring-skip b -2

>> b: [1 2 3 4 5]

>> ring-skip2 b -1

>> ring-skip2 b -2

>> ring-skip2 b 344

Hi, Larry, Nice variation on the theme! Larry Palmiter wrote:

> Here is a different approach to circular addressing of a REBOL > series. The heart of the matter is to be able to skip forward > or backward by an arbitrary number of steps. Here are two > functions which serve that purpose... > Neither of the functions does ANY numeric indexing into the > original series... >

> The first function uses iteratation: > ring-skip: func [s [series!] n [integer!]] [ > ] > ]

>> b: "abcde" == "abcde" >> ring-skip b 5 == "abcde" >> c: tail b == "" >> ring-skip c 0 == "" >> ring-skip c 5 == "e" >> ring-skip c -1 == "e"

>> ring-skip2 b 344

Hi Joel

> Nice variation on the theme!

> Ah, you sneaky fellow! ;-)

> Absent tail-recursion elimination, I'd always use the iterative > version myself (but that's just a personal opinion, and certainly > not something I'd force on anyone else).

>> b: make block! 10000

>> repeat j 10000 [append b j]

>> t: now/time/precise ring-skip b 10001 now/time/precise - t

>> t: now/time/precise ring-skip2 b 10001 now/time/precise - t

> 1) There is a peculiar "singularity" that occurs if the series > argument is positioned at the tail, but not at the head. > >> ring-skip c -1 == "e" > This could be guarded for at the beginning of either function.

>> r: make ring [] >> r/data tail [1 2 3]

> 3) The last example you gave > > >> ring-skip2 b 344 > == [5] > > shows that it's possible to burn lots of cycles with a large > enough second argument.

> Combining all of these ideas, we could have the following at the > beginning of either the iterative or recursive version: > > if tail? s [s: head s] > if any [0 = length? s 0 = n: n // length? s] [return s] > > after which the function will never make needless "round trips".

Larry Palmiter wrote:

> > Absent tail-recursion elimination, I'd always use the > > iterative version myself (but that's just a personal > expression evaluation, which there is not in this case > because the args s and b carry the state...

> The REBOL internal stack for delayed operations is about > 1500 deep, so the example shows that it is does not come > into play. >

> I can illustrate this in more detail if you are interested. >

>> count-tr 10 ;== 10 >> count-tr 100 ;== 100 >> count-tr 1000 ;== 1000 >> count-tr 10000

>> count-tr 10 ;== 10 >> count-tr 100 ;== 100 >> count-tr 1000 ;== 1000 >> count-tr 10000

>> count-tr 10 ;== 10 >> count-tr 100 ;== 100 >> count-tr 1000 ;== 1000 >> count-tr 10000

> BTW ring is also not too happy with series at the tail. > > >> r: make ring [] > >> r/data tail [1 2 3] > ** Math Error: Attempt to divide by zero > ** Where: skip > ** Near: pick _data _pos: _pos - >

> I think I would prefer to just return an empty series for both > the case of an actually empty series (i.e., empty? head s returns > true) which is already handled ... >

> ... and for the case where the current index is at the tail. > This signals a problem to the user in an unobtrusive way. >