[phpBB Debug] PHP Warning: in file [ROOT]/phpbb/session.php on line 590: sizeof(): Parameter must be an array or an object that implements Countable
[phpBB Debug] PHP Warning: in file [ROOT]/phpbb/session.php on line 646: sizeof(): Parameter must be an array or an object that implements Countable
[phpBB Debug] PHP Warning: in file [ROOT]/phpbb/session.php on line 1068: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3839)
[phpBB Debug] PHP Warning: in file [ROOT]/phpbb/session.php on line 1068: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3839)
[phpBB Debug] PHP Warning: in file [ROOT]/phpbb/session.php on line 1068: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3839)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 5129: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3839)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 5129: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3839)
[phpBB Debug] PHP Warning: in file [ROOT]/includes/functions.php on line 5129: Cannot modify header information - headers already sent by (output started at [ROOT]/includes/functions.php:3839)
Extremely large numbers. 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 - Toki Pona Forums

Extremely large numbers. 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Language learning: How to speak Toki Pona, translation problems, advice, memory aids, tools and methods to learn Toki Pona and other languages faster
Lingva lernado: Kiel paroli Tokiponon, tradukproblemoj, konsiloj, memoraj helpiloj, iloj kaj metodoj por pli rapide lerni Tokiponon kaj aliajn lingvojn
janU
Posts: 14
Joined: Sat Mar 03, 2018 4:44 pm
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Extremely large numbers. 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Postby janU » Sun Mar 04, 2018 12:00 am

0 ala
1 wan
2 tu
3 tu wan
4 tu tu
5 luka
6 luka wan
7 luka tu
8 luka tu wan
9 luka tu tu
10 wan ala, or wan ali
11 wan wan, or wan ali wan
12 wan tu, or wan ali tu
13 wan tu wan, or wan ali pino
14 wan tu tu, or wan ali tama
15 wan luka, or wan ali ka
16 wan luka wan, or wan ali luka en wan
17 wan luka tu, or wan ali luka en tu
18 wan luka tu wan, or wan ali luka en tu wan
19 wan luka tu tu, or wan ali luka en tu tu
20 tu ala, or tu sin wan ali
21 tu en wan, or tu sin wan ali wan
22 tu en tu, or tu sin wan ali tu
100 wan ala ala, or tu ali
110 wan wan ala, or tu ali wan ala, or wan kipisi wan sin tu ali
111 wan wan wan, or tu ali wan wan,


Extremely large numbers:

100000 10^5 luka ali

100001 10^5 + 1 luka ali wan

500000 5 X 10^5 luka sin luka ali

500001 5.00001 x 10^5 luka sin luka ali wan

1000000 1 X 10^6 luka wan ali

1000001 1 X 10^6 + 1 luka wan ali wan

5000000 5 X 10^6 luka sin luka wan ali

5000001 luka sin luka wan ali wan

602252000000000000000000 (avagadro's number) luka wan kipisi ala tu en tu luka en tu sin tu en tu wan ali

10000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 10^100 (googol, ten duotrigintillion) tu ali ali

1000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000
0000000000000000000000000000000000000000000000000000000000000000000000
000000000000000000000000 10^303 tu wan ala tu wan ali

... or alternatively: wan ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala ala


googolplex wan ala ala ali ali

googolplex^googolplex wan ala ala ali ali ali

googolplex^googolplex and one wan ala ala ali ali ali wan

☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐ wan ala ala mute ali wan ala

☐☐☐☐☐☐☐☐☐☐☐☐☐☐☐ wan ala ala mute ali wan ala ala ali ali ali (a lot)

janKipo
Posts: 3064
Joined: Fri Oct 09, 2009 2:20 pm
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Re: Extremely large numbers. 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Postby janKipo » Sun Mar 04, 2018 8:32 am

Some sketch of the system would help here, examples only point the way.
In general, no system far from the standard Western (American) is going to succeed. I can,t tell how close this is.

janU
Posts: 14
Joined: Sat Mar 03, 2018 4:44 pm
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Re: Extremely large numbers. 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Postby janU » Sun Mar 04, 2018 11:20 am

So basically, one way to read the number is to just read out the digits.

For 0 through 9, I used:
0 ala
1 wan
2 tu
3 tu wan
4 tu tu
5 luka
6 luka wan
7 luka tu
8 luka tu wan
9 luka tu tu

This means that 11 would be wan wan, and 19 would be wan luka tu tu.
This becomes a problem a few times once you get into the twenties and fifties,

21 would be tu wan
22 would be tu tu

51 would be luka wan
52 would be luka tu
53 would be luka tu wan
54 would be luka tu tu

To avoid confusion, I added in the word "en", to make 21 tu en wan, and so on. If there is some other way to say numbers 1-9 it would make the whole thing a lot easier.

Next, to say larger numbers without having to read the whole thing out, I used the same pattern from scientific notation.
For example,

1 * 10^5 is one hundred thousand. So this would be luka ali. I used ali to mean 10 to the power of what ever number comes before ali.

5 * 10^5 is five hundered thousand. Or luka sin luka ali I used sin to mean multiplication.

Now there are two more ways to expand further, the first is by simply adding the number(s) on to the end, so one hundred thousand and one would be luka ali wan.

Then there is the way that is used in scientific notation.

1.1 * 10^6 means one million one hundred thousand, so I used kipisi to mean the decimal point. wan kipisi wan sin luka wan ali

I know made it sound way too complicated here, but it really is not much more difficult to learn than any languages number system, and it follows a pattern.

janMato
Posts: 1545
Joined: Wed Dec 02, 2009 12:21 pm
Location: Takoma Park, MD
Contact:

Re: Extremely large numbers. 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Postby janMato » Sun Mar 04, 2018 4:46 pm

Yeah, but can you express:

bodhisattva (बोधिसत्व or बोधिसत्त) —10^37218383881977644441306597687849648128
ref: https://en.wikipedia.org/wiki/History_of_large_numbers

since a number is a specific thing as specific as a jan Mato (there can only be one!), why not use proper modifiers, e.g.

nanpa Posisapa

mi wile e moku pi ma Mesiko kepeken suli pi nanpa Posisapa.

janKipo
Posts: 3064
Joined: Fri Oct 09, 2009 2:20 pm
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Re: Extremely large numbers. 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Postby janKipo » Sun Mar 04, 2018 8:59 pm

How does your desire for Mexican food use a very large number? For what? (Wherdja get that one for bodhisattvas? Really long gone!)

TNTErick
Posts: 6
Joined: Wed Jun 26, 2019 9:10 pm
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Re: Extremely large numbers. 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Postby TNTErick » Mon Jul 01, 2019 3:36 am

My proposals:
1. Count with the preexisting words with doubledigits. That means we tear down a decimal digit into two, five and anything else. The first digit indicates if there is five, ie: ala or luka. The second is 0~4, ie.: ala, wan, tu, tu wan, tutu.

So here's how we count:
ala
wan
tu
tu wan
tu tu
luka (ala)
luka wan
luka tu
luka tu wan
luka tu tu
wan ala ala.

1234: wan ala-tu ala-tu-wan ala-tu-tu.
3.14159: tu-wan lili ala-wan ala-tu-tu ala-wan luka-ala luka-tu-tu.

2. another proposal is not using any words at all, as we have precisely 10 consonants in toki pona.
The series 'kstnpmjlw represents the meaning 0~9, and the vowels are listed as aeiou.
0 e'a
1 eka
2 esa
3 eta
4 ena
5 epa
6 ema
7 eja
8 ela
9 ewa
10ke'a.

1234 kositena.
3.14159 takanekipowu.

janKipo
Posts: 3064
Joined: Fri Oct 09, 2009 2:20 pm
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Re: Extremely large numbers. 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Postby janKipo » Mon Jul 01, 2019 4:59 pm

Well, of course I like the abacus number system (biquinary) but not the mix with thee additive digits. I would rather have two more digits. (‘si' and ‘po’, say). The binary code for digits is a simplification in some ways but makes for even longer numbers. And dropping the initial ‘ala’ sets the whole scheme off right at the start. So I prefer my version of the same general idea. I also like order-of-magnitude words to deal with long complex cases. All that aside, this is one of the better suggestions.

The second system is in some ways even better, except that it can’t be done. The second syllable of a word cannot begin with the null consonant. (basic rule). To be sure, the null consonant is occasionally a glottal stop between words, but not consistently and never within a word. On the other hand, except when reading out strings of digits (phone numbers, say) zero is almost never required, because the place is specified for each digit, without needing to rn through all the zeros. But the rest of the words here are generally impossible by the other rules of phonology: there cannot be any of ‘ji’, ‘wo’, ‘wu’ or ’ti’ and many of the remaining syllable are already assigned standard tp words, which we should try to avoid mucking with if possible. At best, the system could word with ‘a’ and ‘e’, but that is not much help.
Why are the consonants not in alphabetic order (or some other reasonably obvious order)? Adding memory issues to. the rest of the system seems just self-defeating.
This system takes up to 100,000 very tidily (previous problems aside) but does not suggest any way to extend from there on. (The obvious way to do it is just to start over again, with an ‘a’ digit come just before a ‘u’ one telling us that ths addition has taken place. The similar treatment of decimals is brilliant.)
What is the ‘e’ before the digits for? Just to warn that these are numbers?
I really like the compactness and clarity of this system and wish I could think of a dodge around the phonological issue, but in the dozen years or so since something like this first came up, no one has managed a workable suggestion (even noting that the forbidden syllables only need be absent in certain positions doesn’t help, since as digits, they have to occur in those positions, too.)
Here is a germ, however. Treat each digit as a. CVCV pattern with the same C (the digit) and the Vs being ‘a’ and ‘e’, in a fixed code to cover the cases through E4. This unfortunately doubles the length of a number. But we actually only need to do this for four numbers, ‘ji, wo, wu, ti’. The trick now is to get a CVCV pattern, especially a VV pattern, that does not occur. For a single iteration of the system, ‘ae’ satisfies the condition. But, of course, no pattern will work for an iterated system (above E5) unless we mark the beginning of iterations and that turns out to be hard, but probably not insurmountable.

jan Lopata
Posts: 14
Joined: Wed Feb 26, 2020 4:42 am
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Re: Extremely large numbers. 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Postby jan Lopata » Fri Feb 28, 2020 7:42 am

toki!

mi sin tawa toki pona la...

...so take this with the appropriate dose of salt. That said, here's my analysis and resulting approach:

Given (?) that 0-9 are covered, it seems to me that we need to consider:
* Everyday counting numbers up to 100, or perhaps 1,000.
* Accounting numbers into the millions, billions, trillions, etc.
* Scientific numbers.
* Decimals
* Negatives
* Fractions
* Powers
* Imaginary numbers?

Standard decimal notation breaks numbers up into digits and thousand-groups. That's also how we express ordinary numbers in words - hundreds-tens-and-ones thousand-group by thousand-group until we get to millions, thousands and then ones. We gain efficiency by simply omitting unfilled places (i.e. we say twelve thousand and four, omitting zero hundred and zero tens).

If we follow that pattern, we first need a solution for numbers up to 999 and a way of expressing thousand groups. We have a word for group already: kulupu. We also have a word for hundred, albeit overloaded, in ali. If we overload mute to mean ten, we can express numbers up to 10^10 like this:

42: nanpa mute tu tu en tu
259: nanpa ali tu (en) mute luka en luka tu tu
12,004: nanpa mute (wan) en tu pi kulupu (wan) en tu tu
123,456,789: nanpa ali (wan) (en) mute tu en tu wan pi kulupu tu en ali tu tu (en) mute luka en luka wan pi kulupu (wan) en ali luka tu (en) mute luka tu wan en luka tu tu

That last one is a bit of mouthful, but then so is one hundred and twenty-three million, four hundred and fifty-six thousand, seven hundred and eighty-nine.

In 259 the 'en' is optional as in this context 'mute' following hundreds is unambiguous.
Similarly the 'wan's in 12,004 are optional because we can infer unit values for the placeholders.
In that last example, the first 'en' is technically still optional, but highly recommended if omitting the 'wan' as it could otherwise be read colloquially as twenty-hundred (which technically wouldn't be allowed if this approach was adopted generally, but then neither are two-digit hundreds exactly best practice in toki Inli and how often have you heard that construction? We should allow for such colloquialism and expect 'en' after unit 'ali'.

For negative numbers we could use anpa: nanpa anpa mute tu en wan = -21. 'ala' could work too, but following 'nanpa' it suggests not-a-number and following the digits we have the potential for scope confusion - does 'nanpa mute tu en wan ala' = -21 or 19? Hence my preference for up-front anpa - an under-number.

For decimals, I like the 'lili' approach. 'insa' might be even better, I think. Then normal protocol is just to list digits:
nanpa tu wan lili/insa wan en tu tu en wan en luka en luka tu tu en tu en luka wan en luka ... = 3.14159265...
compare
Three point one four one five nine two six five...

For fractions we could use 'supa' or 'linja': nanpa tu supa/linja luka = 2/5. c.f. 'Two over five' or 'two bar five'.

For powers we could use 'sewi' or 'wawa': nanpa tu wan (pi?) sewi/wawa luka = 3^5. c.f 'Three to the power (of) five' or 'three to the fifth (power)'

Putting all that together, Avogadro's number would be:
'nanpa luka wan insa ala en tu en tu en wan en tu tu en ala en tu tu en luka tu tu pi mute wawa pi mute tu en tu wan'
compare:
six point zero two two one four zero nine times ten to the twenty-third.

That leaves imaginary numbers. There my instinct is to go for 'sona' to express i: nanpa luka wan en sona anpa luka tu = 6-7i

ona li sona pi nanpa mute mute pi mi
ona li pona ala pona tawa sina ali?

mi tawa!

janKipo
Posts: 3064
Joined: Fri Oct 09, 2009 2:20 pm
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Re: Extremely large numbers. 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Postby janKipo » Fri Feb 28, 2020 2:34 pm

This goes into the file, better than many, worse than some: too long, occasionally too complex. Continues to try and mix the tp system with a real number syste, with usually muddling results. Nothing strikingly new, except ‘anpa’, which isn’t oo wonderful.

jan Lopata
Posts: 14
Joined: Wed Feb 26, 2020 4:42 am
[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Re: Extremely large numbers. 1000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000

Postby jan Lopata » Fri Feb 28, 2020 6:15 pm

jan Kipo o, toki!

ona li pona tawa mi e ni: sina toki tawa mi.

It has occurred to me that 'lon ala' might be better for imaginary numbers - except that then you have ambiguity between 'lon (ala ...)' and '(lon ala) ... '. Perhaps 'en (nanpa) lon ala pi ...' ?

As I said, I'm new to toki pona, so the only proposals I've seen really are the ones in this thread. Is there a repository of other ideas somewhere? I by no means think my proposal is unique or perfect. I'd be surprised if something similar hadn't been proposed before. I do think it's better than the others in this thread though (with all due respect to their creators).

I'm curious as to why you think any of these constructions are too long? I deliberately gave English equivalents to demonstrate that, while they are shorter in most cases due to the unitary digit names, they are similarly structured and none-the-less long when written out in words. The aim, as I see it, is not to get to numeral-like efficiency. For that it makes more sense for toki pona to adopt the Arabic numeral system like the rest of the world. My aim is to get to a similar level of efficiency as English (or other natlang) numbers written or spoken out in words. Perhaps we're shooting at different targets?

Your comment that it 'mixes the tp system with a real number system' makes no sense to me. It is a real number system. Fundamentally there is only one. Perhaps you meant counting system? But then, I still don't understand the sense in which 'the tp system' would be in any sense 'not real' or opposed to real? Reading between the lines, I don't think this approach is any more mixed with any other language's way of thinking than the English system is with the German, or French or most other natlangs. The aim of toki pona, as I understand it, is not to be deliberately contrary. Where a problem has been solved in other languages and the solution works in toki pona, why not adopt it to the extent that it makes sense in toki pona?

One might argue for using a base other than ten, I suppose, but as I said, I think we're (almost?) universally culturally attuned to base ten, so to me it makes sense to take that as a constraint. Even if we accept base 5 for example as culturally more toki pona, we still need magnitude tags and the rest; we just drop 'mute' and use 'luka' as the base. Binary and ternary could get away with fewer tags perhaps, but they blow up too fast to be realistically viable, I think. Ternary does have some appeal given that 'ala', 'wan' and 'tu' are the only pure number words we are given to work with. It would be quite a mind-shift to start thinking in threes, nines and twenty-sevens rather than tens, hundreds and thousands, but as a native system it could work.

Can you explain what you find "muddling"? I may have missed something (it's very possible) but I thought I had considered all the possible internal ambiguities and got the word orders right. We might need a more explicit counting system tag than simply 'nanpa' (e.g. 'nanpa pona' cf. 'sitelen pona') to distinguish from ordinals and less precise scalars (e.g. 'nanpa mute' for 'many numbers' or 'the many-th'), but if there are other issues please point them out.

I don't think the syllable approach is viable, as it effectively adds extra words to the toki pona lexicon. It seems to me that that would be cheating. jan Sonja has defined the tool-set and quite deliberately not included unique names for each decimal digit. I take that as a hard constraint (although I do have some sympathy for the 'si, po' proposal so that we would only have two-word compound digits instead of threes). Given (and perhaps it's not the case) that the multi-word names for digits are already widely accepted, toki pona will inevitably have number expressions that are longer than languages with unique unitary names for each digit if we aim to express numbers in base ten (or indeed in base two, three or five which will naturally blow up faster anyway).

Given that we're aiming for a base ten system, a way of expressing tens seems necessary. We can't use prefixes or suffixes (-teen, -ty) as that too would be breaking the rules of toki pona. Adding a word might be valid in this case, but it's not necessary if we simply overload (or perhaps contextually define a precise limit to) 'mute', which already has that meaning, inter alia. 'kulupu' is also a candidate, but it's longer, and thus better suited to a higher-order grouping.

Simply stringing together 'luka', 'wan', 'tu' and 'ala' doesn't work due to ambiguity of place value. The 'en' solution I've adopted is more-or-less the same as that suggested by jan U and is, I think, as efficient as we can expect for strings of digits. Using 'mute', 'ali' and 'kulupu' as magnitude markers, allows us to skip places if they're empty, rather than uttering a string of 'ala's to indicate place. 'One million and one' is undoubtedly easier to parse than 'one zero zero zero zero zero one'. Other groupings (e.g. hundreds, which would obviate the need for 'kulupu') and other markers ('sewi'?) could be used, but thousands is (again almost?) universally conventional, so why buck the norm? Using 'kulupu wan', 'kulupu tu' etc. is cleaner than English with its unique terms for each of the first several thousand groups (thousand, million, billion, trillion...).

I don't think using scientific notation for what I've described as accounting numbers makes sense. We don't describe salaries in terms of ten to the power five or six for example in English - accounting numbers are large, but still in a sense 'human-scale' or 'everyday'. Scientific notation li pona ala for that use case. Also jan U's approach to this is, I think, problematic. If I read the post correctly, 'luka wan ali' the example for one million, is also the suggested term for 'sixty'. An unambiguous term for the exponent is therefore needed, just as we use 'power' in English. Then to distinguish scientific notation from a simple exponent we need to be explicit about the base, hence 'pi mute wawa pi'.

Similarly the proposals for fractions, negatives and imaginary numbers are really no more complex than English. Alternative tags could be used of course, but I don't think they can be made much more efficient.

Again, I'm not so arrogant as to think my approach is entirely novel, or perfect, or that it can't be improved upon, especially after learning the language for just a week! I'm also aware that there's possibly a level of ambiguity around joining this pattern of numbers into sentences. Compared to the other options in this thread though, I do think it's better, and I don't think it suffers badly when compared to English or any other natlang, to the extent that I know their spoken number systems (which, to be fair, is limited even for the limited cases I am somewhat familiar with).

I regret that this post probably comes off as a bit prickly and defensive. I guess there is probably an element of defensiveness to it, but my aim is to be analytical about the problem at hand, which I find interesting. I am genuinely interested to see any systems (or elements of systems) that you think are better and to understand why.

mi tawa!


[phpBB Debug] PHP Warning: in file [ROOT]/vendor/twig/twig/lib/Twig/Extension/Core.php on line 1107: count(): Parameter must be an array or an object that implements Countable

Return to “kama sona toki”

Who is online

Users browsing this forum: Bing [Bot] and 2 guests