Category Archives: Thoughts

Hardship creates greatness

Life is so very complicated, is it not? Well of course the answer is it is and it isn’t… Sometimes the answer one is looking for isn’t anything like the true answer, and most of the time the real answer points to something much more subtle… much more profound:

I hope you like the picture! It was a bit of an accident… But I think it’s beautiful. At the time, I called it “Eternal Rose” probably because I was obsessed with eternity at the time ;) It isn’t really an eternal rose… In fact it isn’t really a rose. It’s square, and wound into the red clouds around it. But I couldn’t exactly have called it “Square picture that looks like a rose in a sea of red cloud that reminded me once of eternity”… now could I?

On that note, let’s start with a rose. Let us animate that rose. It has the will to choose. Now of course it grows naturally from good things… water, sunlight. It needs them to survive. And if something really bad were to happen to that rose, it would be crushed and die. It is really a very fragile thing. However, if something painful, if something annoying, if something hard were to befall the rose, what would become of it?

Now, remember, our rose can choose. It can choose to shrivel and die under hardship. It can choose to give up. But with a little fear, but with more than a little bravery, our rose can not only exist like the normal plants beside it, but it can thrive. It can claw it’s way through the dead log that has fallen on top of it, and stretch its way into the light.

Would it not then be a greater rose?

Culture and Change

α: What exactly does one mean by culture?

β: By culture, one is referring to the form of a people. Just like a jug is a specific form of glass, so is culture a specific arrangement of people. Therefore this is clearly a very wide-ranging term and covers everything from language to specificities. An example of the latter extreme would be the fact that such a town in Wales has a wonky signpost near it’s oldest train station. Of course, when one refers to culture, one is generally referring more to the former type of culture (language and customs) but for the sake of coherence and clarity, it seems to make more sense to define culture more widely.

α: It would seem that culturess are all equally meritorious, since any evidence to the contrary would, by definition come from a person who had grown up in one culture, and is therefore tainted by that lens. Even a person who grew up between two cultures would really be the product of his own pidgin culture, and would therefore not be able to see beyond that.

β: The assertion that a person cannot truly abstract one’s-self from what one is accustomed goes against the very meaning of being human. Whether or not any particular abstract generalisation can be contested, but there is no reason why any given person cannot take an objectively valid position by abstracting one’s own experience.
Further, I would argue that all cultures are not equally meritorious, but rather that some cultures are, in fact, better than other cultures.

α: Are you asserting that some cultures have moral superiority over other cultures?

β: No, definitely not! Morality is really another matter entirely. The goodness of badness of a person isn’t so much dependant on how one’s prosperity or natural talent, but rather what they do with it, and the free choices they make with the cup they have been given.

α: So is culture then measured by prosperity?

β: Well, yes, but I would prefer to expand on that, as I think the answer is more subtle.
Culture is, like a good jug, best measured by how it fulfils it’s purpose. Now a jug’s primary purpose is to hold water and pour it without issue. It also has secondary aims like looking beautiful and clearly showing how much water remains, but these should be satisfied with the fullness of the first aim.
However, Culture’s final purpose is to spiritually enrich it’s people. This means to draw them to the transcendentals of Truth, Goodness and Beauty; consequently: God. And in the same way as the jug, culture has secondary objectives like Economic and Social goals, but also in the same way, these should flow from the fullness of the first aim.

α: How can a culture tend towards, or gain such value?

β: If a culture was truly perfect, I think it would be quite clear. However, one possible indicator would be how long the culture has existed without major change. A truly old culture would have been touched by all the wise hands that perfected her over the ages.

α: So then what makes a culture bad?

β: Well, a culture that has experienced great change would have the detailed perfection that time brings it. Of course, this observation does not bode well on our modern world, where culture seems to be changing at a much faster (and possibly more destructive) rate than it ever was before. So whether or not these great changes are good, this of course means that it cannot have been enriched by the process I have been describing.

α: Ah, but what does the reader reckon?

On Subtlety and Complexity

What’s the difference between explaining something in a more complex way as opposed to a more subtle way? After all, both explanations will inevitably be longer, and more complicated. Isn’t subtlety therefore just as complex as complexity?

The example I’m going to use is that of of faith, hope and charity. At first, they all seem fairly similar. Having faith in someone can also be seen as having a strong hope in them; In this wikipedia article, faith is seen as being aligned with goodness (which is otherwise thought of as charity); what’s worse: a modern rendition of charity is the word “love” (which sounds more like trust/hope).

I think perhaps a way of disentangling this confusion is with three very fundamental concepts: Truth, beauty and goodness. Now if you think about it, these are actually really fundamental concepts. They run through everything we know, and anything can be described in terms of them, like a cup:

For example, in front of me, I have truly have a green cup, that because of it’s elegant (beautiful) design is good for holding water (or coffee, in the case of the picture). Something is truly described as what it really is; Something is beautiful when its form follows its function; And something is good when that function is fulfilled.

Now if we back up a bit and look at these two trios side-by side, things start to get interesting. Faith clearly maps with truth, independently of either hope or charity (something simply to be known). The next obvious connection is that of Charity and goodness (“it is in giving that we receive”). And last, but not least, we can see that Hope is left with beauty. This is the analogy that I find most fascinating. Does beauty make one hopeful? Is one who has not hope blind to beauty? I think perhaps simply pondering those questions will do the comparison more justice.

The point is, the ideas of faith hope and charity are clearly different, but they can be quite hard to clearly wrap one’s head round. However, one doesn’t need to break them down (complicate them) in order to understand them more, but instead try to squash and stretch them a bit, until the “shape” of the idea is just right.

The definition of complex is consisting of multiple parts. Subtlety, in contrast is any distinction made that does not break a thing down. As you can see, the distinction between Faith, Hope and Charity is therefore subtle (extremely so), but ironically, trying to explain how it is has proved to be somewhat complex!

Euler Project: Challenge #3

Ok, so a while back (I don’t remember exactly when). I tried to get into the Euler Project. What it is is a series of difficult mathematical (programming) challenges. When I first tried it, I solved the first two challenges, and couldn’t progress much further.

Anyway, I was recently on a bit of a programming spree, and gave challenge #3 another shot. Instead of coding my solution in Javascript, I have now switched to Python (a newer, lower level, yet more elegant, programming language). This post is an explanation of how I solved it, so if you don’t want the solution spoiled, go and figure it out yourself (then please come back here to tell me how inefficient mine is).

The exact problem, as stated on the website, is:

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

As you can see, it is quite a nicely stated problem since it gives you a number you can test out before trying to compute the highest prime of the monster 12-digit number. Initially, I went about coding my solution in a fairly obvious way (pseudo code)

loop bigNumber:

  if number%bigNumber == 0 (i.e. if there is no remainder, then it’s a factor) then
   loop through factor to check if it has factors. if it has none, then it’s prime!

Now, this logic worked fine for the relatively small 13195 (in 0.011 seconds, I might add) but when I threw the huge number at it, the program just hung (sat there, showing no result). After examining it in more detail, I found that it was simply going to take too many life times to check all the factors.

However, I knew there must be a solution that didn’t involve a supercomputer, since I know a guy who solved this problem. Back to the drawing board…

My basic problem was one of efficiency. So in my second version of the program, I changed the program in two different ways. I manually multiplied the number (also known as chunking, a mistake in hindsight, since the computational equivalent of long-division is, in fact, faster). The second change I made was a bit more complicated, but I personally found it fascinating. So, please humour me for a moment with this explanation:

Let’s find out if 13 is a prime number.
So we’ll check the potential factors one by one:

  1. 2 times 2 is 4
  2. 2 times 3 is 6
  3. 2 times 4 is 8
  4. 2 times 5 is 10
  5. 2 times 6 is 12
  6. 2 times 7 is 14 (greater than 13, so we’ll jump to the next number)
  7. 3 times 2 is 6
  8. 3 times 3 is 9
  9. 3 times 4 is 12
  10. 3 times 5 is 14 (greater than 13, so we’ll jump to the next number)
  11. 4 times 2 is 8
  12. 4 times 3 is 12
  13. 4 times 4 is 16 (greater than 13, so we’ll jump to the next number)
  14. 5 times 2 is 10
  15. 5 times 3 is 15 (greater than 13, so we’ll jump to the next number)
  16. 6 times 2 is 12
  17. 6 times 3 is 16 (greater than 13, so we’ll jump to the next number)
  18. 7 times 2 is 14 (greater than 13, so we’ll jump to the next number)
  19. 8 times 2 is 16 (greater than 13, so we’ll jump to the next number)
  20. 9 times 2 is 18 (greater than 13, so we’ll jump to the next number)
  21. 10 times 2 is 20 (greater than 13, so we’ll jump to the next number)
  22. 11 times 2 is 22 (greater than 13, so we’ll jump to the next number)
  23. 12 times 2 is 24 (greater than 13, so we’ll jump to the next number)

Now, since none of the numbers we’ve checked multiplied neatly into 13, we can conclude that 13 is a prime number. However, did you notice that after 4, every single potential factor we checked had already been checked in reverse?

For example, 5 times two (line 14) had already been checked (as 2×5) on line 4!

By simply ending the sequence when we start to see the same number again, we half the number of steps needed. If we do this for a bigger number, like 23, we cut it down by 6 sevenths! So as you can imagine,

There were a few other efficiencies I implemented (like not chunking, for example) and there might even be more still (like looking into how the program does long division, and trying to make it easier relative to the problem). But as it turns out, this simple change knocked the program run time from multiple lifetimes to about 3 seconds! So yes, I did find the highest prime number that factors into 600851475143 and I hope that you can too!

I really enjoyed this challenge, and can see myself attempting more in the future (even reattempting the ones I’ve done in order to do them better). I also see myself switching to a lower level language (like C), so that I can program an even faster and more efficient solution (even though it will make doing so more complex). Perhaps this project can be my doorway into really understanding the truly complex mathematics which has hitherto evaded me.

More Toki Pona

One day I’ll get sick of this constructed language once and for all, but for the moment, there still seem to be some things that bring me back to Toki Pona. I had a more thorough read of the book today, and frustratingly read through the “Toki Pona Proverbs section”, which managed to concentrate all the things that I didn’t like about the language…

And don’t get me wrong, the sound of the words doesn’t bother me that much. My current solution (though technically breaking the phonetic rules) are simply to change the stress patterns of the language. So instead of saying TOki POna LI TOki POna, one says toKI poNA li toKI poNA, which personally I find sounds a lot better.

No what bothers me is the shallow philosophy that seems to sit in the background of The Toki Pona Book: Truth is Relative, Simplicity is Goodness, non-essentials are bad (literally “Ike). So instead of rehashing all these frustrations, i decided to write a Toki Pona “sequence” (it doesn’t display enough structure to be called a poem, but it might just resemble one):

pona li pona ala nanpa ali
 wan ijo li pona ala e ali
 wan li pona e oko
 mute ijo li ike e ala ali
 oko li oko e mute pona
 mute ali li ike ala
 mute li pona
 wan wan li ike ala
 wan li pona
 pona li pona ala
 ike li ike ala

And no, don’t worry. This time, I wont be daft enough to leave you without a translation, even though it is rough, and won’t carry the same tone as the (extremely ambiguous) original:

simple is not good always
 one thing does not make good all
 one does good to the eye
 many things do not bad to all
 the eye sees a lot good
 not many is all bad
 many is good
 one one is all bad
 one is good
 simple is not good
 non-essential is not bad

If you concluded that that made very little sense, don’t worry. You’re probably right!

The Meaning of Friendship/Affection: Half-baked thoughts

I like to think about the nature of friendship. A while back, I read CS Lewis’s “The four loves” and for a long time used it as a lens to understanding relationships. Though now I have dropped the first and prefer Fulton Sheen’s three types of love, I do like the idea that some types of relationships are fundementally different to others, though not necessarily better or worse.

I’ve recently been watching a TV series. In this series, the main character is an evil manipulative murderer. However, every morning, he goes to have breakfast at this cafe of a fellow who knows nothing about him. However, he treats the cook well, pays generously, and they have a nice chat every once in a while. In one episode, the cook found a newspaper attacking the protagonist, and without looking into whether it was true or not (those reliable newspaper;), he burned it. He burned it because he was the protagonist’s friend, and he really cared for the protagonist, independent of how evil the protagonist was.

And then the thought hit me: The cook is a friend to the protagonist, even if he’s not necessarily a friend back. This implies that a friendship can be one-sided.

The first of the four

As stated in the top of this article, CS Lewis asserted four types of love, but Fulton Sheen only three. For a while (when I first wrote this post) I rejected the first of CS Lewis’s: Affection (a simple love or non-animate things or even some people). However, I have recently gone back on this idea, and this is why:

Every morning I walk to work at a ceirtain time. As I walk, I always pass a bearded guy on a bycicle going in the opposite direction and a blonde-haired lady with headphones (who I think is a librarian). Later on, I consistently see a family with three children also going the other way. Now, I never talk to these people, and I probably never will, but they nevertheless have begun to form a part of my daily routine. I have began to get used to walking past them. I think perhaps this simple feeling is what CS Lewis was expressing with the first of his four “loves”.

So… what do you think is the true meaning of friendship or affection?

En Français

Bonjour. Ça, c’est ma premier post sur le blog completement en français. Pardonnez-moi pour les plusiers des problemmes que j’ai, mais je pense que c’est important ecrire en Français pour continuer apprendre.

Pour sûr, j’aime des langues (si on peut voir de ma poste avant de cette poste), mais il y a plusieurs de manneirs on peut apprendre une langue. Pour example, actualemment, je utilise le site s’appelle: Lingq. J’aime ça beaucoup, et je pas c’est le meilleur pour moi dans cette moment. En le passé, j’ai utilise Duolingo, Memrise, et plusieurs des autres choises.

Alors, c’est tout pour mainetenent. Ciao! ;)

A Language Review

The nice thing about delaring one’s self a linguaphile is that one can be sure that one is, even if one doesn’t earn the lofty title of “polyglot”. In light of this, and as amateur(ist?) as it may be, I would therefore like to Review a constructed Language (conglang): Toki Pona. As I’m not very experienced with this reviewing business, I’ll try to keep it short.

Toki Pona is (famously) an extremely light (~120 word) language with minimal grammar. It’s made up of very few (very easy to pronounce letters) and can be learned relatively quickly. I would like to start by saying that I don’t speak/understand Toki Pona that well at all. However, I have studied the language a little, so I do have a little to say.

What I do like about the Language:

  • I like the lightness of the language. 120 words adjective/adverb/noun/verb interchangability. A regular/simple grammar. All these factors are very appealling.
  • More so than that, I thoroughly enjoy the constructive nature of concepts in Toki Pona: Is a house a “place for life”, or “four flatnesses that give light”? The creativity that this leads to is brilliant, and it has a lot of poetic potential.
  • I like the subtractive colour system in Toki Pona. It’s very elegant, and mathematical (In fact, it feels much more Lojban than the rest of the language).

What I don’t like:

  • The language sounds childish – I think the sound of a language means a lot. Natural languages seem to find their own personalities and ruts when developing, therefore obtaining their own coherent feel. However, Conlangs have to try and nail that “feel” straight away, so don’t generally turn out as well. Now why I don’t think Toki Pona suffer’s from Esperanto’s problem (trying to be so broad it’s consistently wierd), the sounds it does make, to me, sound rather childish. And I find this rather offputting. N.B. There is actually a solution to this, in that one could swap out the words, or play with the consonant flexibility that Toki Pona offers (e.g. swapping out all the “T”‘s for “D”‘s). I simply haven’t tried it.
  • My #1 gripe with the language: The word “Pona” means both “good” and “simple” – This desroys the language for me (in it’s original form anyway). The authors obsession with K.I.S.S. kills sublety (e.g. it’s equation of the animal text with “mu”) and goes so far to assert that the ultimate form of goodness is simple. I find this philosophically lazy and blind to the beauty of complexity. This is my single biggest gripe with the language, and for me, it seriously hurts what Toki Pona has going for it.

Yes, I could swap the words for better sounding words, and I could pick and choose definitions, but then it wouldn’t be Toki Pona (or atleast the one ye’re all familiar with)… would it?