Raw Notes on Hardy’s Apology

August 25, 2018

Preface. Reading is a form of communication. It follows that one who loves reading loves socializing. Just that this particular mode of communication goes one-way only and not real-time. One ridiculously good aspect deriving from the one-way property is that it doesn’t matter how great the author was, the obscure reader entitles himself to an advantageous post, where he freely points his finger or makes satirical comments without consequences. The great body of my notes are of this worthless type. Haha! Usually I strive to write my book report coherently, focusing on the most important subject that got me thinking. But this booklet, albeit small, contains many a profound idea that branches out and is hard to merge. So this time, I go all casual and post the discrete set of raw notes \footnote{edited and expanded} in the following. There will be additional comments on one plot line regarding my conversion though.


Before Section 10 it was mostly me enduring personal attacks, if I remember correctly. There are remarks here and there that I could relate to. But all that ambition/immortality talk is alienating.

10 A painting may embody an ‘idea’, but the idea is usually commonplace and unimportant.

Never noticed this. It rings true. Just look at all the nudes, landscape, still life, mythological/historical paintings. The painterly effect that wraps the idea is usually more important than the idea itself in our appreciation of the artwork. In contrast, a piece of mathematical work has no paintbrush or words to dress itself up, only the idea in and is itself.

Beauty is the first test: there is no permanent place in the world for ugly mathematics.

This line is vehemently opposed by the twitter sphere – where I got the idea to have a look at this booklet in the first place. But one doesn’t have to take it as an offense as if Hardy meant that “ugly” mathematics do not contribute or have no place. Just not permanent place. In the long run, inevitably people will find more elegant proofs for the same thing. So those get to go into textbooks, and the “ugly” is replaced and hence loses its temporary place.

14 I do not know what is the highest degree of accuracy ever useful to an engineer—we shall be very generous if we say ten significant figures.

Thanks for your generosity. MATLAB default eps is 2.2204e-16. Not far.

As regards Pythagoras’s, it is obvious that irrationals are uninteresting to an engineer, since he is concerned only with approximations, and all approximations are rational.

Well, to this I have no objection. Control engineers love rational functions! It’s not to say there aren’t infinite-dimensionals in the control theory literature. Actually, they extensively study delay. But if an average engineer can get away with a rational approximation, why not.

At this point, I had yet to be exposed to his shocking belief. So I asked, isn’t mathematics a model of, hence an approximation to the physical reality? Which one is the ultimate? I would say the physical. In the physical world there is no infinity, an apparent contradiction with the existence of infinity in mathematics. So an engineer approximates true mathematical solutions, but is it further from the physical reality than the true mathematical solution is?

15 isolated curiosities… These are odd facts… nothing in them which appeals to a mathematician.

The two examples taken from Mathematical Recreations are to illustrate superficial theorems. They look a lot like that Hardy-Ramanujan number. I wonder if he would get upset at being attributed a trivial theorem to. But we may comfort him in saying, this attribution is more to the memory of you guys’ peculiar deathbed conversation than to the actual mathematical merit of the discovery itself. Even without resorting to this, he deemed his numerous early papers insignificant anyway. So he had enough unimportant results to not notice the additional one.

16 “It is the large generalization, limited by a happy particularity, which is the fruitful conception.”

A quote from Whitehead. Typically poetic, full of ambiguity, love, and passion. I could see his thoughts dancing. Delightful! read more …


Coyote Is Going Along

April 11, 2018

A new federal agency, dedicated to the destruction of predators… aimed to kill every predator of every species in a region… [Dan Flores, Coyote America, 2016]

Extermination, destruction, eradication, extirpation… these words blatantly went into state policy titles. For someone growing up with population ecology common sense, it is beyond ridiculous to see, not too long ago into the past, a governmental agency trying to eliminate the entire “predator” category from the ecological hierarchy.

Forest service, national park service, fish and wildlife service… these names today automatically project green and friendly mental images, referring to probably the most harmless governmental departments. Who would have thought they had such a dark history during the late 19th and early 20th centuries?1

These near past events serve as a warning sign that is still beckoning to us: how zeal wedded with ignorance is surely to produce madness Ahab style. One would think after the Endangered Species Act, wild animals in general were to cast behind them the darkest era of their history, and to ride the turning tides triumphantly into the future. Wrong. If my eyes are not deceiving me, the red wolf recovery program is still on at this very moment – the one that actually led up to the Act itself. One defines a specific animal to be a species, then finds it to be endangered. In the name of purity, some other canids like coyote, whom red wolves naturally have genetic exchange with, simply lost their right to exist. Layman’s questions aside2, the chilling methodology aside3, one never ceases to be exasperated by blind human convictions.

Also noteworthy is the social significance the particular scientific advance in ecology rapidly brought about, which today I have so naturally taken for granted. Back then the coyote research was done in a highly politicized environment, entangled in a web of industrial interests – in this case those of the ranchers and hunters – much like what climate scientists have to face today, as was pointed out in the book. I wonder how climatology will look like in the eyes of the near future. Does it cast a similar curve of acceptance rate that quickly converges to a common wisdom steady state? Has it morphed into a new wave of public movement?

Despite all the atrocities revealed by the book, its overall style is actually quite witty, and also dotted with suspension. The author’s personal encounters with coyotes were most beautifully written. The poignant reflection of the detachment shown by that killer child, awakens my own deep remorse for similar degrees of cruelty. The wooden call episode let me relive the moment of mixed mutual feelings – those of curiosity and fear that seem to epitomize the entire subject of man and nature.

If the Old Man Coyote, “a whirlwind biophysical force with a large capacity for taking sensuous pleasure in life”, who embraces “no religious tradition beyond being alive” but “sacred existence”, and “teaches delight in being alive in a world of wondrous possibilities”, sounds too much of artificial romanticism than a sober observation, then there is this; if among all the tales and accounts there is a single story to remember, then it is this:

A coyote trot along a trail with a sprig of sagebrush in its mouth. At repeated intervals it had tossed the sprig joyously into the air, caught it, then trotted on.4

1 Compared to that, the “desert” of pine trees created by the JNF looks too innocent to be called even a mistake.

2 A species being a species by definition does not breed with another species. If coyotes interbreed with red wolves, how can they be two different species and one of them endangered species?

3 The technique “using morphology measurements and recorded howl profiles” instantly alarms me by a frightening association with the Nazi studies of differentiating human races for malicious purposes. What the author related to was Crania Americana, which at first I presumed was less harmful as I had never heard of it before. But it seems to be recognized as an important work for scientific racism.

4 Turning over the last page, don’t I also want to swing back my head and howl to the million stars!


The Kafka Museum Visit

November 16, 2016

As I was reading about the route Kafka used to take everyday to school accompanied by the family chef, suddenly the strains of HaTikvah was heard. It may not be much of a surprise since Kafka was known to have wanted to make aliya, the strange thing is that barely passing 8 bars, the music deviated from what I know so well. It then became apparent that this is not the Israeli national anthem, or a remix of it.

Recalling that the music of HaTikvah was adapted from some pretty pedestrian folk tune, I went to the Wikipedia page in hope of finding some confirmation that the presently playing piece was also a derivative of the same source. There, the name Smetana struck me familiar. Wasn’t that splendid hall where I listened to that underwhelming concert inside the municipal house called Smetana Hall? – It’s probably not the Prague Symphony Orchestra FOK’s fault, but my insisting in going to the concert after a whole day’s hike to blame. Now as the second movement of Smetana’s symphonic poem set, Vltava, greets me again, my hypothesis is validated. For some time, I enjoyed the discovery of the hidden links between these initially unrelated dots scattered all over my trip. But it seems to be a well known fact domestically.

Now as I think of it, isn’t it most suitable to choose this piece of music for that short film of Kafka’s Prague? On one hand, the HaTikvah-like melody alludes to his Zion heart, on the other, a Czech rendition reflects his cultural identity. By the way, this is not the only occasion where the museum designers show genius choice of music. Firstly I was met with some non-trivial ambient music in the introductory part. And close to the end in the literary analysis section, some spooky metal sounds are heard accompanying Kafka’s hand injury drawings made for his insurance company, creating a creepy absurd space. I would say the museum is quite experimental sonically and visually.

They also offered scholarly and deep interpretations for Kafka’s work, which were difficult to chew. To be honest, when I read Metamorphosis, I hardly saw anything beyond the storyline. But I’ll have plenty of chances to read between the lines now that I bought a set of three books compiling Kafka’s short stories from the museum shop – almost as impressive as the Autechre EP box that I got at the live show!

On a somewhat remotely related note, the nude with arms raised (and armpit hair exposed) by Pablo Picasso actually reminded me of George Samsa’s sister at the end of Metamorphosis, stretching herself to receive the infinite generosity from the sunshine as much as she could; her parents suddenly realize that here is a full fledged young woman ready for the future. This is not to say that I finally start to whole-heartedly appreciate that drawing. Although admittedly, Catherine’s explanation helped a lot towards that end. She says naivism tries to unlearn the academic training and focuses on the essence of what one wants to convey through childish paint strokes. In this particular drawing, I indeed starts to see the innocence, youthfulness and all the signs indicating the fresh positive, instead of singling out the grotesque squiggles supposedly representing her hair and hands. We also agreed that his intentional neglect of making her face pretty and leaving the natural underarm as is were an explicit challenge to typical modern viewers such as us, who are knowingly but irresistibly conditioned to popular media dictation of what is considered to be feminine beauty.


From Forrester’s World Dynamics

September 18, 2016

The first half of the book is roughly a documentation of the model being simulated. I didn’t complain because of an early warning that conventional birth control will prove to have little effect on improving the final undesirable equilibrium compared to that without, a method I had imagined as a silver bullet to today’s major world problems.

In the result discussion chapter, I found out I wasn’t entirely wrong about my favorite method. The usual birth control programs do not set a constant birth rate, but which is subject to influences from other variables such as material standard of living, pollutions etc, manifested by their corresponding multipliers. That’s why the simulations faithfully report that with a transient rise of standard of living following a birth control policy, the incentives for increasing birth rate becomes even stronger. This result forces me to clarify myself that what I actually mean by birth control is to set a rigid birth rate independent of other system variables, which might require something like the womb system in Ergo Proxy on the implementation side, as my totalitarian nature quietly creeps up1.

Another thing I shall bear in mind is that there are other modes of disasters that cannot be suppressed by reduced population alone. In fact, the author views capital investment and pollution as primary leverage points and birth control the secondary tool – not the other way around as is my belief. I never really understand what capital investment means as I never comprehended money and its movement. Let’s say that it’s directly associated with industrialization. Then based on the assumptions of this model, the simulation result indicates that fewer people does not lead to hampered capital investment. Consequently pollution comes out to be the destroying force. Therefore birth control even in my stricter definition is not the silver bullet. A comprehensive program exercising self-restraint on multiple fronts including not only reproduction but also economic development, emerge as an attractive idea.

Recall that this is the state-of-the-art in 1970, it amazes me to see that people today are still spouting the ugly idea that technology is the savior of mankind. And I’m more ashamed of myself than amazed at them that I didn’t see the fallacy until the book clearly spells it out. In contrast to this indifference that new insights were received with, ancient ideas such as self-discipline have never been adopted by the mainstream either. I see traces of environmentalism in Greek mythology already, as the Greeks were temporarily confined in a small world centered around Greece so the transition from golden to bronze ages mostly as a result of human multiplication were perceived; certainly there were a couple of great Chinese thinkers who ages ago saw through the vanity of the rushing and blindly excited expansionists, tech-enthusiasts, growthists2… Oh yeah, there certainly is a possibility that we can escape from the confinement of the earth and continue to grow in some other earth-like planets. But it’s exactly those who insist in letting expansion go unchecked and willingly accept the consequential rising violence and danger of war as fated – some of whom by the way I personally know (!) – that are diminishing this possibility of space exploration by diverting huge funds to the defense causes. read more …


Gone On the Road

July 7, 2016

Finished On the Road by Kerouac*. Throughout the majority part of the book, I wasn’t particularly interested. Rundown shacks, ragged lives and beaten souls everywhere. My skin turns greasy automatically when imagining walking in their shoes. On top of that was a not-so-friendly language wielded only by college dropouts – I’m not referring to the tech nerds – a bizarre consequence of street talk coming from a mind drenched in years of literary activities. On the other hand, I didn’t get particularly bored either because, as it was my book on the road as well, I only turned a few pages while waiting at a bus station.

But towards the end, somewhere before the Mexico trip, I had become fascinated by Dean’s madness. He “digs” whatever he sees with attention of monstrous intensity like laser beams; every trifle that is going on around him warrants his equal devotion; only he could see and let the godsent revelation flood through him and eventually reach us like a torrent. The outward manifestations are constantly sweaty face, bulbed eyes, throbbing veins, rubbing of his belly and a finely selected vocabulary of “Yass, yass! Wow! Man! Phew!” ranging from howling to moaning. It would have seemed pretty dumb in the beginning, but now that his contagious spirit makes sense to me… Yes, only Dean can “dig” the way beyond what the word itself intends to mean.

Just as I thought by now I was fairly used to the gross ways of life they are leading, the tropical bug T-shirt episode pushed it to a newer level. But the Mexico trip really had me hooked – it’s really not at all about those drug and sex thingies, but the thoughts that emerged from a fierce spring that never runs dry: how they make of the landscape and various people they met – something that never happens to me when I am traveling**. At the height of it, I was informed that the awful Dean left the fever stricken Sal. And shortly after was their last meeting. Friends that had done so many crazy things together could just part forever like that without a warning. In contrast to the frantic rushing, the final few words sound markedly quiet, poignant as though they were written down after days of meditation. And then, profound sadness engulfed me.

* James Zabiela was the one who introduced this book to me.
** Because after all, I am of an entirely different breed