ジャンル: サイエンス・ロジック
英語難易度: ★★☆
オススメ度: ★★☆☆☆
うーん、取っ掛かりは読みやすい本かと思いましたが、やっぱり難しかったですね。 数学の基礎知識が無い状態で英語で読むのは難易度が爆上がりで、完全に着いていけず… 少なくともブルーバックスとかの入門書で、言葉の定義だけでもベースを仕入れておかないと、目が滑る滑る。 もっといろんなジャンルの洋書をたくさん読みたいのになあ。 出生率が僅差で男子の方が多かったことに対して神の摂理であると主張する人々に対する反証のあたりや、P-Valueのとこなんか、とても面白そうなんだけど理解できていません。 対数log と素数のところも、ちょっと大変。針を落とした時のAdditiviy のとこなんか、さっぱり。 完敗でしたー。
(2014年発刊)
メモポイント
とは言え、いくつか印象に残ったフレーズがあったので、備忘メモとして記します。
⚫︎ 有名な生存バイアスのお話。 第二次世界大戦中、敵の攻撃を受けた戦闘機の損傷箇所を分析して最も損傷の多かった部位(主翼と尾翼部分)を装甲補強しようとした分析官がいた。それに対して統計学者Waldは損傷を受けていない箇所を補強するように主張した。つまり研究対象となる損傷のあった戦闘機はその箇所が傷ついても何とか帰還できているのだが、それ以外の箇所が損傷した戦闘機は既に墜落していたからである。
The armor, said Wald, doesn’t go where the bullet holes are. It goes where the bullet holes aren’t: on the engines.
Wald’s insight was simply to ask: where are the missing holes? The ones that would have been all over the engine casing, if the damage had been spread equally all over the plane? Wald was pretty sure he knew. The missing bullet holes were on the missing planes. The reason planes were coming back with fewer hits to the engine is that planes that got hit in the engine weren’t coming back. Whereas the large number of planes returning to base with a thoroughly Swiss-cheesed fuselage is pretty strong evidence that hits to the fuselage can (and therefore should) be tolerated. If you go to the recovery room at the hospital, you’ll see a lot more people with bullet holes in their legs than people with bullet holes in their chests. But that’s not because people don’t get shot in the chest; it’s because the people who get shot in the chest don’t recover.
⚫︎ これぞ、ベルカーブ。 自然界に溢れる正規分布の不思議さよ。神の摂理か。
The bell curve/gendarme’s hat is tall in the middle and very flat near the edges, which is to say that the farther a discrepancy is from zero, the less likely it is to be encountered. And this can be precisely quantified. If you flip N coins, the chance that you’ll end up being off by at most the square root of N from 50% heads is about 95.45%. The square root of 1,000 is about 31; indeed, eighteen of our twenty big thousand-coin trials above, or 90%, were within 31 heads of 500. If I kept playing the game, the fraction of times I ended up somewhere between 469 and 531 heads would get closer and closer to that 95.45% figure.
It feels like something is making it happen. Indeed, de Moivre himself might have felt this way. By many accounts, he viewed the regularities in the behavior of repeated coin flips (or any other experiment subject to chance) as the work of God’s hand itself, which turned the short-term irregularities of coins, dice, and human life into predictable long-term behavior, governed by immutable laws and decipherable formulae.
⚫︎ 大数の法則。 コインの裏表が出る確率。が過去の結果に対してバランスを取ろうとするわけじゃない。
That’s how the Law of Large Numbers works: not by balancing out what’s already happened, but by diluting what’s already happened with new data, until the past is so proportionally negligible that it can safely be forgotten.
⚫︎ パスカル曰く。神が存在する確立を至福となる期待値で表す。存在可能性がいかに少なくても、その至福の度合いが無限大である限り、期待値としてはプラスとなる。 しかし、ヴォルテールはこの概念には重大な欠陥があると反論した。
Pascal doesn’t make any such dodgy numerical move. He doesn’t need to. Because it doesn’t matter whether that number is 5% or something else. One percent of infinite bliss is still infinite bliss, and outweighs whatever finite costs attach to a life of piety. The same goes for 0.1% or 0.000001%. All that matters is that the probability God exists is not zero. Don’t you have to concede that point? That the existence of the Deity is at least possible? If so, then the expected value computation seems unequivocal: it is worth it to believe. The expected value of that choice is not only positive, but infinitely positive.
Pascal’s argument has serious flaws.
パスカルは神の実在性についての証明を求めているのではなかった。 信じる事に価値があるかどうかについて論じたまでである。
Pascal is not offering evidence for God’s existence at all. He is indeed proposing a reason to believe, but the reason has to do with the utility of believing, not the justifiability of believing.
⚫︎ テレンス・タオが、世間一般の天才数学者伝説に違を唱える。 みんな、ラマヌジャンやエルデシュのイメージに引っ張られがち。
The popular image of the lone (and possibly slightly mad) genius—who ignores the literature and other conventional wisdom and manages by some inexplicable inspiration (enhanced, perhaps, with a liberal dash of suffering) to come up with a breathtakingly original solution to a problem that confounded all the experts—is a charming and romantic image, but also a wildly inaccurate one, at least in the world of modern mathematics. We do have spectacular, deep and remarkable results and insights in this subject, of course, but they are the hard-won and cumulative achievement of years, decades, or even centuries of steady work and progress of many good and great mathematicians;
