A Formula for Economic Calamity一帖經濟蕭條的解藥?
The market crash of 2008 that plunged the world into the economic recession from which it is still reeling had many causes. One of them was mathematics. Financial investment firms had developed such complex ways of investing their clients' money that they came to rely on arcane formulas to judge the risks they were taking on. Yet as we learned so painfully three years ago, those formulas, or models, are only pale reflections of the real world, and sometimes they can be woefully misleading. 2008年股市崩盤使全球陷入經濟蕭條，如今仍餘波盪漾。探究經濟蕭條發生的原因，我們發現數學是其中之一。金融投資公司早就發展出一套複雜的方法來運用客戶的資金，儘管晦澀的公式無法符合現實，金融投資公司卻還是把這些公式做為投資依據。然而，如同我們三年前學到的慘痛教訓，這些公式跟模型只是反映了真實的市場，而且有時候，甚至會誤導大眾。
It was the supposed strength of risk models that gave investment firms the confidence to leverage their bets with massive sums of borrowed money. The models would tell them how risky these bets were and what other investments would offset that risk. Yet the huge uncertainties in the models gave them false confidence. 正是因為風險模式帶給投資公司的假想支持力，讓公司有信心能平衡賭金與巨額借款，雖然這些模型會顯示公司下的賭注風險有多大，以及提供其它能補償該風險的投資，但是隱藏在模型裡的極大變數卻給了公司錯誤的信心。
With so much at stake, in the past three years financial firms have spent tens of millions of dollars in buttressing their models of investment risk in the hope that new ones will preclude anything like the 2008 collapse from happening again. But that may be a vain hope or a case of wishful thinking. Experts in financial models have serious doubts about whether risk models can be improved in any fundamental way. What this means is as obvious as it is scary: banks and investment firms are leading the global economy into a future that is at great risk of repeating the past. 鑒於危急關頭，過去三年來，這些金融投資公司已經砸下數千萬元在支撐投資風險模型上，並希望新模型能避免往事重演。但或許這是徒然的幻想或只是一廂情願，財經專家嚴重懷疑風險模型是否有根本的解決方法，答案明顯且令人害怕：銀行和金融投資公司正使全球經濟陷入處境為難的未來─重蹈覆轍。...