这是一次非常有趣的谈话,so I thought I'd write here about a few things that came up.
Mathematics likes to think of itself as a very certainty-based business.如果你“用数学证明了某件事”,then it's supposed to just be true.没有IFS或BUTS。Complete certainty.
当然,在实践中,人类所写的证据有漏洞。Somewhere between the imprecision of ordinary language,and the difficulty of really thinking through every possible eventuality,几乎不可避免的是,任何发表的长期证据都是不完美的。即使有一大群人来检查它,并不是每个错误都会被发现。
I suspect that what was imagined at that time was that by finding the smallest universal machines one would discover some "spark of computation"—some critical ingredient in the rules necessary to make universal computation possible.(At the time,可能还有“生命的火花”或者“智慧的火花”可以在系统中找到。)
I remember that when I first heard about universality in the Game of Life in the early 1970s,我认为这并不特别重要;这似乎只是一个聪明的黑客。
但几十年后,建立了整个框架一种新的科学,I have a quite different view.继续阅读
And so as part of commemorating the fifth anniversary of一种新的科学今年5月14日,我们announceda25000美元奖金用于确定该图灵机是否实际上是通用的。
I had no idea how long it would take before the prize was won.一个月?A year?A decade?A century?Perhaps the question was even formally undecidable (say from the usual axioms of mathematics).
But today I am thrilled to be able to announce that after only five months the prize is won—and we have answer: the Turing machine是事实上是普遍的!
物理是我的第一个领域(事实上,我成为a card-carrying physicist when I was a teenager).当它发生时,the talk I just gave (for the欧洲随机几何网络)是我一个老朋友组织的物理合作者.
Physicists often like to think that they're dealing with the most fundamental kinds of questions in science.But actually,what I realized back in 1981 or so is that there's a whole layer underneath.
There's not just our own physical universe to think about,但整个宇宙都有可能存在。
如果要做理论科学,最好是处理一些明确的规则。但问题是:什么规则?
现在我们有一个很好的方法来参数化可能的规则:尽可能的计算机程序。And I've built a wholescienceout of studying the universe of possible programs–and have discovered that even very simple ones can generate all sorts of rich and complex behavior.
好,that's turned out to be relevant in modeling all sorts of systems in the physical and biological and social sciences,在发现有趣的技术方面,等等。
But here's my big hobby question: what about our physical universe?它能按照这些简单的规则操作吗?
Bridges have a long history.早些时候,只有少数类型似乎已经被使用。But with the arrival of iron structures in the 1800s there was a kind of "Cambrian explosion"不同类型的桁架桥:
But what is the very best bridge structure,从稳健性的角度来说?There's a huge universe of possibilities.但到目前为止,only a tiny corner has been explored–and that mostly in the 1800s.
我们的2007NKS暑期学校大约两周前开始的,and one of my roles there was to show a little of howNKS完成了。
过去,在任何一种生活方式下展示这都是非常不现实的。But with computer experiments,and especially with数学软件,that's changed.And now it's actually possible to make real discoveries in real time in front of live audiences.
我做了几十次“现场实验”现在(here是2005年的一份报告)。My scheme is as follows.在实况实验前几小时到几分钟,我提出了一个我很确定以前没有研究过的话题。然后我要确保在我真正面对现场观众之前,不要去想它。
然后,一旦实验开始,我发现东西的时间有限。Just by running数学软件.最好是在观众的帮助下。偶尔也能从网上的参考资料中得到一些帮助。
But then,不知何故,things almost always manage to come together.我们设法发现了一些东西。这通常很有趣。(根据我在第一所暑期学校做的现场实验,现在仍有论文发表,回到2003)
I usually make my first live experiment at each Summer School be a piece of "pure NKS": an abstract investigation of some simple program out in the 金宝博188投注computational universe.
今天的CPU有数百万个组件。But the Principle of 金宝博188投注Computational Equivalence implies that all kinds of vastly simpler systems should also support universal computation.
好,也许我太感情用事了。Or too steeped in history.或者太幼稚的品牌。但对我来说别无选择。这归功于过去20年来我们所建立的所有基础,我们仍然称之为我们今天所建立的。”数学软件."
Realistically,我想十年后数学软件1.0 just to realize what a powerful thing we had in数学软件.
我们一直在谈论”symbolic programming”,它如何让我们统一许多不同的想法和领域。But sometime around the mid-1990s it began to dawn on us just what an amazing thing symbolic programming actually is.
我们开始认为,如果人们真的用符号编程尽一切所能的话,在计算上可能达到一个全新的水平。
好,that was an intellectual challenge we couldn't resist.大约十年前,we embarked on seeing just what might be possible. 继续阅读