The apparently imminent discovery of the Higgs boson by scientists at CERN will have at least one quirky side effect that appears to have gone entirely unremarked until the appearance of this blog post — it threatens to inflict fatal collateral damage to the brilliant, eccentric and infuriating Omega Point Theory proposed by the physicist Frank Tipler.
Tipler, who is not a crackpot, once published a book called The Physics of Immortality, purporting, on the basis of orthodox physics plus some plausible auxiliary assumptions, to establish the existence of an omnipotent, omniscient, omnipresent and altruistic “being” who will one day resurrect everyone who has ever lived to eternal life.
The first step toward that startling conclusion is the assumption that our descendants will not allow all life to come to an end. This in turn will require them to control the evolution of the Universe so that it doesn’t collapse in anything that human beings perceive as a finite amount of time; Tipler argues that they’ll quite plausibly have the technology to do that. But all this future tinkering with the shape of the Universe has consequences that (in a very rough sense) radiate backward and forward through time. From this and some highly technical but more-or-less standard physics, Tipler manages to conclude the existence of an Omega Point — a place where (again speaking roughly) all the information in the Universe is stored. Writing in 1994, Tipler never considered the possibility that the Omega Pont might be located in Mountain View, California. Instead, he stressed that in its omniscience, it’s something very like God.
Continue reading ‘This Particular God, at Least, Appears to Be Dead’
The ever-insightful philosopher Peter Smith has a number of interesting things to say about abortion, but I found one of those things particularly striking — partly because I don’t recall ever having thought of it before, and partly because, in retrospect, I don’t see how I could have failed to think of it.
Namely: The argument is made that zygotes/embryoes/fetuses, even at a very early stage, have the full moral status of human beings. Yet if that were true, surely we’d want to divert a substantial portion of the medical research budget away from relatively minor scourges like, say, cancer, to the spontaneous abortions that take the lives of something like 30% of these full-fledged humans. In a typical year, there are about 8 million cancer deaths worldwide; the number of early-stage spontaneous abortions must be at least twice that.
In Smith’s words:
very few of us are worried by the fact that a very high proportion of conceptions quite spontaneously abort. We don’t campaign for medical research to reduce that rate (nor do opponents of abortion campaign for all women to take drugs to suppress natural early abortion). Compare: we do think it is a matter for moral concern that there are high levels of infant mortality in some countries, and campaign and give money to help reduce that rate.
Smith is struck by the fact that this attitude is very widespread; I am more struck by the fact that it seems to be very widespread even among those who characterize themselves as pro-life.
Continue reading ‘Moral Matters’
Bertrand Russell, that most rational of men, was nonetheless plagued by intermittent depression and the occasional nightmare. Including this one, as reported by Russell’s confidante, the mathematician G.H. Hardy:
[Russell] was in the top floor of the University Library, about A.D. 2100. A library assistant was going round the shelves carrying an enormous bucket, taking down books, glancing at them, restoring them to the shelves or dumping them into the bucket. At last he came to three large volumes which Russell could recognize as the last surviving copy of Principia Mathematica. He took down one of the volumes, turned over a few pages, seemed puzzled for a moment by the curious symbolism, closed the volume, balanced it in his hand and hesitated….
Principia Mathematica, to which Russell had devoted ten years of his life, was his (and co-author Alfred North Whitehead’s) audacious and ultimately futile attempt to reduce all of mathematics to pure logic. It is a failure that enabled some of the great successes of 20th century mathematics. And — the first volume having been published in December, 1910 — this is its 100th birthday.
Continue reading ‘Lord Russell’s Nightmare’
This is an extremely elementary post about numbers. (”Numbers” means the natural numbers 0,1,2 and so forth.) It is a sort of sequel to my three recent posts on basic arithmetic, which are here, here and here. But it can be read separately from those posts.
Today’s question is: Do numbers exist? The answer is: Of course, and I don’t believe there’s much in the way of serious doubt about this. You were familiar with numbers when you were five years old, and you’ve been discovering their properties ever since. Extreme skepticism on this point is almost unheard of among mathematicians or philosophers, though it seems to be fairly common among denizens of the Internet who have gotten it into their head that extreme skepticism makes them look sophisticated.
Let me be clear that I am not (yet) asking in what sense the natural numbers exist — whether they have existed since the beginning of time, or whether they exist outside of time, or whether they exist only in our minds. Those are questions that reasonable people disagree about (and that other reasonable people find more or less meaningless.) We can — and will — come back to those questions in future posts. For now, the only question: Do the natural numbers exist? And the answer is yes. Or better yet — if you believe the answer is no, then there’s obviously no point in thinking about them, so why are you reading this post?
Continue reading ‘Basic Arithmetic: On What There Is’
Like everyone else I know, I am of course a longtime fan of the webcomic XKCD. But somehow it took me until last week to become aware of the frequently brilliant competitor Luke Surl, of which the above is a delectable example. What else out there am I missing?
Hat tip to Harry Brighouse of Crooked Timber.
Click here to comment or read others’ comments.
Yesterday we started a conversation about whether mathematics is invented or discovered. Today I’ll give you my three best arguments for “discovered”. And to focus the discussion, I’ll talk not about mathematics generally but about the natural numbers (0,1,2, and so forth) in particular.
I believe the natural numbers exist, quite independently of whether anyone’s around to think of them. Here’s why: First, we perceive them directly. Second, we know non-trivial facts about them. Third, they can explain the Universe. In more detail:
Continue reading ‘Real Numbers’
Is mathematics invented or discovered? In my experience, applied scientists often think of mathematics as a human invention, while actual mathematicians (with a few notable exceptions) feel sure that mathematics was always there to be discovered. (Of course, it’s sometimes hard to tell how much of this is genuine disagreement and how much is a language barrier.)
I’ve just finished reading an excellent book by Mario Livio which is entirely about the invention/discovery question, though he’s chosen the (somewhat unfortunate) title Is God a Mathematician? Much of the book is a lively romp through mathematical history, with a well chosen mix of biography and exposition. Although he parts company with them in the last chapter, Livio gives a more than fair hearing to the many great mathematicians who have insisted that they are discoverers, from Pythagoras through Galileo, G.H. Hardy, Kurt Godel, and the contemporary Fields Medalist Alain Connes (among others). Here, for example is Connes:
Continue reading ‘Jellyfish Math’
The Intelligent Design folk tell you that complexity requires a designer.
The Richard Dawkins crowd tell you that complexity must evolve from simplicity.
I claim they’re both wrong, because the natural numbers, together with the operations of arithmetic, are fantastically complex, but were neither created nor evolved.
I’ve made this argument multiple times, in The Big Questions, on this blog, and elsewhere. Today, I aim to explain a little more deeply why I say that the natural numbers are fantastically complex.
Continue reading ‘Non-Simple Arithmetic’
As I mentioned the other day, I’ve recently (at the direction of my old friend Deirdre McCloskey) been reading some of the work of John Polkinghorne, the physicist-turned-theologian who seems to write about a book a week attempting to reconcile his twin faiths in orthodox science and orthodox Christianity.
Although Belief in God in an Age of Science is a very short book, it is too long to review in a single blog post. Fortunately, though, much of the non-lunatic content is concentrated in roughly the first ten pages, so I’ll comment here only on those.
Polkinghorne begins in awe. He is awestruck by the extent to which our Universe seems to have been fine-tuned to support life; this is the subject matter of the much-discussed anthropic cosmological principle. To take just one example (which Polkinghorne does not mention): The very existence of elements other than hydrogen and helium depends on the fact that it’s possible, in the interior of a star, to smoosh three helum atoms together and make a carbon atom; everything else is built from there. But it’s not enough to make that carbon atom; you’ve also got to make it stick together long enough for a series of other complicated reactions to occur. Ordinarily, that doesn’t happen, but now and then it does. And the reason it happens even occasionally is that the carbon atom happens to have an energy level of exactly 7.82 million electron volts. In fact, this energy level was predicted (by Fred Hoyle and Edwin Salpeter) before it was observed, precisely on the basis that without this energy level, there could be no stable carbon, no higher elements, and no you or me.
Continue reading ‘Life, the Universes and Everything’
After the philosopher Daniel Dennett was rushed to the hospital for lifesaving surgery to replace a damaged aorta, he had an epiphany:
I saw with greater clarity than ever before in my life that when I say “Thank goodness!” this is not merely a euphemism for “Thank God!” (We atheists don’t believe that there is any God to thank.) I really do mean thank goodness! There is a lot of goodness in this world, and more goodness every day, and this fantastic human-made fabric of excellence is genuinely responsible for the fact that I am alive today. It is a worthy recipient of the gratitude I feel today, and I want to celebrate that fact here and now.
Continue reading ‘Giving Thanks’
Logicomix is—I am not making this up—a graphic novel (that is, what we used to call a comic book) about Bertrand Russell and the writing of Principia Mathematica. Implausibly enough, it succeeds, making rather gripping drama out of the twentieth century crisis in the foundations of mathematics. The technical issues are portrayed clearly and accurately (a novice reader could learn a lot from this book) but never coldly; this is above all a saga about human obsession. I even like the device where the authors themselves appear as characters, trying to figure out how best to present this stuff. It works.
But there’s one part I find almost impossible to believe is accurate; maybe a reader can set me straight. The novel begins in 1939 and proceeds by flashback. In 1939 we see Russell, a lifelong pacifist confronted by the Nazi horror, being shaken to the core by the realization that his beloved Logic does not contain the answers to all of life’s problems. Can there be even a shred of truth to this? Surely the man who devoted his youth and over 300 printed pages to proving that 1+1=2 must always have been well aware that formal logic has its limitations as a practical guide to life.
Continue reading ‘Principia Mathematica: The Comic Book’
