Relay-Version: version B 2.10 5/3/83; site utzoo.UUCP Path: utzoo!mnetor!seismo!caip!sri-spam!nike!ucbcad!ucbvax!cdx39.UUCP!jc From: jc@cdx39.UUCP Newsgroups: mod.ai Subject: Re: "Proper" Study of Science, Conservation of Info Message-ID: <8608201406.AA26083371@rclex.UUCP> Date: Wed, 20-Aug-86 10:06:56 EDT Article-I.D.: rclex.8608201406.AA26083371 Posted: Wed Aug 20 10:06:56 1986 Date-Received: Tue, 16-Sep-86 18:58:36 EDT References: <8608010557.AA11269@ucbvax.Berkeley.EDU> Sender: daemon@ucbvax.BERKELEY.EDU Organization: The ARPA Internet Lines: 93 Approved: ailist@sri-stripe.arpa [The following hasn't any obvious AI, but it's interesting enough to pass along. Commonsense reasoning at work. -- KIL] > The ability to quantify and measure ... has profound implications ... > > ... A decade from now it's likely that none of our bodies > will contain EVEN A SINGLE ATOM now in them. Even bones are fluid in > biological organisms; ... OK, let's do some BOTE (Back Of The Envelope) calculations. According to several bio and med texts I've read over the years, a good estimate of the half-life residency of an atom in the soft portions of a mammal's body is 1/2 year; in the bones it is around 2 years. The qualifications are quite obvious and irrelevant here; we are going for order-of-magnitude figures. For those not familiar with the term, "half-life residency" means the time to replace half the original atoms. This doesn't mean that you replace half your soft tissues in 6 months, and the other half in the next six months. What happens is exponential: in one year, 1/4 of the original are left; in 18 months, 1/8 are left, and so on. Ten years is about 5 half-lives for the bones, and 20 for the soft tissues. A human body masses about 50 Kg, give or take a factor of 2. The soft tissues are primarily water (75%) and COH2; we can treat it all as water for estimating the number of atoms. This is about (50Kg) * (1000 KG/g) / (16 g/mole) = 3000 moles, times 6*10^23 gives us about 2*10^26 atoms. The bones are a bit denser (with fewer atoms per gram); the rest is a bit less dense (with more atoms per gram), but it's about right. For order-of-magnitude estimates, we would have roughly 10^26 atoms in each kind of tissue. In 5 half-lives, we would divide this by 2^5 = 32 to get the number of original atoms, giving us about 7*10^25 atoms of the bones left. For the soft tissues, we divide by 2^20 = 4*10^6, giving us about 2 or 3 * 10^20 of the original atoms. Of course, although these are big numbers, they don't amount to much mass, especially for the soft tissues. But they are a lot more than a single atom, even if they are off by an order of magnitude.. Does anyone see any serious errors in these calculations? Remember that these are order-of magnitude estimates; quibbling with anything other than the first significant digit and the exponent is beside the point. The only likely source of error is in the half-life estimate, but the replacement would have to be much faster than a half-year to stand a chance of eliminating every atom in a year. In fact, with the exponential-decay at work here, it is easy to see that it would take about 80 half-lives (2*10^26 = 2^79) to replace the last atom with better than 50% probability. For 10 years, this would mean a half-life residency of about 6 weeks, which may be true for a mouse or a sparrow, but I've never seen any hint that human bodies might replace themselves nearly this fast. In fact, we can get a good upper bound on how fast our atoms could be replaced, as well as a good cross-check on the above rough calculations, by considering how much we eat. A normal human diet is roughly a single Kg of food a day. (The air breathed isn't relevant; very little of the oxygen ends up incorporated into tissues.) In 6 weeks, this would add up to about 50 Kg. So it would require using very nearly all the atoms in our food as replacement atoms to do the job required. This is clearly not feasible; it is almost exactly the upper bound, and the actual figure has to be lower. A factor of 4 lower would give us the above estimate for the soft tissues, which seems feasible. There's one more qualification, but it works in the other direction. The above calculations are based on the assumption that incoming atoms are all 'new'. For people in most urban settings, this is close enough to be treated as true. But consider someone whose sewage goes into a septic tank and whose garbage goes into a compost pile, and whose diet is based on produce of their garden, hen-house, etc. The diet of such people will contain many atoms that have been part of their bodies in previous cycles, especially the C and N atoms, but also many of the O and H atoms. Such people could retain a significantly larger fraction of original atoms after a decade. Please don't take this as a personal attack. I just couldn't resist the combination of the quoted lines, which seemed to be a clear invitation to do some numeric calculations. In fact, if someone has figures good to more places, I'd like to see them.