Talk:Half-life/Archive 1

Archive 1

Archive 2

Measuring the half lifes

Given that the half-life of Tungsten is so long and that decay is therefore a very rare event I would like to ask how it is possible to accurately measure its half life? For example if a reasonable mass of Tungsten only has one theoretical atomic decay a year there is a real statistical chance (by random variation) that none or more may occur and so one would surely need to measure over an unfeasible period of time (of unfeasible mass)? Also such a low rate would surely be masked by contamination and background radiation or re-absorption of emitted particles? Could an explanation of the method be added as a link? [ManInStone].

I think Bismuth has an even longer half-life that Tungsten.—The preceding unsigned comment was added by 194.176.105.39 (talk) 13:48, 5 April 2007 (UTC).

Right heres a problem to put all this into context. The half life of bismuth is 19*10^18 years. Its molecular mass is 208.98040g•mol−1. Accordingly there are about 2.87108E+27 atoms in a ton of bismuth. How long would I have to observe the one ton mass in order to be 95% sure that I would observe a single disintigration (assuming there were no technical problems to observation of every event)? --ManInStone 08:21, 18 May 2007 (UTC)

I had a go at this but soon got bogged down in the maths. According to my rough and long winded calculations you would have a fifty percent chance of seeing one decay on the first day. Can anyone shed any light on this problem?

From the question on the exponential decay page: the equation is dN/dt = γN = [ln2/t(1/2)]N. If t(1/2) is 1.9e19 years = 6e26 sec and N is 2.9e27, then dN/dt is 3.35 disintigrations per sec. From here, you have to know that you need to calculate from the Poisson distribution the 0.05 probability time for 0 events, when gamma (expected event rate) is 3.35/sec, is exp-(γ*t), where the lamba here is the total expected event rate for our entire mass, not the one for each atom. So 0.05 = exp-(3.35*t). Solve for t and you get a time about 0.893 sec. You have to wait that long for a 95% chance to see a single disintigration with an expected rate of 3.35/sec. SBHarris 02:07, 28 July 2007 (UTC)

yeah... seriously most half lives are older than chemistry —Preceding unsigned comment added by 141.149.13.22 (talk) 20:08, 22 April 2008 (UTC)

Misleading 'a'

To say that the constant 'a' is negative in the case of exponential decay leads to a very confusing developement (imho): the standard is to use the decay constant $\lambda$, which is positive: $\lambda ={\frac {ln(2)}{t_{1/2}}}$. One should write the exponential law as $x(t)=x(0)e^{-at}$, and so there is no need to talk about the constant being able to absorb the minus sign, which is actually incorrect! (if $a$ absorbs the minus sign, it becomes positive, that's indeed what we see in the last formula: $t_{1/2}={\frac {ln(2)}{a}}$ since ln(2) and $a$ are positive. And since $a$ is positive, there should be a minus signe in the exponent of the decay law). To make things even easier to understand, one may use N instead of x, it's probably a more natural way to represent the population of radioactive isotope which is an integer. (I leave it to other people to make the changes: my English is not very good).

---

I agreed with the above point, but the whole article needs some work IMO. I have flagged it as needing attention. The discussion on the half-life usage in physics seems to talk about lots of points that don't belong here. Perhaps these bits should be integrated into the radioactive decay article?

The structure doesn't seem that great either - there are lots of major headings containing only a sentence or two of description.

I don't understand the section on its usage in population calculation. Could someone clarify this or else remove this section.

There are probably other problems that I have forgotten... Bobbis 18:52, 26 Oct 2004 (UTC)

Of "particles", "substances", "radioactivity" and the like

People like to use these words in this article, but strictly speaking, none of them have anything to do with half-life. Half-life is a purely mathematical (theoretical) property of the likewise mathematical phenomenon of exponential decay. The differential equation that describes exponential decay crops up in a bunch of places; see Exponential decay for a list (which I'm sure is less than complete). --Smack 05:02, 10 Nov 2004 (UTC)

A little more simplicity might be in order

Imagine a high-school student -- or anyone who did not take more than first year college math. Do you think they would get anything from this page or the one on exponential decay?

I think the table is needed on BOTH pages, but even more so on the half-life page -- as it is more likely anyone who was not mathematically advanced would go there first.

Anyone who was able to understand what has appeared on these pages would NOT need to look up the terms.

No? --JimWae 04:35, 2004 Dec 20 (UTC)

I see two viable options: a) leave this article as it is, or b) put a thorough discussion of exponential and radioactive decay here. (I disregard any intermediate compromise solution, as it would frustrate both your goals and mine to an equally great extent.)

I rewrote this article with Option A in mind, by purposely stripping it of everything not related to this narrow subject. My hope is that the references to Exponential decay and Radioactive decay are prominent enough that people who see this article and wonder where all of the information is will go there. Option B would involve simple duplication of material presented elsewhere, which encourages divergent evolution. --Smack 18:07, 20 Dec 2004 (UTC)

P.S: If you want to make this subject more clear to those with weak mathematical skills (or even short attention spans for math), I see no reason why you shouldn't. I just have concerns about the way it's done. --Smack 18:12, 20 Dec 2004 (UTC)

• I still think the simple table would make this a much more useful article for the overwhelming majority of readers. Those who understand the math here, would never need to look up the meaning.--JimWae 20:55, 2004 Dec 31 (UTC)

What meaning?

I agree that this article is not very helpful. I don't intend it to be helpful for most people. It does not stand alone, except for narrow purposes. People who come here with general questions are better off at Exponential decay, and I think we should do our best to make sure they go there. The more general content we put here, the less likely that is to happen. --Smack 18:45, 3 Jan 2005 (UTC)

Encyclopedia articles should be accessible to those who might open the page, not just be technically correct. Most people will more likely go to half-life first than exponential decay. Even if they manage to click on exponential decay after going to half-life (but why that link rather than any other there?), they are first going to see stuff way too technical for them there too. There is no real danger of significantly different versions with that table. If somebody understands either page, they already know what half-life means--JimWae 07:03, 2005 Feb 18 (UTC)

You're right, exponential decay is not referenced prominently enough for inexperienced readers. I'll tweak the intro paragraph a bit.

You're also right that that article is not very accessible to the non-mathematical. IMO, the way to resolve that problem is not to slap half-hearted stand-in explanations of exponential decay onto other articles, but to write a qualitative treatment of the topic into the main article's introduction. If you consider yourself capable of doing that, please do so. I wouldn't trust myself with the task. --Smack (talk) 03:45, 20 Feb 2005 (UTC)

half-life decay to infinity

So in theory radioactive substances cannot complete decompose, as it constantly halving, in practice though i doubt this as one single atom will obviuosly become another substance after some time and none will be left, so what do we believe? 19:50, 10 December 2005 (UTC)

Why do you think it will "obviously" decompose? An unstable atom can, in principle, go on indefinitely without falling apart. It's very unlikely to do this, but it can. --Smack (talk) 22:21, 14 December 2005 (UTC)

Hey High School Student Here...This is mind bogoling....Slayerx675 19:16, 1 May 2006 (UTC)

Just to make sure this is clear. The maths is talking about probability. In one half-life, roughly half the atoms will decompose. The most likely result is half of them decomposing. Once you get down to one atom, it has a 50/50 chance of decomposing every half-life. Think of it like throwing 100 coins in the air, and every coin that lands face-up has 'decomposed'. Each time you do it, about half the coins should 'decompose'. When you only have one coin, it obviously doesn't land as half-heads each time, it is either heads or tails. You have a 50/50 chance of it landing heads. Skittle 15:04, 13 June 2006 (UTC)

Request for Mediation

Removed old mediation tag - it died two months +/- ago. Vsmith 22:35, 1 May 2006 (UTC)

Well, I'm just a kid and checked this out because I'm a fan of the videogame. Anyway, I think that an atom could decompose by 1/2 again and again and again. what I am wondering about is that if it could completly compose to nothing what would happen to the empty space? My guess is that it continues the curved path by halving itself on the X axis every time it goes down one unit on the Y. I think it will do this forever and to infinity. (Based on junior high science and pre-algebra).

An unstable (radioactive) isotope will decay along a decay pathway until it become a stable atom (such as lead) at which point the decay stops. I think you are confusing theoretical probability theory with the actual mechanics of radioactive decay. This appears to be a common point of confusion judging by other posts on this general topic.

--ManInStone 08:34, 18 May 2007 (UTC)

Table of values

I move to remove the table. --Smack (talk) 03:25, 21 March 2006 (UTC)

Keep the table and maybe expand to show the pattern in fractional form (1/2)ⁿ. This needs to be aimed at the general reader rather than just catering to the math geeks :-) Vsmith 22:35, 1 May 2006 (UTC)

After # of Half-lives	Percent of quantity remaining
0	$(1/2)^{0}$
1	$(1/2)^{1}$
2	$(1/2)^{2}$

The contributor who originally added the table intended precisely to cater to the general reader. If I understand it correctly, your proposed version would cater only to the profoundly stupid. I think that very few readers would find a table of this form to be helpful at all. --Smack (talk) 18 May, 2006

I like the current table in the article. It doesn't help me, but I think it illustrates the basic principle of half-life, to people who do not understand it, better than any accurate, encyclopedic words possibly could. Skittle 15:06, 13 June 2006 (UTC)

Derivation

Hi,

You (fresheneesz) remarked in an edit comment at Half-life that you're moving the derivation to the talk page, but the talk page's edit history shows no edits by you. Where did it go, and why did you remove it at all? I've placed your talk page on my watchlist, so you may reply right here, to keep the discussion all in one place.

P.S: You can use the five-tilde (~~~~~) feature for the timestamp at the top of this talk page. --Smack (talk) 02:43, 9 June 2006 (UTC)

Hmm, yea I guess I never did end up pasting the derivation to the talk page. Whoops.. I did it now. I removed the derivation because it wasn't clear, and I guess I didn't think it was very helpful. I can't remember my reasoning, but I didn't think it derserved the space it took up.

Do you think the derivation should stay? Sometimes, its better if derivations like that appear at the bottom of a page, or if they appear on a separate page all together. Oh and thanks for the five-tilde tip. Fresheneesz 03:30, 9 June 2006 (UTC)

I think that a section at the end of the page would give it the right amount of prominence. I originally put it in the beginning because I needed it for the formulas, but that point is moot now that we have a whole section just to define the term. I'll put the derivation back, then. --Smack (talk) 03:48, 9 June 2006 (UTC)

Sounds good, I'll copy this discussion to the talk page of half-life. Fresheneesz 03:56, 9 June 2006 (UTC)

Here is the derivation:

Quantities that are subject to exponential decay are commonly denoted by the symbol N. (This convention suggests a decaying number of discrete items. This interpretation is valid in many, but not all, cases of exponential decay.) If the quantity is denoted by the symbol N, the value of N at a time t is given by the formula:

$N(t)=N_{0}e^{-\lambda t}\,$

where

• $N_{0}$ is the initial value of N (at t=0)
• λ is the decay constant, a positive constant.

When t=0, the exponential is equal to 1, and N(t) is equal to $N_{0}$. As t approaches infinity, the exponential approaches zero.

In particular, there is a time $t_{1/2}\,$ such that:

$N(t_{1/2})=N_{0}\cdot {\frac {1}{2}}$

Substituting into the formula above, we have:

$N_{0}\cdot {\frac {1}{2}}=N_{0}e^{-\lambda t_{1/2}}\,$

$e^{-\lambda t_{1/2}}={\frac {1}{2}}\,$

$-\lambda t_{1/2}=\ln {\frac {1}{2}}=-\ln {2}\,$

$t_{1/2}={\frac {\ln 2}{\lambda }}\,$

Thus the half-life is 69.3% of the mean lifetime.

Definition

This is not the definition of half-life:

$t_{1/2}={\frac {\ln(2)}{\lambda }}$

It's a correct relationship but not the definition of half-life. Jclerman 04:56, 9 June 2006 (UTC)

Do you care to mention what the "definition" is? 71.238.35.126 23:47, 12 November 2007 (UTC)

After you care to read the article's first sentence: "The half-life of a quantity whose value decreases with time is the interval required for the quantity to decay to half of its initial value." Jclerman 11:10, 13 November 2007 (UTC)

Opinions unsourced

These opinions need to be verifiable from peer-reviewed sources:

Most people understand the concept of half-life quickly and are usually first introduced to it in an introductory chemistry or biology course. The extra logarithmic factor, however, is often considered mathematically unpleasant because it leaves room for an additional source of computational error. Nearly all textbooks beyond the introductory level, especially in physics, consider half-life to be archaic and use mean lifetime instead.

Jclerman 00:17, 11 June 2006 (UTC)

The rationale for the deletion of the quoted statements (unsourced and subjective) follows the discusion of the terminology given in [1]

Jclerman 00:13, 18 June 2006 (UTC)

Verification requested...

How old is an archeological site according Carbon 14 dating where the half life of Carbon 14 is equal to 5,730 years and there is only 25% as much Carbon 14 in an archeological sample as a recent sample?

$h=5,730$

Where h is the half life of Carbon 14

$p=.25$

where p is the percent or portion and is defined by:

$p=1/{2^{n}}$

and n is defined as the number of half lives

$n={\frac {\lg \left({\frac {1}{p}}\right)}{\lg \left({2}\right)}}$

and age is defined as

$age=h*n$

1. Option Explicit
2. Dim h As Double, p As Double, n As Double, age As Double
3. Private Sub Form_Load()
4. h = 5730
5. 'Where h is the half life of Carbon 14
6. p = 0.25
7. '(where p is the percent or portion) and defined by'
8. 'p = 1 / (2 ^ n)
9. 'and n is defined as the number of half lives
10. n = Log(p) / Log(.5) (or n = log(1/p) / log(2))
11. 'and age is defined as
12. age = h * n
13. Debug.Print "Half-life", "Percent", "Half-lives", "Age"
14. Debug.Print h, p, n, age
15. End Sub

Can anyone verify the accuracy of this conclusion and method so that it may be posted to the article page? Thanks.

...IMHO (Talk) 19:57, 12 June 2006 (UTC)

That's not necessary. See Radiocarbon_dating#Computations_of_ages_and_dates. --Smack (talk) 23:47, 12 June 2006 (UTC)

Its necessary for readers (especially young readers) who have learned how to write a computer program but not yet learned fancy mathematical symbols which ar only meant to awe strike and confuse them them instead of helping them get on with the business of learning science and saving higher mathematics for higher mathematics. ...IMHO (Talk) 01:35, 13 June 2006 (UTC)

Then forget all formula for your example: 50% ~ 5730yrs x 1 = 5730yrs; 25% ~5730yrs x 2 = 11460 yrs. Keep adding 5730yrs and halving the activity for each half-life. Jclerman 02:04, 13 June 2006 (UTC)

By whatever method is used kids still need a variety of optional methods for comparision before then can grasp what the symbols are all about and before they reach middle age. ...IMHO (Talk) 02:12, 13 June 2006 (UTC)

...and that is what teachers are paid for. However, an encyclopedia is not a teacher - rather it is a source of information and the article provides valid information. Now, I'll agree that the calculation method presented in the article is a bit much for those without some background in math manipulations, logarithms and rate laws. But, as I said up front, that's why we have textbooks and teachers.

Now for your calculations. The general approach works, but it seems you have an error:

p = (1/2)ⁿ

log p= n·log 0.5

n = (log p) /(log 0.5) ... (not log 1/p)

That's my simplified approach for easing students into the concept. If they can find the calculator log button they can do it.

However, all that does not belong in the article. Wikipedia is not a how to... Vsmith 02:48, 13 June 2006 (UTC)

There are two entirely different "how to" reasons. The first is to offer a means of simplifying and softening the explanation of a concept and thereby reducing the learning curve. The second is far more detailed an is for the purpose of actually doing the task over and over again in the real world. A reputable online encyclopedia embraces both kinds of “how to” explanations by including the first kind within the article and by providing a link to the second, which in the case of the Wikipedia would be to the Wikibooks and the Wikibooks:How-tos_bookshelf. ...IMHO (Talk) 03:10, 13 June 2006 (UTC)

Thanks for the reference to the Wikibooks. However, don't rely too much on them. They have a misleading module on the application of logs to radiocarbon dating. I just entered my comments (see below) on a module written, without teacher assistance, by a high-school student. Jclerman 03:42, 13 June 2006 (UTC)

And likewise for the change from log(2) to log(.5) above. Computer wise it gets rid of a division which as I recall from my computer classes of many years ago is far slower than a floating point multiplication. The important issue here, however, is to mold the Wikipedia to the variety of minds out there versus trying to get them to mold to the Wikipedia. Symbolic math is great but once math markup becomes functional and an actual programming language on its own there is no way that it can compete except perhaps for display of math in the form it has taken over the past centuries. What is especially important to realize is that most people have been seduced by the power of a computer to do math and would rather have formulas provided to them in a form that they can plug into their personal computers and get answers with right away so its important to use the universal, all inclusive, comprehensive approach and provide formulas as if all of these were but different languages so that all will be accommodated according to there individual leanings. While Log(1/p)/log(2) might work for me and Log(p)/log(.5) might work for you they both work for the computer. BTW I had previously run a "simplify equation" command under Mathcad 12 and it did not do the conversion to log(p) and Mathcad 12 has made a lot more money than me. ...IMHO (Talk) 08:10, 13 June 2006 (UTC)

Please correct the following in the math module of the Wikibook

<<Half-life is a very commonly used application on exponential decay. Half-life also has a special k. >>

The half-life is a quantity, not an application.

<<The element Carbon-14 has a half-life of 5730 years. When will a 100 gram sample be reduced to 20 grams?>>

A sample of 100 gram is not reduced to 20 grams. You won't be able to notice any change in mass.

Please, don't teach erroneous concepts. Jclerman 03:42, 13 June 2006 (UTC)

Sounds like the student did not do any proof reading in the first sentence and has a complete misunderstanding of how little carbon-14 is actually involved. Atoms would be a far more appropriate measure than grams since there are approximately one trillion carbon-12 atoms for every carbon-14 atom. To do grams you would need a carbon object weighing 100 trillion grams before you could extract 100 grams of carbon-14. However, if you start off with 100 trillion atoms of carbon-12 and 100 atoms of carbon-14 then after 5,730 years you would still have 100 trillion atoms of carbon-12 but only 50 atoms of carbon-14 and 50 atoms of nitrogen-14. So even though weight is not an appropriate unit the student's idea may be correct. It would take 13,305 years for 80 atoms of carbon-14 to be converted to nitrogen-14, leaving only 20 atoms of carbon-14. After 38,069 years all of the carbon-14 would be gone and converted back into into nitrogen-14 from whence it came. ...IMHO (Talk) 09:38, 13 June 2006 (UTC)

Nice try. But,

• Carbon-14 is never completely gone. It decays exponentially ad infinitum.
• How come we date samples as old as 60,000 yrs if all C-14 is gone after 38,069 yrs?

Jclerman 10:57, 13 June 2006 (UTC)

Huh? Are you sure you should be editing any of these pages??? Sorry to tell you this but...

1. There are only a finite number of carbon-14 atoms in any living organism when it stops breathing.
2. Some samples start off with more than 100 atoms of carbon-14. In other words it depends upon sample size. However, even though all atoms of carbon-14 will in any sample eventually be converted into nitrogen-14 by the process of Beta decay the generally accepted reliability limits for measuring any of the residual atoms of carbon-14 left in any reasonable maximum size sample taken from an organism that was once living is about 8 half-life cycles or around 50,000 years max. You can reverse the calculation and do a growth analysis to find out just how big an organism would have to be to start off with in order to extend the number of cycles beyond 8.

Think about it this way. If you only have one atom of carbon-14 and another 5,730 years goes by (plus or minus 40 years) how many atoms of carbon-14 will you have left? As soon as carbon-14 replacement stops in an organism (as the result of the organism no longer breathing) replacement of carbon-14 atoms taken in from the atmosphere stops and there is nothing to counteract the decay process. Since carbon-14 atoms (or any atom for that matter) can only be divided in number down to the number of one eventually no matter how many atoms you start with you will end up with only one atom and in another 5,730 years in the case of carbon-14 (plus or minus 40 years) that last atom of carbon-14 will be gone - converted back into nitrogen-14 from where it came. ...IMHO (Talk) 15:32, 13 June 2006 (UTC)

Since you hinted that I shouldn't be editing, you probably do not see me fit to discuss your comments. So, I won't discuss them. However, for the sake of others that could be misled, I will point out the more important areas of misunderstanding and let the readers resolve them if they wish so in the literature about the relevant topics. As somebody else said, wikipedia is neither a classroom nor a manual, but just a pointer to topics and to related references.

This is the partial list:

• No organism incorporates carbon-14 by breathing.
• The counting statistics needed for dating is based on exponential statistics of random decays, not valid for small number of atoms.

• This is the article on half-life, thus dating methods consist of counting radioactive decays, not C-14 atoms.
• A single atom can decay at ANY time, irrespective of the isotope's half-life.
• The age limit can be extended not only by increasing the sample size but also the counting time.
• Certain amount of decays per second (specific [radio]activity) are needed to be detectable above the background.

Jclerman 20:42, 13 June 2006 (UTC)

Item 1 above. Plants breath c02 with some of the c atoms being c-14 and animals eat plants. Item 2 above. I will leave it to you to determine the probability of transformation in respect to half-life for only a few atoms. C-14 decay for even only a few atoms will happen eventually because it is an unstable isotope. Item 3 above. Radioactive decay results in a decrease of c-14 atoms and an increase in n-14 atoms. While only the names and characteristics change the total number of atoms stays the same. The only way to understand why there is less radioactive emission is to understand why there are fewer atoms of c-14. Item 4 above. True. If you have only one atom of c-14 it might transform into n-14 immediately or wait awhile but eventually it will decay. I'll leave it to you to determine the probability of it not transforming within 2 of its half-lives. Item 5 above. we probably agree on sample size and counting but without your definition of both terms I can't comment. Item 6 above. True. But this number appears to be arbitrary and dependent upon equipment calibration, sensitivity, proximity, components of the surronding environment, etc. To be an editor you not only have to understand a topic but understand why others do not and how to bridge the gap for their benefit rather than your own. ...IMHO (Talk) 03:32, 14 June 2006 (UTC)

Half-life comprehension and computation...

The following discussion moved from Wikipedia:Reference desk/Science. Arbitrary username 19:47, 13 June 2006 (UTC)

Ever get board with mathematicians who insist on using symbols instead of real world tools like computer code? Go to the article on Half-life and you will see what I mean. Here is a less awe striking solution to learning what Half-life is all about and how it is used to compute the age of a sample: How old is an archeological site according Carbon 14 dating where the half life of Carbon 14 is equal to 5,730 years and there is only 25% as much Carbon 14 in an archeological sample as a recent sample? $h=5,730$ Where h is the half life of Carbon 14 $p=.25$ where p is the percent or portion and is defined by: $p=1/{2^{n}}$ and n is defined as the number of half lives $n={\frac {\lg \left({\frac {1}{p}}\right)}{\lg \left({2}\right)}}$ and age is defined as $age=h*n$ Option Explicit Dim h As Double, p As Double, n As Double, age As Double Private Sub Form_Load() h = 5730 'Where h is the half life of Carbon 14 p = 0.25 'where p is the percent or portion and is defined by' 'p = 1 / (2 ^ n) 'and n is defined as the number of half lives n = Log(1 / p) / Log(2) 'and age is defined as age = h * n Debug.Print "Half-life", "Percent", "Half-lives", "Age" Debug.Print h, p, n, age End Sub Don't bother trying to add this easy to understand example to the Half-life article though. Somebody over there wants to keep it a secret. Try adding this niffty example to the Wikipedia article on Half-life. ...IMHO (Talk) 01:42, 13 June 2006 (UTC) I'm sorry, but I really don't see a question anywhere in that rant, nor do I even see cited evidence of your attempts to get this information into the page yourself. The reference desk pages here are a sort of reference desk, not a place for resolving a dispute about article content. Your best bet would be to discuss your concerns on the Talk:Half-life page. If you aren't satisfied that your opinion has been considered, there are other formal ways to resolve the dispute. DMacks 02:12, 13 June 2006 (UTC) And who might you be to take such an authoritative stand when there is no dispute. Like the cave man twins in the Gieco ad say "You need to do your research next time." ...IMHO (Talk) 02:36, 13 June 2006 (UTC) IMHO, a good place to rant is in a blog. If you want to ask a question, feel free, if you have a problem with the article, do what DMacks said.  freshofftheufoΓΛĿЌ  03:33, 13 June 2006 (UTC) Here we go again... another member of the science reference desk social club who can't resist adding their two cents. ...IMHO (Talk) 04:17, 13 June 2006 (UTC) IMHO, what are you talking about? You post a rant into the wrong place, people ask you not to, and you get pissed off. There's no need to get snarky with anyone here. Better places for this discussion include the talk page of the article (as you're already doing) and Request for Comment. — Asbestos | Talk (RFC) 05:29, 13 June 2006 (UTC) Its not a rant. Your neural nets have been overly programmed in that direction and now see everything that way. It is instead just a nice little intro into an otherwise totally boring improvement for the ordinary user who might be just a bit curious as to how they did that calculation to find a date using carbon dating on that National Geographic Hominide episode but could otherwise care less - certainly less than to be required to get a degree in higher mathematics first. ...IMHO (Talk) 06:59, 13 June 2006 (UTC) So why is this here instead of in the half-life article? —Bkell (talk) 09:29, 13 June 2006 (UTC) "insist on using symbols instead of real world tools like computer code?" -- how is computer code any less a set of symbols than mathematical notation? Needing to clarify an article is one thing, but substituting one arcane notation for another (particularly another which is tangentially related at best) isn't a clarification. — Lomn Talk 14:57, 13 June 2006 (UTC) I did not say substitute. In fact that is my point. Some students learn to program in Basic long before they ever see their first mathematical symbol. Think in terms of such articles as presenting to such students the same opportunity as the Rosetta Stone provided for various cultures long ago in terms of not only translation but in terms of opportunity to learn a new language. By using a multiplicity of notations not only does an article serve a wider audience but it permits various components of that audience to learn something new. ...IMHO (Talk) 17:51, 13 June 2006 (UTC) I request that this conversation cease or continue in a more appropriate place. ike9898 17:54, 13 June 2006 (UTC)

Improper deletions

This article can not be used to prevent other users from obtaining a complete comprehension of half-life in the same manner as a member of a trade or artisan guild might try to hide techniques or methods of performing some function. An explanation of half-life can not be limited to only a very technical or mathematical version or explanation of the process. Half-life decay can not be presented here in the same way as a tradesman or artisan would withhold a simple explanation from a patron for the sole purpose of mystifying the topic and keeping the ordinary user from comprehending the topic fully. Such censorship can not be permitted. For this reason deletion of example data, compute code, and simple arithmetic intended to clarify the process and results of Carbon-14 to Nitrogen-14 half-life decay for other users is not acceptable. If such deletions continue then they must be assessed as vandalism an pursued accordingly. ...IMHO (Talk) 04:54, 19 June 2006 (UTC)

• User:GangofOne added this comment within the text of your table: (This example isn't very realistic. 1E+308 atoms of C14 has a mass of 2E+282 kilograms. The Earth's mass is only 5E+24 kilograms.)
• The physics is unrealistic for this and other reasons, and the numbers you post do not appear to reflect your description of the table.

Both the physics and the mathematics are relevant and important here in response to Jclerman's statement that the process of half-life decay in a sample never ends but rather proceeds ad infinitium. This table is verification that no matter how large a sample of Carbon-14 one starts with that the process of half-life decay will eventually terminate. ...IMHO (Talk) 14:26, 19 June 2006 (UTC)

• IMHO the whole matter belongs to this discussion page, and sans personal atttacks so I've transferred the table to the following section.

Jclerman 07:34, 19 June 2006 (UTC)

Nice try to prevent inclusion and clarification of the topic. Recognition that your actions are vandalism does not mean that it is a personal attack. However you are the one who must be held accountable for any act of vandalism thus necessitating the use of personal pronouns. My fault is in warning of an impending complaint rather than making the complaint outright. ...IMHO (Talk) 14:19, 19 June 2006 (UTC)

User:Pce3@ij.net aka IMHO, the absurdly long table you added was quite innappropriate as well as OR. Its removal was not vandalism and Jclerman is not trying to hide anything.

A teacher often has to simplify concepts to help students understand, however, simplifying requires an understanding of the concept to avoid introducing errors. Your posts above illustrate a lack of basic understanding of the concept of radioactive half life and basic biochemistry. Your attempted clarifications, though well meaning I'm sure, had the opposite effect by adding incorrect information and flooding the article with absurd calculations. Now, I'd suggest that you be cautious with your accusations of vandalism and other personal attacks and carefully consider related Wikipedia policies. Vsmith 14:53, 19 June 2006 (UTC)

Here is the table referred to above

Computational Data (demonstration of half-life results)

(Note: This chart is limited to a maximum value of1E+308 using Microsoft Excel Spreadsheet.)

Beginning with a total sample size of 1E+308 atoms of Carbon-14 and zero atoms of Nitrogen-14 we can track the progress of decay (or transition of Carbon-14 to Nitrogen-14) over 1025 half-life cycles of 5,730 years each or 5,873,250 years. (Notice that the process of Beta decay which results in the transition of Carbon-14 to Nitrogen-14 is not the same as the process of fission and the change involves only a decrease in whole Carbon-14 atoms to whole Nitrogen-14 atoms. Thus an end point is reached in 1024 cycles with a starting sample size of 1E+308 at the point their continued division results in less than one Carbon-14 atom.) Also please note that the total number of relevant cycles we can investigate is limited by 1.) sample size (which is in this case 1E+308) and the threshhold of distinction between sample emmissions and background radiation.

(This example isn't very realistic. 1E+308 atoms of C14 has a mass of 2E+282 kilograms. The Earth's mass is only 5E+24 kilograms.)

The purpose of this example is not only to show computational or mathematical results of half-life computation but to show the basis for refuting Jclerman's claim that half-life is an infinite rather than a finite process. ...IMHO (Talk) 15:17, 19 June 2006 (UTC)

Transition of Carbon-14 to Nitrogen-14

Cycle	Atoms of Carbon-14	Atoms of Nitrogen-14
1	1E+308	1
2	5E+307	2
3	2.5E+307	4
4	1.25E+307	8
5	6.25E+306	16
6	3.125E+306	32
7	1.5625E+306	64
8	7.8125E+305	128
9	3.9063E+305	256
10	1.9531E+305	512
11	9.7656E+304	1024
12	4.8828E+304	2048
13	2.4414E+304	4096
14	1.2207E+304	8192
15	6.1035E+303	16384
16	3.0518E+303	32768
17	1.5259E+303	65536
18	7.6294E+302	131072
19	3.8147E+302	262144
20	1.9073E+302	524288
21	9.5367E+301	1048576
22	4.7684E+301	2097152
23	2.3842E+301	4194304
24	1.1921E+301	8388608
25	5.9605E+300	16777216
26	2.9802E+300	33554432
27	1.4901E+300	67108864
28	7.4506E+299	134217728
29	3.7253E+299	268435456
30	1.8626E+299	536870912
31	9.3132E+298	1073741824
32	4.6566E+298	2147483648
33	2.3283E+298	4294967296
34	1.1642E+298	8589934592
35	5.8208E+297	17179869184
36	2.9104E+297	34359738368
37	1.4552E+297	68719476736
38	7.276E+296	1.37439E+11
[sic..]
985	6.11624E+11	1.635E+296
986	3.05812E+11	3.27E+296
987	1.52906E+11	6.54E+296
988	76452955627	1.308E+297
989	38226477813	2.616E+297
990	19113238906	5.232E+297
991	9556619453	1.0464E+298
992	4778309726	2.0928E+298
993	2389154863	4.1856E+298
994	1194577431	8.3712E+298
995	597288715	1.6742E+299
996	298644357	3.3485E+299
997	149322178	6.6969E+299
998	74661089	1.3394E+300
999	37330544	2.6788E+300
1000	18665272	5.3575E+300
1001	9332636	1.0715E+301
1002	4666318	2.143E+301
1003	2333159	4.286E+301
1004	1166579	8.5721E+301
1005	583289	1.7144E+302
1006	291644	3.4288E+302
1007	145822	6.8577E+302
1008	72911	1.3715E+303
1009	36455	2.7431E+303
1010	18227	5.4861E+303
1011	9113	1.0972E+304
1012	4556	2.1944E+304
1013	2278	4.3889E+304
1014	1139	8.7778E+304
1015	569	1.7556E+305
1016	284	3.5111E+305
1017	142	7.0222E+305
1018	71	1.4044E+306
1019	35	2.8089E+306
1020	17	5.6178E+306
1021	8	1.1236E+307
1022	4	2.2471E+307
1023	2	4.4942E+307
1024	1	8.9885E+307
1025	0	1E+308

The personal attack was transferred here

This is not a personal attack but rather being labeled as such in an effort to diminish the truth of what is being said. ...IMHO (Talk) 14:31, 19 June 2006 (UTC)

Accusations of lying or deception are personal attacks - please refrain from using such language. Vsmith 15:18, 19 June 2006 (UTC)

As with a charge of slander in the real world they are not unless false. ...IMHO (Talk) 02:27, 20 June 2006 (UTC)

From User:Pce3@ij.net (who signs IMHO) to User:Jclerman :

You do not own the Half-life article.

You can not use this article to prevent other users from obtaining a complete comprehension of half-life in the same manner as a member of a trade or artisan guild might try to hide techniques or methods of performing some function. You can not limit an explanation of half-life to only a very technical or mathematical version or explanation of the process. You are presenting half-life decay here in the same way as a tradesman or artisan would withhold a simple explanation from a patron for the sole purpose of mystifying the topic and keeping the ordinary user from comprehending the topic fully. Such censorship can not be permitted. For this reason deletion of example data, compute code, and simple arithmetic, such as the data you have deleted which clarifies the process and results of Carbon-14 to Nitrogen-14 half-life decay is not acceptable. If you continue to practice such vandalism an official complaint will be pursued against you. ...IMHO (Talk) 04:49, 19 June 2006 (UTC)

See a long discussion of the computations, above, [2] which had already been moved from elswhere, with contributions from other users. Jclerman 08:03, 19 June 2006 (UTC)

See also

For continuation of this topic go to:

• Talk:Half-life computation. This discussion explains the rationale for creating a new article.
• Half-life computation. New article which contains the misleading and erroneous table being discussed in the current page, above. This table is misleading, among other points, by the fact that its numbers contradict the narrative describing, for the layperson, the transition process. BTW, such a table does not calculate the half-life. It uses its experimental value to attempt a calculation of the decay process based on a hypothetical model.
• An alternative table. This is mathematically more correct than the table subject of the current discussion, although equally physically unrealistic. It was authored by User:GangofOne as a comment/correction to the erroneous table. This link contains other comments related to this discussion.

This table is not "more" mathematically correct but only represents a smaller sample size and is not a comment/correction by User:GangofOne but rather a table generated using the same algorithm and a different software.

One point at a time. First, the tables, their algorithms and software. The obvious differences between the two tables, are as follows:

• In aka IMHOs table the number of atoms of C-14 that decrease during each cycle is not equal to the number of atoms of N-14 that result of the transformation according to the narrative describing the proposed model. Verification: addition of the C=14 and N-14 numbers is not a constant number.
• In GangofOne's table the decrease of C-14 is equal to the increase of N-14. Verification: addition of the C-14 and N-14 number of atoms is a constant number equal to the initial total number of atoms. This corresponds to the narrative describing the model proposed and, thus, it is mathematically more correct. Jclerman 22:16, 19 June 2006 (UTC)

(Minor factual correction. I did not make that table. --GangofOne 01:56, 20 June 2006 (UTC))

The issue here is not the tables anyway or who created them or how since the facts they are intended to illustrate can be reproduced by virtually anyone using virtually any method. The issue here is the fact that sample size (whatever number of Carbon-14 atoms that are started with) will eventually result in no Carbon-14 atoms and a number of Nitrogen-14 atoms equal in number to the sample size of Carbon-14. In other words only integer division can be represented here since no decimal places are involved and consequently the process of radiocative decay of Carbon-14 will eventually terminate when there are zero atoms of Carbon-14 remaining rather than Carbon-14 radioactive emissions continuing ad infintium as User:Jclerman claims. ...IMHO (Talk) 02:42, 20 June 2006 (UTC)

What User:Jclerman either fails to comprehend or to accept is that the process of decay is not infinite in absence of replacement of atoms for all element transformations based on Beta decay and must be calculated using integer rather than floating point variables and jargon. Suggesting or commenting that the process of radioactive decay for a finite amount of Carbon-14 is infinite is irresponsible and inaccurate science and/or mathematics. The entire basis for this discussion has been to provide User:Jclerman with an opportunity to correct his conceptual and mathematical thinking in this regard so that the article might correspondingly represent the truth. Yet User:Jclerman still refuses to acknowledge these facts even in the face of computational evidence which these tables represent. Radioactive emissions from a finite sample of Carbon-14 do not continue ad infinitium as User:jclerman claims but cease when all atoms of Carbon-14 are transformed into atoms of Nitrogen-14. All User:jclerman need do is acknowledge this fact and make such a declaration in the article so that the article will reflect the truth. The half-life computations which serve as evidence of the facts can remain in the new article so that layman users who are seeking a simple method and knowledge of half-life computation will have a resource they can use. ...IMHO (Talk) 21:06, 19 June 2006 (UTC)

• Comments about alleged censorship. Discussion related to deletions from the half-life article by an alleged guild and how to circumvent them.

Jclerman 17:34, 19 June 2006 (UTC) Jclerman 20:37, 19 June 2006 (UTC)

• More about policies.

Jclerman 11:15, 20 June 2006 (UTC)

One point to remember, the percentage of C14 that decay in a half-life, say, is MOST PROBABLY a half, but since this is a statistical statement, it is not say that it is EXACTLY a half. Any given C14 atom decays independently of any other atoms around it, and can exist for many half-lives. For instance, in the table, some of the C14 you started with lasted over 1000 half-lives, over 5,000,000 years, and it is possible that some at the end of the list will last another 5,000,000 years, (although that is not the MOST PROBABLE outcome.) The usefullness of half-live and ratio C14/N14 measurements are greatest when there is sufficient numbers of both to give a valid, ie most probable, outcome. --GangofOne 02:06, 20 June 2006 (UTC)

The table has no business in the article, for many reasons. It's cumbersome and inaccurate. A simple graph would do much better. --Smack (talk) 03:12, 21 June 2006 (UTC)

I would agree that a simple graph would do fine except that the issue is neither graph nor table but rather that basing the results of either one on decimal instead of integer variables in the case of half-life computation being applied to the Beta decay of Carbon 14 is incorrect. If the resolution of a graph derived from integer variables was sufficient to clearly indicate that the decay of Carbon-14 terminated at zero amount regardless of starting sample size (unless infinite) then use of a graph would be fine with me but in this case even a table is insufficient to convince User:Jclerman that Carbon-14 decay does not proceed ad infintium as he or she contends but rather terminates when the amount of Carbon-14 reaches zero. Neither a table or a graph will convince him or her of this. What is necessary instead of a graph or table is the ability to comprehend and acknowledge the facts. ...IMHO (Talk) 04:04, 21 June 2006 (UTC)

It's (I hope) obvious that the issue of decay and rates becomes moot when the amount of ¹⁴C reaches zero. But given 1 atom of it, it is not true that at one t_1/2 later (or at one instant before) that atom will decay. Your equation may find that and a table (that isn't wrong) may indicate it, but that's not how nuclear decay happens (as has been explained a few times now). And the table is wrong--it's mathematically not even close to correct for the equation even accounting for round-off and integer vs non-integer math and ignoring all physical applications. DMacks 05:33, 21 June 2006 (UTC)

I was assuming that the "editors" and readers of the half-life article had at least a certain elementary level of knowledge and were therefore capable of understanding a few basic scientific and mathematical facts. Now I find myself back teaching forth grade science in order to get this point across but if such is the level of miscomprehension then all I can do is to repeat the following and say nothing else. The values in the table are not intended to be precise but are only intended to illustrate the fact that application of half-life to a discrete atomic structure is different from the application of half-life to an analog charge on a capacitor. On the one hand the computation must use integers because the items they represent are discrete whereas in the case of a charge on a capacitor decimal variables must be used because voltage is measured as an analog value. Consequently the application of a half-life computation in the case of discrete values like atoms will result in termination when the last atom has decayed while on the other hand the consequences of the application of half-life computation in the case of a voltage is that the process of half-life decay will (in theory) continue ad infinitum because the capacitor (in theory) will always retain a residual charge regarless of how small it becomes. Half-life computation when applied to atoms must use integers. Half-life computation when applied to voltage must use decimals. One process is finite while the other process (in theory) is infinite. To verify this simply create another table using decimal values. ...IMHO (Talk) 07:12, 21 June 2006 (UTC)

See [3] where an independent tutor suggested in 2003 how to test the behavior of the last atom. Validation of physics models consists in comparing the expected behavior with experimental observations of real physical systems. The tutor's article describes how you can test yourself the validity (or not) of the exponential formula for small number of atoms with a simple experiment. Physics describes nature. When a formula can mimic nature we accept the model and use it. In radioactive decay, the exponential model does not apply for small number of atoms (or small number of atoms are not within the domain of validity of the formula or equation or table). The DIY experiment uses pennies. Also in [4] In other web pages they use m&m candies, e.g. [5]. A similar experiment is performed in college with isotopes of a very short half-life, e.g., see Fig 5 in [6]. See how to write a computer program that simulates radioactive decay including the required randomness in [7]. Jclerman 08:43, 21 June 2006 (UTC)

This [8] is yet another example of how misinterpretation and reliance upon publications as the basis for accepting an invalid concept leads to such a situation as we have here. What these articles address is the rate (based on probability) of decay and rather than the fact or reality of decay. The articles are about probabilistic measurement to determine the rates of decay versus being about the fact of decay in regard to science. While the rate of atomic decay may be probabilistic the fact of atomic decay is deterministic. None of the articles deny that in eventuality the last atom will decay. A deterministic rather than a probabilistic experiment with real atoms of short half life such as [9] requires that the presence of a single atom of the isotope be measurable and distinguishable from other isotopes and impurities. What you are failing to comprehend as evidenced by [10] is that the existence of unstable radioactive isotopes like Carbon-14 is like the existence of living and dying organisms. Just as each living organism will eventually die so will an unstable radioactive isotope. While the duration of life may differ among the same organisms and the rate of decay or dying may be measured probabilistically all of the organisms will eventually die. Consequently the process of decay or dying is terminal and entirely independent of the rate at which it proceeds. As with a living population of organisms which do not reproduce radioactive isotopes which are not replenished will eventual cease to exist regardless of their half-life or rate of dying or decay. ...IMHO (Talk) 14:01, 21 June 2006 (UTC)

A minor aside—the process of discharging a capacitor necessarily involves the movement of discrete particles as well, and strictly speaking isn't continuous either.

As Smack noted on your talk page, Pce3, modelling either radioactive decay or an electrical circuit as exponential decays works quite well with large samples, but it is dangerous to take either model literally when you're down to a (statistically) small sample. When dealing with just a handful of particles the model doesn't tell you how many (undecayed atoms or electrons) will be left after a period of time with any certainty—it only gives an expectation value. As long as we're clear that the formulae here generate an expectation value and aren't meant to be taken literally, I don't see the problem. TenOfAllTrades(talk) 13:27, 21 June 2006 (UTC)

The following had been deleted by User:Pce3@ij.net from User_talk:Pce3@ij.net. It was transferred here for completeness because it had been recently referred to by user TenOfAllTrades. User:Jclerman

First of all, the article is entitled "Half-life," not "Decay of carbon-14." If you would read the introductory paragraph, you would see that the article relates and applies to much more than a particular chemical isotope. For a more thorough treatment of the subject, please see Exponential decay.

Be that as it may, your main point is incorrect. Exponential decay does not depend on the number of items present. Let's say that I have one atom of carbon-14 in a jar. The exponential decay formula, with N=1 at t=0, predicts N<1 for t>0. Now, you say that this is nonsense - you can't have a noninteger number of atoms in a jar. But I say that it's not nonsense. The number that we get out of the formula does not represent the actual number of atoms; it represents the expected value of the number of atoms. The actual value may be greater (one) or less (zero) than the expected value.

In fact, the exponential decay formula for numbers of atoms greater than one is also an expected value. Say we have two atoms of carbon-14 in a jar. Physics allows both of those atoms to sit there for millions of years without decaying. They're not likely to do so, but it's important to note that they can. Although your table specifies numbers of atoms to arbitrary accuracy, in fact all the decimal places beyond the first few mean very little. For most practical purposes, they're just an exercise in arithmetic masturbation.

--Smack (talk) 05:04, 21 June 2006 (UTC)

My concern is not about what you do with your own body. Please keep such personal comments away from the Wikipedia and to yourself. ...IMHO (Talk) 14:44, 21 June 2006 (UTC)

I suspect that Smack's comment about 'arithmetic masturbation' is meant in the commonly-used (and very informal) sense of 'playing with numbers', and has nothing to do with a personal habits. Could you address the substance of the remark? Would you agree that the formulae presented here represent an expectation value rather than an absolute measure, and if interpreted that way the notion of a fractional result is reasonable? TenOfAllTrades(talk) 14:54, 21 June 2006 (UTC)

Bottom line is that the computation of half-life can be done with integer variables or with decimal variables to reflect that the population which is decaying or dying is made up of discrete individuals, each with a finite life expectancey, or that the "population" is infinitely divisible such as a number line versus points on the number line. I don't know how to make this point any clearer. ...IMHO (Talk) 15:04, 21 June 2006 (UTC)

←dragging back to left margin← The point is that by the time you get down to so few individual particles that a choice of discrete versus continuous variable makes a difference, the model is near-meaningless. You're saying that in reality, a particle is always decayed or not-decayed; this is absolutely true. However, in the exponential decay model, we can only talk about a most probable outcome: an expectation value. Given a single atom of a radioactive isotope, we can come up with a probability distribution which describes the time by which it is most likely to have decayed, but we cannot predict – at all – when that decay will take place. For a single particle, the probability that a decay will take place is actually constant with time; the odds that a decay will occur within the next second are the same no matter what second you examine, until the particle decays. The actual decay event could fall exactly at one half-life, but just as easily at 0.1 or 10 half-lives. There's no way for a single nucleus to count its neighbours and check its stopwatch, as it were. In your giant table of values, the last few rows read

time (half-lives)	undecayed atoms
0	16
1	8
2	4
3	2
4	1
5	0

That's an accurate representation of the expectation values, but actually relatively unlikely to happen so precisely in real life. It's a stochastic process, and you might well see this

time (half-lives)	undecayed atoms
0	16
1	7
2	3
3	1
4	0
5	0

Or even this

time (half-lives)	undecayed atoms
0	16
1	8
2	7
3	3
4	1
5	1
6	1
...	...
12	1
13	0

Suggesting that modelling with a discrete (integer) variable is more 'real' just isn't true; you're still modelling a stochastic process. The model just doesn't give you an integer output—it's only producing expectation values. TenOfAllTrades(talk) 15:27, 21 June 2006 (UTC)

You still have no idea of what you are talking about or the reality of what I am saying. ...IMHO (Talk) 15:32, 21 June 2006 (UTC)

Table of Comparison

Half-life Computation

based on

Variable Type

Decimal	Integer
(voltage)	(atoms)
38.48451001	38
19.242255	19
9.621127502	9
4.810563751	4
2.405281875	2
1.202640938	1
0.601320469	0
0.300660234	0
0.150330117	0
0.075165059	0
0.037582529	0
0.018791265	0
0.009395632	0
0.004697816	0
0.002348908	0
0.001174454	0
0.000587227	0
0.000293614	0
0.000146807	0
~	~

suggestion :

I suggest that, if there are no new arguments and/or facts, we conclude here the current discussion. REMINDER: The fate of the table is being decided together with the fork article, at Wikipedia:Articles for deletion/Half-life computation.

I have no objection to deletion of the "fork" article or exclusion of a table based on integer variables so long as the difference between the use of integers and the use of decimal variables and their results in terms of termination versus continuation ad infinitum is acknowledged and explained and that unstable radioactive isotopes are admitted to be mortal on behalf of future readers. ...IMHO (Talk) 15:28, 21 June 2006 (UTC)

The problem is that a given atom of an unstable radioactive material can last for an arbitrary length of time. A half-life indicates the probability that an atom may decay within a given period of time; it does not compel the atom to decay—ever. The half-life (and associated exponential decay theory) are models and nothing more. Using an integer representation to imply that it actually is some sort of count is misleading; all that the half-life calculation gives you is an expectation value. The very small decimal value generated after many half-lives have elapsed represents the small probability that the atom has not yet decayed. By all means emphasize this fact in the article, but it is flatly incorrect to imply that the use of integers in the calculation will give a result in some way superior, more accurate, or more 'real'. TenOfAllTrades(talk) 01:33, 22 June 2006 (UTC)

"Validation" section

I think that a practical discussion of how half-lives work in late generations is a great idea; however, this section as it presently stands is pretty rough. Since it appears fairly contentious, I'll post thoughts here for now and hold off on the boldness.

1. The present content simply looks bad. WP:MoS is needed regardless. Specifically, italics and bold text are overused.
2. Several external references appear superfluous. Most notably, the "this site shows how to program..." is a homework assignment, not an explanation. I feel the pennies/m&ms links are sufficient for the purpose
3. The soliloquy on "physics is nature, formulas do things, other stuff happens" is far outside the scope of the article
4. Perhaps most importantly, the section fixates on atomic decay and its implications, far more specific than the subject of half-lives at large.

In short, this section is better suited to radioactive decay; specifically, as addenda to Radioactive_decay#Decay_timing where the distinction between predicted and observed (and the necessity of integral) quantities of substance is already discussed. — Lomn | Talk 20:54, 21 June 2006 (UTC)

This is the talk page and not the article page. It is inapproriate to apply the rules which apply to articles to discussions of those articles. The fact that half-life may be computed using integer variables to represent discrete decay and decimal variables to represent continuous decay are highly relevant to the article. You need to spend less time in your Ivory tower and more time down here on Earth. ...IMHO (Talk) 02:40, 22 June 2006 (UTC)

Please try to remain civil. Snide comments about "ivory towers" and "being on earth" do not help improve the article. I intentionally did not check authorship of this section so as to avoid possible bias -- it's simply a bad section, in my opinion, as it stands currently. Because it's contentious, I'm discussing my problems with it here first.

As for relevance, I feel an in-depth discussion of the particulars of calculations for integral decay are better suited to articles that focus on integral decay; that is, radioactive decay. Continuous decay isn't particularly interesting (from an expansion standpoint) because it simply mirrors the mathematical definition in all particulars. — Lomn | Talk 03:01, 22 June 2006 (UTC)

There's nothing wrong with the ideas that the section expresses, per se. The trouble is that the text rambles disjointedly and makes little sense. Furthermore, some of these ideas, such as the one about "validation of physics-math models" don't belong in a specialized article like this one (because it really should keep a narrow scope, even though people keep stuffing it with extraneous goodies). In fact, it may even be good to write a separate article on validation of physics-math models or something like that, if we don't already have one. --Smack (talk) 18:41, 25 June 2006 (UTC)

Schroedinger's cat

Mentioning it in the "see also" without any pointer within the text of the article and without any "half-life" being mentioned in the cat's article, puzzles readers like myself who wondered what the relationship and purpose of the link was. The proponent should edit the article as to make the "connection" obvious to the reader. BTW, consider that this article is about half-life as the time to reach half of an initial quantity that decreases with time. It was never intended to discuss the timing of the last element because in origin it dealt with decays of very large number of elements. Perhaps a reference to the cat would be more suitable in a more general article about decay. Anyhow, the proponent could try drafting/editing one or both of these approaches, then re-insert the link. Jclerman 19:54, 24 June 2006 (UTC)

major revisions complete

The Half-life computation article has undergone substantial revision which has hopefully addressed everyone's concerns. If you have any further comments after looking at the article again, please list the items you do not like, make whatever comment you have and please be specific and allow time for further revision. If there is any reason I can not comply with your wishes then I will let you know the reason why. ...IMHO (Talk) 12:18, 25 June 2006 (UTC)

Proposed merge

I can see no reason for four articles on this subject. As it stands, we have

1. Exponential decay
2. Half-life
3. Elimination half-life
4. Biological half-life

All four describe the same mathematical process with small variations that could be covered in sections. All the material in #2 is also in #1, except for the "Validation" section and the dubious statement that half-life has a meaning for non-exponential decays. If what is meant is that the term is sometimes pressed into service for elimination processes above the point where the liver is saturated, that should be said more explicitly.

Is there an actual reason for so many virtually-identical articles? I don't see them as focused, just redundant. Robert A.West (Talk) 20:16, 25 June 2006 (UTC)

I think a merge of exponential decay and half-life would be okay, and perhaps a merge of biological half-life and elimination half-life. Although they are related, I think merging all four articles into one would not be a good idea. Biological half-life has a lot of content that is specific to it and it would be odd to include it in a combined article. Also, I think a single article might be confusing since there are subtle differences in the terms. I suggest that there be a single talk page for the discussion to take place at. -- Kjkolb 04:19, 26 June 2006 (UTC)

One advantage of a diversity of articles is that each may deviate just slightly enough from another to allow comparisons that make comprehension of half-life computations a lot easier than a single article with the methodology and mathematics condensed into a precise and yet virtually incomprehensible (at least for the layman) result. So long as such an article would include a grade school level explanation with examples for each application then I think it would be a great idea. Here is an example of what I would like to see:

Usage example for the laymen

Where p is the percent or portion of Carbon-14 in a sample:

$p={\frac {1}{2^{n}}}$

and where n defines the number of Carbon-14 half lives in an archaeological sample:

$n={\frac {\ln \left({\frac {1}{p}}\right)}{\ln \left({2}\right)}}$

and where age of an archaeological sample is defined as

$age=h*n\$

Specifically:

Where h is the half-life of Carbon 14:

$h=5730\$

and the percent or portion of Carbon-14 in the archaeological sample is 25%:

$p=.25\$

and the number of Carbon-14 half lives equal to:

$2={\frac {\ln \left({\frac {1}{.25}}\right)}{\ln \left({2}\right)}}$

then the age of the archaeological sample will be:

$11,460=5730*2\$ years

...IMHO (Talk) 06:53, 26 June 2006 (UTC)

Also you may wish to look at the extremely wide variety of papers (1,340,000) regarding the application of half-life outside the Wikipedia starting with Google Scholar List of Google Scholar half-life application papers ...IMHO (Talk) 10:23, 26 June 2006 (UTC)

Actually, I think it might be better to keep biological half-life and elimination half-life separate or to name the combined article something like biological and elimination half-lives, so that the terms are not seen as equivalent. Anyway, a discussion about merging half-life and exponential decay was recently concluded at Talk:Exponential decay. The merge was clearly opposed. I think the tags should be removed unless there is something different about this merge proposal. The argument seems to be the same, so I don't know what that would be. -- Kjkolb 11:27, 26 June 2006 (UTC)

The problem is is that application of the concept of half-life is now so diverse that it would be impossible to merge every article that utilized the concept. The Google Scholar half-life list above references over one and a quater million papers. A far better idea would be to classify articles beginning with the basic divisions used for the reference desks maybe even going so far as to incorporate the Dewey Decimal System if not one of our own. Is what I am proposing to classify the entire Wikipedia? Yeah! ...IMHO (Talk) 11:45, 26 June 2006 (UTC)

I think that elimination half-life should be retained since it is the correct terminology in pharmacokinetics. Almost all drug-related articles (with Template:Drugbox) link to this page as an explanation of the half-life field in the infobox. I other disagree with the merger generally since, as others have said above, each of these half-life articles concern related, but distinct concepts. Perhaps part of the reason why a merger was proposed was because the biological half-life page is badly in need of a cleanup. -Techelf 11:35, 27 June 2006 (UTC)

Merge "biological" into "elimination" or vice versa, but keep the rest. If an article with 'half-life' in the title loses focus, it needs to be trimmed, not merged. For instance, much of what people try to include into this article really belongs at Exponential decay. Likewise, some of the content at Biological half-life should probably go under Clearance (medicine). --Smack (talk) 23:43, 27 June 2006 (UTC)

Single place to discuss: RfC? =

I know that Request for Comment tends to be a place where people go when they are fighting, but I agree with Kjkolb that there should be a single place to discuss this, and I can't think of a better place to do it. What do others think? Robert A.West (Talk) 11:52, 26 June 2006 (UTC)

Seems like this is as good a place as any unless maybe it would be the science desk or villiage pump proposals. ...IMHO (Talk) 11:55, 26 June 2006 (UTC)

Per Robert A West, RfC is indeed the correct place to ask for additional comment on articles. Just put a short summary of the dispute (in terms as neutral as possible) on the appropriate article dispute page—in this case, Wikipedia:Requests for comment/Maths, science, and technology. For discussing a merger to this article, or any other content issues, this talk page is as good a place as any for a centralized forum. TenOfAllTrades(talk) 12:33, 27 June 2006 (UTC)

I'm for merging Half-life and Exponential decay, tough there's really no reason to cram the others together. The two concepts share significant conceptual overlap, and it would be good for organizational purposes to more clearly destinguish between Half-life and Half-Life. 70.48.151.133 00:50, 28 June 2006 (UTC)

I agree that elimination half-life and biological half-life are similar concepts and could be merged. The inclusion of exponential decay and half-life would however be incorrect. The concepts may be the similar mathematically, they are distinctly different. The exponential decay is a strictly mathematical concept. The concept of half-life again, is a general concept, most widely know for describing radioactive decay, but should not be restrained to such. Finally the biological half-life, which is a mathematical model describing the passage of material through the body. It is not the same as radiological half-life and should not be confused as such. Although the three examples share a common mathematical formula the concepts are unique. Dav1s 75 00:41, 13 April 2007 (UTC)

Graph

A graph should accompany the chart in the intro. — Omegatron 23:07, 15 September 2006 (UTC)

There is a graph at Exponential decay, to which this article refers as prominently as it can without being unseemly. As for the chart, I still think that we should remove it. --Smack (talk) 03:25, 17 September 2006 (UTC)

By what logic? — Omegatron 17:01, 17 September 2006 (UTC)

Because the table actually tabulates exponential decay. This article is supposed to be narrowly focused on half-life, to avoid duplicating exponential decay more than necessary. I'm partly inclined to resolve your objection backhandedly by moving the table to that article, which has a graph but no table. --Smack (talk) 00:20, 18 September 2006 (UTC)

I don't understand why you think that. Both should be in both. — Omegatron 00:42, 18 September 2006 (UTC)

Seems there's room for both in both, why the limitation? The graph 'tho seems a bit misleading as it shows the first two lines aparently zeroing out rather than approaching zero asymptotically (is that spelled right, looks wierd?) - may be a resolution problem. Vsmith 01:19, 18 September 2006 (UTC)

It's not a resolution problem; the lines do actually disappear when they hit the x-axis.

I don't like the idea of "both in both." We have "room" (m:Wiki is not paper) to put the entire Exponential decay article here. But we don't – why? --Smack (talk) 03:55, 18 September 2006 (UTC)

Ok. After that, we'll also have to take the space shuttle pictures out the NASA article, the Arc de Triomphe pictures out of the Paris article, the lightning picture out of the electricity article, ... — Omegatron 04:44, 18 September 2006 (UTC)

What is the point of this article?

Pictures of the space shuttle belong in NASA, because NASA is a major topic that relates very closely to the space shuttle. Half-life, however, is not a major topic. It's a scrappy little topic, subsidiary to Exponential decay. However, someone casually familiar with scientific literature could easily fail to realize this. People tend to use the word 'half-life' without explicitly referring to exponential decay; the former has become a metonym for the latter. (If you doubt me, just compare the two articles' Whatlinkshere pages.) Noting this fact, let's consider how we can distribute content between the two articles.

1. I find that this situation smacks of Category:Redirects from related words: the same way that we redirect Atheist to Atheism, we might consider redirecting Half-life to Exponential decay. But the terms differ too much for us to do that.
2. Discuss the topic extensively at Exponential decay. Since half-life is a scrappy little topic, give it a scrappy little article, and send people to the longer article if they want to know more.
3. Discuss the topic extensively at both places. This would create the nightmare task of keeping information synchronized between two long articles. I hope nobody actually espouses this option.
4. Discuss the topic extensively here, and keep a stub at Exponential decay. I abhor this option. I believe that populistically substituting a commonly-used name for the correct name compromises our scientific integrity.

Each approach has its problems, of course, but I'll assume for the sake of argument that everyone agrees with me that option 2 has the fewest. That leaves us with the problem of how best to implement it. Note that, because of the metonymic usage, many people go looking for Half-life when they actually want to know about Exponential decay. Thus, we need to make it clear that there's more information outside this article. Which leads me to the point I've been trying to make all along: the more information we have here, the more likely people are to think that this is all we have. --Smack (talk) 16:52, 18 September 2006 (UTC)

Sure, there are related articles and some should be merged/changed into disambiguation pages. But which ones?:

• Half-life
• Half-life (disambiguation)
• Radioactive decay
• Exponential decay
• Elimination half-life
• Biological half-life
• Effective half-life
• Half-life of knowledge
• Reaction half life
• Context-sensitive half-life

Maybe merge Half-life's content into the appropriate articles, move Half-life (disambiguation) to Half-life, given a sentence or two of description, and then link to all the various field-specific meanings?

Otherwise, merge all the field-specific meanings into Half-life. We definitely shouldn't be duplicating content. (But we should duplicate images and graphs where appropriate.) — Omegatron 17:50, 18 September 2006 (UTC)

• RE: "the more information we have here, the more likely people are to think that this is all we have"
  • Using that line of reasoning, one should keep only the simplest explanation here - including the simple table - and remove all the complex math to the exponential decay article - rather than arguing for removal of the simplest material --JimWae 18:23, 18 September 2006 (UTC)

I think that all of the specific half-life articles represent the metonymic usage that I'm talking about. They should be dicdefs referring the reader elsewhere. For instance, Biological half-life should point to Clearance (medicine).

JimWae: I have judged successive additions to this article by how much they relate specifically to half-life, as distinct from exponential decay. I have let the specifically half-lifey things stay, and tried to remove the others. You have a point, but I can't say offhand which approach I like better. --Smack (talk) 18:40, 18 September 2006 (UTC)

Simplified Formula

The formula:
$N=N_{o}e^{-\lambda t}\,$
could be simplified to:
$N={\cfrac {N_{o}}{2^{({\cfrac {t}{t_{\frac {1}{2}}}})}}}$
by substituting the value of lambda in terms of half-life:
$\lambda ={\cfrac {ln2}{t_{\frac {1}{2}}}}$ Just wanted to know if you wanted to include it somehow.
—Preceding unsigned comment added by 69.223.47.102 (talk • contribs)

Why would we want to do that? I think that that version looks awful. We could fix up the TeX markup like this:

$N={\cfrac {N_{o}}{2^{\left({\cfrac {t}{t_{\frac {1}{2}}}}\right)}}}$

but then it still look pretty wonky. --Smack (talk) 20:15, 1 December 2006 (UTC)

$N(t)=N_{0}2^{-t/t_{1/2}}.\,$ in the article exponential decay where both formulae are shown, and their scaling is mentioned.

lambda has physical meaning. Don't change this article. --Jclerman 05:13, 2 December 2006 (UTC)

I don't think the way it looks matters, but if the formula works, it should be changed. --199.43.172.254 14:13, 19 March 2007 (UTC)

Nonsense. You are not a physicist, sure. Go change E = m.c.c; it's simpler because doesn't need superscripts and "it works". Jclerman 01:19, 21 March 2007 (UTC)

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