Half-life Download Free
Hebe Newnam
Half-life (symbol t) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable atoms survive. The term is also used more generally to characterize any type of exponential (or, rarely, non-exponential) decay. For example, the medical sciences refer to the biological half-life of drugs and other chemicals in the human body. The converse of half-life (in exponential growth) is doubling time.
The original term, half-life period, dating to Ernest Rutherford's discovery of the principle in 1907, was shortened to half-life in the early 1950s.[1] Rutherford applied the principle of a radioactive element's half-life in studies of age determination of rocks by measuring the decay period of radium to lead-206.
Half-life is constant over the lifetime of an exponentially decaying quantity, and it is a characteristic unit for the exponential decay equation. The accompanying table shows the reduction of a quantity as a function of the number of half-lives elapsed.
A half-life often describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition that states "half-life is the time required for exactly half of the entities to decay". For example, if there is just one radioactive atom, and its half-life is one second, there will not be "half of an atom" left after one second.
Instead, the half-life is defined in terms of probability: "Half-life is the time required for exactly half of the entities to decay on average". In other words, the probability of a radioactive atom decaying within its half-life is 50%.[2]
For example, the accompanying image is a simulation of many identical atoms undergoing radioactive decay. Note that after one half-life there are not exactly one-half of the atoms remaining, only approximately, because of the random variation in the process. Nevertheless, when there are many identical atoms decaying (right boxes), the law of large numbers suggests that it is a very good approximation to say that half of the atoms remain after one half-life.
In second order reactions, the rate of reaction is proportional to the square of the concentration. By integrating this rate, it can be shown that the concentration [A] of the reactant decreases following this formula:
The term "half-life" is almost exclusively used for decay processes that are exponential (such as radioactive decay or the other examples above), or approximately exponential (such as biological half-life discussed below). In a decay process that is not even close to exponential, the half-life will change dramatically while the decay is happening. In this situation it is generally uncommon to talk about half-life in the first place, but sometimes people will describe the decay in terms of its "first half-life", "second half-life", etc., where the first half-life is defined as the time required for decay from the initial value to 50%, the second half-life is from 50% to 25%, and so on.[7]
A biological half-life or elimination half-life is the time it takes for a substance (drug, radioactive nuclide, or other) to lose one-half of its pharmacologic, physiologic, or radiological activity. In a medical context, the half-life may also describe the time that it takes for the concentration of a substance in blood plasma to reach one-half of its steady-state value (the "plasma half-life").
While a radioactive isotope decays almost perfectly according to so-called "first order kinetics" where the rate constant is a fixed number, the elimination of a substance from a living organism usually follows more complex chemical kinetics.
For example, the biological half-life of water in a human being is about 9 to 10 days,[9] though this can be altered by behavior and other conditions. The biological half-life of caesium in human beings is between one and four months.
The concept of a half-life has also been utilized for pesticides in plants,[10] and certain authors maintain that pesticide risk and impact assessment models rely on and are sensitive to information describing dissipation from plants.[11]
In epidemiology, the concept of half-life can refer to the length of time for the number of incident cases in a disease outbreak to drop by half, particularly if the dynamics of the outbreak can be modeled exponentially.[12][13]
In his Software that Fits in Your Head talk, Dan North defines the half-life of software as (I'm paraphrasing) "the amount of time required for half of an application's code to change so much that it becomes unrecognizable."
The upsides of a short code half-life are significant. Imagine how much better your life would be if your application's code always reflected the most accurate, up-to-date understanding of the problem at hand. Think about how much costs would go down if you never had to navigate dead code. Consider the value of having of an application that is free of speculative additions that were thrown in to support features that will never arrive.
Code is read many more times than it is written. Writing code costs something, but over time the cost of reading is often higher. Anyone who ever looks at a piece of code has to invest brain-power into figuring out what it does.
Dead code and speculative cruft make it hard to decipher the intention of code. It follows that you can reduce overall costs by optimizing code for reading rather than writing. The easiest code for subsequent readers to understand would be frugal, i.e. it would be simple, correct, and without embellishment.
I suspect, however, that I'm preaching to the choir. I suspect that you already believe everything stated in the prior paragraph. It's not that you disagree that it would be a good thing to have frugal code, it's that the applications that you work on are so far removed from this ideal that you despair of ever reaching it.
In my experience, most applications are a mess. Successful business rely on long-lived applications that endure a constant barrage of new requirements. Changes are commonly made under urgent time pressure, which drives applications towards disorder. As entropy increases, it becomes harder and harder to add features except by way of one more hack. The accumulated mess leads to hacks, hacks lead to more hacks, and then you're in a loop. Velocity gradually slows, and everyone comes to hate the application, their job, and their life.
If it makes you feel any better, there's a way in which having a big mess is a sign of success. The reason your competitors don't have messes is that they went out of business. You won, and your prize is an application that betrays the ravages of time.
And, as if that's not alarming enough, I fear that the coding culture that led to your current success may be dooming you to future failure. If your existing application impedes change, nothing good will come of doing more of what you've done. If this is the state you're in, it's time to change how you write code.
The parts of your applications that change the most also cost the most. These dynamic parts are often fundamental to your business. They are the result of lengthy, evolutionary development, and suffer from never ending churn. You depend on them the most, yet they are hard to understand, and only getting worse.
Vast other swaths of your application are likely equally unpleasant, but relatively stable. This stability essentially makes them free. It's not ugly code that costs money--it's change. Ugly code just exacerbates costs.
Time is in appallingly short supply. The good news, however, is that you're not obligated to fix things that aren't costing you money. The most efficient way to improve long-lived applications is to focus on the code that churns--this is where your efforts most pay off. For maximum effect, commit to crafting solutions that are both frugal and easily replaceable.
The last item above is key. Code that isn't easy to replace doesn't get replaced, instead it gets expanded. Its conditionals get bigger. The number of class names it knows about grows larger. These sorts of expansions tightly couple the code you're changing to other parts of your application. This coupling makes it difficult to swap in alternative implementations, which it turn leads to a long half-life for the code.
Unstable code that has a long half-life inevitably accumulates cruft. This complicates the code, and programmers hesitate to neaten what they don't understand. The trick to maintaining frugality over the course of many changes is to insist on code that's easily replaceable. Achieving replaceable code necessitates developing a culture that values polymorphic objects and loosely-coupled code.
You have a bargain with other programmers about how you will write code. Your current application is this bargain made manifest. If you're finding that the original pact has outlived its usefulness, the first step to improving your life is to start talking to one another about how you wish you were writing code. Dan's talk, and the idea of the half-life of code, can spur this discussion.
The 2nd Edition contains 3 new chapters and is about 50% longer than the 1st. Also, because 99 Bottles of OOP is about object-oriented design in general rather than any specific language, this time around we created separate books that are technically identical, but use different programming languages for the examples.
99 Bottles of OOP is currently available in Ruby, JavaScript, and PHP versions, and beer and milk beverages. It's delivered in epub, kepub, mobi and pdf formats. This results in six different books and (3x2x4) 24 possible downloads; all unique, yet still the same. One purchase gives you rights to download any or all.
Half-life in the context of medical science typically refers to the elimination half-life. The definition of elimination half-life is the length of time required for the concentration of a particular substance (typically a drug) to decrease to half of its starting dose in the body. Understanding the concept of half-life is useful for determining excretion rates as well as steady-state concentrations for any specific drug. Different drugs have different half-lives; however, they all follow this rule: after one half-life has passed, 50% of the initial drug amount is removed from the body. The characteristic decreases of drugs over time have long been studied in a field known as pharmacokinetics and are depictable by basic differential equations. Most clinically relevant drugs tend to follow first-order pharmacokinetics; that is, their drug-elimination rates are proportional to plasma concentrations.[1] In contrast, a few drugs follow zero-order elimination in which the drug amount decreases by a constant amount over time regardless of initial concentration (i.e., ethanol). This article will focus on first-order half-life elimination as it is the most frequently encountered in clinical practice.
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