“Thoughts are things.”
Yes, there is much “evidence” that thought is the incipient evidence of things to come. Thought, then, is the literal foundation stone of all we will ever know, be or have.
A simple example is answering the question, “What would you like to order?” You respond by reading the menu item which names your desired meal — a written thought — and soon that food you named is handed to you on a plate.
Another example is the professional who is asked, “When did you decide you wanted to be an engineer / doctor / captain?” The answer is very often recounted as a long-ago thought, formulated in the mind of a small child who had no access to anything but her own imagination, where she formed and nurtured the thought.
And, what of the person who opens a sailing magazine, sees a boat he’d like to own, and he begins to tell himself and then to tell his friends, “I’m going to have a boat like that.” And, five years later, when he is entertaining those same friends on his new boat, the thought has become the thing that initially resided only in the thought, acknowledged and said to himself at first.
“Thoughts are things.”
In the very least, they are the beginning of things. For, thinking turns our attention toward what we think about, to the exclusion of other things and shines a brighter light and focus upon that subject of our thinking.
Now, this can be a promise or a threat, depending upon where we are getting our thoughts and toward what outcome we are looking.
Sometimes, when we are looking in a scary direction, we become fixated by sensitization to stare at what we don’t want to have happen. Yet, our forever thinking mind continues to contemplate, then ruminate and brood, upon the object of our attention. Following this, it is not uncommon to feel fearful that we are condemned to reaping that thought’s unlovely harvest.
Here’s a how to look at this in a way that keeps the mind free and untroubled by the incessant ebb and flow of thoughts. Consider that in order to keep a thought constant in the mind, a lot of energy must continually be injected into the thought. To do this, requires the person to continually turn her attention in the direction of the thought and think it again. To do this, often takes getting into a similar emotional state as before, use the same or similar words, and envision the same unlovely outcome.
To do this – to put all of this energy and take all of these steps reanimating the thought in our minds about an outcome we do not want to experience — is exhausting. Unfortunately, when the mind feels exhaustion, it is less capable of shifting into a new perspective and will yield to a dominant, persistent thought it has become familiar with.
The good news is, the inverse is as true. As we turn from the invitation to ruminate or think again and again about an unlovely outcome, we treat the thought just like nature treats a radioactive substance: by withdrawing energy from it, it quickly loses its power over us by half lives.** In the case of a thought, that energy is in the form of attention, which we simply, now, focus in another direction. A thought robbed of supportive energy, dissolves, diminishes and ultimately disappears simply from lack of attention.
And, lastly, to ensure that we become as fixated on the new other direction as we had once been on the old thought, allow yourself in idle moments to live in and animate the desired outcome. See it, feel it, taste it, smell it and hear it.
And doodle it. Make yourself a doodle-a-day. Every day, make a quick-sketch doodle that represents all of, or some aspect of, your desired outcome.
Any time your mind avers and heads in the direction of what you do not want, pull out your doodle and give it your attention for half a minute. That’s all you need to disrupt an unlovely thought from taking hold of your dear mind. Thirty seconds of your attention just calmly looking at your doodle-a-day. Just like a captain at sea or a pilot in the air, do this simple course correction and be assured that you are destined to reach the port of your heart’s desire.
** Probabilistic nature of half-life
Simulation of many identical atoms undergoing radioactive decay, starting with either 4 atoms per box (left) or 400 (right). The number at the top is how many half-lives have elapsed. Note thelaw of large numbers: With more atoms, the overall decay is more regular and more predictable.
A half-life usually describes the decay of discrete entities, such as radioactive atoms. In that case, it does not work to use the definition “half-life is the time required for exactly half of the entities to decay”. For example, if there are 3 radioactive atoms with a half-life of one second, there will not be “1.5 atoms” 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%.
For example, the image on the right 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.
There are various simple exercises that demonstrate probabilistic decay, for example involving flipping coins or running a statisticalcomputer program.
Formulas for half-life in exponential decay
An exponential decay process can be described by any of the following three equivalent formulas:
- N0 is the initial quantity of the substance that will decay (this quantity may be measured in grams, moles, number of atoms, etc.),
- N(t) is the quantity that still remains and has not yet decayed after a time t,
- t1/2 is the half-life of the decaying quantity,
- τ is a positive number called the mean lifetime of the decaying quantity,
- λ is a positive number called the decay constant of the decaying quantity.
The three parameters , , and λ are all directly related in the following way:
where ln(2) is the natural logarithm of 2 (approximately 0.693).
|[show]Click “show” to see a detailed derivation of the relationship between half-life, decay time, and decay constant.
By plugging in and manipulating these relationships, we get all of the following equivalent descriptions of exponential decay, in terms of the half-life:
Regardless of how it’s written, we can plug into the formula to get
- as expected (this is the definition of “initial quantity”)
- as expected (this is the definition of half-life)
- , i.e. amount approaches zero as t approaches infinity as expected (the longer we wait, the less remains).
Decay by two or more processes
Some quantities decay by two exponential-decay processes simultaneously. In this case, the actual half-life T1/2 can be related to the half-lives t1 and t2that the quantity would have if each of the decay processes acted in isolation:
For three or more processes, the analogous formula is:
For a proof of these formulas, see Exponential decay#Decay by two or more processes.
There is a half-life describing any exponential-decay process. For example:
The half life of a species is the time it takes for the concentration of the substance to fall to half of its initial value.
Half-life in non-exponential decay
Main article: Rate equation
The decay of many physical quantities is not exponential—for example, the evaporation of water from a puddle, or (often) the chemical reaction of a molecule. In such cases, the half-life is defined the same way as before: as the time elapsed before half of the original quantity has decayed. However, unlike in an exponential decay, the half-life depends on the initial quantity, and the prospective half-life will change over time as the quantity decays.
As an example, the radioactive decay of carbon-14 is exponential with a half-life of 5730 years. A quantity of carbon-14 will decay to half of its original amount (on average) after 5730 years, regardless of how big or small the original quantity was. After another 5730 years, one-quarter of the original will remain. On the other hand, the time it will take a puddle to half-evaporate depends on how deep the puddle is. Perhaps a puddle of a certain size will evaporate down to half its original volume in one day. But on the second day, there is no reason to expect that one-quarter of the puddle will remain; in fact, it will probably be much less than that. This is an example where the half-life reduces as time goes on. (In other non-exponential decays, it can increase instead.)
The decay of a mixture of two or more materials which each decay exponentially, but with different half-lives, is not exponential. Mathematically, the sum of two exponential functions is not a single exponential function. A common example of such a situation is the waste of nuclear power stations, which is a mix of substances with vastly different half-lives. Consider a sample containing a rapidly decaying element A, with a half-life of 1 second, and a slowly decaying element B, with a half-life of one year. After a few seconds, almost all atoms of the element A have decayed after repeated halving of the initial total number of atoms; but very few of the atoms of element B will have decayed yet as only a tiny fraction of a half-life has elapsed. Thus, the mixture taken as a whole does not decay by halves.
Half-life in biology and pharmacology
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 in blood plasma of a substance to reach one-half of its steady-state value (the “plasma half-life”).
The relationship between the biological and plasma half-lives of a substance can be complex, due to factors including accumulation in tissues, activemetabolites, and receptor interactions.
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, though this can be altered by behavior and various other conditions. The biological half-life of cesium in human beings is between one and four months. This can be shortened by feeding the personprussian blue, which acts as a solid ion exchanger that absorbs the cesium while releasing potassium ions in their place.