Saturday, January 26, 2013

Day 12 - Fundamentals of Physics - 1.6 Estimations and Order of Magnitude

You are welcome to check out my previous blogs within the series “Fundamentals of Physics

In physics, as in life, we find ourselves having to make estimations in order to get an approximation as a general view of the situation, we might not have all the accurate details, we actually never do - thus, everything in physics is only accurate up to a degree of error, this degree of error can be anywhere from small to big where as in every situation we will demand or compromise on a different degree of accuracy / error.

Physicist love approximations, in this chapter we will speak of estimations within the quantity as the order of magnitude, this is similar to what we discussed in chapter 1.4 Dimensional Analysis, where we had to use our common sense in understanding the dimensions of the quantity / problem, as the nature of the quantity and the relationships within the problem, to gain more access to it as an initial step in solving the problem - here, in this chapter we are looking at a different form of estimation, here the estimation will be in regards to magnitude, as we outline a general size / amount / quantity, and thus are able to have more access to understanding the situation, in regards to the size / amount / quantity

When we speak of "order of magnitude" we are referring to the power of 10, how many time 10 multiples with itself - though again, like we've seen before - this is a random choice and has no profound physical meaning, it is just very convenient to calculate within the decimal system, as the power of 10 is: 10, 100, 1000, 10000 and so on, as well as 0.1, 0.01, 0.001 … and so on - you will find this method to be very easy and practical. For those that are not familiar with this - a simple way to know what is the power of magnitude of a number is to count how many digits it has, before or after the decimal dot, and depending if the number is larger than 1 or if it is a fraction, thus between 0 and 1.

For instance, the number 123,345,456 - we will first round this number down to be 100,000,000, a much easier number to work with, and in regards to the order of magnitude both 123,345,456 and 100,000,000 have the same order of magnitude, the same amount of digits, if you will - now lets count how many zeros appear after the initial digit -we have 1 and 8 zeros following, thus the order of magnitude is 10 in the power of 8.

We can do the same with fractions, 0.1 is 1/10, thus we can say it is equal to 10 in the power of (-1), 0.01 is 10 in the power of (-2), and so on, so now lets take it into practice, lets take for instance the number 0.000976 - we will round this number up to be 0.001 and now it's clear to see that the order of magnitude is 10 in the power of (-3).

You might ask yourself, "but, now that we do all our calculations on the computer why would we need to round the number if the computer can make an accurate calculation? that's true, this exercise will be implemented when you are not using a computer, as you are just organizing the information and making the general estimations and approximations, and you don't want to be distracted by the specific numbers, because maybe it doesn’t matter if it's more or less a few thousand when you are speaking of billions, so it gives you the opportunity to have a clean number to work with, without losing the relevant data, which is the order of magnitude rather than the exact number.

Estimations in physics is a cool tool to use in order to understand the general outline of a problem without having to go through, look for, or calculate all the specific details - then, once we have the approximation we can determine if we require to investigate any further to find a more accurate and precise solution.

Speaking of the order of magnitude is very relevant when comparing two quantities, as it will show if they are in the same order of magnitude, thus, approximately the same size, or if there are a few orders of magnitude difference, this is relevant in physics because many times if there is a big difference in order of magnitude one can decide to neglect the small quantity because it is too small in comparison to the bigger one and thus is considered to have close to zero effect on the problem - we saw this when we discussed the atom, as we saw that the proton's mass is 2000 times larger than the electrons mass, and thus when calculating the mass of the atom we ignore the mass of the electron because it is three orders of magnitude smaller and thus irrelevant. Of course there might be some calculations that the level of accuracy must be higher and then they will be as accurate as possible, it depends of the need of the experiment. Another example to grasp this point is money, if you have 1004 dollars, the 4 dollars seem insignificant, as they are 3 orders of magnitude smaller, same would be if you had 75 million dollars, or if you had 750 million dollars, the difference is only one order of magnitude and see what a big difference it does, an the other hand if you have 75 million dollars and then lost some money and have now 69 million, it's in the same ball park, same order of magnitude.

Once you get the simplicity and practicality of this method you can take on real life problems and estimate them roughly to gain access and insight into the point. Such as, how many people can the earth sustain - ask yourself what information you will need and research it, such as how much surface of productive soil does the earth have, how much land it takes to feed one person for a life time - gather the information and round it up, multiply the relevant quantities and figure it out.

As I've said in my previous blog, a number, an amount, rarely has any value if it is not placed in relation to something, thus, when we are given a number, in order to give it meaning we must compare it to something, for instance, if we want to know how many people are malnourished in the world we will find that it is estimated to be 925 million people which can be expressed as the approximation by saying that the order of magnitude of 10 in the power of 9, though It's hard for us to even grasp how much that really is - so lets see if we can get an idea through relating it to other amounts that we are more in touch with: The most populated city in the world in Shanghai, populating approximately 18 million people, the order of magnitude is 10 in power of 7, that is 2 orders of magnitude less than the order of magnitude of hungry people in the world - so you can imagine that if you take all the people in Shanghai 100 times, that is the amount of people that are malnourished. New York City's population is approximately 10 in the power of 6, that would mean to take all the people in New York 1000 times and deprive all of them of nourishment, or take a school of children, we can estimate a school has about 1000 kids in it, so the amount of people that are malnourished in the world is equal to the amount of kids in 100,000 school full of children being hungry - just to try and grasp how many people are malnourished - you should know that in all of the united states there are less than 100,000 public school, this means that there are more people starving in the world than there are students in USA - that's an insanely large amount of people - now, wouldn't you say that if we can calculate this, and grasp how many people we're talking about, don't we now have a responsibility to find solutions - we can use our common sense, and can now calculate within making rough estimations within finding our the order of magnitude of land we need, of founding we need, how much we need to limit our consumerism and / or the destruction of our land, and so on.

By using estimations we can take responsibility and educate ourselves through using common sense to assist us in becoming more aware of what is going on here, in our reality - when we hear that in South Africa alone, a woman is raped every 17 seconds - you can now make an approximate calculation and find out how many women are being brutally raped every year, you can calculate how many have been raped through out your life time, you can compare this number to the population of your city and assess how many of your cities would it take to reach that insane amount of tragic abuse - now that these numbers have more of a personal meaning you can ask yourself what can be done, how can we change this - but obviously you couldn't have asked yourself that before you knew the extent and vastness of the problem. Thus, it is each of our responsibility to utilize the tools provided to us, to investigate our reality, to get ourselves out of the bubble we comfortably exist in, within justifying that we do not know, and that it's difficult calculations, because through any thread of data that comes your way you can utilize critical thinking, ask yourself questions, don't take the numbers / quantities for granted, make yourself familiar with what that number means to you, find a way to reach that order of magnitude through value and quantities from your life experience, become aware of what is here as the first step towards taking self responsibility for it.

This is a cool tool to utilize because in many cases we find ourselves overwhelmed with the vastness of information, and we can thus justify not approaching a problem because we don't have enough information, or that we can't see the exact details, or that we are simply intimidated by these big numbers - this method shows us that we can approach any problem with the data that we have, and through utilizing the power of magnitude estimated approximation, we can come closer to understanding the problem - we don't know what will open up once we start investigating, thus we mustn't allow the experience of overwhelmingness to direct us, limit us, and prevent us from using what we do know, to approach any problem or situation that presents itself.

When walking the desteni process we find ourselves in such situations many times, where we see a pattern we participate in, but at a first glans it appears to be too big and too detailed and we don't have access to all the points within it, so many times we will push the point away within justifying that we cannot see it yet, though, within the principle of estimated approximations, we now know that whatever information we do have is within our responsibility to explore and investigate, knowing that we will not come to the final solution from the get go, though knowing that within this initial investigation we will be able to see the problem from a new perspective, as we will be able to see one more layer of depth into ourselves - whatever will open up we do not yet know, thus we have a responsibility to explore it, and from what open us, even though it is a generalized estimated approximation, we will be able to move to the next step and the next step and so on, until we are satisfied that we "hit the spot", that we see our participation and responsibility within and as the pattern / character / behavior - thus we walk this process one step at a time, using what we have access to, as true scientists, dedicated to turn every rock until we have turned the one that will lead us to the next phase of our investigation.

Within walking process, many being participate in the "I don't know" or "I can't do this" characters - we must realize that yes, at the moment we "do not know" but it is merely because we are not allowing ourselves to truly investigate in self honesty and actually find out - not realizing that we must take that first step, that first leap into the, what seems to be, unknown, as we will find that within ourselves, in self honesty we have known all along, but we have masked ourselves from seeing ourselves - thus, we must allow ourselves to start, as in a generalized estimated approximation - if I don't know exactly what I am feeling / experiencing / thinking / remembering, I will find the general experience / feeling / memory, and investigate it, as what is here, within realizing that only through walking the point will the next point / layer open up and thus, we cannot expect to know before we have set foot I the journey to life, as exploring and investigating ourselves into the unknown, to come out of it a living expression of "know thy self".

Thus, feel free to make approximations and estimations as you walk the process in order to gain access to the next, deeper layer of yourself, commit yourself to open up what is here and not follow blindly the experience of overwhelmingness, but rather realize that it is a process, and as the physicist you must start with the approximation, and then become more and more specific until you are self honestly satisfied that you are done with the point, and move on to the next.

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