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This evening, the Newton School Committee and the Newton Teachers Association (NTA) bargaining teams reached a tentative agreement on a new four-year contract. The contract will require ratification from NTA members and a majority vote of the School Committee.

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Answer (1 of 37): Read this before applying to Newton school. Never ever join Newton school, I will share my experience below and you will understand why ! Let me share my experience….. I applied to Newton school after reading many many advertisements on Instagram. It&#x27;s a 6 month duration cou...

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The Newton School | 103 followers on LinkedIn. The Newton School is an innovative, private, non-profit elementary school in Sterling, Virginia currently serving students in K-8th grade. Our school focuses on students who may have a difficult time reaching their full potential in a traditional ...

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Ed. Department at Newton North High School. The course taught students how to produce biodiesel, make fused plastic bags, and grow algae that would later be processed into fuel. The biodiesel was sold to a recycling company as well as the community at large. This program was the first of its ...

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Think of a few random numbers. Numbers like 8, 12, 876, 93 ...These are random numbers in biology, and these seemingly simple numbers hold keys to the most profound mysteries of the universe--- ourselves. To be more specific (and less dramatic), not the numbers but the process through which numbers have been produced have serious implications. For example, one can ask some fascinating questions like Are these numbers really random? Am I likely to come up with the same numbers if asked for random numbers in the future? How does our brain produce these random numbers? Is it likely that the brain has just tagged a few numbers as random? Is there an algorithm involving random processes like rolling dice going on unconsciously in the brain? Are our thought processes free? Is there such thing as free will to start with? All of you would have rightly noticed that these are the questions for which we do not have satisfactory answers at the moment. Some of you would believe that science will ultimately find out the correct answers to these questions, and till then, there is no need to beat the bush and create hype. Most of you might not realize that science has a few answers and a few leads where a little more effort can answer some profound questions. At the end of this post, I will propose an experiment that you can perform at home to probe your thought processes. Meanwhile, let's talk about some random processes. Perceived randomness is not random Let’s look for random numbers in the mechanical world out there. These are the outcome of random processes like the toss of a coin or roll of a dice. There are other random phenomena like the number of red cars crossing an interchange in a day, the number of meteorites entering our atmosphere, etc. Then there is the output of (or any other routine of your favorite computer language). The last one is surely not random because it is the output of an algorithm. The algorithm will produce the same numbers if it starts its calculations from the same 'seed' number. These are, in fact, pseudorandom numbers.  Good for all practical purposes, but completely predictable and thus not exactly random. numpy.random.rand() Most of the randomness we experience in our lives is in fact pseudo-randomness, caused by the lack of information. Take the other example—the number of red cars crossing an interchange. The person waiting at the interchange may find the appearance of a red car as a random process, but a person having the live traffic view of the region through a satellite will know how many red cars will cross the interchange. The process, which is apparently random for one observer, is completely deterministic for another observer with more information. This is a general feature for most of the randomness we experience in our daily life. The apparent randomness is due to a lack of information. Now think of the toss of a coin. The result is again apparently random. But do you really think that we can fire a rocket in space and exactly determine when and where it will land on Mars but can not predict the outcome of the toss of a coin? Are the laws governing the motion of the rocket so different from the ones that determine the movement of the coin? Indeed it is not the case. The same laws of physics prevail in two cases. The only difference is that we lack precise information regarding the dynamics of the coin when it is tossed. Not that the information is not there. We simply do not bother with the effort of retrieving it and pretend that nature has made a random decision for whatever purpose the coin was tossed. Indeed the video footage of the first few fractions of a second of a coin just tossed through a fast movie camera can decode the dynamics of the coin and can predict the outcome of the toss. The same is true for the roll of a dice, your favorite lottery, or most of the random processes you can think of (pun intended). This is because the laws of nature we experience in our daily life ( for simplicity, Newton’s laws that we study in high school) are deterministic. If you know the initial conditions (positions, velocities) of the objects of interest and the forces acting on these objects, you can precisely determine the future dynamics of the objects. Anything appearing random in this domain is due to our lack of access to the information. The information is there. We just need better technology to record and process that information. Casinos may run out of business in near future when our smartphones will start predicting the outcome of the dice while it is still rolling. This means that in a couple of decades in the future, the toss of a coin and roll of a dice may not serve any more than does abacus today. We would have the required technology in our smartphones capable of resolving the dynamics of the coin in a fraction of a second and predict the outcome. A few quick snapshots of the roll of a dice and our phones will predict the outcome of the throw. Maybe there are people making such apps right now. Maybe there are people making money in this way right now. But for more humble ones like us, a natural question is how we will play casinos in the future? Or start matches? Or win lotteries? And for those of you, I present pure naked raw randomness--- quantum mechanics. Meet true randomness is a theory that deals with the description of nature at the most fundamental level. This is the level where we deal with the building blocks of matter and energy, atoms, molecules, electrons, photons, etc. At this level, nature behaves very differently from how it appears in our everyday life, as we will shortly see. Quantum mechanics A quantum coin Think again of the toss of a coin. But this time, it is a quantum coin, for example, the spin of an electron. Electrons are part of the building blocks of matter.  These are the genie we have released from the magic teapot with the difference that we can make more than three wishes. Everything around you that moves makes noises and is not a baby is running on electrons. The electrons have a property called spin. The measurement of the spin of electrons is quite easy. All you have to do is to pass the electron near a wedge-shaped magnet. The magnetic field of such magnet exerts a force on the electron, and the electron is deflected in one or the other direction depending on its spin. When the experiment to measure the spin of an electron is performed, we find that it has only two possible values. We label them as the head (spin-up) and tail (spin down), and we have got ourselves a quantum coin. If you now toss the quantum coin, you will again get a random output, either head or tail. But the difference from the classical (the one we discussed earlier) is that the indeterminacy is not due to any lack of information. We know everything there is to know about the electron, and still, there is no way to predict if the spin measurement will result in spin up (head) or spin down (tail). Every event in the quantum world is a roll of dice. This is in contrast to the classical coin, where randomness was due to a lack of information. This is the first mystery of nature at the quantum level. Nature does not allow us to know when and which fundamental interaction between the building blocks of matter and energy will take place. Every event happening at this level is a roll of dice. In fact, this aspect of quantum mechanics has been part of a lively debate since the beginning of the theory. Many people, including Albert Einstein, were not happy with the indeterministic description of events at the quantum level. You must have heard his famous quote, “ ”. He believed that the theory was incomplete and likely missing some hidden variables that would restore the classical world, like determinism in the quantum world, when added to the description. God does not play dice However, countless experiments in the last 100 years have ruled out the possibility of these hidden variable theories. And our best understanding of nature at the quantum level is the one provided by quantum mechanics, which in principle does not allow us to predict the outcome of the toss of a quantum coin. The key point up to this point is that for a classical random process, the information is present but may not be accessible, but the quantum process is inherently random. There is no missing information. Armed with this understanding of random processes in the classical and quantum worlds, we are ready to explore the really big questions in the biological world. First, you can appreciate that the free will absent in the deterministic world of classical laws can be restored thanks to the indeterminism in the quantum world. The only thing we have to explore is to look for quantum signatures in the brain's functioning. Many people have suggested this before, but present-day technology promises experimental verification. We might soon hear fantastic news from people doing quantum biology. Design in disguise? Then there is this other question that I wish to talk about. Consider life. There are two dominant theories regarding the emergence of life on this planet. Either we are part of some intelligent design, or life emerged on the planet as an accident, and through random mutations, it evolved into all the life forms we witness today (and sadly, the ones we have eradicated from the planet). Science naturally favors the second view. But most of the people who favor the scientific view do not realize that there is still the possibility of the design in their worldview. This is because we still have to determine if the processes causing mutation in a genome are governed by classical or quantum laws. If classical laws can satisfactorily model these mutations, then these are not random. These are deterministic processes for which the information, aka design, was already present. Whether someone had that information (The almighty God?) or not is a separate question and can be subjectively answered. What can be objectively ascertained is that a design was available. This is a unique perspective on the natural selection vs. intelligent design debate that a physicist offers. More research in quantum biology and exploration of quantum signatures in genetic mutations will tell if we are part of a design or result of truly random accidents. Quantum biology will reveal if we are designed. Lastly, I wish to propose an experiment to explore the thought processes as I promised. With some patience and a lot of courage, you can easily do this experiment at home. Take a piece of paper and write a few random numbers on it. Fold the paper and put it in a box. Put the box aside. Now, wait for a couple of weeks. Meanwhile, do not try to recall the numbers you have written. Obviously, do not open the box. After a couple of weeks, take another piece of paper, again write a few random numbers on it, and put it in the same box. Again wait for a couple of weeks and repeat. Over an extended period of time (say a year or six months), you would have a lot of folded papers in the box. Now open the box and look at all the random numbers you have written over time. Are they all random? Are there some favorite random numbers? Are there patterns? Is there a design?

Natural Selection Vs. Intelligent Design: A Physicist's Perspective

প্রাকৃতিক নির্বাচন বনাম। ইন্টেলিজেন্ট ডিজাইন: একজন পদার্থবিজ্ঞানীর দৃষ্টিকোণ

Natürliche Selektion vs. Intelligentes Design: Die Perspektive eines Physikers

Selección natural vs. Diseño inteligente: la perspectiva de un físico

Sélection naturelle contre. Conception intelligente : le point de vue d'un physicien

प्राकृतिक चयन बनाम. बुद्धिमान डिजाइन: एक भौतिक विज्ञानी का परिप्रेक्ष्य

自然選択 vs.インテリジェントなデザイン: 物理学者の視点

자연 선택 대. 지적 설계: 물리학자의 관점

Seleção Natural vs. Design Inteligente: A Perspectiva de um Físico

Естественный отбор против. Разумный замысел: взгляд физика

Doğal Seçilim Vs. Akıllı Tasarım: Bir Fizikçinin Perspektifi

Chọn lọc tự nhiên Vs. Thiết kế thông minh: Góc nhìn của một nhà vật lý

自然选择与智能设计：物理学家的观点

ISAAC NEWTON

MATHEMATICAL MEMORIES: NEWTON'S BINOMIAL THEOREM

Situations Given a number of total students in a school and you want to know if all the students fit in an assembly ground, you need to know how many lines need to be formed at a minimum. Given the dimension of a door, you need to know how big plywood can be passed through the door. You can’t do these without one thing — square root. Whether it is finding the square root of a number or square root of a sum of squares, a function (or command) to find the square root of a number is needed. Easy? OK, easy. We have built-in functions (or commands/buttons) in our calculators, computers, programming languages, mobiles and everywhere to calculate the square root. Yes, that can be done in a straight forward way. But what if you are in a place where electricity is not available and your gadgets are dead? Help me … Yes, I am rescuing you from that situation if the day comes. I am bringing your old friend Newton (and Raphson too), whom you loved a lot during your school days. Probably, some of you hated too seeing his name everywhere — from math textbook to physics textbook, from classical mechanics to heat and thermodynamics, and from optics to cubics. I remember his name in the GK book too. Algorithm Take a reasonable guess (approximate root) for the square root. Add the approximate root with the original number divided by the approximate root and divide by 2. x_i := (x_i + n / x_i) / 2 Continue step 2 until the difference in the approximate root along the iterations is less than the desired value (or precision value). The approximate root is the square root we want. Whiteboard demonstration Let’s see it in the whiteboard now with . n = 4 Fig: Newton method for calculating the square root of 4 It is well known that there are two square roots and we ignore the negative square root here. The negative square root can be calculated easily by taking the first approximation near to the negative square root. So, this is it — the recipe for the rescue — but I don’t stop here as my computer science, python, mathematics loving readers are expecting to see more. Let’s start with the Python code. Python r = x
    precision = ** ( ) abs(x - r * r) > precision:
        r = (r + x / r) / r : def mySqrt (x) 10 -10 while 2 return Why don’t you implement it in your system? Newton’s method Newton’s method, also known as Newton-Raphson method is a root-finding algorithm that produces successively better approximations of the roots of a real-valued function. The approximations of the root go as: x_(n+1) = x_n - f(x_n) / f’(x_n) is the rough approximation of the root done at the first and the successive approximations go as x_0 x_1, x_2, …. is the function whose root is to be determined and is the derivative of the function. f(x_n) f’(x_n) Description For a close enough approximation , the better approximation of the root typically can be found by drawing the tangent to the graph at and finding where the tangent intersects the -axis. x_n x_n x The equation of a line with slope passing through would be: m (x_1, y_1) y - y_1 = m (x - x_1) Here, the tangent is the line, derivative, , is the slope and is the point. f’(x_n) (x_n, f(x_n)) So, y - f(x_n) = f’(x_n)(x - x_n) As the better approximation will be of the tangent, put and solve for . x-intercept y = 0 x_n -f(x_n) = f’(x_n)(x - x_n) or, x - x_n = -f(x_n) / f’(x_n) So, x = x_n - f(x_n) / f’(x_n) ………………. (1) This is Newton’s method for approximating the root of a function, f(x). Let’s see now if we can come up with the algorithm provided above using the general formula. Newton’s method for square root If we have to find the square root of a number , the function would be and we would have to find the root of the function, n f(x) = x² - N f(x). Here, the value at is: f(x_n) x = x_n f(x_n) = x_n² - N And, the derivative at the point is: f’(x_n) = 2 * x_n Now, the better approximation can be found using (1). x_(n+1) = x_n - (x_n² - N) / (2 * x_n) x_(n+1) = x_n - x_n² / (2 * x_n) + N/ (2 * x_n) x_(n+1) = x_n - x_n / 2+ N/ (2 * x_n) x_(n+1) = x_n / 2+ N/ (2 * x_n) x_(n+1) = (x_n + N/ x_n) / 2 This is how the algorithm for finding square root of a number comes. Integer square root of a number Integer square root of a number is the floor of the square root. The algorithm can be modified a little to find integer square root of a number. The condition here would be . The algorithm terminates when the approximate squared is less than or equal to N. while approximate * approximate > N The iteration relation here is: where // is integer division. x_(n+1) = (x_n + N // x_n) // 2, Proof of correctness First, let’s prove the . correctness for the while condition The iteration relation is: x_(n+1) = (x_n + N // x_n) // 2 It can be written as: x_(n+1) = floor((x_n + N / x_n) / 2) For and . So, a ≥ 0 b ≥ 0, a + b ≥ 2 * sqrt(a*b) x_(n+1) ≥ floor(2 * sqrt(x_n * N / x_n) / 2) or, x_(n+1) ≥ floor(sqrt(N)) So, x_(n+1) ≥ intsqrt(N) Therefore, the value of the approximation never goes below the value of . intsqrt(N) Now, let’s prove that . the approximation is monotonically decreasing Let’s find the difference x_(n+1) - x_n. x_(n+1) - x_n = (x_n + N // x_n) // 2 - x_n As is less than or equal to (based on while condition), N // x_n x_n (x_n + N // x_n) // 2 ≤ (2 * x_n) // 2 So, x_(n+1) - x_n ≤ (2 * x_n) // 2 - x_n As is an integer, i.e x_n (2 * x_n) // 2 = x_n. x_(n+1) - x_n ≤ x_n - x_n So, x_(n+1)-x_n ≤ 0 Hence, the sequence is monotonically decreasing. {x_n} The values and are equal only when is equal to and that is when we find the solution and the while loop gets stopped. In all other cases, the sequence is strictly decreasing. x_(n+1) x_n N // x_n x_n {x_n} Hence, the correctness of algorithm to calculate the integer square root is proved. Numerical Analysis — EndNote Numerical analysis is the field of algorithms that use numerical approximation for the problems of mathematical analysis. Ranging from engineering and physical sciences to life sciences, social science, medicine, business, and arts, scientific computations are being applied everywhere. The rise in computing power has encouraged and enabled the use of realistic mathematical models in science and engineering and numerical analysis is required for the detailed implementation. This is an example of numerical analysis, where we use Newton’s method to calculate the root of the function. There are two things that excite me about numerical analysis. Complex functions and equations can be solved which otherwise would be unsolvable. The algorithms can be programmed and automated making the solution easier to implement, reproduce and package. Did you too find interesting? If so, comment here your favorite numerical analysis algorithm. numerical analysis

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