# Category Archives: tutorial

## Quick reminders about the leap day

I explained the difference between the sidereal day and the solar day in a previous post (one of my popular posts). A sidereal year is the time taken by the Earth to orbit the Sun once with respect to the fixed … Continue reading

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## How to archive a blog

I care deeply about the preservation of self-expression.  Archiving people’s labor of love and preserving them for posterity is good for society. With commercial art, music and writing there are more avenues for preservation but nobody cares about archiving the … Continue reading

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## Parity transformation changes helicity

This post is the continuation of the Parity Transformation tutorial where I demonstrated the parity transformation in 2D by using the shape of letter L. Figure (1) The image to the left of the vertical axis is the reflection of the letter … Continue reading

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## Parity Transformation

In physics “parity transformation” is a special kind of reflection. Parity transformation cannot be expressed as a rotation. Do not confuse the parity transformation in physics with the parity concept in mathematics. Let be a function and the parity transformation … Continue reading

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## On the photon frequency

Image credit We know photons exist. We also know how to manipulate photons collectively. Our technology has now advanced to the level where we can even manipulate the individual photons. But, if you ask me “what is a photon?” I … Continue reading

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## Network Externalities

When I first heard the term “network externalities” I was kind of embarrassed that I did not know the meaning of this cool sounding term. The person who mentioned it to me said that it was a term used in economics. Later, … Continue reading

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## Difference between duality and superposition in physics

This is a follow-up on an earlier posting titled “Meaning of Duality in Physics.” I request that you read that article first. The reason is that the the meaning of “duality” in physics is very different from the common meaning … Continue reading

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## Superposition Principle of Quantum Mechanics

Classical superposition principle Classical waves pass through each other. For a medium with linear restoring forces, any local displacement of the medium will be equal to the displacement represented by the linear combination of the displacements produced by the interfering … Continue reading

## π Day

March 14 is the day. Coincidentally, March 14 is also the birthday of Albert Einstein. The best encyclopedic resource for anything related to mathematics is Wolfram MathWorld which is created, developed and nurtured by Eric Weisstein. I have tremendous respect … Continue reading

Posted in mathematics, society, tutorial

## Circular Resonators

I would like to bring your attention to the wonderful educational web pages maintained by Jens Uwe Nöckel http://pages.uoregon.edu/noeckel/circles For me, the most important lesson was the fact that we can view (construct) a concentric circular wave as superposition of … Continue reading

Posted in physics, tutorial |

## Light reflecting off water is polarized

The glare which is due to the polarization of the reflected light by nonmetallic surfaces bothers people but sometimes it turns into a blissful vision. Image credit: unpolarized light bouncing off the surface of water becoming horizontally polarized. I enjoyed … Continue reading

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## QM wavefunction and its many interpretations

Mathematical formalism known as Quantum Mechanics (QM) describes the outcomes of measurements performed with elementary particles when they interact with each other or external fields. Measurement is the key concept in QM. Measurement is like taking a snapshot of the … Continue reading

Posted in philosophy, physics, prediction, probability, science, tutorial

## Short Descriptions of Quantum Field Theory

Lisa Randall Warped Passages, Harper Perennial (2005) “Quantum field theory, the tool with which we study particles, is based on eternal, omnipresent objects that can create and destroy those particles. These objects are the ‘fields’ of quantum field theory. Like … Continue reading

Posted in physics, tutorial |

## Geometric Algebra (1)

Geometric algebra is not to be confused with algebraic geometry. Geometric algebra is also known as Clifford algebra which has many applications in physics and engineering. Algebraic geometry, on the other hand, is a branch of abstract mathematics. Geometric algebra … Continue reading

Posted in mathematics, tutorial |

## Save these physics tutorials (2)

I am very physics focused these days. It is too bad that I am not an academic physicist and I have to work 1o hours a day on boring subjects to make a living. It is a shame that academic … Continue reading

Posted in physics, tutorial

## Save these physics tutorials (1)

There is redundancy in the mathematical description of physical reality. The redundancy has been increasing exponentially since the beginning of the 20’th century. We have different theories to describe the microscopic and macroscopic phenomena, for example. I am not talking … Continue reading

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## Geometric interpretation of sqrt(-1)

I wrote a post titled Euler rule is almost mystical where I mentioned the Cotes-Euler identity Euler rule is a special case of the Cotes-Euler identity. represents the rotations of the complex unit vector. This provides a natural interpretation for … Continue reading

Posted in mathematics, tutorial |

## Biquaternion

In the previous post we have seen that a quaternion is defined as where and , , , are real numbers. Biquaternion The biquaternion is a complexified quaternion where , , , are complex numbers. The basis elements , , … Continue reading

## Quaternion

Quaternions are 4-dimensional generalizations of complex numbers. It can also be said that the basis elements , , of a quaternion are 3-dimensional generalization of the pure imaginary number . William Rowan Hamilton discovered quaternions in 1843. After many years … Continue reading

Posted in mathematics, tutorial |

## Golden Number and Lucas Sequence

The golden number is . There is extensive literature on the golden number which is also known as the golden ratio. The exposition in Wolfram Mathworld [http://mathworld.wolfram.com/GoldenRatio.html] is excellent. John Baez gave an interesting exposition [http://math.ucr.edu/home/baez/week203.html]. Mario Livio’s book “The Golden … Continue reading

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## Three-Leaved Rose

Simple is beautiful. This universal principle is valid in mathematics and geometry too! Equation for three-leaved-rose (trifolium) in polar coordinates is r = a cos (3θ ) where “a” is a constant and the angle θ is measured from the … Continue reading

Posted in geometry, tutorial |

## Phase enables relativity

Physicists are experts at assigning new meanings to the terms established in common language. I mentioned the term “dual” or “duality” before. In common language dual means two. In physics dual means equivalent. Physicists use the word “phase” in different … Continue reading

Posted in geometry, mathematics, physics, science, tutorial

## Euler rule is almost mystical

In his wonderful book “Road to Reality” Roger Penrose mentions that the Euler rule is “almost mystical” because it relates the 5 fundamental numbers 0, 1, i, π and e to each other. The Euler rule is a special case … Continue reading

Posted in mathematics, tutorial |

## i raised to the power of i

Remember the general rule Using this rule we can compute i raised to the power of i remember that and

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## How to insert vertical space in the WordPress editor

Sometimes it is necessary to control the vertical spacing in your WordPress blogs, especially around inserted pictures. My solution is the following: In the WordPress editor go to the HTML mode (the tab labeled as “Text”) and insert this command … Continue reading

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## Platonic Solids Revisited

I will not talk about Sacred Geometry. This is a tutorial on geometry. I guarantee that if you read this tutorial you will learn at least one fun fact that you did not know before. How many 3-dimensional geometric objects … Continue reading

Posted in geometry, tutorial |

## Conditional Probability

The concept of conditional probability is not properly taught in schools. Bayes formula is mentioned but the table technique is rarely discussed.  It is important to point out that the conditional probability table is an implementation of the Bayes formula. … Continue reading

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## How to Compute Standard Deviation in One Pass

Unbiased Estimator of Sample Standard Deviation The formula for the sample standard deviation is where N is the number of data points in your sample. The first formula is known as the unbiased estimator of sample standard deviation. This is … Continue reading

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## Notes on Galactic Motion

Our galaxy (Milky Way) is one of the spiral galaxies. Our solar system is located in one of the spiral arms. The Milky Way is like a flat disc (diameter: 100000 light-years, thickness: 1000 light-years). The thickness increases at the galactic center. Our … Continue reading

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## Uncertainty is Highest at 50:50 Odds

Bernoulli Experiments Experiments with only 2 outcomes are known as Bernoulli experiments. Examples are: Heads or tails in a coin toss Win or lose True or False Yes or No Binary code 0 or 1 The list is not limited … Continue reading

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Academic institutions in America are dominated by scientific materialists. This does not stop the courageous pioneer scientists who work on consciousness. Knowing the circumstances I cannot stress enough how courageous these scientists are.  One of these academicians is David Chalmers who … Continue reading

## On Information, Surface, and Volume

You may have read Michael Talbot’s book “The Holographic Universe.” He talks about two ideas: a) brain as hologram b) universe as hologram. In this article I will comment on the speculation of physical universe being a hologram. Talbot credits … Continue reading

Posted in physics, tutorial |

## What is Dimension?

I use the word “dimension” in my writing quite often. I did not get a chance to clarify what I mean by it. The word “dimension” has multiple meanings in various contexts and it is worth spending few minutes to … Continue reading

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## LaTex Book Template with Fancy Header

You can typeset books using LaTex which is free software. There is no free lunch, however. Installing the software and learning LaTex requires a lot of effort. Don’t be discouraged. Remember, you can produce publication quality books using LaTex. I … Continue reading

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