# Category Archives: 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 models and theories that are complimentary. I am not talking about complimentary theories. We … Continue reading

Posted in physics, tutorial |

## 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

Posted in mathematics, tutorial | Tagged , , ,

## 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 ab  = e(a ln(b)) Using this rule we can compute i raised to the power of i ii = e(i ln(i)) = e(i πi/2) = e(-π/2) = 0.207879576…. remember that ln(1)=0 ln(i)= iπ/2 and

Posted in mathematics, tutorial | Tagged

## 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

Posted in tutorial | Tagged ,

## 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 |

## Tutorial

LaTex Book Template with Fancy Header What is Dimension? Uncertainty is highest at 50:50 odds Notes on Galactic Motion How to compute standard deviation in one pass Conditional Probability Platonic Solids Revisited How to insert vertical space in the WordPress … Continue reading

Posted in tutorial | Tagged

## Essays by Suresh Emre

A new synthesis of Spiritual Philosophy is presented in Definitions and Summary of Soul Monism I volunteer for the Renaissance Universal (RU) movement. A Vision for a Universal Renaissance. The complete list of my articles is given in http://sureshemre.wordpress.com/index/

## 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

Posted in tutorial |

## 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

Posted in tutorial | Tagged

## 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

Posted in physics, tutorial | Tagged ,

## 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

Posted in tutorial | Tagged

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

Posted in tutorial | Tagged , | 1 Comment

## 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

Posted in tutorial | Tagged , , ,