Today I gave a math lesson to my five-year-old son and stumbled upon a mathematical property that I did not know of. It turns out that any square number is a sum of two triangular numbers. My experience illustrates that the best way to form abstract ideas is to start with concrete examples.

During the lesson, I used these two toys: Subtraction Abacus by Melissa & Doug and MathLink Cubes by Learning Resources. They were helpful to see the patterns.

Subtraction Abacus by “Melissa & Doug”

One-sentence summary: I explain why an exponential scale was invented, and how it compares with the older scales based on ratios of integers.

It is the continuation of the article on the mathematical nature of musical scales. In that article, we have used ratios to come up with a division of an octave. We have given Latin names to musical intervals (or ratios of frequencies): Octave as 2/1, Tertia as 5/4, Quinta as 3/2, Quarta as 4/3, Tone as 9/8, and Semitone as 16/15.

In American English, the tone, tertia, quinta, and quarta intervals are familiarly known as second, third, fourth, and fifth notes of a basic scale. However, I will use the Latin names for reasons described in the previous article. …

Blaise Pascal studying the cycloid, 1785, Louvre

Here is the story of how I became an atheist and stopped fearing God. My transformation occurred through exposure to three philosophical ideas over several years. The first idea was that I could rely on my mind rather than on a say-so of experts. The second idea was that arbitrary claims do not require proof. And, the third idea was that one should hold his knowledge at certainty rather than at 99% probability. I have learned all three from Ayn Rand and Leonard Peikoff.

I have considered myself to be an atheist even before this transformation. I grew up in…

Raised by Wolves is a science fiction TV series directed by Ridley Scott, the same man who directed Blade Runner. The setting is a devastating war between Mythraics versus atheists. I was intrigued the moment that I heard of a show about atheists, and rushed to buy an HBO subscription to watch it.

The historical Mithraic Mysteries was a mystery religion that competed with Christianity in the 3rd century CE. It was based on the god of the sun Mythras whom the Romans imported from Persia. …

This article goes into technical details concerning Elliptic Curve encryption.

Public and private key cryptography is a recent invention from the late seventies that did not occur to our creative predecessors. Instead, they relied on symmetric encryption schemes which requires both sides to know the encryption key.

The earliest of such schemes is Scytale, a device first mentioned in 7th century BCE by the greek poet Archilochus. In this scheme the secret was in the width of the stick on which a strip of ciphered text is rolled on.

Scytale (image from Wikipedia)

Since then there were a series of innovations in the complexity…

At Smarking, we use the Amazon Web Services (AWS) infrastructure. We help organizations improve the efficiency of parking lots, and to do that we need to communicate with their computing systems. However, these organizations, which include hospitals and universities, often run closed private networks. Outside vendors like us may access those networks only through an IPSec-based VPN.

Is it possible to create an IPsec tunnel from an AWS Virtual Private Cloud (VPC) to a network outside of AWS? The use case that AWS supports well is connecting your own on-premises network with the VPC. Thus, in naming components, AWS uses…

Religion is a Ponzi scheme, whose currency is faith. And, I am not talking about money. Although money is a key factor driving religion, I want to focus on faith alone. There are two levels to my claim.

The first level is individual. The longer a person stays within the confines of faith, the harder it is for him to admit that it’s wrong. But, his own rationality, which he still has and uses in daily affairs, continues to challenge him. Consequently, he must buy-in even more into faith. This is a never-ending cycle which bursts when he is in…

Names of keys on a piano

One-sentence summary: In this article I will explain the math for the Just intonation and Pythagorean tunings for the diatonic major scale (all the white keys on the piano).

In the preceding article The Physical Nature of Musical Sound I have talked about how air vibration affects a human eardrum and causes the perception of sound pitch. I used a piano as a case study, noting that there are metal strings inside the piano that vibrate at different rates. The vibration frequencies to which the strings should be tuned, is the subject of this article. …

At Smarking we receive data from third-party vendors. This data comes in various formats: XML, CSV, Excel, PDF, and JSON, and we use an Extract-Transform-Load (ETL) process to store the data in our database. This kind of ETL process is used by many organizations that ingest data from external sources. What are the security considerations pertaining to this process?

The security issue is that a third party may unintentionally provide data laden with exploits. This can happen if the third party accumulates but does not filter free-form data submitted by users. Such data may include names, street addresses or free-form…

Whitfield Diffie and Martin Hellman are researchers who invented a safe method to communicate a password. Their 1976 paper opens with the following:

WE STAND TODAY on the brink of a revolution in cryptography.

The development of computer controlled communication networks promises effortless and inexpensive contact between people or computers on opposite sides of the world, replacing most mail and many excursions with telecommunications. For many applications these contacts must be made secure against both eavesdropping and the injection of illegitimate messages. At present, however, the solution of security problems lags well behind other areas of communications technology. …

Boris Reitman

The course of history is determined by the spreading of ideas. I’m spreading the good ones.

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