Archive for the ‘Patterns’ Category

Patterns in Society

One of the most intriguing things about Mathematics is the patterns that can be found within the subject. It is possible to use a formula from one equation across the board and apply it to something else. It certainly helped me to make sense of the subject when I was at school as there seemed to be connections woven throughout the area of Mathematics.

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Patterns have always fascinated me, and it’s interesting to look into previous events and try to predict what might happen in the future. In terms of society, the ‘Arab Spring’ is also something that I have become interested in over the last couple of years. It could be argued that the uprising across Africa and Western Asia stemmed from the War in Iraq, and the citizens of these countries were inspired by the overthrowing of Saddam Hussein.

From there, the citizens of countries such as Egypt and Libya revolted against their respective leaders, with varying degrees of success. The media is now obviously focused on events surrounding Syria and it remains to be seen whether there will be some sort of intervention from outside forces; of course this all depends on the Western media’s portrayal of the issue.

The uprising in Egypt was generally successful, compared with that in Libya. Although the majority of the people of Libya, and Western leaders, got what they wanted, there is still unrest in the country where opposing forces are still fighting and the newly appointed provisional parliamentary republic is having trouble enforcing their control on the country.

It is important to look at the patterns of the past to determine what the future holds for the country of Syria.

Further Information

Harry Collins – Using a VPN to Communicate in Middle East and Africa – US IP Proxy

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Military Pay Chart a Marvel of Mathematics

This 2013 military pay chart is the result of a complicated algorithm of pay considerations based on a members rank and length of service.  The charts origins are a feat of mathematics.

Military pay charts are available through multiple different websites. However, understanding or locating all the different types of pay and allowances can seem like an overwhelming task, because currently there are over 70 different types. The most simple and straight forward to locate is the base pay chart.

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Whether the active duty member is enlisted, commissioned officer, or a warrant officer the different ranks equate to a pay grade. The pay grades translate uniformly across all the different branches of the military. Beyond the individual’s pay grade, the amount of time in service is also a factor of pay. For every two years of service the active duty member receives a slight increase in pay. This last bit of information can be difficult to decipher because after certain number of years a pay grade will hold steady until the end of the chart. The reason for this occurrence is that if a member is unable to attain the next higher pay grade, then the individual is discharged from service. It works in a similar way to some European forces, in particular check out the French armed forces, although you’ll need a French IP address to check online.

The pay grade will traditionally appear on the left side of the chart in descending order the hierarchy, while the time in service will appear along the top running from left to right, least to greatest. To obtain a member’s base, simply locate his or her pay grade on the left, and follow the row over until the column that reflects time in service is attained.

However, base pay is not the entirety of what an active duty member’s Leave Earning Statement, LES, reflect for the monthly monetary amount paid to the individual.  Military members are entitled to Basic Allowance for Subsistence or BAS which can be found on a different chart.

Basic Allowance for Housing, also known as BAH, is paid to the active duty members that have earned the privilege to not be required to live in the barracks. Since, the different military bases/posts and duty stations are located in areas that have varying costs of housing prices, BAH amounts will increase or decrease depending on the surrounding area’s market. In addition, large sums of BAH are allotted to the individuals that have achieved higher ranks, and there is difference in the amount between a single active duty member with no dependents, and one that has dependents. It should be noted that having additional dependents beyond one will not increase the amount BAH.

Cost of Living Allowance, or COLA, is also meant to help the active duty member be able to maintain living in areas where the cost of living is higher than the base pay, and all the other allowances could sustain. When changing duty stations, both the amounts allotted for BAH and COLA should be understand so that the member can understand the options for housing.

Finally, there are Special Pay(s) that certain active duty members warrant. Some occupations within the armed services are deemed more hazardous than others. Thereby, all who perform these occupations are entitled to hazardous duty pay. When active duty members go into combat zones, they are awarded combat pay, and there are many more allowances and pays. For this reason the military pay chart quickly becomes a complex thing to understand.

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The Science Behind Loan Amortization

Understanding how loan amortization works can be a bit tricky, even for math-minded individuals.

These days, most people would rely on mortgage amortization in order to repay all their debts. Mortgage amortization is considered as a situation where the principal balance of a mortgage is gradually reduced over time as the borrower makes monthly or periodic payments. However, some people find it difficult to keep up with the scheduled payment for amortization. This causes delays and more expenses on the part of the borrower. Fortunately, there are already several tools that can help people manage their monthly amortization payments properly and on time.  Depending on where you live they should be accessible but it might be worth investing in as smart DNS proxy if you are getting blocked at all.  One of these tools is none other than the famous amortization calculator.

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Understanding the Use and Function of Amortization Calculators
An amortization calculator is a very useful tool that can help you make payment schedules that are easy to follow. The calculator can provide a detailed table of your amortization that can be used to keep you updated with your repayment. All you have to do is to enter all the features of your mortgage, which includes the amount of the loan, the interest rate, the date the loan starts, and as well as the terms of the loan. A reliable calculator can provide a table that shows the breakdown of your payment every month until the entire debt is covered. The calculator can also provide an abbreviated table that shows a detailed description of your previous monthly payments and the annual total for the rest of the years for your mortgage.

Using this unique calculator is actually not difficult. The data boxes to be filled out are properly labeled to help you know the right information or detail to encode. Aside from this, the calculator also does not require a lot of steps in order for you to get your schedule of payment. This schedule can help serve as your guide to keep you reminded of your deadlines. In addition to this, most calculators also provide you a schedule for pre-payments. These pre-payments are very useful since they can help you save more money just by adding a small amount to your monthly payment requirement. These are just some of the wonderful benefits of using these calculators.

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Pattern in Wine Vintages

I think we all remember seeing a copy of the Farmer’s Almanac at some point in time right?  I was having a discussion with a guy who owns a 90 point wine club and he was telling me that despite all of our scientific advances, there are still a number of wineries which use the type of old school tools that so many people in my generation think are an absolute joke.

In any case, it was interesting to hear the pros and cons of using every available resource.  While you might think that having something like the Farmer’s Almanac would be worthwhile because after all, the goal is always to make better wine, you lose some respect within the industry these days by using those type of tools.  It isn’t really something that I agree with, but it is clearly something he has thought about a lot and talked about with a ton of people so what can you do other than simply respect his opinon and move on?

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Math, Patterns and Chiropractic Care

I think I’ve mentioned before, but I have some family in Miami.  In fact, I travel there enough to visit that I actually have a small insurance policy in the state of Florida. My Miami Chiropractor is one of my favorite doctor’s that I’ve ever met for a few reasons.  To start, like me, he loves patterns and the way they influence our lives.

He was saying that he has found a new way to treat back pain and it seems to work based on his testing.  What he does, is as much about allowing movement as it is about lining up our spines.  He said that the vast majority of his patients which suffer a significant injury had some significant swelling before the injury occured.  He now tries to reduce that swelling before treating the patient at all!

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Wine Patterns

We all know that a turmoundous number of patterns that we track were originally found in the natural world.  Those patterns help many of us to find out how the wider world works.  For a wine a month club there are quite a few other things going on as well when it comes to patterns and pattern breaking!

First, we know there are sales clusters.  Depending on who wrote your website, it might speak more closely to someone living in a specific region of the country, or a certain income level.  These are things which you need to know and track over time to be successful.

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A Basic Introduction to Cryptanalysis

When you look at a cryptogram for the first time, they nearly always look rather daunting after all how are you expected to decipher all that code!  However there are certain techniques that can make the task much less daunting and in some senses it is actually quite fun to work them out.

One of the most basic procedures is that of frequency analysis.  In fact without this technique you won’t get very far in understanding any of the procedures behind substitution cryptanalysis. So let’s try and briefly explain what’s behind this technique in an effort to expand our mathematical education.

Cryptanalysis relies on the fact that all letters of a specific language have specific characteristics or personalities.  To the ordinary observer all the letters might look fairly similar, but to the analyst they will know the specific traits and characters of each individual letter.

 

GJXV EHRT NUCOT WMOHY UWGK HWIE

GJXV EHRT NUCOT WMOHY UWGK HWIE

GJXV EHRT NUCOT WMOHY UWGK HWIE

GJXV EHRT NUCOT WMOHY UWGK HWIE

GJXV EHRT NUCOT WMOHY UWGK HWIE

GJXV EHRT NUCOT WMOHY UWGK HWIE

GJXV EHRT NUCOT WMOHY UWGK HWIE

GJXV EHRT NUCOT WMOHY UWGK HWIE

Don’t try and decipher this example though – there’s nothing there.  The cryptanalyst would initially begin by counting each letters frequency and it’s contacts (the contacts are the letters which are adjacent. They would then construct a frequency table based on the text.  This can then be compared with a standard frequency table based on a similar number of words.  This table will list the likely frequency of each individual letter – i.e how often it would be expected to appear.
Unfortunately it is rarely as simple to line up your standard frequency table and the one you created to solve the cryptogram.  They are very unlikely to be identical even for the reason that they will be based on a different number of characters.  However it is surprising how little relative frequencies shift from one piece of text to another.  You will almost always find e,t,a,o,n,r, i, s and h in the high frequency areas whereas d,l,u, c and m will normally be found in the medium frequency group.
It’s useful to see how the basics work in encryption, especially if you use such technology to protect yourself online.  For example I can use a technology to spoof my IP called a Virtual private network which creates an encrypted tunnel between the client, effectively hiding the IP address of my client.
Using frequency you can narrow down to distinct groups each individual letter, often with very accurate results.  However you need more than this to focus more specifically on a possible solution and this is where ’contacts’ are important.  Every letter has a cluster of associations that are likely to occur.  In fact an experienced cryptanalyst can spot these associations almost without thinking when presented with a frequency distribution and a tally chart.
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Math and Design

Those who are creative often shy away from math. This is partly the fault of many education systems around the world that at an early age make young people choose between the humanities and the sciences. I cannot remember at school anyone who choose both math and art as their specialist topics. In the Renaissance as in ancient Greece the two disciplines were seen as complimentary.

Leonardo da Vinci was not only an outstanding artist he was also a draftsman, an inventor and a mathematician . He looked for the mathematical formulas that underlay beauty. It is da Vinci that bought the idea of the golden ratio to many people’s attention. It is found throughout nature and is one of the most fundamental principles of design. The golden ratio seems inherently ‘right’. It can be expressed in math as:

 

 

 

 

 

 

From this formula you can get a rectangle that can inform the design of tables, whiteboards and also the spacing of sections on a website.

Another mathematical aspect to design can be found in the Fibonacci sequence of numbers:

1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89 etc.

This sequence is derided from adding the last two numbers together to get the next number in the sequence. Thus 1 +2 =3. 2+3 =5. 3+5=8 and so on. It is interesting to note that the bigger the numbers get the closer their relationship conforms to the golden ratio.

The Fibonacci sequence is particularly useful for graphic design. It gives us the correct proportions between font sizes and also the relative values for column sizes. For website design it is good to start with a content width of 987 pixels to make it easy to calculate the relative sizes of columns.

Finally, modern design has been greatly influenced by fractals. These are mathematically governed images that appear to magnify at each iteration. It is like the zoom on a camera; only with fractals the image quality never becomes blurred. Designers often have fractals moving and /or  rotating with each iteration to produce striking effects.

It is clear from these 3 examples that much of the best design is mathematically based. The more we can use math in design the easier it will be on the eye. For website design maths can be a powerful to grab the user’s attention.

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Math and Music


Music is written in a notational form that can be easily converted to mathematical symbols. Through doing so it soon becomes apparent that the basis of all music that is commonly thought of as ‘beautiful’ uses repetition.

A motif in music is introduced and then it is repeated and altered. The setting up of expectation of repetition in music and then fulfilling or dashing that expectation explains the dynamic of music. It is a series of patterns essentially that is behind the aesthetics of all music from chamber music to death metal.

This sets up an interesting question: is it possible to write music that is totally absent of pattern? This is different to random music – rather music that has patterns but no pattern is repeated. To do this math is needed.

John Costas was hired by the US Navy to solve the problem with the sonar ping. For the ping to work a sound with patterns where no pattern was repeated was needed. He solved the problem by using the Prime Number Theory developed by Evariste Galois. Each component of the ping was mathematically related to the next but no pattern was repeated.

The speaker in the talk (Scott Rickard) used the work of Costas that borrowed from Evariste Galois to write a piece of music without repetition. It should be the ugliest piece of music ever written as it is devoid of repeating patterns.

In a sense this music realizes the dream of the composer Schoenberg in his movement called ‘the emancipation of the dissonance’.

After listening to the talk and musical piece on TED it is worth reading the comments
(http://www.ted.com/talks/lang/en/scott_rickard_the_beautiful_math_behind_the_ugliest_music.html) as it details some of the key points of what is pattern? How does the mind perceive pattern? How is math converted to music?

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