If you own a laptop or a desktop, then at some point or the other you may face problem with its functioning. The problem may be technical or software related.
There are a lot of computer repair services available online that you can avail to solve all your system related problems.
Online computer and laptop repair services are becoming increasingly popular as they are not only easily available but also very efficient.
Before selecting an online computer repair service professional, it is important to look for the type of services they offer.
These online centres usually offer a number of services including LAN/WAN setup, fire wall and email security backup, installation of antivirus software, internet issues, hardware repair services, data backup and recovery and window OS installation and troubleshooting.
The main advantage of hiring a professional computer repair technician online is that they are accessible 24/7.
So if you face a problem at odd times, you need not to worry.
You can call these professionals who have good experience and can work remotely with you to solve issues with the system. They are experts and have required skills to fix any hardware or software related problem.
By contacting them, you need to follow their guidelines on how and what to do; this helps you get good knowledge about the possible solution.
Online computer or laptop repair services offered aim at exceptional customer satisfaction. Also these services save you from the hassle of standing in a long queue outside a shop, and hence help to save a lot of time. They can offer you the best possible solution of the problem by gaining access to your computer remotely.
There are several remote computer repair services available online and it is important to select one that is not only quick and effective but also affordable.
Most of these offer services for both home and business users.
They also have customized services to cater to specific needs.
It is very important to do some research online to find the best service provider who can offer you quality services.
It is always good to check the track record of the company in handling queries.
You can also read the testimonials and feedback left by the customers who have taken their services earlier.
Online computer repair services offer a lot of benefits to customers which have contributed to their rising popularity. They help you save a lot of time as well as money, both of which are very precious.
Monday, 29 December 2014
Choosing the Perfect Prom Dress
Choosing the perfect prom dress can be a fun, rewarding process.
Looking through magazines for the latest fashions is a great way to start. Flip through magazines at home with your friends, or make a trip to the bookstore. There are many fashion and prom-related magazines out there, and they will give you an idea of what styles you like.
You want to be comfortable with what you are wearing on your special night, so look for styles that match your preferences and personality. Romantic Styles: If you are the romantic type who falls for the Greek Goddess look, consider all white, empire style gowns.
Also, think fairytale-inspired dresses in rose or pink shades.
Consider curling your hair and wearing it down, and placing a delicate, intricate pin in your hair. You can also look like an angel in a flowing dress with one-shoulder.
Sophisticated Styles: If you are sophisticated and love all black prom dresses, go for it.
Accessorize with big, crystal earrings with a splash of red.
Also, look for black dresses with sequins, or black dresses with bright, attention-grabbing sashes.
They are fun, flirty, and daring.
Victorian Style: If you loved to play dress up as a child, you may favor the Victorian style.
Victorians tend to favor the layers of tulle and lace that come with the beautiful full ball gowns.
Look for vintage lace, in pinks and yellows.
Victorian style dresses are also fitting if you have a narrow waist and a womanly-lower body.
Sweet and Simple: If you love the simplicity of fashion, a simple, strapless chiffon gown would be perfect for you.
It's flirty because you can show off your shoulders, and it's also elegant and classy.
You do not have to worry about beads, sequins or fancy designs with this style.
Since a simple chiffon gown is, for a lack of better words--simple, feel free to get your hair styled in an up-do and wear flirty, fun heels.
Sexy Dresses: If you have a great figure and want a sexy look, go straight for the straight--straight gowns that is.
Silky, slinky and soft fabrics will look fabulous on you. These fabrics will show off your figure and show the latest of trends.
Look for a combination of other fabrics and unique cuts that will help you achieve a sexy prom dress look.
Colors: Prom dresses come in every color imaginable. Remember to look for colors that you like, not what everyone else is wearing.
This year should be easy because there is an abundance of colors to choose from.
Bright yellow and black, orange, emerald green and purple have made big come backs this year.
Prints: If you are fashion forward, look for prom dresses with big oversized patterns and bright colors.
We traveled for over 3 months throughout the world looking at different gowns and designs, and we were most impressed with the fashionable prints for 2009 prom dresses.
These prints are unbelievably gorgeous, and you have to see them to believe them.
Be sure to look at our collection of prom dresses and formal evening gowns online.
Our 2009 collection is filled with limited edition prom dresses that will impress even the pickiest of picky.
We can help you find the perfect prom dress for 2009.
Looking through magazines for the latest fashions is a great way to start. Flip through magazines at home with your friends, or make a trip to the bookstore. There are many fashion and prom-related magazines out there, and they will give you an idea of what styles you like.
You want to be comfortable with what you are wearing on your special night, so look for styles that match your preferences and personality. Romantic Styles: If you are the romantic type who falls for the Greek Goddess look, consider all white, empire style gowns.
Also, think fairytale-inspired dresses in rose or pink shades.
Consider curling your hair and wearing it down, and placing a delicate, intricate pin in your hair. You can also look like an angel in a flowing dress with one-shoulder.
Sophisticated Styles: If you are sophisticated and love all black prom dresses, go for it.
Accessorize with big, crystal earrings with a splash of red.
Also, look for black dresses with sequins, or black dresses with bright, attention-grabbing sashes.
They are fun, flirty, and daring.
Victorian Style: If you loved to play dress up as a child, you may favor the Victorian style.
Victorians tend to favor the layers of tulle and lace that come with the beautiful full ball gowns.
Look for vintage lace, in pinks and yellows.
Victorian style dresses are also fitting if you have a narrow waist and a womanly-lower body.
Sweet and Simple: If you love the simplicity of fashion, a simple, strapless chiffon gown would be perfect for you.
It's flirty because you can show off your shoulders, and it's also elegant and classy.
You do not have to worry about beads, sequins or fancy designs with this style.
Since a simple chiffon gown is, for a lack of better words--simple, feel free to get your hair styled in an up-do and wear flirty, fun heels.
Sexy Dresses: If you have a great figure and want a sexy look, go straight for the straight--straight gowns that is.
Silky, slinky and soft fabrics will look fabulous on you. These fabrics will show off your figure and show the latest of trends.
Look for a combination of other fabrics and unique cuts that will help you achieve a sexy prom dress look.
Colors: Prom dresses come in every color imaginable. Remember to look for colors that you like, not what everyone else is wearing.
This year should be easy because there is an abundance of colors to choose from.
Bright yellow and black, orange, emerald green and purple have made big come backs this year.
Prints: If you are fashion forward, look for prom dresses with big oversized patterns and bright colors.
We traveled for over 3 months throughout the world looking at different gowns and designs, and we were most impressed with the fashionable prints for 2009 prom dresses.
These prints are unbelievably gorgeous, and you have to see them to believe them.
Be sure to look at our collection of prom dresses and formal evening gowns online.
Our 2009 collection is filled with limited edition prom dresses that will impress even the pickiest of picky.
We can help you find the perfect prom dress for 2009.
Masters Degree Online
Online masters degrees are a great option for people looking to get a graduate education, but without the flexibility that traditional degrees require.
For people with existing jobs and family commitments, online degrees offer a way to pursue an education without sacrificing other important aspects of their career and social life.
Online programs give you the ability to choose from any school rather than being limited to colleges in your local proximity.
This can be a very big advantage because you can choose a school that meets your educational needs as well as your budget. An online masters degree program isn't for everyone. It takes a lot of work and self discipline to sit at a computer day after day and do coursework. Some students find they cannot operate without the social aspects of a classroom and daily interactions with other students and teachers. Learning styles vary, and it is well worth it to be honest up front about what you need in order to achieve peak academic performance.
Don't overlook the educational experiences that occur outside of the actual lecture. Many people find that these are the underpinnings of their ability to stay focused and achieve academic results.
Most people will benefit by taking a class or two online before committing to a long term program. Be wary of schools that want you to simply pay for an entire degree up front.
Take a few classes that will benefit you regardless of whether you complete the degree and get a feel for the online learning environment and for your ability to concentrate at home surrounded by daily distractions of friends and family.
For people with existing jobs and family commitments, online degrees offer a way to pursue an education without sacrificing other important aspects of their career and social life.
Online programs give you the ability to choose from any school rather than being limited to colleges in your local proximity.
This can be a very big advantage because you can choose a school that meets your educational needs as well as your budget. An online masters degree program isn't for everyone. It takes a lot of work and self discipline to sit at a computer day after day and do coursework. Some students find they cannot operate without the social aspects of a classroom and daily interactions with other students and teachers. Learning styles vary, and it is well worth it to be honest up front about what you need in order to achieve peak academic performance.
Don't overlook the educational experiences that occur outside of the actual lecture. Many people find that these are the underpinnings of their ability to stay focused and achieve academic results.
Most people will benefit by taking a class or two online before committing to a long term program. Be wary of schools that want you to simply pay for an entire degree up front.
Take a few classes that will benefit you regardless of whether you complete the degree and get a feel for the online learning environment and for your ability to concentrate at home surrounded by daily distractions of friends and family.
The Child Care Diploma an Essential Qualification
If you are interested in working with children in any capacity it would be wise to take a training course in child care.
The most comprehensive course with a highly valued qualification is the Diploma for Children and Young Peoples Workforce or as it is simply known the Child Care Diploma.
This highly valued course combines theoretical knowledge and understanding with workplace assessment which sets the child care diploma above many other qualifications.
Child Care Diploma - Knowledge and Understanding This part of the course comprises 21 modular units covering a vast amount of essential knowledge that you will need to understand and apply in the workplace.
For example it covers:- 1.
Understanding - Child development, safeguarding children and young people as well as how to support positive outcomes with them 2. Supporting - Children's health and safety as well as their need to achieve their learning potential, speech and language 3.
Promoting - Equality and inclusion in their environment, physical activity, communication, learning and development and creativity 4.
Developing - Positive relationships The Childcare Diploma is listed on the QCF (Qualifications and Credit Framework) and just by completing a valid theory course you will gain the 65 credits needed for the qualification on completion of the work placement assessment. Extrapolate Childcare Diploma - Workplace Assessment This is where the application your knowledge and understanding comes under scrutiny.
Normally you will need a placement (paid or voluntary) of around 100 hours in order to be assessed across the various areas that the child care diploma covers and ensure you have indeed grasped what you need to know in order to look after children and young people in a proper and fitting manner.
In order to be assessed you will need to gather evidence of the practice of essential skills you have learned from the theory part of the course. This evidence then needs to be documented and verified by a qualified (level 4 and above) on site worker.
It will encompass: 1.
Observations of children and young people's activities 2.
Witness statements of your work within the workplace 3.
Professional discussions you have been engaged in 4.
Observations of tasks completed by qualified child care workers Once having completed both the theory and practical assessment to the satisfaction of your course tutor you will then gain the coveted CYPW Child Care Diploma How to Find a Suitable Child Care Diploma Course Care is needed when sourcing a course to ensure that you are engaging in an authentic training programme. The internet is the most convenient way of finding such education.
Simply enter Childcare Diploma or CYPW in Google and course suppliers will be listed.
Check that the course is listed on the QCF and that both the theory and practical aspects are included. Do not always enrol in the cheapest training make sure that the college provides tutor support and allows enough time to complete the two sections (theory and practical).
The most comprehensive course with a highly valued qualification is the Diploma for Children and Young Peoples Workforce or as it is simply known the Child Care Diploma.
This highly valued course combines theoretical knowledge and understanding with workplace assessment which sets the child care diploma above many other qualifications.
Child Care Diploma - Knowledge and Understanding This part of the course comprises 21 modular units covering a vast amount of essential knowledge that you will need to understand and apply in the workplace.
For example it covers:- 1.
Understanding - Child development, safeguarding children and young people as well as how to support positive outcomes with them 2. Supporting - Children's health and safety as well as their need to achieve their learning potential, speech and language 3.
Promoting - Equality and inclusion in their environment, physical activity, communication, learning and development and creativity 4.
Developing - Positive relationships The Childcare Diploma is listed on the QCF (Qualifications and Credit Framework) and just by completing a valid theory course you will gain the 65 credits needed for the qualification on completion of the work placement assessment. Extrapolate Childcare Diploma - Workplace Assessment This is where the application your knowledge and understanding comes under scrutiny.
Normally you will need a placement (paid or voluntary) of around 100 hours in order to be assessed across the various areas that the child care diploma covers and ensure you have indeed grasped what you need to know in order to look after children and young people in a proper and fitting manner.
In order to be assessed you will need to gather evidence of the practice of essential skills you have learned from the theory part of the course. This evidence then needs to be documented and verified by a qualified (level 4 and above) on site worker.
It will encompass: 1.
Observations of children and young people's activities 2.
Witness statements of your work within the workplace 3.
Professional discussions you have been engaged in 4.
Observations of tasks completed by qualified child care workers Once having completed both the theory and practical assessment to the satisfaction of your course tutor you will then gain the coveted CYPW Child Care Diploma How to Find a Suitable Child Care Diploma Course Care is needed when sourcing a course to ensure that you are engaging in an authentic training programme. The internet is the most convenient way of finding such education.
Simply enter Childcare Diploma or CYPW in Google and course suppliers will be listed.
Check that the course is listed on the QCF and that both the theory and practical aspects are included. Do not always enrol in the cheapest training make sure that the college provides tutor support and allows enough time to complete the two sections (theory and practical).
Top Bachelor Degrees Up For Grabs Online!
Do you thirst for a brand new experience in the field of studying? Or are looking for an online degree program that suits your taste, needs, and skills? Well, you've come to the right place, for this article provides you an overview of top online degrees to choose from.
If you have already gathered credits from your previous school-traditional or online, need not worry, because you can actually transfer the credits you earned from that degree to the new program you want to enroll in.
Plenty of three- to five-year online degree programs are available, and are acknowledged by most colleges worldwide. One of the top online degree programs is a degree in Business Studies.
This course is favored by most students for it offers great opportunities for them to immediately land on a job after graduation. In fact, there is an unlimited array of related jobs across the globe. The most well-known and sought-after degree is the Bachelor of Science in Administration (BSBA). Such course not only trains students, but also provides them with opportunities to work either or both in public firms, or in the private sector. The degree program specializes in such fields as finance, marketing, information management, operations management, and organizational behavior.
There are plenty of universities that offer top online degree programs in the field of Business Studies.
Keiser University is one of the universities that are accredited by the Commission on Colleges of the Southern Association of Colleges and Schools. They ignite their students for careers that are made for growth and demand. They have what they call a "one-class-at-a-time" policy, which allows busy students to have more time to focus on their studies, and develop the skills needed for them to excel on a certain field.
Keiser University offers top online degree programs in such courses as Accounting, and Marketing.
Administration in Finance, Administration in Human Resources, International Business, Management, and Capella University is a university that is accredited by the Higher Learning Commission, and is a member of the North Central Association on Accreditation and School Improvement.
It also offers top online degree programs in such courses as Science, Business Accounting, Bachelor of Business Finance, Degrees in Science majoring in Business, Science degrees majoring in Business (Human Resource Management). Kaplan University, located in Davenport, Iowa, is accredited by the Higher Learning Commission, and a present member of the North Central Association Commission on Accreditation and School Improvement.
Kaplan University offers such online degree programs as: Bachelor of Business, Bachelor of Business Finance, Bachelor of Accounting, Bachelor of Management of Information System, and Bachelor of Business Security and Assurance.
If you have already gathered credits from your previous school-traditional or online, need not worry, because you can actually transfer the credits you earned from that degree to the new program you want to enroll in.
Plenty of three- to five-year online degree programs are available, and are acknowledged by most colleges worldwide. One of the top online degree programs is a degree in Business Studies.
This course is favored by most students for it offers great opportunities for them to immediately land on a job after graduation. In fact, there is an unlimited array of related jobs across the globe. The most well-known and sought-after degree is the Bachelor of Science in Administration (BSBA). Such course not only trains students, but also provides them with opportunities to work either or both in public firms, or in the private sector. The degree program specializes in such fields as finance, marketing, information management, operations management, and organizational behavior.
There are plenty of universities that offer top online degree programs in the field of Business Studies.
Keiser University is one of the universities that are accredited by the Commission on Colleges of the Southern Association of Colleges and Schools. They ignite their students for careers that are made for growth and demand. They have what they call a "one-class-at-a-time" policy, which allows busy students to have more time to focus on their studies, and develop the skills needed for them to excel on a certain field.
Keiser University offers top online degree programs in such courses as Accounting, and Marketing.
Administration in Finance, Administration in Human Resources, International Business, Management, and Capella University is a university that is accredited by the Higher Learning Commission, and is a member of the North Central Association on Accreditation and School Improvement.
It also offers top online degree programs in such courses as Science, Business Accounting, Bachelor of Business Finance, Degrees in Science majoring in Business, Science degrees majoring in Business (Human Resource Management). Kaplan University, located in Davenport, Iowa, is accredited by the Higher Learning Commission, and a present member of the North Central Association Commission on Accreditation and School Improvement.
Kaplan University offers such online degree programs as: Bachelor of Business, Bachelor of Business Finance, Bachelor of Accounting, Bachelor of Management of Information System, and Bachelor of Business Security and Assurance.
The "People" Aspect of Data Security
Although your staff may be the most important aspect of your business, when it comes to data security, they could potentially be the weakest link.
Because many cybercriminals are well versed in how to avoid firewalls and sidestep encryption, relying on your staff to protect your system files and information exponentially increases the possibility of a data breach. When employees are not aware of data security protocols, you are exposed to a great deal of risk if even one of them commits a mistake.
Phishing emails - ones that ask for personal or work-related account information like bank account or passwords - are still popular nowadays, even with countless information campaigns from companies and the government.
The reason for this is that hackers really only need one individual to provide details; after that, accessing your data will be like slicing butter with a hot knife. When this happens, hackers can obtain more information that they need by taking over the employee's account and posing as him or her.
Because of this, your paradigm on data security should shift from a computer-centric to a people-centric one.
Hackers only need to find a single way to enter your system and take advantage of the most vulnerable aspect of your data security: the potential for human error.
Because data and security breaches often become apparent only after the event, educating your employees about data protection is important, now more than ever. It is also important to note that securing your system files and information is beyond password-protecting their PCs.
Personal computers are only one small barrier from a hacker. Once they get access, it's open season on your files and systems.
Staff education through informal conversations with your staff can serve as a great starting point.
Proper verification process should also be implemented especially with legitimate-looking emails that raise initial suspicion.
Employees that deal with customers directly are one of the most affected by phishing emails because they tend to open and respond to emails that look official, without considering the risk.
When employees think twice about providing information in response to suspicious emails, it helps you avoid getting trapped in a bad situation that could cost your business more than just time and money.
Other strategies for protecting your data include tracking of attempted data security breaches and hiring specific employees dedicated to this task alone.
Similarly, employee awareness on potentially damaging computer practices as well as regular reminders or updates on network security protocols does not only serve as a great "investment" but also as a better, more impenetrable barrier from hackers and other individuals that may be planning to do unsavory things with your company data.
Because many cybercriminals are well versed in how to avoid firewalls and sidestep encryption, relying on your staff to protect your system files and information exponentially increases the possibility of a data breach. When employees are not aware of data security protocols, you are exposed to a great deal of risk if even one of them commits a mistake.
Phishing emails - ones that ask for personal or work-related account information like bank account or passwords - are still popular nowadays, even with countless information campaigns from companies and the government.
The reason for this is that hackers really only need one individual to provide details; after that, accessing your data will be like slicing butter with a hot knife. When this happens, hackers can obtain more information that they need by taking over the employee's account and posing as him or her.
Because of this, your paradigm on data security should shift from a computer-centric to a people-centric one.
Hackers only need to find a single way to enter your system and take advantage of the most vulnerable aspect of your data security: the potential for human error.
Because data and security breaches often become apparent only after the event, educating your employees about data protection is important, now more than ever. It is also important to note that securing your system files and information is beyond password-protecting their PCs.
Personal computers are only one small barrier from a hacker. Once they get access, it's open season on your files and systems.
Staff education through informal conversations with your staff can serve as a great starting point.
Proper verification process should also be implemented especially with legitimate-looking emails that raise initial suspicion.
Employees that deal with customers directly are one of the most affected by phishing emails because they tend to open and respond to emails that look official, without considering the risk.
When employees think twice about providing information in response to suspicious emails, it helps you avoid getting trapped in a bad situation that could cost your business more than just time and money.
Other strategies for protecting your data include tracking of attempted data security breaches and hiring specific employees dedicated to this task alone.
Similarly, employee awareness on potentially damaging computer practices as well as regular reminders or updates on network security protocols does not only serve as a great "investment" but also as a better, more impenetrable barrier from hackers and other individuals that may be planning to do unsavory things with your company data.
Sunday, 28 December 2014
Length, Area, Volume - Do We Need Them?
An important tool one can use to understand different concepts is the question, "Do we need them?" Here, by "we", I mean all of humanity as a whole.
That is, can you think of a scenario outside of the examination room where a person would feel the need to invent the concept in question? Of course, if a concept exists in the text books of today, the first person who invented it could not have possibly been motivated by doing good in an exam that tested that concept.
It is often useful to imagine yourself in that person's shoes and think of the reason that led him to the discovery. Let me demonstrate.
Volume.
We all know that volume of a cuboid is length times breadth times height and volume of a sphere is four-thirds of pi times its radius cubed.
But do we really need to define this quantity called volume? Do we really need all these formulas to compute it? Let's put ourselves in the shoes of a possible inventor of the concept. Imagine you live in a world where no one knows how to compute the volume of different objects.
The ruler of your kingdom is a man who takes interest in art and architecture. He visits his friend in Egypt and is fascinated by the pyramids.
On his return, he summons you to the court and orders you to build an exact replica in your own kingdom. He also informs you that his good Egyptian friend has kindly agreed to supply you with one million bricks.
Are one million bricks enough to build an exact replica? It is clear that to answer such a question, you need to calculate the volume of the pyramid, the total volume of all the bricks combined and see which one is bigger.
So, here we go. Here is one situation where you really need a formula for volume.
In general, volume is a quantity that is preserved under deformations of shape, as long as the deformations do not include compression and expansion. For example, if you take a huge object, chip out a small portion of it and reattach it at another location, the total volume of the object will not change.
Thus the question, "Can you deform an object in some way so that you end up with another given object?" can be answered by calculating the volumes of the two objects and comparing them.
So given a large piece of clay, if you are asked to build an exact replica of an object out of it, you should compare the volumes and see if it is possible.
Alright, it's clear now that we do need something, some kind of formula that puts a number on an object so that when we compare the number on one object and the number on another object, we can figure out if one can be deformed without expansion or compression to get the other.
But do we really need the specific formulas we are taught in school? That is, are they really the unique solution to the problem of deciding whether one object can be deformed to get another? Let's think of that formula in an abstract way for a while and let's say the formula is a person and let's call him The Volume God.
Whenever you want to calculate the volume of an object, you show it to The Volume God.
He inspects it for a while and puts a number on it with the Holy Stamp. This number denotes the volume of the object.
Thus, given some clay, and given an object, if you want to build an exact replica of the object, you show the clay and the object to The Volume God, get them both stamped and compare the two numbers. If the number on the clay is bigger, you go ahead and build the object otherwise you complain to your king and ask for more clay.
One day, The Volume God feels slightly mischievous and decides to confuse his people. He decides that instead of putting down the correct volume, next time he is shown an object, he is going to add 10 to the correct volume and stamp it with that number instead.
Thus when shown a cuboid, he started stamping it with 10 + (length x breadth x height) instead of just length x breadth x height. Of course, people had full faith in him and his Holy Stamp and so no one doubted the number.
Surprisingly though, nothing changed.
The Volume God's mischievous plans had absolutely no effect on the people.
The reason is that no one was ever interested in the absolute number that The Volume God stamped on objects. People were only interested incomparisons between two numbers and the comparison never changed.
If a number was less than another, 10 added to the first one was also less than 10 added to the second one. But wait a second. Doesn't this mean that we don't really need the exact formulas that we are taught in school? That if we add some arbitrary number to all the formulas, as long as the number added is consistently the same, we will never know the difference in the real world? Perhaps the volume of a cuboid should have been 10 + (length x breadth x height) then and the volume of a sphere should have been 10 + (4/3 x pi x radius cubed)! All these conclusions are correct if all we ever do with volumes is compare them.
However, we do use volumes for more than just comparisons.
Let's go back to the example of building objects out of clay.
Suppose you are shown an object and a bucket of clay.
Your clay supplier tells you that he can provide you with as many buckets of clay as you want to build an exact replica of the object. How many buckets should you order? You can answer this by getting more demanding towards The Volume God. So you go and pray to him thusly: "It would be great if you could write numbers on these objects such that just by looking at the numbers not only can I figure out if the second object can be deformed into the first, but also, how many of the second objects I would need to build the first object.
Amen." The Volume God agrees and stops adding 10 to the numbers. So now, to decide how many buckets of clay you will need to build an object, you show the object and the bucket to The Volume God and divide the number on the object by the number on the bucket.
That's it. All your problems are solved and the world lives happily ever after.
Wait.
Not ever after.
After only a few days, The Volume God gets mischievous again.
Since he did not want to add 10 to all these numbers and disappoint his followers, he decides to multiply all these numbers by 10.
And once again, surprisingly, nothing changed.
No one noticed the difference.
If one number is less than another, of course, 10 multiplied by the first one is also less than 10 multiplied by the second one. Also, the result you get on dividing one number by another is exactly the same as the result you get on dividing 10 times the first number by 10 times the second number.
Since comparison and division were the only things people did with volume, The Volume God's new mischievous plans had no effect on the world. So does it mean we can freely change the formula for volume of a cuboid to 10 x (length x breadth x height) and the volume of a sphere to 10 x (4/3 x pi x radius cubed) and in general, multiply all formulas for volume by 10 and nothing will ever change? This time, it's actually true.
The exact formula for volume does not mean anything until you specify what unit you are measuring it in.
Multiplying all formulas by 10 is equivalent to defining a new unit and measuring all the volumes in that specific unit. Going back to the question we started with, do we really need all these formulas for volume? Yes, we do, up to multiplication by some constant, or in other words, up to specifying the unit. I leave the similar question about length and area for the reader to ponder.
Why, for example, would anyone ever need the formula for the area of a circle?
That is, can you think of a scenario outside of the examination room where a person would feel the need to invent the concept in question? Of course, if a concept exists in the text books of today, the first person who invented it could not have possibly been motivated by doing good in an exam that tested that concept.
It is often useful to imagine yourself in that person's shoes and think of the reason that led him to the discovery. Let me demonstrate.
Volume.
We all know that volume of a cuboid is length times breadth times height and volume of a sphere is four-thirds of pi times its radius cubed.
But do we really need to define this quantity called volume? Do we really need all these formulas to compute it? Let's put ourselves in the shoes of a possible inventor of the concept. Imagine you live in a world where no one knows how to compute the volume of different objects.
The ruler of your kingdom is a man who takes interest in art and architecture. He visits his friend in Egypt and is fascinated by the pyramids.
On his return, he summons you to the court and orders you to build an exact replica in your own kingdom. He also informs you that his good Egyptian friend has kindly agreed to supply you with one million bricks.
Are one million bricks enough to build an exact replica? It is clear that to answer such a question, you need to calculate the volume of the pyramid, the total volume of all the bricks combined and see which one is bigger.
So, here we go. Here is one situation where you really need a formula for volume.
In general, volume is a quantity that is preserved under deformations of shape, as long as the deformations do not include compression and expansion. For example, if you take a huge object, chip out a small portion of it and reattach it at another location, the total volume of the object will not change.
Thus the question, "Can you deform an object in some way so that you end up with another given object?" can be answered by calculating the volumes of the two objects and comparing them.
So given a large piece of clay, if you are asked to build an exact replica of an object out of it, you should compare the volumes and see if it is possible.
Alright, it's clear now that we do need something, some kind of formula that puts a number on an object so that when we compare the number on one object and the number on another object, we can figure out if one can be deformed without expansion or compression to get the other.
But do we really need the specific formulas we are taught in school? That is, are they really the unique solution to the problem of deciding whether one object can be deformed to get another? Let's think of that formula in an abstract way for a while and let's say the formula is a person and let's call him The Volume God.
Whenever you want to calculate the volume of an object, you show it to The Volume God.
He inspects it for a while and puts a number on it with the Holy Stamp. This number denotes the volume of the object.
Thus, given some clay, and given an object, if you want to build an exact replica of the object, you show the clay and the object to The Volume God, get them both stamped and compare the two numbers. If the number on the clay is bigger, you go ahead and build the object otherwise you complain to your king and ask for more clay.
One day, The Volume God feels slightly mischievous and decides to confuse his people. He decides that instead of putting down the correct volume, next time he is shown an object, he is going to add 10 to the correct volume and stamp it with that number instead.
Thus when shown a cuboid, he started stamping it with 10 + (length x breadth x height) instead of just length x breadth x height. Of course, people had full faith in him and his Holy Stamp and so no one doubted the number.
Surprisingly though, nothing changed.
The Volume God's mischievous plans had absolutely no effect on the people.
The reason is that no one was ever interested in the absolute number that The Volume God stamped on objects. People were only interested incomparisons between two numbers and the comparison never changed.
If a number was less than another, 10 added to the first one was also less than 10 added to the second one. But wait a second. Doesn't this mean that we don't really need the exact formulas that we are taught in school? That if we add some arbitrary number to all the formulas, as long as the number added is consistently the same, we will never know the difference in the real world? Perhaps the volume of a cuboid should have been 10 + (length x breadth x height) then and the volume of a sphere should have been 10 + (4/3 x pi x radius cubed)! All these conclusions are correct if all we ever do with volumes is compare them.
However, we do use volumes for more than just comparisons.
Let's go back to the example of building objects out of clay.
Suppose you are shown an object and a bucket of clay.
Your clay supplier tells you that he can provide you with as many buckets of clay as you want to build an exact replica of the object. How many buckets should you order? You can answer this by getting more demanding towards The Volume God. So you go and pray to him thusly: "It would be great if you could write numbers on these objects such that just by looking at the numbers not only can I figure out if the second object can be deformed into the first, but also, how many of the second objects I would need to build the first object.
Amen." The Volume God agrees and stops adding 10 to the numbers. So now, to decide how many buckets of clay you will need to build an object, you show the object and the bucket to The Volume God and divide the number on the object by the number on the bucket.
That's it. All your problems are solved and the world lives happily ever after.
Wait.
Not ever after.
After only a few days, The Volume God gets mischievous again.
Since he did not want to add 10 to all these numbers and disappoint his followers, he decides to multiply all these numbers by 10.
And once again, surprisingly, nothing changed.
No one noticed the difference.
If one number is less than another, of course, 10 multiplied by the first one is also less than 10 multiplied by the second one. Also, the result you get on dividing one number by another is exactly the same as the result you get on dividing 10 times the first number by 10 times the second number.
Since comparison and division were the only things people did with volume, The Volume God's new mischievous plans had no effect on the world. So does it mean we can freely change the formula for volume of a cuboid to 10 x (length x breadth x height) and the volume of a sphere to 10 x (4/3 x pi x radius cubed) and in general, multiply all formulas for volume by 10 and nothing will ever change? This time, it's actually true.
The exact formula for volume does not mean anything until you specify what unit you are measuring it in.
Multiplying all formulas by 10 is equivalent to defining a new unit and measuring all the volumes in that specific unit. Going back to the question we started with, do we really need all these formulas for volume? Yes, we do, up to multiplication by some constant, or in other words, up to specifying the unit. I leave the similar question about length and area for the reader to ponder.
Why, for example, would anyone ever need the formula for the area of a circle?
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