Mathematics is important in day to day life, no matter what people tell you. Even shopping involves numbers and a basic grip on how they work will stop you getting screwed by unscrupulous shop keepers (to add a bit of fear to the post) or simply allow you to make better choices about value for money.

The important thing about maths for day to day use is that the feel is more important than the actual number.  It is less important how much cheaper something is than which is cheaper.

Most maths, at least when I was taught it at school revolved around learning a bunch of laws and then picking the right law to solve a question.  A typical maths question at high school might look like this:  D = (C + B) / A where A = 1, B = 4, C = 12 (in this case D = 16) and at University the game doesn’t change much.  The question now becomes prove the statement and then put some numbers in (also the statements become a lot harder).  This ‘filling in the pieces’ method to mathematics is not a good way to learn maths for the real world.  It’s rare that you get a problem where you know all the information and nothing else.  Often you have an information overload and even more often you don’t know everything you need to.  What is important is the ability to deconstruct the problems.  In computer programming, for example, this is called abstraction.  The process of breaking down a complex problem into a series of smaller problems.  For the rest of this post, I will show you how you can deconstruct mathematical problems and make them easier.  By being able to deconstruct maths into manageable chunks, you get a better idea of the underlying principles rather than simply learning a load of laws and cherry picking the right one at any given time.

The Deconstruction Method

Let’s take an example,  14 × 18 × 29.  This is a complicated multiplication and unless you know your 14, 18 and 29 multiplication tables, you aren’t going to be able to get the answer straight away.  Let’s start to deconstruct this by taking the first two numbers and multiplying them.  (14 × 18 ) × 29.  We won’t worry about 29 until later.  Is this the simplest form of the question?  No.  I want to break this down so that people with the most basic knowledge can work this out in their heads so let’s go further. ((10 + 4) × (10 + 8 )) is an equivalent way of writing this and is much simpler.  The benefit of this is that multiplying a number by 10 is as simple as putting an extra zero on the end of it.  This statement is the equivalent of 4 multiplications, 3 of which are by 10, (10 × 10) + (10 × + (4 × 10) + (4 × 8 ), or (100 + 80 + 40 + 32) or 252.

Our first multiplication problem is now 252 × 29.  Again we can deconstruct this into something far more manageable, (200 + 50 + 2) × (20 + 9), which is another far more simple set of multiplication to do than 252 × 29.  Now we have (200 × 20) + (200 × 9) + (50 × 20) + (50 × 9) + (2 × 20) + (2 × 9).  Some of these numbers are quite complicated but can be broken down even further.  (200 × 20) becomes (2 × 10 × 10 × 2 × 10) or (2 × 2 × 10 × 10 × 10) or 4000,because the order in which numbers are multiplied does not matter.  I will leave you to figure out the others but if you sum those values properly you will get the correct answer.

Why Deconstruct?

Deconstruction of problems gives a better feel for the underlying principles rather than the set of rules learned by rote in some maths class a long time ago.  It can be helpful in real life situations where you might not have the specific rule to apply and might not know all the information.  Having a feel for numbers and the way they work is something that comes with practice.  Maths is a muscle and like any other muscle in your body it needs to be exercised regularly for it to grow, but it is important to do the right kinds of exercise.  If you want to be a power lifter, there’s no point going on the treadmill and if you want to be good at maths there is no point learning a bunch of rules and trying to apply them when necessary.

Another Example

Here’s an example of a real world problem from applied maths.  I will talk you through the stages of solving the problem so you can see how to deconstruct a real problem into it’s component parts.  This method is designed for problems like this, less to do with pure mathematical questions.

If I were teaching a class of students this method, I would encourage them to discuss each of the stages amongst themselves and get them to critically analyse the questions and methods that each child suggested.  I would then get them to do the experiment themselves and compare the results to what they calculated.  Not only does this encourage mathematical and logical reasoning but it also encourages the children to talk to one another, discuss their ideas and select the best.

A water tank is being filled with water.  How long does it take to fill to the top?

There are two immediate questions here.  How big is the tank?  How much water goes into the tank in a second?  Once you know this you know everything you need to get the answer, but we don’t know that.  All we have is a tank and some water.  Next question…

What shape is the tank? The tank is a cuboid (simple example).  Now we have something to work on.  What is the volume of a cuboid?  Height times width times base or (for a cube) height times height times height.  What is the height?  I don’t know.  How can I know?  Measure it.  What is the measurement?  1 meter.  So we have a tank with dimensions 1 × 1 × 1 meter, or 1 cubic meter.  That’s the simple question.

How much water leaves the pipe in one second?  How can I measure this?  Get a container with a known volume, say a half litre glass and time how long it takes to fill.  Half litre glass is filled in about 5 seconds.  The rate is then 0.1 litre per second. 1 litre is 0.001 cubic meters.  0.5 litres is 0.0005 cubic meters and 0.1 litres is 0.0001 cubic meters.  The rate the water flows from the pipe is 0.0001 cubic meters per second.  So how long does it take to fill the tank?  Well if the rate is 0.ooo1 cubic meters per second, in 10 seconds there will have been 0.001 cubic meters and 10,000 seconds later, the whole 1 cubic meter will have been filled.

Experiment versus theory is important.  Experimental accuracy is something that is never discussed until graduate level physics and other applied mathematics courses.  In the description above I added an uncertainty by saying half litre glass is filled in about 5 seconds.  The error in this measurement gives an error in the flow rate value which gives an error in the overall answer.  Understanding that the answer you calculate might not be the answer you get is something that I personally had a hard time getting my head around and feel is often overlooked in all but the highest level of courses.

I recently got dropped from my PhD place. This sucks. I could rant about a whole bunch of stuff I’m unhappy about with the decision but that wouldn’t serve any purpose or give any value to anyone so I’m going to hit you with some weird shit that I’ve started to notice to me since this happened.

Closure

I have not had any closure on the matter.  My supervisor has not even bothered to write me an email saying she’s disappointed in me or thanking me for my work or that she’s sorry it’s not worked out or even that she’s trying to appeal my case because the department was unable to give me the tools I needed to do my work.  I’m pretty angry about that but here’s the interesting thing.  I don’t think it is because this kind of behaviour is rude and disrespectful but more because it doesn’t give any closure.  I’ve been left hanging on a thread with no idea what’s going on after simply being told “we’re done here” by someone else.  I hate this hanging around in limbo.  I need to be able to move on.

I think it’s important when you reach a transition point in your life to close off any previous ties which link you to your old life.  That’s not to say you should tell all your friends to fuck off and die and that you hope you never see them again.  That’d just be stupid and unnecessary.  On the other hand it’d be weird to just wander off somewhere without telling anyone what’s going on.  My purpose is no longer Physics.  I know that but there is still some lingering uncertainty in the matter.  No doubt I would be happy to work in Physics again in the future, although for a different department at a different University, but I need to know that everything is finished, finally and totally.

Lack Of Purpose

David Deida once said that a man must be on his purpose.  I’ve always had a purpose until now and never truly understood what he was saying.  Even when I broke my leg and was rehabbing, my purpose was to rehab it as quickly as possible.  Secondly, my purpose was to accrue as many X-Box gamer points as possible and achieve top level on Battlefield Bad Company.  I now have no reason to get up in the morning.  I hate this but I’m still not going to get up and walk around for no reason.  My bed is warm and I can think a lot there.  I feel like I’m in the worst funk of my life and there’s nothing I can do about it.  I’m stood in a night club looking around and seeing really stunning women and just thinking ‘meh’.  Even before I’d think ‘my god she’s stunning, I need to go talk to her NOW’ (sometimes I might even go talk to her).

This apathy is worrying.  I really don’t know what I will do next.  Nothing is inspiring and I don’t have my usual spring in my step, clarity of thought and bright eyes (by the way, Cassadiaga is an excellent album by the artist Bright Eyes, linked at the bottom).  The closest thing I can get to a purpose is completing West Side For Skinny Bastards weight training program.  But that doesn’t count, it’s just lifting weights and a goal to bench press 110kg, whilst important, is not something to live one’s life for.  I can’t even go running because I try to keep my slightly fragile knee together for playing American Football.

David Deida is spot on when he talks about purpose.  I don’t feel whole.  Something is missing that was there before.  I need a new purpose but I think I’m being held back by the lack of closure from the last purpose.  I honestly don’t understand how unemployed people can exist like this.  I feel like half a man.  I feel pathetic and weak, traits I don’t value and don’t want to be embodying.

Regrets

One thing I most definitely noticed was that I was not the person the most saddened by this.  In fact I was a little relieved.  I’ve been having to deal with some total nonsense associated with the project which I most certainly didn’t sign on for and I will be happy to see the back of that.  I’ve also been disillusioned with the project for a long time.  I don’t feel that it was worth my time for the most part.  That I could be helping the world and humanity so much more by doing other things.

The next question is clearly do I have any regrets and I can honestly say my only regret is taking the project on in the first place.  It was a bad decision based on emotion over logic and I was not as thorough as I could have been.  I also naively expected that when I was told I would be able to pursue my interest in theoretical modelling, this would be the case.  This now frees up my life to find a purpose that I am more passionate about and pursue it with total presence, undistracted by little things.  Star formation, whilst interesting in it’s own right, will not save the world and my work might have made the lives of a few people more complete but wouldn’t have really affected me either way.

Any other regrets?  Absolutely not.  I went through the course until now with a clarity of purpose and although there were times when this was slightly clouded, it didn’t take much to make it clear again.  By acting honestly and consciously through my own true intentions I was able to do exactly what I wanted to do in the way that I felt it was best.  This is the power of having a purpose and being on it.

David Deida also said that sometimes ones purpose changes and when this happens, it is important to get out with the minimal stress to those around you.  I don’t feel that this has been the case.  I have left too many open threads in my work which need closing off.  I have no intention of finishing this myself, especially considering I’d be doing it for free (something I’d have been happy to do before I started the research and had to deal with the nonsense), but I would like to know that the work will be done in the future or that they are closing the project.  Once I know this I will most likely put star formation to bed in my mind and my only exposure in the future will be if someone writes about it on the BBC website.

Lessons

So what have I learned from this that I can share with my readers?

1. A purpose is mandatory.  Life without a purpose is a life of mediocrity.  It is wishy washy and indecisive.  Compared to the alternative, a life of clarity, consciousness and decisiveness there is no competition.  If you are living a life with purpose, you will appreciate this.  If you can’t very quickly identify what your purpose is now, perhaps you should try and find one.  There is an exercise here which I may try again later this week.  It didn’t help me last time but I believe it really will now I have no clear purpose, or am not aware of my purpose.
2. A purpose can change.  When a purpose changes it is important to tie up the old purpose in a clean and efficient way so you are not held back by old anchors to it.
3. Decisions to do with purpose need to be based on logic as well as emotion.  Just because something seems right does not always mean it is right.  It’s important to make mistakes and to learn from them so abandoning all emotion is a bad idea but a decision based purely on the emotion of the moment can be more trouble than it’s worth
4. Acting honestly and consciously, doing what you believe to be for the best at all times, gives you strength through adversity.  It would be so easy to beat myself up and question every action I took over the last year, many of which were very unorthodox.  I have total faith in myself however and know that I did the right thing so I am not beating myself up in any way.  There are people I wouldn’t mind getting my hands on though
5. Failure is OK.  This is probably the first major thing I’ve ‘failed’ at but I’m still alive and breathing.  I will pull through this and probably sooner rather than later.

The thing that has really struck me has been the weirdness and emptiness that I have felt without a purpose and how I really don’t like it.  I want my purpose back as soon as possible!  A life without purpose is no good to anyone.  You owe it to yourself and I owe it to myself to live a life with purpose and ambition, wether that purpose is to be a good parent to your children or to make millions by buying up incorrectly priced securities on the international markets.  This post struck a chord with you?  Perhaps you need to think about your purpose, if it’s really the best one for you or if you’re kidding yourself.  GET ON IT!

Let’s face it.  Our country is fucked up at the moment and I fully believe that the Conservative Liberal Coalition was the best general election result for the country and i hope that they will drag us out of the mess created by the Labour government and their inept leader Gordon Brown, but I still think I could do a better job than any of the politicians that are currently running the country.  Unfortunately I will never have a chance to govern because I don’t believe in playing the party political game to get in power.  I’ve decided to call myself the individualist ‘party’ in a nod to Ayn Rand, who’s book The Fountainhead has inspired a lot of my sociological views.

So for shits and giggles, I have decided to outline exactly what I would do if someone came to my front door tomorrow and told me that I was to be running the country for the next five years.  This is a radical approach to governing a country and since it will never come to pass, I can be as honest as I want.  Today I am going to write about my key political points and education.  This will form the foundation of the future work I will write

Individualist Party Key Points

The individualist political ‘party’ values the individual above all else.  Above state, government, region and family.  All policies reflect this.  It is our aim to create an environment where people can achieve their full potential.  We believe that each human being is born equal and capable of greatness but that many will struggle to achieve this.  We do not just believe that the current system is not maximizing the potential of individuals but (often unintentionally) taking huge steps to limit and diminish humanity and it’s potential.

The individualist political ‘party’ is not only pro Europe and pro America, it is pro World.  The individualist party recognizes that due to recent technological advances and the inevitable future progress the world will continue to get smaller and smaller.  Rather than try and fight the change and lose, I believe it is important to embrace the change and look for the opportunities that will inevitably present themselves.  Globalization is happening, now.

The individualist ‘party’ is not just secular but atheist.  The leader (me!) does not believe in God and will not allow anything that is not tangible or disprovable affect policy.

The individualist party is a party for life on Earth.  For creating the best possible Earth it can.

The individualist party views the world as a place of abundance, not scarcity.  We believe that opportunities will present themselves in many different forms for those who are looking for them.  The individualist party encourages people to look for these opportunities and not to simply be blinkered.

The individualist party is not a nice party.  It believes that if you screw up you need to live with the consequences.  The individualist party, if it had been governing at the time of the financial crisis, would not have bought out the failing banks or any other industries for that matter.  The individualist party believes that in the ashes of destruction, new life is created.  New businesses would have formed with far stronger infrastructures and better managers.  This situation would have been preferable to the current one.  The party understands that people could have lost all their money and doesn’t care.  The party thinks that they should have taken better care of it while they still had it.

The individualist party is anti trade union and would eradicate their existence from the face of the planet by whatever means necessary including a rocket full of unrepentant members aimed at the sun.  It is fiercely pro Capitalist.  The party is anti any form of collectivism and believes that the best creations come from individuals working at their highest level.  The party’s goal is to help people to access their highest level as consistently as possible.

Education

I believe that education is the key to success but that the education system currently employed in the UK is (often irreparably) damaging the children being put through it.  The current system is designed to make children into good soldiers for the army.  Times have changed.  Needs have changed.  The education system has not.  Our schools have barely progressed since the time of Charles Dickens as illustrated in this quote.

Now, what I want is, facts. Teach these boys and girls nothing but Facts. Facts alone are wanted in life. Plant nothing else, and root out everything else. You can only form the minds of reasoning animals upon Facts: nothing else will ever be of any service to them. This is the principle on which I bring up my own children, and this is the principle on which I bring up these children. Stick to Facts, sir!

- Charles Dickens Hard Times

The scary thing about the current education system (2010) is that it is still exactly the same as it was back then, without caning.  This is not acceptable.  We need to gut the education system and rebuild it from the ground up, starting by identifying what type of graduate we want to produce at the end of their time in our system.  I value problem solving and creative thought and I want any education system I produce to be geared towards creating people who can think independently and logically whilst remaining creative.  I want the people who leave my system to have an understanding of the world and how it works, now.  I want them to be confident with business and finance.  I want them to have some level of emotional intelligence.  I want them to develop character.  I want them to be strong people who can go out and contribute to the world and humanity whilst living for themselves and those that they care about.  I want to create an education environment which I can be proud to send my children to.  I am not proud of what we have at the moment.

Theory

The current education can be neatly written like this.  C = A + B, A is 5 and B is 6, find C.  I propose a new structure, which can also (conveniently) be simply written.  What is C?  The difference may not be immediately apparent but this method of solving problems is far more realistic and helps develop a person’s ability to identify and solve problems.  Without the knowledge of what A and B are, or even that A + B = C, the student is forced to work them out for themselves.  C is still 11 but the way the student gets there is different.  The student is forced to ask questions and decide what is relevant in the current situation.  The ability to filter lots of information and identify and use that which is important, discarding the rest, is important in today’s culture of information overload.  My work as a scientist has revealed this to me.  As an undergrad you are asked questions of the first type, where all you need to do is be able to remember an equation and identify which number goes where.  eg a 1kg weight sits in limiting equilibrium on a slope angled at 30 degrees from horizontal, what is the coefficient of friction?  As a post grad you are asked the more realistic second type of question, what is the temperature of a cloud of dust in a nearby star forming region?  This applies to other subjects too, not just sciences but essay subjects.  Essay structures are taught and if you can identify the relevant piece of information from a text and slot it into this framework you will do well (I dropped less than 10 marks on 2 A Level English exams).

It is a method for passing exams, it is not a method for learning.

The old subjects will all be gone and replaced with the following streamlined areas of study

• Humanity – replacing history, law, philosophy, religion language, literature
• Logic – replacing science, maths
• Identity- replaces citizenship, PSE, psychology, philosophy
• Creation – replaces art, music, technology
• Finance – self explanatory
• Sport and Physical Education

Because of the philosophy of how subjects are taught, the subjects themselves need to be streamlined.  More time is needed by each subject and I have no desire to increase the length of the school day.  The humanity section is designed to help people understand humanity as a whole.  A question might be “Was George W Bush a good president?  Why might someone disagree with your answer?”  The student would have to define good and bad, find evidence for their point of view, critically analyze their evidence and try to provide a counter argument.

In logic a question might be “How long does it take to fill a tank with water” where the students would be encouraged to discuss the physical properties of the tank and how it is being filled, arriving at a conclusion which is testable.

The aim of Identity is to get students to think who they are and how they can live in positive ways.  It also aims to create emotionally intelligent people who understand the world and how people and they themselves act and why.

Creation encourages people to create.  Whether they want to create music or art or sculpture or create a table or a circuit, this is their chance to really express themselves.

Finance is the study of economics, business and money.  With money being so important in todays society the failure to teach children about money is almost criminal in my opinion.  We cannot expect our children to make good money decisions if they have no understanding of money in the first place.  The history of finance and it’s implications and lessons would be studied as well as the applications in the real world.  An example question would be “You are in control of all aspects of the finance in 1980’s Argentina.  Your aim is to make the country a financial superpower.  What do you do?”

Sport and Physical eduction is so unbelievably important to humans in general.  It will be mandatory for all children to partake in a minimum of one hour of physical exertion at school a day.  I also believe that the psychological effects of competition are beneficial and should be encouraged.  It will also help to build the identity element of ‘fit and healthy’

Implementation

Implementation of a whole new education system or environment is not easy.  I am under no illusions about this.  The start will be to retrain the teaching staff from junior school to sixth form.  Universities and infant schools will remain reasonably constant but encouraged to adopt the more progressive and student involved method of delivering educational material I am advocating in this article.

After retraining, a teacher support and social network would be set up so that all teachers participating in the scheme would be able to share ideas, challenges and solutions.  The emphasis will be on the individual teacher to work to create new and inspirational material based around their own passions but they should not be made to feel isolated and powerless to help in a system that will be new and challenging to them.  This support network will also encourage those with the natural ability to be ‘Prime Movers’ of teaching to flourish.  This teaching environment is not designed for the teachers to cram information from some standard book into their students’ heads but to encourage the creativity and passion of both student and teacher.

In Closing

This revolutionary method of teaching would improve the lives of the people it teaches and would make the schools a more fun and inspiring place to be, where people are allowed to follow their passions and give their gifts to the world.  The following is a list of books which I have read and have inspired the creation of this article: