Growing Need for VPN Encryption Solutions

There’s little doubt that the internet has developed incredibly over the last couple of decades. In the earlier years we were amazed at a few 256 colour pictures or some complicated ASCII art. Nowadays you can stream Ultra high definition movies through our computers or Smart TVs without a second thought.

There is one area though which has remained largely the same, and that’s the security infrastructure available by default on the internet. The primary security is supplied in much the same way as the end of 1990s in the form of SSL (secure socket layer). However this security is actually very vulnerable particularly if you’re using internet access points from untrusted sources. This could be anywhere from the local library to an wifi access point in your airport. We are completely reliant on these connections being secure and properly configured to ensure the security of our personal details when we use them.

Most of us now regard a VPN service as an essential resource for performing anything on the internet. In the event that you travel and make use of access points in places like hotels, cafes and airports – using a VPN is practically vital. If you do not then it’s virtually inevitable that eventually you’ll be the victim of some sort of cyber crime.

Among the main issues with these free Wi-fi points is that they are nearly always installed and set up with somebody without any appreciation of computer security. Many surveys have found a huge proportion of these devices are installed with default settings. Only the larger chain organisations are likely to have some specialized staff able to manage these appropriately and even then this isn’t often the case.

Think of all the places you make use of free internet access, who supports the connection do you imagine? Who would you get in touch with if there was a problem? In most cases the information would be extremely difficult to locate as they are probably set up in flying visit then some obscure telephone support at the end of the phone. In smaller companies it’s often the dreaded – ‘mate who knows a bit about computers’.

It’s the reason that all these access points are so appealing to identity thieves and cyber criminals. Here’s just a small choice of the primary issues:

  • Central Access Points used often by thousands of people to check out secure sites such as e-mail, banking, paypal and so on
  • . Frequently poorly set up with minimal security.
  • Allow access to seize all sorts of data using Man in the Middle style assaults.
  • Enables anonymity for attackers who don’t even have to present if they hack into the router.

They’re definitely a huge attraction for organized identity thieves for example who can take all sorts of data if they are able to hack into the router. The other well-known method is to simply put together a free internal access point in the same location and give it a similar name. Setting up this someplace near a hotel lobby or coffee shop means you can steal peoples information while they surf. This attack is often referred to as the “evil Twin” attack making use of a phony access point.

If someone compromises an access point or gets you to connect to a phony one then your data is in genuine difficulty. Forget about SSL or HTTPS all these can be bypassed if they have control of the access point you are actually using. Pretty soon the cyber criminals can have emails accounts, banking details as well as all sorts of private details.

Your only hope is to include your very own personal layer of file encryption which protects account names and details – when it comes to this you need a VPN. Now over the years many people have been using proxies and VPNs for a variety of reasons. However for individuals travelling then the overriding priority should be safety and security. The best VPN for BBC iPlayer like this one might not really be the best VPN to keep your web connection secure for instance.

Lots of people use Smart DNS systems to bypass geo-blocks on well-liked media sites however these should be steered clear of. Although they can work for bypassing blocks they offer no security whatsoever and there is no encryption layer added to any of the connections. The Smart DNS services are not secure nor where they designed to offer any online protection.

The same could be said for all the specialised proxies you find for sale too. A proxy will hide your identity to some extent from the website you are visiting and your ISP. It will provide virtually no security against any other kind of middle man attacks. Even some of the highly specialised ones such as the best rotating proxies used for retailing bots don’t really help. You can invest hundreds of dollars in the best rotating proxies you can buy, yet without a file encryption layer you are nevertheless at risk.

Thankfully there are some VPN solutions which provide the best of both worlds. They supply a proper level of security and provide the ability for streaming UK TV or other media sites. Firstly avoid those who sell themselves as TV watching services, they won’t take the security side seriously. They’ll likewise probably have slower servers as all the users will be continuously streaming online video through them. Look for service providers who stress the security of their system, make sure they don’t keep logs and have proper grown up responses to privacy issues.

Mathematical Concepts – Vedic Mathematics

Sometimes it’s easy to forget that there are different methods of achieving the same goal. Most of us from Western educational systems have learnt mathematics in a very similar way right from primary school to undergraduate level. However that doesn’t mean it’s the best way and there are certainly alternatives especially in the field of mathematics. One of the most famous is the method known as Vedic Mathematics, which I first learnt about in the remarkable BBC documentary – The History of Maths. You may be able to still access on the BBC iPlayer however you will need a residential IP based in the UK to be able to watch it. There’s more help on this at the end of the article if you need it.

What does Vedic mean?

In the introduction to the book Vedic Mathematics Sri Tirthaji describes two senses in which Veda can be understood. The first is as ancient scriptural texts and the second is as true knowledge.

The Vedas are perhaps the oldest known ‘texts’ and form the source of spiritual, philosophical, moral, ethical and secular teachings of the Hindus. It is not possible to determine their age because they were handed down by word of mouth, although they are thought to be more than five thousand years old. The Vedas were originally consisted of three texts – Rigveda, Samaveda and Yajurveda – each dealing with different aspects of human development and conduct. A fourth Veda, Atharvaveda, was included at some ancient epoch. At a time when the power of memory became insufficient amongst the protectors of these verses the Veda were written down. This may have been earlier than 1000 BC.

Each Veda has two portions, one dealing with prayers and mantras and the other (Brahmana) describing the meaning and procedure of the prayers and mantras. The sutras of Vedic Mathematics are supposed to be within an appendix portion (Parishishta) of the Brahmana section of the Atharvaveda. Sri Tirthaji did not give a precise reference for the sutras and to date nobody has found all of them. There are a number of possible reasons for this discussed below.

True Knowledge

The second meaning of Veda is true knowledge which is alive today and relevant to our lives. There are certain principles of conduct, for example, which would appear to be common to all races and religions and applicable at all times throughout history. To cite one example, there is a law written in the hearts of men by which it is natural not to seek harm of anyone. Both the Hindu principle of Ahimsa and the Christian ethic, “Love thy neighbour as thyself”, are direct expressions of this law.

This great principle is as relevant today as ever, irrespective of the date when it was first expressed. What really matters is its permanence and its relevance to the society in which we live. Similarly, with the Vedic mathematical sutras, it does not matter when they were first expressed. The important questions are, are they relevant and how can we not let them be forgotten?

What Sri Tirthaji appears to have discovered is how these sutras apply to the mathematics of his day. This is no doubt the reason for a good deal of arithmetic and algebra. He also applies the sutras to differential calculus, a relatively modern mathematical tool. This fact alone suggests that although the laws expressed by the sutras are unchanging the application of those laws changes with time just as the understanding and nature of mathematical expression evolves or devolves.

Recent research has discovered that the Vedic Mathematical sutras are applicable to any area or topic within mathematics, ancient or modern. The reason for this is that the sutras describe common mental processes of the human mind rather than particular mathematical fashions. For example, the sutras can be found at work within classical Greek geometry, the theory of determinants, in Chaos theory or even in Catastrophe theory.

Additional Reading:
Accessing the BBC – Do BBC Block Live VPN

Dutch Education Ministry Introduces Bitcoin into Syllabus

One of the constant criticisms that is often leveled at the education system particularly in dealing with scientific subjects like mathematics is that it is not made relevant to today’s world. Now in some cases this is difficult, as more advanced mathematical concepts are difficult to apply to real world scenarios. Of course, we can make basic principles like arithmetic very relevant as those skills are needed for almost everyone in day to day life. But what happens when we get a little bit more advanced? How do we engage with pupils to make the subject interesting in the context of the curriculum.

There are examples though from across the world how educational authorities are trying to incorporate modern concepts in the the teaching of maths. After all it’s common sense to include modern concepts into a subject like mathematics that is developing all the time. Demonstrating how maths can be used to solve modern day issues is the best way to make it relevant and interesting. For example studying the algorithms required in rotating residential proxies is something that can be used in today’s digital economy. Below is an example of a country taking a pro-active approach to introducing such concepts into their maths curriculum by covering things like Bitcoin. It refers to some questions revealed from some Dutch examination papers.

According to a rough interpretation of the test paper circulating on Reddit, students were actually presented the following question introduction:

” Bitcoin is actually a digital currency which simply exists online. It has already existed since January 1st, 2009, and can be used as settlement method in webstores and for other internet services. Bitcoin is not, like regular money, made by a reserve bank. On the other hand, every bitcoin that exist are created by having computers take part in dealing with distinct mathematical problems. This works as follows: anybody can easily run particular software on his or her computer that participates in solving such a mathematical problem. The operator of the computer system that solves the problem is given 25 (recently created) bitcoin as a reward. Simply because it was the situation that in 2014 this kind of a problem is resolved every 10 minutes, 25 new bitcoins were literally created every 10 minutes. On January 1st, there were (approximately) 12.2 million bitcoin.”

Following from the preceding overview, students were actually asked to deal with five separate mathematical problems. The questions asked that students “determine in what year the amount of bitcoin went beyond 18 million,” “determine from which year during the prize will be actually less than one bitcoin,” “identify the largest amount of bitcoin which can be in circulation,” in addition to presenting addition challenges based upon the formula used to resolve the aforementioned questions.

Netherlands Warming Up to Cryptocurrency

Dutch Senior High School Exam Comes with Bitcoin-Themed Questions. The test has actually been presented to students following increasing recognition of cryptocurrency on the part of Holland’s establishments.

Throughout March, the Court of Amsterdam determined that bitcoin provides “properties of wealth” while adjudicating a civil rights case concerning an individual pursuing settlement from an unfinished agreement concerning bitcoin mining. The law court concluded that “bitcoin represents a value and is transferable” and “therefore shows features of a property right. A case for repayment in Bitcoin is, for that reason, to be regarded as a claim that qualifies for verification.”

Earlier this month, the ambassador of the Dutch Blockchain Coalition, Rob van Gijzel, demonstrated a nationwide blockchain research agenda, which had been ordered by the Dutch Ministry of Economic Affairs and Climate Policy. The ministry had established a designated board, TopTeam ICT, entrusted with studying the potential legal, economic, and ethical significances of disseminated ledger technology in the Netherlands.

It’s vital that mathematics takes part in these modern day concepts especially when they are directly relevant. It also makes it easier to attract talented students from related subjects towards the study of mathematics. For example if computer students realise that the importance of maths to installing, configuring and deploying things like privacy or sneaker proxies with residential IP addresses then it’s more likely to attract those students.

The Beginning of Maths History

The history of mathematics is actually a long and involved story. Indeed many degree courses have specialised lectures on just this subject, however it is possible to identify the highlights especially if you focus on a specific section of the timeline. The story reaches backs in to the very annals of human history from before records began. Indeed it is not long after human dialect develops, it really is safe to assume that people start counting – and that fingers and thumbs provide nature’s abacus. The decimal system is actually no accident. Ten has been the basis of the majority of counting methods in history.

When any type of record is really needed, marks in a branch or a stone are the typical solution. In the very first enduring traces of a counting system, numbers are developed with a repeated sign for each group of 10 followed by another repeated sign for 1.

Math can not easily develop up until an efficient mathematical system is in place. This is a late appearance in the story of mathematics, calling for both the principle of place value and the concept of zero.

Because of this, the early history of mathematics is that of geometry and algebra. At their rudimentary levels the two are simply mirror images of one another. A number expressed as two squared can likewise be described as the area of a square with 2 as the span of each side. Similarly 2 cubed is the volume of a cube with 2 as the length of each dimension. The subject is obviously important and perhaps the application of geometry can be visualized more easily than any other branch. If you look at any plans, engineering drawings or even those diagrams on the ‘tactics board’ from the Match of the Day stream on your computer, then it’s simple to see the various geometric patterns develop.

Babylon and Egypt: from 1750 BC

The very first surviving examples of geometrical and algebraic calculations derive from Babylon and Egypt in about 1750 BC

Of the 2 Babylon is much more advanced, with quite complex algebraic problems featuring on cuneiform tablets. A common Babylonian maths question will certainly be expressed in geometrical terms, but the nature of its solution is essentially algebraic (see a Babylonian maths question). Due to the fact that the numerical system is awkward, with a foundation of 60, calculation depends largely on tables (sums already worked out, along with the answer given for future use), and numerous such tables endure on the tablets.

Egyptian mathematics is much less advanced than that of Babylon; but an entire scroll on the subject endures. Referred to as the Rhind papyrus, it was actually copied from earlier sources by the scribe Ahmes in about 1550 BC. It incorporates brainteasers for example, problem 24: – What is the size of the heap if the heap and one seventh of the heap amount to 19?

The papyrus does introduce one essential element of algebra, in the usage of a basic algebraic symbol – within this case h or aha, meaning ‘quantity’ – for an unknown number.

Pythagoras: 6th century BC.

Ancient mathematics has actually reached the modern world largely through the work of Greeks in the classic period, building on the Babylonian custom. A leading figure among the early Greek mathematicians is Pythagoras.

Above is the solution of the famous Rhind Papyrus problem as demonstrated on YouTube. In around 529 BC Pythagoras moves from Greece to a Greek colony at Crotona, in the heel of Italy. There he establishes a philosophical sect based upon the view that numbers are the underlying and changeless truth of the universe. He and his supporters soon make exactly the sort of breakthroughs to bolster this numerical faith.

The Pythagoreans can show, for instance, that musical notes vary in accordance with the duration of a vibrating string; whatever length of string a lute player starts with, if it is doubled the note consistently falls by precisely an octave (still the basis of the scale in music today).

The devotees of Pythagoras are also able to prove that whatever the shape of a triangle, its three angles always add up to the sum of two right angles (180 degrees).

The most famous equation in classical mathematics is known still as the Pythagorean theorem: in any kind of right-angle triangle the square of the longest side (the hypotenuse) is equal to the sum of the squares of the two other sides. It is actually unlikely that the proof of this goes back to Pythagoras himself. But the theorem is typical of the accomplishments of Greek mathematicians, with their primary passion in geometry.

This interest reaches its peak in the work compiled by Euclid in about 300 BC.

Further Reading:

There are some great Maths documentaries available online and from the world’s premier broadcasters.  Watch out for the History of Maths from the BBC, it’s not on the BBC iPlayer application at the moment but it’s repeated quite often and then added to the archive.  If you’re outside the UK then you can use this article to access – Watch UK TV Online – which shows how to use a VPN to hide your location and access from anywhere.

The Mathematics of the Beautiful Game

When we look at the news and see how companies like Cambridge Analytica are controlling our world through analysis of big data, it can be quite concerning. Mathematics is becoming increasingly important in all works of life largely to to analyse and process the huge amount of data that is currently available.

Over the last decade or so this has also started to filter into professional sports particularly the high profile professional ones like football. Sometimes when you watch your favorite team fail to impress yet again there seems to be little planning behind their performance. However at the top of the game this is not strictly true. Mathematics obviously doens’t control the game of football but it is used to help managers, players and staff maximise their performances in a host of different areas.

The focus is of course using mathematics to give a team an competitive edge. This is in the form of analytics, algorithms and numerous statistical models in various sections of the game. It all sounds incredibly high tech and modern but the origins of using statistics in football is actually quite old. IN the 1950’s a gentleman names Charles Reep, a retired RAF officer who loved football decided to try and help his beloved Swindon Town.

How did he do this? Well he took out his notepad and started analysing the players – making notes about movements, positions, tactics and their setup during the fame. His goal was to try and identify small changes which could be made to help his team score more goals.

This was literally decades ahead of his time. Now as we approach the 2018 World Cup, this sort of analysis is actually commonplaces in football. If you tune into any football programme you’ll see a bewildering range of statistics about the game virtually as you watch on screen. Certainly on the UK football shows on Sky TV or if you’re streaming Match of the Day online like this, then you’ll get loads of statistics literally at the push of the button.

The biggest football teams in the world all use advanced systems of collecting data, analysing them and producing metrics and reports on all aspects of the team and their players. There is an element of using algorithms in bringing success to the football fields.

Ironically going back to Charles Reep – his team had little interest in the statistics that he was producing. However another team did decide to take it further employing him as an adviser, that team was Brentford Town. The West London side were struggling with relegation and used all his recommendations which indeed seemed to make a huge impact on their results. Brentford were saved from dropping down a division and he was considered something of a hero to Brentford fans.

Reep however was not popular among other football fans partly because of how his data suggested the game should be played. His data suggested that the majority of goals scored came from moves involving three or less passes. In essence he suggested the most effective way of winning a football game was to play the much maligned ‘long ball’ game. Basically to maximise their chances thy should hoof the football forward and hope for a knock on or lucky break.

Football teams now take this sort of data very seriously and the revolution of ‘big data’ is increasingly being employed by teams at all levels of football. Indeed commercial data companies like SAP are starting to get involved in managing the data produced by actual games and training of professional football teams. The training is the obvious target initially because you can analyse and modify training much more than you can the actual game. Crunching and analysing the data means you can look at the strengths and weaknesses of each individual player and adapt their training to maximise their performances.

Additional: How to Watch Match of the Day Online

The Search for Absolute Zero

There were many great physics breakthroughs in Victorian Britain and a host of pioneering scientists. One of the most famous was born as William Thomson although he is known as Lord Kelvin throughout history. Probably his most famous practical achievement besides his work on hear and energy was helping to build the first transatlantic submarine cable used for the transmission of telegraphs.

Absolute zero is literally the envisioned point at which a material is actually so cold its own particles stop moving. Absolute zero in itself has actually never been achieved, neither in nature nor in the laboratory. Yet researchers have come very close. It really may be impossible to get to absolute zero, and also if we did we might not recognize due to the fact that absolutely no thermometer could determine it.

When we determine the temperature level of anything we are recording the average energy of the particles which make it up. Temperature level suggests precisely how quickly the particles are vibrating or moving around. in a gas or liquid, molecules are actually free to travel in any course, and frequently bounce off one another. So temperature is connected to the mean speed of the particles. Inside a solid, atoms are secured in a latticework structure, really like Meccano held together by electronic bonds. When this becomes hot, the atoms are energetic and agitate around a great deal, like wobbly jello, while sitting in their positions.

The concept was illustrated in several documentaries which were aired originally on the BBC, as part of their Physics season.  I think the programmes are now available on Netflix although I’m unsure of which region it is on.  If you need to switch locales on Netflix you’ll need an account plus a VPN with a residential address. This company provide residential IP addresses –, although they can be quite expensive.

As you cool down a material, its atoms move much less. Within a gas their speeds drop; in a solid their vibrations are reduced. As the temperature level drops further and further, atoms move less and less. If cooled sufficiently, a material might become so cold that its atoms cease moving absolutely. This hypothetical still point is called absolute zero. The concept of absolute zero was actually identified in the 18th century simply by theorizing a graph of temperature level and energy to zero. Energy rises steadily with temperature level, and the line linking the two quantities can be projected backwards to discover the temperature at which the energy reaches zero: -273.15 degrees Celsius or -459.67 degrees Fahrenheit

In the 19th century, Lord Kelvin contemplated a new Pressure temperature range that commenced at absolute zero.
Kelvin’s scale effectively took the Celsius temperature scale and repositioned it. So, instead of water freezing at O degrees Celsius it does so at 273 kelvins and boils at 373 Kelvins (equivalent to 100 degrees Celsius) Today, the majority of chemists use kelvins to measure temperature.

Further Reading: Useful Article: Match of the Day on iPlayer

Mathematics Shows on TV

I love science programmes particularly those about maths and physics, but it’s an area that is often neglected by many of the large media companies. Naturally they are difficult subjects and hardly likely to attract big audiences for the commercial channels, although some broad casters do go out of their way to cover such topics. There is an ongoing PBS TV collection (additionally numerous books as well as an internet site) called “Closer to Reality”. It is hosted by neuroscientist Robert Lawrence Kuhn. He’s featured in one-on-one interviews and panel discussions with the cream of the cream of today’s cosmologists, physicists, theorists, theologians, psychologists, etc. on all the Huge Inquiries surrounding a trilogy of broad topics – Cosmos; Awareness; Definition.
The trilogy jointly dealt with truth, room as well as time, mind and also awareness, aliens, theology et cetera as well as on. Below are a few of my discuss among the general subjects covered, mathematics. It’s nearly as good as some of the classic mathematics shows on the BBC from the last decade although you’ll have to buy them on DVD or perhaps use a UK TV VPN to access on BBC iPlayer.

Is Math Eternal?

Simple, complex, gorgeous, classy, awful, describes all, success story, fundamental bedrock, and so on. These are words as well as phrases usually related to mathematics, specifically appeal and stylish. That in itself does not make maths infinite.

I suspect that whatever the legislations, concepts and relationships of physics were to end up being, there would be some sort of maths to cover it. However, a lot of our maths births no connection to our physics – inverse dice relationship for instance.

Is Math Eternal 2?

Just what is the condition of mathematics? Is maths eternal?

Mathematics has no standing outside of the human mind. So mathematics is just as everlasting as the duration that human minds exist. Math is a development of the human mind (since I recognize of nothing else life type that uses mathematics in any type of abstract type of means) to assist people in dealing with the many (also invented) complexities of human culture (like trade, commerce as well as economics). Math offers useful applications like navigating and also offers getting as well as predictability in the environment that rule the human roost. Math is a not-thing since it has no physical residential properties and can not be spotted using any of your sensory apparatus. Naturally if we remain in a Simulated (Virtual Reality) Cosmos then we completely exist as, and also in, a mathematical construct.

Of course maths could also be the development of extraterrestrial intelligences, so mathematics could linger permanently in the universes as long as there are smart life kinds around to utilize and abuse their mathematical creations.

Is Mathematics Invented or Discovered 1?

IMHO, mathematics is a not-thing, an abstract idea that’s the invention of the human mind. Mathematics has none of the residential properties that we associate with points. Things can be uncovered; concepts are developed. One plus 2 equates to 3 (1 +2=3) is nothing. Pi is nothing. The square formula is nothing. Mathematical theories are not things. Math could not be found with any of the five detects, and even with instrumentation that prolongs our sensory abilities past that which our sensory apparatus could pertain to terms with. Math is an useful tool certainly, though several possible maths that could be typically aren’t. We browse around for and also embrace the kind of maths that fits in with just what we observe, with exactly what is useful, and also chuck just what does not suit into the rubbish container. So the gravitational force can be accounted for by an inverted square legislation, however not by an inverted cube legislation, so the inverse dice connection is taken into the rubbish container. Then we doubt the appeal as well as beauty of the inverse square regulation describing the means the gravitational force operates over range as well as forget about the non-beauty as well as non-elegance of the inverse dice law. As an aside, appeal as well as beauty are not legitimate clinical or even mathematical terms. You won’t discover them in any kind of scientific or mathematical thesaurus no matter just how frequently scientists as well as mathematicians utilize them according to most of the meetings here on “Closer to Fact”.

Is Math Invented or Discovered 2?

The collection of all possible mathematical equations is as close to infinity as makes no chances so it should not be unusual that a part of those needs to by coincidence reflect what takes place in the real world like the inverse square law for the propagation of electromagnetic radiation and gravity. That implies that mathematics is an invention as well as not an exploration. If there were actually this broad fantastic globe of a near unlimited number of mathematical relationships awaiting exploration as something part and parcel and essential to the cosmos, then one wouldn’t anticipate that the large majority wound up having no significance to the cosmos at large as well as the regulations, principles as well as partnerships of physics that crack the whip.

John Simmons –
Additional –

The Mathematics of the Drunken Walk

Lectures on statistics are not always the most exciting ones in the world of maths however certain subjects tend to attract students attention.  One of those is of course alcohol, and not in the over indulgence and problematic way where you end up taking a drug like this one called Selincro to combat it’s effects.   It’s actually revolved around a concept called the Drunkard’s Walk a famous mathematical concept.

It can be best explained in a theoretical example about a drunken man who was walking way too close to a cliff for someone in that state.  The idea is that from his starting position a single step forward would send him over the cliff.   He takes completely random steps oblivious to his own safety in any direction.  His probability of taking a step away is 2/3 and of taking a step towards the cliff is 1/3.  The mathematicians problem – what are the drunkards chance of escaping the cliff?

It’s a classic problem but actually touches on some advanced statistical topics. The particular topic is centered around Stochastic Processes which covers these ‘random walk’ issues, the specific name is called a Markov Chain.

Stochastic Process – a random process which explains how a system or process changes over another unit (commonly time).

Random Walk – a path derived from a series of completely random steps in some defined mathematical space.  Our example is the very drunk man tottering on the edge of a cliff.

Markov Chain – a random walk which actually maintains independent events.  That is the next event is not dependent or related to the previous one.  The drunken man has to be so drunk that his position and last action has no bearing on his next step!

The mathematics of this situation is of course all related to probabilities and how likely the man is to survive his reckless behaviour.   The simplest point is the beginning where he is one step away from the edge, the probability of surviving the next step is 2/3 and he has a 1/3 chance of stepping over the edge.

After that of course it get’s more difficult as the man if he survives will be moving away from the cliff edge and buys himself some time.   The easiest way to visualize this situation is to draw a chart of the probabilities with all the possibilities.  This has to include his relative position from the cliff and an assumption about where he ends up and what position is safe!

The problem is actually not that complex but it can seem so purely because there are so many possibilities after the initial even.  The secret is to define the chart with the possibilities and then try and generalize the problem in order to create a formula. This has to include the probability of stepping towards the cliff edge and stepping away.

To solve these problems you normally define the expected probability of the event you are trying to measure.  So in this case it would be defining the probability of falling from the cliff – say P1.

Without too much detailed analysis we can get to the formula as follows:

P1 = (1-P) + (p*P2)

Here the variable P2 is the probability of falling from the cliff on a path consisting of 2 steps!

John Welcome

Mathematics Key to 4D Printing

Although some of us are just getting our heads around the amazing potential in 3D printing, the next step is already on the horizon.    A leading mathematician has started working on the formulas required to step into an extra dimension!

Three D printing is already revolutionizing all sorts of areas from manufacturing, medicine to science and engineering.  It’s now fairly simple and inexpensive and has the potential to create all sorts of intricate objects quickly and cheaply.   There are printer parts in our machines and indeed people are having printed body replacement parts transplanted into their bodies with great success.

However there is always a next step, and now mathematicians are working on taking us in to the world of 4d printing.  Just to clarify we are talking about the possibility of fabricating objects with a programmable shape over time.  It’s always been theoretically possible however no-one had really starting looking at working through the complexities involved.

This seems to be changing as Professor Pasquale Ciarletta from Milan has just published a paper in ‘Nature Communications’ where he has started working through the numbers about a specific problem with this.  The professor has been focusing on how to control the sudden nucleation of localised furrows in the soft solids produced in 3d printing.

The advantages and possibilities of these developments may not be initially apparent.  However in addition to the advantages to the field of engineering there is huge potential to have the ability to design and print objects which can morph over time.  The paper related the development to the field of development biology as particular interest.  Here we could look at things like tissue morphogenesis and other areas such as issues in the brain or tumour control.

Ciarletta has acknowledged that there are great complexities behind making this work.  There has already been lots of experimental investigation of the issues involved – the physics behind the concept of ‘creasing’ being particularly challenging.  His study proposes a unique mathematical approach to predicting the experimental conditions required to trigger the onset and how creases change over time.  This is the key to being able to control their appearance on a specific scale and ultimately to be able to print them in 4d.

There are parallel advancements being made in the area of 3d printing too.  You can already sit down and watch the football on Match of the Day live like this on a completely 3d printed television set.  It is also now possible to edit specific printed objects after they have been created.  This is achieved by repeatedly changing the colours of 3d printed objects after thy have been printed.

The concept is currently being developed under the name ColorFab and it involves using a specially created 3d printable ink which can actually change colour under certain conditions – primarily after being exposed to UV light.  This of course has a time delay currently estimated at around 20 minutes, however the researchers are hoping to improve on this substantially in further development.

Further Reading: Available on British TV

The Life of John Napier

John Napier was born in the year of 1550 at Merchiston Tower in the City of Edinburgh in Scotland.  He dies at the age of 67 on April 4, 1617  in his home town of Edinburgh, Scotland.  If you were to choose a top ranking table of world mathematicians then Napier would almost certainly feature in it.   He spent much of his life including his work as an Alma mater at the University of St Andrews where he was also a Doctoral adviser.  Of course as any school child will probably  know he is most famous for that little book of Logarithms.  However he was a man of many talents and he is also famous for such things as Napier Bones and the introduction of the Decimal Notation. John Napier of Merchistonalso signed as Neper, Nepair, nicknamed Marvellous Merchiston, was a Scottish landowner known as mathematician, physicist, and astronomer. He was also actually the eighth Laird of Merchiston. His Latinized name was Joanne Nepero or Joannis Neperi.  However we know him know as John Napier and is certainly best known as the discoverer of logarithms.

John Napier was featured in the recent BBC’s history of mathematics which you can still get on the BBC iPlayer for a few weeks.  If you’re outside the UK then this article entitled How to Watch UK TV from USA should help, you just need to hide your location and it all should work perfectly.

He also invented the so called Napier’s bones and made common the use of the decimal point in arithmetic and math. Napier’s birthplace, Merchiston Tower in Edinburgh, Scotland, is now part of the facilities of Edinburgh Napier University. After he died from the effects of gout, Napier’s remains were buried in St Cuthbert’s Church, Edinburgh. Napier’s father was Sir Archibald Napier of Merchiston Castle, and his mother was Janet Bothwell, daughter of the politician and judge Francis Bothwell, Lord of Session, and a sister of Adam Bothwell who became the Bishop of Orkney. Archibald Napier was 16 years old when John Napier was born.

As was the common practice for members of the nobility during that time, John Napier didn’t enter schools until he was 13. He didn’t stay in school very long, however. Little is known about those years, where, when, or with whom he might have studied, although his uncle Adam Bothwell wrote a letter to John’s father on 5 December 1560, saying I pray you, sir, to send John to the schools either to France or Flanders, for he can learn no good at home, and it is believed that this advice was followed. In 1571, Napier, aged 21, returned to Scotland, and purchased A castle in Gartness in 1574.

On the death of his father in 1608, Napier and his family moved to Merchiston Castle in Edinburgh, where he resided the rest of his life. Advances in maths – His work, Mirifici Logarithmorum Canonis Descriptio contained fifty seven pages of explanatory matter and ninety pages of tables of numbers related to natural logarithms. The book also has a fantastic discussion of theorems in spherical trigonometry, commonly known as Napier’s rules on circular parts.

Jim Hamilton. Watch BBC iPlayer in Spain