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As a Muslim American, I was shocked by the Christchurch mosque shootings in New Zealand that took the lives of 50 completely innocent people and injured scores of others in March. The tragedy was made more sickening by the fact that the alleged gunman, reportedly a white supremacist, live-streamed the first attack on Facebook Live.
The fact that the attack happened during the Muslim Friday prayer, a religious service I attend regularly myself, left me deeply shaken and heartbroken. Besides privately grieving for those who perished in Christchurch, I also attended public rallies to show solidarity with the victims in the aftermath of the carnage in New Zealand.
But there's something you won't see me doing: Calling for a crackdown on what some deem offensive speech on social media — and a crackdown on what some consider extremist right-wing speech on social media in particular, as many have called for in the wake of the tragic Christchurch mosque shootings.
I know this may surprise some people. As I said, as a Muslim, I was particularly outraged by the slaughter in New Zealand. But I'm not outraged to the extent that I believe that:
- Censorship of speech, whether by governments or near-monopolistic social media corporations, is an appropriate response to extremism; and
- censorship of speech is an effective way to combat extremism.
To be clear: I applaud the swift action of Facebook, Twitter, YouTube and other social-media sites to take down videos of the Christchurch shootings. Indeed, Facebook reported it removed or blocked 1.5 million videos in the first 24 hours after the attacks.
To me, these videos were nothing more than sick snuff films; pornographic videos of actual murders of innocent human beings. There's simply no place for such vile videos on social media.
I also believe there's no place, anywhere and at any time, for people to threaten and openly call for violence against others on social media. There are common-sense limits to free speech — and that limit is reached when it comes to encouraging and advocating violence.
What I oppose is the censorship of controversial speech, versus dangerous speech, and I believe we unfortunately crossed that line on social media even before the New Zealand mosque shootings.
Most of us have now heard of social-media firms cracking down on, say, right-wing conspiracy theorist Alex Jones and the blocking of sites and posts by other conservatives.
Some may dismiss the complaints of conservatives that they are being unfairly targeted by social-media giants, but to do so ignores a potentially serious problem.
Conservative sites and posts that are not espousing violence are getting shut down or removed by social-media giants because their views are deemed offensive, not necessarily dangerous. And all this is happening in a somewhat arbitrary and potentially biased manner.
After the Christchurch tragedies, one of my concerns was that the justified removal of the mosque-shooting videos from social-media sites would lead to further censorship policies — and, sure enough, that's what happened.
Late last month, Facebook announced that it intends to ban content that glorifies white nationalism and separatism, a major policy shift that's slated to begin early this month.
But do we really want to go down this road? Do we really want huge social-media sites defining what is and what isn't white nationalism and separatism — what is and what isn't glorification of such causes? More importantly, do we really want social-media companies defining what's offensive and controversial speech in general?
I've dedicated a large amount of my academic time studying true online extremism on social media. And by true extremism, I'm talking about truly dangerous views espoused by groups like ISIS that glorify death and terrorism and that explicitly encourage violence on a mass scale against others.
These are the truly dangerous groups and sites we need to keep our eye on moving forward, and it's not easy keeping track of them on social media and in other dark corners of the internet.
The bottom line is that we have to get smarter and more realistic when it comes to dealing with extremist views on social media.
While it is important to prevent the spread of content that directly endangers people's lives, we need to be careful and differentiate between those expressing clearly violent views from those simply expressing controversial views.
Social media companies should take action to protect us from direct harm, not become arbiters of what is and isn't offensive. When it comes to free speech versus online extremism, we shouldn't throw out the baby with the bath water.
Tauhid Zaman is associate professor of operations management at the MIT Sloan School of Management. His research focuses on solving operational problems involving social network data. Some of the topics he studies include predicting the popularity of content, finding online extremists and geo-locating users.


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Recently I switched my brand from ServiceKey to CEO Warrior.
Why did I make the switch? One reason is because I wanted to express, through my brand, something that I've been thinking about for a while: there's a massive difference between business owners. On one side of the spectrum you have struggling entrepreneurs who are just trying to get through the day. On the other side of the spectrum you have massively successful people who run a business.
When you compare put both of those people into the same room, you might call them both "business owners" but in reality you are looking at two VERY different people:
• The struggling business owner is working hard – running the treadmill or, to use another analogy, perhaps feeling like they're bailing water on a sinking ship.
• The ultra-successful business owner also works hard – but they're like a master juggler who is able to keep many knives in the air at once without more than a simple touch of the knife to keep it in rotation.
We normally call both of those groups "business owners" but I wanted to express the vast difference between the two. So the ultra-successful business owner is someone I call the "CEO Warrior".
The difference between business owners and CEO Warriors can be seen in what they think about:
• Consider the mindset of most business owners: they're thinking about "how will I make payroll?" and "how will I get more customers?" and "how do I keep my team busy?"
• Now compare this to the CEO Warrior. They're thinking "what systems can I build?" and "how can I get leverage?" and "how can I grow my business?"
A business owner thinks small. Yes, even if you run a busy business, you're still thinking small. Consider a CEO like Jeff Bezos of Amazon or the late Steve Jobs of Apple. Do you think they are wondering how to get more customers or how they will keep their team busy? No, they think bigger things – things that still address customer acquisition and team productivity but on a bigger scale.
Being a CEO Warrior doesn't automatically eliminate the struggle or the challenges you face. However, being a CEO Warrior changes what you think of your business and the actions you take. Rather than bailing water, you start juggling knives (to mix my metaphors!) and your business takes on an entirely different feeling.
What is CEO Warrior? Here's how I define it…
• CEO Warrior is a mindset. It's a way of thinking and acting and living. It's a way to run a business. It's a way to view opportunities and challenges.
• CEO Warrior is an aspiration. It's a new way of thinking about your role in your company and how your influence as a CEO Warrior can help you achieve that aspiration.
• CEO Warrior is a call to action. It's a commitment to fierce, relentless action – like a warrior in battle who pushes himself beyond his limit so that he emerges victorious.
Become a CEO Warrior and see your entire approach to business and life transform!
Are you SERIOUS about no longer treading water and MOVE your business forward WARRIOR STYLE? Find out more about Mike's Warrior FAST TRACK Academy!

subset: commoncrawl


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Think about this: We use our eyes to take in 90% of everything going on around us. All other senses combined are just ten percent.
Wouldn't it be nice to know your eyes are helping you react to and absorb everything they possibly can throughout your day? But how can we show our doctor how we're using our eyes, to make sure this is the case? There's new technology that does just that: it performs a multitude of tests in the form of eye-tracking "video games," each taking only a few minutes to complete. The resulting reports provide valuable insight into how a patient's eyes and brain are functioning. It's called RightEye, and it helps EYEcenter optometrists and vision therapists to better assess patients of all ages and vision levels.
During her years as a tennis coach, RightEye co-founder Melissa Hunfalvay read a statement that changed her perspective on vision:
'Elite level tennis players do not watch the ball.'
"It confused me at first, because 'watch the ball' is a fundamental concept in sports," Hunfalvay said. "I started to realize then, that experience teaches us where to look.
"Experienced tennis players watch the arm as it comes forward on a serve: this helps them anticipate where the ball's going to go," Hunfalvay continued. "Inexperienced players wait and watch for the ball, and this doesn't allow enough reaction time. The same is true in soccer, football, baseball--the list goes on."
Have you ever seen a teenager drive? They often don't look past the hood of the car. But experienced drivers look 20 feet ahead. If you text and drive, you look at the same places as inexperienced drivers. Statistics on both athletics and distracted driving tell us that where we look matters. Tracking eye movement can provide this information quickly and accurately.
Where you're looking can help you anticipate better and improve your safety. But our eyes also tell us how we look at something. Doctors assessing head injuries ask patients to follow a finger with their eyes. We can now re-create this test using eye-tracking: the paths your eyes follow allow us to see differences between someone who has had a concussion and someone who hasn't.
Our eye movements can also reveal if we're seeing clearly. To read effectively, our eyes need to converge. There are times when this fails to happen, and that's called "convergence insufficiency." It's one of many eye conditions that aren't tested for during basic vision assessments, like those provided in most schools. Using eye tracking technology can give us this information within a few minutes.
Think of the implications of missing the opportunity to assist kids with reading, and potentially misdiagnosing them with attention disorders because they look around the room instead of at their work. We might think they have trouble focusing, but really what they need is reading glasses.
RightEye is a solution for these kids, for adults, for athletes, for patients recovering from a concussion. Since many health and vision conditions are identified through eye movement, tracking it can help us assess your vision like we've never been able to before. Click here for more information about RightEye tracking technology, and call us or click here to schedule a screening.
The content on this blog is not intended to be a substitute for professional medical advice, diagnosis, or treatment. Always seek the advice of qualified health providers with questions you may have regarding medical conditions.


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Published 2009 Revised 2018
1. In the beginning ...
Knowledge about the possible beginnings of human mental development comes from research on the co-evolution of language and the human brain. The central idea that comes out of this research is that mankind, uniquely, is what is called a 'symbolic species'. That is, we have the ability to make ideas 'visible in the mind'. This means we can create, manage, manipulate and blend images in ways
that help us to form new relationships and produce new concepts.
We can only speculate on the earliest stages in the development of mathematics but we do have evidence which shows that we have the power to visualise and represent physical objects in our mind. This power is seen in the representations of counting, bartering and building activities of early civilisations. In particular, our perceptions of symmetry seem to have produced many kinds of geometrical representations in different cultures.
In these images, a square pattern has been divided into different areas, making rectangles or triangles.
In the above two images, other shapes have been produced, leading to speculations about relationships between numbers and areas, and it is thought that the elementary number theories of the Pythagoreans might have been generated by images like these [see Note 1 below].
Further manipulation, dissection of squares and rearrangement, leads to images of right-angled triangles and the familiar relationship between numbers and areas. For example:
|In particular, the Papyrus has a series of problems showing how to solve what we could call 'linear equations' by a method that became commonly used by merchants throughout the Mediterranean countries for some three thousand years, called the 'Method of False Position'. It is used for all kinds of calculations involving comparison of values and quantities. This method still appeared in school text books in the early 20th century.
|In a quantity and its $\bar{4}$ (is added) to it so that $15$ results
A quantity is added to a quarter of itself and the answer is $15$
Calculate with $4$
You shall calculate its $\bar{4}$ as $1$. Total $5$.
You begin by assuming $h = 4$,
so, as the left hand side is $h + \frac{h}{4}$
this gives $4 + 1=5$:
$h = 4$ does not work as it gives an answer of $5$ not $15$.
Work with $5$ to find $15$.
\ . $ ~~~~~5$
\ $2~~~~10$
$3$ shall result.
|Now take the $5$ and divide it into $15$ to get $3$.
Multiply $3$ times $4$
\ $4~~~~12$
$12$ shall result
|Multiply the $4$ by $3$ to find the result you want, $12$.
. $~~~~12$
$\bar{4}~~~~~ 3$ total $15$
The quantity $12$ its $\bar{4}~~~3$.
Total $15$
|So, $12$ add a quarter of $12$ is $15$.
In modern notation, the problem looks very easy: $$h + \frac{h}{4}=15$$
We begin by using $h=4$ which immediately makes the fraction $\frac{h}{4} = 1$
So the left hand side is $5$, but we need $15$.
If by using $4$ we obtain $5$, what do we need to use to get $15$?
|The sundial was one of the first instruments used for measuring time, and the properties of the right-angled triangle were well known to ancient people (Problem 56 deals with similar triangles). The slopes of pyramids and other sloping surfaces were measured by the 'seked' - the horizontal distance measured for every cubit of height.
Visualising a triangle like this would make the problem much simpler and the ratios could then easily be compared. $$\frac{\mbox{'}h\mbox{'}}{15}=\frac{4}{5}$$
So, for the denominator of the right hand ratio to be $15$, we need to multiply the numerator and denominator of the ratio $\frac{4}{5}$ by $3$.
For two squares of the same size, it is easy to see how to combine the areas to make one square, but not obvious for squares of different sizes.
"If it is desired to combine two squares of different measures, a [rectangular] part is cut off from the larger [square] with the side of the smaller; the diagonal of the cut-off [rectangular] part is the side of the combined square."
"Alternatively if it is desired to combine two squares of different measures, a rectangle is formed with the side of the smaller [square] [as breadth] and that of the larger [as length]; the diagonal of the rectangle [thus formed] is the side of the combined square."
These instructions clearly show a knowledge of the 'Pythagorean relation'.
The base line for the altar was always East - West and careful and precise interpretation of the instructions enabled the priests to build the falcon 'fire-altar'.
Length, Width.
I have raised, length and width. Surface: $252$
I have put together length and width: $32$
$32$ put together,
$252$ surface: $18$ length, $14$ width
The problem and answers are stated,
and the method is described.
|This is the way of doing it:
|Here is the arithmetic:
|$~~~~~$break off half of $32$: this gives $16 $
|$~~~~~$raise $16$ by itself: $256$
|$~~~~~$leave out the surface: $256 - 252 = 4 $
|$~~~~~$find the side of this square $4$: it is $2$
|$~~~~~$put together $16$ and $2$: $18$ length
|$~~~~~$tear out $2$ from $16$: $14$ width
|$16 - 2=14 $
|I have raised length and width. $~~~~~ 252 $
|$(16+2)(16-2)=252 $
The visual thinking behind the calculation appears to have gone like this:
We have the area of a rectangle, $252$;
We have the sum of its length and width, $ 32$ (the semi-perimeter);
We know from practical experience (see diagram above); that by removing a small (red) square from a larger (blue) square, we can make a rectangle.
So, if we make the side of the large square half of $32$; then the area of the large square will be $256$.
Now take away the rectangle, (area $252$), and we are left with the small (red) square.
Geometrically, this will always work whatever the lengths of the sides concerned. Arithmetically , the problems were arranged so that the numbers used in the calculation always resulted in a perfect (red) square.
Many more examples like this have been discovered, and as well as the underlying geometrical visualisation, there is also the clear emergence of an algorithmic process . The Babylonians had established one of the important essential aspects of problem-solving. They had established a method for solving particular types of area problems , and it was this method that was taken over by later generations of scholars and eventually developed into the algorithm we use in classrooms today.
|The red side of the rectangle is brought into line with the upper blue edge by drawing an arc (radius r ). The (red + blue ) line is bisected to find the centre of a circle, and a semi-circle is drawn. The side of the square required is the green vertical line.
|In this diagram there are three similar right-angled triangles, APB in the semicircle, AXP and PXB. The coloured sides of the triangles correspond to the diagram above. The relationship shown is the equivalence of corresponding ratios.
The six cases of equations were:
In our notation:
Compared with the Babylonian word problem in section 5 above, this is another case where the semi-perimeter of the sides of the rectangle are given, so that the area of the square made with half the root is larger than the area of the rectangle. In this case the algebra of his first solution is:$$\frac{10}{2}-\sqrt{\frac{10^2}{4}-21}$$
and his second procedure is $$5+\sqrt{5^2-21}=7$$ which gives the diagram opposite, where the $7 \times 7 = 49$ fills the empty space.
Evidence for this kind of activity is deduced from fragments of writings by the early Pythagoreans. Also, the elementary number theory in Euclid Book VII. Katz (1998) has a section on the Pythagoreans (pp. 48-51)
The dating of early Indian mathematics has always been controversial. As with other civilisations it was basically an oral culture, and what was written down appeared long after it was first conceived. Added to this the Indian scholars wrote on palm leaves that rotted away quite quickly in the humid climate. Documents were copied and copied many times, so we never have the original text and it is virtually impossible to reconstruct the early history of Indian mathematics with any certainty.
Quoted from Kim Plofker's chapter on Indian Mathematics in Katz (2007 p.387).
Both quotations are from the Baudhayana - Sulbasutra (c. 1,000 - 500 BCE) in Kim Plofker's chapter 4 in Katz 2007.
Evidence for this geometrical basis comes from recent research into the language and culture of the period by a group including Jens Hoyrup from Roskilde University in Denmark and Eleanor Robson from Cambridge.
This is my version of the problem using Hoyrup's (1984) Babylonian 'word list'. See also Pedagogical Notes item 5.
The 'Pythagorean' diagram on the right hand grid in section 1 above has a rational area of 5 units, and non-rational sides.
Heath, T. L. (1963) A Manual of Greek Mathematics. Dover (original Oxford University Press, 1931)
'Mal' was Euclid's word for 'wealth' (the unknown).
A Dihram is a unit of currency, still used in the Arab Emirates.
All translations in this section are quoted from Berggren, Chapter 5 in Katz (2007).
Arcavi, A. (2003) The role of visualisation in the learning and teaching of mathematics. Educational Studies in Mathematics 52 (3) 2003 (215-224)


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It's been a glorious summer, which has made for some heated work in the brewery! That has meant that all of the Old Sawley Brewing Company team have particularly enjoyed their summer holidays this year, taking a break from the intense heat of the brewhouse.
Head Brewer Roo headed over to Lanzarote and couldn't resist the opportunity to visit a local brewery. A busman's holiday is a fantastic thing when you are a brewer! He went to the artisan brewers, Los Aljibes which is on the easterly side of the island. Brewer Gav showed him around, and happily there is also a restaurant and bar on site so there is plenty of opportunity to sample their wares!
Gav is living the dream in Lanzarote having moved over from Bolton. As you can see from the photo, demand is outstripping capacity and so he is looking to move the brewery to get more space. Currently they are offering a dark, a Pale Ale, an IPA and an APA. Roo tried some from the conditioning and was very impressed with it.
Roo really enjoyed the opportunity to talk brewing with colleagues in a different country, comparing notes on technique and practice. Los Aljibes have to use reverse osmosis on their water, do not filter unless bottling and pack their beers full of hops!
Meanwhile, our Business Development Manager James also enjoyed the opportunity to jet away.
James' research was enjoying a lovely Free Dive IPA from Copperhead Brewery of Tampa whilst watching the sun set over the Gulf of Mexico. We can't help but think that this research was not quite as in-depth as Roo's but it certainly makes us jealous!
Of course, someone has to hold the fort while all of this gallivanting takes place! This meant it was time for Liam to step up to the plate - with his first solo brew (under Mark's watchful eye). He brewed our signature ale, Little Jack. But how does the student match up to the master? Time will tell...