Education and Architecture

It seems to me that one of the things a teacher can do to "re-enchant" education is draw his students' attention to the world we live in, and to the world we have built around us - the language of form in architecture. We can connect this easily with mathematics, geometry, astronomy, music, and history. An article by philosopher John Haldane in The Catholic Herald for 30 August 2009 even gives us a way to connect it with biology.

The architects of classical antiquity and of renaissance and later neo-classicism were resolute humanists. For them, man and measure go together, either with man being the measure of all things, or else in his measuring cosmic order through his ability to discern mathematical sequences, ratios and parallels.

The principle architectural expression of this abstract ordering is the façade or wall divided into parts: surface and spaces defined by classical geometry. When competently conceived and executed such schemes are undeniably pleasing, like the rhythm of a well-ordered rhyme. But the inspiration is less to do with what is observed in nature than with what is reasoned to through mathematics and philosophy. The Gothic, by contrast, takes its key from the living world of ordered growth. From beneath the earth the germinated seed breaks through, first establishing a stem, then branching, next putting out leaves and buds, then in turn producing flowers and fruits. The order is not one of mathematical design but of organic progression; and it pre-exists invisible but immanent within the seed.

Like plants, Gothic buildings grow out of the earth and are developed upwards, drawing material from below but reaching for the light. They represent a recognition of the order of nature and an identification with it; acknowledging and seeking to imitate divine design.

Of course, the "living world of ordered growth" is itself a mathematical order, and the Gothic masons probably understood it as such. Nevertheless, Haldane is absolutely right that in a Gothic cathedral we easily imagine ourselves "standing beneath the canopy formed in an avenue of over-lapping trees, or imagine the undersides of the leaves of those trees." And it is surely true that "the power of England's Gothic cathedrals to prompt wonder at the order of nature and to encourage speculation about the source of that order is not altogether diminished. Hundreds of years on from their first appearance they remain sources of theological inspiration and reminders of the possibility of integrating intellect, imagination and sense in the embodiment and recognition of religious meanings."

Born in Britain but living in California, the architect Christopher Alexander believes that architecture should be rooted in a profound understanding of the human person as spiritually transcendent, yet intimately related to the cosmos. His book series The Nature of Order (2004) opens with an assault on the mechanistic idea of order, which he traces back to Descartes in the seventeenth century. He argues against this idea that matter and space possess degrees of life, because the elements of which they are made relate to each other as mutually supporting “centers”, making the whole more than the sum of its parts. He illustrates this by means of the patterns in a Turkish carpet and the architectural and decorative features of buildings like the Alhambra and Chartres Cathedral.

Alexander defines fifteen structural features that correlate with degrees of life. This enables him to become quite practical in his recommendations. The examples he chooses are eclectic, ranging from mud huts to palaces, from Shaker furniture to Persian glassware, from electrical discharges to cell walls, from the branches of plants to the cracking of mud and the formation of crystals and feathers. He suggests that his approach offers a way beyond Hume’s fact-value distinction. Our feeling-response to things, properly discerned, is an objective measure of their structural wholeness. The implications of all this for education remain to be explored.

Take a look at the "50 most extraordinary churches in the world" and see if you agree with your friends on which are the most beautiful!

The beauty of mathematics

For many of us, “mathematics” and “beauty” sit oddly together. We may remember math as boring or even frightening, but hardly beautiful. Yet math is the key to science, and science dominates our age. And there is another way to look at it.

The single most compelling reason to explore the world of mathematics is that it is beautiful, and pondering its intriguing ideas is great fun…. To study the deep truth of number relationships feeds the spirit as surely as any of the other great human activities of art, music, or literature. -- Calvin Clawson

This quotation is taken from p. 239 of a wonderful book called A Passion for Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality, by Clifford A. Pickover. It is full of games and quotes and ideas that parents and teachers will find useful to get kids of all ages and all backgrounds interested and involved with maths and geometry. Pickover himself believes that “mathematics is the loom upon which God weaves the fabric of the universe” (p. 53).

Looking back on the maths classes I sat through as a kid, I can't help wishing I had been taught the subject not as a collection of seemingly arbitrary rules and procedures but (1) historically (starting with Pythagoras), (2) aesthetically (in relation to music, painting, architecture), and (3) symbolically (with a view to qualities, meanings, analogies inherent in numbers and shapes) - not to mention (4) playfully.

The religious and secular use of numbers are related, as I tried to show in The Seven Sacraments (Crossroad) as well as in Beauty for Truth’s Sake. The numbers particularly prominent in Christian tradition are 1, 2, 3, 4, 7 10 and 12. One is the source of all other numbers, 2 is the beginning of multiplicity, there are three divine Persons and three theological virtues, four cardinal virtues and four Gospels, seven sacraments as well as seven days of creation, ten commandments, twelve apostles and twelve tribes. And all these numbers are interrelated: 7 is 3 plus 4, 10 is 3 plus 7, 12 is 3 times 4. So in a way the fundamental structural numbers only go as high as 4, and all the others are made up from these. That takes us back to the sacred Tetraktys of the Pythagoreans, whose influence on the Christian tradition has been underestimated.

There is a fascinating article by Karen Kilby called MATHEMATICS, BEAUTY AND THEOLOGY that I recommend to your attention if the subject interests you. (Just follow the link.) And I also want to mention "The Curriculum of Beauty" by David H. Albert and Joyce Reed in Life Learning magazine. Albert writes:

Our children have within themselves, or so I am led to believe by my experience of them, an inner yearning for the beautiful, a potential wonderment and a delicious longing and love and trembling waiting to be empowered on its quest. This yearning is not likely to be fulfilled in a high school hallway or on the shopping mall checkout line. So what if we were to set as our task – as parents and as educators – acquainting our children with the beautiful without and the cultivation of the beautiful – the yearning – within? How might we go about our homeschooling lives differently if we were to conceive of what we are doing as primarily an aesthetic task?

Light

Education is a never-ending process – or should be. And what we learn depends largely on what catches our imagination. Not long agoI learned something by chance that changed the way I look at the world. Like many people, I grew up with the idea that the light by which we see things emanates from a source, bounces off the thing I am looking at, and collides with a cell in my retina. Not true, apparently. When a photon hits something, it is absorbed. This energy is then radiated back again as light: not the same photons, but new ones. In a way, then, the whole world is glowing. The leaves on the trees are alight. Your eyes are (almost literally) shining like stars.

Such a world is much more alive, more beautiful, it seems to me, than the passive, lumpen world I previously inhabited. Matter is active in revealing its colours and shapes to our eye. I think St Denys would have appreciated this. The way light is passed on by matter is an analogy for the way spiritual illumination is passed down his hierarchy of angels: each angel makes the light his own, and illuminates the others by his own gift. It also echoes the pattern of the Trinity, the supreme three-dimensional act of love. In love each gives to the other, each receives from the other. When we see anything, it is because a photon has been received, and a photon given. Light is gift.

Universal Search is Here!

I posted about Universal Search and what you need to do to get ready for it and stay on top of your search results in the beginning of the year. If you don't recall or if you just started following me then you can look at the post located below:

http://myseogal.blogspot.com/2009/01/are-you-ready-to-go-universal.html

I remember getting some negative feedback from those who thought what I was saying was bologna or thought what I was saying was insignificant or didn't apply to them because they already had this website marketing/SEO thing in the bag.

Well good for them!!!! Goody two shoes...... (P.S. I love those type of people, they make me want to work hard at proving them wrong!)

Well guess what guys, Universal Search is here now and very visible in the searches.

Go ahead, do a search, search about anything. Nine times out of ten I bet you will see a variety of options for your search. Unless you're searching something about pet rocks??

You may see Google's Shopping results first or paid advertising, nothing new there. Then you may see a display of images that are related to your search (this is part of the Universal Thing I've been talking about), then videos (Yup, still part of the Universal Search thingy), then the search results.

Now let's go over some things and answer a couple of questions and when I mean a couple I mean a couple! I'm not going to go deep into this right now. Please feel free to read my first post about it to find out more detail about it and what you can do to stay on top of your search results:
http://myseogal.blogspot.com/2009/01/are-you-ready-to-go-universal.html

Here's a common question I get all the time:

How do I get my images to show up in the search results?

Here's a quick tip:
When you upload pictures to your website. Are the images name something like IMG25687? or AzBe25E? Well if they are, CHANGE THEM. Unless someone is searching for an IMG25687 then the chances of you showing up in the search results is very, very, very slim. Try naming your image with your keywords in mind.

Example: If your image is a picture of a giraffe print purse, optimize or name your image with those keywords when you save it to your harddrive or your My Pictures located in your My Documents. Upload them to your website, then go to your Webmaster Tools in your Google Account and include your images in Google's Search. You can do this in your Settings in your Google Webmaster Tools. You can also create a sitemap with your images included and upload it to your Webmaster Tools.

How do I get a video to show up in the search results?

The same goes for videos. Make sure your video file is named with your keywords in mind. Add the videos to your site and to popular video sites like Youtube who just so happen to be owned by Google (wink, wink).


These two tips plus others included in the post I did a while back are really beneficial to your online search results success!

So work on getting those images optimized and those videos uploaded to your site!

Carla Phillips
My SEO Gal
http://myseogal.com
Got a Question or need help? Contact My SEO Gal Today for a FREE SEO Quote.

10 Absolutely Awesome Advertising Tips!

When you aren't seeing any orders coming in or when you are starting to bite your nails due to the current economy. It's a normal reaction to start looking at things that can be cut in the budget like marketing. Marketing should be the LAST thing on your list to cut out. If you make that choice to cut out marketing you are taking a huge risk of crashing faster than you thought you already were!

Marketing your business and attracting new customers should be an ongoing process, not something you do one month and then forget about for three or four at a time. You will never see a sale at that rate! Below are a list of low cost to free advertising options so you can succeed online.

1. Join the Social Networking Sites: This is a must. If you haven't gotten around to joining social networking sites like Facebook or Twitter. Now is the time when you should sign up for an account to market your products or services. Social Networking or Bookmarking Sites are great ways to generate traffic and to start a buzz about your business. They are free to use and get tons of traffic each month.

2. Be prepared for Peak Seasons
   You must be prepared for peak seasons. The holiday shopping season is already here!!! Do you have your holiday items on your site? Do you have your holiday newsletters and sales lined up. If not, don't start running around, pulling out every strand of your hair off your head. Simply sit down and write out your plans for this holiday shopping frenzy. What new products or services are you going to offer. Are they holiday themed products or are they gifts for people or pets even? Have a service that you offer to other businesses? Create a holiday package just for your customers. Offer a discount or an incentive. Research seasonal keywords that people are already using for the type of products or services you have to offer.

3. Unique items or services : Make sure that you have unique items or services offered on your site. Take a look at your competitors site and see what they are offering and what they aren't offering. Try to find products being offered by manufacturers in your niche that your competitors do not have yet. Don't forget about the “Small Business Owners”! Small business manufacturers have the most unique products and are looking for retailers to help distribute their products. Contact them to see if you can get a sole contact with them to sell their products online. If you do land a contract, make sure to state it in your products description. You can use words like “Exclusive” “Only Available” or Available Online Only. If your product is online available online then a buyer who is interested will be more inclined to make a purchase.

4. Get on top of your SEO: If you haven't done so yet, make sure to put SEO on your calender before the month is over. You really don't want to be left out in the cold or finding yourself closing shop the first of the year due to no sales. Take some time to research your keywords in your niche. If you don't take the time to properly optimize your site, just remember this big tip: YOUR COMPETITION WILL!

5. Reward referrals
   As you may know, some businesses thrive from referrals. I have found that one of the best ways to get referrals is by having others help you find customers for you. You can do this by offering a rewards program or a referral program. You can either give out free merchandise, give a discount off of their future purchases, or offer a percentage of your sales. It all depends on your the type of business you have and what you can give away. Now be realistic. Don't offer a 50% cash incentive if you can not afford to pay the incentive. If you send out a newsletter, include a section in your newsletter where your customers can tell a friend or you can set up a form on your site that will allow your customers to enter in the names of their friends. When you get a new customer from the referral, make sure to send the person a personalized thank you note along with their reward.

6. Send out a newsletter: Have a sign up form on your site and give a discount for those who sign up. Make sure the discount is automatic. You can do this by doing a custom thank you page and include the coupon code in the thank you message. It's important to keep your customers up to date on sales, contest, and new products. Keep your newsletter simple and straight to the point. Your newsletter can be themed based where you send out information that is geared toward one specific type of product or service. Make sure to get permission from everyone you send out a newsletter too and make sure to give them an option to unsubscribe from your newsletter. You don't want to take the risk of getting to many spam marks or you will not be able to send out newsletters because your email address will be marked as a SPAM address.
   
   

7. Sponsor a Giveaway or Do a Giveaway:

   Sponsoring a contest or doing one yourself is an excellent way to advertise your site. This is also a great way to collect email addresses, mailing addresses and any other information you would like to use to in the future. I have done plenty of contest advertising for clients and they ended up with over new leads over a period of a month. You can also participate in blog contest events. There are tons of blogs out here that offer Blog Hopping events. Make a note of all of the events and make sure you include your site or blog in the hopping event. You can gain a lot of exposure to your contest and website.

8. Start a Blog
   I should have posted this tip before the giveaway tip?! If you don't have a blog make sure to add that to your To Do List. A blog is another great way to bring traffic to your sites. More and more searchers are looking to see if a website has a blog when they visit sites. A blog is a good way for them to get to know more about the company they want to purchase a product or service from. You can keep your customers informed about any sales, new products or upcoming events you are having. Be as natural as possible with your post. Don't sound like a robot when you are promoting your advertising. Make your post as friendly and as engaging as possible.

9. Groups and Forums

   Join groups and forums that are related to the type of products you have to offer. Many forums will allow you to post your url in your signature. Be very cautious when using this as a method of advertising. Forum members do not like when a business gets on a forum and starts to post links to their site with no other communication. This is known as SPAM and most hate it, so stay away from it. If you join any forums or groups on Yahoo, Google or MSN. Make sure you are there to learn or contribute. Respond to questions that you are familiar with, especially those that pertain to your niche. Become an authority figure on the topic and people will start to respect you and even look for your comments.

10. Team up with like minded businesses or people:
    Find people online and offline who are within the same niche as you or who have a passion for the type of products or services you have to offer. If you sell pet products, team up with pet lovers or groomers. If you sell baby products, team up with new mothers, play groups or day cares in your area. If you are in the website designing niche, team up with hosting companies, SEO'ers, or other website designers. You can offer discounts to anyone you team up with for your products or services. Establish life long relationships and watch your business grow!

If you have read through these 10 tips and are thinking that all of them sound great but you just don't have the time right now. Times are hard right now for a lot of people and they just aren't shopping the way they were a year ago. Although money might be tight right now for a lot of consumers the need for making money is continuous. Try setting aside two to three hours each week to start focusing on advertising your business. When you actually take the time to market your business, and start to see a change in new orders, then believe me, you will be glad you did!

Carla Phillips

My SEO Gal

http://myseogal.com

Long Term SEO : Keyword Research Plus Long Term SEO = Online Sucess

Long Term Keyword Research leads to Long Term Search Engine Ranking Results

I spend my days and nights working on a lot of websites from all different type of niches and I am constantly reminded of the importance of keywords. It really all comes down to obtaining the coveted top 10 listings for your most profitable keywords in the major search engines, of course Google is the one that most seek out and freak out about.

Since your keyword rankings can make or break your online marketing plans. You have to be consistent and keep your keywords on the first page of the search engine result pages or SERPs. It's all about getting top keyword rankings and staying there. You can do this will Long Term SEO.

If you're trying to target extremely competitive and profitable keywords you will definitely have your work cut out for you. You will have to have the type of mindset that it's going to take time, and you are going to have to have patience. Then again, if you have money in the bank like Daddy Warbucks and time to build and buy links to get you to the top spots then you might be there in no time, MIGHT. Google has frowned upon link buying and is/has taken steps to fight it, although there are some who still use this form of link building to obtain top ranking position, doesn't mean that it's the right thing to do. Why take the risk of Google finding out? If you want to rank for those “competitive” keywords, you are going to have to expect to spend months if not years, getting to those top listings.

Long Term SEO is the way to go!

Most website owners who are just starting out and honest website owners want to take the proper yellow brick road to the top and earn those top rankings by providing good quality content that your website visitors will actually find useful and beneficial. These “honest” website owners build links and target their keywords in a natural way, by creating articles, having keyword enriched content, writing ebooks, working with blog owners, targeting social networking sites and building their brands, which in return will build backlinks or one way links to their sites.

One way to help you achieve long term keyword rankings in the top results is by building one way links. You will start to gradually see over time that these links will build up those highly competitive keywords you are trying to target and your rankings will go up in the search engines. Searchers will find your content on the web and start to bookmark it or share it with others in their social networking groups. They can share your information, content, products or services on sites like Kaboodle, Stumble Upon, Facebook, Twitter etc. and your rankings will move up even faster. I'm a fan of social networking sites and definitely believe that you should focus on creating content on your blogs or websites that will make others want to share it or come back to it to see what else you are going to say or provide.

Building links and keyword marketing has become very competitive. You may have noticed some of your competitors holding the top positions on a consistent basis. This is because they are focusing on targeting their keywords in their website content, focusing on obtaining backlinks or one way links to their sites using those keywords and working on their SEO campaign on a long term basis.

Google is always changing, as you may have noticed lately. You may see a site listed on the first page of their search results one day and then gone the next or you may see a page rank at a 3 one day and then a 1 the next. You really have to stay on top of your game if you want to keep your keywords in the top positions. It really all comes down to making quality content that web surfers will find beneficial or think that they need.

Overall, once you have taken the time to tackle your SEO plans and no longer run from them your long term SEO will end up working for you in the long run as long as you keep promoting your site and using your keywords in your content, and link titles. Make sure to target hundreds of keywords, but don't use them all on one page! Make a list of the main keywords for your site, then make a list of keywords for each one of those main targeted keywords. Once you have narrowed down two or three for each page. Then start incorporating them into your website pages, products etc..

If I have learned anything over the years that I have been working on SEO, one thing always remains true and that is PERSISTENCE! You must keep at it and don't give up. It's going to take months if not years to get to the first page especially for very competitive keywords, but if you can see the big picture it is so worth it in the end.

If you need some help with finding keywords that are being searched for on a daily basis, I have listed some keyword tools that I use everyday and they are free:

Keyword Discovery

Google's Keyword Tool

Word Trackers Free Keyword Tool

So take a deep breath and an aspirin. Make a to do list to start focusing on Long Term SEO and building one way links to your site and you will be on your way to success in no time.

Sincerely,

Your SEO Gal

Carla Phillips

http://myseogal.com

Reconnect with nature

The word “ecology” was coined only as recently as 1873, by the German zoologist Ernst Haeckel. He based it on the Greek word oikos meaning “house, dwelling place, habitation” (plus, of course, logos). But though the scientific study of ecology, referring to the complex inter-relationships of biological entities with each other and with their environment, is a modern development, the traditional worldview has a great deal to say on the matter. The medievals did not possess posters showing the fragile earth floating in a dark sea of space, but they were deeply aware of the inter-relatedness of the natural world, and of man as the focus or nexus of that world, which they expressed in the doctrine of correspondences. It was, of course, more poetic than scientific in its formulation, but it expressed a profound insight that remains valid, and the present ecological crisis could only have developed in a world that has forgotten it, or forgotten to live by it. The cosmological principles underlying the quadrivium, even today, can help us learn to dwell more wisely in our common home.

James S. Taylor’s Poetic Knowledge: The Recovery of Education encapsulates the wisdom of the Integrated Humanities Program taught at the University of Kansas in the 1970s and 80s. Taylor writes, for example:

“The implications for education, especially for learning in the poetic mode, as a result of the Cartesian revolution should not be difficult to trace since modern education is dominated, in one way or another, by its influence. Any school of philosophy that claims that one particular science (mathematics and scientific method in the case of Descartes and his followers) must be applied to all other subjects of knowledge, will impose a formal rigor upon the entire curriculum, eliminating even the contemplative nature of mathematics and science. Sooner or later, it is all reduced to ‘facts.’ This approach bypasses the contemplative nature of knowledge, leaving the student disconnected from his nature and the nature out there.”

It is not Taylor’s conviction – and it is certainly not that of Beauty for Truth's Sake – that we can or should do without “rigor” in science or in education; just that we must keep things in right proportion. Contemplative, or poetic, or intuitive ways of knowing can give profound insights into reality. Any education that fails to integrate such knowledge is liable (as most of our schools demonstrate) to produce men and women alienated from their own full humanity and from nature itself.

Sacred geometry

The vesica piscis is one of the most important figures in sacred geometry, and symbolically speaking an image of the source of life. It may best be described as a lens shape formed by intersection of two circles with the same radius, intersecting in such a way that the center of each circle lies on the circumference of the other. The name in Latin means the bladder of the fish. The shape is also called, somewhat more poetically, mandorla ("almond" in Italian).

The Mandorla halo, often seen in religious art enclosing Christ or his Mother, is also often taken to represent the womb, and to have been associated with the power of giving birth, since it was used to generate many other numbers and forms, beginning with three and four, the triangle and the square. In Christian art, the area where the two circles overlap may be taken to represent the Incarnation, the beginning of the union of divine and human natures.

The figure was the subject of intense mystical speculation among the Pythagoreans and their successors. The mathematical ratio of its width to its height is the square root of 3, the ratio 265:153 being the best possible approximation to this square root using small whole numbers. As a result the number 153 was sometimes called “the number of the fish”. It is probably no coincidence that the number 153 also appears in the Gospel of John (21:11) as the number of fish Jesus caused to be caught miraculously after his resurrection. The writer of the Gospel would hardly have recorded the number if it had not been believed to be highly significant, and its occurrence is suggestive of a Pythagorean or Platonist influence.

But why as a Catholic do I speak of “sacred geometry”, a term so associated with the New Age movement? I believe that, as the Pope says in The Spirit of the Liturgy, the “mathematics of the universe… comes from the Logos, in whom, so to speak, the archetypes of the world’s order are contained.” And I agree with Michael S. Schneider that children miss out if they are exposed to numbers merely as quantities instead of qualities, each with a distinct character, connected with all others in endlessly fascinating patterns. Such patterns can awaken us to a world of wonder and beauty, and point to the underlying harmony between science, art, and religion.

As you might see from the Comments, Charlotte Ostermann and others are adapting some of these ideas for Catholic homseschoolers. If you are interested to find out more, add a comment of your own, or get in touch directly. In the sidebar you'll find a section where I plan to collect useful ideas for what to do with younger kids to get them interested in all this - not just in geometry, but in the whole process of learning and the development of a vision of how everything connects together.