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The first Horse Boy 1 workshop at Stal Tilburgs, Bergeijk, The Netherlands
8 oktober 2018
Blog by Ellen Schuringa
Eager, dreams & self care
8 oktober 2018
Blog by Ellen Schuringa
Eager, dreams & self care
The first two days were the most intense collaboration, critical analysis of practices, envisions, planning, future design discussions, brainstorming work I have ever done. Yes, other workshops have this type of work, but New Trails Learning Systems is different. Even the personal stories of our trainers and leaders are emotionally laden, incredibly powerful and humbling, and still, these folks give and give and give!
Our first ever Horse Boy Method workshop in Norway took place on 1 and 2 September 2018 in Fåvang. The workshop was hosted by our Horse Boy practitioner Emma Helleman at her magical care farm Mattisborgen IPT Gård. She did an amazing job at preparing her farm and horses, Alex and Tindra, for the 6 participants in the workshop.
Having a traumatic brain injury can be limiting and frustrating. Simple task become a challenge and memory can play daily tricks that are not enjoyable at all and make one feel like a fool.
One of our veterans has come a long way from almost never speaking to conversing and opening up after long trail ride in canter and especially after learning to jump. After one of those successful jumping lessons where Clue was just a charm and made sure the rhythm and joy of jumping was truly experienced by the soldier rider, the father of three came up to me and shared. He loved jumping, and he mentioned how happy and relaxed it made him. He said it kept him going, and Clue is saving his life.
Raven's Guardians movie night at New Trails.
When your house is a mess, when your children need rides to activities, your spouse had a rough week and needs a shoulder to lean on, the dogs needs their vet appointments, and make sure you fit in your dentist appointment you have not had for a year, and oh yes, bills are due and the fridge has mice coming out desperate for food- on top of that, if you have a child that needs a little extra attention, make sure you spend time, maybe ensure therapies needed, relaxation time and special parent kiddo time, while keeping up at work- WOW- what are these mortals doing to themselves???
We are very happy to announce that Bianca Rimbach became a certified 1 star Horse Boy Method practitioner.
Bianca Rimbach is both a devoted 5th grade teacher using all our Movement Method principles in her classroom on a daily basis and works with Wounded Warriors and their families at the USAFA Equine centre in Colorado Springs.


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Cited by Barron's as one of the top financial websites to visit on the weekend, Financial Sense® provides educational resources to the broad public audience through editorials, current news and resource links on salient financial market issues. Begun in 1985 as a local talk radio program, Financial Sense® Newshour is now a free weekend broadcast available through the site and in iTunes with host Jim Puplava and top financial thinkers.
Financial Sense® also offers a weekly premium broadcast with interviews from leading money managers, investors, analysts, and authors on the markets and economy as part of its FS Insider service.

subset: commoncrawl


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A Christmas Resolution Three minutes to midnight. I'd spent the year trying to stay off the big man's list. Or at least keep on the right side. Sure, I robbed that old lady—I needed the cash, but I did put 12 percent of my take in the church offering box. Heck, even the Good Book … Continue reading Flash Fiction: A Christmas Resolution
Tag: flash
How much pressure can one head take?
I had a headache for about six hours today. I did this sketch in Flash MX as a form of therapy. It didn't work.


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Carnival spirit
PUBLISHED: 14:00 08 September 2012
A TOWN is set to benefit from three events to be put on this month - including an annual carnival and a civic service.
Axbridge will see a procession of floats on the theme of nursery rhymes make its way through the town on September 22, from 1-3.30pm, with prizes for the best floats handed out in The Square.
Later, at 6pm, a barbecue will be held at The Rising, by The Church of St John The Baptist in The Square. Tickets, priced £2.50-5, are available from Axbridge Butchers, Post Office and chemist.
On September 23, a civic service will be held in the church in The Square by Gill Slocombe, chairman of Sedgemoor District Council at 11am, with a performance by Axbridge Singers also planned.


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Forklift Resume Template – forklift cv template, forklift operator resume templates, forklift resume, Determing the best Forklift Resume Template to obtain tasks is not really something to ignore. Considering there are numerous varieties of resume on the market, you need to ensure which one to pick, and which one matches your want the most. Is more details regarding this.
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Wave 35 in perfect conditions with 2x250 hp Honda
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Paraplegia caused by invasive spinal aspergillosis
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A 40-year-old woman with a history of multiple sclerosis (MS), asthma, and Crohn disease suddenly developed paraparesis, which was attributed to MS. She had received infliximab for Crohn disease 14 days prior to the onset of paraparesis, as well as methotrexate and corticosteroids in the more distant past for asthma. Eight months later, she developed progressive upper extremity weakness and sensory changes. Physical examination revealed flaccid paralysis in both lower extremities, and sensation was absent below T3. MRI revealed an edematous spinal cord from C5 through the conus and multiple enhancing extramedullary masses (figure, A). Spinal cord biopsy revealed a caseating granuloma with fungal hyphae morphologically consistent with Aspergillus species (figure, B), although cultures were negative. Chest and abdomen CT performed within 3 days of hospital admission revealed no source of aspergillosis. Despite 7 months of therapy with voriconazole and caspofungin for presumed spinal cord aspergillosis, gradual progression of the spinal cord lesions was noted on MRI. Nine months after switching to posaconazole, she remains clinically stable with no further radiographic deterioration by serial MRI scans. There is a risk of granulomatous infections following tumor necrosis factor antagonist therapy,1 which may be caused by invasive fungi2 and may present with severe neurologic manifestations (figure).
1. Wallis RS, Broder MS, Wong JY, Hanson ME, Beenhouwer DO. Granulomatous infectious diseases associated with tumor necrosis factor antagonists. Clin Infect Dis 2004;38:1261–1265.OpenUrlAbstract/FREE Full Text
2. Warris A, Bjorneklett A, Gaustad P. Invasive pulmonary aspergillosis associated with infliximab therapy. N Engl J Med 2001;344:1099–1100.OpenUrlCrossRefPubMed
Disclosure: The authors report no conflicts of interest.
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Published March 21, 2007
- Petros C. Karakousis, Johns Hopkins University School of Medicine
- Shelley S. Magill, Amita Gupta
- Paraplegia caused by invasive spinal aspergillosis
Published March 21, 2007
- David N. Alexander, UCLA
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News on Politics and Religion with Rants, Ideas, Links and Items for Liberals, Libertarians, Moderates, Progressives, Democrats and Anti-Authoritarians.
Saturday, October 29, 2005
Coloradans facing the woes of TABOR
As part of the national conservative agenda TABOR is pushed for all governments, after 13 years Colorado is debating repealing it.
The misnamed taxpayer-bill-of-rights measures place severe limits on government spending growth no matter the circumstances. Supporters advocate private colleges, private schools, toll roads, fees for parks and other libertarian measures as they become unaffordable to government (the not so hidden agenda of TABOR.)
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Children require extra care during winter. Their immune system is continuously growing, so they are more likely to get cold and other winter diseases. From food to clothes you need to check everything from the harsh weather. You must consider ways to increase your child's immunity to keep them safe in winter. Apart from that, there are other lifestyle and dietary changes that you must make to protect children from cold weather.
Tips for winter clothing
- Kids have delicate skin, hence you should buy clothes with soft wool which does not lead to any kind of allergy or rash.
- Sweaters are not the only thing you must buy. Socks, hat, gloves, and earmuffs.
- You should not make unnecessary layers of clothes.
- Wash woolen clothes with soft detergent and make sure that it removes all possible germs.
- Do not allow kids to stay in wet clothes.
- Kids Do not have the same tolerance for cold-like adults.
Dietary tips for winters
- Diet so plays a vital role in keeping kids warm during winters.
- You can make soups for your children. It is healthy and will definitely keep your children warm.
- Sweet potato is very famous during winter. You can give sweet potato to your kids. Make sure you serve it hot to your kids. So you can squeeze a lemon and sprinkle some salt to enhance the taste.
- Do not give your child coffee or tea due to the presence of coffee. You should give hot milk or you can give hot chocolate sometimes.
- Nuts and seeds are other healthy option which you can serve your kids. Nuts are really good in winter as they are loaded with nutrients. Nuts can be both served as morning or evening snack. It is also a healthy snacking option.
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Winter skincare for kids
- Apply moisturizer on your child's body every day after they take a bath to keep their skin hydrated.
- You can give them a hot oil massage but do not heat the oil too much. Use only warm oil.
- Sunscreen is required in winters as well.
- You can also apply oil on your body before a bath to maintain the hydration.
Read more articles on Children's Health.
For more related articles, download OnlymyHealth app .


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Furniture 101: Buying And Caring For Your Home Furnishings
It's not difficult knowing what it takes to buy furniture. You just need the right knowledge to ensure you are doing it in a manner which saves you time and time.This article will provide you with that; use the tips included wisely.
Furniture is something that can cost you quite a hefty price tag. That is one reason that used is usually a good deal. You will find used furniture readily available at thrift stores, garage sales or consignment shops. You can always reupholster furniture reupholstered if necessary. This will allow you to save a bit of cash.
The end of summer is really the best timeframe to buy outdoor furniture. Many stores want to sell summer items to make space for winter items. This is when they make prices cheaper so they're more affordable.
Don't neglect trying some haggling when you can't ask for a lower price on furniture. Most furniture stores have a huge markup on their furniture up by as much as twenty percent. If you can't haggle, take someone with you that will help you negotiate the price.
Always test a recliner or rocker before you bring it home. It can be difficult to get a replacement from certain furniture stores.
Furniture that you choose should be your priority choice. Neutral items make it easier to change and art. You can have more options as the years progress.There are quite a few neutral options that you can add to your home.
Always know how much space you're about to get furniture for. It doesn't matter if you're buying a side table or a bed, always make sure the new furniture will fit the allotted space. Guessing can turn out badly.
Inspect the legs on a piece of furniture prior to making your purchase. The chairs legs should be hefty and joined to the frame. Wooden legs are the most durable, rubber or plastic, metal and rubber legs also scratch flooring.
Make sure you plan a clear budget before you go furniture shopping. There are many different prices for similar pieces of furniture. You can end up spending much more than you can afford if you don't have a budget. Knowing up front the maximum you can spend helps to keep you from over spending.
Choose durable when you shop for furniture. You need to maximize your buyer power by choosing pieces that it is built to last. Furniture can be expensive and you have to select things that will last you. Metal and hard wood items will last for a long time.
Online research is good for ascertaining price ranges, colors and attributes, but it can't give you the ability to actually touch and examine the furniture. This is the only way you can personally test out the furniture pieces to determine whether or not they are right for comfort and physical appearance.
Check the condition of furniture before accepting it.You don't need to get rid of a sofa that is sagging in the middle just because your friend no longer wants it. You may not want to put out money for a new piece, but a poor quality item may be more trouble than it is worth.
Check out the classifieds online for free items. You may just find some amazing pieces. A lot of people just throw away old furniture that could have been refinished or cleaned up. A bit of elbow grease can turn these furniture pieces into a great deal.
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Learn the various kinds of wood are used for building furniture. You won't want to pay for fake wood.
Always think about what your family's opinions in mind when you're purchasing furniture. They must live with the pieces in the same way that you will, so it's best to get things that everyone can enjoy so that they will respect the furniture more.
Try shopping for furniture around the end of the month. You can get an excellent deal during this way.
Go for understated colors in your furniture colors. You do not want to wind up with trendy pieces that could go out of style quickly. You can be trendy when you're picking out everything else in the home,
You don't have to buy furniture in the same style as your old or current pieces. You can add new updated pieces that compliment your older style.
When buying couches, take off the cushions and then push down the base. Do its coils push down and spring back right away? If so, then the sofa is worthy of consideration. If they don't, they are probably worn down and the sofa should not be bought.
When shopping for cushions, be sure that they are not too soft and that they have removable covers on either side that match. While they may be more expensive, they last longer. Look for machine washable covers.
What must you know to shop for furniture like a pro? The answer is utilizing the excellent advice presented here. By doing this, you will discover that your furniture-shopping endeavors are much more successful. Turning this situation around is what you need to do in order to succeed with it.


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In order to raise your likelihood of getting a teaching appointment once potential, you will need to ship your resume along with application package to each school area on your town, no matter if any places are available or not. The trick is always to ship the application package to just about every college district into your town. Our sample resume is really a superb example of this way you are able to present years of housekeeping experience for this managerial functionality. Search for sample resume templates that can give you a very good thought and advice about ways to compose a very excellent resume cover letter from the world wide website.
Third, you will likely have to undergo cough testing to ascertain if, so, you own a mold allergy. Cleansing equipment after and before every use to help keep the spread of illness has been realized by the nursing staff. If you are on the lookout for a very good deep cleaning every approximately every week, then you may probably will need to employ someone having a reasonable amount of encounter who has completed with the desired duties earlier. Housekeeping is actually a job which involves almost any mix of cleaning tasks. To create a fantastic housekeeping resume, then you should highlight your own efficiency, cleanliness, potential to comply with guidelines, along with client service abilities. Housekeeper restart samples can assist you decided in regard to what to cite. A house-keeper that focuses on pet maintenance cleaning may possibly be quite a good choice in the event you get a four-legged pal in the home.
You've likely took a few activities to creating your resume, resume cover letter, and also internet software, to keep in mind to create the rankings. You want to take care of the cover letter right towards the college superintendent. In the event you created a general cover letter, you only ought to have to alter the speech and Superintendent name.
Once you have got a meeting with a individual, you have created your own first impression, and as they state you never possess the opportunity to develop a very first impression! Go through the issues and try to recognize ways which you are able to exhibit your work aide or potential employer which you are in possession of a balanced group of communicating skills which will help you perform exceedingly well at your future job. In the event the work meeting is right for a swift food restaurant, just a little far additional casual is nice, such as khakis and pull shirt. It is always useful to prepare yourself beforehand before to enjoying a job interview. In addition, it's going to aid you in getting ready for the true interview with the possible company.
Skills you get started drafting your own sanity. It is helpful to add skills that you already have over a restart. Ensure you're acquainted with all the current job search talents and tactics out there. Hence, you need to cite the center abilities like ironing and cleaning at the peak of their restart. In the event you need assistance with a restart, then see the Career Center at your school and request help.
Match your skills to this organization or job you are looking for. For instance, you can drop a parttime occupation causing you to get a complete time livelihood elsewhere. If you should be prepared for work then you are prepared to become always a leasehand. If you wish to apply to get a housekeeping job, it's necessary to showcase your own abilities and knowledge on your own resume. If you are searching to get a Coding trainer occupation, you will need to showcase your skills and talents accordingly.
You may possibly put in an application for a job where they company was searching for some body to upgrade the business web site with pictures however doesn't always have the chance to accomplish it himself. A summer project is an incredibly first measure to make your career! Obviously, you won't likely to strike a summer occupation that satisfies every one your requirements, but you must attempt to locate a summer job which meets just as far as your demands as you are able to. Really, the correct summer project will soon undoubtedly be beneficial to you in learning crucial skills such as for example being instantaneous, the best way to keep up a schedule and managing your finances.
The job environment is rapid plus it might be hot. If you have got past archery experience, then obtaining a brand new job needs to become straightforward. If you don't have previous archery encounter, you will need to use examples in your other professional adventures or private life to demonstrate you'll be an essential worker. To acquire a professional resume created, you will have to devote a substantial amount of money. Talk about your thoughts with people that are experienced childcare professionals.
Adding waste elements to your landfill is just another kind of treatment providers. Many companies are large and also possess locations across the us, even though other bigger organizations might just have 1 salon. In addition, they employ individuals to simply perform a few hours each and every night to clean places of work. The absolute top writing businesses will not only utilize surveys to consider about the restart. A superb approach to be sure that your resume is perfect is to request the help of an expert resume writer. It really is tough for an composing services to make sure that a job since there are lots of factors that will influence the last selection. A amazing means to make sure you're dealing with a reliable service will be always to check their BBB rating.
Determine that which graphics you want to decorate your own card. Purchase a visit to the website of the retailer from that you want to get a card. For instance, it is possible to get an gift card from lots of retailers that may send the gift-card right to your recipient. For an extra fee, you may add gift cards, also. When picking the theme and fashion, you're ready to begin producing the home gift card.
In the event that you really will need to take action different, you might even make handmade cards that have shocking messages inside them. Predicated around the type of card you have to make, you also can look them in such a fashion. The segments of a greeting card card is only one of the absolute most critical things you should learn before making one.
Glue a lace ribbon into the borders of this picture on front area of the card make it appear to be nicer. An card will be repeatedly, and not always in a way that jibes using the standard translation. After deciding a design motif, you need to decide on the method that you will make your greeting card. Establish a home office business in which you are ready to generate your homemade cardsto market your small business enterprise, and handle administrative and advertising tasks. Personalized credit card You can find a great deal of personalized greeting cards on several different internet sites today.
Photo or no graphic that you are guaranteed to find yourself with a card you will enjoy. Just bear in mind that probably the most important portion of an greeting card is the way you cared enough to ship you. The cards really are useful as a method to think about the more profound problems encompassing the query readily offered. Writing child cards will be quite a quite special time for all of us else involved. Present your loved ones associates habit cards to demonstrate how much you really care.
At the current occasions, handmade cards are frequently employed. Keep in your mind the signatures of tarot card cards are quite unfastened. About the flip side, you also can download your own cards from the net web and publish off them yourselves. Add some details you prefer to surface on your enterprise card, like your cellular contact number or physical address. Your business cards need to reveal that you're a responsible personal, that you could provide references when your parent requests to receive them and that you're knowledgeable. Whenever you're finished, you are going to have a practical digital small business card that keeps its formatting with an picture in accordance with your contact details.
As you personalize your own cards, then you're able to choose the type of design you want, together with the date in case you want the card to put in the mail. Once you have bought an account to get the identifying graduate, have just a small time for you to create something special and thoughtful. Enclosure cards may be used for any range of purposes. The titles are available in many of dimensions, colours and newspaper shares. Studying greeting cards which are already on the market provides you a feel for exactly what consumers and greeting card organizations want to know more about. In Western nations and increasingly in various societies, even many individuals traditionally mail seasonally themed cards to their own buddies and household in December. In addition, you will find tons cards that will act as the basis for creating your own personal style and layout.
Include a point about how you will make use of this gift. A lot of men and women will not actually think about giving a talent unless there is a greeting card attached. You might also create an internet gift without using a present template. A anonymous card or gift stipulates the opportunity to exhibit encouragement or provide aid, just because you're inspired to achieve that. A birthday compliments would be really a great means to present your very best friend exactly how far you care about her to her special instant.
Many men and women opt touse costly envelopes for business mailings. Becoming able position to receive homemade cards is this kind of fantastic experience. Today , a number of you'll delight in the common pastime of creating your own greetings cards.
If you are finally satisfied along with your message, then you certainly are in a position to compose it down to the greeting card card. Although others may think that it's really hard to compose a greeting material, it doesn't have to be difficult if you just take a while to practice writing down your personal message onto the sheet of newspaper. You will write a customized communication on the interior of the cardeven in case you decide on the one that includes an printed material in the front.
You've got to inspire and reward teachers to prevent burnout and boost the absolute best instruction environments. Thus teachers, for people with no established goals, it's the chance to write a while and increase your workout. Not all English teachers are going to get exactly the same resume. They could make an effort and foray in different areas or build new principles and skills. Just as they need to motivate students to keep engaged, teachers also ought to get engaged. A substitute instructor is somebody that teaches college students, if the normal teacher isn't obtainable because of some motives. The college pupils have a great deal of attention-span issues, and it's challenging to create sure the kid is concentrating around the lesson.
If you're an experienced candidate, you must furnish an employer combined side most of the current specifics of one's prior work and achievements. Some companies also search for interns who'd be prepared to connect the company and when given a shot. Most employers are actually about the lookout for reasons perhaps not to join you personally.
Practice the contact details with the contact details regarding this individual to whom you're going to be covering the correspondence. A letter of interest is one of many absolute most crucial and crucial cover letters that should accompany resumes, certificates and other formal records that will make up the contents of a work program. It's mandatory that you personalize the restart along with cover letter in light of your own requirements. In the event of this measure, it's important to send out a resume cover letter together with the resume. Prior to your restart, it's the cover letter that's going to become seen and that's the reason it has to be written with extreme care. Writing great cover letters is just a potent solution to gain the biggest market of the future employer and doubles your own likelihood of finding the work that you dream about.
The interested person ought to really have a great command over language and should own a high confidence degree. Be-ing between tasks isn't ideal. Any knowledge you've got ought to be mentioned. By contrast, a nicely crafted resume highlights your own capability to produce a excellent product. Let your composing be expert and as stated by the demands of the employer.
Resume is just a succinct proof of your professional travel, also it plays a valuable part in virtually any task job interview. It is likely to also incorporate details about some expert memberships which you've init. It is imperative to include advice regarding the instruction certifications in a teachers resume.
Employed being a hospital housekeeper will provide you with the responsibility of keeping the hygiene and cleanliness of a hospital. There are an variety of functions and obligations primarily based on practical expertise level. The component of the instructor stays the exact same inside our current society.
Your resume should clarify just what you did, and also the way you propose to measure your effectiveness. Instructor Resume should become well drafted record. Going through the above account executive resume sample should've provided you insights regarding creating your own resume.
In the event you've ever grumbled, I'm never very likely to discover work that works by using my instruction, you are not lonely. Alternatively, you should tailor your resume for every work which you apply for. Thus, it really is a hard endeavor but in the event you should be passionate about serving persons, afterward it is not difficult to control all the obligations. Maybe not only the candidates which are re-iterating their presentday project's description and stating X number of all years of working experience within the enterprise. It was really impressive to discover the amount of work done, though LeWagon is not yet 1 year-old. Find methods to assist teachers wind up time in order that they usually don't get overwhelmed. The commencement of one's resume is devoted to explaining your skills as a housekeeper.
In case you have some work experience as a professional assistant, it is likely to become simpler that you obtain work at the enterprise. For the post of the hospital housekeeper, it's important that you include all the experience which you have in relevant subjects. Your encounter, educational qualifications, and ability collection are a few of the absolute most essential things which you will want to concentrate on. You'll get absolute wisdom and hands-on experience whilst still growing or boosting the relevant abilities needed for HR pros and other organizational leaders. My comprehension of the plastic company is incredibly slender. Present your abilities and experience well and they'll speak louder than the most flattering image. Maybe not merely are you really able to develop several sorts of knowledge from these organizations, but furthermore, you are exhibiting potential companies you are just one eager to dedicate themselves into your project.
Try and recall , even caffeine might cause withdrawal signs or symptoms. The danger of reduction will be more than off set by the potential to get a significant gain. In this manner, your maintenance restart experience section looks a complete much better. It's only employed for pain management that necessitates typical dosing (within this scenario, each and every 12 hours). After that, choose the people that you'd like the potential employer to pay attention to, and set them at a unique skills department. Outline the way that your company operates. Once everyone was welcomed into your dealership, it is the proper moment to discover what your buyer needs to get a car or truck.
The different offender may possibly possess precisely the specific things to supply you with. The exact first candidate is aware the way to promote . These credentials are now termed differentiators. You are able to opt to seem for one or both predicated on your eligibility and abilities. You need to stick to the syllabus for every one of those articles extremely minutely to have the ability to answer all of the concerns. Enrol within an institute you will find several reputed institutes for instruction to successfully acquire govt projects.
Some might want certain key words. You must keep an watch about the recruiting forces and vacancy announcements. You can't ever hear music that doesn't harken back into your own social encounter. The makeup of the objective statement can be quite challenging, as most people simply do not know what to incorporate from this announcement. A mixture of education and expertise is acceptable at case the real estate specialist can demonstrate the crucial job capabilities. Brain Storm amounts which you will comprise. This free auto mechanic project description sample template will find a way to help you bring an innovative and knowledgeable automobile mechanic to your organization.
Being a leasehand you are getting to become accountable for the majority of the total labor about the rig. You can find assorted sorts of servicing workers, using a variety of kinds of manners a person keeps an equipment. Fully being a real care worker supplies you with a great deal of pros. Most companies require home specialists to induce, thus a legal driver's permit often is crucial, and you also may possibly be required to find yourself a motor automobile. For example, prospective companies will love to realize that you just built your company from GroundZero by buying a certain quantity of properties within a certain space of time. Just before you meet with a possible employer, utilize this exercise moment with a friend to expel some fear or doubt in regards to the job interview practice.
A driver restart aim is that the exact first thing that a potential employer experiences about the work candidate. Drivers have to maintain a position to keep exceptional records and documentation. Day care centre van motorists provide transport and supervision for kiddies.
The job of care worker may be helpful for you personally. Does the work offer you funds, but nonetheless, it also allows you to conserve a good deal of itas possible certainly do your repairs. Writing a fantastic program vitae objective is vitally crucial for obtaining a fantastic task. If you're prepared for hard work then you're well prepared to be always a leasehand. Or perhaps it is the right time to see grandmother and grandpa for a lot of occasions. You have to receive yourself a new prescription each moment; point. It's the time scale of maintenance specialists.
Yes, even if it's the case that you do eventually quit accepting Oxycontin, then you will require to slowly taper down seriously to reduce withdrawal signs. Furthermore, prescriptions for Schedule II medication are interested in being hand written and can't be called in, but under specific ailments. Do exactly what you can under your own physician's oversight. Your doctor is going to be better able to help you handle your pain when they are able to discover a feeling of what you are going right through.
The interview procedure is more full of style evaluations and queries formulated to establish your appropriate job skills. If you have no experience, explain you are looking for an entry-level position at which you might learn on the job. However, job training would be the best way to acquire the acceptable practical experience to ascertain if you've got what exactly is necessary to be considered a Freight agent. It really is perfect to people that possess minimal expertise from the specialization. Right, you say, but I would like to demonstrate my soft skills far as well, plus it could be really hard to measure them. Simply take a look at the care resume example at the onset with the guidebook to appreciate how it performs in training.
When it has to do with solving math troubles, you definitely should really have the ability to use short cuts confidently. There is additionally an instance resume and a sample restart to get mechanic project hints on how best to conduct an job search. The exact first case includes everything. The plumber sample project description can be employed to help you make work advert that'll draw in candidates that qualify for the position.
The wonderful elegance of many of the themes makes Shopify a very exceptional place for ecommerce websites. If you work a beauty shop, a software organization, or freelancer advertising consulting organization, you wish to develop a referral program that provides you with with a regular flow of new customers. Regrettably, some gyms are somewhat very likely to reduce on the possibility to own my own friend workin their impression. A trainer additionally needs to be ahead-of-the-game when it's to do with fitness investigation, since even something as invisible as a customer's mental condition can have a noticeable effect on their present-day wellness. Along with knowing the aftereffects of assorted kinds of work out regiments, he also needs to know appropriate nutrition, very helpful exercise environment, and even a bit of psych. Prove you are the sort of trainer that's actively interested in each and every person's individual situation. Anybody could use a exercise pro, from boring job employees who need a rest from their daily regular to business executives trying to shave a couple pounds off their mid riff.
With no a single, you most likely will not acquire a meeting. The practice interview can help one to tweak any dilemma areas for you. Most manuals are made like this.
Educating Skills It is not adequate to fully grasp how to do exercise sets or what exercises they are tripping. Describe what metrics you have to reach to be able enough to be cash flow break . You should devote if you would like outcome, they triumphed. The procedure is more pretty easyaspie, which makes it simple for each man to participate. Now that you realize why referrals and referral apps can certainly help your business, it is the right time and energy to find tactical. Otherwise, it is certainly likely to be stressful for a referral program to remove. Whenever you look for a referral promoting program, be sure you imagine about something that works for your brand.
A referral can be really a trusted recommendation from somebody else. Meanwhile, the referrals are among the most essential growth drivers for most programs. The optimal/optimally method to have referrals is to give excellent merchandise and alternatives.
Eventually, to deliver an outstanding pitch is to tell a terrific narrative and this narrative needs to be supported by the most acceptable outline. Customer-service also needs to become always a concern on manuals with out lots of food service experience, so make sure that you emphasize that practical encounter in resumes which do not have a lengthy history. Organizations shut their doorways all the time. If you operate a advertising firm or a small, regional provider, you have the capacity to to learn from Ritika. If you are unable to have a whole portfolio that we can look at, then this is definitely a reddish flag.
Make it a portion of one's very own exclusive manufacturer. You have to be specialized in exceptional services and merchandise at all times. Providing excellent product and providers is also the exact first step in building an efficient referral application. For example, you can realize that you omitted an essential sample content. Free samples available on the net are something a kind of drive you in the right direction. You'll notice a range of the templates are free of charge to utilize and many others be expecting a premium account.
The greater that your practical comprehension of this project, the more inclined you have to be hired. A exercise trainer's task isn't just to show to you the suitable way to transport out particular physical exercises or even to design a program for the requirements, however keep you on track mentally to reach your own exercise goals. As the job may demand more income or a greater title, you have showing up and perform that job every day. Touring requiredThis occupation is about travel along with being away from home for long amounts of period. Even in downtime, then you also should be in a position to obtain work to do. Then it is the right time to choose the form of project you'd like to create.
Getting attention, obviously, is measure one in completing the purchase. Other skills may also be time management and leadership abilities. About the flip side, strong abilities, also known as social or societal abilities, would be the ones which you own as private traits or you also get through expert encounters. When it has to perform breaking skills into classes, you can find two sorts of skillshard and tender.
You need to specify the objective is vital, when it ought to be completed and also an general outline of those steps to achieve this. The purpose should be attainable. Personal objectives are part of numerous expert processes and papers. Writing personal objectives will not will need to be part of a formal record or program. Putting a deadline makes an atmosphere of urgency, which are going to be able to assist you to work to accomplish your personal intent. Setting targets too high often leads to annoyance instead of as much drive to endure with unique aims. Setting reasonable targets is substantially like putting attainable objectives.


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Flocons de Sel: Nature's Table
Very Kerri Travels | Megève
Every day, I feel lucky to work in an industry I genuinely love. Fabulous food, bevs and vibes are all key to a successful restaurant business which will survive its first year, but it's the personalities behind them which separate the good from the best in the world.
My favourite spot to date is Osteria Francescana in Modena; there are moments from our dinner there, like THAT Parmesan, which I will remember forever. For a few reasons, like your mortgage, it's sort of like a one off, or maybe twice if you're very lucky. Flocons de Sel in little old Megève, on the other hand, is the place you could return to many times, knowing it will be a tremendous experience on every occasion.
Why Uber when the restaurant sends a car to pick you up from your hotel? Because no reason. We're whisked up the mountain through fairytale scenes and just as we're settling into our gorgeous window table, big beautiful snowflakes start to fall. You couldn't write it lads.
Delicate snacks, like nutty mushroom carpaccio, and soufflé bread delight. Lest we forget all the fresh bread, with salted butter, no less to indulge in. Whilst Darty gets personal with beetroot gnocchi, a bowl of salsify ribbons (courgetti is so 2016) with lashings of smoky bacon and black truffle arrive; and it's like the most indulgent carbonara ever. I'm the clear winner here, not that it's a competition. A considered smack of citrus cuts through beautifully rich scallops and fresh lake char is light and dreamy.
It all starts to get a bit loose once we've demolished the cheese trolley, which didn't stand a chance, by the by. I have a hankering for dark choc, so go off piste with the dessert menu, asking for something chocolatey, if possible. A while later, someone totters over with an apple and caramel brittle combo in martini glasses. "So much for the chocolate", we think, and tuck in.
I'm downing an espresso, when a procession of chocolate arrives from the kitchen, well this is a surprise. One dish is even introduced as 'like a painting', but it's the giant dark choc soufflé dusted with a snowflake which wins The Turner Prize, for me. Oh, and maybe the dark chocolate sorbet, too.
Whilst Emmanuel Renault modestly refers to his establishment as 'an alpine chalet', I think of to it as the most down-to-earth restaurant delivering outstanding hospitality experiences, day in day out. Osteria Francescana has a tough battle to fight for my top spot, which is covered in salt flakes right now.
Five Very Kerri things about Flocons de Sel
- Eh, the chauffeur service
- On point Sommeliers
- Cheese trolley to sink a battleship
- All the dark chocolate
- Not a rule or bit of stuffiness in sight


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Why in the discussion?
India, white backed vulture, which is in a highly endangered category, will release 8 cherished captive guards with tracking device. With the help of these devices, the causes of the death of Gidda will be known and due to that, the deaths of other Gidhs can be prevented.
Important facts
- These vultures were planted in the Jatayu conservation breeding center and they will be left in Bir Shikha Sanctuary, where the Bombay Natural History Society (BNHS) is working towards declaring it 'Vulture Safe Zone'.
- This satellite tag will also show that these birds are treating normally from the other nearby species in the wild or not?
- If death has not been recorded due to the poisoning of these 8 birds in 2 years then 20-25 birds will be left in the wild every year.
- In South Asia, for the first time in November 2017, the Government of Nepal and the National and International Conservation Organization left the white-backed white Giddhs in the desert with a highly distressed category.
Other related facts
- Jatayu Conservation Breeding Center, Bir Chikshak Wildlife Sanctuary is situated on the border.
- This is a joint project of Haryana and Bombay Natural History Society (BNHS), which was established in 2001.
- It was formed in India to investigate the severe degradation of the 3 severely endangered 'Gips species' .
- 9 species of Vultures reside in India. Out of this, there has been a terrible decline in the population of 3 species such as The White Backed, Log Build and Slender Build Vultures which was more than 90% in the mid-1990s.
- This bird has now been included in the critically endangered category.
- In South Asia, the main reason for the extinction of these giddies is the 'Diclopenoch' painkiller drug used in the treatment of cattle . When the vultures eat the dead body of the cattle treated with Diclofenoc, their kidneys stop functioning.
- The Government of India has banned its therapeutic use since 2006.
Why in the discussion?
The two-day global Cooling Innovation Summit will be organized in New Delhi on November 12, 2018.
Important point
- This summit is the first of its sort of solution focused, in which experts from all around the world will be united and looking for concrete steps to deal with the huge loss to the climate due to the rising demand of room air conditioners.
- This conference will be jointly organized by the Department of Science and Technology, Government of India, with the support of Rocky Mountain Institute, Alliance for the Energy Efficiency Economy (AEEE), Conservation X Labs and CEPT University.
- During this summit, the 'Global Cooling Award' will be launched, which is a challenge related to mission innovation and aims to accelerate the development of residential cooling (cooling) solutions, which is the minimum of the current standard solution on the climate The fifth part will be affected.
- Global Cold Rolling Awards and Innovation Summit will be attended by prominent speakers from around the world, including explorers, philanthropists, venture capitalists and other industrialists.
Global Cooling Award
- The 'Global Cooling Award' is a competition with global reach and participation, which aims to develop such a cooling technology, which will require very little energy to be operational, in which the refrigerant will be used and the ozone depletion And this will also reduce the impact of global warming. Not only this, the equipment will also be economical in case of large-scale construction.
- To invite remarkable ideas from around the world for this award program, the attention of the whole world will be drawn to this.
- Those awardees will be congratulated by presenting this innovative product and they will also be given necessary encouragement and support.
- This award will also be able to create a collaborative platform which will be able to use the capabilities of researchers so that public research can contribute significantly in promoting innovation and it has a positive impact on social and economic terms.
- Through this award, not only will those who make significant contributions to clean energy related research and development will be congratulated, but it will also motivate young researchers to develop innovative products in the field of clean energy so that clean environment or climate From the point of view, this world can be better.


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Open carry advocates and gun violence prevention groups will face off Thursday night in Old Pasadena as an out-of-town firearms group brings its protest of Assemblyman Anthony Portantino's bill to ban open carry to the lawmaker's home turf.
South Bay Open Carry is calling on its pistol-packing members to descend on ix Tapa Cantina at 7 p.m. to demonstrate against Assembly Bill 144, which would close a loophole in state law that allows unloaded firearms to be openly carried in most public places. The group's Western-themed "wanted" poster promoting the event bears a picture of Portantino and a call for supporters to "support your Second Amendment rights: together we can make it happen."
Members of the Brady Campaign to End Gun Violence and other groups are organizing a counter protest.
AB 144 cleared the Assembly Public Safety Committee on a 5-2 party-line vote last


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Homogeneity through Time – A Follow-up Paper to Questions at the
Royal Society Scientific Discussion Meeting: The Nature of Mathematical Proof
With a Rider on the Dimensions of Physics
During a discussion session at the above meeting I asked a question in which I raised the matter of homogeneity through time when procedures moved from mathematics to computer aided proofs. The concept seemed to perplex at least some of the participants. In effect it is the confounding of variables which manifests itself with the passage of time. The first use of this term of which I am aware was by Keynes in respect of mathematical economics, as described in the paper.
I consider the concept to be of such fundamental importance that after thinking it through again I have set it out in full below.
The methodology which I use starts with the assumptions inherent in the use of number and mathematics. This requires a detail which some of those skilled in the art may find laborious, but it allows me to add more concisely the successive assumptions which illustrate the concept of homogeneity through time. The descriptions are non-mathematical, because mathematical terms all come with their own definitions and connotations. In some ways this is what is being challenged, and so we need to begin at the beginning.
In a collection of numbers in no particular order such as:
1 2 5 3.2 …… 21
the number 1 is a conceptual entity which has unit value everywhere and at all times. It does not grow or shrink or change into something else, whether in the same place or in another place. The most succinct description of this is that it is homogeneous through time and space.
For most purposes it is unnecessary to state that something is homogeneous through both time and space, because if it is homogeneous through time, then it is probably also homogeneous through space within our frame of reference. The proof of this is to move to another place an infinitely small step at a time. What starts homogeneous through time, remains homogeneous through time at each step. The exception is that for analysis which addresses the nature of time itself, it may be necessary to consider homogeneity through space in its own right. This is considered below.
From the definition of the number 1, it can be seen that the number 2 is simply two units of 1 in additive association i.e. 1,1 or (1,1) or 1+1. The same is true of the other numbers. Decimals are conceptual entities which are defined as identical and equal to one tenth of the unit, and as such are similarly homogeneous through time etc.
Describing the number 2 as a symbol which represents 1 in additive association with 1 takes us back to ancient Mesopotamia, when arithmetic evolved to keep accounts on clay tablets of their equivalent of bushels of grain in granaries. One bushel was one stroke, two bushels two strokes etc. However, when the number reached five, it was marked for convenience of reckoning with a diagonal stroke which signified a defined bundle of strokes. This was in effect a new symbol. So
which is not so very different from the notation used by the Romans.
The notation:
0 1 2 3 4 5 6 7 8 9
was a later invention from the Middle East, whence the term arabic numerals.
Units may be added or subtracted using either convention. So
3 + 2 = 5
On the basis of addition and subtraction, they may also be multiplied or divided. They may be ranked in order of magnitude. They may be used with the power notation i.e. 32 is the same as 3 x 3.
Negative numbers may be accommodated by considering them as on the other side of a balance, so that their magnitude is in effect subtracted from the value on the first side. Operations on the other side of the balance are carried out in the same way as on the first side, but the result is retained on the negative side. Double negatives are accommodated by performing the operation on the negative side of the balance, and then bringing it back, so that the result is on the positive side.
All this is trivial and generally accepted.
b. Algebra
Algebra uses a symbol such as x to represent a number, so that operations may be carried out without the labour of arithmetic. If the collection of numbers above is represented in algebraic symbols, each number would have to have a separate symbol, such as x1, x2, x3 and so on. Addition and subtraction would lose the convenience of numerical notation, because even if x1 has a value of 2 and x2 has a value of 3, there is no algebraic symbol for 5 and they would have to stay as x1 + x2 ,which loses the point of the symbols.
The solution is to use both arithmetic and symbols in association together as multiplicative entities, and to express all numbers in terms of a number of xs: so 2x, 5x etc. The result is that all the operations which apply to arithmetical number can be applied to an algebraic number. They can be added, subtracted, multiplied, divided, adopt negative values, be expressed as powers etc. The essential point is that both the number and the symbol are treated as numbers multiplied together, even if one is not specified. So:
2x multiplied by 3x is the same as 2 multiplied by x multiplied by 3 multiplied by x
which by reordering is the same as:
2 multiplied by 3 multiplied by x multiplied by x
which is
6 multiplied by x multiplied by x
which is 6x2.
The symbol x is called a variable. Arithmetical values do not have to be substituted for x until the end of the operation. In fact they may not have to be substituted at all to provide meaningful relationships.
There may be a symbol y which represents a relationship expressed in terms of x at every value of x, which is described as y = f(x). The values of y for each value of x may then be plotted on Cartesian co-ordinates to show the shape of the function e.g. straight line, parabolic, exponential etc.
Since the algebraic symbols represent numbers, algebraic functions are homogeneous through time.
c. Non-numerical entities which are homogeneous through time.
Since x is an undefined numerical entity, it is natural to substitute other entities which are homogeneous through time in algebraic equations. Indeed that is where it all began, with Mesopotamian bushels of wheat. Undefined entities fall into two categories: discrete and continuous.
i. Discrete
An example of a discrete entity which is homogeneous through time might be an apple. An apple is a discrete entity if it designated as such conceptually. The description does not mention size or shape or flavour. An apple comes as a whole conceptual unit which is homogeneous through time. Apples, of course, are real entities, and in this form they are certainly not homogeneous through time. But conceptually they are homogeneous through time, since otherwise we would not be able to talk about them without identifying the particular apple in question. 'Apple' is the symbol.
The arithmetic then deals with 1 apple, 2 apples, 3 apples etc. Numbers of apples may be added and subtracted, and they may take on negative values as above.
However, they may not be meaningfully multiplied or divided in their associated form: twice 2 apples means 4 apples, but 2 apples multiplied by 2 apples is a meaningless concept. Similarly (2 apples)2 is meaningless; (22 apples) is 4 apples.
The sequence of logic is:
- This calculation is about apples.
- The arithmetic or mathematics is performed to give a number or algebraic expression without the appearance of 'apples'.
- The answer is expressed in terms of a number of apples.
'Apple' is not a substitute for the algebraic x.
ii. Continuous entities.
A continuous entity here means something like kilogrammes of gold. Discrete golden entities would be gold coins. By comparison weight is a continuous variable, even if it is expressed in kilogramme units. (Entity may not be quite the right term here, but no obvious alternative springs to mind).
The same analysis applies as to discrete entities. Weights of gold can be added, subtracted, and ranked in order of magnitude. They can be given negative values as on the other side of the balance. They can meaningfully take the double negative.
But they cannot be multiplied or divided; 2 kg of gold multiplied by 3.2 kg of gold is a meaningless concept. By comparison 2 kg multiplied by 3.2 is certainly meaningful i.e. 6.4 kg.
The reason for selecting gold as the example of a continuous entity is that gold is to all intents and purposes homogeneous through time. It does not shrink or grow or turn into something else with the passage of time, which is one reason why it has always been such a valuable commodity. Its material homogeneity through time is the parallel of the conceptual homogeneity through time of the apple. The result of the calculation is expressed in terms of numbers of kilogrammes of gold.
d. Variables which are non-homogeneous through time
The above discussion prepares the way for the main burden of this paper, the mathematical handling of entities which are non-homogeneous through time. The most graphic introduction is an invented example from economics, the consumption of alcoholic beverages in Utopia.
The data are:
1 2 3 … 21
this time in millions of litres/yr.
The same analysis applies as to gold. Litres of beverage can be added, subtracted, ranked and take negative values, always provided in this case that the result of the calculation does not give a negative consumption. But they cannot be multiplied or divided.
However, each figures refers to a year. They are a time series, even if the order in which they are written does not necessarily represent sequential years. Nor do they represent a simple concept or material which is homogeneous through time, because they are aggregates with a composition which may change with time.
For instance, during the year represented by the first figure, 1, the composition may be 2% wine and 98% bitter beer. On the other hand the figure of 3 million litres a year may represent 3% wine, 27% lager and 70% bitter. If they are consecutive years and not just a random collection, the picture may look as follows:
Composition %
These are not so much abstract points as a commentary on the socio-economic dynamics of Utopia over five years. As prosperity increased, more wine was drunk. As thirsty heavy industries declined, and those remaining were relatively less prosperous, less bitter was drunk. Lager consumption increased with the rise of the spectator. Consumption is an aggregate which is non-homogeneous through time.
A number of observations distinguish non-homogeneity through time from homogeneity through time.
i. The analysis of necessity refers to a particular place (non-homogeneous through space).
ii. There are problems in forecasting the next point in the series. There would be problems even if the trend for consumption were a straightforward mathematical function. The reason is that the 2005 figure, when it comes, has a significant new component in the form of 5% of some completely new beverage.
iii. There are interactions of these data with other series in the Utopian economy, for instance the demand for potato crisps. It may be socially obligatory to have a packet of crisps with a can of lager, in which case consumption of the two are linked.
iv. Changing technology plays a significant role in the changes of composition which occur. The invention of the can with a ring pull makes a considerable difference to who drinks what and where. Similarly the invention of the widget.
v. Aggregates of such series across the whole economy are the basis of Gross Domestic Product (GDP). To produce a variable which can be aggregated, supply and demand are expressed in terms of the money spent or expected to be spent on each item. Money is continuous and homogeneous through time by definition, so that it is analogous to the above example of gold. This device makes the algebraic operations possible, but the underlying socio-economic dynamics remain, hidden beneath the blanket of money.
vi. No relief is to be obtained by breaking the data down to something more 'fundamental', say the figures for wine, unless that is the goal of the analysis, because the question then becomes: red or white, wine bar or supermarket, aperitif or table etc? Nor can one specify the consumer more precisely in this sense; there is nothing more unpredictable than the individual consumer. You just have to choose the goal carefully, and live with the imprecision.
That is not to say the figures are meaningless, or the series not worth recording. It depends on what one is trying to achieve. The point is that calculation may be necessary but it is not in itself sufficient.
e. Keynes and mathematical economics
The first use of the term non-homogeneity through time of which I am aware was by Keynes, who was unhappy with the application of algebraic functions to his new economic model because economic "material is, in too many respects, not homogeneous through time" (1, 2). He thought it could not substitute for keeping 'at the back of our heads' the necessary reserves and qualifications.
I have no way of knowing how far he pursued the idea, but I have extended it to economic theory in my own book The Scale and Scope of Economics (3). Conventionally economic theory considers only economies of scale; the assumption is that processes are scaled up without changing their basic nature, rather like multiplying them by two i.e. they are homogeneous through time.
However, this assumption is far from true. Notional economies of scale are often, though by no means always, outweighed by the diseconomies which are introduced by changes of scale, such as difficulty of process control, problems of management of organisations of increased size, increased problems of location and environment, problems of learning to operate larger equipment, problems of security of supply of inputs, and so cost of down-time, problems of insurance etc.
None of these problems is insuperable, if the effort is worth it, but they all have to be taken into account when the costs are reckoned in decision-making. This is in addition to the hardware- or scale-related costs. They are factors which depend on people and time, whether in the enterprise or in the environment in which it is intended to operate, and they may not all be foreseeable. They are non-homogeneous through time. Rather than always using the cumbersome term non-homogeneous through time in this context, I use the neutral term 'scope' to distinguish it from 'scale'. It is scope which changes with time. Hence economies or diseconomies of scope. Hence the 'scale and scope' of economics.
There is a problem of summarising these two aspects of economic systems mathematically. To describe the economy as a function of time is trivial, because it must be so. However, it may be possible to decompose the system into scale and scope subsystems. Scale applied to operations depends only on current conditions i.e. output varies with current input prices depending on current demand, which varies with time. This is the production function. However, all the aspects of processes which are non-homogeneous through time are continually being addressed to bring improvements i.e. the process is evolving through time; it is changing in scope, another function of time. These two functions, scale and scope, are not independent; each gives rise to the other. Perhaps the best way to describe them mathematically is as some kind of product.
Another way of describing this process of evolution is 'learning system', as described in my book A Degree of Freedom, which sets out a new, non-mathematical analysis of systems thinking (4).
Non-homogeneity through time is the unplanned or unavoidable confounding of variables in a statistical sense which manifests itself only with the passage of time. In a snapshot at any particular time it may simply be an undetected heterogeneity. It is the changing composition of the heterogeneity through time which may cause confusion. Economics is only one, perhaps exaggerated, example.
In practice there are very few systems which may be considered as absolutely homogeneous through time, whatever is planned. People are non-homogeneous through time. Apart from fashion, they respond to what they believe to be threats and opportunities in the environment. They may have an optimistic or pessimistic outlook by nature, they may be influenced en masse by random events beyond anyone's control. This affects the outcome of all processes in which they are involved, whether in planning, execution or interpretation, whether safety procedures or management or university admissions, whatever the mathematical principles applied. All living things have this susceptibility: animals driven by hunger, plants suffering from drought, and even insects and microbes, the great survivors. Evolution itself is the result of non-homogeneity of populations through time.
Even wider, it applies to everything in the physical world subject to entropic degradation. Non-homogeneity arises from two sources. First, the system being described may itself be non-homogeneous, say a rocky structure containing flaws, a building or a piece of equipment. How these behave may depend on where they are located and how long they have been in existence. This may not become apparent until something snaps. Such phenomena are non-homogeneous by their very nature, like the weather.
Secondly, systems for obtaining inputs may be far from clearly and uniquely defined, especially in an evolving society and with changing technology. Similarly the systems for interpreting the outputs may be far from unambiguous, even if reproducible. Hence the 'scientific' or experimental aspect of computer proofs, even if they are free of bugs.
This points up the difference between the conceptual and the actual with respect to proof. Mathematics is always conceptually homogeneous through time and space, because that is how it is conceived. No one develops an axiom or a theorem to be valid only in a specific place or with an expiry date. They may later be shown to be false or they may be extended by the application of further mathematical reasoning, but their proof is what they set out to prove everywhere and at all times: QED.
The consequence is that mismatches must arise when the mathematics is applied to systems which are non-homogeneous through time. Things do not turn out quite as calculated, because they do not match the assumptions on which the proof is made. Even if they do now, they will probably not later. The passage of time will reveal the differences. Under these circumstances the term proof must mean proving the use of the mathematics in the sense of putting it to the test i.e. the percentage 'explained'.
That is not to cast aspersions on the use of mathematical proofs of any sort. Sometimes the most fruitful analyses are the most difficult because they deal with inputs which are non-homogeneous through time. Rather it is to conclude that the goals and limitations need to be clearly understood at all stages; calculation is not enough. There is no substitute for understanding, experience and insight.
Mathematicians may be allowing themselves a certain amount of satisfaction that at least their theorems are above the hurly-burly according to this analysis; it is only when they have to be translated into systems and perhaps computing that consideration must be taken of the complexities of non-homogeneity through time. However, that may be a little premature.
Sooner or later mathematics has to address change as a function of time. But time is nothing without an event to mark it (Einstein). Events mark the passage of time, whether they are homogeneous or heterogeneous in a static sense, as in a snapshot; it does not matter if the heterogeneity has no time to change. If there are no events, there is no time; there is no way of knowing.
The way of measuring time is to provide a sequence of evenly spread events. Even this implies that you can follow the intervals between events. You watch the pendulum throughout its swing, and note when it passes a fixed point, which is the event. All clocks here on Earth are arranged to produce the same interval of time, the second, whatever physical phenomenon is used.
However it cannot be assumed that any particular phenomenon is homogeneous through space. Indeed it is known that the interval of time measured by a pendulum would vary from place to place on the face of the Earth depending on the force of gravity on which it depends. This is also true more generally. As the clock moves from position to position in space, the phenomenon on which it is based may be influenced by, say, gravity, magnetism etc. This may be true of electromagnetic phenomena as a satellite leaves the surface of the Earth and heads out of the Solar System. The interval of time which it produces may then vary from place to place in space; it may be non-homogeneous through time. Another way of describing this is that space may be differentiated as far as this particular phenomenon is concerned.
These qualifications may be true of the currently used interval of time which is based on an electromagnetic phenomenon, because it is considered to be a fundamental property of atoms and the speed of light, both homogeneous through time. However, there are indications that the standard time interval may not be as immutable as thought; it could turn out to be a 'gold standard' in which 'gold' was found not to be homogeneous through space. An even more sobering thought is that these days all units of distance are measured in terms of time.
Nor can we assume that this applies only to space 'out there'. What about the subatomic space which fills atoms? Or nuclei? Atomic clocks provide the phenomenon which we use to describe the macroscopic world i.e. atoms, molecules and the structures we perceive, but the internal structure of atoms also changes with time, whether through the motion of subatomic particles or by some outside interference.
Moreover, there is no reason to assume, as Relativity does, that all physical phenomena used to make clocks would be identically affected as they move out into space. For example, different phenomena might be more, or less, affected by gravity or magnetic fields etc in the same locations in space. The result would be that space is differentiated differently for each phenomenon.
When clocks leave the place where they are all calibrated against each other, those based on different phenomena would then behave in different ways and produce intervals of time of different length. Perhaps it would be better to look at the stars, which is where it all began, but an interval of time derived from them must contain all the celestial movements which are not only elliptical with long time periods but precess to boot: orbits around the Sun, motions of the Sun etc. A second which was a fraction of a year, as at present, would not be the same as a tenth of the same fraction of 10 years, because of annual variation. Nor would it be the same in a different 10 year period.
Finally, one might ask why bother with clocks and physical phenomena at all in mathematics? Why not treat time as just another continuous variable? But time is nothing without an event to mark it (Einstein, again). No clocks, no events, no time! You must have a clock to have a variable.
It seems probable that a phenomenon such as exponential decay of a radioactive isotope would remain exponential throughout time and space, because the number of radioactive nuclei which decay in a population depends only on the number present at the time, as far as is known. The exponential curve as such would remain homogeneous through space as well as time. In this case it would just be the constants which varied (!), because they are all calibrated in Earth intervals of time i.e. seconds. This is because there is no way of timing the rate of radioactive emissions other than with a clock calibrated effectively in seconds.
A possible solution which I have proposed is a radioactive clock with a decay curve which is exponential and therefore homogeneous through time, but which does not rely on measuring rates of decay in seconds with another, conventional timepiece. Such a radioactive clock would give intervals of time which were Absolute, the same everywhere and at all times. It could then act as a Universal standard.
The methodology is as follows: to specify an interval of time in terms of a number of counts; to derive a parameter of decay which is dimensionless because it relies only on number, i.e. it eschews the second and the phenomenon used to measure it; and to obtain successive intervals of elapsed time of the same absolute length by calculation (5).
Such a clock would require, in the first instance at least, extensive evaluation and international agreement before it could become a standard.
A.C. Sturt
Guildford, Surrey, UK
25 October 2004
Physics uses equations such as:
where m is mass, t is time and d is length. The other symbols in the equations are either constants or derived from m, t, and d.
The symbols m, t and d are variable values of what are called the dimensions of the equations for the purposes of dimensional analysis. Dimensions are denoted as follows:
Since the symbols represent numerical quantities of these dimensions, they can be used in all the same operations as x in algebra. They can be added, squared and multiplied. They can be differentiated and integrated.
It certainly works, because these equations of Newton's enabled him to predict the motion of the planets very precisely. In fact this sort of equation is the working basis of all scientific and engineering calculations.
However, it is worth pointing out the assumptions which underlie the algebraic operations.
Thus 3t means 3 units of time-interval, on the assumption that the time-interval does not vary through time and space. This is reasonable for homogeneity through time because that is how clocks are devised, but what about space? Similarly 2d means 2 distance-intervals, on the assumption that the distance-interval does not vary through time, which is reasonable, because that is how the distance-interval is defined. But again, what about space?
In fact we know that the assumptions break down at velocities through space which approach the speed of light. Acceleration of a mass is no longer proportional to applied force, and in fact there is a limiting velocity beyond which mass cannot be accelerated, the speed of light. No longer a straight line relationship, it appears to be asymptotic i.e. a hyperbola (6).
The Theory of Relativity is based on the hypothesis that the algebraic relationships still hold good for measurements taken by anyone travelling at the relativistic speed,
i.e. they are homogeneous through time and space, but the observed discrepancies in everyday experience occur because the dimensions change with velocity. All the dimensions change together; it is a question of frames of reference.
In Relativity mass increases and time dilates as velocity approaches the speed of light. Clocks slow down, and so seconds grow longer by comparison with the standard time-intervals. Metres grow longer, but only in the direction of travel. It is not the dimensions which are homogeneous through time and space, but the algebraic relationships which depend on them. As pointed out above, these algebraic relationships are composed of variables which in fact signify number. Thus the Theory of Relativity seems to try to have it both ways.
An alternative which I have proposed in my series of papers (7) is that both the dimensions of physics and the fundamental physical phenomena, such as electromagnetic radiation, are homogeneous through time and space. Discrepancies are observed at relativistic speeds because the equations themselves, which have been derived under our local conditions, do not adequately represent physical behaviour under all conditions in the Universe. In other words we have not fully evaluated the nature of the fundamental physical phenomena to which they refer.
Examples of this may be the inverse square law for light and gravity It is suggested in another paper that there may be an unsuspected phenomenon at work, namely deflections of microentities (8). Nor are these likely to be isolated instances. Departures from the equations which we might expect to apply everywhere at all times may be exposed as our focus of attention shifts to the extremes of astronomical distances or the world of fundamental particles.
1 December 2004
1. John Maynard Keynes quoted in Keynes by D.E. Mogridge 1976 Fontana Collins, London and Penguin, New York.
"Economics is a science of thinking in terms of models joined to the art of choosing models which are relevant to the contemporary world. It is compelled to be this because unlike the typical natural sciences, the material to which it is applied is, in too many respects, not homogeneous through time."
2. The General Theory of Employment, Interest and Money by John Maynard Keynes 1936. Chapter 21, Section III p297:
"It is a great fault of symbolic pseudo-mathematical methods of formalising a system of economic analysis, such as we shall set down in section VI of this chapter, that they expressly assume strict independence between the factors involved and lose all their cogency and authority if this hypothesis is disallowed; whereas, in ordinary discourse, where we are not blindly manipulating but know all the time what we are doing and what the words mean, we can keep 'at the back of our heads' the necessary reserves and qualifications and the adjustments which we shall have to make later on, in a way in which we cannot keep complicated partial differentials 'at the back' of several pages of algebra which assume that they all vanish."
3. The Scale and Scope of Economics by A.C. Sturt 1984 http://www.churingapublishing.com/
4. A Degree of Freedom by A.C.Sturt 1993 http://www.churingapublishing.com/ p34.
5. Radioactive Clocks: a Basis for the Absolute Measurement of Time by
A.C. Sturt 30 July 2003. http://www.churingapublishing.com/radio_1.htm. See also patent application.
6. Mass in the Universal Inertial Field – A Revised Version by A. C. Sturt
18 September 2003 http://www.churingapublishing.com/numass_1.htm
7. The Timeless Universe, Light and Mass and A New Model of Physics – Foundations http://www.churingapublishing.com/
8. Light and Gravity Inside and Outside Solar System: Potential Consequences of 'Particle' Deflection Hypotheses. Submitted for publication. To be made available on churingapublishing.com website.