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Latest News

The Best Methods to Train Your Dog

The Best Methods to Train Your Dog

A dog is often seen as man’s best friend. Any pet owner would want their dog to behave at their best. But when your dog starts chewing on the morning[…]

Read more
Low Platelet Counts

Low Platelet Counts: The Causes of Low Platelet Counts

Individuals who have low platelets experience bruising easily and the blood does not clot as it should. Many people with low platelets often have to take medication, have surgery or[…]

Read more
Where to Find a Cheap Car Rental, San Francisco

Where to Find a Cheap Car Rental, San Francisco

Finding Cheap Car Rentals in San Francisco Can Save You a Lot of Money Looking to find a cheap car rental in San Francisco? This is possible, if you know[…]

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From Our Blog

The Best Methods to Train Your Dog

June 7, 2021
The Best Methods to Train Your Dog

A dog is often seen as man's best friend. Any pet owner would want their dog to behave at their best. But when your dog starts chewing on the morning paper or gnawing at your leather shoes, you should start taking action immediately. What are some ways you can train your dog? Even if you're not an expert trainer, you can still apply these methods with your pet:

Train Your Dog

Patience is a virtue. Yup, the old cliché is true when it comes to training your pet dog. Be it training your pet not to gnaw at your shoes or not peeing on the couch, patience is the key. If you take on training your pet while you're in a bad mood or you're too tired and exhausted from work, you may end up delaying training your pet for several months. Your pet won't respond well to bad temper, and so you will you as training is the least bit easy. To get more information concerning dog train: click here.

Never hit your dog or use physical force just to make your pet dog obey you - it won't. You'll indirectly teach your pet how to fight back and he/she won't obey any future training you will do. The best way to make a dog follow is through patience and by keeping a calm yet authoritative voice. Don't forget to play with your dog - it's a great way to boost your dog's self confidence.

Be prepared for some slips. If you are potty training your pet dog, be prepared for some slips every now and then, especially during the first few days. This is normal and you should not be disheartened. Just keep your consistency and don't give up on your pet. In a few more days or week's time, you will be pleasantly surprised by the progress your pet dog is showing.

Reward your pet. Every time your dog poops where you want him to or does things the way you want them done, don't forget to give them a nice tasty treat. Words of praise accompanied with petting like he/she is the best pet dog in the whole wide world also do a big difference. Your pet dog will feel valued and he/she will know that they did the right thing, as is bound to repeat it not only for the treat, but for your affection as well.

Making your pet feel valued and loved is a great way to make your pet follow your commands. Just remember to keep your cool as the first few days of training will be rough. Don't give up on your pet - your training will be rewarded.

Article Resource: Leslie Bautista

Low Platelet Counts: The Causes of Low Platelet Counts

June 6, 2021
Low Platelet Counts

Individuals who have low platelets experience bruising easily and the blood does not clot as it should. Many people with low platelets often have to take medication, have surgery or a blood transfusion to help treat their condition. Low platelets causes bruising easily and the blood from clotting properly. There are several conditions that could cause a person to have a low platelet count.

Rheumatoid arthritis.

Rheumatoid arthritis which is also known as RA is well-known condition that can cause low platelets. Rheumatoid arthritis affect many people each year. Over an extended period of time rheumatoid arthritis can cause other medical problems such as tendons, cartilage and ligament damage.


Lupus is a systemic autoimmune disease that can affect any part of the body. It isis a very serious condition and causes the blood platelets to drop dramatically. The occurs when autoimmune system attacks its own tissue instead of the virus or bacteria in the body. There are treatments to help with the low platelets that are associated with lupus.


Bacteria in the blood.

Anytime bacteria is found in the blood this is a very serious problem. It can also be very dangerous and can lead to extreme illness in the person and sometimes death. The condition is very rare but can strike anyone at anytime, find more info.


Different type of medications may cause a person's platelet count to drop. Antibiotics and diuretics can cause the immune's system to destroy the body's platelets. It is important to take medications the way they are prescribed by a health care professional.


Anemia affects millions of people each year. A person who is anemic have a very low blood count. This condition can happen in both the young and the old. Individuals who are anemic experience different type of symptoms such as fatigue, nausea, and wounds that are slow to heal. Anemia happens when the body have a low number of red blood cells.


Leukemia is a type of cancer that is found in the bone marrow. This condition occurs when the bone marrow produces a large number of abnormal white blood cells. The white blood cells then do not function properly in the body to help fight off infections. There is different type of treatment to help with the symptoms associated with leukemia, but the process can be long and ongoing for years.

Viral infections.

Viral infections are hard to treat, and there is usually no cure for virus. There are many viruses that affect many people each year. But there are some very serious ones such as HIV that can cause the platelet count to become seriously low. Individuals with these low platelets brought on my such viruses can cause other types of dangerous infections.

Where to Find a Cheap Car Rental, San Francisco

June 5, 2021
Where to Find a Cheap Car Rental, San Francisco

Finding Cheap Car Rentals in San Francisco Can Save You a Lot of Money

Looking to find a cheap car rental in San Francisco? This is possible, if you know where to look. Here is information on where you should and shouldn't go to get a cheap car rental in San Francisco, as well as additional tips to make sure you get a good deal.

Where You Won't Find Cheap a Car Rental in San Francisco

Hertz has vehicles running in the upper $30 range. While this is ok, this is not the least expensive and it's not the most expensive either, it's middle of the pack. Avis has vehicles starting in the $52 -72 range and Budget starts at mid $60.00.

If you are looking to find a cheap car rental in San Francisco, you should look somewhere other than these places.

Where You Won't Find Cheap a Car Rental in San Francisco

Where You Can Find a Cheap Car Rental In San Francisco

Enterprise really has the lock down in terms of price and getting a cheap car rental in San Francisco, this source. The absolute lowest price you can get starts at under $30, at the Cesar Chavez center located on 45 Charter Oak.

Other places you can get a cheap car rental in San Francisco are at Union Square, located at 222 Mason St and at the Moscone Center, located at 727 Folsom St. They start at under $31 are also great places to find a cheap car rental in San Francisco.

Where you decide to go depends mainly on where is closest and convenient to you. As an added service, Enterprise will also pick you up and afterwards drive you home.

Do Not Rent From the San Francisco Airport

The airport is the last place you will want to go if you want a cheap car rental in San Francisco. Dollar starts vehicles at the mid $100 level and Hertz starts at the mid $110 level.

Some people believe that going to the airport might get them a cheap car rental because they deal in volume. This simply isn't true because renters at the airport put themselves at the mercy of the car rental companies. The companies charge more because of their convenient location and the long hours they are open.

If you feel like you really need to get a vehicle from the airport and do not have any other choice, at least check the discount websites like Priceline for bargains.

Some Locations Allow Bargaining

Some Locations Allow Bargaining

A lot of car rental locations teach their associates to negotiate in order to book more deals and to take customers from their competition. While not everyone likes to negotiate, knowing how to negotiate can potentially secure a cheap car rental in San Francisco.

Do Price Checks Online

Prices do change occasionally do to various reasons. It's always good to compare sometimes to make sure you secure a cheap car rental in San Francisco

Online Discount Coupons Save Money on Cheap Car Rentals

If you are serious about getting a cheap car rental in San Francisco, you should look into using car rental discount coupons. With the right know of where to get them and how to apply them, you could save potentially 20 - 30% on your rental or at least get free upgrades.

Free Memberships Save Money

Another way to secure a cheap car rental in San Francisco is through memberships. The offers and discounts are unadvertised to the general public and are sent to your email. Sometimes, however, the discount coupons will still save you more money, so you have to compare these two.

Book Early

Don't put yourself at the mercy of the time element. The closer you book your reservation to when you need it, the more they can charge you for your vehicle, even if their lot is completely filled with vehicles.

Expect To Pay More During Summer Time

Everyone wants to travel during the summer time and prices go up, even when gas is expensive and the economy is running slow. If you want to get a cheap car rental in San Francisco, use the above strategies to offset this.

Is Car Rental Insurance Important?

Many people think declining car rental insurance will make sure they get a cheap car rental in San Francisco. This might be the case, but not in all situations. You should understand how car rental insurance can actually save you money in some situations before you decide not to take it.

If You Rent Because your Vehicle is Totalled Or You Need a New One

If You Rent Because your Vehicle is Totalled Or You Need a New One

Often many people rent cars because their vehicle was totalled in an accident or for other reasons, will need one soon. If this is the case, sometimes it's worthwhile to look into buying a used rental vehicle because they're very well maintained and are well priced.

Disney Vacation Club (DVC): Disney’s Timeshare Benefits & Costs

June 4, 2021
Disney Vacation Club

Disney Vacation Club (DVC) is a vacation program that operates as a timeshare program with a twist – members purchase “points” when they buy into a DVC property. These points are renewed annually, and can be spent on different Disney resorts and rooms, for different lengths of stay, and at different times of year.

DVC can be a solid investment for guests who travel frequently to Walt Disney World Resort, Disneyland Resort, or other locales. That said, everyone’s situations vary and individuals should carefully consider how DVC operates, its costs and benefits, and other considerations before purchasing.

For an introduction to DVC, read Disney Vacation Club (DVC): Disney’s Timeshare Program

Disney Vacation Club – Cost Benefits

Disney Vacation Club Cost Benefits

DVC has two major benefits, the first being the anticipated, long-term savings for frequent Disney guests. The value of DVC points is set at the purchase price, while prices at Disney resorts increase between 5 – 10 % annually.

Depending on their traveling habits, then, Disney guests can save money through DVC. Disney’s website notes the cost of buying into DVC, on average, is equal to approximately seven Disney family on-site vacations go here.

DVC membership includes discounts on the following:

  • Annual Passes and Premium Annual Passes
  • Walt Disney World water parks, DisneyQuest and Pleasure Island
  • Disney restaurants (select restaurants)
  • Recreational programs and theme-park tours
  • Disney resort room rates for cash (non-DVC) reservations

DVC members enjoy resort perks regular Disney guests don’t that can save money: free high-speed Internet access, free self-service laundry, and no additional charges for more than two adults in a DVC room.

Note: DVC member discount programs are subject to change, although DVC points don’t.

Disney Vacation Club – Vacation Benefits

Another type of DVC benefit involves vacation planning. DVC’s points system offers flexibility. Members needn’t commit to staying at one particular Disney resort on a set schedule. DVC points may also be used at other, non-Disney resorts.

A complete list of other DVC member benefits is given to owners when they check into their DVC resort, but include:

  • Early booking privileges, 11 months in advance for a home resort, and 7 months in advance for other locations
  • DVC Member Services, for toll-free, vacation-planning assistance
  • Pool hopping privileges between Walt Disney World resorts (some exclusions and conditions apply)
  • Freedom to purchase the Disney Dining Plan or cook in their unit’s kitchens

Disney Vacation Club – Considerations

In addition to considering their traveling habits and financial obligations, Disney fans should be aware of several considerations.

Perhaps the most important thing to understand is DVC is not a real-estate investment but a prepaid vacation plan. While members do purchase a deeded real-estate interest in DVC, they don’t own their points forever. Points expire in 2042, 2054, 2057, or 2060, depending on a member’s DVC home resort. Ownership may be transferred to other parties in consultation with DVC.

Total initial and ongoing costs for DVC should also be considered. Initial purchase costs are factored as a minimum of 160 points at $112 per point, excluding closing costs, for a total of $17, 920 plus any financing costs and interest. DVC members also pay annual dues, calculated by number of points. Yearly dues increases are roughly equivalent to increases in Disney resort rates, though that rate is not guaranteed.

Disney promotes DVC’s cost effectiveness and convenience. That’s not always the case. While DVC members may stay outside their home resorts, it’s often not cost effective or convenient to do so – especially for non-Disney accommodations. Booking during peak Disney travel periods or for other popular destinations can be difficult. DVC points must be booked or banked within a certain period or they expire.

Other considerations are lifestyle changes. They may be directly tied to finances –loss of income, retirement, educational bills, or medical expenses – or more general – shifting vacationing interests, relocation, or changes in family structures. There’s also the “Disney exhaustion” factor, when a DVC vacation no longer appeals.

Disney Vacation Club – DVC Research

Buying into Disney Vacation Club is a lengthy, sometimes complicated process, especially because members may buy directly from Disney or through DVC resale agents. Initial research can be conducted at the Disney Vacation Club website or by visiting the DISboards DVC forum.

Guests seriously considering DVC should stay at one or more DVC resorts before attending a DVC presentation. Guests may reserve a room directly through Disney or rent points from a DVC member, the latter which helps demonstrate how the DVC points system works.

Gloucester IT Services & Support

June 3, 2021
Gloucester IT Services

Computer Parts, Networks and IT Supports in Gloucester and Bristol

Today is an era of technology; every company, large or small, relies on computers to provide satisfactory performance. It can be very frustrating when your computer starts and it takes forever to start or stop and wait a long time before finally ending. When teams do not work according to the standards you should probably start to go crazy over them, and not the fault of his team, is a sign that it's time for maintenance or repair may, if your IT service provider found a few defective. It's really a great challenge not only for yourself but for all computer users to keep computers fully guaranteed against the risks many new every day.

qualified service of Gloucester

It 's hard enough to choose a qualified service of Gloucester and Bristol computer repair service providers.If you are also looking for quality work at a nominal price, this task becomes even more difficult.

Computer repair markets are very different in Gloucester and Bristol, which is why it is necessary to attempt to repair computers, specializing in computer sales, computer repair, computer upgrades, computer services, websites, graphic design and marketing of organic SEO. These companies are sure to have unique solutions for every computer user, as it consists of a number of well-trained and qualified technicians.

Gloucester and Bristol computer repair companies usually offer a variety of services and benefits. Some of them are: the personal computer, laptop and Mac computer repair, installation and network configuration, maintenance and upgrades, virus and spyware removal, Internet and broadband, e-mail and configuration, training and technology consulting (in most cases, free consultation, but not always), tailored for personal computers, software installations and configurations, the personal computer tune up services, cash cleaning, cleaning portable, against a slow and slow and unresponsive, blue screen errors, problems starting and stopping, troubleshooting operating systems, to replace the screen if they are broken or dim or lines of them, charging and power problems, and many, many other services.

Computer Support Gloucester

Many computer repair companies in Gloucester and Bristol also offer free pickup and delivery of equipment. This offer is not surprising sounds tempting, but be imposed only if you trust the company because there are many fraudulent repairs business equipment, then it is better that they know.But i think you are going to get the best recommendation than you ever got here. A great site that i am personally familiar with and would like to recommend you is
Gloucester Computer which is famous for IT & Computer Support Gloucester.

Whatsapp vs. Hangouts

June 1, 2021
Whatsapp vs. Hangouts

That’s right. Hangouts vs. Whatsapp. Why not iMessage? Easy. Because it’s only on Mac operating systems, ergo, defeat. This is about cross platform messaging apps that anyone can use. Skype? Let’s face it, Skype operates mainly on video calls and is an old time contender. This is about the two most used 3rd party messaging apps. So, sit down and watch (read) the match. The judges wait silently for the bout to start and the referee… Wait, where is the referee?

Round 1 - Functionality


Whatsapp is based solely, completely, and utterly in the world of messaging. Remember AIM? Imagine it got hit with gamma rays and started having big green anger problems. The advantage is that Whatsapp doesn’t require an account, just a phone number. Google apps on the other hand requires the user to have a Google + account. There is still some privacy in the user experience when it comes to Whatsapp and in that regard it stands alone.

Google Hangouts offers messaging, text messaging, group messaging, voice calls, video calls, and straight up phone calls. Sick. That’s one hell of a hand. Whatsapp offers messaging. Plain, lean messaging. You can only use one device on it as opposed to Google Hangouts which syncs all your different devices into one.

When it comes to functionality, it’s up to the user and what they need. If you want it all, Hangouts is the way to go. If you want dedicated messaging, Whatsapp is for you, Additional resources

Round 2- Platforms

For an app to succeed nowadays it needs to be about at cross-platform as you can get. If they could make apps for old SNES machines I’m sure they would bring just a few more customers, myself included. Both Hangouts and Whatsapp are offered for a variety of operating systems and this round is bound to be a draw or based specifically on your needs.

Whatsapp offers their app on Android, iOS, Blackberry, Windows Phones, and Symbian. That is pretty much all of the smartphone operating systems. It isn’t offered on any desktop style platforms but who knows what’s in store for Whatsapp’s future after Facebook jumped into the picture.

Hangouts boasts a similarly diverse array of operating systems but in a different context. It can be used on iOs and Android smartphones but outside of that it is only available on Mac’s OSX, Windows, Linux, and the web.

For those of us on the go, which is pretty much everyone these days, we need options. Not just some. We want them all. Neither of them have it all but in this case Whatsapp is the most versatile app when it comes to mobile use, which it is designed specifically for. IOS and Android are the most popular but that doesn’t mean you leave out the little guy, does it?

Final Round - Users

According to a post by Econsultancy earlier this year, Google+ had achieved 1.15 billion users. The only downside was that only 35% of them are active. That’s around 402.5 million users. That means that only 402.5 million users could be using Hangouts, seeing as how you need to have a Google+ account to utilize it. This was around February of 2014 and the numbers vary depending on the website you go to.

Whatsapp hit 500 million in April 2014 and 600 million in August 2014. That’s a lot of users. Zuckerberg, the Facebook one, says that he can see Whatsapp reaching 2 or 3 billion users while still being ran independently from Facebook. Now, that’s a lofty goal but seeing that Whatsapp developed it’s over 600 million users in just five years I believe it could be possible that they surpass the Facebook user average. It’s clear that as of right now this round is going to go to Whatsapp.

The Judges Decision

The Judges Decision

It turns out that the reason we couldn’t find the referee is because there isn’t one. The judges also left and joined the crowd around the ring. The fight was good and it’s going to go well beyond just these three rounds. These apps are highly controversial when being compared and in the end it’s only the fans who can decide. Whether you want the app that does it all or the app that is streamlined for its exact purpose it’s up to you. Both Whatsapp and Google Hangouts can be downloaded from the app store on whichever device you have. Unless, that is, you want Hangouts and you have something other than iOS or Android.

Improving Manufacturing Performance with a Few Simple Numbers

May 30, 2021
Improving Manufacturing Performance with a Few Simple Numbers

Business leaders are constantly in search of data regarding their business. Manufacturing professionals especially value so-called "hard" business data as a means of completely understanding and separating profitable operations from unprofitable ones. In today's Information Age, discover more, there seem to be as many different ways of measuring manufacturing performance as there are types of equipment in the manufacturing industry.

Efforts to measure what a machine or work center is doing, however, sometimes obscure what is not being done, lost opportunity that if corrected would yield significant returns and may only require little investment. But how can "lost opportunity" be measured, let alone understood? Fortunately there is one metric that concisely and easily communicates multiple opportunities in a comprehensive manner - OEE.

Overall Equipment Effectiveness

OEE is an acronym for Overall Equipment Effectiveness. OEE is expressed as a percentage, with 0% representing no effectiveness and 100% the equivalent of manufacturing perfection. The OEE calculation is the product of three other percentages - one each for Availability, Performance, and Quality. The formula

can be written like this:

(A%) x (P%) x (Q%) = OEE%

Implemented properly, OEE is an ideal indicator of an area's current work rate compared to its absolute potential and drives focus to the areas of greatest opportunity. Understanding and implementing OEE requires a thorough understanding of its three basic elements.

Availability: Work center Availability essentially measures the amount of time the machine was in use, compared to the time it should have been in use. An important (and somewhat confusing) component of Availability is Net Operating Time. What is Net Operating Time? It is the time left after subtracting

all the time when work will NOT be scheduled: Holidays, planned shutdown periods, weekends, etc. All time within a calendar year when work is scheduled equals Net Operating Time. On a weekly basis, this may be 120 hours (24 hours x 5 days) or 168 hours (24 hours x 7 days). Time not spent producing is tracked and reported as Availability. Typical availability losses include changeover time, preventive maintenance windows, and employee lunch/breaks.

For example, let's assume we have machine scheduled to work eight hours each shift (Net Operating Time = 8 hours). On a particular shift, the machine is down 30 minutes for a changeover and one hour due to employee lunch/breaks - what is the machine's Availability? Subtract the losses from the Net Operating

Time (8 - 1.5 = 6.5), then divide by the Net Operating Time (6.5 / 8 = 81.25%).

Performance: Work center performance is the most easily grasped of the three OEE metric components, as many manufacturing managers already measure machine output in some respect. In simple terms, Performance is the percentage of actual parts produced vs. the theoretical parts that should have been produced in the same time-frame. The key difference for most managers is that existing run standards may not be a truly theoretical and are instead "historical", incorporating downtime and other inefficiencies which skew the data lower than what the machine may actually be capable of producing.

As an example, let's assume our machine has a standard production rate of 200 units per minute (or 96,000 in 8hrs). How much output should we expect in our Availability example above? If you said 78,000 (200/min. x 60 min/hr x 6.5hrs of operating time), you passed! However, if during our 6.5hr shift the machine was down 45min. for troubleshooting & repair, our output would be reduced further. Let's say we only produced 61,000 parts for this particular shift. Our Performance calculation would yield 78.2% (61,000 actual / 78,000 theoretical for the 6.5hr run time).

Quality: The Quality component, like the Performance component, is a discrete and is relatively easy to comprehend. Your machine or process is making something, and each "something" is either of acceptable quality ("good") or not ("bad"). The Quality component of OEE measures the percentage of "good" parts compared to the total number ("good"+"bad") of parts produced. Many manufacturing facilities heavily scrutinize the output of each work center (the "good" number), but far too few measure or have the ability to measure the volume of rejects.

One last example with our fictional machine: In our Performance example above, the machine only managed to produce 61,000 parts. How many of them were good? Did we assume they were all good? Suppose upon examination only 56,000 parts passed inspection. Our Quality rate would then equal 91.8% (56,000 good / 61,000 total).

As stated earlier, OEE is the product of Availability, Performance, and Quality. So, now that we have example data, let's calculate the OEE of our machine during the shift in question:

OEE = (81.25%) x (78.2%) x (91.8%) = 58.3%

losing over two-fifths of our machine's

Okay, so what does 58.3% mean? Basically it means we are losing over two-fifths of our machine's ability to produce. More importantly, we know where these losses are occurring, so we can investigate these areas further, find out why and take action to improve them. Best of all, we will be able to see (through continued OEE monitoring) the impact our actions have on the machine.

Through a few simple measurements, OEE can quickly bring to light a work center's true performance capability, highlight opportunities for improvement, and over time measure the impact of changes.

Philosophy of Numbers in Math

May 29, 2021
Philosophy of Numbers in Math

Do numbers exist only in the human mind? Could they be "living" in a Platonic realm somewhere? Do numbers simply exist as symbols on pieces of paper? What is the precise existence of numbers anyway?

Philosophers been arguing over the true nature of mathematics and numbers for thousands of years. But in my view, Platonism still holds up as the most truthful theory, despite the many new ones that have popped up in recent times concerning this age-old problem. Platonism can be defined as... numbers and mathematics are abstract concepts that have an independent existence apart from the symbols or terminology used to represent them; i.e. the number Pi = 3.141592653... existed somewhere in the "Platonic realm" long before any human ever discovered its practical purpose here on Earth.

mathematics exists simply

In the book, What Is Mathematics, Really? By Reuben Hersh (Oxford University Press, 1999) Hersh puts forth the proposition that mathematics exists simply as a social activity performed by a certain class of humans who gradually work (make experiments and notice patterns, prove and conjecture, write papers and books) to gradually build up a body of knowledge called 'mathematics' that is continually added to, debated over, expanded upon, etc. Hersch calls his new theory of mathematics, 'humanism.' But personally I am not convinced, as none of the arguments in the book seemed strong enough to counter the following argument.

Say a new form of life arises in the future somewhere in the Black Eye Galaxy (NGC 4826; which was discovered in 1779 by Edward Pigott) and the "aliens" there call themselves "Quorfs." Say these quorfs gradually develop a system of counting, but instead of numbers they call them "miglets." Time goes by and gradually the quorfs develop rules for their miglet system and eventually notice rules and laws governing their behavior. Surely at some point the Quorfs will notice that some miglets are not divisible by any other miglets (primes), while others do have divisors (composites) and then they will notice a whole host of rules, laws, and properties for their miglet system.

Even if the Quorfs live in a 5-dimensional world and have eight "digits" on six major appendages and use a base-24 counting system, doesn't it seem plausible that eventually they will discover the same "laws" and "rules" that our number system has? Only they will call things by different names? (The scientists at NASA believe this is true, which is why they send out primes in capsules to deep outer space in search of extraterrestrial intelligence.) Hence, even after the human aspect and any earthly subjectivity has been removed, there will remain some objectivity pointing the way to a realm of forms living in an independent reality, where the concept of numbers lives and waits for anything possessing intelligence to discover.

Ludwig Wittgenstein, one of the greatest philosophers ever to take a breath, said that the laws of mathematics are not self-enforcing, so if people agreed to do mathematics a completely different way than our present method, they too would be correct in whatever rules they happened to formulate. For example, Wittgenstein said that 8 + 3 is not truly equal to 11 in absolute reality, but that it's just the way we humans have done things so far; and that other cultures could do it differently. But to me it seems that "necessity" has dominion here. That is, practical, real-world necessity determines whether 8 + 3 = 11, instead of any group's opinion that 8 + 3 equals 11.

Do we humans apply numbers to the universe arbitrarily just so we can make sense of it? There are slightly more than 365 days in a year, about 365.242, which obviously is not a precise integral number. But 365.242 is still a number, just as Pi = 3.141592653589... is a number that's irrational and transcendental, yet highly useful.

There is also a debate in the world of mathematical philosophy concerning whether numbers are discovered or invented. Formalism is a theory in philosophy that says mathematical statements actually have no meaning at all, but they are simply collections of symbols whose overall forms and proofs may have some useful applications, but other than that they are meaningless. In other words, formalism says that mathematicians merely manipulate symbols on pieces of paper, following their own arbitrary rules, but that it really makes no sense in an ultimate way.

Constructivism is another philosophical theory related to mathematics, but is has a more complicated definition, which I will have to quote: "... in the philosophy of mathematics, [constructivism is] a broad position (encompassing both intuitionism and formalism but also going beyond them) which holds that mathematical entities exist only if they can be constructed and that proof and truth in mathematics are co-extensive. Constructivists oppose the realist (or Platonist) view that mathematical objects or truth exist independently of human procedures. This has the consequence that certain classical results whose proof rely on Platonic assumptions are not constructively valid." - From The Blackwell Companion to Philosophy.

The definitions above bring me to a story which may help elucidate things further: I used to be addicted to submitting integer sequences to the Online Encyclopedia of Integer Sequences. Occasionally I would construct a sequence that was highly artificial. At those times it seemed that I was "inventing" mathematical objects instead of "discovering" them. I had plenty of sequences rejected from the OEIS because of my arbitrary constructions. Around this time I also learned of the concept of constructivism and became intrigued with the idea and wanted to believe in it. But I couldn't persuade myself it was true enough to actually leave Platonism behind.

In other words, I wanted to believe that constructivism was true since that would make all mathematical activity "contrived" or "arbitrary," and that discovering something "beautiful" wasn't as important or as special as it seemed. But I couldn't actually make myself believe in constructivism since my natural intuition kept telling me that people made mathematical discoveries whenever they "did" mathematics. But I still liked the idea of people constructing mathematics, and I still do.

Here is an example. The mathematical work I engage in now consists mainly of being a "prime hunter," which means I search for large 'probable primes' - those that pass a Fermat test but that cannot officially be certified prime since no one knows an elegant algorithm for doing it, and then I submit the probable primes I find to a math database. One of my favorite polynomials that has brought forth an abundance of probable primes is this:

n# * 10^(n+k) +prime(n+j)

Which consists of a primorial: #, powers of 10, and the addition of a small prime on the end. With each new search I regularly change the values of the k's and j's and usually find more primes. This polynomial has been exceedingly lucrative in terms of plucking primes out of the Platonic realm, even though I'm not sure why it works so well. I suspect it has something to do the multiplication of many small primes, the abundance of 2's and 5's from the powers of 10, and finally the addition of a prime on the end which increases the chances of finding another larger prime, etc. But I cannot prove this polynomial any more effective than another simpler more elegant form.

philosophical meandering

My main point however is that the polynomial above would appear quite ugly to a real mathematician! But I still think it's nice. Why? Because it works and it's slightly more complicated than other prime polynomials! Now here's the main point: Did I create this form of mathematics? Or did I discover it? It feels like I created it since the polynomial seems so artificial, inelegant, and unattractive. But my intuition says that the actual primes it gathers are already lurking out there and that I'm discovering them. There is no way to prove it one way or another.

So, despite much philosophical meandering, the Platonic Realm in my view is where numbers still seem to exist. And even though I am intrigued by the idea of constructivism, my intuition still says that I'm a Platonist. Perhaps you would like to pick up a book or two on mathematical philosophy and determine which belief you subscribe to.

Animals on Chinese Military Rank Badges: Nine Different Animals Depicted on Military Mandarin Squares

May 25, 2021
Animals on Chinese Military Rank Badges

Unlike the civil ranks, whose squares could be purchased towards the end of the Qing dynasty (1644-1911), military positions were prized by the Manchu army, and it is unlikely that ranks were sold to the conquered Chinese. Also upper-class Chinese disliked and were uninterested in the military positions of the Manchu, so were unlikely to covet these squares which were confined to those stationed in the provincial garrisons and to Manchu quarters in the larger cities.

Mythical Animals

Animals used on military squares were mythical, as suggested by the use of flame motifs usually surrounding the beast. They were often embroidered without any attempt to obtain a true likeness. It is useful to see illustrations of them in order to distinguish the different animals.

The mythical Qilin was the first rank for a military mandarin and it is thought to have great wisdom. The animal is often found in Chinese art and mistakenly called a unicorn by Western writers. It is a composite beast, with a dragon's head, a pair of horns, hooves, the body of a stag covered with large blue or green scales, and a bushy lion's tail.

The Lion for the second rank resembled the Buddhist "snow lion" in late Qing. It was a large white animal with green curly mane, back crest and bushy tail. Earlier examples had a blue body.

Realistic and Unrealistic Depictions

Realistic and Unrealistic Depictions

The Leopard, the third rank, bore closest resemblance to a live animal except at end of dynasty when the spots became faint circles. Sometimes had a circular star with radiating lines on its forehead. Another realistic animal was the Tiger, the fourth rank, with stripes correctly depicted, except at end of the Qing dynasty when stripes became comma shaped lines. It often had the Chinese character for 'prince' on its brow.

The Bear for the fifth rank, bore no resemblance to its real prototype being depicted with a blue body, green mane, bushy tail and white paws. It looked very similar to a lion, except in later examples of Qing, when the mane was straight and the lion's curly. The Panther for the sixth and/or seventh rank, was shown as a yellowish catlike animal with a white chest; no distinguishing markings, find more info.

Low Ranking Military Rank Badges

The Rhinoceros, the seventh and/or eighth rank, was a completely mythical creature better described as the Chinese unicorn. It was shown to be cow-like with a large horn on the back of the head, curling forward between the ears, and a long thin tail. The last and eighth rank was the Sea Horse, not a small marine animal, but the legendary horse of the sea.

Rank Badges Destroyed

When the Revolution overturned the Qing dynasty in 1911, the provincial garrisons were the first places to be attacked. Military officials, afraid of being recognized, burnt their squares and other marks of identification. Furthermore, these badges had no value in the new government, whereas the civil officials often backed the new regime in the hopes of keeping their property intact.

Therefore low ranking military rank badges which would have belonged to provincial soldiers who would have destroyed them means that the eighth and ninth ranks are extremely rare and therefore expensive.

Review: Nozbe Task Management Software

May 19, 2021
Nozbe Task Management Software

Nozbe is a task management software that was introduced in 2007 and has since been gaining acclaim through various websites and bloggers. I have been using Nozbe exclusively for six months and although I have looked for and tried cheaper task management options, I have found none that can compete with the features found in Nozbe . This task management platform offers many features, but these are a few of the features that I have come to appreciate the most:

Task Management Software

  • Flexibility of the interface.
  • Integration with Google Calendar
  • Free applications.
  • Ability to work with a team.

In recent years David Allen's (2001) GTD approach (n.p.) to task management has been gaining more and more followers. Nozbe offers the kind of flexibility that is needed in order to implement the GTD approach to task management. I have come to find the many ways to organize content through Projects, Contexts, and Actions particularly useful in setting up my system.

Nozbe not only offers a stand alone calendar within the program, but it also offers integration with Google Calendar. When set up Google Calendar will display all of your tasks and offers reminders when tasks are due. This is a great way to keep all of your meetings and tasks in one place.

If Nozbe only consisted of its web based platform it would be a great option. The good news is that it doesn't stop there, Nozbe offers free applications for various phones and computers. While I generally use the application on my Mac to keep track of my day to day responsibilities, I have found the iPhone app to be very easy to use on the go to remember things and keep track of daily tasks.

Nozbe is the ability to work

One of the newest additions to Nozbe is the ability to work with your team on tasks even if they do not have a Nozbe account. I am currently learning more and more about this feature and testing it out with my team. So far I have found that it is an extremely useful and beneficial tool so long as you educate your team on how to use the software.

While Nozbe is not a perfect task management solution, I have yet to find any solution that fits my needs more. At first I hated the idea of paying for Nozbe , with so many free options available. After trying them all I have concluded that you get what you pay for. If you are looking for a great system to get things done look no further than Nozbe .

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