Archimedes was fascinated with large numbers. He famously decided to find a number to count how many grains of sand there were. The greek numbering system was a challenge though. They used letters in place of numbers. A=1, B=2, C=3, etc. Therefore, it was difficult to count very high. Before Archimedes, the largest number in the Greek number system was 10,000, which they called a myriad. While a myriad is great for counting armies, or people, it was hardly large enough to count sand! So Archimedes set to work. He was comfortable working with the area of shapes, such as the area of a square, 4 times 4 is 16. Archimedes used this idea to a far greater effect. He created a new set of numbers using this idea. Numbers of the "first order" would be a myriad times a myriad, which would be 100 million. Numbers of the "second order" would be 100 million times 100 million, which comes to a 1 followed by 16 zeroes! Now archimedes had a system to count the grains of sand. He calculated one would need a number of the "eighth order" to count the grains of sand, or a 1 followed by 64 zeros!
10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 (I hope I counted right) For most people this would be good enough. Archimedes, delighted with his discovery, set about to see how large of a number he could create. He used a new system, called periods, to make numbers so large we can never use them. Numbers of the "first period" could represent numbers as large as a 1 followed by 800 million zeros!! If your writing a book of zeros, this would take the same number of pages as 1000 harry potter books combined! Numbers of the "second period" would be a 1 followed by 64,000 zeros! Still not content, he continued until he reached a number larger than anything we can possibly count in the universe: his so called beast number. Archimedes called it "A Myriad Myriad units of the Myriad Myriad Order of the Myriad Myriad period. This is a 1 followed by 80 quadrillion zeros!!! To put this in perspective, an atom is so small it can only be seen with a super super powerful microscope. How many atoms do you think are in the universe? Scientists believe the universe holds about 1 followed by 80 zeros worth of atoms. This is tiny compared to a 1 followed by 80 quadrillion zeros! There is nothing in the universe that even comes close to this number.
However, infinity is still larger!
Saturday, September 12, 2015
Thursday, September 10, 2015
Do you like Apples? *crunch*
Who me? I love apples! They are a great spring / summertime fruit, and quite delicious. My personal favorites are braeburns and fuji, they have the crunch and the flavor. However, for the fall, I like granny smiths. Why? Because they go into one of America's favorite desserts, apple pie. I'm kind of hoping the bunnies make some soon. If not, I shall make one. You can tell I'm munchy. I actually plan to discuss Apple's recent Livestream event / 2015 Keynote.
Apple, as many of you know makes Iphones, Ipads, laptops, desktops, and watches. Every year they release a new line of updated products for us all to drool over. In case you missed it, here is a quick recap of their major announcements for the coming year:
To start with, I'm going to back up to spring. Apple released a new macbook line of thin, lightweight laptops with a single USB Type C connector. This magical little connector is designed to charge the laptop, connect to external displays, hard drives, dvd drives, and all manner of peripherals. In short, it plans to replace all other connectors in the future.
Fast foward to the Summer, and Apple announced it's new set of Operating systems: iOS 9, and OS X El Capitan. These new OS's add more features, including a split screen (borrowed from Windows 10) all new mission control, spotlight (competing with Cortana, another windows 10 product) seemless integration with all your devices, and of course, the new metal platform underneath the hood. iOS 9 promises all this for the iPhone, and iPad. Both are slated to release in late September.
But the real excitement with Apple is their September annual announcement of new hardware! It was these Keynotes Steve Jobs was famous for, when he released products such as the ipod, iphone, ipad for the first time. These keynotes became legendary. This year's keynote was distinctly toned down, mostly announcing updates for previous systems. That's not to say we're disappointed (well maybe a little). Anyway, here are the highlights:
1) New software and apps for the Apple Watch. I don't follow the watch as closely, but a better user interface, more health tracking apps, and a better system to sync with your iphone are the main things.
2) New Apple TV. This got a round of applause. The apple TV has been due for a makeover for some time, and Apple has finally delivered. The update includes a faster processor, touch sensitive remote, and a wealth of new features to make it more user friendly than ever before. Features include voice activated commands, capability to play games using iphones as remotes, and advanced searching capabilities. The new box will cost about 150$, or 200$ for the larger storage drive.
3) Ipad Pro. A super large iPad, mimicking the Surface Pro. This ipad is 12.9 inches across, almost the size of a macbook air! It is very light, boasts a faster processor, and of course, the new iOS 9. It can be used with a featherlight keyboard, but does NOT use the full system OS like macbooks. This was a bit of a disappointment. The Surface Pro comes with a full feature windows OS, why shouldn't the Ipad Pro do the same?
4) Apple Pen?! This was by far the biggest surprise (and controversy) of the show. A pen accessory made specially for the iPad series to write with, draw with, and otherwise interact with. Steve Jobs famously made a statement in 2010 that "If you see a stylus they blew it". So why is apple making this pen 5 years later? The answer is Jobs may have been referring to a pen as the only way to interact with a device. Palm Pilots of the 90's used pens, but you could not use your finger. Apple is bringing back the pen for specific tasks that fingers are simply not precise enough for: like drawing. Used in this way, the pen makes sense. However, apple fans are torn. This isn't exactly the big new announcement like when the ipad came out, or an iphone.
5) iPad Mini 4. They very quietly mentioned the iPad mini 4 is coming out, but didn't go into detail. this is possibly the last mini they will be releasing.
6) Just a few notes; Apple spent much of their presentation bringing in guests to demonstrate how the new products can be used with updated software packages such as Adobe, WarHammer, hospitals, and others. Overall, it just felt a little anti-climatic. But again, some years are like that. My thoughts? Wait on the Ipad pro until you are sure you want the full-sized ipad with the same iOS software, give the apple pen a pass unless you are an artist or writer (and prefer to write with a pencil than a keyboard). The apple tv is the product I'm personally most excited about. It comes with enough new features that it may be worth the upgrade.
That's it for Apple's Keynote!
Get ready to update your devices with the new OS9 and OS X El Capitan! Or, wait for the bugs to be fixed, then update. :)
Woof!
Apple, as many of you know makes Iphones, Ipads, laptops, desktops, and watches. Every year they release a new line of updated products for us all to drool over. In case you missed it, here is a quick recap of their major announcements for the coming year:
To start with, I'm going to back up to spring. Apple released a new macbook line of thin, lightweight laptops with a single USB Type C connector. This magical little connector is designed to charge the laptop, connect to external displays, hard drives, dvd drives, and all manner of peripherals. In short, it plans to replace all other connectors in the future.
Fast foward to the Summer, and Apple announced it's new set of Operating systems: iOS 9, and OS X El Capitan. These new OS's add more features, including a split screen (borrowed from Windows 10) all new mission control, spotlight (competing with Cortana, another windows 10 product) seemless integration with all your devices, and of course, the new metal platform underneath the hood. iOS 9 promises all this for the iPhone, and iPad. Both are slated to release in late September.
But the real excitement with Apple is their September annual announcement of new hardware! It was these Keynotes Steve Jobs was famous for, when he released products such as the ipod, iphone, ipad for the first time. These keynotes became legendary. This year's keynote was distinctly toned down, mostly announcing updates for previous systems. That's not to say we're disappointed (well maybe a little). Anyway, here are the highlights:
1) New software and apps for the Apple Watch. I don't follow the watch as closely, but a better user interface, more health tracking apps, and a better system to sync with your iphone are the main things.
2) New Apple TV. This got a round of applause. The apple TV has been due for a makeover for some time, and Apple has finally delivered. The update includes a faster processor, touch sensitive remote, and a wealth of new features to make it more user friendly than ever before. Features include voice activated commands, capability to play games using iphones as remotes, and advanced searching capabilities. The new box will cost about 150$, or 200$ for the larger storage drive.
3) Ipad Pro. A super large iPad, mimicking the Surface Pro. This ipad is 12.9 inches across, almost the size of a macbook air! It is very light, boasts a faster processor, and of course, the new iOS 9. It can be used with a featherlight keyboard, but does NOT use the full system OS like macbooks. This was a bit of a disappointment. The Surface Pro comes with a full feature windows OS, why shouldn't the Ipad Pro do the same?
4) Apple Pen?! This was by far the biggest surprise (and controversy) of the show. A pen accessory made specially for the iPad series to write with, draw with, and otherwise interact with. Steve Jobs famously made a statement in 2010 that "If you see a stylus they blew it". So why is apple making this pen 5 years later? The answer is Jobs may have been referring to a pen as the only way to interact with a device. Palm Pilots of the 90's used pens, but you could not use your finger. Apple is bringing back the pen for specific tasks that fingers are simply not precise enough for: like drawing. Used in this way, the pen makes sense. However, apple fans are torn. This isn't exactly the big new announcement like when the ipad came out, or an iphone.
5) iPad Mini 4. They very quietly mentioned the iPad mini 4 is coming out, but didn't go into detail. this is possibly the last mini they will be releasing.
6) Just a few notes; Apple spent much of their presentation bringing in guests to demonstrate how the new products can be used with updated software packages such as Adobe, WarHammer, hospitals, and others. Overall, it just felt a little anti-climatic. But again, some years are like that. My thoughts? Wait on the Ipad pro until you are sure you want the full-sized ipad with the same iOS software, give the apple pen a pass unless you are an artist or writer (and prefer to write with a pencil than a keyboard). The apple tv is the product I'm personally most excited about. It comes with enough new features that it may be worth the upgrade.
That's it for Apple's Keynote!
Get ready to update your devices with the new OS9 and OS X El Capitan! Or, wait for the bugs to be fixed, then update. :)
Woof!
Thursday, September 3, 2015
Crash Course in Today's Processors
Hello and Happy Thursday Everyone!
Today, I bring you a list of today's processors and microprocessors! If you are looking to buy a new phone/tablet/computer/laptop, one of the most important components is a processor, the main "brain" of the unit. Where Ram, and Hard Disc space are usually upgradeable, the processor is more or less built into the machine from the start. Therefore, it is important to know what kind of processor you are buying, because to replace it, you may just need to replace the whole unit.
Desktops, of course you can replace the processor in, providing you buy a similar processor to fit the motherboard. :)
Desktops, and most laptops use one of two brands of processor: Either an Intel chip, or an AMD chip. These two companies have been rivals for decades. Here is a quick pro-con list of the two companies before we get into specifics:
Intel Pros,
Speed: byte for byte, Intel chips are usually faster than AMD's chips, there is a wealth of technology under the hood that accounts for this, but we won't get into that too much.
Compatibility: Intel chips work with many more motherboards and system boards than AMD. Intel has the majority on the market here, so other companies build more total boards to accommodate intel's chips than AMD's chips.
Cooling: Intel chips tend to use less power, and get less hot than AMD chips. If you like a cool laptop, or if you are environmentally conscientious, you may want an Intel chip.
AMD Pros,
Graphics: AMD has invested a lot of money into built in graphics on their chips, they own ATI, a graphics company, which gives them the ability to really take advantage of AMD / ATI graphic combinations especially in their laptops.
Price: AMD is well below Intel in price, some of their chips can be a 100$ or less than a compatible Intel Chip.
Overclocking: If you are the sort of gaming rabbit who can't resist playing with factory specifications and want to overclock your processor, AMD is built for overclocking. Just be sure to stick it in the freezer or add a water-cooling system to it!
Now for some more details:
Intel:
About 6 years ago, Intel made a huge naming switch when multi-core processors first came on the market. Instead of the P-4 processors, or duo / dual core, they renamed their main line the Core iX:
Core i-3
Intel Core i-3's stands for their low end processor, a dual core processor, which basically means two small processors built to run like 1. These are very low power, so devices with these will tend to have a longer battery life than the larger cores. These also have the least amount "brains" or Cache to them. The larger the cache, the more the processor can handle at once without slowing down. An average cache for an i-3 is about 3mb. Another way to think of it is how many programs do you have open at once? A core i-3 can have three small programs open at once, or one large program, like photoshop.
Core i-5
Intel Core i-5's is their middle of the road processor, a dual core, (sometimes quad core if it's a desktop model). These run like 4 small processors built into 1. These take a little more power, and won't last as long on a single charge, but they are also faster. They average about a 4-6mb cache, or 6 programs open at once, or 2 large programs open at once. They will also cost a little more.
Core i-7
The cream of the crop. A core -7 can have up to 8 cores, or 8 processors built into 1! They cost quite a bit more, and will drain power quickly, but are much faster. They average about a 8-20mb cache, or 8-20 small programs open at once, or 3-4 large programs open. This is for someone who wants a lot of power to run video editing, large computations, high end computer games, or lots of programs open simultaneously.
Every couple years, Intel releases a new version of these Core processors. They have model names or generation numbers. a 3rd generation will be faster, and more energy efficient than a 1st generation for example. This year, they are releasing their 6th generation set, codenamed Skylake. This new generation promises a lot of new features that haven't been seen in processors before:
1. Built to work with wireless charging!
2. Built to drastically change the speed and capability on the fly depending on whether you are running on battery or plugged in.
3. Built to use all those newfangled cords, like the thunderbolt 3, and the usb type C connectors you may (or may not) have heard about.
4. Support for new RAM types also coming out soon!
5. A catch-up to AMD, it can now overclock easier without overheating and blowing up your house.
6. Just plain faster than the old models.
For those of you wondering, I have matched up the generation numbers with the fancy codenames Intel uses:
1st Generation: Nehalem
2nd Generation: Sandy Bridge
3rd Generation: Ivy Bridge
4th Generation: Haswell
5th Generation: Broadwell
6th Generation: Skylake
AMD took a little longer to begin catching up to intel, and had to do a lot of research, to develop a whole new line of processors, but their results were quite impressive. Their numbering system is a lot more complex, so I will simply give some general details on their lines:
Most of AMD's newer processors are part of the FX series, which include 4 Core, 6 Core, and 8 Core processors:
4 Core: AMD's Quad Core processors are their lower end series, and run similar to Intel's Core i-3 models.
6 Core: AMD's Six Core processors are the middle end series, and run similar to Intel's Core i-5 models.
8 Core: AMD's Eight Core processors are the high end, and lightning fast. They run similar to Intel's Core i-7 models, but usually have built-in graphics cards and can outstrip a stock Intel chip on graphic related tasks.
For those of you wondering, I have matched up the generation numbers with the fancy codenames AMD uses:
2011 Generation: Llano
2012 Generation: Trinity
2013 Generation: Richland
2014 Generation: Kaveri
2015 Generation: Carrizo
AMD's Carrizo line is their newest line, and will be competing with Skylake. Both companies are trying to enter the mobile device market.
Okay, that's about it for the Laptops and Desktops. We know that AMD and Intel want to enter the mobile market. So... what does the mobile market look like?
Apple has been using a Company called ARM for their chips, usually named A4, A5, A6, etc. These chips have vastly different abilities, but the chipset is the same.
The Android Devices have used a variety of chips, the most popular being Qualcomms Snapdragon series, Intel Atom chips, and Broadcom, or other chips by ARM. There is a new player on the marked, Nvidia, known for its graphics chips, is working on a Tegra chip to work in phones and small devices.
Without listing heaps of specs on every individual processor, let me take this in groupings:
Apple has been using, and will probably continue to use the A Series. Their latest chip is the A8 and the A8x, which is a 3 Core processor, with 2mb cache. What does this mean? It's about on par with a low power Intel Core -3, while being more energy efficient.
Samsung, and other Android companies have been using a blend of ARM's Exynos chips, and Qualcomms Snapdragon chips. The ARM exynos chips are comprable to Apple's A series, and the snapdragon chips are specially designed for anything ranging from cell phones to tv chips.
I look forward to seeing how AMD and Intel may break the trend with moving to the mobile market.
Well, that's all for now, enjoy!
Today, I bring you a list of today's processors and microprocessors! If you are looking to buy a new phone/tablet/computer/laptop, one of the most important components is a processor, the main "brain" of the unit. Where Ram, and Hard Disc space are usually upgradeable, the processor is more or less built into the machine from the start. Therefore, it is important to know what kind of processor you are buying, because to replace it, you may just need to replace the whole unit.
Desktops, of course you can replace the processor in, providing you buy a similar processor to fit the motherboard. :)
Desktops, and most laptops use one of two brands of processor: Either an Intel chip, or an AMD chip. These two companies have been rivals for decades. Here is a quick pro-con list of the two companies before we get into specifics:
Intel Pros,
Speed: byte for byte, Intel chips are usually faster than AMD's chips, there is a wealth of technology under the hood that accounts for this, but we won't get into that too much.
Compatibility: Intel chips work with many more motherboards and system boards than AMD. Intel has the majority on the market here, so other companies build more total boards to accommodate intel's chips than AMD's chips.
Cooling: Intel chips tend to use less power, and get less hot than AMD chips. If you like a cool laptop, or if you are environmentally conscientious, you may want an Intel chip.
AMD Pros,
Graphics: AMD has invested a lot of money into built in graphics on their chips, they own ATI, a graphics company, which gives them the ability to really take advantage of AMD / ATI graphic combinations especially in their laptops.
Price: AMD is well below Intel in price, some of their chips can be a 100$ or less than a compatible Intel Chip.
Overclocking: If you are the sort of gaming rabbit who can't resist playing with factory specifications and want to overclock your processor, AMD is built for overclocking. Just be sure to stick it in the freezer or add a water-cooling system to it!
Now for some more details:
Intel:
About 6 years ago, Intel made a huge naming switch when multi-core processors first came on the market. Instead of the P-4 processors, or duo / dual core, they renamed their main line the Core iX:
Core i-3
Intel Core i-3's stands for their low end processor, a dual core processor, which basically means two small processors built to run like 1. These are very low power, so devices with these will tend to have a longer battery life than the larger cores. These also have the least amount "brains" or Cache to them. The larger the cache, the more the processor can handle at once without slowing down. An average cache for an i-3 is about 3mb. Another way to think of it is how many programs do you have open at once? A core i-3 can have three small programs open at once, or one large program, like photoshop.
Core i-5
Intel Core i-5's is their middle of the road processor, a dual core, (sometimes quad core if it's a desktop model). These run like 4 small processors built into 1. These take a little more power, and won't last as long on a single charge, but they are also faster. They average about a 4-6mb cache, or 6 programs open at once, or 2 large programs open at once. They will also cost a little more.
Core i-7
The cream of the crop. A core -7 can have up to 8 cores, or 8 processors built into 1! They cost quite a bit more, and will drain power quickly, but are much faster. They average about a 8-20mb cache, or 8-20 small programs open at once, or 3-4 large programs open. This is for someone who wants a lot of power to run video editing, large computations, high end computer games, or lots of programs open simultaneously.
Every couple years, Intel releases a new version of these Core processors. They have model names or generation numbers. a 3rd generation will be faster, and more energy efficient than a 1st generation for example. This year, they are releasing their 6th generation set, codenamed Skylake. This new generation promises a lot of new features that haven't been seen in processors before:
1. Built to work with wireless charging!
2. Built to drastically change the speed and capability on the fly depending on whether you are running on battery or plugged in.
3. Built to use all those newfangled cords, like the thunderbolt 3, and the usb type C connectors you may (or may not) have heard about.
4. Support for new RAM types also coming out soon!
5. A catch-up to AMD, it can now overclock easier without overheating and blowing up your house.
6. Just plain faster than the old models.
For those of you wondering, I have matched up the generation numbers with the fancy codenames Intel uses:
1st Generation: Nehalem
2nd Generation: Sandy Bridge
3rd Generation: Ivy Bridge
4th Generation: Haswell
5th Generation: Broadwell
6th Generation: Skylake
AMD took a little longer to begin catching up to intel, and had to do a lot of research, to develop a whole new line of processors, but their results were quite impressive. Their numbering system is a lot more complex, so I will simply give some general details on their lines:
Most of AMD's newer processors are part of the FX series, which include 4 Core, 6 Core, and 8 Core processors:
4 Core: AMD's Quad Core processors are their lower end series, and run similar to Intel's Core i-3 models.
6 Core: AMD's Six Core processors are the middle end series, and run similar to Intel's Core i-5 models.
8 Core: AMD's Eight Core processors are the high end, and lightning fast. They run similar to Intel's Core i-7 models, but usually have built-in graphics cards and can outstrip a stock Intel chip on graphic related tasks.
For those of you wondering, I have matched up the generation numbers with the fancy codenames AMD uses:
2011 Generation: Llano
2012 Generation: Trinity
2013 Generation: Richland
2014 Generation: Kaveri
2015 Generation: Carrizo
AMD's Carrizo line is their newest line, and will be competing with Skylake. Both companies are trying to enter the mobile device market.
Okay, that's about it for the Laptops and Desktops. We know that AMD and Intel want to enter the mobile market. So... what does the mobile market look like?
Apple has been using a Company called ARM for their chips, usually named A4, A5, A6, etc. These chips have vastly different abilities, but the chipset is the same.
The Android Devices have used a variety of chips, the most popular being Qualcomms Snapdragon series, Intel Atom chips, and Broadcom, or other chips by ARM. There is a new player on the marked, Nvidia, known for its graphics chips, is working on a Tegra chip to work in phones and small devices.
Without listing heaps of specs on every individual processor, let me take this in groupings:
Apple has been using, and will probably continue to use the A Series. Their latest chip is the A8 and the A8x, which is a 3 Core processor, with 2mb cache. What does this mean? It's about on par with a low power Intel Core -3, while being more energy efficient.
Samsung, and other Android companies have been using a blend of ARM's Exynos chips, and Qualcomms Snapdragon chips. The ARM exynos chips are comprable to Apple's A series, and the snapdragon chips are specially designed for anything ranging from cell phones to tv chips.
I look forward to seeing how AMD and Intel may break the trend with moving to the mobile market.
Well, that's all for now, enjoy!
Subscribe to:
Posts (Atom)