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Quantumaniac is where it’s at - and by ‘it’ I mean awesome.

Over here I post a ton of physics / math / general interesting posts in an attempt to make your brain feel good. My aim is to be as informative as possible, all while posting fascinating things that hopefully enlighten us both a little to the mysteries of our truly wondrous universe(s?). Plus, how would you know if the blog exists or not unless you observe it? Boom, just pulled the Schrödinger’s cat card. Now you have to check it out - trust me, it said so in an equation somewhere.

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Modeling the Price of Different Sized TVs

It really started with a joke.

“Oh, you need a new TV? You should get a 70 inch. Wait, what about the 80 inch TV? Well, those quite a bit more expensive than the 70 inch TV”

I really hadn’t looked carefully at TV prices so I wasn’t aware that the price increased dramatically with size. I’m aware now.

You can probably guess what comes next. Yes, I need to go to Amazon and look up the prices of different sized TVs. Now, there is a problem comparing TVs of different sizes. You could have a 42 inch TV with more features than a 60 inch and that could have an impact on the price. What I need are TVs that are the same model except for size. Fortunately, I was able to find some models just like that from Sharp, Samsung and Vizio. Along with this, I have the lowest prices for the different size ranges as advertised by the Walmart website.

Screenshot 1 18 13 1 50 pm

The different brands seems to be similar enough that we can look at this all as one set of data. So, what happens when you double the size of a TV? Does the price also double? No. A 40 inch TV is much less than half the cost of an 80 inch TV. Well maybe the size is proportional to the area of the TV.

First, let’s look at the listed “size” vs. the actual area. The standard measurement for a TV is to give the diagonal distance from one corner to the opposite. We also know that a standard HDTV has a 16:9 aspect ratio. Maybe this diagram will be useful.

Screenshot 1 19 13 7 56 pm

It doesn’t matter how big your TV is. If it’s an HDTV, the ratio of height to width will be 9/16. Here, I just have some constant in there (a) to get the actual size. Using the Pythagorean theorem, we can find the length of the diagonal based on the side lengths – you can see that parameter a survives. But this isn’t really right either. I want the area in terms of the quantity s (which I am using as the length of the diagonal). From this expression, I can get an expression for a in terms of s:

Screenshot 1 20 13 11 12 am

I probably shouldn’t have evaluated that square root since it looks like I will just square that value anyway. Now for the area (which I will label as A).

Screenshot 1 20 13 11 25 am

Let’s just check this really quickly. What if I have a 40 inch TV? It would have a height of 19.61 inches and a width of 34.86 inches. This would give it an area of 683.6 inch2. Now, if I use the above formula with a diagonal of 40 inches, I get the same value.

Now for the plot of TV price vs. screen area.

Screenshot 1 20 13 2 43 pm

That doesn’t look as linear as I would like it to be. Look at that 80 inch TV. It doesn’t fit very well with the linear function comparing area and price.

More Data

That doesn’t really improve anything. My last option is to forget about my first assumption. What if the different TV manufactures follow different models? Here is a plot of price vs. screen area for the Sharp, Target, and average Walmart TVs with separate linear fits.

Screenshot 1 21 13 7 59 am

This gives three different price functions for TVs in terms of screen area.  (Yes, I know I left off some of the brands of TVs – but they mostly fit with the lower sized models so I left them off for a cleaner graph)

Screenshot 1 21 13 8 03 am

What does this tell us? First, if Walmart sold a TV with no screen (zero area) – it would cost you -$21.64. Yes, they would have to give you money. This could be my new job – buying zero-inch TVs and collecting the money. But really, does this make sense? Yes. It must mean that if they are basing the price on the area of the TV then they are subsidizing this price. Otherwise, your Target TV would cost 21 dollars more. And look at the Sharp TVs. They have a zero-inch price of almost $4,000. Of course, maybe this just indicates the sale price of these devices and not an actual price. What do I know? I am just making up economic stuff here.

So, How Much? 

In this case, I have a question in my mind. What if there was a 100 inch TV? How much should that cost? What about a 200 inch TV? Of course, these are the diagonal measurements and not the area. So, let me re-write the price function in terms of diagonal size (s) instead of the area.

Screenshot 1 21 13 8 26 am

Now that the price is a function of size, I can just plop in the size to get a price. With this, a 100 inch TV should cost $10,706. A 200 inch TV would cost $54,806 dollars. That’s a serious TV. Now, this is just using the Sharp price function since I have data for larger TVs from them. What if Walmart made a 200 inch TV with their same pricing model? It would cost just $4,888. Not too bad.

One more thing. What if you want a free TV? How big would a Sharp TV be if it was free? Here, I can put in a price of zero dollars and then solve for the size.

Screenshot 1 21 13 8 35 am

That’s bigger than the TV I have right now. OK Sharp, I will take my free 52 inch TV. I will even pay for the shipping. Just send me an email and I will give you my address.

Oh – someone is probably going to ask if they can use my data.  Sure.  Here it is in a Google Docs spreadsheet.  Have with it.

Source: Dot Physics

The Real Difference Between Our Presidential Candidates
This, perhaps more than any other simple, undeniable fact - clearly shows the difference between President Obama and Governor Romney. Seeing who supports each candidate can easily give you a better sense of what, and who, these candidates stand for. While Romney is proudly and substantially backed by banks, financial institutions and investment firms; the President is supported by educational institutions and technologically based, forward-thinking companies. Interpret this as you will. 
As the infographic says, the organizations themselves did not donate, rather the money came from the organizations’ PACs, their individual members or employees or owners, and those individuals’ immediate families. Organization totals include subsidiaries and affiliates.

The Real Difference Between Our Presidential Candidates

This, perhaps more than any other simple, undeniable fact - clearly shows the difference between President Obama and Governor Romney. Seeing who supports each candidate can easily give you a better sense of what, and who, these candidates stand for. While Romney is proudly and substantially backed by banks, financial institutions and investment firms; the President is supported by educational institutions and technologically based, forward-thinking companies. Interpret this as you will. 

As the infographic says, the organizations themselves did not donate, rather the money came from the organizations’ PACs, their individual members or employees or owners, and those individuals’ immediate families. Organization totals include subsidiaries and affiliates.

How Much are Olympic Gold Medals Worth?

As far as the value of the raw materials in them, this varies from Olympiad to Olympiad.  For the current 2012 Olympics in London, the medals are the largest of any in Olympic history, weighing in at 400g for the gold medal.  Of this 400g, 394g is sterling silver (364.45g silver / 29.55g copper) with 6g of 24 karat gold plating.  At the current going rate for gold and silver, this means a gold medal in the London Olympics is worth about $624, with $304 of the value coming from the gold and about $320 coming from the sterling silver.

Of course, athletes can often get much more than this selling the medals on the open market, particularly for momentous medals, like the “Miracle on Ice” 1980 men’s U.S. hockey team gold medal.  Mark Wells, a member of that team, auctioned his medal off in 2012 and received $310,700 for it, which he needed to help pay for medical treatment.

Most auctioned medals don’t go for nearly this much, though.  For instance, Anthony Ervin’s 50 meter freestyle gold medal won in 2000, even with all proceeds going to the victims of the Indian Ocean tsunami, only sold for $17,100.  John Konrads’ 1500 meter freestyle gold medal won in 1960 only sold for $11,250 in 2011.  This is a great return in terms of what the raw value of the materials are worth, but certainly nowhere close to Mark Wells’ medal.

Gold medals in the Olympics weren’t always made mostly of silver.  Before the 1912 Olympics, they were made of solid gold.  However, they tended to be much smaller than modern medals.  For instance, the 1900 Paris gold medals were only 3.2 mm thick, with a 59 mm diameter, weighing just 53g.  For perspective, the London 2012 medals are 7 mm thick, with a diameter of 85 mm and, as mentioned, weigh 400g.  The 1900 Paris gold medals at today’s value of gold are worth about $2685.  For the 1912 games in Stockholm, the last year the gold medals were made of solid gold, the value of the gold medals at current prices of gold would be $1207.86.

If the current 2012 Olympic gold medals were made out of solid gold, they’d be worth about $20,266 each.  This may seem do-able, considering how much money the Olympics brings in, until you consider just how many medals are awarded during each summer Olympics.  For instance, in these 2012 Olympics, about 4,700 medals will be given out, so over 1500 gold medals. At $20,266 each, that would be just shy of $32 million dollars for the gold medal materials alone.

As it is, with the current gold medals having about $624 worth of materials, then $330 for the silver medals (93% silver, 7% copper), and $4.70 for the bronze (which are mostly made of copper, with a very small amount of zinc and tin), about $1.5 million is still being spent on the materials alone for the medals awarded, not to mention the cost of minting them.

Bonus Facts:

  • Strict guidelines are set for the minting of Olympic medals.  For instance, for gold medals the silver must be 92.5% pure silver (with 7.5% copper), and they must include at least 6g of gold for plating the medal.  They also must be at least 3mm thick and 60mm in diameter.
  • Nobel Prize gold medals really are made of mostly gold.  Today they are made with 24 karat gold plating and 18 karat green gold (gold with a small amount of silver) for the rest.  Before 1980, they were made from 23 karat gold.
  • The practice of giving out gold and silver medals is thought to have its origins with the military.  Before a standard set of military awards were created, it was common to reward soldiers (in a variety of militaries throughout the world) for special achievements by giving them gold and silver medals.  For instance, in the United States, special awards were given to commanding officers in the form of gold medals and the officers under that commander would receive silver medals.
  • The gold medals at the 1992 Barcelona Olympics, being smaller than the current medals (Barcelona medals at 9.8 mm thick, 70 mm in diameter, weighing 231g) are only worth about $484 at the current price of gold and silver.

(Source: todayifoundout.com)

New Space Company May Solve World’s Economic Problems

This Tuesday, a group of billionaires and former NASA scientists will announce Planetary Resources Inc., the first asteroid mining company in history. They claim they will “add trillions of dollars to the global GDP” and “help ensure humanity’s prosperity.”
The group of investors and scientists on board this enterprise is impressive:

…including Google’s Larry Page & Eric Schmidt, Ph.D.; film maker & explorer James Cameron; Chairman of Intentional Software Corporation and Microsoft’s former Chief Software Architect Charles Simonyi, Ph.D.; Founder of Sherpalo and Google Board of Directors founding member K. Ram Shriram; and Chairman of Hillwood and The Perot Group Ross Perot, Jr.

Harnessing the resources of asteroids is not a crazy proposition and the return of investment could be amazing. So much that they are convinced they can “add trillions of dollars to the global GDP.” More importantly, this may solve many of our material needs as resources on Earth keep dwindling fast.
But is it doable? There are no details yet, but if they are going to invest millions of dollars on it, you can be sure it is doable and it will be profitable. They don’t have to travel to the asteroid belt to grab them. There are many passing near Earth that may be accessible. In fact, there are already plenty of plans on scientists and engineers’ drafting boards.
Needless to say, and despite the fact that it will probably take some years to achieve their goals, this is all extremely exciting. If they are successful, it will truly be a new dawn for humanity.
We will be covering the press conference live, which will feature Charles Simonyi, Planetary Resources, Investor; Eric Anderson, Co-Founder & Co-Chairman, Planetary Resources; Peter H. Diamandis, M.D., Co-Founder & Co-Chairman, Planetary Resources; Chris Lewicki, President & Chief Engineer, Planetary Resources; Tom Jones, Ph.D., Planetary Scientist, Veteran NASA Astronaut & Planetary Resources, Inc. Advisor.
It will be held in the Museum of Flight in Seattle on Tuesday, April 24 at 10:30am PDT.

New Space Company May Solve World’s Economic Problems

This Tuesday, a group of billionaires and former NASA scientists will announce Planetary Resources Inc., the first asteroid mining company in history. They claim they will “add trillions of dollars to the global GDP” and “help ensure humanity’s prosperity.”

The group of investors and scientists on board this enterprise is impressive:

…including Google’s Larry Page & Eric Schmidt, Ph.D.; film maker & explorer James Cameron; Chairman of Intentional Software Corporation and Microsoft’s former Chief Software Architect Charles Simonyi, Ph.D.; Founder of Sherpalo and Google Board of Directors founding member K. Ram Shriram; and Chairman of Hillwood and The Perot Group Ross Perot, Jr.

Harnessing the resources of asteroids is not a crazy proposition and the return of investment could be amazing. So much that they are convinced they can “add trillions of dollars to the global GDP.” More importantly, this may solve many of our material needs as resources on Earth keep dwindling fast.

But is it doable? There are no details yet, but if they are going to invest millions of dollars on it, you can be sure it is doable and it will be profitable. They don’t have to travel to the asteroid belt to grab them. There are many passing near Earth that may be accessible. In fact, there are already plenty of plans on scientists and engineers’ drafting boards.

Needless to say, and despite the fact that it will probably take some years to achieve their goals, this is all extremely exciting. If they are successful, it will truly be a new dawn for humanity.

We will be covering the press conference live, which will feature Charles Simonyi, Planetary Resources, Investor; Eric Anderson, Co-Founder & Co-Chairman, Planetary Resources; Peter H. Diamandis, M.D., Co-Founder & Co-Chairman, Planetary Resources; Chris Lewicki, President & Chief Engineer, Planetary Resources; Tom Jones, Ph.D., Planetary Scientist, Veteran NASA Astronaut & Planetary Resources, Inc. Advisor.

It will be held in the Museum of Flight in Seattle on Tuesday, April 24 at 10:30am PDT.

(Source: Gizmodo)

Wonderful Geometric Shapes Made from Currency

Kristi Malkoff is a Canadian visual artist - in her series titled Money Pieces, Kristi uses an assortment of colourful currency from around the world, folding and manipulating bills into wonderful geometric shapes.

What is Googol? 
Google, the company founded by Larry Page and Sergey Brin in 1998 - is one of the most influential corporations of our time. However, where does the name come from? Mathematics, of course - these guys were at Stanford, it must be connected to math. 
A googol, which they later changed to Google, is 10100. For the non-mathematically inclined, that is 1 with one hundred zeroes after it. The intent was so symbolize the enormous amounts of information that would be available to the site’s users. Actually, the company was originally named ‘Backrub,’ but it was eventually changed because, well, come on - it’s just silly. Google actually originated from a simple misspelling of googol - but it stuck. 

What is Googol? 

Google, the company founded by Larry Page and Sergey Brin in 1998 - is one of the most influential corporations of our time. However, where does the name come from? Mathematics, of course - these guys were at Stanford, it must be connected to math. 

A googol, which they later changed to Google, is 10100. For the non-mathematically inclined, that is 1 with one hundred zeroes after it. The intent was so symbolize the enormous amounts of information that would be available to the site’s users. Actually, the company was originally named ‘Backrub,’ but it was eventually changed because, well, come on - it’s just silly. Google actually originated from a simple misspelling of googol - but it stuck. 

There are 10^11 stars in the galaxy. That used to be a huge number. But it’s only a hundred billion. It’s less than the national deficit! We used to call them astronomical numbers. Now we should call them economical numbers.

Richard Feynman

Physicists in the Money
There are a number of famous Physicists who have been featured on currencies, including Isaac Newton, Michael Faraday, Galileo Galilei, the above Albert Einstein, and many more. Check it out here; really interesting. 

Physicists in the Money

There are a number of famous Physicists who have been featured on currencies, including Isaac Newton, Michael Faraday, Galileo Galilei, the above Albert Einstein, and many more. Check it out here; really interesting. 

(Source: )

essentialisinvisible asked
Stuff like that is why the USA is in debt though...

The USA, unfortunately, is in fact in quite a lot of debt. However, the portion of the debt that is caused by the NASA budget, and programs such as the James Webb Space Telescope, is infinitesimally small - and I have to disagree with you. If NASA’s complete budget were to completely disappear, there would be no appreciable savings to the U.S. Government. In fact, Americans spent more last year on items such as pizza and pet food than the government spent on NASA. 

According to a number of different estimates, the average consensus is that we spend about $8 billion every month funding the Afghanistan war alone. Every nine weeks, the Afghanistan war has already used an amount equivalent to NASA’s yearly budget. NASA’s 2012 budget? $17.9 billion, that’s lower than 1% of the entire U.S. spending budget. The Department of Defense, including the Department of Homeland Security, receives more than 40 times NASA’s budget every year. While I’m not saying that a strong military and defense system is not important, it’s very easy to see how excessive this is. The United States spends more on its military than the next fifteen biggest defense spenders put together.

It is a proven fact that every dollar spent on space exploration returns $8 to the U.S. economy thanks to advancements in technology. In order to explore space and find our place in this universe, new technologies must be created - which stimulates the economy for the long term. New technologies = new jobs, which are crucial for recovering from a recession like the one we’re in now. Additionally, one cannot argue that the quest for knowledge and discovery is invaluable. By funding the space program, we can better understand the universe around us, and our home here on Earth. 

While I do understand your point, and completely agree that the U.S. Government does wastefully spend money in many places, I do not believe that NASA is one of these. NASA, and space exploration in general, is the key to the future - both technologically and philosophically. 

A Senate subcommittee announced some great news today. Despite announcing a slight decrease in NASA funding, the long-questionable fate of the James Webb Space Telescope has been decided!

NASA will receive all necessary funding for a 2018 launch of the telescope! In 2012, the project will receive $530 million. This telescope is going to be incredible, I can’t wait to see what we will discover with it. 

A Senate subcommittee announced some great news today. Despite announcing a slight decrease in NASA funding, the long-questionable fate of the James Webb Space Telescope has been decided!

NASA will receive all necessary funding for a 2018 launch of the telescope! In 2012, the project will receive $530 million. This telescope is going to be incredible, I can’t wait to see what we will discover with it.