I guess that means I am coming out of the closet.
What will my family think?
Actually I do not even know if my family cares, outside of my brother who is a Lakers' fan (perhaps I should ask the rest of them who their NBA teams are).
However, since it is time for the best part of the season, I can start to care myself. The last time I claimed a team was in my middle or high school époque and that team was the Charlotte Hornets. Even then, I did not watch many games. I guess you could say the Heat are my NBA team much like the Preds are my NHL team, the Titans are my NFL team, and Arsenal is my EPL team. It is not so much that I cheer for any one of them or have any REAL connection to any of them. For whatever reason, I just hope they win and if I have the chance I check their scores to see if they did.
I am going to be completely honest here and the truth hurts. Sports are a form of entertainment and simultaneously inconsequential. Do not get me wrong, benefits are derived from sports. One could argue the economic advantages of sports or any one sport and in doing so, one would likely find I completely agree. All I am saying is that it really does not matter, in the bigger picture, whether one team wins or loses. Except for the job security of those employed by that team at the time, whether they are players, coaches, or the front office. Let me ask this question in earnest: If a team loses or wins does it really affect our lives? Maybe we have a bad (or good) day, possibly a bad (good) week, but ultimately life returns to normal, what it would have been without 'the game'. Sometimes I wish that sports were not merely a distraction for me, like for those employed in the industry.
The Heat dropped game 4 to the Knicks (87-89), but the Heat are still up 3-1 in the series. Staying alive with this win, the Knicks also ended a 13 game playoff losing streak. It is extremely likely that they are just delaying the inevitable, the Knicks have struggled all season against the Heat. The Knicks are just outmatched by their opponent and that is when they are completely healthy. This is a Knicks team that is dealing with several injuries. Amare Stoudemire, as most probably know, missed game 3 after suffering a laceration to his hand as a result of punching a glass fire extinguisher case on the way to the locker room after the loss in game 2. Jeremy Lin has been out recuperating from knee surgery on April 2nd. In game 1 the Knicks lost Iman Shumpert, its top perimeter defender, to a torn left ACL and lateral meniscus. Baron Davis was also limited from a back injury, before suffering a knee injury in the second-half of game 4 that keep him from returning. It is not likely, from the looks of the injury, that he will return for the series. Although, it does not seem that anyone will officially know anything until tomorrow, when he should be getting an x-ray of the knee.
Therefore, for an already out-gunned team at less that 100%, pushing it to a game seven seems unlikely. I am okay with a game 5 in the sense that it gives the Heat a chance to put the series away at home in front of their fans, like a little bit of an extra treat. However, at the same time it is a little worrisome from an injury stand-point. The Knicks forced a game 5 off of a 41-point performance by Carmelo Anthony. That is very unlikely to happen another three times. Stoudemire played in game 4, although he was obviously bothered. Especially noted when he nearly lost the ball out of bounds on what should have been an easy two points. Fortunately he managed to recover and despite bad position he drew a foul or at least the call. He still managed to come away with 20 points 10 rebounds and an assist. The good news for the Knicks is that his hand should only get better.
Despite a monstrous performance from Melo, the Knicks barely escaped the Heat. Dwayne Wade missed a three at the buzzer. Which I am not convinced was the best shot to take, from the best shooter. I watched LeBron James the whole time Wade had the ball and I just had to accept that James looks a lot better with the ball in his hands. It is not like the Knicks put the Heat in a position to respond very often, but it seemed that if ever they did, James was the one to respond and what a statement he can make! I suppose that is one of James' criticisms, although I do not really agree with it. I 'think' James would have been the better option to have the ball to create or if he was going to shoot a three, I could hope then Wade would have enough time to crash the board. Realistically, no one knows. I would not be surprised if James gets double teamed, but even then I hope a pass to the open man creates an easy bucket. Nevertheless, if Wade or anyone on the Heat tied the game with a two, which they should have attempted considering the horrific three-point shooting on the evening, I think the Knicks lose in overtime.
If the Knicks come back to Miami with a nothing to lose attitude and push it as hard as they can, the Heat will go as hard as the Knicks do. That is what worries me, I do not want to see anyone injured, period. I cringed when I saw Baron Davis go down today. Jeremy Lin might feel pressure to come back too soon, when he would be better off accepting that his season is over and continuing to recuperate for next year. Congratulations to the Knicks, as they say, with this win you kept your chances 'alive'.
Good luck Heat, do not feel too bad if I continue to not watch too many games. As it turns out, I do not bring a whole lot of luck as a viewer/spectator.
Sunday, May 6, 2012
Wednesday, May 2, 2012
How did you get those numbers?
I have been taught, by way of the Internet, that "I haes maths". (sorry that should have read "teh interwebz"). All joking aside, I have some innate ability for math. However, like most normal people I avoid ridiculously high levels of math. Let's reserve that for the actual geniuses. It is notable, however, that I did have "college algebra" as well as descriptive and inferential statistics. And just in-case any one is curious, but definitely NOT to brag, I got a high mark in each class (all 'As').
I am with everyone else though, at this point in time, even the most basic math ability is lost outside of the realm of academics. There are not a lot of people going around asking about the slope of a line and there are not very many asking about your z-score, on anything. To top it all off, when I was in grade school taking an average of 10 numbers was slightly more difficult than '=AVG(A1:A10)'. Therefore, even if there were, computers are available to solve all our problems, from a purely computational stand-point. But, I digress.
With my basic affinity for math, I see formulas. It is just the nature of numbers they are, formulaic. In the real world when a number of things generate a number, perhaps of possible outcomes, there is a formula to predict this number. Now any one that has read this far should be sufficiently prepped to understand the dilemma at hand.
I pulled up to Sonic drive-in today, unfortunately I noticed most all of my favorites are now off the menu. However, they have always been the place for uniquely mixed (non-alcoholic) drinks. Nowhere to my knowledge can you add as many flavors to your drink than at a Sonic, especially here in Bowling Green, Kentucky. Maybe they feel like that is their competitive advantage. I feel like a competitive advantage is the way those ice balls paired with their Styrofoam cups maintain a low temperature for hours under normal circumstances. Anyway, I ran into this sign:
And as I look at the sign in picture form, I realize that it is impossible to read anything but the number. Zut alors! I will paraphrase the tiny text. It said something to the effect of this is how many flavor mixtures available (398,929). This made me curious. This is a very precise number, but as they say, 74.9 percent of all statistics are pulled out of the air. Okay, I made that up (no not the joke, the number used as the statistic; I know, not very original). It made me curious because given the number of combinations, theoretically one should be able to predict the number of flavors. One could also count the flavors off the menu board, but that is too easy.
My first thought, from the way the sign read, was that they are only counting mixes added to drinks, therefore the number is not inflated too much. If you think about this you will understand what I mean. If they have 1 beverage and 2 flavors they have 4 possible drinks OR the non mixed drink, two drinks + 1 flavor, and the drink + both flavors. Make that 2 beverages and 2 flavors and it gets complicated. I was assuming it was simple though. So I thought simple, a factorial! Literally, n! when n = number of flavors. It was simple and wrong, but I did not know it yet. I grabbed my calculator and took a few guesses. I narrowed it down to 9! = 362,880 clearly that is not right and 10! would be 3.6 million. Not to mention, sonic has more than 9 flavors. How would you get ONLY 36k more possibilities? It just is not feasible. The local Sonic I was at had 17 flavors, see picture below. Using this method, we are looking at 17! = 355.7 trillion.
Something was wrong anyway, I had to think about it on a smaller scale. Two flavors = 4 possibilities, see above, BUT 2! = 2. Let's think about this, what is three flavors: the beverage, 3 single flavored mixes, 3 double flavors, 1 triple flavor. = 8 (3! = 6). I can probably do this one more time, but after that it gets really tedious. Four flavors: the beverage, 4 single flavors, 6 double flavors, 4 triple flavored and one full flavored beverage. To be honest, I knew that I was dealing with combinations or permutations or something like that, but I could not remember what they were called simply that they were easier to plug into the TI-83 than worry about plugging in numbers to the equations.
Somehow I managed to figure out what I knew that I did not know. I could remember the calculator function dealt with a C and a P that's about it. After reading up on it, I realized it was combinations, because basically permutations are combinations where order matters. In other words AB and BA are two distinct possibilities. Cherry-vanilla Dr. Pepper is the same as vanilla-cherry Dr. Pepper, order does not matter. There is a problem though, combinations deal with a number of distinct items taken k at a time. Where k is equal to the specific number of flavors one must put in their drink. Clearly this eliminates everything but one combination when there are clearly more possibilities. For instance, no flavors, one flavor, two flavor, three flavors, etc. Well I knew what had to be done, Σ or =SUM if you prefer.
Once again, I figured out what I knew I did not know. I found and scanned this page for what I was looking for, perhaps they explain it better than I have/will, for those that are interested. Needless to say, I know have the information I need to figure out the answer, but there is still a simple question to be asked.
Concerning whether beverages mix: If we assume beverages don't mix the number of possible drinks simply "doubles" flavor possibilities with each marginal increase of a beverage, however, depending on taste beverages could theoretically be mixed. Either way the equation is generally the same, the sum of all the differences of n distinct things (or as previously described the sum of all possible combinations; this is equal to 2n). To add single beverages to the sum of all the differences of n distinct flavors we multiply by the beverages, because each beverage has every possible flavor combination in common. Therefore, 2nf * b, where b = the number of beverages and nf is the number of flavors. The difference is only what we are considering distinct. When there are only 2 flavors, the single beverage is irrelevant because the lack of both flavors (one distinct difference) is the beverage alone. Therefore if we add more beverages, than just one, we can consider the formula for mixing beverages to be 2nf + b. Mixing those with each other and the flavors is a possibility then that increases what is distinct and remember this results in an exponential increase in possibilities. If you want to think about it logically you can consider that beverages and flavors are actually two separate differences of n distinct things, but ultimately combining them for a total of distinct differences would be the same as treating them like one distinct difference to begin with (2nf * 2nb).
To put it simply, Sonic's numbers are arbitrary. Neither too big to require an explanation, nor too small to mitigate the shock factor. After figuring this all out I sought Google's infinite wisdom and found this. Since, I do not exactly agree, who is right? Well there is a chance we both are. Different Sonics at different times, options might have changed. I did not look into it. Then again, my maths is (or was) not good enough to know the answer right of the cuff and I am not betting a million that I eventually got it right. Nevertheless...
I may have taken a little longer than normal to place my order, however, with 16 flavors (-1 for cherry vs diet cherry) and 13 beverages (that I "counted"; I did not include slushies and the link I provided apparently did), I had a perfectly good excuse. There were a lot of possibilities to eliminate. One might say the raspberry sweet-tea I got was one in 536.9 million (229), but no matter the number it was delicious.
In the end, let's be honest though, 0-2 flavors is probably the norm and most of us are less inclined to ask for a "suicide" when someone else has to make it. So realistically, plausibly, there are approximately only 200 typical combinations and even those could include Powerade pineapple chocolate.
Since it is not my first choice, I cannot give it an accurate number. Can you?
I am with everyone else though, at this point in time, even the most basic math ability is lost outside of the realm of academics. There are not a lot of people going around asking about the slope of a line and there are not very many asking about your z-score, on anything. To top it all off, when I was in grade school taking an average of 10 numbers was slightly more difficult than '=AVG(A1:A10)'. Therefore, even if there were, computers are available to solve all our problems, from a purely computational stand-point. But, I digress.
With my basic affinity for math, I see formulas. It is just the nature of numbers they are, formulaic. In the real world when a number of things generate a number, perhaps of possible outcomes, there is a formula to predict this number. Now any one that has read this far should be sufficiently prepped to understand the dilemma at hand.
And as I look at the sign in picture form, I realize that it is impossible to read anything but the number. Zut alors! I will paraphrase the tiny text. It said something to the effect of this is how many flavor mixtures available (398,929). This made me curious. This is a very precise number, but as they say, 74.9 percent of all statistics are pulled out of the air. Okay, I made that up (no not the joke, the number used as the statistic; I know, not very original). It made me curious because given the number of combinations, theoretically one should be able to predict the number of flavors. One could also count the flavors off the menu board, but that is too easy.
My first thought, from the way the sign read, was that they are only counting mixes added to drinks, therefore the number is not inflated too much. If you think about this you will understand what I mean. If they have 1 beverage and 2 flavors they have 4 possible drinks OR the non mixed drink, two drinks + 1 flavor, and the drink + both flavors. Make that 2 beverages and 2 flavors and it gets complicated. I was assuming it was simple though. So I thought simple, a factorial! Literally, n! when n = number of flavors. It was simple and wrong, but I did not know it yet. I grabbed my calculator and took a few guesses. I narrowed it down to 9! = 362,880 clearly that is not right and 10! would be 3.6 million. Not to mention, sonic has more than 9 flavors. How would you get ONLY 36k more possibilities? It just is not feasible. The local Sonic I was at had 17 flavors, see picture below. Using this method, we are looking at 17! = 355.7 trillion.
Something was wrong anyway, I had to think about it on a smaller scale. Two flavors = 4 possibilities, see above, BUT 2! = 2. Let's think about this, what is three flavors: the beverage, 3 single flavored mixes, 3 double flavors, 1 triple flavor. = 8 (3! = 6). I can probably do this one more time, but after that it gets really tedious. Four flavors: the beverage, 4 single flavors, 6 double flavors, 4 triple flavored and one full flavored beverage. To be honest, I knew that I was dealing with combinations or permutations or something like that, but I could not remember what they were called simply that they were easier to plug into the TI-83 than worry about plugging in numbers to the equations.
Somehow I managed to figure out what I knew that I did not know. I could remember the calculator function dealt with a C and a P that's about it. After reading up on it, I realized it was combinations, because basically permutations are combinations where order matters. In other words AB and BA are two distinct possibilities. Cherry-vanilla Dr. Pepper is the same as vanilla-cherry Dr. Pepper, order does not matter. There is a problem though, combinations deal with a number of distinct items taken k at a time. Where k is equal to the specific number of flavors one must put in their drink. Clearly this eliminates everything but one combination when there are clearly more possibilities. For instance, no flavors, one flavor, two flavor, three flavors, etc. Well I knew what had to be done, Σ or =SUM if you prefer.
Once again, I figured out what I knew I did not know. I found and scanned this page for what I was looking for, perhaps they explain it better than I have/will, for those that are interested. Needless to say, I know have the information I need to figure out the answer, but there is still a simple question to be asked.
Concerning whether beverages mix: If we assume beverages don't mix the number of possible drinks simply "doubles" flavor possibilities with each marginal increase of a beverage, however, depending on taste beverages could theoretically be mixed. Either way the equation is generally the same, the sum of all the differences of n distinct things (or as previously described the sum of all possible combinations; this is equal to 2n). To add single beverages to the sum of all the differences of n distinct flavors we multiply by the beverages, because each beverage has every possible flavor combination in common. Therefore, 2nf * b, where b = the number of beverages and nf is the number of flavors. The difference is only what we are considering distinct. When there are only 2 flavors, the single beverage is irrelevant because the lack of both flavors (one distinct difference) is the beverage alone. Therefore if we add more beverages, than just one, we can consider the formula for mixing beverages to be 2nf + b. Mixing those with each other and the flavors is a possibility then that increases what is distinct and remember this results in an exponential increase in possibilities. If you want to think about it logically you can consider that beverages and flavors are actually two separate differences of n distinct things, but ultimately combining them for a total of distinct differences would be the same as treating them like one distinct difference to begin with (2nf * 2nb).
To put it simply, Sonic's numbers are arbitrary. Neither too big to require an explanation, nor too small to mitigate the shock factor. After figuring this all out I sought Google's infinite wisdom and found this. Since, I do not exactly agree, who is right? Well there is a chance we both are. Different Sonics at different times, options might have changed. I did not look into it. Then again, my maths is (or was) not good enough to know the answer right of the cuff and I am not betting a million that I eventually got it right. Nevertheless...
I may have taken a little longer than normal to place my order, however, with 16 flavors (-1 for cherry vs diet cherry) and 13 beverages (that I "counted"; I did not include slushies and the link I provided apparently did), I had a perfectly good excuse. There were a lot of possibilities to eliminate. One might say the raspberry sweet-tea I got was one in 536.9 million (229), but no matter the number it was delicious.
Since it is not my first choice, I cannot give it an accurate number. Can you?
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