Just some stories, lessons learned, and plans. Mostly for saving the experience before I forget by making it explicit, and lessly I can't fall asleep.
Was listening to Warren Buffett today, he said "But we never looked back, you can only live life forward anyways". And that sounded like a great idea.
There is not a whole lot to say. Things started off wonderful, as usual, but as we find out more of each other it seems like a good idea to stay separate. I initiated the leaving, from the beginning I know if we were to ever break up, I'd have to be the one who does it. I thought I could open her up, make her try new things with me and feel affections. Yet after a year she is still resolute on her barriers, determined to "not get hurt" and afraid of laying out her emotions while my overflowing feelings filled the moat around her fortress. She had never laid out her heart against mine, and mine was getting cold being out there alone for long long times. So I had to go, the worries and thinking are hurting my confidence, and it is unhealthy to be not confident. Now once in awhile I still look at her windows across the street from where I live, contemplating in the room beyond which I will likely never visit again, but it is purely out of habit.
That happened a month ago, and time is slowly regenerating my health over time. Although you feel scarcely any better than yesterday, I do feel like a living man compared to last month this time. Sometimes I wonder if I regretted of leaving her. I reflected on the things I learned after the break up, such as ask for help from her or be more patient or don't take it too serious. All of them might saved the relationship. But then I thought such maturity and lessons can only be learned by reflecting on the break up, so be it. Overall I have learned that, at least for me, you need to admire each other, and willing to fix issues between the two when the arises by putting in efforts. In the end, it was a good experience (hopefully she feels the same), although it did not end well, we had plenty good times while at it, and those times I will never forget. + Show Spoiler +
Now aside from relationship, life has been treating me very well. I had the fortune to visit Germany for a week to attend a computer science workshop. The weekend before we visited a friend in Geneva, which has the clearest lake I have seen, and it was a joy to swim in it. While at the workshop the food was amazing, this is what I get to eat for breakfast every day. + Show Spoiler +
and a day off to visit Berlin. I had the pleasure of taking pictures with these outrageous Bears... + Show Spoiler +
of course, drinking beer on the sidewalk and cheap turkish food is always a plus in Berlin. I'd post picture on the tourist attractions such as the wall or what not, but I'm sure there are better pictures of those online.
Now I'm back, and it's time to go back to work, and try to finish the camera ready version of the paper by monday. School starts next Thursday, so I have 3 days off!
The following semester is goign to be my last semester as an undergraduate student. I shall enjoy it well by taking hard classes and learn! I might join a choral so I can better understand how to sing harmony. I was going to write more but alas I need to get back to work early tomorrow, and now I must sleep! I hope you are doing well, whoever is reading, and is feeling happy, perhaps hopefully happy with a full stomach!
That will be all. I guess I now learned a thing or two about relationships, if you have a specific question regarding it, I can try to answer them in this thread.
And it's been awhile since I posted a math blog, so here is a puzzle I made up for you to chew on: + Show Spoiler +
Quick math puzzle I just made up, it's should be light and good:
Suppose you have a test tube of size 2 oz, and it is filled 1 oz worth of chemical. You want to clean the test tube with 1 oz of water.
The catch is that 1 oz of liquid must remain in the test tube at all times. i.e. you cannot empty the test tube past 1 oz. Therefore, your only hope is to dilute the chemical as much as you can. What is the best you can do?
That's all!! Ciao Ciao.
P.S. friend wrote a song which is fairly pertinent to the topic, original composition.
Quick math puzzle I just made up, it's should be light and good:
Suppose you have a test tube of size 2 oz, and it is filled 1 oz worth of chemical. You want to clean the test tube with 1 oz of water.
The catch is that 1 oz of liquid must remain in the test tube at all times. i.e. you cannot empty the test tube past 1 oz. Therefore, your only hope is to dilute the chemical as much as you can. What is the best you can do?
Sorry to hear things didn't work out. I like your moat and fortress metaphor.
I'm confused about your math puzzle. Is the goal to get 1 oz of pure water in the test tube? The best that I can think of is to keep filling the tube with water, mixing, and emptying it halfway, then you'll keep halving the amount of chemical every iteration.
Quick math puzzle I just made up, it's should be light and good:
Suppose you have a test tube of size 2 oz, and it is filled 1 oz worth of chemical. You want to clean the test tube with 1 oz of water.
The catch is that 1 oz of liquid must remain in the test tube at all times. i.e. you cannot empty the test tube past 1 oz. Therefore, your only hope is to dilute the chemical as much as you can. What is the best you can do?
if you have c chemical at some point and add w water, the proportion of chemical is now c/(1+w). After mixing and pouring, you have c/(1+w) chemical left.
Let us say we have n pours/mixes, then we must maximize the function (1+w_1)(1+w_2)..(1+w_n) subject to w_1+w_2..w_n=1. By am-gm, each term should be equal so w_i=1/n.
So the result is 1/(1+1/n)^n, take limit as n->infinity to get 1/e.
On August 21 2011 04:10 blankspace wrote: if you have c chemical at some point and add w water, the proportion of chemical is now c/(1+w). After mixing and pouring, you have c/(1+w) chemical left.
Let us say we have n pours/mixes, then we must maximize the function (1+w_1)(1+w_2)..(1+w_n) subject to w_1+w_2..w_n=1. By am-gm, each term should be equal so w_i=1/n.
So the result is 1/(1+1/n)^n, take limit as n->infinity to get 1/e.
Seeing the bears again... they really do look like ¯\_(ツ)_/¯...
Also, the least amount is clearly 1/infinity. First you pour in 1oz water, so you have 1/2 chemicals You pour half away and fill it up with water again, so you have 1/4 chemicals Then pour half away and fill it up again, 1/8 chemicals Continue until infinity.
Sorry to hear what happened with your girl, but you did the right thing - I don't think it's worth dragging on a relationship when one of the two never opens up.
Last semester of undergraduate eh? What are your future plans?
On August 21 2011 04:10 blankspace wrote: if you have c chemical at some point and add w water, the proportion of chemical is now c/(1+w). After mixing and pouring, you have c/(1+w) chemical left.
Let us say we have n pours/mixes, then we must maximize the function (1+w_1)(1+w_2)..(1+w_n) subject to w_1+w_2..w_n=1. By am-gm, each term should be equal so w_i=1/n.
So the result is 1/(1+1/n)^n, take limit as n->infinity to get 1/e.
I am very confused. What does this number mean? I am not a mathematician so I do not want to argue with your math as I'm sure it's perfect. However what does that number mean? is 1/e the concentration of the chemical? And if it is the concentration then what are the units? As far as I understand math 1/e~0.368. Are you saying that the most dilute that you can get it is 1/3 amount of chemical left? This is obviously not true at all so what am I misunderstanding? If this derails the thread too much feel free to PM me. I am very interested in understanding this problem
I am an analytical chemist so dilutions are pretty much my life and I can tell you that the chemistry answer to this problem is if you dilute the chemical an infinite number of times you will eventually have no chemical left. It doesn't matter if you always leave 1oz in the flask. Eventually you will dilute the solution to where you have 1 molecule of your chemical left and then that molecule will get tossed out and you will have pure water. (assuming perfect mixture every time, and assuming the chemical doesn't stick to the flask etc...) And actually it won't even take that long to get a pure water solution. Assuming that you get a perfect mixture every time and that you throw out exactly half of your chemical every time, and for calculation's sake let's say that you have 1 mole of chemical (instead of 1 oz just so we can get a precise number to make the calculation easier) it looks like you will get pure water on your 81st rinse, assuming when there is only one molecule left it gets discarded with the rinse and does not stay in the flask.
First, the number e can be defined as the limit of (1+1/n)^n as n goes towards infinity. e is about 2.718 (this is easily calculated from another definition of e = 1+1/1!+1/2!+1/3! etc...). You can show that the expression increases as n increases but the most it can get to is about 2.718 no matter how big n is.
Next, you're right that if we had infinite water we could dilute the chemical to zero. For example, add 1 oz of water and mix/pour so chemical is now 1/2 oz. Add 1.5 oz of water, mix and pour so chemical is now 1/4 oz. Do this forever and the chemical approaches zero.
However I think what you overlooked is the fact that you only have 1 oz of water. Less water means less dilution. (for a more extreme case, if you only had 1/1000th oz of water, you could barely dilute the chemical).
First, the number e can be defined as the limit of (1+1/n)^n as n goes towards infinity. e is about 2.718 (this is easily calculated from another definition of e = 1+1/1!+1/2!+1/3! etc...). You can show that the expression increases as n increases but the most it can get to is about 2.718 no matter how big n is.
Next, you're right that if we had infinite water we could dilute the chemical to zero. For example, add 1 oz of water and mix/pour so chemical is now 1/2 oz. Add 1.5 oz of water, mix and pour so chemical is now 1/4 oz. Do this forever and the chemical approaches zero.
However I think what you overlooked is the fact that you only have 1 oz of water. Less water means less dilution. (for a more extreme case, if you only had 1/1000th oz of water, you could barely dilute the chemical).
If you only have 1 oz of water then you can only dilute it to 1/2 of it's original concentration. It would be impossible to dilute it any more than that. (Using a highly simplified meaning of the word "concentration")
I'm still not clear on what the actual number that you gave as the solution to the problem actually means. You said that the lowest dilution of the chemical possible is 1/e which means that it is ~1/3 of the original concentration. However if you just add 1oz of water to 1oz of chemical then the chemical will be 1/2 of it's original concentration (here again we are simplifying what "concentration of the chemical" actually means or else we are just assuming that 1 oz of the chemical is molar equivalent to the 1 oz of water).
Also if you look at my solution you would not need to dilute to infinity to get rid of all of the chemical as long as you're throwing out half of your solution with every dilution.
"If you only have 1 oz of water then you can only dilute it to 1/2 of its original concentration"
nope, look at this example: first put in 1/2 oz water into 1 oz chemical. Mix and pour out to 1 oz. Since 2/3rd of the solution was chemical, now we have 2/3rd oz chemical, 1/3rd oz water. Now pour in the remaining 1/2 oz of water. We get 2/3rd oz chemical out of 3/2 oz total, so the proportion is 4/9th. Pour out and we have 4/9th oz of chemical remaining.
Notice that if you plug in n=2 to the formula 1/(1+1/n)^n, you get 4/9th.
basically the more iterations of the process (i.e n gets bigger), the smaller the fraction gets. 1/e, as I said before, is the limit as n gets really really big.
Also if i understood everything correctly a discreet solution exists and you do not need to take n to infinity. 1 oz of water has approximately 1E24 molecules of water. So you can actually plug in the right number and it will be more then 1/e so technically you were still wrong (and of course this doesn't even take into account the fact that the water and the chemical are probably not molar equivalents of each other which of course means that the formula you used wouldn't work anyways)
On August 23 2011 05:30 FryBender wrote: Got it. This makes sense now. Thank you.
Also if i understood everything correctly a discreet solution exists and you do not need to take n to infinity. 1 oz of water has approximately 1E24 molecules of water. So you can actually plug in the right number and it will be more then 1/e so technically you were still wrong (and of course this doesn't even take into account the fact that the water and the chemical are probably not molar equivalents of each other which of course means that the formula you used wouldn't work anyways)
And then we still only would have a probability that the last molecule of the chemical is poured out... it might forever be in the container, always being in the half that stays in. Seems like a task for chaos theory :p
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(and of course this doesn't even take into account the fact that the water and the chemical are probably not molar equivalents of each other which of course means that the formula you used wouldn't work anyways)
