Tag Archives: Interesting Observations

Interesting Observation: Better Late Than Never

You all probably have heard the phrase “Better late than never” at least once in your lifetime; if not, well, it’s better late than never to learn it. Either way, a friend recently said it to me, and I was about to reply “yeah, of course, it’s always better late than never,” when I realized something: “What if it was my execution?” :/

Imagine the executioner coming to your jail cell to fetch you; he unlocks the door, binds your hands, and as he leads  you to the guillotine, he says, with an apologetic look on his face, “I’m really sorry that it has taken so long to get your execution set up, we’re usually not this sloppy; but, you know, better late than never, right?”

~ George

Interesting Observation: Happy New Year!

A new year has started! There. That’s a pretty interesting observation if you think about it, so the post must be finished. Sign: ~ George. Done.

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Not really 🙂 As you probably know, it’s a the start of a new year. You can tell because of all the people saying “Happy New Year!” all the time. I’ve said it myself a few times, but I started wondering what we were actually saying when we said “Happy New Year” to people. If you look closely, it isn’t actually a sentence at all, just a noun plus two adjectives. Saying “Happy New Year!” to people is grammatically the same as yelling “Purple Tin Piano!” at them.

Of course, we aren’t yelling “Purple Tin Piano” at them, and of course we mean something more than “adjective adjective noun”. What we omit when we say “Happy New Year” is the two words “Have a”. When we add those words, we get “Have a Happy New Year”, which is a complete sentence. We just drop the verb to make it easier to say. Furthermore, “Have a Happy New Year” is still leaving out a bunch of words. What we actually mean is “I wish that you may be happy throughout the rest of this new year.” No wonder we shortened it.

Anyhow, as if I haven’t said it enough, Happy New Year! (However you want to read it) 🙂

~ George

Quotable/Interesting Observation – The Cycle of Tiredness

If you run too long you’ll get tired and want to walk. If you walk too long you’ll get tired and want to stand. If you stand too long you’ll get tired and want to sit. If you sit too long you’ll get tired and want to lay down. If you lie down too long you’ll get tired and want to get up and run. This is the Cycle of Tiredness.

~ George

Interesting Observation: Thanksgiving isn’t a Money Holiday

Recently I was talking with a few friends about the fact that stores are selling Christmas supplies long before Thanksgiving even started, when one of them pointed out that Thanksgiving isn’t really a money-making holiday. Apart from the famous Turkey and other foods, along with pilgrim supplies, there really isn’t much for the stores to sell you. Easter has eggs and candy; Halloween has costumes, decorations, and candy; valentines day has cards and chocolate; Christmas has decorations, gifts and candy; even 4th of July has fireworks. Thanksgiving has none of those; it is perhaps one of the more “pure” of the widely celebrated (national) holidays, that is, it is not a commercial holiday. Just thought this was something cool to think about.

~ George

(Later the conversation turned more humorous with us discussing ways to make Thanksgiving into a money holiday. You can see my post on that conversation here)

Interesting Observation: Average Day

When someone asks you what you like to do, you usually don’t reply with the things you do most often, whether because they’re not fun (school, work), everyday (eat, sleep), or boring to talk about (watch TV, use the computer, play outside, etc., although they can be interesting to talk about, they aren’t very noteworthy). The more usual reply would be something more specific and interesting, like I would say “Swim Team and Piano”, because those are more interesting replies than “using the computer”. In general, it’s the highlights that we talk about, because for the average person the average day is merely average : )
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(Yes, I wrote this whole thing primarily so that I could say that last line 🙂 )
 ~ George

Ponderings from Math Class

One of the things that has me so tied up for time is my math class, precal/trig in one semester (5 credits!). However, during class I often think of random questions or observations, and I think that instead of making a post for every single one, it’d be better if I just make this single post and keep updating it. If I make a post based on something in here, even better! Quite a few of these will probably only make much sense in my head, but since half the point of this blog is to make people think about things they wouldn’t usually think about, I think it’ll work :). Anyhow, on to the ponderings…


(1) First off, every time I hear the word “pondering” I think of a joking definition made by a past teacher of it. Someone asked what pondering meant, and he replied something like, “pondering is what it’s called when someone wanders around making ponds, the word explains itself, you see.” 🙂


(2) What if 4 > 4 was somehow a valid statement? (((I actually have a way to make it so, but it involves something that I’m not anywhere near posting)))


(3) 1 = 1/1 = 2/2 = 3/3… Somewhat similar to the last question, what if it wasn’t exactly equal, or in some way it wasn’t true. They actually aren’t exactly the same, after all; you type them different, so if you were to measure the bit count of them they wouldn’t be equal


(4) How can you have $i ? Is it equal to $1? $-1?


(5) A joking quote from the teacher: “I’m pointing big!”. What would that actually mean? “Point” means a specific place, but point “big” could mean a general direction, or what?


(6) Interesting Observation: It is impossible to plot a perfect graph, because there is always a smaller number to calculate


(7) Interesting Observation: In precal, you are told that the only numbers you have to worry about being undefined are dividing by zero (infinity), even roots of a negative number (i), taking log of a negative number (also i), and taking log of zero (infinity again). However, you also can’t do this: 0^0, which is undefined (note: not infinity or i, “indeterminate”; even Wolfram Alpha can’t figure it out: http://www.wolframalpha.com/input/?i=0%5E0). So if you had a problem in which you needed to find the domain of 0^x, the answer would be {x|x<>0}. Also, a^0 = 1 = a/a, so 0^0 = 0/0, which is also indeterminate.


 

(8) Funny comment my teacher made: “Now back to more pleasant things, like math!” (after a conversation about exponential growth and Ebola)


 

(9) log base a of x = y is equivalent to a^x=y, so long as x>0 and x≠1, both of which are impossible (at this level of math?), for example, log 0 = y would mean that 10^SomeRealNumber = 0, but what if it worked? Same with log (-100) = x, which means 10^x=-100, although I think that one is possible with imaginary numbers


 

(10) Interesting Observation (that I’m positive lots of people know): You can have any base for a number system (ours is base-10) and still use decimals, it just depends on when you shift over a decimal. For example, our base 10: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 (one 10), 11 (1 and one 10), 12 (2 and one 10)…; base 8: 0, 1, 2, 3, 4, 5, 6, 7, 8 (one 8), 11 (1 and one 8), 12 (2 and one 8), 13, (3 and one 8)…; also, base 12: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, a, b, c (one c), 11 (1 and one c), 12 (2 and one c)….

It can get pretty hard to imagine, but you could do it, especially if you were raised on it


 

(11) 0 < 8 > 0 is a perfectly valid statement, but is there any context in which it would be useful? At the very least it’s symmetrical 🙂


 

(12) It’d be interesting to create a problem that has an exact answer and is made up of whole numbers, yet the exact answer is 20 digits long (and not just a irrational number, like e, or a fraction, like 1/3). Also, if you wanted to be mean, you could say that the answer has to be exact, and nobody would trust that their calculator wasn’t just rounding to the 20th decimal, causing everybody would think they just had to restate the problem instead of giving an exact decimal.


 

More to Come!

~ George

Interesting Observation: Social Norms

Having participated in a discussion about social norms recently, I realized something that I don’t think anyone else there picked up on.

There are way more social norms than we usually think there are. Many things are social norms, even if we wouldn’t think they are. To help identify a few, here’s the definition which I’ll use:

A social norm is something the majority of society does/finds normal

Using that definition, you can find more social norms by realizing a few things about them:

  • Possibly the easiest to realize, something can be bad and still be a social norm (slavery in pre-civil war ear, for example, and smoking nowadays)
  • The next easiest to realize might be that something can be the right thing to do and still be a social norm (not interrupting someone who is talking is the right thing to do, and a social norm; it’s also a social norm to let the other person talk sometimes so that they don’t need to interrupt you in the first place)
  • Less easy to notice, something can be both common sense and a social norm (driving on the right side of the street, for example, is a social norm. Obeying the law is too,  although for some laws (such as the speed limit), it has become the social norm to not strictly obey)
  • Even harder to notice, something can be nearly unnoticeable and still be a social norm (eating 3 meals a day is a social norm, and so is waking up before noon during a weekday)
  • And the strangest of all, something can be “of course you don’t do that” and still be a social norm (of course we don’t randomly punch people in the face, but it’s still a social norm. Not punching someone in the face is, after all, “something the majority of society does/finds normal”)

The last one is the most interesting to think about. There are so many things which are “yeah duh, of course we don’t do that”, which I hadn’t even thought of as social norms. Of course we don’t randomly set fire to forests. Yes, it’s common sense. Yes, it’s the right thing to do. Yes, it seems crazy to even think about doing on purpose. And yes, it’s a social norm.

~ George

Interesting Observations – “Proven Beyond Doubt”

It’s possible for something to be “proven beyond doubt” without actually being true. After all, for a long time entire countries believed that the Earth was the center of the solar system, and it didn’t even occur to them to doubt. This is obviously false today, but in that time and in that place an Earth-centered universe was “proven beyond doubt”. Along similar lines is the phrase “That many people can’t be wrong!”, which, when you think about it and how often that isn’t true, sounds too foolish even to argue against.

~ George