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Today I have signed the intent to adopt my 5th and 6th child. My joy is stifled only by the reality that my parents are not here to share it with. I want to pick up the phone, call them and let them know they are about to be grandparents again. This may be my last adoption. My family may be complete. And what a beautiful family it is. How blessed I feel. My babies. Never would I have imagined that I would be a mother – much less to 6 beautiful, smart, kind and talented little people. I can’t help but think about how happy my mom would be. Heaven knows she would have spoiled them beyond words. My dad would have too. I regret that my little people will never get a hug and a kiss by my mom and dad, but… they know them. We keep their memory alive – in a healthy way. We talk about who they were and what they were like… we talk about how they loved and how much they would have loved each of them. We visit their graves and my kids all take little gifts – a drawing, a special rock, a flower or a toy that they want to share. They leave these little momentos and it touches my heart. Good kids… On second thought maybe mom and dad do know. Maybe they had a hand in it all after all, or at least perhaps they are watching and smiling.
First of all: I got the job!
My new supervisor called today- he sounds awesome- and talked about when training starts and some just regular logistical things. I start September 26th with 6 other newbies! He says it’s 22 weeks of intensive classroom style training to start where you are given an increasing number of real cases. I’m super excited. I’m seriously not able to articulate the amount of excitement I have for this change in my life. It’s going to change everything.
If you read the last entry you may have been thinking, Olivia… don’t go over to Pauls house- it’s a trap all he wants is to sleep with you. And I’m not going to say you’re wrong. I know he just wanted me back to borrow for a moment not to keep and I had my own motives and was willing to accept the situation. I was just really curious to see the house, it was in development (and town for that matter) that he wasn’t considering before so I wanted to see it. So, of course, it starts off with a tour and I immediately realize, “Wait, where are your drums?” He had a lovely $8,000+ drum set that he just loved. Being a “heavy metal drummer” was part of his identity. When realtors would say “There’s room for your drums in the garage” he would act like they proposed to put his first born son in the dog kennel. ”I needed another five thousand...” he sold his drums. In order to buy the house…. he sold…. his drums. I still can’t really believe it. He said he had to make a decision and that he rarely used them anyway and that the band would never really do anything. Oh my gawd I didn’t even consider the band- the band that I had to tolerate on Wednesday nights, the band members we joined in the worst road trip ever (due to Paul not the other members lol).
Yes, he sold the drums but there was a solid 300% increase in the number and variety of gis for martial arts since I last was there.
I’m annoyed that I even know it’s called a gi. He also bought new couches. He had the worst ugliest couches in his old place they were awful. come to find out he actually did move them into the new place. He only replaced them after the move.
So, ok, those are things I found interesting and wanted to sort of know. Now for the things that surprised me. I’m not mad at him anymore. I kind of expected to walk in and feel standoffish immediately. I don’t know if it’s because he’s the first person I fell in love with or if there’s just some unique chemical thing about him that makes me feel comfortable. For example at one point I needed to take a bit of a shower…. he’s a dude with a new house so he has no shower curtains which he thinks he doesn’t need because the shower has a glass door…. whatever. The point is I was fine just washing up with him watching me. He always did that- and it’s not in like a creepy way or super sexual way he just looks me over and comments on my body somehow just like “you’re looking slim” “wow you have amazing skin” and of course a playful reference to a sexualized area from time to time. It’s one thing to be comfortable naked while you are being sexual with someone- but it’s completely a whole other thing when you’re just comfortable naked with someone.
No, I can’t ever trust him again… and I know there’s no future there… but I don’t know, I think I just need to acknowledge that there’s a loss there and I would be lying if I said I wasn’t worried that I’ll never have this level of comfort with another person again. It’s a scary prospect for someone like me who didn’t even think that was possible for me to have with someone- now there’s this notion of what if he was the only one, and now it’s ruined.
I had to get up really early to get to work on time. He seemed really concerned, I told him before we went to bed that I would be getting up super early. He actually walked me to the door. He got out of bed at 5:45 am to walk with me 20 feet- he was not doing that shit at the end of the relationship, I had to wake him up for a kiss goodbye and he was not sitting up for it. He texted me first thing when he got up for the day a couple hours later and then he called me on the center phone… he used to do that early on in the relationship, you know: Back when he thought he loved me. So when he did that I was just confused. I wasn’t able to take the call my coworker just said all confused, “Some guy called for you, said his name was Paul??” Like what did he think was going to happen? What did he want out of all this and didn’t he already get it?
Later he was asking about what I thought of the place and I gave him some feedback and when I said something about getting some decorating going he said “That’s where you come in” so…. what? He wants me to help him feng shui his place? I’m not an interior decorator- that’s not a hobby of mine. I actually don’t really like doing it- I always have richer tastes and they change so often. When we were together he would talk about this house he wanted and what amenities he wanted and then he’d say, “And you will make it a home not just a house with your touch.” At the time I loved that. But he is not privy to my touch right now- nor will he ever be, he has forfeit my domestic touch…… it’s just apparently if I’m not with anyone and he calls….. maybe I’ll be willing to pretend…..
So… first day of school for my kiddos was today.
LOVE my class!!! LOVE them.
First day is always crazy. It was a little crazy. Went by SUPER fast. Which is good. We’ll build into it, though. ;) A few young ones this year, which always makes a HUGE difference. ;)
My two girls have had 3 days back to school. So far, they’re having a great time!!! :) They love seeing their friends every day. They’re both LOVING their teachers this year (that ALWAYS helps!!!). Just, all around, going well.
B and I have been talking QUITE a bit more. :)
So, he’s a cop here. And my co-worker is married to the sheriff here. So, she’s all sorts of interested.
Also, I just wanna hang out with him. I’m pretty excited about this one. (last couple/few I haven’t been all too thrilled about- but was all “well… I suppose I should probably at least TRY to enjoy myself, ya never know!” and… they weren’t the greatest of matches)
And, let’s be real….
I haven’t slept with someone in so freaking long. NOT that I am up for that right NOW. But I’d sure like to make out with someone.
I know that even more than making out, I do want a relationship. I am ready for one. It’s been a long time. A year and like a few months since I’ve been in a relationship. I’ve toyed around with the idea of dating again and not.
I’ve finally gone on a couple of dates. Now, I’m ready to be in a relationship. I am. :) I want to.
See…. all in due time. ;)
My friends told me I’d get to this point. I was skeptical. hahaha…
I want to work on my classroom right now but some guy is in here installing a sink. So it’s like… I can’t really do a whole lot. He’s kind of “in the way” of anything I want/need done.
Infinity is something not really understood by many but still used as if it were understood. The two most prevailing ideas are 1) it is a really big number, and/or 2) it’s a concept, not a number.
With regards to 1, this isn’t well defined. What is a number? Is it something you count on your fingers and toes? Then 0.5 isn’t a number. Is it something you define a range, say, all the numbers between 0 and 1, and then just extend positively and negatively to include things like “everything between -5 and +5” and so on? This is a bit better, but then you have issues like “well what is a number divided by 0?”
Ultimately, a number itself is a very ambiguous term, and it’s not a very well defined one within mathematics (or even by the average person. Go ask someone what a number is—if you’re clever, you’ll always have a “number” that seems to not be included in the definition). You might as well try and precisely define “red” as a color we see—you can’t, and you can’t even prove my red is your red, even if their light wavelengths are the same.
The best we have in the mathematical world is a set of various names of various types of numbers. Natural numbers are your counting numbers, 1, 2, 3, etc. Whole numbers also include the number 0 (this is probably the most ill-defined set for a few ugly reasons). Integers also include all the negative numbers. Rational numbers include any two integers that can be divided (anything divided by anything except 0), which basically says “decimals that stop or have a repeating pattern). Irrational numbers are only those numbers with decimals that have no real pattern or repetition. And real numbers include both rational and irrational and are basically the “parent” of everything. Its sibling is the complex numbers which include the grossly named “imaginary” numbers, or the even roots of negative numbers (like the square root of -1, the definition of the imaginary number i ).
With regards to 2, well, you’re on to something, but not really. You might as well hold up two apples and say “this apple is more apple-y than that apple.” What are you saying? Nothing intelligent, I promise you.
So where does infinity fit into all this? Well, we have two other types of numbers: cardinal numbers and extended real numbers. Extended real numbers are just a “convenience,” wherein we simply take the real numbers and just take them all the way to infinity. This is the idea of infinity most people are aware of. And there are clearly defined rules:
Infinity + Infinity = Infinity
Infinity * Infinity = Infinity
0 – Infinity = -Infinity
Infinity * -Infinity = -Infinity
Infinity / number not 0 = Infinity
Infinity + or – number = Infinity
-Infinity + or – number = -Infinity
However, there are two caveats when allowing such an extension:
Anything divided by infinity isn’t defined (an engineer will tell you this is 0. An engineer doesn’t understand numbers any more than a janitor does, I promise you. The difference is that a janitor knows this, and the engineer believes otherwise). Also, infinity minus infinity isn’t defined (and there’s no way around this).
Engineers came up with the concept, too, that a number divided by 0 is infinity (or a negative number divided by 0 is negative infinity). See the previous parenthetical for what engineers know about numbers. With regards to this, we know that 1/X as X approaches 0 converges to infinity (or negative infinity if it’s -1/0, or either if it’s any other number divided by 0). But limits and numbers aren’t really the same—limits give numbers, but they aren’t numbers. A bank gives you money, but it isn’t money, if you need an analogy.
The other type of number is the cardinal number, and cardinal numbers are perhaps the most important numbers for the real person (even if they don’t realize it), and in nearly 100% of situations, they are identical to normal numbers. Cardinal numbers measure things. They aren’t just mere numbers—they are actively doing something, namely measuring something.
How much liquid is in your cup? How much square feet is your home? How much more do you prefer to this show over that show? You may give a number (or an abstraction for that final question), but you’re measuring something, and this is cardinality.
Extended real numbers only have two infinities: a positive one and a negative one, and if you come up with a positive infinity and I come up with a different one, they are the exact same.
Cardinal numbers are different. How many counting numbers are there? 1,2,3,4,… Infinity, right? Well, now what if I count by 3s? 3,6,9,12,… Infinity of those, too! But they clearly aren’t the same infinity—one appears to be smaller than the other because it’s excluding some numbers (indeed, counting by 3s excludes an infinite number of numbers and is still infinity itself, which gives itself erroneously to the possibility that Infinity – Infinity = Infinity).
Take it a step further. How many numbers are there just between 0 and 1? Or 0 and 0.0001? An infinite number! Now what about ALL the numbers ever! Is this the largest infinity? (No, actually, there are infinitely many infinitely larger infinities than the infinity of ALL the numbers EVER. Isn’t that neat?).
We do know some things, though. We certainly know that the counting infinites can be ordered. I know that 3,6,9,12,...’s infinity is smaller than 1,2,3,4,5….’s infinity. I don’t know by how much (other than by infinity, which is useless), but “logic” and “common sense" make sense here. And I also know that all the numbers’ infinity is larger than these two.
The first two have infinites known as “alephs.” The 1,2,3,4,5,… infinity is known as “aleph naught,” which is a strange looking N (the aleph) and a little 0 under it (the naught). We have other alephs, like aleph-1, aleph-2, etc. for other counting things. The infinity that includes decimals, say, all the numbers between 0 and 1 (or any two numbers X and Y), we call this c. The letter c, specifically lowercase.
And you might think it crazy, but we know that all cs are equal. There are an equally infinite number of numbers between 0 and 1 as there are between 2 and 17, or -1000 and 47287827827871870. Here common sense eludes us, but this is a mathematical thing.
As for the big infinity for all numbers ever, we conveniently just call that one infinity with the normal sideways-8 symbol. This is the not the largest infinity, but it is the one most people are familiar with, so it makes sense to give it the same symbol as we give the extended real number infinity.
Now, with cardinal numbers, you can’t operate on them. I can’t add two measures. Do you think it makes sense to add 3 liters of water and 4 square feet? No, it doesn’t. You might say “Well, why don’t I add 3 liters of water and 6 liters of water?” But you’re not adding measurements anymore! You’re actually just adding the quantities 3 and 6, and then you’re “keeping” the measurement that they both share! “Why don’t we just add the quantities of 3 liters and 4 square feet and keep the measurement they share?” They don’t share a measurement, and you’re not allowed to assign a measurement arbitrarily (or do you really think you can just hold up 4 liters of water and say “this is 4 miles of water” and expect anyone to believe you?).
In fact, ANY time you’re adding measurements together, you’re actually just adding the numbers inside the measurements and then slapping the measurement to the answer. In math, this is 4 feet + 7 feet = (4 + 7) feet = 11 feet. This makes more sense than you might think!
Go back to kindergarten or first grade, when you learned to add and subtract. You have 3 apples, Timmy gives you 2 more. What did you do? You counted to 3, then you counted 2 more. You added the quantities first, and only after you were done did you bother putting on the measurement (here, “apples”) on it.
So you can’t operate on measurements: no adding, subtracting, dividing, or multiplying. So infinity doesn’t mean much except as a measurement, and this is where the idea of “infinity is a concept, not a number” really comes from.
But infinity is a number.
The real question is, what on Earth is a number?
If you can answer “what is a number” in a very precise, rigorous way, you’re going to actually solve a lot of open problems in mathematics and philosophy that have never been solved before, some of them having nothing to do with numbers or math in the slightest. ...And people have tried very hard to answer this or a very similar question (specifically, “what is an object within a set of objects?”).
I’m sorry, but I don’t believe in you enough that you’ll actually come up with the answer. :(
i am going to guess that you said this to me around the time of your breakdown, when you started getting really emotional.
we were talking about the growth of our friendship, how it had changed and progressed over the years, and i mentioned that our “boss/employee” dynamic had really defined the first few years of our friendship. how i often felt like a commodity, a “peon,” and how i was always slightly scared of your temper, and the position of power you had over me.
and you asserted that you had always considered me a friend, that our friendship was more important to you than what use i could be.
this last winter was a hard one for you. losing your relationship last fall definitely was quite a blow, but the following deterioration was anything but a natural progression – most people don't follow, or skulk, wheedle or threaten their ex under the guise of “staying friends.” you kept making bad decisions, and i kept asking you why. you couldn't answer, and you couldn't stop; that should have been my red flag. i guess after eight years, the flag looked minor.
when you called me to weep, i answered, no matter what i was doing. when you said you needed someone to listen, because you couldn't stand being alone, i drove for an hour to be there, and stayed up all night before going to work the next day to make sure that you didn't have to feel isolated.
and over these months, you seemed to open up. you told me you loved me. you encouraged me to try to get myself some help and support. i thought i was seeing you turn into a better person, suffering, but expanding, and learning.
i thought you were learning to care about me.
maybe you only suggested therapy for me because you knew i would need the support once i found out the truth. if thats the case, that is the only altrusitic, empathetic, human thing you did.
your betrayal spanned the entire time you were “having your breakdown.” you did despicable things, having me handle your personal life and items, the entire time completely aware that you were doing the worst thing to me, and that the subterfuge could only go on for so long.
while you made soulful, teary eye contact and repeated over and over how important i am to you, it was all just a cover for the person you are: weak, selfish, inconsiderate, manipulative, disgusting.
it wasn't incidental. it wasn't accidental. you know how i know? because you kept trying to fuck me. which honestly would have made me...i don't know. when i found out about your big secret, i was very sick over it for months. if i had let you fuck me while all this was happening behind my back...i don't know how sick i would have gotten. maybe too sick to recover.
because when i found out the truth, i had to handle it. i had to get rid of you, and make sure everyone was safe from you. but i thought about suicide a lot. a lot-a lot. being logical was extremely difficult. i don't know how much worse it would have been if i had let your rancid cock inside of me.
and that's how i know it was intentional. fucking me would have made the betrayal entire.
you really must have wanted to end our friendship pretty definitely.
soooo. thats a chunk of my summer.