I stand on the edge of a cliff, a place I've been to before several times. All the roads I follow lead me here. In the past I was afraid of where I ended up, couldn't believe my path ended here...turned my head and created another path, away from the cliff's edge, too dangerous. Invariably, given what I'm writing about, those paths led me back to the same spot. I've tried so many diversions now I can't help but recognize these alternative paths for what they are, diversions.
Last night I was out with a woman I've been with several times before. Every time she comes over and we sit on the couch I realize why I never commit to her. She just sits there, sobs about her life into a pillow cushion. I have the means to help her, I know she wants this, but I can't do it, I don't want to. She's easy, she's available, but she's not what I want. I'm not willing to claim what I do want despite knowing with near absolute certainty I have the power to create and have what I want.
In the moment I wake up I remember my lady friend left last night without us doing anything. We were in the bed and I just couldn't bring myself to consummate the night with her. I heard her get up as she thought I was sleeping. I saw the other bathroom light turn on, stay on for a while, and turn off. I heard the door open and close. I peeked out a window blind and saw her in her car, engine on and ready to go. I open the door intending to ask her what she's doing, to come inside because it's cold. But in that moment I knew I had a choice. To choose what I really didn't want, or let her go and free myself to go after what I really do want. I close the door without stepping outside. She doesn't see me, I watch her drive away. I've made my decision.
In the moment I woke up I realized all of this. I realize I have the power within me to create the relationship I want. I realize how my not having it is connected to my running away from my own power. Rather than seize it, I deny it and choose a bottom-feeder -- haha, no offense meant, inside joke. Because I choose to deny who I am and what I'm capable of, by falsely choosing humility over recognizing my power, I've created the situation with this woman and others. So much is coming together and making sense to me.
It's scary to me to claim my power, to recognize what I'm capable of in confidence because my ego knows that'll be the death of it. It's spent lifetimes investing my energies into the maintenance of itself. It doesn't want to go. I realize why: it wants acknowledgment. It doesn't want all of its efforts to be wasted, for it all to have been for nothing. I smile and feel so loving inside as I realize this. That's all it wants, acknowledgment. I tell it it hasn't been for nothing. That we've learned so much together, that I won't forget the adventures and the service it's brought me. Since my ego is me it knows I mean what I say. It knows I love it and won't let its existence fade into obscurity. I ask it to join hands with me, merge with me as we begin another grand adventure. I ask it to be loved with all my heart and join back with me, a piece of me I saw too long as separate.
So much is making sense to me. I imagine telling my spiritual midwife this. I imagine writing and sharing this. This is a special moment for me. A simple realization is when it's all going to change. It's nowhere near as dramatic as I had imagined. :) No precipice to jump over, no fanfare, no theatrics. There never was a precipice. I get that now, lol.
Bleary-eyed, but it's released. Truth be told I'd rather not release it right now, but, since Mozilla went ahead and released Firefox 4 I felt I had no choice. Version 3.0t3 is, at this point, more or less the successor to LastTab 2.2 so I'll be releasing it on Mozilla's Add-ons site shortly. I seriously didn't get anywhere near the time I would rather have to dogfood the new features, but such is life and a promised release on the weekend. Hey, it's still technically the weekend, lol. I unexpectedly ran into issues that just had to be corrected before release.
Aside from the gripes I actually am happy with the new Enhanced Menu popup. I had always planned on adding this popup, but as I got into creating it I realized I really miss the binding features of WPF. So I included a primitive version of a data binding engine. Some parts of the Enhanced Menu are bound to each other so it simplifies the coding some. I didn't have time to fully flesh it out the way I want for this release, but I eventually plan on using it for the options dialog and other parts of the extension as appropriate. Might even see about releasing it as a separate download.
Something new to LastTab is what I'm calling content detection for the previews. Like the data binding engine this was a completely unplanned feature. Now that I have a widescreen monitor I noticed how much space I was staring at in the previews and got curious about getting rid of it. Starting investigating the DOM and how to spot the real content on a page. Over a few weekends -- when I had time to work on LastTab -- it became my little obsession as I saw how neat it was. Perfect it ain't, which is the prime reason I included an option to turn it off, but I think over time it'll get better. Overall I much prefer it to the standard "show everything" previews. It'll really come into play with the planned all previews popup and help give each tab more distinctiveness, since the previews will be different dimensions.
|Content Detection Comparison
One other new thing about previews in LastTab is how the size of the previews are specified. Previously you would specify an integer width. I decided to eliminate this in favor of a monitor resolution dependent scale. I thought this would be more user friendly in the sense that you can use a slider to specify the preview size.
Okay, time for sleep.
I've been noticing more people coming to my blog using Firefox 4. There is a version of LastTab compatible with Firefox 4 on my web site. I haven't made it available on the Mozilla Add-ons site because I've discontinued work on LastTab 2.x series in favor of 3.x. I haven't considered it functionally equivalent enough to version 2.2 to release it there yet. Version 3.0t3 will be released this weekend and is functionally equivalent enough to version 2.2 that I'll release it to Mozilla Add-ons.
Despite the title this is not, I suspect, going to be a dating adventures post. Rather it's really going to be what I've learned about myself and life as a result of pursuing a woman. Since I view life as a classroom I try to distill lessons from my experiences. I think I'll go the bullet point route in offering up said learnings this time.
Say what you feel
A friend had turned me on to Steve Pavlina's site some time back, and one post in particular stood out to me in the midst of feeling down about this woman. Basically it was just about not playing the dating game, trying to guess intentions, and just outright say what you feel. I did this with this woman, but as usual when calling I got the voicemail, so left a voicemail saying I was interested in her beyond friends. It was actually a very tough thing to bring myself to do, I was shaking before and after the call. But oddly I had a strength when I was saying it because it was the truth. I was comforted by the fact that I was simply telling her what I already felt. I was thinking after the call my shakes were due to me being truly honest about something I would usually keep hidden. Almost like removing the caked on dust on something that's been too long dormant. That's how my energy body felt to me. I was finally letting my energy flow through my blue ray energy center instead of impeding it.
Since then I've been coming back to this lesson from different ways. I'm starting to settle on this woman is probably stringing me along, not maliciously, but because she has a hard time saying no. She told me this when we first started talking, in relation to her family wanting her to do something that she didn't really want to do, and then making up excuses as to why she couldn't do it even though she had already agreed. She is a very nice person and very friendly, but I see now how such behavior is actually hurtful in its own way. At least if you're doing it out of a desire to not hurt the other person by not saying how you truly feel. There's nothing wrong by being honest, in expressing what you already feel. If you think it'll hurt the other person to say what you know they don't want to hear, take comfort in knowing you'll just be expressing your truth. It's taken me experience – and this experience with this woman in particular – for this lesson to truly be learnt. Having experienced both sides of this honesty issue I feel I have a more balanced view on it.
Generally speaking I might say lying to protect someone from the truth is not a wise thing. It's akin to trying to put out a fire with a fire. The ends do not justify the means. It may be difficult, incredibly so, to speak a truth you know another doesn't want to hear. But if you think you're sparing them that hurt, just know you're trading it for another. Again, it's taken me experience to learn this, but it's been reinforced to me that nothing bad truly comes from being honest.
Face reality, not a fantasy
Another lesson I've learned in regards to pursuing this lady is the importance of honestly dealing with yourself and not living with delusions. One of the first things I thought about after calling this woman and expressing how I truly felt about her was how I could no longer live in a delusion. No longer could I fool myself into thinking she's interested in me when there are signs she isn't. This isn't to say I discount this possibility, even now, it's just the delusions I'm talking about are more of a cognitive dissonance. Ignoring and minimizing things that don't support what I want to see, preferring things that support what I want to see, no matter how small or infrequently they occur.
It's hard to give up on someone that you really like, it's especially hard when they give you signals that you can interpret in a way different from what they intend – e.g. they can't say no. All the unreturned phone calls, the excuses for not being able to do something go flying out the window when they smile and talk with you so freely. When you're in the midst of such a state it's hard to get out, let alone even notice you're in it. I think this is why women stay with abusive boyfriends. "I can change him." "There are times he's nice to me, he doesn't really mean it." It's a powerful drug.
The mystic in me thinks about this in regards to reality creation. I think it is necessary to imagine what you want to create, to give it energy, breathe life into it so to speak, in order for your dreams to come about. But I guess the more balanced view I'm coming across now is to notice what you create and not just what you want to create. If you fall off your bike don't pretend you didn't. Accept that you did, try to analyze why, and then try again to ride without falling. I suppose another idea that comes to mind is there's nothing wrong with failure, not achieving what you set out to achieve. Nothing to be ashamed of.
Don't act contrary to what you want
This is a relatively recent lesson. I was taking an elevator down at work to go take a walk – ya know, feeling bummed. When it got to the first floor it bobbed up and down like the cable was going to break or something. I got out a floor earlier and just walked to the ground floor. Later when I got back to the building I had a thought to just take the stairs up. If I did that that would take me past this lady's cubicle and so I might have to face her and I didn't really want her to see me in the sad state I was in. So even though I actually really wanted to talk to her, since she was the reason why I was bummed, I ended up taking the elevator back up and didn't talk to her. The next day when I was thinking about this I realized if what I really wanted was to talk to her I shouldn't take steps that are contrary to this. Regardless of what reasons I may present to myself to justify my behavior, that doesn't change the fact I'm acting opposite from what I want.
It's been a common behavior pattern of mine to become emotionally self-destructive and get into a downward spiral when things don't go my way. I presume to know what the other person is thinking and act on that, instead of what's actually happened, things they've actually said. Now I see more clearly how such behavior hasn't helped me. Prematurely cutting off communication with someone is usually what happens. Which, in light of what I've learned, is not at all what I really want. I really want to talk to the person, I just get hurt and lash out in unproductive ways.
The following day I decided to ask this lady if we could go for a walk so I could talk to her outside of work. I can't say the end result of the talk we had significantly changed anything, but I at least felt better. I was doing what I really wanted to do: talk to her and ultimately date her. I had that same shaky feeling I had when I told her how I felt about her when I asked for the walk. It's what I really wanted to do, but for too long I've denied myself from expressing such behavior. I think I'm on the right track. Nothing bad truly comes from expressing your truth.
I've mentioned before how I think people are fragmented beings, how we aren't fully aware of ourselves. These experiences, and the lessons I've been learning from them, have been shedding light and clarity on what that means in terms of day-to-day actions. One of the biggest obstacles I've been noticing to becoming more aware of these lessons is fear, fear of humiliation, fear of not knowing something you think you should already know. That last one seems a bit comical to me now, how can you feel bad for not knowing something you don't even know you should know. But yet I've gotten that thought from others before, "you should know these things at your age by now". Depending on how someone processes that thought it can be a great stumbling block in knowing, integrating, and accepting yourself. Living to the expectations of others instead of being yourself. You'll never find yourself if you keep looking to someone else.
I'm really happy about something that happened today, even if on the surface it sucked.
There's a lady I've been trying to pursue for a while at work before my contract ends. It's been hard to gauge how she feels about me. She's very friendly with people, we've had lunch before, she mentioned having dinner, playing tennis. The first time I called after getting her number she never answered or called back. I hate talking to her during work because she's busy and it seems I can't call after work. So today I decided to walk over to her cubicle, the first time talking to her since calling. She said hello and had a I'm-busy-please-leave look. Being at work I asked if she was busy, she said yes, and I left after some pleasantries.
I'd been feeling terrible the days between calling and today, going back and forth over how she feels and the situation. One thing I noticed then was how similar some other girls I've known may have felt when I never followed up on their advances. Seemed like it was my turn to be in their shoes, to experience what they may have felt. I felt a similar karma situation today. There was a guy at this same job that would come over to my cubicle nearly every day toward the end of his contract. It always used to annoy me because I wanted to get back to work, hated being interrupted. I remember the I'm-busy-please-leave looks I used to give him, I remember the slightly sullen rejected look his expression changed to from his initial excitement. Heh… I still talked to him because I did enjoy it.
Having the feeling of stepping in his shoes I have to say it sucks. :) But it took having a similar experience of my own to really feel prompted to change my behavior. Now that sad feeling of knowing you don't need someone but you want them, and they don't want you, has hit home. I actually feel more inclined now to make time for people whereas I would've felt annoyed. Outwardly my actions might appear the same since I did talk to that guy, but the motivation would be different. That's the key thing I think. Change on the surface is easy, because usually it isn't real. The real changes, changes in consciousness, those are harder.
But the thing I'm most happy about today is that I feel I've done everything I can in regards to this lady. I don't feel the emotional anguish anymore, there really is happiness now. Not at the possibility nothing will happen with her, but that I was true to myself, I followed my heart and I know it.
I've read before it takes courage to do that, to explore the shadowy areas of yourself, the areas you feel ashamed to express. I never used to believe it much, thought it was just empty feel good talk people said. But I have to say being true to yourself is really one of the tougher things I've attempted in my life. The world encourages a sort of conformity of thought. As you progress from that you have multiple thoughts you can conform to, labels: biker, hippy, geek, etc. Further still is being, you. No labels, no framework to fall upon to inform you how you should be. Nothing to tell you if you're doing things right or wrong. The line from the Matrix comes to mind, "The Matrix can not tell you who you are." It really is amazing how invisible some of these labels are. You can be a conformist and not even realize it.
I really would like things to work out with this lady, she's a lot of what I want: physically attractive, is feminine and likes to dress up, not afraid to get dirty, into health and raw foods, exercising, smart. But I'm happy if nothing happens. Actually today the situation reminded me of a wonderful dream. I wake up and want to hold the feeling but it fades. I want to have the same dream the next day but it doesn't happen. All I can do is enjoy what I had for what it was, a wonderful experience. In a sort of real life dream I've been in an emotional state that set me up to learn lessons about myself. Perhaps that was the whole point of feeling this way about this woman. Maybe not, who knows. Either way it's a wonderful experience, something I can enjoy for what it has been.
Reading the title to Lauryn Hill's first album was probably the first time the idea of being misinformed entered my awareness. It's kind of funny to think about now but up until then I just never really questioned certain aspects about life. Some years later I was at a rally and someone I worked with mentioned you can't trust the news. It was shocking to hear, "What, Peter Jennings is lying to me?" impossible I thought. He seems so trusting. Around the same time a friend said she didn't consider herself an American. "Preposterous", I thought, "you live in this country!"
But certain ideas never leave you once they take root. Your mind drifts to them when it wanders. The ideas grow and grow until one day you start to question, "Is it possible I'm not being told everything by news anchors, is it possible they're lying to me?"
In terms of health I've always been skeptical of mainstream approaches, preferring natural approaches whenever possible. Didn't take me long to get a reverse osmosis water filtration system installed to avoid consuming fluoride. And so with my focus on questioning mainstream health ideology I thought I was immune to being lied to. One of the insiders, one of the few who've figured out the world is a scam. It was kind of nice thinking I had secret knowledge, even if told everyone who would listen what I knew.
So it's been quite an eye opening experience to come across the web site of Wade Frazier. I first came across his site while Googling about fluoride to post a comment to a news article on Yahoo. Figured I already knew what he was talking about so I would just scroll through his article to find the fact I was looking for. That was a few weeks ago and I'm still reading, riveted at what he's uncovered.
Did you know the United State's conquest of America was a lot like what Hitler did to the Jews? Of course not, you're probably thinking, Hitler was evil. But Americans killed many many natives in order to make the United States what it is today. It's not really secret knowledge, every American knows this land was already populated when European settlers came, but what happened to the natives…
The specifics of Wade's site, though utterly fascinating to me, aren't really what interests me the most. No, it's my mindset I had going into it. Thoughts I've never had, ideas I've never questioned. Why didn't I ever think about the sheer numbers of natives that used to live on this land. Why didn't I ever wonder how it's possible for the United States to have issues with obesity when other countries face issues of starvation. Why didn't I ever wonder why we spend so much money maintaining military bases around the world when we have people living in poverty here.
The more I read the sadder I get really. It really does feel like I'm learning the truth about history and the world for the first time. When I was a kid I used to wonder sometimes how did planes know to fly where they went, why did certain stores close and not others. "Things just happened" I thought. But I wondered. Now it's becoming clearer there are specific people that make things happen. There is no invisible hand that regulates the market or economy, there are specific people that do this, usually for their own benefit. Things don't just happen.
Every now and then I try to challenge myself to mentally calculate numbers. As I improved at this over the years I noticed that division was always especially vexing so I usually just forgot about it and went about my day. Just yesterday I decided to put my mind to it to come up with a more efficient way of mentally dividing numbers than long division. After I was all proud of myself :) I thought about sharing everything I've learned about arithmetic to make it easy for myself. I searched Google for the phrase "easy arithmetic" and came up with solutions that, to me, seemed tricky. By that I meant they relied a lot on rules that applied in particular instances but not generally, for instance squaring a number that ends in 5. This was different than how I had been teaching myself which relied more on the relationships between digits. I won't necessarily say that what I'll say below is the fastest way of performing arithmetic, and it's probably not even unique to me. I'm just sharing it in the name of exposure. Since I was never taught this it's likely there are others who don't know about it either. So that's my main reason for writing this.
Fundamentals: Digits & Relationships
What I'll be saying here will probably seem terribly obvious but it's critically important to explicitly state these ideas since they're fundamental to what comes later. These are not rules per se, so no trickery, rather they're simple definitions of our number system.
- There are 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
- There is an ordering to the digits. 0 is less than 1, which is less than 2, and so on.
- The digit 0 represents no value.
- The operation of addition is transitive. That is 2 + 3 gives the same answer as 3 + 2; the order is unimportant.
- The operation of subtraction is intransitive. That is 2 - 3 does not give the same answer as 3 - 2. However, the only hurdle to transience is the sign of the result. 9 - 4 = 5. 4 - 9 = -5.
- Subtraction is the opposite of addition and vice versa. If I add 4 to the number 2 I get 6. To get back to 2 I just subtract what I added, 6 - 4 = 2.
- The operation of multiplication is simply repeated additions.
- The operation of division is simply repeated subtractions.
This is sort of a sub-classification to the above, but I thought to give it proper space and not just make it a bullet point. A number is not a digit, it is a collection of them. But even then there are fundamental relationships to observe. Our numbering system is based on 10 digits, thus it's called base 10. (There are numbering systems involving 8 and 16 digits so they're base 8 and base 16. In case you're curious base 16 involves using letters A - F after 9.) So in base 10 numbering successive digits in a number are a reflection of powers of 10 increasing from the decimal. Since I really don't need to involve the technical definition of powers in this article I'll restate that to say successive digits in a number are a reflection of increasing numbers of zeros from the decimal.
So the number 2 reflects zero 0s after it.
The number 10 reflects one 0 after it.
If I have the number 20 what I really have is the number 10 multiplied by 2 and added to 0.
20 = (2 * 10) + (0 * 1)
19 = (1 * 10) + (9 * 1)
538 = (5 * 100) + (3 * 10) + (8 * 1)
2429 = (2 * 1000) + (4 * 100) + (2 * 10) + (9 * 1)
- This is not trickery, this is just fundamentally how you get numbers bigger than the highest digit.
Now when you see the number 2429 you probably don't think you're implicitly performing multiplication and addition, but you are. And this fact is what makes arithmetic of numbers really easy!
Another sub-classification to the fundamentals section. In the methods I'll list below many intermediate numbers are used to store parts of the solution. Because I developed all this to perform mental arithmetic being able to remember many things is critical. So to emphasize: use your memory. You can be creative in this. For instance it can help to remember 103 by the fact it's 3 from 100. Exactly which direction from 100 isn't critically important because you're really trying to impress the number 103 in your mind, 3 from 100 is just a reinforcing thought. When I say be creative I make my numbers flash, glow, spin around, whatever it takes to hold the memory of the number intact in my mind.
- Whatever you do, it is critically important you remember the original numbers you're performing operations against.
Of course you could cheat and actually write numbers down to make things easier. :P
Let's say you want to do:
Instead of adding each individual digit and carrying leftovers instead break apart the numbers into their components.
49 = 40 + 9
27 = 20 + 7
Because addition is transitive it doesn't matter a bit the order in which you add the numbers! Mentally it's easier for me to work with numbers with zeros on the end which is why I break them apart. So:
+ 20 + 7
---- + ---
So instead of directly adding 27 to 49 I employed two intermediate additions to get two intermediate answers. The final step is to add these intermediaries.
Again, working with zeros makes this much much easier. Generally speaking this reduces arithmetic down to single digits since 0 has no value. And again, this is not involving any kind of trick, instead it's relying on the relationships of digits.
378 = 300 + 70 + 8
247 = 200 + 40 + 7
300 70 8
+ 200 + 40 + 7
----- + ---- + ---
500 110 15
At this point if you feel confident in your mental abilities simply stop and add 500 + 110 = 610 + 15 = 625. However to illustrate how breaking apart numbers to make them easier to work with has no bounds I'll continue.
500 = 500
110 = 100 + 10
15 = 10 + 5
+ 100 + 10 5
----- + ---- + --
600 20 5
At this point you can literally see the answer: 625. How far you take this splitting apart is up to you. I've found the more I practice doing calculations the less I need to mentally break apart the numbers. Mentally I employ animations of the numbers, I visualize for instance 10 spreading away from 110 so I have 100 and 10 as distinct numbers. Because addition is transitive this is possible.
Subtraction is made easier by reframing the operation. Instead of subtracting one number from another, instead think of the numbers as being on a line and you're moving in successive steps from a source to a destination: the number of steps you have to make is the answer of the subtraction. Convince yourself of this by mentally subtracting 3 from 9. The answer is 6. In terms of the reframing: the source number is 3, the destination is 9, and the number of traversed steps is 6. If instead you had to subtract 9 from 3, 3 - 9, rely on the fact that although subtraction is intransitive the only thing stopping it from being so is the sign. So reverse the numbers so that you still start at 3 and move to 9, 9 - 3, but remember to change the sign when you get the answer. Instead of getting 6 you get -6.
The point of this reframing is to help with higher order numbers and something I call filling in or spackling, similar to filling in cracks in your walls. Let's say you have to do:
Remember you're always moving from a smaller number to a larger, so you'll be moving from 128 to 297. Again, working with zeros is much easier. So how far do you have to go from 128 to get to the nearest zero number? 2 steps puts you at 130.
128 + 2 = 130
Float this number 2 away in your memory somewhere, it's part of the answer. So now you want to move again to the nearest zero, in this case 200.
130 + 70 = 200
Again, float this number 70 away, it's part of the answer. Because it is part of the answer it's up to you if you want to add it to the 2 you previously floated away, or hold it in memory as a distinct number. So now there are only 97 more steps from 200 to get to 297, the destination.
200 + 97 = 297
You could either float this number 97 away as part of the answer, or you could go in smaller steps and instead do:
200 + 90 = 290
290 + 7 = 297
As you can see it's up to you and how good your memory and concentration skills are. Because addition is transitive it doesn't matter a bit how you add the numbers. If you never added any of the intermediaries you'll have this final addition to perform
Which, if you want, you can look at as
+ 90 + 7
---- + ---
So that means your final answer to 297 - 128 = 169. This all works because addition is an opposite operation to subtraction. So 128 + 169 = 297 - 169 = 128. It's just that previously you stated the problem differently, as a question. What needs to be added to 128 to get 297: 297 - 128 = ?.
First let's get definitions down since we're no longer simply adding. In the operation 9 * 7 the 9 is the multiplicand and the 7 is the multiplier. Essentially 9 will be added 7 times. Because adding is involved, and addition is transitive, you can say 7 * 9 is 7 added 9 times to get the same answer. Frame it however you want just keep in mind that one number specifies the number of additions to perform, the multiplier, and the other is the number to be multiplied, the multiplicand. So, higher order numbers.
Take the multiplier, in this case 97, and break it apart so you're working with zeros.
97 = 90 + 7
Because the operation of multiplication involves repeated addition what we're really trying to get at by 98 * 97 is what is the answer when 98 is added 97 times. If we instead choose to do 90 additions first and then 7 more later on it doesn't matter, the answer is the same.
x 90 x 7
---- + ----
At this point you'll see we now have two distinct multiplications to do, plus an addition; how's your memory! You can make this easier by breaking down numbers even more:
98 = 90 + 8
90 8 90 8
x 90 x 90 x 7 x 7
---- + ---- + ---- + ---
Again, because order is irrelevant when it comes to addition you can break the problem down and build it back up to the solution in the manner easiest for you. When dealing with multiplying something that has a zero on the end it can be easier to reframe it.
90 = 9 * 10
So when doing 90 * 90 it's really 9 * 9 and move the zeros to the end. Technically you're not simply moving the zeros to the end, you're multiplying a power of 10 to the number like you're supposed to (9 * 9) * (10 * 10), but mentally it's easier to simply move, or stack, zeros.
90 8 90 8
x 90 x 90 x 7 x 7
---- + ---- + ---- + ---
8100 720 630 56
So now the answer to 98 * 97 is the addition:
Remember you can spread apart numbers if it mentally makes it easier to see what's going on
8100 = 8000 + 100
720 = 700 + 20
630 = 600 + 30
56 = 50 + 6
Add however you want
+ + 50 6
---- + ----- + ---- + ---
8000 1400 100 6
Although that 1400 could be spread away I'll just write the answer to be 9506. Don't believe that's the answer? Whip out that calculator then, haha. Again, no trickery, you're relying on fundamental relationships between digits so this method works with any kind of number regardless of how big it is, or what the final digit is, or etc. Although it seems to be a lot of calculations involving lots of intermediate answers, the more you practice the easier it becomes. Working with zeros makes it easier to simply see the answer with very few calculations going on.
In a similar sense to how I reframed the operation of subtraction I'll reframe the operation of division. If you have a bunch of objects the operation of division answers the question: how many groups of objects can I get with each group being a certain size. Like the higher order operation of multiplication definitions are important with division. The population of objects is called the dividend and the size of each group is called the divisor. In the operation 10 / 2, 10 is the dividend and 2 is the divisor. 10 objects taken 2 at a time gives 5 groups. For higher order numbers forget long division, instead rely on digit relationships.
To tackle this we're going to rely on the fact that addition is the opposite operation of subtraction. So the divisor, 28 in this case, we'll add 2 to it to get 30 since numbers with zeros on the end are easier to work with. It's important to keep in mind how big we've made each group of objects, we added 2. So that means in our final answer each group will have 2 more items in it than it should. So to undo our adjustment to the problem we'll subtract out those 2 items from each group. This will be the multiplication of 2 by whatever the group count we get. So mentally remember this 2. So now we have.
/ 30 (28 + 2)
Like subtraction division involves moving from one number, 0, to another, 359 in this case, but instead of going 1 at a time we move in multiples of the divisor, 30 in this case. This involves multiplication. Your goal is to find the number of steps, or groups as I reframed the division operation, it takes to get to 359 without going past it. By working with a number with a zero on the end you can ignore the end digits and simply rely on single digit multiplication; remember your multiplication tables? :) If I start at simply 10 then 10 * 3 = 30, add in the zero means it's really 300.
30 * 10 = 300
Since 300 is less than 359 we haven't exhausted the number of steps we can take, but just float away that number 10 as part of the answer. Now the problem becomes reduced to going from 300 to 359, 59 steps taken 30 at a time. Intuitively you might see you can only do this 1 time. But the general solution remains the same: successively move in steps of the divisor until you move to the destination or if you would move past it, don't. Every time you move float away the number of steps as part of the solution. So in our case we moved a total of 11 steps to 330, with 29 remaining.
/ 30 (28 + 2)
11 remainder 29
Now we have to undo the modification we made to the divisor to make it easy to work with. We added 2 objects into each group so we have to take them out.
2 extra objects per group * 11 groups = 22 squeezed out objects.
Add this back into the remainder we were working with:
29 + 22 = 51
Again, to do the addition you can mentally spread out the components of the numbers and add them in different ways. Now the 51 remaining is more than our true divisor of 28 which means we can move some more steps, at least one. You can either choose to divide 51 / 28 or intuit a subtraction, it's up to you. Using division
/ 28 / 30 (28 + 2)
---- ~ ----
1 remainder 21
21 remainder + (1 group * 2 extra per group) = 21 + 2 = 23 total remainder
So we got one extra group from the previous remainder of 51 with 23 remaining. This is less than our true divisor so we're done. 359 / 28 = 12 23 / 28 is the final answer.
Depending on why you're engaging in the division operation this may be enough for you, it really is the answer. But if you want the customary decimal notation instead of a fraction read on.
Fractions & Decimals
The number 5.75 is a decimal but it's really an encoding of two concepts. The 5 represents a whole amount of units, whereas the 0.75 represents some portion of a unit. This is a fraction of a unit, or said another way a percentage. So 0.75 is the same as 75 / 100. Hey, look at that, division! So seeing how we got 23 / 28 in our above calculation, in order to get the decimal equivalent we simply divide.
The issue here is that the divisor starts out bigger than the dividend. To do the calculation we simply give the dividend 0s until it's bigger than the divisor. Every time you add a zero like this you're adding a number to the right of the decimal point, keep track of this. So
23 / 28 becomes 230 / 28
The same methodology outlined above works here except you'll be engaging in successive rounds of division to calculate successive decimal digits.
/ 28 / 30 (28 + 2)
----- ~ -----
First round of division gives
/ 30 (28 + 2)
7 remainder 20
2 extra objects per group * 7 groups = 14 extra remainder + 20 = 34 total remainder
Intuit there's only 1 group of 28 in 34 so 34 - 28 = 6.
8 remainder 6
This means the first number after the decimal is 8, 0.8. Adding this in to our previous whole number of 12 means we have 12.8.
At this point you'll simply repeat what we've done since now we have 6 / 28 instead of 23 / 28. However many decimal places you want to go is up to you. If you ever come upon a situation where your remainder matches your divisor, 28 / 28, then you simply add 1 to that round's group total and you're done. If at any point you discover you're working with the same amount of remainder that you had in a previous step then stop because you have a repeating decimal. It'll repeat from the first time you came across that remainder amount to where you're currently at.
This was a question I woke up with last week.
So I learned something today: other people have things to teach me! Haha. It's not a new lesson of course, but there is always the euphoria with having a revelation, even if I've had the same revelation many times before.
There's a guy at work I dig into a lot, he was the subject of a previous post. I was looking at some code I had written and discovered he had refactored it. (Non-techies, this is improving the code.) Even though the code technically belongs to the company I work for there's a sense of personal ownership: I wrote the code. So when I saw he changed it I was teed off and immediately set about changing it back because I felt I had already written it good.
"How dare he improve upon my work! That's simply not possible!"
After I was done I took a step back and wondered if I was fossilizing, becoming resistant to new ideas; maybe I should investigate the worth of what he had done I thought. So I did. Went on Google, Stack Overflow, and other sites to get different opinions on code styles, asked someone at work who likes to talk about these things. In the end I kept some of my old code style, but was open to adopting the new one this other guy had done. As in many things software related each code style has merit beyond style, which is why I didn't wholeheartedly adopt the new approach. But still, it was a revelation of sorts: this guy I always believe I'm superior to actually has things to teach me if I would lower the ego a bit and actually listen.
As a side note. There's another friend at work who's been teaching me some different lessons, non work related, in regards to relating to women and really people in general.
When I say teaching I don't really mean these people are sitting me down on a stool and saying, "See this here? This is important." No, what's really happening is they're just living their lives as feels natural to them, completely oblivious to the fact that they're teaching me. It's my response to seeing such different behavior to what feels natural to me that prompts me to go into study mode. I'm probably going to get a bit more direct than I usually get in stating my world view, but these other people are like mirrors. Me viewing different aspects of myself made manifest in others. It's really amazing that I can think of myself as complete in certain ways but yet come upon moments where I realize how incomplete I am. Were I to only develop software in a way that feels natural to me, it would take an extraordinarily long time to come upon an equally worthy style that someone else feels is natural. Similar to being open and friendly to other people. Being able to watch this behavior so effortlessly flow out of another greatly speeds my acquisition of such behavior.
Truly it could be said other people are catalysts of ourselves. Catalyst in the truest biological sense. Noun. Chemistry. A substance that causes or accelerates a chemical reaction without itself being affected.
I've been meaning to write this for a while but was never able to because I never had the right mood when I was in front of the keyboard.
Today I was thinking about someone at work I somewhat frequently spar with because of his programming designs. I won't get into my specific reasons as that'll sidetrack what I want to talk about, but suffice to say I highly believe I'm right and that he's highly wrong. But today I was getting excited about planning for a programming task. All these ideas I've had in mind for a while I'll get a chance to implement them. It's fun! That's also when I started thinking about this other guy. He actually really enjoys development as much as I do. But I was thinking today how boring it would be if someone like me were constantly telling him to not do something the way he wants, but this other way instead. These opinions of mine I do believe are valid enough to bring to his attention to change, and I do. But...I'm killing his joy.
There really are some lessons in life that others can't learn for you. You can read it in a book until you're blue in the face, but you'll never grasp it, not really, until you live it. It's as if you need to be given a chance to do what you think you would never do. Until you have that real visceral choice, an experience that makes you truly question yourself, the learning doesn't really take root.
The overarching lesson for me in all this is a proper, or balanced, way of expressing myself. Not impressing my will upon others. The sun has enough energy to burn, but it can moderate it to warm. It's a tricky thing finding that balance between being a doormat and not expressing myself, and becoming a tyrant and lording over others. I think the thing I learned today is the importance of letting others be as they will be. It's their joy to experience and live as they please, regardless of what I feel about their form of joy.
An image that's always come to mind when I think about this concept are children in school. I imagine an 8th grader correcting a 3rd grader, frequently. While the 8th grader may be absolutely right in his teachings, the 3rd grader isn't learning, isn't enjoying being alive. Someone else is appropriating their joy of discovery from them. Besides, at some point the 3rd grader will become an 8th grader. The lessons will be learned, regardless of the road to get there.
The amount of corruption in this country, and the world, beggars
the imagination. I'm going through email and came across a link
describing the American College of Nutrition (ACN) wanting to merge
with a similar organization, the American Society for Nutrition
(ASN). ASN apparently manages the Smart Choice food labeling
system, and Fruit Loops got it. A food that's 41% sugar and made
with partially hydrogenated oils. Turns out ASN receives major
funding from the same companies who might receive the label. So ACN
wanting to merge with ASN is a bit fishy, and definitely doesn't
seem to be in the best interests of nutrition knowledge.
As a consumer it would be easy to just trust the label, Smart
Choice, and feel good about eating all that sugar. It's crazy how
often you have to delve into the truth of matters on your own and
not just take what's said at face value. As potentially tiring as I
might find having to verify everything myself, it honestly seems a
I was thinking about nature and how the body constantly wards
off bacteria, viruses, and other organisms that want to consume it.
It's only when you die that they win and you start to decompose.
The price of living is eternal vigilance, against bacteria et al.
Stars have to constantly generate enough energy to keep gravity
from collapsing them. Seems nothing really does exist in a vacuum.
You check your brain at the door and something else will happily
fill in for it.
The society we have really is of our own making. Too many of us
have become complacent in taking responsibility for it. So that
leaves a huge vacuum that a few, namely corporations, fill in for
I've been kind of intrigued by the major arcana of the tarot since reading about its relationship to the archetypical mind in the Law of One. Below is an image I've created to express what I know. Probably the biggest thing to note is the division between the mind, body, and spirit of 21 of the cards, or archetypes. Secondly the 7 classifications: matrix, potentiator, etc. So you have Matrix of the Mind, Transformation of the Body, etc. There are pairings that were expressed as useful for contemplation as well: matrix and potentiator, catalyst and experience, and transformation and great way. I've colored the cards to illustrate these pairings; the colors chosen were subjectively chosen by me for clarity in an image and were not expressed in the book. You'll notice the significators aren't paired with any archetype in their group, rather they were suggested to be seen in relation to The Choice, card 22.
Briefly the archetypical mind would be the blueprint of life. In terms closer to home how you learn or evolve. The matrix being all that is in potentiation. The potentiator that aspect that initiates. Catalyst being that which is initiated; creation or a situation. Experience, experience of the catalyst. The significator the most efficient use of the catalyst. Transformation seems to be the change brought about; learning. The great way I might say I see as bias gained, a path formed, as opposed to random movement.
You can choose to see yourself as a flag blown in the wind; you can also choose to see yourself as both the wind that blows and the flag that is blown.
This reality creation stuff is pretty interesting. This I say after sunning myself outside, feeling the wind and warm sun against me, watching a cat frolic and hunt down bugs. I'm going to be given the opportunity to help interview for a position we have on our development team this week. I see it as an honor to be chosen for this. It's something that I've always wondered how I would do at, and simultaneously something I've feared. Feared mainly for messing it up, being in a role that I've never been in before. It was interesting for me to note the differing ways of seeing this opportunity being in this sunny environment.
It's possible to see it as inevitable and without much meaning needing to be attached to it. Given the constant churn of developers on this team, due to a company policy of a set duration of time a contractor can work, I'm a senior developer and thus qualified to interview someone. Still, I see it as an honor since it isn't necessary that I was chosen, especially since full-timers usually do this. The same situation, two possible interpretations; a choice must be made. That, I believe, is the most important thing to note: choice. We always have it. Frequently, I suspect though, this realization isn't always apparent.
I have an opportunity to experience something that I've always wanted to experience. An inevitable situation given what I've described above, or the manifestation of a heart's desire? The thing about reality creation I've begun to notice is that it somewhat flies in the face of the scientific method. The observer is the observed. This isn't quite like saying a human is the eagle being observed. :) But rather finer forces. In the scientific experiment of the truth of reality creation the observed outcome is determined by the desires of the observer. If you're familiar with quantum physics on some level this will sound familiar. The issues become elevated beyond simply asking what is possible and onto what is desired.
This heart's desire I mention is a tricky thing itself. It becomes more important to acknowledge the totality of who you are in determining this thing called heart's desire. By totality I'm thinking of the division of consciousness colloquially termed consciousness and subconsciousness / unconsciousness. The amount of energy, or intention, directed at an outcome determines the outcome chosen. So if you've got some aspect of yourself that you're unaware of for the most part who knows what you'll create for yourself. Definitely puts knowing yourself among the more important tasks to accomplish. Much much more to learn for me.
You know, it occurred to me today I really don't have much idea of
what my spirit is. There's the idea that we have a mind, body, and soul;
I'll use the term spirit. It's fairly obvious what the body portion of
that trinity is. The mind portion too, fairly obvious, your
consciousness: intellect, feelings, emotions, intangible things. But the
spirit portion I have a much tougher time getting a grasp of. If the
body has its way of perceiving the world, the mind its own way, then the
spirit would have its own way as well. The best definition I've come
across of spirit describes it as a shuttle between us as an individual
and the whole.
It's kinda odd when I think about it now that it's
taken me this long to realize how much I don't know of the spirit, even
though it is a part of me as much as my mind and my body. I have to
imagine the miraculous things you read about in history are achieved via
the spirit. My imaginations of communicating with my higher self as
well. One thing I'm realizing I'll have to be careful of, should I
choose to explore more of my spirit, is to let it be what it is. That
is, don't approach it from a mind or body perspective. Sort of like how
the mind is not the brain, that's a body perspective.
Beliefs are a funny thing. Whatever the truth of them they have a very real affect on you. They guide your thoughts, in turn your actions; they're the blueprint of you in a very real sense.
So a couple of days ago I was at work talking with a friend and co-worker when he mentioned a conversation he had with a lady I have the hots for. We talk about her a lot but this particular day I was pissed and didn't want to hear it. (Side story: The previous day as I was walking in the hallway I saw her but she looked down to pretend she didn't see me. We've had some other pretend I don't see you moments in the past, from both of us, so it wasn't completely unexpected. But still, it hurt some to see her do that.) So, I was pissed when my friend was talking so exuberantly about her.
As I get more in-tune with myself as I age I'm starting to recognize patterns within myself, and one hit me as I was talking to my friend. It's a sinking feeling in my stomach, like even my throat is being pulled into a pit in my stomach. I notice it happens when I engage in a pattern that's self-destructive but yet one I feel I must force myself to take. Beliefs in action. This particular belief has taken a while to pin down but I've identified it for the most part. Whenever there's something that I want but I'm hesitant to reach for, if I experience any kind of hardship in an attempt to reach, then I adopt a stance that me or the other person would be better off if nothing happened.
One of the ways I use to work through things is to hold internal dialogue with myself. This day I imagined I was talking with me, my higher self. He, me, shared a different perspective on the situation, one from outside an incarnation. He mentioned how once this incarnation is over all I would be able to do is review it, not make any changes. He assured me that from the vantage point of a fuller view of the situation I would be amazed how easy it is to solve. By solve I mean choosing a different path from what I usually engage in. Right now I feel burdened by the accumulation of baggage, I feel I have to carry it. But I could just not. There's nothing forcing me to engage in behaviors that don't benefit me except my belief that I have to; oftentimes because I don't even realize I'm choosing. He also pointed out that instead of conducting a life review and wishing I had done something differently, what I really felt in my heart I would rather do, I actually can make changes now because I'm still living this life.
That's also when I realized what a great treasure it is to be alive. We can choose.
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