From a given point to draw a straight line touching a given circle.
Let TeX Embedding failed! be the given point and TeX Embedding failed! the given circle;
thus it is required to draw from the point TeX Embedding failed! a straight line touching the circle TeX Embedding failed!.
For let the centre TeX Embedding failed! of the circle be taken; [Prop 3.1]
let TeX Embedding failed! be joined, and with centre TeX Embedding failed! and distance TeX Embedding failed! let the circle TeX Embedding failed! be described;
from TeX Embedding failed! let TeX Embedding failed! be drawn at right angles to TeX Embedding failed!,
and let TeX Embedding failed!, TeX Embedding failed! be joined;
I say that TeX Embedding failed! has been drawn from the point TeX Embedding failed! trouching the circle TeX Embedding failed!.
For, since TeX Embedding failed! is the centre of the circles TeX Embedding failed!, TeX Embedding failed!,
TeX Embedding failed! is equal to TeX Embedding failed!, and TeX Embedding failed! to TeX Embedding failed!;
therefore the two sides TeX Embedding failed!, TeX Embedding failed! are equal to the two sides TeX Embedding failed!, TeX Embedding failed!:
and they contain a common angle, the angle at TeX Embedding failed!;
therefore the base TeX Embedding failed! is equal to the base TeX Embedding failed!,
and the triangle TeX Embedding failed! is equal to the triangle TeX Embedding failed!,
and the remaining angles to the remaining angles; [Prop 1.4]
therefore the angle TeX Embedding failed! is equal to the angle TeX Embedding failed!.
But the angle TeX Embedding failed! is right;
therefore the angle TeX Embedding failed! is also right.
Now TeX Embedding failed! is a radius;
and the straight line drawn at right angles to the diameter of a circle, from its extremity, touches the circle; [Prop 3.16. Porism]
therefore TeX Embedding failed! touches the circle TeX Embedding failed!.
Therefore from teh given point TeX Embedding failed! the straight line TeX Embedding failed! has been drawn touching the circle TeX Embedding failed!.
Let TeX Embedding failed! be a circle about TeX Embedding failed! as centre and TeX Embedding failed! as diameter;
I say that the straight line drawn from TeX Embedding failed! at right angles to TeX Embedding failed! from its extremity will fall outside the circle.
For suppose it does not, but, if possible, let if fall within as TeX Embedding failed! and let TeX Embedding failed! be joined.
Since TeX Embedding failed! is equal to TeX Embedding failed!,
the angle TeX Embedding failed! is also equal to the angle TeX Embedding failed! [Prop 1.5]
But the angle TeX Embedding failed! is right;
therefore the angle TeX Embedding failed! is also right:
thus, in the triangle TeX Embedding failed!, the two angles TeX Embedding failed!, TeX Embedding failed! are equal to two right angles: which is impossible. [Prop 1.17]
Therefore the straight line drawn from the point TeX Embedding failed! at right angles to TeX Embedding failed! will not fall within the circle.
Similarly we can prove that neither will it fall on the circumference;
therefore it will fall outside.
Let it fall as TeX Embedding failed!.
I say next that into the space between the straight line TeX Embedding failed! and the circumference TeX Embedding failed! another straight line cannot be interposed.
For, if possible, let another straight line be so interposed, as TeX Embedding failed!, and let TeX Embedding failed! be drawn from the point TeX Embedding failed! per pendicular to TeX Embedding failed!.
Then, since the angle TeX Embedding failed! is right,
and the angle TeX Embedding failed! is less than a right angle,
TeX Embedding failed! is greater than TeX Embedding failed!. [Prop 1.19]
But TeX Embedding failed! is equal to TeX Embedding failed!;
therefore TeX Embedding failed! is greater than TeX Embedding failed!, the less to the greater : which is impossible.
Therefore another straight line cannot be interposed into the space between the straight line and the circumference.
I say further that the angle of the semicircle contained by the straight line TeX Embedding failed! and the circumference TeX Embedding failed! is greater than any acute rectilineal angle,
and the remaining angle contained by the circumference TeX Embedding failed! and the straight line TeX Embedding failed! is less than any acute rectilineal angle.
For, if there is any rectilineal angle greater than the angle contained by the straight line TeX Embedding failed! and the circumference TeX Embedding failed!, and any rectilineal angle less than the angle contained by the circumference TeX Embedding failed! and the straight line TeX Embedding failed!, then into the space between the circumference and the straight line TeX Embedding failed! a striaght line will be interposed such as will make an angle contained by straight lines which is greater than the angle contained by the straight line TeX Embedding failed! and the circumference TeX Embedding failed!, and another angle contained by straight lines which is less than the angle contained by the circumference TeX Embedding failed! and the straight line TeX Embedding failed!.
But such a straight line cannot eb interposed;
therefore there will not be any acute angle contained by straight lines which is greater than the angle contained by the straight line TeX Embedding failed! and the circumference TeX Embedding failed!, nor yet any acute angle contained by straight lines which is less than the angle contained by the circumference TeX Embedding failed! and the straight line TeX Embedding failed!. --
TeX Embedding failed!. From this it is manifest that the straight line drawn at right angles to the diameter of a circle from its extremity touches the circle.
It may be considered slightly heretical of me to say so, given the media hype and government drives surrounding exercise promotion, but I am of the belief that exercise is a waste of time.
It really is. The only reason that artificial exercise is a necessity, is because our bodies have evolved under the pressure of exercise being a requisite survival skill. This means that there was never a selection pressure to optimize the body for situations in which exercise wasn't the norm, and therefore not surprisingly the body goes wrong in absence of exercise. If you don't exercise your body enough, it is the evolutionary equivalent of putting a niche species into a different environment in which it is less successful. It's no surprise then that all kinds of problems ensue.
I wish the damned thing was just maintain itself. The evolution of a self-maintaining body may have arisen if we had of had lifestyles that required an equal measure of long periods of intense activity followed by long periods of non-activity. Then selection pressure might have favoured those whose bodies maintained themselves better during the inactive periods, especially so if there happened to be some fatal danger present in the active periods which would require a high level of physical fitness to endure. Alas this didn't happen, hence our bodies have not really evolved to cope with long periods of inactivity.
Obesity, heart disorder, diabetes, depression, and lethargy, among others, can all be caused by a lack of exercise. So to borrow an expression from Chistopher Hitchins, for the sake of any biblical fanatics reading, Some Design!
Every benefit of exercise: the endorphins, getting fresh air, being outside, etc, are all simply norms that the body actually expects. This is the environment in which the majority of our evolution was accomplished. If you want to feel normal, do a lot of exercise.
So whilst it may be a bullshit that we have to do it, the upside is it will make you feel better than if you don't do it. I don't want to be overly negative about it, there isn't enough time in life for that kind of thinking.
Speaking of thinking, I think that future robotic humanoids will not have our body problems. You know, sometimes I wonder to myself that the body might be better equipped if it had a better GUI:
Except of course it wouldn't look as shit. I think the following features would be useful:
Well, I'm sure you can think of better and more interesting ways the body could be augmented with useful features. Note that I'd want these evolved into the brain de-facto, not some cheap addons from Intel or whatever.
Just wrote to my MP regarding Gary McKinnon:
Dear Richard Benyon,
I write from Newbury, West Berkshire.
I am writing to you regarding the conduct of our nation in the case of Mr Gary McKinnon. Gary is accused of "hacking" into various US computer systems. Regardless of the extent to which he is guilty of these crimes, all the accusations are with reference to actions taken on our soil, within the jurisdiction of our country. Crimes committed or suspected of being committed within our jurisdiction, should likewise be tried within our jurisdiction, by our judicial system. The US request to have Gary extradited, should therefore be met with a flat refusal, on the grounds that the actions he is accused of, were committed here.
I am afraid that our country has given itself over in this manner to acting as a sergeant under the US, in obeying its every request. This is a threat to our sovereignty and integrity, and must be resisted.
Please then, I urge you to sign Early Day Motion 2388, with regard to this case, of which more information can be found here:
I think I have been clear enough in the email. But to reiterate, I don't care if he is guilty or not, I simply object to extraditing any of our citizens for actions taken within our borders. I suppose one could argue that computer hacking transcends borders, but I would argue, that the physical act of hacking occured in the UK and thus should be tried in the UK.
This is my warning that there may be patches of downtime with this website, as I am a newbie admin.
The server was running dog slow the past day, so don't vote on that poll just yet.
The reason it was so slow was that I was running 32 php-cgi processes! Like I knew that was a lot, hehe. So my memory was overloaded and everything was crashing.
I sorted that out about 30 mintues ago, but then I rebooted to find my linode wouldn't boot! oh shit. Luckily it was just stuck booting, which I was able to discover by using the console that linode provides on the admin website for emergency purposes. There were lots of error messages about the file system being read only.
The problem was ACL: Access Control Lists, a fine grained method to control security of files. I had enabled it yesterday without realizing that my default kernel doesn't support it. It has to be loaded after boot. So upon boot my /etc/fstab was trying to mount the drive with ACL enabled which fucked things up.
Fortunately the fix was easy, I just removed the acl option from /etc/fstab and rebooted, and then of course remounted the partition enabling acl after boot. I've now added this post-boot remount to /etc/rc.local so hopefully it should do it automatically next time. Phew! I wipe my brow in pantomime fashion.
Things are going well. I installed postfix, courier, some spam filters, and squirrelmail today. So now my email is back up and running. Still to do is to migrate ashleyinjapan, which is a wordpress based website, and to migrate the email accounts I setup for my family.
I have a bit of a computer high. There is something about working with command lines and text files all day. You know, computers are funny, programming and stuff is regarded as complicated work, but it is so addictive and fun. Sure its frustrating sometimes, but it is nethertheless so compelling and absorbing it sometimes feels like one can work on it almost indefatigably.
I used to think, oh programming and computers are so easy, and take it all for granted. What I realize now is that us geeks find it easy but other people don't find it easy. I didn't really learn this until I tried to do things which I wasn't very good at, and then I saw how people differ. I'm glad that my "special skill" so to speak is in computers.
Well I finally finished migrating this website to the linode. It didn't take me all this time since my announcement, its just I only found the time to do it this weekend. It has taken perhaps one day to do everything.
Yes, what a nice poor quality webcam shot.
Word of advice. When you setup your own server, don't decide that it might be a good idea to use access control lists to set the permissions for each file that needs to writable by the webserver, just use group permissions. If you do decide to use ACLs you will have some headaches. For one thing editing files under vim destroys the ACL each time, and for another, any archiving you do will have to be done with STAR.
Despite this, almost everything seems to be working. DruTeX math rendering is now fixed TeX Embedding failed!.
Gallery2 is still working, after upgrading it and sorting out its file permissions.
The only thing that doesn't work is image uploading via the WYSIWYG editor CKEditor that I use for editing blog posts. This is pretty annoying obviously. It appears to be some file permissions problem due to the before mentioned dumb decision to use ACLs. I'll solve it at some point, or perhaps just ditch the ACLs all together.
The website should be a lot faster now since I'm using Lighttpd and have a proper virtual server at linode.
I will try and play with the performance options over the coming weeks.
In case you are interested, this is the process I had to go through to setup the webserver:
I think the easiest thing in the world would be to make the webserver run under the same user that the content belongs to, then everything would work without any fucking about. The only advantage to not doing this, that I can see, is that it allows more control over which content the webserver can change. But since drupal accesses the mysql database directly via the webserver, which is where most of the content is stored, this actually seems pointless in retrospect... Any thoughts?
... I wrote this whilst flying to Las Vegas a couple of weeks ago ...
I'm on a plane, not with any snakes thankfully. Those damn snakes.
I ended up going to Gatwick early, last night in fact. My reasoning for this, was the precendent set a couple of weeks ago when, due to the weather induced traffic chaos, it took me 5 hours to travel 32 miles.
Consequently I ventured the trip to Gatwick early, so as to protect myself from such a recurrance, given that the possibility of such an occurance was fighting for prominence in my growing list of anxieties.
I stayed in a place called "The Aintree", which was a bed and breakfast operated by a woman of plain but kind character and middling age. And by middling age I mean perhaps 40 or 50.
The Aintree http://www.aintreehouse.com/ was a satisfactory stay. Albeit a little expensive (£45).
I left for Gatwick after a hearty ye olde English Breakfast at approximately 9AM today and arrived at Gatwick Airport a prompt 10 minutes later.
My flight was scheduled to leave at 11:20 but it was delayed until 13:45. It was later delayed further until about 15:00 due to obscene security measures, and then we sat on the runway for aeons until presently whereupon we are in the air and it is 16:53. We have been in the air for about 15 minutes.
At the airport I was subject to two full body searches, and my trainers were inspected twice. Every passenger flying to Las Vegas had to undergo a full body search upon entering the "gate waiting area" in addition to the usual searches and metal detector scans that occur upon departure lounge entry. They also perfomed full hand-baggage bag searches on everyone.
Isn't it wierd how terrorists have such a hard-on for Aeroplanes? You'd think, given the relative lack of security on other forms of transport, that they might appeal more as targets. I guess not. Well not yet anyway.
Terrorists will continue to be generated and there will undoubtably be more attacks. If it isn't Aeroplanes it will be something else.
After the christmas bomber, they have decided to rush through the implementation of the naked scanners. If you haven't heard, there exist some microwave scanners which almost reach the pervert superhero's dream of being able to see through clothes. They are sufficiently advanced as to be able to show up a meat and two veg or a cameltoe.
But of course liberty must be sacrificed for security.
Yes, it was Benjamin Franklin who said "They who can give up essential liberty to obtain a little temporary safety, deserve neither liberty nor safety."
But to borrow from Noam Chomsky. We are only supposed to revere great people, not read them. Stupid isn't it.
Sure, I don't want to get blown up, but I'm not scared of it. The risk is so low that it isn't worth my time. Besides, I have plenty of other things to worry about that take precendence. I am of course speaking with some tongue in cheek re my last sentence, for worry is a burden that likes to be encouraged. Call it a virus of the mind, like many others, it persists because it encourages me to fuel it, and I abide.
On the plane, there are approximately 100 seats unoccupied. Lucky us. I have two seats to myself right now. I moved from my original seat. I tried to move before we took off, but one of the cabin ladies told me to go back because of "weight distribution". This was of course a sham reason, for my new position is better from the perspective of weight distribution, I can see this. And besides, I formerly chose my seat prior to flying, online. And I expect many others did. And so unless we all got lucky and chose a perfect distribution of weight, I find the excuse highly unlikely. If it were really "weight distribution", then surely we would have all been assigned new seats once it transpired that 100 seats had been freed up. I said "weight distribution!", and then she said "oh well the pilot knows where everyone is sitting". Fuck knows what the real reason for not letting me move before take-off was. That is, if there was any reason at all. On the way back the weight distribution issue came up, but this time they actually moved people around. Presumably then it is a real issue. But the first time, I'm sure it was a lie since they moved nobody, and like I said, my new position was more even.
In the "gate waiting area" before we left I heard a bizarre explanation of "aerodynamic theory" in the words of the protagonist. It went something like this:
"hey bozza, do you know anything about aerodynamic theory, you know, how a plane flies?"
"nah jobba, nuffink."
Jobba went off and got a pen and paper and came back to the window in the waiting area where I was sitting.
"Well bozza, you see the wing yeah, well yeah air particles. <pause> Air particles. <pause> The wing yeah it splits, it splits em, it splits the air particles in half. And then they join up on the other side. And 'cause this curve on top is longer, and its shorter under, then well the air particles, they travel faster underneath and this makes them lighter and so the wing lifts up".
I was tempted to correct him, but he looked like the kind of guy who wouldn't appreciate such a lesson.
This reminds me of something. Some people I feel, like to boast about what they know, and bully and belittle those that know less. You know the sort. Well I want to tell you that I am not one of those people. I just thought it was a funny explanation of flight worth sharing. And I think he thought he was genuinely spreading truth. At least he was appealing to reason to backup his claims, which is a good start.
I was reading a book from a friend lately called "What are you optimistic about?". It is a collection of short one or two page entries from eminent scientists and philosophers regarding what they are each optimistic about.
It is a good an uplifting read. I've been too negative lately, to worried about the world and its seemingly dead-end direction. But I was seeing things from a biased perspective.
The world is pretty fantastic actually, you just have to see it.
One thing I have picked up on, when reading this book, is that many of these eminent scientists think the same way that I do. I should point out, that I use the word eminent, only to indicate that they didn't just pick a bunch of criminals off the street to provide entries. Of course, eminence is as Fenyman said "epilettes", a badge of honor bestowed by someone else to indicate worth. I think normal people are just as valuable, but its good to have a strong source to feed to those who value "eminence" heavily, when in a debate.
Well anyway. What I realized is that many of these people think like I do. Not exactly of course, but what I mean is, they value reason. They value reason and they don't like lies and evidence-absent claims. Many of the entries are about the death of God and the rise of reason, and this is the kind of stuff I love.
In reading that book, I came to the realization that it is people like us, the reasoners, the thinkers, that have driven civilization forward. And who continue to do so.
As the value of reason continues to grow, the dogmatists and religious, will find that they can ineffectively insulate their victims from the world that surrounds them. The brainwashing that they try and force upon their offspring will take less and less. So we don't have to do anything except promote science and reason, and the religious will simply lose purchase on the rockface of rationality that we are painstakingly shaping. Hopefully they will one day simply fall away forever.
So I am optimistic that the future is bright for society, and that reason is the means by which it will be acheived. Technology will save us from ourselves, and reason will free our minds. This inspires me to keep working on improving technology and advancing science.
Science is too often represented as a cold and heartless machine and the truth is regarded as unforgiving and impersonal.
Yet it is truth and beauty that hit my spiritual nail on the head.
In physics there exist several different types of field, for example: gravitational field, electromagnetic field, and the more recent quantum field.
I believe it to be true that some people are generators of a forth type of field: the stupidity field.
This sounds rude, and perhaps I am rude. But some people I cannot stand to be around because they seem to radiate stupidity.
When I spend a long time around such a person, they start to get inside my head. It is if their stupid and brutish way of looking at the world starts to jostle for attention with mine by the might of its sheer and bloated ugliness.
It sounds crazy, but I am a little crazy when it comes to psychological matters, but it feels like their views and idiocy pollute and corrupt my mind. Does anyone else get this? Do you?
I hate this. I need to learn to concentrate and block out external influence better.