Landscape of Round Holes

Surreal Numbers

Returning to the topic of infinitesimal numbers, which is an example of a surreal number, here is what i have learned:

To create these 'surreal numbers' first you must define what a number is, mathematically.  Now this may come as a surprise to you, but numbers are fairly hard to define. This definition is just one of many, and it goes something like this:

A number is defined by two sets of numbers, where no member of the 'left' set is greater than or equal to any member of the 'right' set.

Math wise it will look like this:    x --> [X_L,X_R];   X_L ¬≥  X_R

(Since every number corresponds to two sets the L and the R are used to designate the two "X" sets from each other when not side by side.)

Now, at first you may have noticed that this definition is self-referential - it uses sets of "numbers" to define numbers, but this can be overcome by starting with an "empty" set of numbers.

So, the first "number", we shall call it a since we don't know what the number is yet, would be:

• a --> [ {  }_L,{  }_R ]

Does it fit the definition? It has two sets of numbers, although both sets are "empty". So are any numbers in the left set greater than or equal to any number in the right set? No, there are no numbers in the left set (greater than, equal, or otherwise).

Now we have a single number with which to define more numbers, they are:

• b' --> [ {  },{a} ]
• b'' --> [ {a},{  } ]
• b''' --> [ {a}, {a}]

Do they also fit the definition? The left set b' has no numbers, so there can be no numbers that are greater than or equal to a (the only number in the right set of b'), ergo, it fits the definition and is a number. Likewise, the a in the left set of b'' cannot be greater than or equal to any number in the right set of b'' because there are none.

At this point b''', as a number, cannot be determined, because there is no way of checking whether or not a is greater than, less than, or equal to a. It sounds funny, i know, but we have to define at least one relationship between numbers in order to define numbers themselves. It has only worked so far because of the "empty" set has no numbers, and we can compare something with nothing without relationship.

Do not fear, tomorrow i will define a relationship and we can continue with this. OK now you can fear. :)

P.S. Interesting to note, there were no actual numbers used in this post, like a "1" or a "2". It has all been letters and symbols

Not about nothing.

What's the opposite of nothing?

Anything.

Something.

Or everything.

Think about it.

Attention: Patients Update Required

Computers.

I have a definite love/hate relationship with them. They are just useful enough not to throw the frustrating things right out the window (is that a pun?). The case i have decided to pick on today are 'updates'. I hate updates. Just when you get used to your computer and all it's little foibles, along comes some update to make new ones. You know the ones: Internet browsers, active X controls, firewall protection, virus definitions, zip tools, audio codecs, spam filters, hardware drivers. Seems like half the time i want to do anything i can't because i don't have some kind of 'update'. Half of those times i just give up on what ever it is i wanted to do, because i know the process will take longer than i want to spend to do what ever it was i wanted to do in the first place, and thats if it goes smoothly.

Case in point, I decided to do a deep and thorough security scan of my computer today. The kind that takes a several hours of 'at the keyboard' work. In keeping with the spirit of the deep scan i wanted to update my virus definitions, which where out of date (see above reasoning) and sinse i was already committed to the time requirement...

I open my anti-virus software, and navigate to the update button, after clicking it, i get an error saying to reinstall the anti-virus software. What? They provide a link to a web site with more info, and apparently the updating portion of my security suite needed to be updated. ( oh, the irony!) Again, they provide a link to do just that, so i click it. The next screen, provided by the browser this time, tells me i can't view this page until i have updated my activeX controls, with, this must be my lucky day, another link to address this (that is a pun). No less than four activeX control updates later i am allowed to see the page to update my updater.

I update the updater, and it went smoothly and relitively quickly, can't remember if it required a restart or not though (i lost count -- read on). Then it was finally time to update the anti-virus software itself, this required a renewal fee, which i already knew and was prepared to pay, but did add to the whole 'chain of events' thing that i am going for here. Permission now payed for i update the anti-virus software, which half-way through informs me that i must re-run the updater when this one is finished. Which of course i did, after the required restart (man, i sure hope the 'restarter' doesn't need an update). I ran the updater two more times before it said all the updating was done, each needing it's own restart. Thankfully somewhere in the three updates the definitions where also updated. To recap, it took four updates to get to the update for the updater so that i could update my anti-virus software three times to update my virus difintions. Fuck me! I had better find Satan himself hiding out in my computer for all the trouble i'm going through.

But, it was finally done, and with no errors! But before you get to excited, i still have to update my anti-spyware , anti-spam, anti-adware, and last but not least, my firewall secruity. Then i can start the actual scanning. I'll let you know how it goes... next week... when i'm done. In a word, i'll give you an... update. :)