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Archive for the ‘Philosophy’ Category

God’s sticky fingers

Tuesday, May 12th, 2009

I’ve written on my old blog about the Google adsense dilemma, but I think it doesn’t apply during the first days of putting Adsense on a site as you need to click an ad once or twice just to convince yourself it’s working properly (not that Google actually pay you any money (if you’re me) for something ridiculous like an ad being clicked on). My choice of ad I did find genuinely intriguing, one linking to the magnificent sounding Cosmic Fingerprints website, and claiming it could prove to me that God exists using :

Тhe Atheist’s Riddle: So simple, any child can understand; so complex, no atheist can solve it.

Which sounds like fighting talk to me. I don’t generally get involved in debates like these – I know where I stand and if people believe in God I don’t really think they really should be swayed by things such as reason and proof as that really misses the point of religion. But this site, published by a guy called Perry Marshall (who knows a thing or two about search engine optimisation) annoyed me as it gives contact details (a forum) and invites you to let him know if you think you can prove him wrong… but these contact details are no longer valid. So essentially he’s presenting something as an ongoing debate he is still winning, when it is anything but. I wouldn’t mind so much, but he’s actively advertising his site!

I must’ve been in a very militant mood at the time as I decided to subscribe to his 5 part emailed proof of God’s existence (Essentially running as follows: Only minds can create codes. DNA is a code. Therefore a mind cretaed DNA, and that mind is God’s) simply in order to get an email address to respond to, and then replied with my counter argument. Which he hasn’t replied to, so I will post it here:

  1. A code can be produced by a human mind
  2. The human mind exists in the universe, and is made of the same stuff as anything else in the universe (albeit arranged in a very complicated manner)
  3. So there exist systems in the universe capable of creating a code
  4. DNA is a code
  5. So there could exist a system in the universe capable of making DNA
  6. The existence of DNA does not prove God exists

So there!

Here are a few other counter arguments I like, particularly the first one:

ps -  Week’s holiday in Riga, if you wondered why the extended silence.

Is stackoverflow a chaotic system

Friday, April 17th, 2009

As I believe I’ve mentioned once or twice, I have been reading Deep Simplicity by John Gribbin. At the same time I have become severely addicted to participating in the riot of discussion over at, the new, and hopefully, self-organised clutter free forum for programmers.

Part of what feeds this addiction is that sometimes you get loads of votes for a mediocre answer, and sometimes hardly any for a great answer, and it becomes a mission… a quest, if you will… to master the beast and always receive great feedback.

Luckily I’ve now managed to get my addiction under control, and it’s all thanks to Deep Simplicity. You see, there is order, where everything is predictable, and there is chaos, where nothing is predictable, and in between there is a thing called (though I don’t think this is quite the official term) self-organised non-equilibrium on the edge of chaos, which is where interesting patterns emerge; things like some regularity in how often ice ages occur, stock market crashes, earthquakes…  loudness of music! When events of a particular size will happen cannot be known, but roughly speaking the log of the frequency of the event is proportional to the log of its magnitude.

The important factors to create a system like this are the following:

  1. Positive & negative feedback mechanisms
  2. The existance of thresholds which, once the system/part of system crosses it, its state suddenly changes in a disproportionate way to the size of the movement across the threshold
  3. A constant soure of new energy (or whatever the equivalent might be. For physical systems it’s energy, but that could mean mass, radiation, motion…)

So the question I ask myself is this: Is Stack Overflow a system on the edge of chaos, where answers getting lots of votes will happen rarely, and getting few votes will happen often, but as to precisely which answer  will get which number of votes… well, that cannot be determined in advance. In particular, if you could have an objective measure of the quality of the answer, this would not indicate it will get a lot of votes; big up-votes just happen at a particular rate to whichever answers are around.

So what qualifies stack overflow as a nearly chaotic system (from the point of view of a user’s movements through the rankings, not individual questions, though the user is the sum of questions and answers):

  1. Positive & negative feedback mechanisms
    If one person votes an answer up it goes up the page, is more visible and gets more votes, and vice-versa. Also the reputation system adds to this.
  2. The existence of thresholds
    If a question gets enough votes it will appear in more places in the site. the same I think is true of answers (this is perhaps tenuous).
  3. A constant soure of new energy
    New users join all the time

I will hopefully not forget to see if I can put together a log plot of the number of users versus their reputation score.

Modern deism

Tuesday, April 14th, 2009

Earlier today I was reading an article on agnosticism with relation to God (itself a response to a better article on how Richard Dawkins, Christopher Hitchens and their ilk are annoyingly agressive in how they promote atheism/put down religiosity (incidentally, Hitchens’ book “God is not Great” has possible the worst written opening paragraph I have ever read – it just screams “I am a twat”).

One comment on the article linked to a site called modern deism, which tries to encourage people to believe in God without believing in religion, essentially making up their own God as they go along. Quite what the point of this is I don’t know. Also, they claim to be in tune with modern thought, incorporating science and all that, but their inspiration for believing in God is that:

The Deist looks at existence and infers that this wonderous thing could not have been an accident.

Which is pretty much the opposite of what a lot of modern science points towards.

Anyway, I was going to quote liberally and try and be funny, but failed at the funny side. But I will leave you with:

Therefore, Deists have a common belief in God based on Reason but the view into the nature of God varies among Deists as this nature is generally unknown to us at this time.

Logic 2.1.1

Tuesday, March 24th, 2009

Further discussion on the logic functions with my good friend Matt, specifically regarding what they could mean, has landed on the idea that a value of, say, 2 or 3 for the truth of a statement X could equate to “X is sooooo true”.

Bearing this in mind, Matt wasn’t happy with the shape of the graph of =>, and further thought has led to the following necessary conditions for a function =>(x,y) (I’ll call it f from now on for ease of typing) which works well with the notion that something can be soooo true:

  • f(x,1) –> 0.5 as x –> infinityx (so if something very true implies something else is true to a normal level, this means the implication is less a preserver of truth: more a diluter (though I set the asymptote as 0.5 as we thought it shouldn’t get closer to falsity than to truth)
  • f(x,0) < 0 for all x > 1 (if x gets more true but y is still not true, then teh implication is, again, less of a truth preserver, though this is debatable. Maybe eqality with zero would be more appropriate.)
  • f(1,y) –> infinity as y –> infinty (similar to the case where x varies and y = 1,  if 1 is immensely true despite x only being a little bit true then the implication is very strongly true)
  • f(0,y) = 1/y for all y > 1 (the thinking here being that if y contiinues to get more and more true, despite no change in x, then the link between y and x should accordingly be weakened)

logic 2.1

Monday, March 23rd, 2009

I have, as promised, found a better form for XOR:

  • XOR(x,y) = x + y -2xy

As I sit here chomping on a chicken wing, I can’t help but feel a touch of disappointment alongside the inevitable satisfaction at completing my mission. The previous solution – XOR(x.y) = (1-xy)(x + y) – was, I feel, more elegabt; the fact we were dealing with x/y symmetry, and that x and y could take only the values 1 and 0, seemed to almost leap out.

Talking of symmetry – I’ve just realised that I didn’t cover x => y, the only asymmetric elemental* logical operator.

So here, deduced by trial and error is the formula:

  • =>(x,y) = xy + 1 – x

I lied though. Because, of course, => is not as elemental as one would hope, so:

x => y <–> NOT (x AND NOT(y)) = NOT(x AND (1-y)) = NOT(x(1-y)) = 1-(x-xy) = xy +1 -x

Thus demonstrating the usefulness of being able to represent logical operators analytically.

Logic 2.0

Saturday, March 21st, 2009

Now, somebody has probably already done this, but I’ll throw in my twopenneth anyway.

Yesterday morning I woke feeling strangely alert, so decided to do some maths. Namely, finding analytical functions of the real numbers taht agree with the logical operators NOT, AND, OR and XOR on the values of 0 and 1, and here they are:

  • NOT(x) = 1-x
  • AND(x,y) = xy
  • OR(x,y) = 1-(x-1)(y-1)
  • XOR(x,y) = (1-xy)(x+y)

Now, the above begs a few questions

  1. Are they any use? Well, I think so. They can be combined and recombined to form an polynomial function LP: {1,0}^n —> {1,0} to represent any logical proposition, where n is the number of elementary propositions. So given the truth or falsity of all these propositions the truth or falsity of the compound statement can easily be deduced
  2. Are these the simplest analytical functions that agree with the logical operators on 1 and 0? Probably NOT, OR and AND are; they’re all quadratic or less. But XOR is a cubic expression, which is unexpected. I can’t help thinking a hyberbolic parabola – quadratic – with the relevant constants shoudl work. Will have a think. *edit – success!
  3. Can they be extended over the reals? Well, yes – they’re analytical! But a good question is ‘What is the real world interpretation of a function like this?’ Extending the factorial function over the reals has proved useful, but would extending logic to things being doubly true, trebly true, negatively true, make any sense? Search me. The functions above could withstand the insertion of a few square/cube roots here and there, thus making the graphs more linear, and maybe they would be more likely to lend themselves to a real world interpretation. But the shapes of the graphs for the non-rooted functions (and probably ones with roots taken) (see below) defy interpretation I think.
  4. What do these functions look like?