From the Glacier
Philosophy, Science, Mathematics and whatever else


The Feast of Corpus Christi, 2008, John and Andrew:


it lies fallow


Happy birthday to me…


Time, motion and change. Aristotle calls time the number of motion. Whilst reading “The Fabric of the Cosmos” by Brian Greene, I stumbled upon a quote:
‘No one has as yet found the definitive, fundamental definition of time, but, undoubtledly, part of time’s role in the makeup of the cosmos is that it is the bookkeeper of change.’

Interesting. . .


Okay, I know when you add relativity to quantum mechanics you get all sorts of ugly infinities. But I was thinking about probability waves yesterday, wondering what they were, and I discovered a little thought experiment. Considering only special relativity, we can take the Lorentz transformations and apply them to a frame of reference. Just to make the mathematics easier, suppose we set the v=.8c, t=1 year and x=1 light-year. This makes all of our numbers conveniently cancel. So supposing I am stationary and the object is moving away from me with the aforementioned numbers. What happens to the distance and time? Well, the xof 1 light-year becomes 1/3 of a light-year, a contraction of 67%. The time, 1 year, becomes 13/15 of a year, a contraction (slowing down?) of roughly 13%. Granted, .8c is astronomically (pardon the pun) fast, but the numbers are easy to calculate for yourself.

Suppose we apply this to the moving photon. As we approach the speed of light, we see that the contraction of distance approaches 100%. Similarly, we see the time dilation approach 100%, that is every instant in time appears locked in the now. So what would we “see” if we were sitting on the photon? Any extension would be contracted to no extension. All time would be present. Wouldn’t, then, all the universe (from the point of view of our photon-easy-chair) past, present, “near”, “far”, all be “here”?


I was thinking about quantum mechanics again. In the standard pop-science book the author usually asks the reader to visualize a flat surface with different heights of waves on them. These waves, unlike water waves which show higher points of energy, for example, actually show in this visualization, the differing probabilities of a particle being found at a different point in space. So when they say that light going through two slits (the standard interference pattern we’ve all seen time and time again) the light and dark patterns represent different places the photon particles land. The reinforcement – “constructive interference” is an increased probability. The dark patterns, destructive interference. But each photon taken in and  of itself, could land on any spots, it is just the averaged out probability of all of them that creates this pattern.

But what kind of waves are probability waves? Unlike water or sound or sports arena waves they do not require a medium. So in this respect they seem to be like electro-magnetic waves. But (due in large part to Bell’s Theorem)  probability waves appear to act in a non-local manner, that is, they propagate instantaneously to all parts of the universe, instead of propagating at the speed of light. So unlike electro-magnetic waves, which are the basis for special relativity, probability waves do not follow with the rules of locality as laid down by Einstein. How then do they (the cognosciendi) maintain these results? Simple. Probability waves are not things, not matter, not substance. Then no ‘thing’ is moving at superluminal speeds.

Where does that leave us? We are familiar with the high school science texts with pictures of the two-slit experiment linked above. But yet, the waves can’t actually be there. So what, exactly, is a probability wave? Do we answer Einstein’s famous quote with: yes, God does play dice?


So, after reading all the b.s. on the internet from last Saturday, the “luckiest” day ever, now we get the b.s. about Friday the thirteenth. Again, it all comes down to how you choose to frame your times and dates. As it stands with the Gregorian calendar, there is a slightly greater incidence of the thirteenth of the month falling on a Friday (14.333…% for Friday the 13th versus 14.25% for Thursday or Saturday the 13th) within any four-hundred year cycle. This is evident that all days (named) cannot have the same days (numbered) probability, because the year is not exactly 52 weeks long. There’s always at least one left over day. So it really strikes me odd that the greatest coincidence of days has bad luck attributed to it. Does this mean that people believe that bad luck is more prevalent? Statistically, it is more common. What a doom and gloom way of looking at the cosmos.

But superstitions are idiotic. Why don’t they call the thirteenth floor of a building the thirteenth floor? Why call it the fourteenth? Just because you call it something else doesn’t change the ordinal numbering.

Well, I’m almost through with work today. I would say that the statistical probability of me cutting myself at work is probably, 1.82:1, that is, I cut myself on an average of 10 times in five and a half days. I have not, however cut myself today (though twice yesterday). Does that make Friday the 13th lucky for me?


I’m sure everybody by now has noticed today’s date. And you know? It pisses me off. All of the enlightened, scientific, technologically advanced, liberal-minded and socially advanced people in this country are no better than prehistoric monkey-men leaping around a fire with sticks (shades of 2001). I’m sure you realized that there is a record number of nuptuals scheduled for today. Why? To take advantage of the “lucky” date. I wonder how many near term pregnant women are getting induced today so that their offspring may have the “lucky” birthday? Horoscopes abound, I even saw an article today on why the number seven is lucky for love. How can a number be lucky for anything? Just because we use a particular convention for a particular number system for particular days (probably to make tax collection easier) doesn’t mean that there is som corresponding reality behind it. What if the Gregorian reform had not taken effect? Then 7-7-7 would have been (since we were orginally an English province) eleven days ago. Does that mean people who married eleven days ago are lucky, but only in a Julian way? And for 170 years Britan and Catholic Europe had different calendars. So would it have been a lucky day for one and not the other? Or for both at different times?

It reminds me of a number question (as do most things). Certain numbers are interesting, others are not. Two is interesting because it is the only even prime. Three is interesting because it is the first odd prime, and so on and so forth. Well then, what is the first uninteresting number? Well, that number would be interesting because it is the least uninteresting number. And so on. Therefore there is no uninteresting number. In the same way every date (with some computation) can be construed in any way. For example, my oldest was born on 10-10-01. Taken in binary, that equals 41. 41 is the 13th prime number, and everybody knows that 13 is unlucky. Thusly, is he doomed to his fate.

What a crock of shit.


Suppose you were still in school and your teacher told you on Friday that you had a pop quiz coming the next week. Now if you were smart, you’d ask her when the quiz was. She’d reply, of course, that if you know when a pop quiz is, it ceases to be a pop quiz. Then you could argue, that it couldn’t be on Friday the next week, because if it were the last day of the week then it wouldn’t be a pop quiz. So if Friday is ruled out, then we could also rule out Thursday, because since we know it can’t be Friday, then by the time Thursday rolls around it can’t be on Thursday either. That leaves three days left, Since we know it can’t be on Thursday or Friday, then it can’t be on Wednesday either, for the same reason. Thus goes Tuesday and Monday by the wayside also, so you could correctly reason, with your teacher, that there cannot be a pop quiz.



I was thinking about orthogonal vector spaces today. (why? who knows) Anyway, from any three vectors we can construct an orthogonal vector space (a right angled vector space if we are using unit vectors, called orthonormal, whatever). This is basically akin to saying we can take three vectors and construct a three-dimensional Cartesian Plane. So I was looking out at work today, taking three distinct moving objects (or two and the direction I was looking in as a third vector) and thinking about constructing spaces based off of these. It is kind of interesting, because we can create a frame of reference out of just about anything. Once my thought experiment lead to the creation of one vector space, I could take all the other motions at work and relate them back to the others. So separating mathematics from causality, I could understand the motion of person A, say, and understand it as linearly dependant on the space I just created. Then making the jump (mentally) from math to reality, I could think about as person as a marionette, controlled by motions of completely unrelated things. Sure, it all falls apart once the person deviates from straight line motion, but if you think about it, most people walk in a pretty straight line. And once they change direction, you can just make that a new linearly dependant vector and let the person keep their puppet status.

Needless to say, I was bored this afternoon at work.