Andrew D. Anderson » Blog » Philosophy

When I was about ten, visiting my mother for the summer in Bullhead City, AZ, I met a man by the name of Mike Anderson. He seemed to me to be rather intelligent, was undoubtedly quite an interesting fellow, and fueled my interest in a number of things that occupied my time throughout that summer and beyond. Most of the things he got me thinking about were “paranormal” – things like telekinesis, out-of-body experiences, and telepathy. In fact, I’m still interested in those things to a certain degree, as they appeal to my desire for an extraordinary existence, but I haven’t spent much time mulling them over lately. Instead, I’ve been thinking about discreet mathematics, which I know very little about, continuity, and the concept of infinity…

This goes back to Mike, because one of the tidbits he once left me to mull over was: “light is like a river, and nothing within the river can go faster than the river goes” – of course, he was trying to explain to a ten-year-old that the speed of light is a kind of universal speed-limit. It sounded neat, I didn’t really fully buy it then, and I’m still not sure if I do now. However, recently, I’ve been having the oddest thoughts about light-speed, midpoint paradoxes, and discreet mathematics. I’m basically under-qualified for discourse in all of the subjects, but let’s bundle them up for a bit and draw out what’s been bothering me.

The midpoint theorem is simple enough, to get from point A to point B on a continuous function you must pass through the points on the function between A and B. There are more rigorous definitions available, but that one should do for now, I hope. So, you walk in a straight line from point A to point B, and you must pass through the midpoint C. The paradox arises that you can never get to point B. There is always a point half-way between wherever you happen to be on the line and where you want to go; you must always get halfway before you can get where you want. You can always get to the midpoint, but you can never get to the end.

Now, here’s the catch, or so I think… for the paradox to hold, there must be a midpoint at every one of an infinite number of divisions. I do not believe that can happen. I’m highly suspicious of attempting to apply the conceptualization of infinity to the actual world. (Calculus is nifty and useful, right, I know… and I don’t think that I take issue with the use of infinity in that sense… as a symbol, or a designator of a mathematical process…) I’m thinking that the world does not have the kind of domain that permits of infinite divisions.

Naturally, things appear to have bounds… movement is bounded by the speed of light, the physical dimensions of objects by the size of atoms (or components thereof)… so that at some point it makes no sense to talk about dividing a step along a natural function. Maybe everything moves in discreet steps, with the number of possible divisions bound by the speed of light. When you try to divide time itself into a segment smaller than light can travel, maybe that just doesn’t make any sense… perhaps it’s an impossibility… and if it is – then maybe the paradox is misleading about the way the world is.

More than that, maybe the idea of infinity is misleading about the way the world is. Maybe the idea of continuity as applicable to the natural world is nothing more than a pleasantry…(though, would it make any practical difference if we changed our way of thinking about the number of possible midpoints on our walk  from our front door to the mailbox?) If we can’t divide time into infinity, then I don’t think we can divide anything else into infinity. It’s like time is the river, and everything that can happen can only happen as fast as time will permit.

Using Mike’s analogy: the speed of time can only bound by the speed of light (because, mustn’t time itself be in the river… or could it be the river?) – and then that’s our actual continuity stopper. We’re not moving continually, we’re taking a bunch of really, really small steps. Really small, but not infinitely so.

What happens at 299,792,459 meters per second? Nothing…? And light’s speed it constant… so we know where it must be at each time between any A and B. Take that with the limited dimensions of the light particle itself… and you have all the bounds you need to prevent the infinite division, or not? We can’t divide to any point that would make that little light particle move faster than it can move. Dammit, is time bound or not? I’m regressing into confusion…

What do yo think? If you’ve read something somewhere that would help me think about the issue further, or have personal insight into what I’m confusing myself over, then please leave a comment and let me know.

My ideal government would be decentralized. The national government would be tiny, maintaining a national military and acting as a mediator between smaller governments. Local governments would hold a great deal of power and local citizens would control the means of production. There would be many powerful small governments, but no centralized big government. No big corporations.

The people would be taxed using a flat sales tax for necessary government services, but extra projects would be funded by inflation-indexed rate-capped government bonds. This way debt would be more fine-tuned by individual communities – and the nation would have less chance of overspending (especially on a national level).

Because communities would own patents collectively (granted by the national government), to foster innovation and productivity, large one-time cash awards and honors should be given to innovators. Say 10x the median income. This would ensure people were still excited about innovating, but prevent multi-billion dollar entities, groups, or people from concentrating power. Because local governments and people would benefit from innovators, they would be highly sought after. The local governments would set wages accordingly to keep and attract promising people. This would ensure that mediocrity didn’t run rampant.

Everyone would own arms, and participate in government/community at some level (even if it was just picking up trash in the park). This would make people feel connected with their community, and likely lead to more voluntary government involvement. Decisions at the local level would be made via direct democracy. State and national decisions would be made via representations. The overarching system would be a republic.

Governments would not be able to turn people away, but they could have policies in place to provide very low wages to new members of the community. Children would also become new members of the community when they were able to vote (which should require some type of national test, rather than an age requirement). This should lead to relatively normalized living conditions, and starting wages would not go too low (to deter new members) if people knew it would also affect their children.

I think that under a system like this, people would be guaranteed basic wages, but innovation would still be highly prized. Communities would become meaningful and cohesive, and people would not be making as many decisions while being removed from the effects of those decisions. Power would be with the people – political and economic power, both.

Whenever we start drawing parallels between men and computing machines we are bound to notice a particular incongruence rather quickly. Namely, men are apparently more indivisible than machines. That is to say, whereas we can talk of a computer requiring some hardware and some software to function, a man cannot be so easily disunited. A man has a brain that we may be tempted to associate with a processor and even memory (hardware), but it is not clear what part of a man we would want to label software. If we point to DNA or RNA, we do not ameliorate our difficulties. For one thing, that “software” creates its own hardware so that it is unintelligible to talk about a man without genetic code. There cannot be a human with “software” but no “hardware”. Of course, on machines today there certainly can be.

I’m not sure that this makes talking about artificial intelligence more difficult, but it may confuse the picture if not mentioned at the onset of a discussion. It can make the term “computer” somewhat ambiguous to the modern mind – and the object of artificial intelligence potentially elusive. If we inspect the hardware of a machine apart from the software, say, powered off – there would be very little of interest going on. If we took the software apart from the hardware, say, printed out – I think we’d have a hard time finding signs of intelligence then too. Only when the software is coupled with the hardware do interesting things become possible. Even when software can be embedded into hardware, it is easy for the concepts to admit separation. This may simply be due to the familiar organization of modern computers, but it may also be indicative of something more interesting – we should at least keep it in the back of our minds.

For now, at least to start, when discussing computers in relation to intelligence, it seems clear to me that we would do well to always discuss them as a bundle of software and hardware to avoid confusion. Despite the fact that one may install some “intelligent” program along many other programs, every program requires hardware to run. It is all too easy to think of the program itself as the sole cause of certain behavior – it should not be forgotten that the hardware is no less important in manifesting that behavior. So we are on the same page, in all that follows, unless I specify otherwise, when I talk of computers or computing machines, I am referring to a hardware-software couple. I am regarding the machine then, in that sense, as indivisible as a man.

This is a way of thinking that comes up occasionally in support of the existence of god. Really, I have more issues with the reasoning than I do with the conclusion. Believe what you will, but please don’t offer up chimeras as cornerstones of that belief. I’m not saying all ideas must be grounded in science, I don’t think that at all, but there mustn’t be all this slight of hand to make an explanation convincing. What follows are a few of my own problems with the “improbability of it all”.

So, the reasoning goes, for every atom to be directed just so, for the temperatures, distances, and elements all to be just as they are in order to support life – the odds of that are mind-numbingly low – god must have intervened to get life going. Further, it is sometimes added, conditions to sustain this fragile state are improbable in their own right. Praise the lord, for making this system!

I’ll start from the last statement and work my way back. Ridiculous. I think we can get rid of the sustenance part all together. We’re in a system that has safeguards built in – we’ve got more-or-less predictable orbits, an atmosphere, a sun that doesn’t move much, and energy that doesn’t just disappear whimsically. The system itself appears to be in a reasonably steady state (at least locally or practically). Most people would agree that seems reasonable. We act on the principle all the time, we constantly rely on a predictable system that is bound by some laws to act as it always has before. (Even if we have little reason to do so, we do rely on that.) Creating a system that’s self-perpetuating might be more improbable than creating one that isn’t, but lets assume that’s what we’ve got. Then we don’t have to deal with the probability of existence second by second, we just account for the potentially increased improbability in the original system itself. Now, we’ve got an even more highly improbable system that basically acts like it doesn’t have many options at all (that it’s law based).

Right, so in making now easier to explain by appeal to yesterday, we’ve made day one more improbable. That’s alright. All kinds of thing are improbable, but reality trumps statistics. You might double-check your numbers upon winning the lottery, you might exclaim “this isn’t happening” because it is so very unlikely, but if it is… well, then it is. Our system looks like that, it looks like it is happening. We rely on it happening systematically, and it looks like it does. So set down your numbers and go for a walk.

Of course, that might not convince you. Fair enough. It’s much more improbable, after all, than winning the lottery. It’s like winning the lottery every day. (Again, if you did, you did… but I see the concern while you didn’t). So what are you saying? That you don’t think this system actually happened on its own. You crunch your numbers, gaze at the astronomically large negative exponent and disregard the sand under your feet. As if the god idea has better odds. Well, I’m a bit short on words for you here. If you’re using math to back up your line of thought, mustn’t you provide two sets of numbers? What calculations can you give for the god claim? What’s more, is that you’re acting like you think the system is self sustaining (or possibly god intervenes every nano-second), at any rate, you’re not constantly double-checking the math. At least we agree on that part. It appears self-sustaining. Come back when you’ve imbued your god model with a probabilistic number. Things will be the same.

If you can actually give me a number, arrived at by convincing methodologies, I’m going to have to assume it’s going to be quite improbable too. And the deal with probability is that its bound to happen sooner or later, so that your god number and the self-organizing system number might both have happened, or at least enough time has passed for either (eternity anyone?). If you could give me a number, I’d probably grant you that possibility. But you’d need to grant me my possibility too. Because we’d both just have an astronomically small number. Then what do we do? Have a cup of tea? Flip a coin? Can I double check your number?

Maybe we don’t need to go that far, maybe there’s another way of looking at this. Consider this before you go… if you happened to be in an improbable system could you actually use it against itself? You use the numbers provided by the system, because that’s where you are. Does it make sense to say that the system furnishing the numbers is improbable? Improbable where? Within that system? I don’t think you can. You’ve got your numbers, but they only work within the system. Not before the system or outside the system. There numbers for here. The way they work, whatever they mean, reaffirms that the system is actual, or at least like it was yesterday. All your logic, words, thoughts, they are not somehow able to be divorced from what we’re in.  They are part of it. So it might make sense to talk about the odds of the Earth being where it is in a universe like we have, but not to talk about the odds of the system itself. That doesn’t make sense.

But in this system things are like they are, seemingly, because of how they were before. The odds of that are pretty good. So the fact we are here in the system is a practical inevitability in this place. In this system. Its part of how it works that we’ve got to be where we are. Even random quark models don’t disrupt the hitting of a golf ball or the smell of sulfur.

But who created the system then? Hell if I know who did… or didn’t, but don’t give me a probabilistic model to talk about meta-system possibilities. Things there need not conform to what you think of things here. It’s an unconvincing argument, on my view. In this system things are apparently deterministic, the probability of here and now is 100%. Now, if you think god is incessantly following his own laws, I don’t think you’d have much to argue with a physicist about anyway. In that case, you’re just giving different names to the same phenomena. (Never-mind the difference in “feel”, you’re then bound to scientific claims about what’s going on inside the system.) We’re all on the same page here in the system. And we’ve got no clue about the meta-system.

What does it mean, fairness? What is fair? Is nature fair, is society fair, how can we go about being fair? Are there levels of fairness and should there be?

It seemed so clear to me when I was a child: fairness is when I got the good things I saw other people get. Fairness was ice cream and toys. Fairness was goodness. Group punishment was not fair, head lice was not fair, and the chickenpox was not fair – because they were not good, I did not want them. I wonder how this early idea of fairness as goodness may linger in my thoughts. I will try and shed my prejudice: fairness may not necessarily be goodness. Bad things may be fair things.

I am also inclined to think of fairness as something rank-able – possibly even quantifiable. “The game is fair only half of the time”, “this game is more fair than that game”, or “make this adjustment to your rules and they will become more fair”. These are certainly ways that are very natural for me to talk about fairness. I should like to try and suspend this way of thinking. A game that can be made more fair may simply be NOT fair. “Unless you adjust your rules they will not be fair”, or “a game that is fair half of the time is not a fair game”. These seem reasonable to me as well, although I tend not to think about fairness as absolute in my everyday life. I’d like to start with the possibility that it might be.

Also, it seems to me that fairness often requires interference. That nature is not fair – although it may be unbiased. It kills some children, it lets others grow up with severe handicaps, or allows others with no troubles at all to grow until a very old age – that does not seem fair. Not only because it does not seem good, but because it seems random. It does not pick the strongest-willed mother to rob of her child – it picks any mother at all – it may pick the weakest mother. Randomness does not necessarily seem fair to me. In some cases it seems that fairness is separate from chance.  I am, however, going to entertain that randomness MAY be fair. I will not dismiss the possibility just because it does not seem intuitive to me.

I occasionally have trouble with the idea that awareness is required for fairness. I don’t intrinsically feel that it is unfair to withhold something from me that I do not desire. This can include good things that I may simply be unaware of. If I don’t know they exist, if I don’t know they can be had, it seems to me that I can’t integrate them into my own idea of fairness. But, I think this is likely the most problematic idea of them all: for it would seem to suggest that enhancing ignorance can enhance fairness – and that seems to pose a real difficulty. At any rate, I am going to consciously consider that fairness may have nothing to do with what I know or can conceive of – it may, after all, not be fair of my peers to keep me in ignorance.

Lastly, it seems much too commonplace to imagine fairness as a common starting ground. If we start out on an equal footing, well that seems fair. I’m not going to assume that is necessarily true. I can imagine a scenario where starting fair does not mean things stay fair – it might mean nothing is really fair but the start itself.

Those are some conceptions of fairness that come easily for me – and because of this I am going to be very cautious with them and make a real effrot to entertain alternatives. This investigation of fariness will be continued in a second part.