Anyone frequent any science or physics forums/groups

Miscellaneous General
141

That’s a good thought. I’ve actually not made the connection between latent theories of the world (social/physical etc.) that Pinker discusses and programming languages. Mathematically speaking, all computer languages of a certain ‘power’ are all equivalent since each can, in theory, simulate all the others. Nevertheless, it is certainly easier to do some tasks in one language (matrix transpose in Matlab) and other tasks in another language (text pattern matching in Perl), etc. I’m designing my own computer language as a hobby… you’ve just sent me back to the drawing boards, damn you!

P.S. I’m in computer engineering (not quite the same thing as software, but close).

Clayton -

142

(Warning: Don’t try to read this unless you’re really patient or something.)

Imagine that the red ball is right in the middle of the picture, and then try to predict where it will go next.

It will move one unit of distance - whatever that means - in one of the whatever amount of directions there are. We can’t narrow the options down to anything but that it will only move one unit. It could move up, down, left, right, up/right, up/left, or whatever. We have no idea what direction in those 360 degrees it will “choose”. But what if we then see it move one unit to the right? Now we know that it can’t do anything but keep moving one “unit” to the right until it hits the right side of the picture and then bounces back toward us.

But let’s go back to the first frame, where we don’t know anything but that it’s sitting right in the middle of the picture. We just talked about what will happen after that frame, but what about what will happen before it? Do we know anything about what the frames were that would have came before it, if we had experienced them? Do we know what we would have experienced if we were to have been there to see what happened before that first frame? Well, we can narrow it down a bit. We can say that the frame directly before the frame that we see right now would have shown us the red ball one unit of distance away from where it is right now, or simply where it is right now. We’re able to know that the frame right before the frame that we’re experiencing right now was either the ball one unit away from where it is right now in any possible direction, or just the ball in the same place that it is right now. In case this is getting convoluted, let me state it in more natural terms. Either the ball came from somewhere adjacent to where it is right now, or it was just always sitting there. But now let’s imagine that we experience another frame, and it’s the ball one unit adjacent to where it is right now. That means that we can throw out the possibility that the ball was just sitting there, and we get back to where we were in the first paragraph.

But let’s talk about those two frames again. Let’s say that the two frames that we have experienced are the ball right in the middle of the picture, and the ball one unit to the right of there. We know that its only course of action could be to continue to the right. Its only option is to keep going toward the right-most edge of the picture, right? No, on second thought, that’s wrong. I came to that conclusion in the first paragraph, but it’s not right. Let me explain why it’s wrong. Well, first, let me say what the real prediction would have to be. We couldn’t say that the ball is definitely going to continue to the right, but only that the ball either went from the left to the right and will continue to the right, or that it went from the right to the left, and will continue to the left. But what the hell? Doesn’t that mean that it would have to go from the middle, to the right, and then jump to the left? No, I smuggled in some baggage when I said that “the second” thing that we would experience. Ah, but how do we know that it was the second thing? What do you have in your memory? In your memory, you don’t have anything but a bunch of frames. Your memory is what puts them in a sequence. Haven’t you ever had the experience of not remembering what just happened, simply because it was so similar to every other time, that you couldn’t put it in a sequence? Okay, that was terribly explained, so let’s start over. Let’s look at an example. Imagine opening your refrigerator, looking through the entire thing, and then pulling some lettuce out. Now imagine asking yourself whether you had any oranges left. Well, maybe you don’t know. But how do you not know? You just looked 3 seconds ago! Well, the problem is that you open your refrigerator so often that there really wasn’t anything “different” about that frame then anything else. Maybe if something was weird, like you saw that some juice spilled, you would be able to remember whether the oranges were there simply by locating the frame where the juice was spilled, and then asking whether the oranges were there. But, if there’s nothing to set it apart - nothing to let you put it in a sequence, you’ll be at a loss.

Okay, this is getting really convoluted. Let me start that paragraph over, but with the new insight that we have to put the frames in sequence in our memory based on experience, and not on any original quality of the frames. The frames don’t order themselves. You have to order them for yourself, based on the regularity. Just like the direction of time comes from the regularity in the sequence of things growing and deteriorating, the order itself comes from the regularity in general. Okay, let’s get back to it. Let’s say that the two frames that we have experienced are the ball right in the middle of the picture, and the ball one unit to the right of there. We don’t know what the order is; all we know is that we remember two frames, where one is the ball being right in the middle, and the second is the ball being one unit to the right of the middle. Let’s ask two questions: What happened before that, and what will happen? What happened before it: Either (1) a frame where it’s in the same place - it never moved, (2) a frame where it’s one unit to the left - it moved from the right to the left, or (3) a frame where it’s one unit to the right - it moved from the left to the right. And what will happen after: Either (1) a frame where it’s one unit to the left - it will move to the left, or (2) a frame where it’s one unit to the right - it will move to the right.

But what happens when we get the third frame? Well, everything falls into place. If it’s one more to the left, then we know that the ball came from the right and will move to the left; and, if it’s one more to the right, then we know that the ball came from the left and will move to the right. That’s it. But where the hell did I get this idea that things can move only one “unit” at a time, and that they can’t change direction unless they hit something else? How did I smuggle that in? Well, I have no idea, but this whole analysis has rested on that “hypothesis”: That things move in straight lines and at uniform speeds unless something interferes. With that hypothesis, 3 frames it all that you need to know exactly what happened and will happen, in our simplified model. But, again, where the hell did I get it? Well, I guess that I would have had to experience a certain amount of situations where only that happened. Or something.

143

"but i actually will give a counterexample that seems to go against this in order to make the point:

<9x9=81 could be used to learn something completely unrelated to human action: i know there are 9 boxes of 9 donuts each in my kitchen, so i can know there are at least 81 donuts there. “there are 9 donuts” is not an action, so although 9x9=81 CAN be a praxeological statement, it doesn’t have to be. so not even all basic mathematics is contained in praxeology.>"

ZB:

Going back to your original statement that “at least most of mathematics is best demarcated as a sub-branch of praxeology,” I would argue that this notion is more comprehensive than you may realize, for the following reasons:

It is not necessary that “there are 9 donuts” be an action for “there are 9 donuts” to be subsumed by praxeology.

We can easily conceive of an action as being comprised of both a means and an end. Means and ends are components or categories of action.

Then, to argue that “there are 9 donuts” is not part of praxeology, it will be necessary to demonstrate or prove that “there are 9 donuts” is neither a means nor an end of action. If “there are 9 donuts” is either a means or an end of action, then of course “there are 9 donuts” is, by definition, subsumed by praxeology.

Your proposition that not all of basic mathematics is contained in praxeology is based on your premise that “there are 9 donuts” is not an action. But if “there are 9 donuts” is either a means or an end of action, then “there are 9 donuts” is contained in praxeology.

Also, for any object X we may assume or suppose, it may not be necessary to answer the ontological question as to what X “is”.

Instead, it may only be required that we consider X “as” a certain thing, or consider X from a certain point of view.

I.e., we may consider X as a means of action, or as an end of action. We may consider X as something an actor is trying to obtain or attain, or consider X as something the actor is utilizing as means.

Then, to argue that X is not part of praxeology, it will be necessary to prove that it is impossible to consider X as a means or end of human purposive activity.

One of the most important passages in Mises touches on this:

“It is of primary importance to realize that parts of the external world become means only through the operation of the human mind and its offshoot, human action. [External objects] are as such only phenomena [of the physical universe] and the subject matter of the natural sciences. It is human meaning and action which transform them into means. Praxeology does not deal with the external world. but with man’s conduct with regard to it. Praxeological reality is not the physical universe, but man’s conscious reaction to the given state of this universe. Economics is not about things and tangible material objects; it is about men, their meanings and actions. Goods, commodities, and wealth and all the other notions of conduct are not elements of nature; they are elements of human meaning and conduct. He who wants to deal with them must not look at the external world; he must search for them in the meaning of acting men.” (Human Action)(emphasis and brackets added)

When Mises writes that human meaning and action transform the external objects of the physical universe into means, he doesn’t mean this in the ontological sense (that in utilizing objects as means, we transform these objects physically). What he means is that for any given object X, praxeology as the theory of action, looks upon object X as a means or as an end of action.

Praxeology need not be founded upon nor preceded by a process of ontological categorization:

Object X “is” the subject of praxeology. Object Y “is not” the subject of praxeology.

Object X “is” a conscious being. Object Y “is not” a conscious being.

Praxeology can be approached as a purely formal endeavor:

If object X is a means, then qrs. If object X is an end, then tuv.

If object X is an acting being, then xyz laws apply. etc…

144

it doesn’t. particulars are lumped together and used that way1, with a few hacks and tricks to approximate generality.

we can then take that bundle of particulars and find certain characteristics common to all (or most) of them, then use those characteristics as guidelines for determining what new particulars should be placed in the category.

in the case of the moving ball, though, i’d guess we have some built-in machinery for recognizing motion and object permanence, as you alluded to. though since part of it is hard-wired in and probably part is learned in childhood, a complete explanation would get messy.

1with this showing up all over the place in typical human patterns of error

145

if you could elaborate on that somehow when you’ve considered it more, i would look forward to it. could methodological individualist assumptions versus collectivist ones, or some similar distinction, result in a different programming language (like for an economics simulator1)? and in what sense is a programming language like a spoken language?

1i really have no clue about this, so make the necessary adjustments to something that would make sense

146

you seem to be suggesting that your memory puts them in sequence for logical or practical reasons, but it seems to me that our memory faculties would just automatically have some method of keeping track of which thing came first and which came next.

this is a bit thorny because we have to keep track of our assumptions.

  • if we are looking from the view of natural objective science, we would say what i said in the paragraph above: “our memories keep track of the order [in terms of actual objective time]”.
  • if we are looking from the individual perspective, we can know nothing of any objective notion of time in the natural universe. at bottom, we are actually noncognitive to such talk. it doesn’t have any meaning at the individual level, from the individual point of view. an individual adhering to strict methodological individualism would have to say time JUST MEANS a series of frames of experience ordered by memory. or heck, he doesn’t even know of “memory” per se, so just a series of frames that feels like its in a certain order, whatever i mean by “feels like”.

and what is an ordering? so as not to smuggle in the concept of time through the back door, i would say it is an certain type of utility prioritization, at least. that’s something as a start; a promise someone made to us “long ago” is regarded as less relevant to our current actions than a promise “a moment ago”. so in one sense it is a prioritization scheme, where we call “more important past happenings” the recent past, and “less important past happenings” the distant past. but that is just one aspect of it.1 what are the rest?

this is why time has been a hard concept to iron out: if we try to do it from the individual perspective, which is ultimately the only valid epistemology, there are a lot of different things going on and going into the concept we summarize in a single word: time.

1and i realize this could be reversed in some cases, but there is a general tendency like that…time heals all wounds, and such.

147

if we are looking from the individual perspective, we can know nothing of any objective notion of time in the natural universe.

Unless you grow up in a closet, you have to deal with physical processes that are ordered in time. You have to deal with other people’s plans and actions when formulating your own plans and actions. I find it hard to imagine a non-invalid person who is unaware of an objective ordering of physical events that corresponds with their memory ordering and with everyone else’s memory ordering.

Even growing up in a closet, you still have a chance of learning the objective ordering of events. For, your own body is a datum external to the human mind and it obeys physical processes.

BTW, I’m talking about the time-like intervals of everyday experience. Space-like intervals have no objective ordering (per relativity theory). I cannot cause something to happen or prevent something from happening 1 light year away in less than a year’s time, no matter how clever or powerful I am. Such an event occuring is objectively neither in my past nor my future; it is outside of both my memory and my influence. Space-like intervals do not involve cause-and-effect; such events are only data to be learned after-the-fact.

148

'guess if you take the idea of a means to its logical end, it really could be the entire state of affairs (Mises) someone is faced with. an axe is my means to chop wood…but really so is gravity, friction, momentum, my arm, the fact that my arm is attached to my body, the fact that i am not in handcuffs, the fact that there is light for me to see by…these are all means if any of them is! why the axe any more of a means than the light?

still, all of those are necessary for me to chop the wood. there being 9 donuts in my car is not necessary for my chopping of the wood. i don’t utilize that aspect of the state of affairs as a means…but then, is it really an aspect of my state of affairs? or, in such cases, is it just an irrelevant nothing?

ok wait, i think i got something: “there are 9 donuts” has meaning to me in the present moment only as far as it is relevant to whatever action i am taking now. specifically, if i just try to collect random facts that may at some point be useful to me, and this seems a habit of most humans, “there are 9 donuts” is going to be relevant to me for chopping the wood…orrrr maybe not?

nah, this is it: eureka! (maybe). it’s really that there’s this state of affairs, whole and undifferentiated. it is state of affairs A, and it includes an unchopped block of wood, a whole slew of other things…and 9 donuts in my car. i want to change this state of affairs to a state of affairs B that includes a chopped block of wood, that same whole slew of other things…and that same 9 donuts in my car. i don’t care about the 9 dounts really, but if we look at the entire state of affairs as whole and undifferentiated, then we cannot say anything other than that i am “utilizing” or “working” or “acting on” state of affairs A to change it to state of affairs B. then all of A is the means and all of B is the end. that is with no subdividing of the two states of affairs down into specific parts like the axe or the light or my arm or the donuts. then once i reach B, it becomes my new means, and i select a new action to reach state of affairs C, my new end. and so on. or something like that?

it is as if the current instantaneous frame of your experience is your means, the entire thing, not any one part of it, and the next (or next next next…) frame of your experience that you anticipate or hope your present action to accomplish is your end, and each end achieved becomes a new means because it is now your present frame of experience that you will act on to try to get something even better, or at least less worse.

in some ways it’s a very unenlightening way to think of means and ends, but it could perhaps have its uses?

Means / Ends
149

What’s an “objective notion of time in the natural universe”?

Interesting suggestion.

Have you ever been somewhere so many times that your memories of being there run together such that you can’t pick out a frame from your memory and have any idea when you experienced it?

If you only went somewhere once in your life, and you remember slipping and falling in that setting, you can go to the next step and ask when you went there. But, if you went somewhere 10,000 times, and you remember slipping and falling in that setting, what the hell is there for your memory to latch onto? Absolutely nothing. But what if you see something weird, such as somebody dressed as an 80’s tennis player in the sequence of frames? Well, then your memory might have something to latch onto.

If the ordering were native to the frame, that wouldn’t be a problem. But the ordering isn’t native to the frame. We order our memories based on their regularity. When do people dress like 80’s tennis players? Halloween! We learn that through experience, so we know that seeing that person in the sequence of frames where we slipped and fell makes it likely that it happened on Halloween. And then maybe you remember leaving somebody’s house (where a pumpkin was on the front step) and then getting to the place where you slipped. Oh, that means that it was on the Halloween that I went to that person’s house… and so on, until you recreate a simplified sequence up to the current time.

But, wait, I just smuggled in an order right there. I remember leaving their house and then getting to the place where I slipped? Isn’t that an order? How did I know that the frame where I was leaving their front step was before the frame where I slipped? Either by the same method, or maybe there’s something automatic at the lower levels. Not sure yet.

150

Well, the word “language” is somewhat misleading in the phrase “programming language.” Obviously, computers don’t “speak” or even communicate with one another in the way that humans or even other animals do.

A programming language is only a language in the technical, computer-scientific sense of being (in the most general sense) a subset of all strings drawn from the “Kleene-star” (length-wise lexicographic combinations) of a finite alphabet. Languages are frequently defined in terms of acceptance by a machine, that is, “L is the language of all strings accepted by machine M.” A machine need not be physically instantiable (i.e. it can have some infinite resource, such as an infinite tape, etc.) but every machine I’m aware of is physically comprehensible, that is, you can imagine the operation of the machine as a physical device, locally.

There are a wide variety of machine types (and a wide variety of language types) but the most general and powerful machine is the Universal Turing Machine (UTM). Machines which are superficially different in their construction but which can be proven to be formally equivalent (and, thus, to accept the same language) are said to be equivalent and have the same “power”. Any UTM can simulate the operation of any other UTM as well as the operation of any formal machine (a UTM accepts the “Universal Language” which contains every other formal language as a subset).

I said all of that to be able to say that a programming language can actually be thought of as a machine specification. At least, it specifies what kind of machine is required. In the case of the Universal language, the machine specification is “any UTM or equivalent”.

But that’s all really abstract theory. Programming languages are rooted more in practice than in theory (though each individual programming language may borrow heavily from one or more aspects of computing theory). A programming language is almost invariably a transform description, that is, it describes how to transform a set of high-level instructions into a functionally equivalent lower-level set of instructions. For example, if you write a program in C#, it will first compile down to Microsoft’s Intermediate Language (IL), which can then be compiled further down to machine instructions (which are a language which the physical CPU can read and execute). Perl6, similarly, compiles down to Parrot instructions (PASM), which can be run on a “native” (machine language) interpreter that dynamically converts the PASM code to native machine code. Java uses a method call JIT-compilation (Just-In-Time compilation) which is a nifty little trick for squeezing more performance out of interpreted code*.

That’s all background. To get back to your question, programming languages are like spoken language insofar as they are a machine specification. Think of engineering an automobile engine. Somehow, you have to describe all those curved surfaces, the join points, dimensions, functional behavior, and so on. A programming language implies an abstract machine which has a sort of “mental shape”** to it, and it is this “mental shape” that constricts or liberates the programmer by making some things easy and other things hard. Not everything can be easy… unless you’ve invented AI (lol). However, a program language designer can invest sweat equity into his language and save the users of his language the effort of repeating that sweat labor. This is a lot harder than it sounds because you cannot foresee how your language will be used in the wild. You might solve a particular problem in your programming language and it turns out that people want to solve a problem just slightly different than the one you solved for them. In which case, they will simply neglect all that labor you poured into your language (and, if your language isn’t buying them anything else, they might just abandon it for something more useful). Or, you might solve the problem that everybody needs solved, but then you package it in an alien way that programmers find counter-intuitive, backward or otherwise un-aesthetic and they will simply neglect to use it, even though it’s right there for them to use. This is not so much different than the problems facing UI (user-interface) designers for operating systems (or microwaves or DVD players, for that matter).

Clayton -

*The old-fashioned bright-line distinction between compiled code and interpreted code is blurred in modern languages

**The “mental shape” is the implied, abstract machine residing behind the semantics of the language. In C, for example there are these things called “pointers” but pointers assume a certain memory model that is not applicable in other kinds of languages. This gives C a unique “mental shape” from other languages which do not have pointers.

151

When you say “everything”, do you mean just everything in the outside world, or do you mean everything not only in the outside world, but also in your head?

152

quickly: i didn’t use the word “everything” in that quote so i’m not certain i know what you mean, but i guess i would mean neither “everything in the world” nor “everything inside and outside my head”; i would just mean everything in my head (because i am assuming the methodological individualism point of view).

but also, that is just me trying to see if i correctly understood AK or not, so it is all provisional.

no time for a long reply now, but while i’m at it: my “objective notion of time in the natural universe” is, strictly speaking, nonsense from the individual point of view. i mentioned it only because it is of course the common view and i have to deal with that to clarify the discussion.

153

Sorry, I wasn’t clear enough.

Does that “state of affairs whole and undifferentiated” include just what’s in the outside world (the donuts, the wood, and so on), or does it also include what’s in your head (imagining yourself chopping the wood, some bodily sensations, and so on)?

Rough:

You can build your idea of the outside world (the idea that things exist whether you’re there or not, that you can be wrong about what you think is there, and so on) out of the methodological individualism point of view. (When I say “in your head”, I just mean everything that you don’t consider a part of the outside world. But of course the outside world for you (I’m guessing…) is just a model for predicting what 2D image, bodily sensation, or whatever will come next.[EDIT: and whether you’ll like it!])

154

yep both those. although i am noncognitive as to “the world”, that is i guess not the point of your question. yah, everything i am experiencing is my state of affairs, so that would include every impression that i am enjoying or un-enjoying, whether i classify it as coming from within or without.

(sorry others, i will respond in full later)

155

I’m not ready to substantiate this, but I suspect that the ideas of “choice”, “means and ends”, and so on don’t make any sense except when you’re referring to your interface with the outside world.* (Which would mean that your “state of affairs” - your means - would be just what’s in the outside world. If you look at everything - including what’s in your head - there doesn’t seem to be any “choice” left. I just find by the principle of association that my mind transitions from X to Y etc and that’s it. Perfect determinism.)

*Unfortunately you could probably interpret that like 50 ways that I’m not talking about.

Don’t worry about responding to this now if you don’t have time right now…

156

Back to infinity for a moment.

The natural numbers can be defined by positing a “first number”, 1, and a successor function:

s(x) = x+1

s(1) = 2

s(2) = 3

etc.

To me, infinity is the inevitable result of the following question - is there a number large enough to break the successor function, i.e. is there a largest number, or a number which does not have a successor? I think the answer to this is clearly no.

The next question which naturally follows is, how many numbers are there? The answer, in terms of numbers we have already defined, is “no number”. There is no number that says how many numbers there are. But when we list the numbers out: 1, 2, 3, 4, 5… they look perfectly countable. So why can’t we count the whole lot of them, just as if they were a really big barrel of apples? I see no reason why we can’t define a symbol, say Aleph_0 and say, “The number of natural numbers is Aleph_0” especially since there’s lots of interesting things we can then do with this symbol.

Of course, such a magnitude cannot be physically instantiated… yet neither can a geometric plane and nobody has a problem with that. A geometric plane exists only in our imaginations… it’s a shared illusion or shared mental abstraction. Same goes for infinity.

Clayton -

157

I think that is the clearer question.

To me, infinity is the inevitable result of the following question - how many numbers are there?

The answer perfectly consistent with Zang’s posts is this - as many as you want there to be.

158

That’s easily disproven. I want there to be 3 natural numbers.

{1, 2, 3, 4}

QED

Clayton -

159

Okay, let’s see it.

Solid so far.

(Apparent you find it useful to have 3.)

Still solid so far.

(Before you found it useful to have 3, now you find it useful to have 4.)

But can’t you change what you want?

(Looks like you changed what you wanted from one line to the next.)

160

I understand the praxeological aspect of this, and assent to its importance, but I feel that it completely misses the point. We (humans) envision the world in certain, definite ways (see this lecture by Steven Pinker here). These abstract, immaterial ways of envisioning the real, physical world are, I believe, the ultimate foundation of most mathematical constructs. What do we mean when we say “a straight line cannot cross itself”? Do we really mean that a rigid piece of physical substance which is straight (whatever that means) cannot cross itself? Or do we mean something more ephemeral and metaphorical? I don’t think we’re making any kind of statement about the physical world outside of our brain. The formalists try to say we’re merely pushing symbols around, concomitant to certain rules (whatever a “rule” is) and “A straight line cannot cross itself” is simply a statement about the properties of any object which can properly be described by the symbol “straight.”

However, I reject both of these views. I believe what we’re really saying is more like what Pinker is talking about in how we use language to slice up the physical world in very specific ways. What we’re really saying is something more like, “Hey, you know how you envision the essence of straightness in your mind? Well, any object you envision in your mind which you would think of as ‘straight’ cannot cross itself, right?” The rules of the mathematical formalisms that we find “envisionable” and which we, for that reason, find important are not selected arbitrarily, they are selected to conform to these definite ways in which we envision things in our minds.

I think I need to spend some time thinking of specific examples.

Clayton -