Yesterday, navrins pondered a question that has truly profound

[xiphias]

And the REASON it has truly profound implications is that, to me, it's so obvious that nobody would ever think about it -- but that many (most?) people don't, because it's NOT obvious.

He was considering the fact that, in mathematics, you have sets, and you can always tell, except in a very few Goedel-type cases, whether a given entity is in or outside the set.

But that, in real life, there are many sets that aren't like that. For instance, the set of "buildings". I can tell that a towel isn't a building, and my house is, but if someone is building a building, at what point does it turn into a building?

There used to be a tradition/superstition, by the way, that, at some point when the frame was completed, but before the walls were started, someone would drag a small tree up to the top of the thing. And so, by that tradition, you could get an answer -- it's a building after someone's dragged a tree up it.

I haven't seen anybody do that in YEARS, but it brings up an important point. The very category of "building" isn't a real thing. It is something defined by humans, and therefore may be defined in any way we wish.

But it doesn't really exist. The concept of "building-ness". Sure, Plato hypothesized that all categories have actual examples of Platonic forms: that a "chair" is any approximation of the Platonic form of "chair-ness".

But in reality, there is no such thing as "chair-ness" in itself. It is purely a human-created artificial definition. It doesn't exist per se -- it only exists in our minds as an idea.

This has profound implications for Bad Science. A great deal of Bad Science comes from trying to assume that categories are real. For that matter -- a great deal of magic works by manipulating categories and TREATING categories as real.

Inasmuch as categories are things that humans create and exist within our own minds, this actually can have a certain effectiveness -- you CAN manipulate people's perceptions and ways of thinking by manipulating categories as if they are real things.

But I want to go back to Bad Science for a minute -- specifically, creationism.

One of the fundamental tenets of modern creationism is "microevolution exists, macroevolution doesn't."

In reality, there's no such thing as "microevolution/macroevolution". It's all "evolution." But creationists state that things CAN change within their category, but CANNOT change from one category to another. Did Darwin see lots of different kinds of finches with different beaks specialized for different things? Yes, certainly -- but they were all nonetheless finches. Creationists think that a finch can change as much as it likes, so long as it remains a "finch".

Or the evidence that whales have vestigial hip-bones which demonstrate that they are descended from other animals with legs? No problem -- a whale with legs can turn into a whale without legs, just so long as it always remains a whale.

The thing is: Nature has no clue about the terms "finch" or "whale." Those are entirely human-generated concepts. Nature draws no such hard boundaries, makes no such categories, defines no such sets. Humans do that.

And it's very difficult for humans to deal with when reality doesn't conform to our expectations. WE categorize. Therefore, we expect the universe to follow those categories. And that's the basis of a lot of creationist thought.

The second story in the Book of Genesis includes the concept that Adam named all the animals. And creationists believe that -- they believe that, once Adam gave an animal its name, it and its descendants were tied to that name forever and ever. If Adam named a large hippopotamus-like creature "Whale", then it's fine that its descendants include orcas and blue whales and sperm whales, none of which have legs, because they all nonetheless bear the name of the category "whale."

As someone who believes that the Torah has truth, but not literal truth, I DO think that "Adam", meaning "humanity in general", DID give names to every living thing -- but those names do not, did not, never WILL define them. They are names given by humanity, NOT by G-d, and do NOT bear an actual per se reality. Things are what they are -- they are NOT what we call them.

The "magic of names" is a powerful concept -- we have a deep-seated desire to believe that The Word Is The Thing. We WANT to categorize, we want to define, we want to classify, organize, index, and understand.

But the world isn't that simple. It is only our PERCEPTION of the world that even CAN be that simple -- and when we simplify the world to the level that we can deal with it -- and we must do so, because that's all our brains can handle -- we are NOT dealing with what IS real. As human beings, all we ever can do is deal with our own mental models of what is real, which are always, of course, only going to model a subset of what is actually going on.

We need to categorize in order to build our mental models. We need to generalize, to look at objects and classify them as "thing that I shouldn't walk into", "thing I can eat", "thing that is a door", and so forth. We don't, most of the time, need to think about the ways in which the latching mechanism for a car door, the latching mechanism for a house door, the latching mechanism for an industrial door differ. We can just categorize them as "door", and that's fine.

They are all fundamentally different objects. Nature has no reason to deal with them the same way -- icing up could jam the car lock, but not the industrial lock, for instance; wood swelling might make the house door stick, but not the other two. Nature has no concept of the category of "door". Or “eyeball”, or “fur”, or “blood”, or “wing”.

When you consider “scientists” who are creationists, a large proportion of them are “computer scientists”. And objects and categories in computer science are always well-defined. With a very small number of exceptions, based on Kurt Gödel’s work (and looked at primarily as curiosities, things which have little practical use), everything in computer science definitively in or out of any set which is defined in computer science.

Such sets do not exist outside of intellectual abstractions, and I think that the desire to find such things leads computer scientists astray when they try to look at other areas of reality.

Comments

[navrins]

This is completely not where I expected anyone to go with my thought, but I'm happy you did.

Thoroughly tangentially, I don't think computer science is a science. (Despite the fact that I have a bachelor of science degree in it.) It's a field that combines elements of mathematics with elements of engineering... actually, it's mostly mathematics. It's not at all about observing the world to see how it works, or forming testable hypotheses and conducting experiments to test them. It's about reasoning from basic principles to see what logically follows from them. The fact that these principles have some relevance to the programming of computers is interesting, but so is the fact that differential equations have some relevance to the navigation of rockets. It doesn't make either of them a science.

[xiphias.livejournal.com]

I agree that computer science is a) a branch of applied mathematics and b) actually engineering.

And I agree that, for MOST uses, it's not science.

I'm not convinced, though, that it's NEVER a science.

One question, of course, is, "Is mathematics a science?"

And, as I've just written a post -- that's a question about putting an abstract "thing" into an abstract "category" -- and we can answer it however we want, based on how we define "mathematics" and "science."

[rymrytr.livejournal.com]

Of the many definitions of the word "science", one is related to perfection or exactness. For me, math is exact and therefor a "science"...

[rymrytr.livejournal.com]

I was too general there, sorry. I should have been more clear.

The term "science" can have more than one definition through its modifiers.

I can say Math = exact science, while another can say Sociology = not an exact science, and some may say that there are things that may qualify as = not science; even though another might say, "the science-(tific) study of that thing that we say is, in itself, not a science..."

[cheshyre]

In the book Dreaming in Code, Scott Rosenberg points out that the phrase "software engineering" was originally coined to make an ironic statement...

[kiya]

My father was strongly of the opinion that compsci could not be a science because it didn't have a joke. This didn't go over well with my computer-sciencey high school friends (such as donperros and larksdream).

So he was asked what he meant by "having a joke". And thus he told this one:

A physicist, an engineer, and a mathematician are staying in a hotel. In the middle of the night, the hotel catches fire.

The physicist wakes up, sees the fire. Sees in his room that there's a bucket and a bathroom sink, and thus fills the bucket, pours it on the fire, sees that it's still smouldering, does a quick back of the envelope second-order approximation, fills a cup, and pours it on the remains.

The engineer wakes up, sees the fire. Sees in his room that there's a bucket and a bathroom sink, and thus fills the bucket, pours it on the fire, and repeats the process ten more times for adequate safety margin.

The mathematician wakes up, sees the fire. Sees in his room that there's a bucket and a bathroom sink, says, "A solution is possible," and goes back to sleep.


My friends nodded to this joke, and, without missing a beat, larksdream said:

"The computer scientist wakes up, sees the fire, and says, 'IT SHOULDN'T BE DOING THAT!'"

My father promptly admitted defeat.

[navrins]

I applaud larksdream's joke extension and your father's open-mindedness.

[eanja]

Hi, I ran across you on friendsfriends, hope you don't mind me commenting.

A very interesting post. What it also immediately made me think of is the very beginning of the Tao te Ching- there's a line in the first verse that goes "Name's the mother of the ten-thousand things." Which means (based on my admittedly purely western and translated and no doubt incomplete understanding), that the universe is a whole, and that all the subcategories and names we have for things are just created by people because we can't comprehend the universe without breaking it down and simplifying it.

It's been a long time since I thought about Plato- but I reading this, I realized that I have no good idea what fundamentally makes something a chair; you know, as opposed to anything you sit on, which would include rocks and stairs and curbs.

At any rate, you've made me think. So thank you.

[xiphias.livejournal.com]

That's why I think that Plato is fundamentally bullshit: I don't think that there IS a per se fundamental "chair-ness".

And yet -- I recognize a chair when I see one. . . .

[cakmpls.livejournal.com]

I'll bet that if you listed the characteristics of all the "chairs" you recognize, you would find that you do have in mind a definition of "chair."

Off the top of my head, mine is:
(1) It is made by humans.
(2) One human (with perhaps a limitation on size) can sit on it. Perhaps two humans can sit on it, but not more than that, and the two would be sitting very close together.
(3) It is raised off the ground in some way.
(4) It has some kind of back.

[eanja]

Well, yes. After I thought posted above, I thought about it and decided that most likely, a chair is something man-made, made with a primary purpose of being sat on. Personally, I don't think it needs to have a back- I would consider a stool, for example, as a subcategory of chair, and not a completely separate thing. (Hmm- I think your requirement for a back rules out my primary purpose comment- if you don't have a back, you need that part to rule out tables or plant stands or buckets). But I do think you are right about being raised off the ground and probably about being meant for only one person.

[cakmpls.livejournal.com]

This is a really good example of why I am amazed that word-communication ever works at all. If I asked someone for a chair to sit on, and they brought me a stool, I wouldn't be satisfied; "chair" to me connotes that I will have at least some minimal back support.

[eanja]

If someone asked for a chair, I wouldn't bring them a stool unless nothing else was available. Then again, I probably wouldn't bring them a rocking chair or a recliner either, and I also consider both of those as particular types of chairs.

So I suspect it's just a matter or how you subdivide you categories- are there more individuals types of furniture, or more different subsets of chairs.

[rymrytr.livejournal.com]

Makes me think of the Japanese before the European came along. They sat on the floor, basically with their back straight. If a Londoner has said, "Bring me a chair", they would not have understood the concept.

Later on, when they began to attend meetings with Ship Captains and others, and were invited to sit down at the table, they found the "chair" to be uncomfortable, complaining that, for one, it interfered with breathing.

(Rabbit Trail alert): I occasionally see an Asian Gentleman at a local Buffet where I take the Alzheimer's Patient (my Mom). He sits up, his back as straight as it can be, and he sits on about the front half of the chair seat. I, on the other hand, slouch and would be most discombobulated, with out the chair's back. :o)

(Rabbit Trail number 2): Which reminds me of another, very good (audio) Book - Across the Nightingale Floor.

[eanja]

I tend to lean that way about Plato as well. I can accept the idea that there may be universal moral ideas (that's into territory I not qualified to be sure about), but universal physical concepts seems to me to be something that largely provides a convenient excuse for cultural superiority (you guys haven't figured out chairs properly, and we have; therefore, we must be inherently smarter than you.)

I can also recognize a chair when I see one, but it seems reasonable to me that other people might have slightly different, but equally valid ideas of chairs (i.e. poster below, who differs w/ me on whether they needs backs).

[sashajwolf.livejournal.com]

And yet -- I recognize a chair when I see one. . . .

If you haven't read Wittgenstein on family resemblances, I think you might find it interesting.

[ckd]

If I'd read this comment before the End of Summer Party instead of after it, I'd have introduced you two.

[eanja]

Oh, too bad. But I suppose it's possible we'll overlap somewhere else at some point.

[xiphias.livejournal.com]

If you were at the Lefton's, then odds are very good that we will.

[cakmpls.livejournal.com]

I like it all, but especially this:

[W]hen we simplify the world to the level that we can deal with it -- and we must do so, because that's all our brains can handle -- we are NOT dealing with what IS real. As human beings, all we ever can do is deal with our own mental models of what is real, which are always, of course, only going to model a subset of what is actually going on.

(I think that first sentence also works well if one substitutes "G_d" for "the world.")

May I use this as my QOTD and link to your essay?

[xiphias.livejournal.com]

Please do!

[rymrytr.livejournal.com]

Very interesting posts indeed! Makes me a happy boy :o)

I wish I had more time, but I have to leave in a few minutes, but maybe I'll post more later. For now:

You(all) are basically right. In order to communicate with others, we must develop categories and definitions. To my ancestors, the world or concept of chair meant nothing. They sat upon the ground, around the fire, on skins, inside a "building" made of Cedar or skins or twigs and limbs, etc.

As for when a building is a building, I offer that an object, an item of construction or manufacture, such as a Pocket Watch or Oil Painting, isn't a Watch or Painting until the Craftsperson is satisfyed with the out come.

When we create concepts for things that don't exist, we need those concepts, for common understanding between ourselves. For me, "Time" does not exist. It is not a physical thing that can be seen, touched or felt. I believe that there are entities that exist without (outside of) time.

As for Creationists and Evolutionists, I have a "theory" that forces them to the same conclusion regarding the "beginning" of existence, as we understand it.

Gosh, I've got to go, or the Alzheimer's Patient (my Mom) is going to have a fit! :o) I LOVE suppositional arguments (if one can "love" and object)...

[cakmpls.livejournal.com]

To my ancestors, the world or concept of chair meant nothing. They sat upon the ground, around the fire, on skins, inside a "building" made of Cedar or skins or twigs and limbs, etc.

That's probably true for everyone's ancestors, going back to some point or other. I'll bet that at least some humans had a word for "skins that we sit on around the fire" as distinguished from all the other skins used for other purposes. We can expand the concept "chair-ness" to "sit-upon-ness"...

Humans constantly recategorize and rename and invent new categories and names as the physical world changes, as our knowledge and understanding changes. I'm 62, and there are certainly concepts and words that have come into existence just in my lifetime.

[rymrytr.livejournal.com]

I like it! "sit-upon lay-upon cover-with-ness" :o) Just for curiosity, I'm going to check for Cherokee words, related to this idea...

[happyfunpaul.livejournal.com]

Aargh, right now I have no time to reply with substance, but... I'll get back to you. By and large, I agree with your musings, but I'll leave this question in the meantime: What is/are the function(s) of having mental categories?

- PhD guy in cognitive psychology who studied categorization, inductive reasoning, and language

[thnidu.livejournal.com]

One answer, in brief: Being able to communicate about the world in more than just specific references to things in the immediate vicinity.

-- PhD guy in linguistics

[geekosaur]

I would replace "communicate" with "relate"; it's not just language, unless you consider reasoning to be communicating with yourself. (I won't even try to figure out which came first, generalization or language.)

Then again, I lack any formal training in any of this.

[rymrytr.livejournal.com]

Training, Shmaining... That's just some other individual telling you his/her understanding of the agreed-upon meanings of a series or set of concepts. Going back to a post above, "In order to communicate with others, we must develop categories and definitions."

As a person trying to obtain a PhD in Supositional *Abstract Thinking, (from Unseen University, [although I've now lived and studied for more than 770 phases-of-the-moon}), I experiment with "conceptual" communication:

My 12 yr old and I have certain esoteric things we say, that would be meaningless to you, unless I first explained the set.

If he says to me, "should I do this or not?", I may respond with "Chicken Soup".

If he tells me that his knee hurts when he Skateboards a lot, I may say "Doctor, Doctor".

If I ask him a question, expecting a yes or no answer, he will say "Does a one-legged Duck swim in circles?" (Think about it!) Or, he may reply with "Does a Weasel have feathers?"

[Chicken Soup: It may not help but it can't hurt]
[Doctor, Doctor: A guy went to the DR and said, "Doctor, Doctor, it hurts when I do this." The Doctor replied, "Well then, don't do that!"]

I have to admit that this was not, totally my idea. I watched Capt'n Jean Luc Picard wrestling with this problem, on a certain episode, when the people of that planet communicated only in conceptual language. It has turned into a fun game for both Bryce and me. :o)



*ab·stract
adj.
1. Considered apart from concrete existence: an abstract concept.
2. Not applied or practical; theoretical.
3. Difficult to understand; abstruse: abstract philosophical problems.
4. Thought of or stated without reference to a specific instance.

[mattblum.livejournal.com]

Reading your post, I had some serious flashbacks to Ray Jackendoff's Semantics class at Brandeis. Because discussing and writing about what constituted a "building" or a "door" was exactly the kind of thing we did every day. In fact, I specifically recall writing a paper on the semantics of the word "chair."

I strongly suggest anyone interested in the topic to check around to local libraries to see if any has a copy of Jackendoff's books on semantics and language processing, because he really did (and probably still does) have some brilliant ideas.

[rymrytr.livejournal.com]

Thank you, I'm interested!

[rymrytr.livejournal.com]

Speaking of "words", you've reminded me of another (audio) book: The History of the English Language by Michael Drout. It was not all that dry, listing to it, and there were places where I found it most interesting.

He teaches on line as well as at Wheaton College. Things like Beowulf, King Arthur's Grammar, Tolkien, etc.

[mattblum.livejournal.com]

There's a very long history of manipulating labels (for that is what categories are) to serve an agenda. Heck, slavery was justified for many years by simply defining the word "person" to include only those with white skin.

But of course this sort of issue arises all the time, and typically for much more trivial stuff. For instance, I am a bagel snob, and tend to bristle at anything termed a "bagel" that doesn't fit with my personal definition. This includes sweet bagels, though I'm usually tolerant of cinnamon-raisin and the like; I draw the line at things like Panera's "French toast bagel." (My feeling is that, if I want a torus-shaped dessert item, I will have a doughnut.) I bristle, too, at places like Dunkin Donuts calling their torus-shaped rolls "bagels." DD's so-called "bagels" aren't bad; they're just not bagels.

Language is a fundamentally flawed means of communication, because it assumes that both the speaker and the listener define each word being used the same way, which is very often not the case. But it's the best means we've got.

[xiphias.livejournal.com]

Speaking as a bartender: "martini".

I used to be far more restrictive about this. There was a time where I bristled at the term "martini" being used for anything other than gin mixed with white vermouth in a ration between 3-to-1 to 7-to-1 inclusively, and then garnished with olives or lemon twists.

This trend of calling anything served up in a cocktail glass a "martini"? I was deeply disapproving.

Then it was pointed out to me (I use the passive voice because I can't remember where I heard this), that a "highball" was once "whiskey and ginger ale", served in a tall glass over ice. But the term NOW is used to refer to the entire category of drinks consisting of a liquor and a carbonated mixer -- rum and coke, gin and tonic, 7 and 7, rye and Moxie -- all highballs.

I now accept the term "martini" as a general term meaning "a drink which is served in the same manner as a martini", by extention from the use of the term "highball."

I still bristle at "vodka martinis", though.

And I believe that Bruegger's is one of the few places you can get a bagel in the Boston area. I'm not even arguing whether Bruegger's has GOOD bagels -- I'm simply saying that Bruegger's is one of the only places that even has bagels at ALL.

[rymrytr.livejournal.com]

I know you use the the term "white" with the modifier of Recent History, but I add that currently, slavery is on-going in Africa, black on black.

My ancestors practiced slavery, although it was mainly reserved for women and, later, the occasional display and sport with a white male captive.

I'm reminded of the Kings and Queens of Europe too. They and their "Lords" held all the purse strings. You could "work" or not. If not, you could starve or steal and be put to death.

The condition of Women in parts of India, Afghanistan, Iraq, Iran...



Makes me curious. Throughout history, has there ever been a decade where slavery did not exist, somewhere on the face of this planet? (Rhetorical question, that.)

[unquietsoul5.livejournal.com]

Hmmm... when they built the new theater on Mass Ave here in Central Square Cambridge they did indeed do the tree on the top thing, and that was only about 3 years ago, so its still done in many places.

[dancing-kiralee.livejournal.com]

I have a couple responses to this.

1) Good science, as well as bad science, is based on categorization. Newton invented a category of 'things' called 'Forces', and another category of 'things' called 'Matter' and a category of mathematics called 'Calculus' which, among other things, described how 'Forces' and 'Matter' interacted. He didn't so much discover gravity, as invent a way to usefully talk about it's effect; and he did it by creating and defining categories.

2) Language is a protocol. Like all protocols, how things are categorized is decided collectively, not individually. It isn't even decided democratically - I didn't get to vote on the color shades that fall into the category 'blue' or even whether or not 'blue' referred to a category of color as well as a category of emotion.

3) Computer Science is generally considered a sub-category of Mathematics; Mathematics operates on an abstract plane - which means all the categories within it are 'abstract' instead of 'real world' and can be defined precisely (except for specific known exceptions). That makes it different from an observational science (like astronomy or paleontology); and from an experimental science (like chemistry). Because databases are both a part of computer science and our current information management technology, the (false) idea that 'real world' categories can be treated as precise may become more prevalent.

4) For the most part I think you're right. I'm amazed that mathematical categories (like triangle) can have any meaningful association with real world objects and their behavior.

And I'm amazed at the existence of language. The protocol may be determined collectively, but it's interpreted individually; how then do we consistently come to similar enough interpretations that we can communicate?

5) I agree with mattblum when he says, "Language is a fundamentally flawed means of communication, because it assumes that both the speaker and the listener define each word being used the same way, which is very often not the case." but extend it into the way I handle interpersonal conflict.

Someday I'd like to go into that in more depth, but I'm running out of time... perhaps in a couple weeks (big deadlines and a birthday will be soaking my time until then).

Kiralee

[mabfan.livejournal.com]

Read and enjoyed; no comment.

[rymrytr.livejournal.com]

sidhebaap wrote:

Let me probe the other direction, then, if you don't mind: What *else* would you call an exact science, besides mathematics? (I'm thinking of physics here, which seems anything but exact to me, usually.)




Regarding my (mistaken?) statement that Math is an exact science...

You've made me think deeply, about Cats, Math, Outer Space & "Exact Science" and for that, I thank you! :o)