On the self.

[vonFiedler]

You're drawing in differences when you claim that. It's one thing to claim two objects are similar enough, therefore I have two of them. But to define 'half a pie' you have to know what a pie is, then approximate the ratio between the two. The 'half' does not exist until we decide that a pie should be a whole circle. Similarily, I have 3 dollars less than I had 10 minutes ago implies a comparison. The negative difference does not come into play until I claim to have more money in a prior instance.

A pie doesn't half to be a whole circle. As long as there's an understanding of what a whole pie is, there can be a half pie. Like objection said, it's an adjective. The comparison to dollars is irrelevant as I didn't claim that negatives can be seen.

Objection isn't saying that numbers are adjectives because they are intangible, just that when counting things in the real world they are adjectives because they describe real things. Two pies is not two nouns, it's one noun and a descriptor.

 

[cantab]

The 'half' does not exist until we decide that a pie should be a whole circle.

A whole pie has an crust all the way around. Half a pie has a big gap where it was cut with the gravy oozing out.

Is a dream an adjective? Is a black hole an adjective?

A dream is a physical process, a pattern of activity in the brain. A black hole is an object, albeit one that is not properly understood in our current laws of physics.

 

[Jack Jack]

Well, I don't know about english, but in french, there is a class of words called " adjectif numéral " litt. numeric adjective, divided in sub-classes such as adjectif numéral cardinal (un, deux ; one, two), adjectif numéral ordinal (premier, deuxième ; first, second ), adjectif numéral multiplicatif (double, triple; double, triple) et adjectif numéral fractionnaire (demie, tiers ; half, third).

I'd argue that a dream is "what it feels like" to have that pattern of activity in the brain =P.

Edit : In french, adjectives are also pluralised, so from my point of view, that hardly counts.

 

[cantab]

Well, I don't know about english, but in french, there is a class of words called " adjectif numéral " litt. numeric adjective, divided in sub-classes such as adjectif numéral cardinal (un, deux ; one, two), adjectif numéral ordinal (premier, deuxième ; first, second ), adjectif numéral multiplicatif (double, triple; double, triple) et adjectif numéral fractionnaire (demie, tiers ; half, third).

In English we have "cardinal numbers", "ordinal numbers", and "fractions". The fact that "number", and "fraction" can be thus pluralised indicates they can be treated as nouns.

 

[Objection]

Well, it indicates that the words "number" and "fraction" are nouns, but not necessarily numbers and fractions themselves. "Adjective" is a noun too, but "hot" isn't.

Are all non-tangible things adjectives? Is a dream an adjective? Is a black hole an adjective? The numbers can count tangible objects, but they can also be used to convey size and be used in equations and expressions.

No, but all adjectives are non-tangible and do not physically exist. This applies to zero, one, fifty, minus three, half, hot, loud, high, bright and all other adjectives. Numbers quantify nouns, as in "Two apples", "Half a pie", "Thirty-three point six metres" and "Minus fifty degrees Celsius", as well as "Zero kites". We use a numeric system to dictate the values of all numbers and what we can do to two or more numbers to get another number, which can be different but doesn't have to be. Like numbers, the numeric system is not a physical thing, in spite of "system" being a noun.

 

[Scoopapa]

The brain does generate the virtual reality for itself, much in the same way the computer does not generate a virtual reality for itself. The computer generate light on a screen, which is a representation of the electrical process in the chips.

No, they're both doing the same thing. They use sensory "organs" to collect data and specialized "circuitry" to process that data into a form that allows them to respond accordingly to their surroundings. Once again, the thing that separates the brain from the computer is conscious experience. You keep trying to make your argument something other than that, but it simply isn't. We are back at square one, because I have already addressed why saying that the brain can't be the seat of consciousness is erroneous, and you are yet to respond to that argument.

Being introspective means to have access to all the information regarding oneself

Maybe I'm the only one who is naturally unaware of the relative quantity of different neurotransmiters in my different synapses.

...the brain itself, if it is conscious, has access to all this information

This is pure invention, and it's a result of your insistence that consciousness be treated as something supernatural just because we aren't yet sure of its cause. I've already told you that intelligent processes require interaction (i.e. communication) in order to function properly. I wasn't making it up, it's as much a law of nature as gravity. Different parts of the brain do their job by communicating with other parts of the brain. They aren't instantaneously "aware" of the rest of the brain is doing, they simply operate based on the input they receive. The only way they could be aware of the rest of the brain is if they were either:

a. running a perfect simulation of the brain - which is of course impossible, and if it were possible, it would negate the need for the rest of the brain anyway.

b. connected directly to every neuron and able to extract and process data about their states at a high enough rate of speed to create a meaningful analysis of what is happening. We know of no such connections, and once again it requires a part of the brain to be processing the actions of the entire brain, so you have the same problem.

So when I give you an argument that the consciousness happens in the brain, why would you tell me that it must somehow be able to do something that no part of the brain could possibly do? I didn't say "the consciousness is in the brain, also it's supernatural". If the consciousness is part of the brain, there's no reason to expect it can be instantaneously aware of everything happening in the brain. Like every part of the brain and like any aspect of any intelligent system, it has to communicate with the rest of the system.

 

[Morm]

This is grade school stuff (like grade 8 or so), but I can understand it not being all that practical or interesting.

Natural numbers are the numbers 1, 2, 3... that are named such because we can observe them in nature, which I believe is what you were trying to describe.

When I hear numbers, I generally assume real numbers which include 0, negatives, and fractions which also have use in real life but aren't directly observed.

You can claim to have 0 lions. You can claim to have owe someone 3 dollars. You can see part of a pie. But it's fair to say that you don't see the lions, you can't really visualise debt, and you don't see 1/2 of a pie, you see a non-circular pie.

Yeah, basically it's all irrelevant to me and my every day life/thought process. I like your last paragraph, that pretty much sums up what's goin' down here.

 

[TheAmazingFlygon]

Well, I don't know about english, but in french, there is a class of words called " adjectif numéral " litt. numeric adjective, divided in sub-classes such as adjectif numéral cardinal (un, deux ; one, two), adjectif numéral ordinal (premier, deuxième ; first, second ), adjectif numéral multiplicatif (double, triple; double, triple) et adjectif numéral fractionnaire (demie, tiers ; half, third).

I'd argue that a dream is "what it feels like" to have that pattern of activity in the brain =P.

There are no adjectif numéral multiplicatif nor adjectif numéral fractionnaire. They are either un constituant d'un nom composé or a simple adjectif qualificatif or even a quantificateur -- in my humble opinion the quantificateur doesn't exist, it's a simple adjectif indéfini, but that is beside the point.

 

[Jack Jack]

"They are either un constituant d'un nom composé "

I only swear by Maurice Grevisse's Le bon usage. I don't buy all these language reform crap.

 

[chaos]

Kitten Bukkake, since you posted a visitor message saying you don't understand me, I will try to explain better.

The crux of my argument is that numbers are not physical entities. Thus, no number "exists" in the physical sense (although they certainly exist in the mathematical sense?).

Numbers are an abstraction. They are invented by human imagination, and live only in our mind. We can use numbers to MODEL the physical world, but when we make observations of the real world, we are not making observations about numbers. We are using numbers to describe our observations. A slight difference.

Here's an common example of a statement that confuses the physical and abstract. A lot of people say that "the laws of physics govern the universe." This suggests that the equations we have developed physically dictate the unruly universe to work in specific ways. However, the reality is completely different: the universe works like it does, and our laws try to PREDICT what the universe actually does. Our laws are an abstraction over the physical reality of the universe. Abstractions exist to help us reason logically about our observations.

The nice thing about abstractions is that we can apply different ones to the same situation and still come up with the same results. This is because abstractions are not in ANY way connected to the physical universe--they are a way for us as humans to describe the physical universe. Let me show you an example based on one of your posts.

You state that you are observing the number "1" because you have observed a single lion. To me, though, you have observed 2.7182818284590451 lions. That lion walks away, and you state that you now have 0 lions. However, to me, you have 1 lion. You then tell me that because you have 2 lions and 5 turtles, you have observed the number "7" because 2+5=7. However, to me, you have observed the number 1096.6331584284585.

Who is right? We both are. In fact, every true statement you can make about lions and turtles using addition is also true from my point of view. Every false statement in your reasoning is false in mine. We have witnessed an isomorphism, or a truth-preserving "conversion" between two formal systems.

In fact, you can convert from your system of thinking to my system of thinking using f(x) = e^x. And every time you use addition I will instead use multiplication.

When you say you see 1 lion, I am seeing f(1) = e^1 = 2.71... lions.

You say because you see 5 lions and 3 turtles, that you are NOT observing the number 2. We can set this up in your system as

5 + 3 = 2 is FALSE!!!

In my system, we have

e^5 * e^3 = e^2
2980.9579870417283 != 7.3890560989306504

Nope. Not true for me either. We are thinking on different planes, but reaching the same conclusions.

You say that because you see 3 lions, 7 turtles, and 10 dogs, that you are observing the number 20. 3 + 7 + 10 = 20. That happens to be true. Using the isomorphism to my way of thinking:

e^3 * e^7 * e^10 = e^20
485165195.40979028 = 485165195.40979028

We agree again. And as I said before, any statement you make about the world that involves equality and addition will have the same truth value as the equivalent in my system. Which means that you cannot be physically observing a certain number, because by the same logic, I am physically observing a completely different one. Abstractions are cool like that. As long as there is an isomorphism between our ways of thinking, it doesn't MATTER which numbers we use or which operations (like addition) that we use. We agree and disagree on exactly the same things, so you can't logically say that 1 is a more valid observation than 2.71. All that matters is that the abstraction is accurately describes physical reality.

This has nothing to do with the argument, but you may find it interesting. Isomorphisms are not trivial--you can't just make up a translation and assume it will work. For instance, if you were to say you observed 1 lion, and I said I observed 4 lions by the isomorphism f(x) = x + 3 and using multiplication, I would be wrong.

In your system:

1 = 1
1 + 0 = 1

In my system:

(1 + 3) = (1 + 3)
(1 + 3) * (0 + 3) does NOT equal 4.

So, it's not an isomorphism. And our ways of thinking are not the same.

Hope that helps.

 

[TheAmazingFlygon]

"They are either un constituant d'un nom composé "

I only swear by Maurice Grevisse's Le bon usage. I don't buy all these language reform crap.

I don't either buy reform stuff and IMO it is simply a word, however you could analyze it as a constituant d'un nom composé which is why I stated it. For example, demi-heure is a single word; it is not an adjectif numéral fractionnaire added to a word to form a nom composé.

 

[Morm]

My eyes may be burning from Starcraft 2, but I think that was a fantastic post chaos. I find it neat how diverse our mindsets can be yet to an outsider (nonhuman) we'd probably look identical or exceptionally similar.

 

[vonFiedler]

My eyes may be burning from Starcraft 2, but I think that was a fantastic post chaos. I find it neat how diverse our mindsets can be yet to an outsider (nonhuman) we'd probably look identical or exceptionally similar.

If that's what it boils down to, then I already know some people who observe numbers in radically different ways than most do. However, none of them would see one lion and perceive two lions. I know I've been a stick in the mud as of late when it comes to theoretical exercises but as abstract as numbers are lions are not. A singular lion is never multiple lions, or a complex number of lions. Maybe there were just better examples you could have used, such as what's green to me really might not be green to someone else. But one lion isn't two lions. If it was, one vonFiedler would be two vonFiedlers. And then we'd have bigger problems than worrying about abstracts.

 

[MrIndigo]

If that's what it boils down to, then I already know some people who observe numbers in radically different ways than most do. However, none of them would see one lion and perceive two lions. I know I've been a stick in the mud as of late when it comes to theoretical exercises but as abstract as numbers are lions are not. A singular lion is never multiple lions, or a complex number of lions. Maybe there were just better examples you could have used, such as what's green to me really might not be green to someone else. But one lion isn't two lions. If it was, one vonFiedler would be two vonFiedlers. And then we'd have bigger problems than worrying about abstracts.

The words/numbers that he uses to describe the lions he sees are different to yours, but the actual nature of what he's looking at is the same.

Mathematics is a language (arguably the fundamentally purest language), but it is used as way of describing something. An analogy is the idea of units in science.

For example, in my system I might measure a change of 23 degrees; you measure the same change in the system and say it was 41.4 degrees. Of course, mine is in Celsius/Kelvin and yours is in Farenheit. The actual physical change is the same, we just change the way we describe it.

 

[Jack Jack]

If that's what it boils down to, then I already know some people who observe numbers in radically different ways than most do. However, none of them would see one lion and perceive two lions. I know I've been a stick in the mud as of late when it comes to theoretical exercises but as abstract as numbers are lions are not. A singular lion is never multiple lions, or a complex number of lions. Maybe there were just better examples you could have used, such as what's green to me really might not be green to someone else. But one lion isn't two lions. If it was, one vonFiedler would be two vonFiedlers. And then we'd have bigger problems than worrying about abstracts.

In that exemple, lions and Vonfielder are but mere units. If you see a single inch, I see 25,4 mm. Somebody who ate Lions or Vonfielders could see 4 meals in a lion, or 2 in a Vonfielder.

A single lion is not multiple lions, only as long as we measure in lions. If we measure in kg, in m^3 or in any other unit, then all bets are off as to what number it becomes.

 

[vonFiedler]

The words/numbers that he uses to describe the lions he sees are different to yours, but the actual nature of what he's looking at is the same.

1 Celsius is 33.8 Fahrenheit, but a Celsius is a degree of temperature, not a lion. One can be 2.7 in some conversions, but you can't have 2.7 lions. If 2.7 MEAN singular, then it isn't 2.7 in any language. The closest language analogy when we're talking about something that isn't real number would be if the numbers weren't base 10. Then I could point at 18 lions and say it's 21 lions, if my numbers were base 16. But one would still be one. One is kind of a special number.

 

[MrIndigo]

1 Celsius is 33.8 Fahrenheit, but a Celsius is a degree of temperature, not a lion. One can be 2.7 in some conversions, but you can't have 2.7 lions. If 2.7 MEAN singular, then it isn't 2.7 in any language. The closest language analogy when we're talking about something that isn't real number would be if the numbers weren't base 10. Then I could point at 18 lions and say it's 21 lions, if my numbers were base 16. But one would still be one. One is kind of a special number.

It wouldn't be "one"; the use of the number named one is flexible. But it would be singular. The actual count of lions would be the same.

 

[vonFiedler]

One is indeed flexible. 2.7 is not. In the case of the lion, one means singular. 2.7 cannot mean singular. Going back to Celsius and Fahrenheit, that's a good example of an isomorphism because there is no actual count. When there's an actual count, even when singular isn't involved, you'd still need to change the way you count to change the number you see. chaos's example still requires our perception to find x. Someone who automatically converts x to e^x without thinking might amaze you, but that would person would be literally retarded. And yeah, I've meet a few people with odd number senses too.

 

[Objection]

What if the numbers in the person's numeric system go 2.7, 9.4, 6.6, 34.5 ... instead of 1, 2, 3, 4 ... ?

 

[chaos]

You are conditioned to associate the number 1 with a single lion. This is what everyone expects you to answer when someone asks you how many lions there are and there is only a single lion. Mathematics is a tool for rigorous logical communication, so it is very good that we all agree that there is a single lion, or else we would have trouble communicating.

However, our system of describing the world is arbitrary. If everyone agreed that there were "2.71 lion" and used multiplication to "add", you would be the weird one. To them, they are thinking in f(x) = x. You are thinking in f(x) = log x. And they would say you are "literally retarded"--why don't you just think in f(x) = x? You cannot claim that you are correct and they are wrong; using the isomorphism, you all will agree and disagree on every single point. You think zero indicates the absence of something? Why? Because adding 0 to something doesn't change the result? Well, to these people 1 indicates the absence of something. Why? Because multiplying by 1 does not change the result. 0 and 1 are identity elements; the former the identity of addition and the latter the identity of multiplication. If I made up a function and found an isomorphism between your system and this system, 0 would map to the identity of my function.

To these people, 2.71 would be the semantic equivalent of "singular". What does singular mean? The English definition is dependent on our agreed on, yet arbitrary, way of using numbers. Try to define "singular" rigorously and you will find the same properties hold in the e^x/multiplication system. :/

What matters is the semantic properties of mathematical objects, not their syntax. "0" is syntax. The identity element is semantics. Syntax can be relative and arbitrary, but for an isomorphism to exist, and for there to be any basis in logic for what you are thinking, our systems must have the same semantics.

edit: Another example.

As children, they learned that e * e = 7.3890560989306504. You learned that 1 + 1 = 2. They learned their exponentiation tables. You learned your multiplication tables. If you were conditioned as a child to think in these terms, wouldn't you find it weird that someone always made the mental conversion to log x? They would think you had an awfully weird "number sense"...

 

[vonFiedler]

What if the numbers in the person's numeric system go 2.7, 9.4, 6.6, 34.5 ... instead of 1, 2, 3, 4 ... ?

Give me a good reason why someone's numeric system would go like that. I already gave an alternate numeric system with a very logical basis. We were raised to think in tens. A base 9 system would seem very odd to us. You might say "well how do they keep track of it without a good round number like 100?". But they would have 100. It'd just convert to 81 with our base 10 system. I feel like that's kinda what you're trying to illustrate chaos, but taking e to the power of x stretches the example far beyond the ability to take it seriously.

And again, you're talking about theoretical people who were raised that way, but I know real people who think in isomorphisms and regardless of how "correct" you'd say they are they still have to convert to regular numbers to do anything. It's a learning disability, though some can go on to be math geniuses, they have to be able to express numbers in a way that acknowledges one lion.

When you get into the high theoretical and talk about truly alien civilizations being raised certain ways, then why are they using 2.7, an arabic numeral, anyway?

 

[Objection]

Give me a good reason why someone's numeric system would go like that.

Give me a good reason why the most frequently used numeric system on Earth goes 1, 2, 3, 4 ... and it will almost certainly be a valid reason for any numeric system of any kind using any symbols in any combinations. Unless you go for simplicity (but even that is debatable) or popularity (don't you dare).

When you get into the high theoretical and talk about truly alien civilizations being raised certain ways, then why are they using 2.7, an arabic numeral, anyway?

That is what I was getting at, and I only used the symbols that I did because I don't have any more funny-looking symbols on my keyboard. Perhaps I should have tried Wingdings?

 

[vonFiedler]

Give me a good reason why the most frequently used numeric system on Earth goes 1, 2, 3, 4 ... and it will almost certainly be a valid reason for any numeric system of any kind using any symbols in any combinations. Unless you go for simplicity (but even that is debatable) or popularity (don't you dare).

Well see I can count the lions using my fingers that way. More specifically, those are real numbers, integers in fact. Very useful for counting whole objects. The first thing they teach you when you're learning game design is the difference between digital and analog (first day anyway, but that was years ago so maybe first week). Both are pretty vital. With chaos's proposed numeric scheme, there is simply no digital at all. Plus, the numbers you listed I suspect had no pattern whatsoever, but I guess that's irrelevant.

 

[Objection]

Well see I can count the lions using my fingers that way.

You could do that no matter what name and symbol(s) you gave to the number we call "one". This also addresses the next part about 1, 2, 3, 4, etc. being integers - they might not be integers to someone whose numeric system works completely differently.

The first thing they teach you when you're learning game design is the difference between digital and analog (first day anyway, but that was years ago so maybe first week). Both are pretty vital. With chaos's proposed numeric scheme, there is simply no digital at all.

Cool, I hope they teach me that in October too.

Plus, the numbers you listed I suspect had no pattern whatsoever, but I guess that's irrelevant.

And to someone whose numeric system goes 2.7, 9.4, 6.6, 34.5 ... the series 1, 2, 3, 4 ... would have no pattern whatsoever.

There is literally no end to the possible numeric systems one could use. For every rule we have in our current one, there can easily be an equivalent in every other one. Why has today's society adopted this one over all others?

EDIT:

2nd: because we have 10 fingers and because that's the way that caught on.

And we call that number "10" because ...

 

[Aura Guardian]

And to someone whose numeric system goes 2.7, 9.4, 6.6, 34.5 ... the series 1, 2, 3, 4 ... would have no pattern whatsoever.

There is literally no end to the possible numeric systems one could use. For every rule we have in our current one, there can easily be an equivalent in every other one. Why has today's society adopted this one over all others?

1st: unless they saw 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, ...
Patterns can be deduced if you have a large enough sample. And not having a pattern for numbers is, I think, rather unlikely.

2nd: because we have 10 fingers and because that's the way that caught on.

Also, I think this has strayed rather far from the OP.