Misunderstanding basic math concepts, help please?

For the discussion of math. Duh.

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Treatid
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Re: Misunderstanding basic math concepts, help please?

Postby Treatid » Sun Jun 25, 2017 1:54 am UTC

Introduction

We agree that there is a pedantic, technical limit that is unreachable. That, in practice, mathematicians don't hold themselves to a standard that is impossible to achieve.

This impossibly high bar is specified by the Laws of Thought. The 'practical' solution that mathematicians take is to reject the Laws of Thought.

As the Laws of Thought would point out - you can't (shouldn't) both abide by the Laws of Thought and not abide by the Laws of Thought.

{
Restatement (Skip if you like)

There are many different ways this problem manifests and can be described.

Take the propositions (x = y) and (x != y).

The Laws of thought rule out both these statements being simultaneously true (non-contradiction) and either one or the other must be true, not some (x semi-equals y) (excluded middle).

The problem is that we cannot unambiguously assign a single 'meaning' to any of these symbols. For all (x, y, '=', '!=', 'true' and 'meaning') we cannot define them in an absolute sense (nor can we define 'absolute sense' in an absolute sense).

As much as we might be clear that x does or doesn't equal y; we can never pin down a single x or a single y. We can't even specify a single definite meaning of equality. As much as the idea of 'equality' seems intuitive and obvious - when it comes to actually defining exactly and precisely, with no ambiguity, what we mean by 'equality'... we're stumped.

Yet language seems to work despite this limitation. So... something else is going on that doesn't require us to define anything in an absolute sense; that doesn't require us to know what x, y and equality mean in order for our symbol manipulation to be useful.
}

Let's see things from Bob's perspective.

Bob is an intelligent observer within its space; Bob is an integral part of its universe; the rules that apply to Bob's universe also apply to Bob.

Bob senses the world around it and can take actions that influence the world around it.

Bob's thoughts are under the same constraints as the rest of the universe.

Modern Bob categorises. Some patterns have similarities with other patterns. It can be useful to group these patterns together.

It turns out Bob can do pretty much everything using categorisation. Just knowing which categories a new pattern appears in allows Bob to have a pretty good idea of what it can do with that new pattern.

Bob can even think of brand new categories and work out which existing categories of patterns are needed to make the new category of pattern.

Bob, itself, is famous for having recently invented/discovered the category "digital watch" and the sequence of patterns needed to make an instance of one. Everyone agrees that this is a pretty neat idea.

When Bob was Born

Bob came into the world with only himself and his senses. As long as Bob lives (it is liking the idea of immortality), Bob will still be just itself and its senses.

Given Bob's evolutionary history as part of its universe...

At any given moment, the sum total of Bob's awareness, knowledge and being is the product of sensory input.

There is not anything else and there will never be anything else.

Which makes this incredibly simple.

The only basis for categorisation is observation (aka sensory data, patterns).

And everything follows trivially from this.

The only thing we can use to categorise anything is the data we receive from our senses (combined with our current state).

A pattern can only be categorised with respect to other patterns.

The only thing that matters are the relationships between patterns.

--------------------------------------------------------------------------

Epilogue

So... this is just a re-statement of Descartes' "Cogito Ergo Sum". If all we have is sensory data, then we can't do anything that isn't wholly and entirely a consequence of that sensory data.

It is no surprise that there are relationships. The unexpected step off a curb is that there is nothing else; that everything is a relationship and it couldn't possibly be any other way.

In retrospect, this whole thread we have been arguing over whether there is anything that isn't a relationship.

That the argument has been so long and protracted (going back at least as far as Plato) is a testament to how difficult it is to prove an absence ("prove that unicorns don't exist").

Indeed, proof, in the classical (mathematical) sense, cannot exist. However, once we frame the problem correctly and seriously try to think of what a "shape unrelated to any other shape" would be; or what meaning a "size unrelated to any other distance" has; it rapidly becomes apparent that "unrelated" (in some absolute sense) isn't a meaningful concept.

We simply don't have "unrelated" concepts that can be used as a basis for describing other things.

Which leaves us with only relationships to describe other relationships.

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Re: Misunderstanding basic math concepts, help please?

Postby ucim » Sun Jun 25, 2017 2:01 pm UTC

I'm not sure what you are getting at, or what question you are asking. But consider that mathematical statements (or entities, for that matter) are built up in several levels... there are theorems (proven stuff), which rely on axioms (nonproven stuff we assume), which rely on defined terms (words whose definition we formally agree on), which rely on undefined terms (words we wave our hands around and pretend we agree on).

It's pretty clear we have to start with undefined terms because we can only define words using words. Mathematicians know this, and have always known this. Nonetheless, it still brings surprises.

Examples of undefined terms are "line" and "point". We "sort-of" know what they mean and have managed to build an entire branch of mathematics on it. In this branch of math, two nonparallel lines in the same plane will meet at one and only one point. We know what this means, even if it's a bit handwavey. But let's wave our hands a little differently: imagine the surface of a sphere, and think of the word "point" as being the set of two locations at opposite sides of the sphere. The set (north pole, south pole) would be one "point". Now re-think the idea of "line" to be complete great-circle route. This is the path traced by a person who walks on the surface of a sphere without turning.... xe goes around and returns to the same place. That's a straight "line". The equator is a "line", but other lines of latitude are not. (You have to keep "turning" if you try to walk them).

With these new handwavings, two "lines" again always intersect at one "point". But now it means something different. Other conclusions drawn from Euclidean Geometry also have analogues, but they "look different". This is a different geometry (resembling, and perhaps identical to, spherical geometry) but expressed in Euclidan terms.

So, what's a "point"? Different answers lead to different (interesting) math. Neither one is inherently "better" or "more true" than the other.

As for Bob and his digital watch; don't confuse math with science. Math is pure thought. Science is about observation and conclusions drawn from that. Science uses math, but isn't the same thing. Math requires no observations at all, except perhaps the shared observations that allow us to handwave an understanding of undefined terms.

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Re: Misunderstanding basic math concepts, help please?

Postby Treatid » Wed Jun 28, 2017 2:48 am UTC

Ah... Magical thinking. Mathematics has different rules to other sciences because... reasons...

Let me rephrase what you are trying to convey: "Mathematics isn't constrained by the same rules as apply to everything else in the universe." or "Pure thought is independent of the physics of the universe."

I get what you are saying. I've heard much the same regarding mathematics - that it is qualitatively different - a pure science rather than a mucky empirical science. This is a meme that has been handed down through the generations. And there is nothing (beyond human hubris) that supports this idea.

Unless you are invoking an immortal soul it takes a mere moment's thought to realise that our thought processes are intimately tied to the physics of the universe. There is not, and cannot be, a hard distinction between what we think and everything else in the universe.

You sort of recognise this when you concede that communication is an exception to mathematics's specialness - yet at the very same moment you try to pretend that the internal processes of thought aren't subject to the very same limits.

..............................................

Right now you are choosing not to understand because you want to believe that mathematics is special (or that the brain is special (or that you have an immortal soul distinct from your mortal flesh)).

We are at an impasse so long as you think there is some part of this universe (your brain) which functions by a different set of rules to the rest of the universe.

So long as you are pretending that there is a hidden set of rules only accessible to pure thought - you aren't going to attempt to understand a single set of rules that is universal.

There is nothing rational about believing that mathematics (or pure thought) is independent of everything else. I'm certain that you can't even articulate what, exactly, that difference is.

However, I encourage you to try to articulate that difference since I believe the attempt will show just how ludicrous it is to attempt to assert a distinction between mathematics and anything else. Maybe I'm wrong and you can actually describe the distinction you are appealing to. (I don't really believe that. I'm really, really sure that there is no distinction. I think that thought is a direct consequence of the physics of the universe. But you are so convinced that I'm the one who isn't getting it - I'm sure you have evidence to back up your assertion that mathematics is different?).

........................................

I may come across as flippant with this post - but this is a core point. I suspect that there are many who share ucim's assumption that pure thought is fundamentally distinct from (say) empirical sciences. I also think that this assumption is repeated as a mantra without due consideration as to whether it is valid.

I think we need to come to agreement over whether or not this is a justified assumption.

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Re: Misunderstanding basic math concepts, help please?

Postby ucim » Wed Jun 28, 2017 3:13 am UTC

Do you draw a distinction between the abstract and the concrete? The idea of a chair, versus an actual chair you can sit in? This is what I'm after.

Similarly, I draw a distinction between what (for this post) I call an "idea" and what I call a "thought". A thought is the result of the machinations of a brain, which is itself governed by the laws of the universe (which, as we discover them, we call the laws of science). An idea is the (abstract) thing that is the subject of the thought. It is independent of the thought (doesn't require the thought to "bring it into existence"), but it's hard to talk about an idea without actually having a thought.

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Re: Misunderstanding basic math concepts, help please?

Postby LaserGuy » Wed Jun 28, 2017 6:10 pm UTC

Treatid wrote:Ah... Magical thinking. Mathematics has different rules to other sciences because... reasons...

Let me rephrase what you are trying to convey: "Mathematics isn't constrained by the same rules as apply to everything else in the universe." or "Pure thought is independent of the physics of the universe."

I get what you are saying. I've heard much the same regarding mathematics - that it is qualitatively different - a pure science rather than a mucky empirical science. This is a meme that has been handed down through the generations. And there is nothing (beyond human hubris) that supports this idea.


I think it would be more correct to say that mathematics isn't a science at all.

Thought is a direct consequence of the laws of the universe, but that doesn't mean that the content of those thoughts have to be. I could write a book where the story takes place in a universe with completely different laws to our own; that does not mean that the thoughts required to write that story, or the thoughts required to understand it, are alien to this universe. I might venture that a critical feature of thinking in the first place, perhaps the critical feature of thought it the ability to conceive of things that could be, not simply what is.

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Re: Misunderstanding basic math concepts, help please?

Postby gmalivuk » Wed Jun 28, 2017 7:12 pm UTC

This ground has been covered, again and again and again, in this and other threads Treatid has started over the years.
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Re: Misunderstanding basic math concepts, help please?

Postby Treatid » Sun Jul 02, 2017 1:43 am UTC

@LaserGuy: You've drawn an equivalence between mathematics and fiction.

I am inclined to agree with this equivalence. And I don't think it helps your argument. (more below - ucim makes a similar kind of argument).

@ucim: abstraction isn't unique to mathematics. E.G. While biology has specific strands of DNA it equally has the abstract idea of DNA. As such, the distinction you are trying to draw is not that mathematics is abstract - but that mathematics lacks any physical basis (is not empirical).

@gmalivuk: You are right - We've been covering much the same ground for a long time. And making progress (however tortuously slowly).

However, until such time as you once more crush my optimism, I genuinely think that we are on the home stretch now. Right now I'm trying to show that there are no exceptions to Descarte's Cogito Ergo Sum. It is my contention that if we just follow this one idea to its ultimate conclusion then everything falls into place.

I think this is a clearer statement of what I am trying to get to than I've made before (To whit: The only possible thing we have available to us in order to explain/describe sensory data is... other sensory data). As soon as we agree that thoughts, themselves, are sensory data then we are home free.

Turing Machine

A Turing machine will only run programs that it is capable of running (with a Universal Turing Machine able to run all possible programs).

Given that our universe is a Turing Machine (I know quantum computing places a question mark over this assumption - bear with it...) then anything that we observe in this universe is a consequence of the program running on that Turing Machine. A thought is just as much a physical entity as a tree. A tree is composed of electrons , protons and neutrons (or quarks and a splash of energy). A thought must also be composed of the same components, just in a different arrangement.

That is, the only programs that can run on the Universe are programs the Universe is capable of running. Whether it is tree or a thought, it is still constructed from fundamental universe bits.

(Fiction always exists in a physical form - words on a page, frames of a film, vibrations of molecules with audio. Your thoughts exist within the framework of a physical brain).

DNA

A thought is not much different to a strand of DNA. A strand of DNA encodes sequences that change the behaviour of certain molecules. A thought is a set of neural patterns that influence our behaviour (behaviour could be "thinking the next thought", "reading the next line" or "becoming a Machiavellian prince".

What, exactly, is non-physical about a thought?

Laserguy and ucim both suggest that abstraction/fiction/ideas are qualitatively different from the mere physics of the universe; even while conceding that it requires the physics of the universe for them to exist.

The way they both concede that there must be a physical basis - but then attempt to hand wave away the significance of that basis (without providing any reasoning or evidence in support) strongly suggests to me that they believe in the distinction - but now that they think about it - they'd rather not think about it.

From what they are describing it sounds like they may have in mind something like Emergent Features - properties of a system that are not obvious from the underlying rules but emerge from those rules.

However, Emergent Features are not independent of the underlying rules - as such, this doesn't show the distinction they are attempting to assert.

LaserGuy wrote:Thought is a direct consequence of the laws of the universe, but that doesn't mean that the content of those thoughts have to be.

!!!?!!! That is exactly what it means!

ucim wrote:]It is independent of the thought (doesn't require the thought to "bring it into existence"), but it's hard to talk about an idea without actually having a thought.

A very similar sentiment to LaserGuy. And equally an utter non sequitur.

Even if there were thoughts independent of the underlying physics...

It wouldn't make any difference to the argument.

As soon as you try to communicate an idea, it either can be communicated using the physics of the universe (and the restrictions described by Descartes) - in which case the thought never needed to be independent of physics. Or it can't be communicated because the idea cannot be executed within the physics of the Universe.

To the extent that ideas, thought, fiction, and mathematics have been written down (or spoken, or communicated in any form) - they are constrained by the rules of physics.

To argue that there is some form of thought/idea that is independent of physics (and also, presumably, independent of any rules we can conceive of?) is a purely religious argument.

I get that we are inclined to think of ourselves as special - to think of ourselves as the centre of the universe (after all, we are individually the centre of our own awareness). But human thought is only different by degree from other physical process, not different in kind.

I think we are coming to a conclusion

To me, your responses scream: 'religious conviction'. I see that you believe there is a meaningful distinction - but you can't easily express or justify the distinction.

This is good. This tells me that we've clearly identified an unexamined assumption.

So... There are no exceptions to the solipsistic component of "Cogito Ergo Sum" - Our awareness arrives through sensory data. For each of us, our universe is specified solely through that sensory data.

Maybe you feel that there are mechanisms outside 'sensory data' that contribute to or create some thoughts. If you have evidence, we would all be pleased to see that. If you have no evidence then I wish you good luck with your religion.

In all other cases, it is obvious that we only have sensory data available to us and thus our only tool is sensory data.

Moreover, when it comes to communication - it doesn't matter where ideas originate - only that they can be expressed.

Thoughts for the day

How do you describe relationships using things that are not relationships?

A not-related or un-related thing has no bearing on the things it is not-related or un-related to.

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Re: Misunderstanding basic math concepts, help please?

Postby ucim » Sun Jul 02, 2017 3:49 am UTC

Treatid wrote:abstraction isn't unique to mathematics.
I never claimed it was unique to math, merely that it was a property of math. It is possible for something to be abstract (non-physical) even if expressing it requires concreteness. A thought and its expression are different things.

You call that an "utter non sequitur". Not only is it not a non sequitur, it is the key to the whole thing.

Communicating a thought is not the same as executing that thought. (Similarly, though perhaps irrelevantly, communicating a program (e.g. sending the file that comprises it over the internet) is not the same as executing that program (i.e. running the file through the instruction processor))

"Three beans" exists in the universe as a physical thing.
"Three books" exists in the universe as a physical thing.
These two physical things share an idea of "threeness", which, divorced from either beans or books, can be applied to windows, holes, paths, and planets. "Threeness" itself is not physical.

Similarly, a bunch of things in a certan order requires exists as a physical thing, for example a strand of DNA or cars on the highway. But the order itself does not require anything physical. If there are no pink unicorns, and there are no white unicorns, there can still be the idea of a row of alternating pink and white unicorns.

Treatid wrote:So... There are no exceptions to the solipsistic component of "Cogito Ergo Sum"
"I think, therefore I am" is accepted a proof of one's own existence (though it gives few clues as to the properties of this "onesself" that is proven to exist). However, it's not the only thing it proves. The actual thought that I am thinking also has to exist. And the "onesself" that was just proven to exist has to have the capability of thinking that thought. And the conclusion which has just been proved must also ultimately exist.

So, how many things have been proven to exist? How many of those things have properties which can be ascribed to them? Are properties not also a thing? Is quantity a thing?

Jose
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Re: Misunderstanding basic math concepts, help please?

Postby Treatid » Tue Jul 04, 2017 6:14 am UTC

What a glorious Gordian Knot of an argument.

What is your argument?

I can see that you wholeheartedly believe that there exists a distinction and that this distinction is key.

What I don't see is an explanation of what the distinction is, how it arises, what it applies to (in a way that allows me to determine whether the distinction applies to a given subject), AND - why the distinction is relevant?

Yes - there are differences. So what?

You go to some length asserting that there are differences between this and that. This is obviously true. Each human is different to every other human. Each human is also similar to every other human.

Showing a difference (trivial) is not the same as showing that this specific difference leads to this specific result (non-trivial).

"I think, therefore I am"

You argue that 'I' and 'the thought' are independent. But they aren't. Remove the thought and you lose the "therefore I am".

I'm arguing that "sensory data", "thought", and "I" are all aspects of the same bundle.

You are assuming that a distinction exists and then using that assumption to illustrate the distinction.

You can't define the distinction.

You already know this. Your example of points, lines, planes and spheres shows you know the impossibility of defining anything in a definitive manner.

And the reason you can't define anything in an absolute sense is that our only possible measuring stick is 'sensory data'.

Closed Loop

Using a set of symbols to describe another set of symbols is a closed loop. I've thrown this out often enough as a denunciation of axiomatic mathematics.

However, the relationships we can describe using those symbols is not a closed loop. Ucim's illustration of points, lines, planes and spheres works because we are describing relationships - not because the words 'point', 'line', 'plane', or 'sphere' are defined.

Logical Fallacy

I know you believe this distinction exists.

So..., here you are, clinging to the idea of a distinction that you know you can't define; whose mechanism you can't specify - but that you believe must exist.

The only difficulty is your prejudice

Everywhere else in mathematics you would instantly dismiss a claim that "something exists which cannot be described" as being meaningless.

Moreover, even a hint of an exception to "Cogito Ergo Sum" would normally require a very solid argument for anyone to take seriously.

I am certain you understand the principles involved:

The only information we receive is through 'sensory data'. Therefore, the only thing we have to describe one set of sensory data is another set of sensory data.

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Re: Misunderstanding basic math concepts, help please?

Postby Cauchy » Tue Jul 04, 2017 2:54 pm UTC

What does this have to do with your misunderstanding basic math concepts?

The difference between a tree and a thought is that one is an object and one is a pattern. The physical object that the thought is a pattern of is the brain. I don't understand your argument because I skip most of your posts when they turn ranty (which is apparently always), but if you're trying to get a concession that the physical world affects thoughts, then yes of course but not really in the same way as it does a tree. It affects the brain in the same way as it does a tree, but thoughts for instance don't exert gravitational pull. Why don't you go on to the next part of your argument, and if it becomes clear that this distinction becomes important we'll revisit it?
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Re: Misunderstanding basic math concepts, help please?

Postby elasto » Tue Jul 04, 2017 7:13 pm UTC

Treatid wrote:I am certain you understand the principles involved:

The only information we receive is through 'sensory data'. Therefore, the only thing we have to describe one set of sensory data is another set of sensory data.

This is both true and seemingly irrelevant.

Yes it's true that if humans didn't exist, human mathematics would not exist either, but that doesn't mean that the idea of 'oneness', 'twoness' and so on can't be said to have an independent, abstract existence. After all, if aliens exist and they have developed mathematics, there's no doubt that their concept of 'twoness' would be functionally identical to ours, even if their 'sensory data' had little or no overlap with ours...

Therefore, even though mathematical systems can't exist without intelligent agents which live in the real world, the concepts which mathematical systems play with are, in a very real sense, pure, objective and universal. We might give human labels to these concepts, but mathematical concepts are discovered more so than invented...

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Re: Misunderstanding basic math concepts, help please?

Postby gmalivuk » Wed Jul 05, 2017 9:22 pm UTC

The only information we receive is through 'sensory data'.
It's true that we receive information through our senses, but it's false that all the information we thereby receive is sensory data.

Therefore, the only thing we have to describe one set of sensory data is another set of sensory data.
You're confusing the medium with the message.

I'm communicating this sentence to you through light and dark pixels on a screen. That doesn't mean the sentence itself is just pixels. I could communicate the same thing with a pattern of sound waves or (depending on the systems you know) a series of raised dots on paper or a sequence of long and short electrical signals.

Whatever it is that remains the same in all those representations of the same sentence (i.e. in whatever sense those can all be the same sentence) must be independent of any particular sense data you might receive.
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Re: Misunderstanding basic math concepts, help please?

Postby Treatid » Thu Jul 06, 2017 2:49 am UTC

elasto wrote:This is both true and seemingly irrelevant.

Yay! *Does a little jig of happiness*

And, reading between the lines - Cauchy is saying much the same - that he agrees we only have sensory data but doesn't see why I'm making such a fuss about it.

In answer to Cauchy's question: "What is the big deal"

The way we receive and communicate information (via sensory data) determines what and how we can meaningfully communicate.

A specific and extremely relevant example of this is our inability to define anything.

What I'm seeing

Each of you are trying to convince me that there is a difference between this and that - gmalivuk says the message is distinct from the medium, elasto says concepts are distinct from the systems in which they arise and Cauchy says that a tree isn't a pattern in the same way as a thought is a pattern.

However, we know that no-one can define a distinction any more than we can define anything else.

This leads you each to commit much the same logical fallacy: You assume the distinction exists and then use that assumption to try and demonstrate the distinction.

What (I think) you are seeing

The distinction is so obvious to you that you cannot fathom how I'm not seeing it when you point to obvious examples.

Even if we can't define it precisely, one just has to look to see it. (If you perceive the distinction to exist then that is proof the distinction exists, is it not?)

And hence you each commit the same logical fallacy in the certain knowledge that this particular instance isn't a logical fallacy (its obvious, right?)

My goal right now

is to encourage you to realise that a logical fallacy remains a logical fallacy irrespective of how self-evident the conclusion you are trying to demonstrate appears.





.........................................................

Not the next step of the argument

Cauchy has a point that having more context aids in understanding. Knowing the purpose of the argument gives a larger framework for considering the significance of the argument.

However, bringing attention to a Logical Fallacy doesn't require anything outside the Logical fallacy itself (Are you tired of me using the phrase 'logical fallacy' yet?) . I expect a fair amount of deflection and I'm reluctant to provide ammunition for that deflection.

With that in mind:

Ex Cathedra Statements

It isn't possible to define a distinction. More than this - there cannot be any distinction - at all. (There can be differences - but they must stop short of being a hard separation.

In order for A and B to interact they must be a part of the same whole. As such, A and B are aspects of the whole system and cannot be considered in isolation.

For example, Temperature and Pressure are not independent of each other. Both are aspects of the movement of 'particles'.

Likewise, we know that under General Relativity, distance and time are two sides of the same coin.

Further, if we cannot draw a hard line between anything and else... then everything must be an aspect of the one thing.

The one thing

We can label the one thing all sorts of things: Universe, sensory data, relationship, difference, separation, ...

We already think everything in the universe derives from a handful of objects with a handful of rules. Going from that handful of things that it is impossible to define, to one thing that is impossible to define is a tiny step.

Maybe you think that one undefinable thing is much the same as several undefinable things.

Remember - for things to interact they must be related; they must be connected. Things that are connected are, ipso facto, not distinct.

All this depends on the difference between asserting a distinction and showing a distinction.

Philosophy

Yes - this is philosophy. It is also pure mathematics in the best sense. There is a chain of reasoning you can follow that leads to a single inexorable conclusion.

Is there any part of this universe that is not part of this universe? Can you have a thought that is not wholly part of this universe? Can you point to anything that is not part of this universe?

Demonstrate it - don't assert it.

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Re: Misunderstanding basic math concepts, help please?

Postby ucim » Thu Jul 06, 2017 2:57 am UTC

"Cogito ergo sum." I have seen the light and realize that the only thing that I can be certain exists, is myself. I'm not certain at all that you exist. If you exist, you must therefore be part of me. If you are part of me, then there again is just "me" and not "you". So, you don't exist.

I will continue to operate under this principle. It will save me lots of typing.

Jose
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Re: Misunderstanding basic math concepts, help please?

Postby Cauchy » Thu Jul 06, 2017 6:35 am UTC

Cauchy wrote:thoughts for instance don't exert gravitational pull.


With this line, I demonstrate that my distinction exists. There''s no logical fallacy here. Similarly, what's the mass of three? What's the angular momentum of this sentence?

Treatid wrote:In order for A and B to interact they must be a part of the same whole. As such, A and B are aspects of the whole system and cannot be considered in isolation.


Why not? Why can't we consider them in isolation and then also consider them as parts of a whole? I can consider things in multiple different ways.

For example, Temperature and Pressure are not independent of each other. Both are aspects of the movement of 'particles'.


Just because temperature and pressure are not independent doesn't mean that I'm not allowed to consider one or the other in isolation. Like, why wouldn't I be?


I feel like you don't know what the word "distinct" means. And since it's impossible to define things, I guess you'll be stuck that way forever. Too bad.
(∫|p|2)(∫|q|2) ≥ (∫|pq|)2
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Re: Misunderstanding basic math concepts, help please?

Postby Treatid » Sun Jul 09, 2017 2:01 am UTC

Did I say there would be deflection? Nah - no deflection going on here.

@ucim: You are attempting to mock - but, of course we are talking about solipsism.

The whole point is to understand what we can 'know' in the face of "Cogito Ergo Sum". We clearly do communicate and understand things (to an extent) - and the logic of solipsism isn't wrong. So... How and what can we understand given Solipsism?

Solipsism doesn't go away just because you think it is nihilistic.

Your response of "Herp derp solipsism is silly so let's not think about it" doesn't resolve anything. You (and everyone else who takes the same approach) is simply burying your head in the sand because you don't want to face up to reality.

Somehow, despite solipsism, we still have something. So somehow, solipsism isn't as nihilistic as your impression would like to convey.

@Cauchy: To your argument that thoughts don't exert gravitational pull - you can find studies on the mass of a thought.

The mass of 'three' is the mass of the 'particles' that are required to think, or to express the symbols on the screen or paper. Likewise for angular momentum.

(not that a thing having mass (or not) demonstrates that it is connected (or not) to another thing. (Or that we have a sufficiently developed sense of gravitation that appeals to it are automatically founded)).

As for defintions; yes - I can't define anything. Neither can you or anybody else. This isn't my problem - it is everyone's problem.

Re: Thinking about things in isolation: I can see where you are coming from - but...

Standard experimental practice is to control the environment (context) so that only the aspect we are interested in varies. This applies to thought as much as to physical experiments.

This doesn't mean that the context has gone away.

Frustration

I can see that you (and pretty much everyone) are frustrated that you aren't persuading me of the distinction you believe in.

However, that frustration is due to your inability to provide a logical argument to support your belief.

You have a theory that there exists a distinction such that... something or other. This theory is supported by most mathematicians.

For a Theory to be a valid theory it needs to make testable predictions.

What are the testable predictions of your hard distinction? How can I tell what has become distinct from what hasn't? What is the mechanism?

What, exactly, is your theory of distinction, and what does it predict? What property of this distinction makes it relevant to this thread?

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Re: Misunderstanding basic math concepts, help please?

Postby ucim » Sun Jul 09, 2017 4:03 am UTC

Treatid wrote:@ucim: You are attempting to mock
Don't be silly. I don't mock what doesn't exist. But sometimes I talk to myself. That's ok, I'm always listening.

You're This voice in my head is attempting to talk about "knowing", without knowing what knowing is. I'm quite content to know that I can't "know" anything beyond the fact of my own existence. But if I don't want to end with "full stop, end of thought, nothing else matters", I'm forced to make some working hypothesis. I'm ok with that. Maybe it's all pretend. I'm ok with that too, because absent that, there's nothing else to go on.

So, working hypotheses (consider them axioms if you like):
1: There exists an objective reality. (Yeah, QM and all... I'm not convinced that we understand QM.)
2: Within their limitations, my senses communicate this objective reality to me. (i.e. I'm not just a brain in a box. And yeah, I know about optical illusions.)
3: Logic works, and I have a command of it. (Yeah, Kruger/Dunning - do you see a way around it?)
4: Anyone, including me, can be wrong and not know it. (The Pope's doctrine of infallibility is bogus.)
5: I can't remember the fifth one right now, but there is one.

Yeah, I've thought about it.

Treatid wrote:Somehow, despite solipsism, we still have something.
No, "we" don't. I have something, and you might not exist to prove otherwise. Nonetheless, I will pretend there is something, and that I am equipped to find out what it might be.

That is all.

Jose
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Re: Misunderstanding basic math concepts, help please?

Postby morriswalters » Sun Jul 09, 2017 11:14 am UTC

Treatid wrote:Is there any part of this universe that is not part of this universe? Can you have a thought that is not wholly part of this universe? Can you point to anything that is not part of this universe?
The answer to the questions, is that the the point is indeterminate. It falls into a category of things that are possible, in the sense that you can formulate the question. But currently unknown. No more and no less.

Math is what it is. Only mathematicians care about proofs. I care only in as much as I can use the fruit of those proofs reliably. Do they work? The answer is obvious and observable. They work well enough. Mathematics can be used to describe the reality of the solar system sufficiently, for us to launch a probe at Mars, and end up at the surface of Mars, with that probe, so that it has near zero velocity at the moment of contact.
Treatid wrote:In answer to Cauchy's question: "What is the big deal"

The way we receive and communicate information (via sensory data) determines what and how we can meaningfully communicate.
There is even a field of study called information theory. And example of the idea in common use is digital compression of music. Cauchy's shrug may be an indicator that you are covering well walked ground here.

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Re: Misunderstanding basic math concepts, help please?

Postby gmalivuk » Sun Jul 09, 2017 12:13 pm UTC

We're not frustrated because we can't prove something, we're frustrated because the person who least understands the topic is the one getting pissy and condescending despite the superhuman patience some of the other posters have exhibited.

I, alas, am but a lowly mortal without such reserves of patience.
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