Bored? Try this math challenge. :)

"

ScrotieMcB wrote:

To clarify my post before this one: the only knowledge we have without thinking is the raw data provided to us by our senses - which itself is so overwhelming in size that we cannot store it, but stream it. Our ability to meaningfully retain this experience rests upon our proficiency in looking for patterns in this ephemeral stream and then remembering our summaries of them - thus, the single most important aspects of memory are vocabulary, as that is the compression method, and precision in one's language, such that the summaries are not inaccurate.

Im aware of that, yes. Very insightful for those whom are not.

"

ScrotieMcB wrote:

Note that this is a purely personal application of vocabulary, and thus interpersonal compatibility is irrelevant;

Well heres where it gets tricky. With most words, there is an enormous amount of implicit information linked with it. Change that implicit info, and the meaning of the word has changed... yet the symbol of the word remains the same.

Each of us has accumulated different amounts of that implicit information of associated data for each symbol(word). Some of may specifically include or exclude members/properties to the set of that information. Perhaps because we arent aware. Perhaps because we specifically thought through the meaning of the symbol and decided it more correctly maps onto reality (or can be more easily leveraged to accomplish some utility).

With this difference in the exact meaning of a symbol between different entities, "interpersonal compatibility" is an issue to some extent. Being part of a group (mankind as a whole), we draw a large portion of our intellectual power from distributing the processing among the group. We learn from each other. But when the symbols being communicated dont match an individuals representation (of the implicit info); inconsistency, contradiction, and conflict can arise.

In addition there is the added complication that entities may be working against the group (knowingly or not). Poisoning the dissemination of information with inanities, falsehoods, biases, distraction, and spam.

"

ScrotieMcB wrote:

(If SkyCore means his signature, I'm calling it out as bullshit.)

Even a priori knowledge must be thought; although it may not require experience to reason out, it still requires reasoning out - and it also requires language (mathematics uses a distinct language all its own, with "1+1" and "11" (decimal) and "11" (binary) all meaning different things; of course, it's possible to have personal definitions of these concepts without associating them with the conventional symbols).

"

SkyCore wrote:

Thinking in human language is the problem. Words cannot truly represent real 'truth'.

At the deepest level, everything is so interconnected we cannot pull the finite out of this infinite whole without losing the 'real truth'.

"

SkyCore wrote:

Language exists merely to manipulate other peoples version of the truth.

This is the one part of my signature i dont think is fully the truth. I wish i could have expressed it more properly. But i felt it important that people be made aware that communications have an impact on what you think and who you are.

It was not my intention to misinform. Thank you for bringing it to my attention. I will change it when i can find a succinct way of saying the prior.

"

ScrotieMcB wrote:

There is no such thing as a concept which exists independent of thought.

I fully agree. It was meant to highlight just that fact.

"

SkyCore wrote:

Or should i say 'discovered' by an individual because all concepts already exist without need of human thought?

I do believe concepts are created, not discovered. This quote of mine is tightly bound to the context in which the OP expressed belief that math exists outside of the human mind.

Math can and does exist outside the human mind. Having a computer experience senses with consciousness is extraordinarily difficult; having it compute strictly a priori knowledge has been done for years.

Also apes.

"

ScrotieMcB wrote:

Math can and does exist outside the human mind. Having a computer experience senses with consciousness is extraordinarily difficult; having it compute strictly a priori knowledge has been done for years.

Point taken. I misspoke. Math does not exist outside of a 'mind' capable of processing it. The meaning of 'mind' is still very vague.

Btw, the limitation of 300 characters in my signature prevents me from fully elucidating as much of the truth as i wish to confer.

But onto the meat of what you said...

There are two key languages in play for any one person: first, the internal one, where concepts are defined to create an internal symbology such that experience can be condensed with some degree of accuracy; second, the external language used to share concepts labeled by audio and visual symbols with others. Your focus seems to be on the latter when certainly the most important is the former.

Once that is done, it is important to realize that a priori knowledge is fully deductive and a posteriori knowledge is at least partially inductive. The inductive process, formalized by the scientific method, rests upon the idea that no hypothesis can ever be proven, only disproven, and thus the conversion of mere hypothetical to glorified theory is, on a personal level, a matter of faith.

** Edit: The notion that science is this purely social construct with peer review and hypotheses-to-theories via community agreement is completely missing the personal nature of inductive reasoning. A human infant can't even meaningfully interact with their world until they've scienced that the environment they perceive is the same one in which they can control the limbs of their body.**

Yes, we do learn a lot from each other, but the one great failing is not our humanity, but the placement of faith blindly in the (apparent) conclusions of others. Faith management is a tricky business (much like chip management in poker), for we don't really have time to rigorously go over every piece of information we find, experimenting directly to see if we independently reach the same conclusions; instead, we take it as probable that a thing is true because someone else says so, for what other motive could they have? While these borrowed conclusions may be accepted most of the time without such review, to accept them as such all of the time, to never audit even a fraction of them, is foolishness. Critical thinking skills are vital, for at the end of the day, you are responsible for the beliefs you hold which you haven't scienced yourself.

Basically, what you blame language for, I attribute to a failure to keep one's own house in order.

By the way, earlier you were referencing a resource for (a posteriori?) thought; I think faith might be it. One only has so many chips in the poker game of what to believe. Unfortunately we've yet to really quantify it.

"

SkyCore wrote:

I could approach that from the other end and say mathematicians (and everyone in general) are so eager to show off their superiority of understanding that they reject anything not immediately recognized as 'correct' without fully exploring its potential. There is a difference between being wrong and not conforming to expectations. And at a deep level, i find this to be among the most widespread flaw of mankind.

It does slow progress, on the other hand, there's something to be said about being able to rely on a typical line of thinking for usual subjects.

"

SkyCore wrote:

My theory is that the brain (the physical brain, not the mind) requires some sort of resource when thoroughly thinking through something.

It does indeed. It burns a tremendous percentage of your body's energy compared to its mass even when resting, and more so when you are thinking a lot, or staying awake for a long period vs sleeping.

"

SkyCore wrote:

Evolution adapted our brain to unconsciously limit potential wasted thought by dismissing things not fully understand. Thus saving internal resources. If so, perhaps there is a drug which can supply excess resources (or the chemical signals involved in monitoring the resource) to the brain. Or both. NZT??

I'd think there would be quite a bit of concern about having too much free neurotransmitters if they tried to chemically stimulate greater thought ability. I would think that one or more governments have already subjected people to testing along these lines, although I haven't really looked into it.

"

SkyCore wrote:

I also think the majority of people are afraid of talking about new concepts. They have learned a social equation subliminally, a formula for how 'conversations should go'. Discussing self-generated novel abstractions, extrapolations, and relations are not a variable in that formula. Hmm, perhaps because such things are not typically discussed... people dont actually learn that they should engage is such things. I dub this meta-level skill, merphing. Every word that ever existed was fabricated by an individual. Or should i say 'discovered' by an individual because all concepts already exist without need of human thought?

MERPHING verb 1) to think about novel abstractions, extrapolations, and relations.

If this happens while you are sleeping (such as while dreaming) and it is subconscious, then it would be SMERPHING.

The opposite of Merphing (acquiring novel abstractions, extrapolations, and relations) vicariously (such a meme browsing) would be SERPHING.

"

ScrotieMcB wrote:

But onto the meat of what you said...

first, the internal one..second, the external language ... Your focus seems to be on the latter when certainly the most important is the former.

There are different ways to evaluate which is more important.

On one hand, you could be said to value yourself greater than all of mankind. That each individual is more important than the group. That is a moral value. An assertion. A core faith that shapes what we think about and how we frame reality. There is no true or false when it comes to assess moral values. It is well beyond the realm of logic.
For you to say with 'certainty' that something is more important than another without fully framing the context with all the parameters... is a bit bold.

On the other hand, i could evaluate your paragraph to instead mean that with limited individuals, the whole of mankind would be weaker despite having stronger external communication.
But that is just erroneous for most scenarios. Look at ants and bees for an example of the hive doing far more (and being more fit for their environment) than the individuals could independently.

"

ScrotieMcB wrote:

Basically, what you blame language for, I attribute to a failure to keep one's own house in order.

I think you are a level or 2 below what i am talking about. I'm not assigning blame. I'm pointing out limitations. Language is great, we owe virtually everything we hold dear to language.

Think about any single word. That word can be considered true if it loosely maps onto physical reality. Take an apple for example: a physical object. The concept of the apple is more than just an individual unique object that exists at only one spot in time. It is a loose class which can be applied to multiple objects. We can manipulate and change the instances of that class without changing the classification.
But in order to do all of that we need a foundation for what all of that means. And after defining all of that, we have additional meanings which require a foundation. Etc ad nauseam. Everything is built up like a house of cards with just 'apple' at the top. That individual apple card is meaningless without the structure underneath it.
at a subsymbolic level, many of those cards do not even have words with which to reference.

As new information comes to light about apples, we can add more cards underneath it. How it behaves under odd circumstances. New possible shapes. Etc.

But most importantly of all, the utility of the abstraction.
Information is infinite. We can take an individual apple and spends millions of manhours fully describing the position and relations of every atom of it. A pointless endeavor. And no matter how much time we invest, we will never exhaust the possibility space of its interactions with other things. And thus we can never fully articulate the ultimate 'real truth' of the apple. No matter how many cards we add, we can invent another.
Only the subset of information which can be applied towards fulfilling goals is worth pursuing. The problem is, we dont always know the bounds of that subset.

Let me reiterate, it seems you overlooked this:

"

SkyCore wrote:

Thinking in human language is the problem. Words cannot truly represent real 'truth'.


At the deepest level, everything is so interconnected we cannot pull the finite out of this infinite whole without losing the 'real truth'.

It's the triangular numbers: 1, 3, 6, 10, etc...

y = x(x-1)/2

"

Darkfyre wrote:

Ok, now do it for no overlapping lines :)

y = 2x - 3 is my guess, I can't see how to get more than x-3 non-overlapping lines in the centre. Perhaps you can get more by drawing the points with irregular spacing though.

Also, do the lines need to be straight? Because if they can be curved, it's more of a graph theory question than a geometry one.