If I understand your argument, numbers are intuitive because multiple number systems with differing bases have arisen over time. I think this would play into the concept of numbers not being intuitive. I have 10 apples, you give me 1 apple, I have 11 apples. How many apples do you picture me having? Most modern people will picture {A A A A A A A A A A A} sitting before me. I computer would have the picture {A A A} sitting before me. A base 20 system would picture {A A A A A A A A A A A A A A A A A A A A A} before me.

I will concede that a when dealing with a set of counting numbers (consisting of the union of natural numbers and some fractional values, and possibly even integers once a more abstract system of commerce with debt is established) could be considered intuitive. However, the complex number set includes a real number component plus an imaginary component (the square root of -1), which is something that often unused in most people's lives and seems utterly unintuitive. Many irrational numbers are also unintuitive, as are extremely large and small numbers. Perhaps our differing opinion comes from viewing the term 'number' as different number sets?

To be honest, I can understand why people find it incredulous that certain concepts are not intuitive. For example, they have shown that children in Africa who grew up making toys out of spare bits of wire have an "intuitive" grasp towards CAD design. To this child, building wire frame models seems natural, but to many other children who did not have the same education in building physical wire frame models do not have the same grasp of the concept and definitely would not find it intuitive.

I admit that I too have my own biases in these matters, for I have grown up in the USA and have been exposed to certain things. For example, there are certain human rights that I consider "intuitive" in nature, but a person from a collectivist culture would not find "intuitive" (and vice verse). To me this indicates that some of these areas are not intuitive but learned constructs. As such, I regard things labeled as "intuitive" with a bit of skepticism.

I think the terrorists have gotten more then they have lost. We live in fear, giving up our rights and freedoms in order to gain the illusion of "security". Then again, this is a police state's wet dream - a passive, docile, and accepting population who never question. (Meaning population as a whole, we know there are plenty of individuals and small organizations that do question the state.)

I was going to say that any other person trying to pat down a 4 year old would be considered a child molester...

I'm curious if this level of search is unique to US airports - do you know? After all, I may consider taking a bus or train up to Canada or down to Mexico and fly from there - but if this new level of invasive "security" is universal, then I might as well not bother...

First movie that made me cry, and it was over the bleeping robot! Much later in life, I though that guy was a jerk for taking one of the robots (Huey) with him when he committed suicide. I was all like "why? WHY? You could have let him go too!" Yup, now I view Lowell as the kind of guy who kills his family before killing himself.

Do you intuitively know what a continent is? If you said yes, post a reply then check out What are Continents? - then post another reply to that.

As to the measuring cup example: if a number line is so intuitive to a measuring cups, why are so many sets of unmarked 1/4 cup, 1/3 cup, 1/2 cup, and 1 cup measuring cups sold? After all, shouldn't anyone just need a 1 cup measuring cup? For that matter, why need tablespoons and teaspoons? After all, a tablespoon is merely 1/16 of a cup and a teaspoon is 1/48 of a cup. Only those measuring cups that have a number line artificially graphed on them are intuitive - otherwise why even need a measuring cup, as a measuring gallon would be just as easy to use and require a lot less kitchen tools.

I think your examples are putting the cart before the horse. You perceive these things to be intuitive examples of a number line because you already have already been educated in what a number line is. The study mentioned reports that adults in other cultures who have not been indoctrinated/educated in the concept of a number line do not perceive these objects in that manner. This is why we often see scientific research done on things we consider "common sense" - because science cannot assume something is because it is perceived as intuitive, they need to find evidence that it is intuitive. In this case, they have found evidence that number lines are not intuitive.

If you find a white crow, it shows the statement 'all crows are black' is false. Thus, the statement "number lines are intuitive" is proven false by this study. Similarly, your statement of "number lines can be intuitive" has an unspoken assumption of 'assuming you know what a number line is' is a fairly meaningless assertion. In other words, you have found good tools to teach people how to perceive a number line, but if you do not teach them a number line the likelihood of them developing the concept without prompting is low.

So suppose I walk in a circle, such that my 10th step falls in the same location as my first step. Is that circle a number line?

The question you need to ask yourself is this: when I did not know what a number line was did my walking make me intuitively come up with the concept of an rank ordered and regularly interval-ed straight line, or does my knowledge of a number line make me perceive walking as a rank ordered and regularly interval-ed straight line where a step backwards is a "negative" step and a step forward is a "positive" step? What the article shows is the latter is far more likely.

No, not joking. There already have been studies that show different cultures have different counting systems. For example, many cultures will have only the most basic of numbers (1, 2, 3, 4, 5) and then jump into the "many" category. Another example of the non-intuitive nature of numbers? 0. That one took a while to catch on. Third example? Describe to me a forest with -10 trees or a person with -1 apple. Negative numbers were not intuitive either. Notice I am avoiding those wonderful numbers like fractions, irrational numbers (pi, e, the square root of two, etc), and complex numbers (i, the square root of -1... graph that on your number line!) - all of which are not intuitive in and of themselves. Final example? If numbers are intuitive, why does it take so long to teach our young to count? Why do so few people understand the concept of billions and trillions of dollars of debt, or the vast distances of the universe, or the very tiny number which represents the time in which million/billion/trillions of molecules collide and interact when undergoing an exothermic reaction?

No, while you have been educated and indoctrinated into a system of numbers, that does not mean it is intuitive. Or another way to think of it - take the pro basketball player who has taught his muscles how to shoot a 3-pointer... he might argue that it is intuitive, meanwhile someone like me (who couldn't make a freaking free-throw shot) would say that it is definitely not intuitive.

I recently was thinking about being "ageless" in terms of elves recently (as I dusted off my old RPGs). In particular, it was Terry K. Amthor's Shadow World, where there is an island called Namar-Tol. Here they are ruled by dark haired elves who viewed the non-ageless races as lesser. I began to think about what that does to the psyche of a being, and realized how alien the concept is. True, you can die from accident or mayhem, but not likely due to disease as an elf. When you live 10,000 years and a human lives 60, that is .6% of your lifespan. Think of it this way, if you have a 60 year lifespan, what would you think of a creature that claimed to be intelligent but only lived 4 1/2 months? There are so many things these "intelligent" creatures would not understand, like the changing of the seasons - much like the ageless would understand the changing of the climate, rising of mountains, and shifting political powers.

Some would argue that mortality is essential to the human condition. If ageless, we could do wonderful things - but would we be human anymore? Also, if ageless would we still be subject to the ravages of diseases? For example, LDLs lead to cardiac disease and heart attack? Would cancers still occur? As ageless, I would assume you reach physical maturity and stop, so the latter might be less likely, while normal heart failure would not occur while congestive heart failure would. What of those born with disabilities like Down Syndrome? In another reply, someone mentioned what would happen to the personality of an individual over great spans of time - as they forget their past and learn new things, would they still truly be the same person anymore?

Overall, being ageless is an interesting topic - but you are right, it could fill volumes. However, the advent of agelessness for human society could also make quite an interesting series of books. If achieved by technological means (surgery and manipulation of telomeres), that would imply a cost to the treatment - so who would be the ones to receive it? How many would be given that privilege? Would those who discover it and know of it even be willing to share it with the masses? How would those denied access to agelessness react? Yeah, sounds like it could make for quite an interesting series...

Correct. Doctor Giulio Tononi has a hypothesis over sleep and synaptic homeostatis. Think of neurons in the brain as being nodes in a map and the connections they make as being weighted edges of the network map. These weights actually represent vesicles of neurotransmitters of one cell and their corresponding receptors of the other cell, and these transmembrane protein receptors increase the amount of energy for a cell to maintain itself. Synaptic downscaling ( the reuptake of the receptors) occurs at a certain frequency within the brain, and this frequency is replicated by slow wave sleep. In more computer science terms, think of it as all the edge weights being reduced in equal proportions on an exponential scale. Thus the edge weights will be at 1/2^t, but after a certain minimum threshold is breached they can go do a 0 equivalent (ie, the connection breaks).

This synaptic downscaling is vital to maintaining a brain that can continue to learn. If downscaling never occurred then eventually you would reach saturation of your neural connections and all energy would be spent maintaining the current state of your brain. Hence, a person does forget in order to forge new connections.

However, you are right - look how different people become after a mere 50 years. Then again, look at what happens when people can apply 20 or 30 years of experience in a field. Imagine what works of art or discoveries could be completed if someone had 1,000 or 100,000 years of experience in it!

Yes, by immortal - which by definition means "living forever, never dying or decaying" - I do mean "absolutely unkillable". That is the definition of not being immortal.

Tolkien elves and so forth are not "immortal", they are "ageless" - a nuanced difference. Ageless means never dying due to age, which is the most likely outcome of research into organ transplants and telomere manipulation. If you can be killed by accident, homicide, suicide, or disease then you are not immortal - in fact, you are quite mortal or "subject to death" (again, by definition

The term used is very important. If you can be killed by violent means, but not by age, then you are ageless and not invulnerable. If you cannot be killed by violent means, but still suffer the trauma of the injuries, then you are immortal. If you cannot be killed by any means and are also immune to any physical damage, then you are both immortal and invulnerable.

As to fertility rates and population declines, there are other factors such as education and economic status that play into these shifts in numbers. As medical science advances and people live longer, we are tapping more and more resources. Ground water depletion, deforestation, over-farming, and so forth. What are the ethical ramifications of a population boom and the people cannot grow enough food - they could live forever if they have food, so is denying them access to food murder? The same for water and shelter. If then population is to be controlled, who gets to decide who breeds and how much? What does this mean for retirement age? Life in prison sentences? True, eventually it would oscillate from overpopulation to underpopulation, with period of low population and plenty followed by high population and famine - and competition for scarce resources is one of the primary reasons for war.

However, I will also concede, there is a chance that the population will stabilize and the problems will be no greater than they are today. However, I do not have that level of faith in humanity. How can I when I look upon our past and current behavior?

Although not my favorite in terms of story or plot, I do think Torchwood's "Miracle Day" covered the effects of true immortality on the human world pretty nicely. People still got sick, still sustained mortal wounds, and still tried to kill themselves - but they just wouldn't die. What do you do when the human population is still multiplying, still getting sick and transmitting diseases, and still suffering brain-damaging strokes or fall into comas but will not die? What does it mean for our criminal legal system and how would it effect human behavior?

So, yes, I agree - immortality would create far more problems than it solves.

Google is powerful. A simple search for 'define immortal' returns this:

So, yes, immortality does mean the end of death. If you are immortal, you cannot die and do not age - and that, my friend, is a fate I would not wish upon my worst foe.

"Limited immortality" is not just plain old immortality. Immortality means the lack of mortal existence - you cannot be killed or destroyed. Anything can be done to you and you keep going on. A key here - if you are hit by a bus, you can sustain a mortal wound. Hence, immortality would have to at least be an extension of mind uploading (so that your "mind" could forever be preserved). One may argue that if teleportation is actually creating a copy, then immortality would be an extension of two of the technologies on the list. Hence, there is no way immortality could be first.

"Limited immortality" would better be phrased as ageless. The current conclusion based on observation is that those with long telomeres live longer and do not suffer the effects of aging as much, and thus being able to repair these sacrificial ends of your DNA strands should extend your cell life. A person who is invulnerable but not ageless is still mortal, for they can die of old are but not from mortal wounds.

On an interesting side note, we do have a form of "deathlessness" within the human body - and we call these cells cancer cells. On a basic level, the cells malfunction, keep dividing, and fail to undergo apoptosis or cell death. So you can think of cancer cells as either undead zombie cells or, more accurately, ageless "limited immortality" cells.