Something interesting I learned last night. It occurred to me that if real numbers (the set of rational numbers + the set of irrational numbers) enable hypercomputation, and hypercomputation is not possible, real numbers must not exist (physically). A quick google search led me to wikipedia, which confirmed the suspicion: http://en.wikipedia.org/wiki/Real_number#In_physics

In some recent developments of theoretical physics stemming from the holographic principle, the Universe is seen fundamentally as an information store, essentially zeroes and ones, organized in much less geometrical fashion and manifesting itself as space-time and particle fields only on a more superficial level. This approach removes the real number system from its foundational role in physics and even prohibits the existence of infinite precision real numbers in the physical universe by considerations based on the Bekenstein bound.[2]

So, “real” numbers are not so real at all. That’s gotta be some kind of ironic misnomer - an irononomer, if you will.

Also, proof that we are all robots.

...And a quick search of the forum shows I already knew this (http://www.centerforinquiry.net/forums/viewthread/13144/). Haha…you relearn something new every day

Now wait just a minute, domokato.  How can you refer to post #13144 if real numbers aren’t real? 

Occam

Hmmm… I don’t know if this makes sense.

In the first place in physics we work with measured values. These have limited precision, so it does not make much sense to distinguish between real numbers and rational numbers.

In the second place, this holistic stuff is still quite speculative. And if I understand what is meant with the ‘Bekenstein bound’, then, given that the universe is infinite, also makes the distinction between discrete values (‘digital’) and continuous values (‘analog’) impossible.

And in the third place: just imagine one could create a perfect square, and cut it exactly at its diagonal, it is difficult to see that we would not have created a ‘real length’, involving some square root.

It is all a very, very theoretical exercise…

Well, if real numbers aren’t real, then are imaginary numbers not imaginary? 

Who us play word games???  Never. 

Occam

Maybe imaginary numbers are real and real numbers are imaginary.

Sorry, this all too complex for me.

From the same wiki you quoted from:

In mathematics, a real number is a value that represents a quantity along a continuous line.

In that sense, that a real number is “a value that represents a quantity” the question of reality does not arise. What is a number or continuous line is more murky.

Regarding the implications from the holographic principle, from:

http://en.wikipedia.org/wiki/Holographic_principle

In a larger and more speculative sense, the theory suggests that the entire universe can be seen as a two-dimensional information structure “painted” on the cosmological horizon, such that the three dimensions we observe are only an effective description at macroscopic scales and at low energies.

The universe of three dimensions that we observe is also not real. 

I think that this is a potential misuse of the word ‘real’. Probably a description that is more accurate is that when we look at very extreme scales, the way things are described begin to break down for things at extremely distant scales. So, maybe real numbers don’t make that much sense at quantum scales, but at human scales, they do.

T-A is correct.  We have to be very careful to recognize that when scientists choose words to identify a particular substance or concept, it doesn’t necessarily have the same meaning as it does when used in everyday conversation.  The same goes in the other direction, too.  For example, chemists chose organic to identify compounds that contained carbon, mainly because most of them came from life forms at the time.  As many new and very exotic compounds were synthesized, such as the fluorinated monomers to make Teflon, which had no connection with living organisms, they were still called organic because of the carbon in them.  Finally, the people who wanted to avoid the manipulation of food sources by insecticides, fancy growth regulators, hormones, antibiotics, etc., gave these unmodified products the name, “organic”.  Fine word, but with a fair number of different definitions.  But it would be silly to argue about its use in one venue while imposing the definition of a different area.  The same goes for the mathematical use of “real” and “imaginary.”

Occam