Religion bashing

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^^ Correct. To grasp infinity, one must first have a mind with greater than infinite capacity.

That's one of the main reasons I believe in the 'world of forms'.

If math is 'all in our heads' as some people say, so is the (uncountably) infinite set of statements that can be made about the real numbers alone. That doesn't make sense.

The universe presents innumerable interactions and their perceptible effects each of which can present aspects which can be symbolized mathematically. Our limited perceptions and symbolic capabilities can select a few of these phenomena and declare them to be vital and total but it is very unlikely that we can conceive of the whole even though there is nothing supernatural involved. Science is continuously discovering new and important perceptions and new relationships of old perceptions and the integration of these new perceptions are frequently changing our conceptions as to what is important and what has been mistakenly assumed as vital. Mathematics is a symbolic representation of what we know and also what we suspect which may or may not exist. There is no doubt that all math is in our heads for, whatever is recorded, if there are no heads to interpret the recordings, the records are merely a peculiar detritus of a rather odd species.

Why? Cannot an infinite thing be grasped by means of just a few principles? Mathematically, all statements we make are in some sense infinite; if there is no x such that x+1=x, then I have apprehended a fact of an infinite number of things. From a simple rule, we may generate knowledge of many things. That these things are not represented in our minds does not thereby imply that we have not grasped them, because there is naught to them that we do not understand. What great feat of computation do I need to understand the infinity of the natural sequence?

Now, the human mind has not the ability to simultaneously track a number of objects greater than about seven. Can I not grasp things greater than that simply because I do not simultaneously apprehend them all? Of course not.

I think what he's trying to say is that math will certainly never exhaust itself and science will almost certainly never exhaust itself.

Which is true, but has nothing to do with the (well-known) infinities that are around.

I do not doubt that particular properties of infinity can be symbolized and manipulated but the total concept of an infinite collection of anything cannot be contained in a finite mind and emotionally accepted as some sort of superbeing.

It requires a lot of thought

But there are ways

Hell, you can even work with 4+ (spatial) dimensions very easily, which is something you do every time you use Google or Yahoo!, and some people can even visualize these dimensions. That's even harder than imagining infinity.

See?

You can memorize a verbal description or mathematical formula that represents the concept of infinity. But to try to fully understand infinity itself with a finite mind is an exercise in egotistical futility.

For instance, I can describe infinity as an ever-expanding mathematical process without limits, but this is not infinity itself.

As an even further, albeit inverted, model of infinity would be to describe the topography of the Earth in the most minute detail. Sure, you know where australia is, and may even be able to draw a fairly accurate outline of its coast. But there is no way that one mind would have the capacity to memorize the position of each individual grain of sand, as well as an approximation of the velocity of each of those grains of sand, and in turn predict where each of those grains of sand will be and how fast it will be going in the next second.

(... disregarding Heisenberg's uncertainty principle, of course.)

Now consider that each grain of sand is composed of trillions of silicon atoms, and these atoms each have electrons and nuclear components, and each of these components are composed of quarks, and each quark may have even smaller components...

This is called infinite regression - reduction of scale down below the sub-atomic level. And one brain could not possibly contain the position of each quark in each atom of each grain of sand, simply because there are fewer neurons in the human brain than grains of sand in Australia - the data exceeds the available capacity.

Now consider that there is a but a finite number of grains of sand in Australia, and compare that concept that an infinite number of sand grains would fill the entire universe, and you may begin to understand how the human mind fails to fully comprehend infinity.

Only the Infinite can truly understand infinity.

Now we're pissing over semantics.

What about concepts such as fields, or groups, or graphs? In some sense, no one fully understands everything about them, because, amazingly, there's scads of new research on pure mathematical structures every year. And they aren't even tangible.

I really don't see how anyone is getting around the idea that we can't grasp, say, the number of planets in the solar system because they exceed the number of objects a human can keep track of at once. Whenever we move to a greater size we are popping it down to a description which describes its essence. I no more don't understand infinity than I don't understand the number of pennies I have lying on my desk at this very moment.

To claim you understand infinity because you can easily perceive it is an eight letter word I find unconvincing. More or less that is your argument.

The scientists of Galileo's time thought the earth was flat and ridiculed him while the religionists wanted to kill him.
I think it's safe to say that the scientists now don't know everything nor do the religionists so don't bank on what they say so much.

Despite the rumors, a flat Earth was never much popular with scientists. Even the Greeks were aware of the curvature of the Earth. The scientists are well aware they don't know everything and are excited over the prospect of finding out. Religion claims to know everything and doesn't want to hear otherwise.

A flat earth was never much popular, period.

What Galileo got in trouble for was geocentrism vs heliocentrism.

http://www.miraclesofthequran.com/

Well, it looks like the Qu'ran has to be updated again. The latest Scientific American seems to indicate that there was no Big Bang but that the universe expands and collapses in an endless series of repetitions. Maybe Allah has a yoyo for a toy and got the idea that way.