patrick.net

Randy H says

A line cannot split infinitely small unless it is also infinitely large.

What are you talking about ?

These questions were considered long ago by Aristotle and Zeno.

If you start with a line segment one inch long, I don't care how many times you cut it in half, say n times, the resulting length will be an actual nonzero length of exactly 1/(2^n) inches (one over two to the nth inches).

If we can't measure one trillionth of one trillionth of one trillionth of an inch, does that mean that such a small length does not conceptually exist ? I guess this does get tricky if we are talking about actual physical space, but certainly conceptually on a number line we can express lengths as small as you wish.

That is, at least mathematically speaking, infinitely small is easy to grasp, and is not questioned.

But the topic has some depth to it. Rational numbers versus irrational numbers, countably infinite versus uncountably infinite.

Randy H says

A line cannot split infinitely small unless it is also infinitely large. Otherwise it is bounded by constraints, and at some level of arbitrary smallness it will cease to be divisiable. And a line cannot be infinitely large because *infinitely* means it will exceed the contraints of the universe unless the universe is also infinite. If the universe is finite, then the line would consume the universe and the entire universe would only be the line. If the universe is infinite, then everything has already happened and causality is broken.

The axiom of choice would beg to disagree

Randy H says

But I still hold that a line is not infinitely divisiable.

Oh, prey tell, give me the smallest segment on the line from zero to one.

Is .99999999999999...(repeating) equal to one ? If so, than please tell me what is the number that comes right before one ?

And if one represented one inch, what would be the distance between these two "adjacent" numbers ?

Would it be zero ? Well, maybe. But then we do not have the ability to name two such adjacent numbers. For any two arbitrarily close numbers you can come up with, I can easily list infinite numbers that are between them.

Infinity is one of those areas where the empirical may not support the conceptual. Mathematics allows for many concepts which are entirely abstract and exceed the constraints of the physics of the universe. That doesn't mean math is truth and those aspects of the universe are simply undiscovered/undiscoverable. It also means that some math exceeds reality and qualifies as well structured, rational imagination. Infinity is one of those concepts.

Substitute "time" for "line" in your theorem above and suddenly you can no longer rely upon dividing a segment of time 1/2^n because time cannot be smaller than a single chronon.

If nothing is actually continuous, then infinity is reduced to "countable infinity" which simply means it's finite, but really f'ing huge.

So if I hear you correctly, you are saying that "reality" might be an extremely high definition digital computer program (as in the matrix)?

Just kidding.

Randy H says

If nothing is actually continuous, then infinity is reduced to "countable infinity" which simply means it's finite, but really f'ing huge.

I don't get what you're trying to say. I do get that you are trying to agree with Aristotle. Sure, if you want to talk about the number of stars or grains of sand, these things would seem to be finite.

But infinity is simply a concept. Zeno argues basically that motion is impossible without infinity because to get from point A to point B would would have to cross a point C that is half way between A and B. Then to get from point C to point B you would have to cross a point half way between those.etc, etc. Without crossing infinite points you can not get from A to B. REmember, this is how the rabbit loses to the tortoise.

THere are logical paradoxes that try to counter zeno. These are fun and prove only that arguing about infinity can lead to paradoxes about paradoxes.

I get your point about abstraction. And that in reality infinity is not so easy to fathom. This is why we have axioms (or postulates). I have never even seen an axiom that states that infinitely small intervals of time or space exist. But physics and even the idea of using continuous functions to describe reality implies such axioms.

About countable versus uncountable.Countably infinite would be for example the number of integers or rational numbers, because we can come up with a plan for counting (or listing them if you prefer), where as the irrational numbers are uncountably infinite. Both are truly infinite. It's just that the latter is a much larger infinity. (I know, weird, right?).

Speaking of Mythical entities being powerless against certain materials (a recurring theme in Indo-European mythology), how about things they are attracted to?

"But his inwards and his legs shall he wash in water: and the priest shall burn all on the altar, to be a burnt sacrifice, an offering made by fire, of a sweet savour unto the Lord." --Leviticus 1:9

Modern religionists should explain why their all-powerful, timeless, benevolent god cares for a good barbeque. Seems to me a being that existed forever, needs no sustenance, etc. wouldn't have much of a use for a grilled steak.

In fact, this Yahweh cat is alot like Ba'al, Apollo, or Thor in enjoying a little piece of meat presented by his followers from time to time. Looks like over time, this "King of the Mountain" Sky God eventually encompassed all the other Gods, did away with his wife, Astarte/Ashtoret/Ishtar, and become more abstract over time.

This line from Leviticus is an artifact from a previous era when Yahweh, in his original form, was much like any other Indo-European deity. As society became more complicated, they changed their God(s) to fit the times.

Hence, in a society experiencing Euhemerism*, Cosmopolitanism, and Alienation, God was again modified to have an only begotten son whose message was not just to Hebrews, but to the Entire World, who was made to fit into a real time and place, and was a PERSONAL savior rather than one who brought benefits to all society in general.

* Euhemerism is the process of putting mythological beings into a set time and place on Earth. In the early Roman empire, Hercules, Perseus, and other mythological beings, once thought to have existed in a nebulous time and place were given a physical, historical existence in a time and place on Earth and their stories rewritten as actual events.

bdrasin says

A classic Islay malt. Good choice.

I do enjoy a good Islay. At any given time 1/3 to 1/2 of the whisky on my shelf is Islay.

Of course, I always keep Lagavulin stocked.

thunderlips11 says

God was again modified

Another modification would be the preference for cash over BBQ.

And speaking of BBQ and spirits one of my favoite spirits this summer has been Ardbeg Uigeadail it has a strong smoky finish with hints of BBQ and it pairs well with... well, BBQ.

leoj707 says

I do enjoy a good Islay. At any given time 1/3 to 1/2 of the whisky on my shelf is Islay.

Have tried to acquire a taste for them. Don't get it so far, unless it's all about not drinking too much because the flavors are so strong. A lot of peat, right ?

Randy H says

time cannot be smaller than a single chronon.

That's just a theory.

thunderlips11 says

Looks like over time, this "King of the Mountain" Sky God eventually encompassed all the other Gods, did away with his wife, Astarte/Ashtoret/Ishtar, and become more abstract over time.

Yes, it is interesting how Romney's faith of Mormonism has woven the god wife back into the mix with Joseph Smiths "doctrine of Heavenly Mother." Actually in the Mormon faith god has many wives, as will all Mormons -- er, Mormon men that is -- who are deemed worthy enough to achieve godhood themselves.

marcus says

Have tried to acquire a taste for them. Don't get it so far, unless it's all about not drinking too much because the flavors are so strong. A lot of peat, right ?

Yeah, a lot of peat and smoke.

To get used to them I think that it helps doing tastings with non-Islay malts to have a flavor reference point, and yes drinking slow.

Even so it is just not to some peoples taste. A buddy of mine gave me a Lagavulin with 80% left because he just could not finish the bottle.

I tried a less expensive one a year or two ago ( Laphroaig 10yr ) that I still haven't finished.

leoj707 says

Another modification would be the preference for cash over BBQ.

ROTFL

Yes, Yahweh has now taken on the aspects of Mercury, Plutus or Cai Shen.

marcus says

I tried a less expensive a year or two ago Laphroaig that I still haven't finished.

The Laphroaig 10 year I am guessing? I do enjoy it but it is getting close to my tolerance level for drinking straight whisky. Not the best Islay to start on.

The 18 year is much better and by comparison not as heavy on the smoke. Also, the Laphroaig Quarter Cask is a fun change with some additional character from being finished in the smaller cask.

Nerds with Doctor Who and Sim City references, and Whiskey Afficionados. Man, I love this site.

Randy H says

A line cannot... is broken.

What are you smoking and how much does it cost?

marcus says

Is .99999999999999...(repeating) equal to one ? If so, than please tell me what is the number that comes right before one ?

As someone who claims to be a math teacher, you should know that second question is meaningless as the real numbers, like the rational numbers, are of the second order of infinity and the "comes right before" question applies only to countably infinite (1st order infinity) or finite (0 order infinity) ordered sets. That's basic abstract algebra.

I don't know how this thread got off tracked to math and physics, but here are a few facts.

In a continuous space like the mathematical space used in Euclidean geometry, a line segment can be divided in half an arbitrary number of times. A line segment has finite length by definition and is infinitely divisible by the following technique.

Create two circles at either endpoint of the segment with a radius equal to the sequent. Bisect the line segment by drawing another at the two points where the circles intersect. Repeat as many times as you like, even to infinity.

The physical universe, however, is discrete on the quantum level. Matter, energy, space, and time all occur in discrete quantities. For example, the smallest unit of length with any meaning in the classical sense is the Plank Length. And the smallest unit of time, the moment if you will, is the Plank Time, which is the time it takes light to travel the Plank Length in a vacuum.

I would argue that the universe is deterministic even though its not fully predictable and that true randomness does not exist even though the concept is useful in statistical analysis of physical phenomenon. And yes, technically the universe does satisfy the definition of a computer. Put that does not imply that there is a programmer or a purpose to its calculations.

thunderlips11 says

Modern religionists should explain why their all-powerful, timeless, benevolent god cares for a good barbeque. Seems to me a being that existed forever, needs no sustenance, etc. wouldn't have much of a use for a grilled steak.

Why can't a super being enjoy a good bit of meat, no doubt with a glass of scotch? Sounds good to me!

Dan8267 says

As someone who claims to be a math teacher

Okay well, of course I ignored you again the other day because of your obnoxious personality (again).

I unignored just now, because of a bet I had with myself. Will he be:

1) adding to the conversation

2) restating something I said

3) just trying to mix t up with me again - basically criticiszing or in some way asserting again that I'm an idiot.

I predicted correcltly that it would be #2, #3 or a combination of both.

For the record, you are wrong, rational numbers are countably infinite. Since by definition a rational number can be expressed as a quotient of two integers, it's easy to set up a two dimensional matrix or maybe I should say lattice with a description of how you will "count" them.

Irrational numbers are (as I said) uncountably infinite. SO of course the real numbers which include both rational and irrational are uncountably infinite.

To get an idea how much bigger the one infinity is than the other: If you were able to randomly select a real number, the probability that it would be a rational number is zero. That is, there is a zero chance that the number would be rational.

Dan8267 says

the "comes right before" question applies only to countably infinite

This is also wrong. Even for any two rational number you give me, it's simple to come up with one that is between them (actually an infinite number of rational numbers between them).

Dan8267 says

The physical universe, however, is discrete on the quantum level. Matter, energy, space, and time all occur in discrete quantities. For example, the smallest unit of length with any meaning in the classical sense is the Plank Length.

Even if the first sentence is true, I'm not so sure about the second. And the third sounds wrong to me. Plank length is only a theoretical smallest measurable length.

I'm not a physicist, but it seems to me that even if there are fundamentally smallest particles in this reality of ours, I don't see why they cant have an actual length even if the length is far too small to measure. But this is getting away from factual knowledge (at least of mine) and in to speculation. I don't claim to know.

I'll admit it. I'm curious, will Dan admit to being wrong before he puts together a long paper about particle physics for us ?

It could be a break through. If he does admit to being wrong, will it be couched in another of his famous rants about what an idiot I am ?

I really am curious.

(My prediction is that it is not possible for him to do it in a humble way. At a minimum, if he does admit he's wrong - he has to figure out a way to do it where he can still assert how much smarter he is than I ).

I'm looking for some creativity this time Dan. Don't let me down.

Dan, I think the best bet would be a few thousand words about physics showing us how smart you are, with possibly just 8 words acknowledging your error about rational numbers and what countably infinite means.

In perspective the errors will seem small and insignificant.

I think going with that would work fairly well. Not many people are reading this anyway. Don't worry about it.

The original post at the top of the thread says it all.

What's that? THat there are are assholes out there that that are still doing what most people get over at the age of 15 or 16 ?

That is, challenging the logic of religious belief. As I said, the believers know they can't prove their beliefs and don't claim that they can. I guess engaging a religious person in a logical debate about their beliefs can give a person a feeling of intellectual superiority (especially if they are an adolescent).

That's what I think the cartoon is about.

marcus says

As I said, the believers know they can't prove their beliefs and don't claim that they can.

Many, many, many (yes that was 3 "manys") believers believe that they can prove their belief. Volumes are written by believers that think they can prove that they have the one true belief.

Only believers that lean towards the rational acknowledge that religious belief can not (currently) be proven.

http://www.quickmeme.com/meme/3q3sgx/

leoj707 says

Many, many, many (yes that was 3 "manys") believers believe that they can prove their belief.

In all of the respected divinity schools and schools of christian learning including Catholic seminaries, I believe that it's understood that their beliefs can not be proven. Hence the word 'faith.'

Fundamentalists are another story.

[...]

curious2 says

The Templeton Prize is only the latest in a long list, as "proofs" of Christianity go back at least to Medieval times.

The Templeton prize isn't about proving Christianity.

http://www.templetonprize.org/previouswinner.html

http://www.templetonprize.org/abouttheprize.html

curious2 says

The converse also applies: the vehement opponents of teaching evolution are almost exclusively Christian,

THat's really only fundamentalists.

marcus says

In all of the respected divinity schools and schools of christian learning including Catholic seminaries, I believe that it's understood that their beliefs can not be proven. Hence the word 'faith.'

While this may be the case for "scholars" in divinity schools the rank and file overwhelmingly believe that their faith can be "proven". The Catholic tradition is steeped in "proof" that their faith is true -- Jesus ever appear on your toast? Well, other people have so it must be true, right?

Yes, this is contrary to the idea of faith, and often the "proof" they choose to grasp to is simple circular logic, i.e., the bible proves my belief in god is true -- god wrote the bible so the bible is true.

If the majority of religious people believed that their faith could not be proven then we would see a lot less videos like this:
http://www.youtube.com/embed/nfv-Qn1M58I

curious2 says

Actually, the insistence on proving a religious belief seems mostly Christian.

Perhaps the "insistence" on proving their religion is mostly christian, but I don't think this means that other don't think that their faith can't be or isn't proven.

First, lots of non-judeo-christian-islam religions are not mutually exclusive in regards to other spiritual beliefs. So, no need to prove your faith is the "right" one to believe.

Second, I think that in a lot of places the "proof" in the supernatural is just assumed. If Hindu's believed that it was impossible empirically "prove" their faith then the god men con-artists would loose their living. Why would you give money to someone who basically proves that the supernatural exists?

[...]

marcus says

http://www.quickmeme.com/meme/3q3sgx/

Yes, that image is amusing, but there is a fundamental problem with the assumption made by the image -- that Christians don’t actually do anything that merits pissing off an atheist; atheists are getting their panties in a bunch simply because Christians exist.

Do you honestly think that Christians have given Atheists no reason to be pissed off?

Also, it is not that there is something special about Christianity that draws the ire of atheists. Any proselytizing faith that had a huge bulk of members pushing things like intelligent design for science classes would also piss of Atheists.

curious2 says

It will be interesting to see what happens if someone proves conclusively that Jesus never actually lived

No need to for them to worry. Baring time travel, I don't think that can ever be proven.

Mathematics allows for many concepts which are entirely abstract and exceed the constraints of the physics of the universe.

This reminds me of a quote, "Black holes are God dividing by zero."