Energy/Math Discussion

[PGTips]

So in other words, disseminition of information seems an irreversable process. Once you tell a secret, you can't take it back.

To use VelocideX's example, you could kill everyone. That would make it a secret again.

 

[gloggawogga]

^^^ Its going to take alot of work to kill everyone, or even those who stole my secret, and that too is an irreversable process. You need to factor that into the equation. Once the secret gets out, its a mess to clean up.

To make an analogy to the 2nd law, turning on my air conditioner will decrease the entropy within my house, but not of the entire universe. It takes work to run my A/C, and my house is not a closed system. The 2nd law only applies to closed systems.

 

[Grim]

Like I said before, there is a level of uncertainty involved when we are dealing with subatomic particles. The macroscopic world functions according to Newtonian laws. At the microscopic level on the other hand, the quantum world limits any certainty regarding the unfolding physical events.

Because the wave function for large objects is much smaller than it is for particles, we can base laws based on probabilities, which are more solid on the macroscopic level. These probabilities are what we consider information. We can take a look at an object and say give it a certain attribute. However at the quantum level, a particle can simultaneously be in a spin-up or spin-down state and position is unknown. So where is the information contained about this particle's spin and position? Say this particle is an electron and we know its energy, how does this knowledge carry with it the information about the position of the electron?

I do believe however that there is a deeper level to reality where everything is infinitely interconnected. I think that everything is part of a more fundamental 'whole' that we canot comprehend with our level of consciousness. Science is fallible because it constantly proves itself wrong so you can never say something is absolute. It is more epistemological in nature, while there is a big ontological aspect that is left to be dealt with.

 

[yougene]

I found this snippet on wikipedia very interesting regarding information.


"As a more physically scientific definition, information is possibly a property in physics. This is demonstrated by the phenomenon of quantum entanglement where information itself cannot travel faster than light, even if the information is transmitted indirectly. This could lead to the fact that all attempts at physically observing a particle with an "entangled" relationship to each other could slow down, even though they are not connected in any other way other than information.

Another such phenomenon is demonstrated where it was proven that in logic gates, an "AND gate" releases more heat than the "OR gate" does because information is destroyed in an AND gate and simply converted in an "OR gate". This discovery is an important development in research to create efficient and therefore less signal interference in quantum computers, as interference is a major roadblock.

This is often held contradictory to the traditional view that information is merely sensory input subjective to each organism or the human brain."

 

[David]

^^Human's like to think they have an effect on how the universe operates. Without humans though, the world would operate much better.

David, you honestly still don't understand this? Pi can be defined by any one of a zillion formulae: eg,

It's easy to show that this series is convergent and hence it uniquely defines Pi. Defined this way Pi is an exact value, not an approximation. Furthermore, the series gives us a direct method of constructing arbitrarily good decimal (or rational) approximations to Pi.

Still an approximation Zorn. An equation is a representation, not the actual value. 8) You should know this. In the real world things are defined to a point of a value. Pi can't be defined within this point, which is why I don't agree with it. I think it's up to like 1.2411 trillion decimal spaces, and that alters results quite a bit, considering we are dealing with a value between 0.1 and 1. The results could alter the very reasoning behind inflation. This is what bothers me about Pi, is that clear enough? Shit between 0.1 and 0.1 X 10^-100 there is such a difference in how the universe would look. This is where my argument actually stems from. It's not from a lacking of understanding, unlike what seems to be the popular thing thrown at me these days.

There are many ways to do it. One simple way: First, by passing an electron beam (accelerated using a known potential) through a known electric and/or magnetic field and observing the deflection or radius of curvature of the beam, you can calculate the charge charge-to-mass ratio of the electron. This is a common freshman physics labs. Then measure the electron charge, for example using an oil-drop experiment (an intro chemistry lab), and you're done.

Yes, I know that way, and I've read a few others. My point was that smashing the particles is a lousy way to measure something, you can't be sure that the particles you are detecting haven't smashed into another particle, and altered the data. Just something I know doesn't happen often, but that one time could fault on something being missed.

It's like the pissing in the drinking bucket game. Only you're blind and can't see the yellow water.

That method was demostrated here on this local to me school's site.
http://phoenix.phys.clemson.edu/labs/cupol/eoverm/

 

[PGTips]

^^Human's like to think they have an effect on how the universe operates. Without humans though, the world would operate much better.

The first sentence implies you think we give ourselves too much importance, and that we actually have no effect on the universe. Then the second contradicts it saying the world would be better off without us??

Still an approximation Zorn. An equation is a representation, not the actual value. 8) You should know this. In the real world things are defined to a point of a value.

Again, you are confusing real world application and mathematics.

Pi = 4arctan(1)

That is a perfect definition of Pi. You will find no error in its value when using it in mathematics. That is the actual value of Pi. Its a poor series to use if you wish to have the decimal expansion, but the decimal expansion is the same number, but written in a different form.

By your logic, 1/3 is not exact, because if I try and put it into decimals, I'll always have an error. Any calculation with "1/3" in it will be in error. In a computer this is true (given the inherent rounding errors in variables). However, in mathematics it is not true because its a mental construct. (1/3)*3 = 1. Put this into a computer and you might get 0.99999999999999999999999 or 1.00000000000000000000000001, because it can't use 1/3 properly, due to finite memory and processing power. No such restraint exists in mathematics. 1/3 is the multiplicative inverse of 3, so (1/3)*3 == 1.

Shit between 0.1 and 0.1 X 10^-100 there is such a difference in how the universe would look.

Firstly you'd be needing to define your unit length for that to make sense. Secondly, what does that have to do with maths? Yes, in reality the apparent laws for the very big are different to those of the very small, but maths is not reality, and there is no "difference of behaviour". We can examine the very small as easily as the very big.

You are operating under the conception reality defines mathematics, that is wrong!!!

I think it's up to like 1.2411 trillion decimal spaces, and that alters results quite a bit, considering we are dealing with a value between 0.1 and 1. The results could alter the very reasoning behind inflation.

While the "Inflation Parameter" is known to be horribly fine tuned, the 1.2 trillionth decimal place of Pi will have no relevance. Lambda is fine tuned to 125 decimal places, so knowing Pi to 1.2 trillion will mean you're accuracy in Pi is overwhelmingly good to not worry about suddenly "tipping" the scales one way or the other.

Simple way to check. Let your value of Pi = 3.1415927 and then try Pi = 3.1415926. If there's a phase change, go to more decimal places, until the extra places no long cause a change in Inflation, so you know your value of Pi is sufficently accurate to no longer be a factor. This place is reached LONG before 1.2 trillion.

It's not from a lacking of understanding, unlike what seems to be the popular thing thrown at me these days.

Your understanding of black holes was less than "perfect" in that you specifically stated they absorb more energy than they emit, which is not always true, and if a 3 line qualative description of something is your definition of "Perfectly understood" then you've a pretty poor dictionary. As Cex says, it tells us nothing other than the vaguest of vague ideas about a black hole. To have perfect understanding, you should be able to answer any relevant question about something. None of the specific questions Cex said are answered by your "perfect description" (which was in error anyway).

 

[Euler]

Human's like to think they have an effect on how the universe operates.

Erm - we do have an affect on the Universe.

Still an approximation Zorn. An equation is a representation, not the actual value. 8) You should know this.

I will define sqrt(2) to be the positive solution of x^2 - 1 = 0. There is no ambiguity here - there is no room for approximations or errors. I have defined sqrt(2) exactly. Pi is just another such number, and there are billions of ways of representing it. Just think for a second (or possibly more) about it. Sadly, I don't think any amount of explaining will help you.

...alters results quite a bit, considering we are dealing with a value between 0.1 and 1.

Maybe this is the root of your problem David. Pi is not between 0.1 and 1. But, that is another little gem we can add to your collection.

Keep up the good work.

 

[Cex]

Guys, guys.

I think I have it worked out - we've been forgetting something fundamental.

If we take the following fact into account, I believe that all will be explained:

The fact is that, from a mathematical perspective, David is a fucking muppet and no amount of careful explaining will make him understand why he's wrong.

This should lead us to ask the question "Why do we bother with this retard?"

Speaking personally, it's kind of fun. It diverts my attention from more mundane pursuits, like learning some actual maths or physics, and not pulling shit out of my ass with my bare hands. Which, coincidentally, is exactly the opposite of what the D-man likes to do.

 

[sexyanon2]

The first sentence implies you think we give ourselves too much importance, and that we actually have no effect on the universe. Then the second contradicts it saying the world would be better off without us??

Perhaps David's saying that we don't have an effect on the whole universe, and we can't shape it any way we want to on a grand scale. His second statement about the Earth is talking about a much smaller scale, something that we do have control over on a grand scale (in a way, ignoring hurricanes and such).

While the "Inflation Parameter" is known to be horribly fine tuned, the 1.2 trillionth decimal place of Pi will have no relevance.

But isn't it all relative? On a smaller scale, wouldn't that difference be a big one? And even if it isn't a big difference, doesn't that show its imperfection?

Just think for a second (or possibly more) about it. Sadly, I don't think any amount of explaining will help you.

Do you think insults will help? If you are truly trying to explain something to somebody else, belittling them won't do any good.

I will define sqrt(2) to be the positive solution of x^2 - 1 = 0.

You're defining it. What's the numerical value of sqrt(2)?

Now, the equation is true. There's no doubt about it. X^2-1=0 is the same as sqrt(2). But they both represent ideas, not actual numbers. There's no cap we can put on sqrt(2) that defines it. 3/2 = 1.5. We have a cap we can put on that number, thus we have an actual value.

Its a poor series to use if you wish to have the decimal expansion, but the decimal expansion is the same number, but written in a different form.

I think this is what David, or at least I'm, getting at. The decimal expansion is not the same number. There will eventually be some discrepancy, no matter how small, to the decimal expansion of Pi.

Pi = 4arctan(1)

That is true. But you're defining one abstract idea with another abstract idea. Ending numbers (like 0.12 or 15) are concrete. Pi is an abstract idea because it doesn't have an ending number. If you define one abstract idea with another one, the former isn't proven to be concrete.

 

[sexyanon2]

You are operating under the conception reality defines mathematics, that is wrong!!!

Ah. Then that's key. For some reason I thought we were talking about math in relation to reality.

But does mathematics define reality? Or just an ideal reality?

 

[sexyanon2]

This should lead us to ask the question "Why do we bother with this retard?"

Because you have an ego that needs to be filled and this seems to be the easiest way. Flaming also builds the ego, which is why you bother typing out those insults.

That's just psychology if you wanted to know. You can insult me if you want to. But you'll only prove psychology to be correct.

 

[David]

UO

Perhaps David's saying that we don't have an effect on the whole universe, and we can't shape it any way we want to on a grand scale. His second statement about the Earth is talking about a much smaller scale, something that we do have control over on a grand scale (in a way, ignoring hurricanes and such).

Exactly. Some people are not of the proper mindset to understand a concept that is new to them. Either way you pretty much hit the nail on the head there. Patterns, and statistics show that information is always there, even if as humans we chose to deny it, or ignore it.

But isn't it all relative? On a smaller scale, wouldn't that difference be a big one? And even if it isn't a big difference, doesn't that show its imperfection?

You can't expect a good answer from someone that doesn't understand the importance between .1 - 1 as the cosmological constant of light during the first few seconds of inflation. Of course being so horribly fine tuned, with the emphasis on the horrible, it's still a theory, and there are numerous models for it. None are factual, and even the thoughts of gravitation are up for grabs. A system of prediction is not explaining what is going on there. This is the fault of relativity.

Do you think insults will help? If you are truly trying to explain something to somebody else, belittling them won't do any good.

You've never seen a real physics debate, have you? It's worst than that.

You're defining it. What's the numerical value of sqrt(2)?

Now, the equation is true. There's no doubt about it. X^2-1=0 is the same as sqrt(2). But they both represent ideas, not actual numbers. There's no cap we can put on sqrt(2) that defines it. 3/2 = 1.5. We have a cap we can put on that number, thus we have an actual value.

Which has been the complaint the whole time, however certain people would rather sling insults, and throw fits than try to define something with a reason.

I think this is what David, or at least I'm, getting at. The decimal expansion is not the same number. There will eventually be some discrepancy, no matter how small, to the decimal expansion of Pi.

That is the difference between .1 and 1. With going over the 1, the universe spins outward uncontrollably, and falls apart, beneath the other, it creates a 'gravitational' effect, and collapses upon itself. Returning to a singularity. Of course this is only one model, and there are others out there, and some even disagree with the Big Bang, but that always going to be the case.

That is true. But you're defining one abstract idea with another abstract idea. Ending numbers (like 0.12 or 15) are concrete. Pi is an abstract idea because it doesn't have an ending number. If you define one abstract idea with another one, the former isn't proven to be concrete.

nail. hammer. head.

Logic based on a concept with no grounds in reality, but of course it's a perfect system, but not grounded on reality. Yet you want to represent reality with it?????8)

 

[sexyanon2]

Logic based on a concept with no grounds in reality, but of course it's a perfect system, but not grounded on reality. Yet you want to represent reality with it?????

Hmm.. so guys - are we talking about math seperately, not based on reality?

As AN said - math isn't based on reality. Now if math isn't based on reality, then why would you "want to represent reality with it?"

Is it for this ideal factor that one strives for? Like you want to break a plank into thirds. You won't get perfect thirds, but you can get thirds that are the same on an imperfect scale.

 

[compact]

Alright, I hate getting involved in this since it's essentially the Pi thread revisited, but David, I want you to very carefully explain to me what exactly a (real) number is to you. I wouldn't mind hearing what sexyanon2 (or other people without a technical background) have to say as well.

 

[sexyanon2]

A real number has a concrete end. These would include the numbers 5 and 6.15. They exist in our reality. I can have 5 ducks in my pond, or I can cut 6.15 mm out of my ruler.

I cannot, however, cut my ruler into three 1/3's. I will never get exactly 3 thirds of my ruler cut. There will always be a difference between each third.

Sqrt(2) also falls under this category. It simply does not exist in our reality.

Mathematics, altogether, deals with an ideal world. Altogether, I'm talking about Pi and sqrt(2). These ideas, abstract numbers, aren't concrete in reality. We define these numbers in terms of equations or sequences; not in concrete terms.

Pi can be defined by any one of a zillion formulae

I will define sqrt(2) to be the positive solution of x^2 - 1 = 0.

Both ideas are being defined in terms of abstract ideas, or equations. They are not concrete. Like an infinite sequence to define Pi isn't concrete, as it has no concrete end.

Mathematics, aside from reality, is fine. But when you start using mathematics in terms of reality, then there's imperfection. Sqrt(2) defined as x^2-2=0 is perfectly fine. In fact it's true. In the mathematical, ideal world.

 

[Cex]

I cannot, however, cut my ruler into three 1/3's. I will never get exactly 3 thirds of my ruler cut. There will always be a difference between each third.

Please explain why you think you can cut a ruler into 4 equal pieces (since 1/4 = 0.25, a terminating decimal) but you can't cut it into three equal pieces.

And when you fail to do so, please reconsider your argument.

Mathematics, aside from reality, is fine. But when you start using mathematics in terms of reality, then there's imperfection. Sqrt(2) defined as x^2-2=0 is perfectly fine. In fact it's true. In the mathematical, ideal world.

Please explain how you want to model the world, in a sensible enough manner to be able to draw conclusions from it, without using mathematics.

 

[PGTips]

That is the difference between .1 and 1. With going over the 1, the universe spins outward uncontrollably, and falls apart, beneath the other, it creates a 'gravitational' effect, and collapses upon itself. Returning to a singularity. Of course this is only one model, and there are others out there, and some even disagree with the Big Bang, but that always going to be the case.

You keep saying that, yet you have only just specifically refered to what this magical "0.1 to 1" is. Until that point it was just "And if its bigger than 1 it spreads infinitely!!"

Perhaps you'd like to elaborate on that somewhat? Or is it part of your theory and you worry we'll steal your ideas/thoughts .

But isn't it all relative? On a smaller scale, wouldn't that difference be a big one? And even if it isn't a big difference, doesn't that show its imperfection?

As I said before, easy way to check. Put in Pi = 3.14 into your equations, and find your values for various cosmological constants. Then try 3.15 (the "real" value of Pi is between those two), and find your values of these constants. Now see if there has been a sufficent change for the equations to suddenly say something different.

Keep increasing the decimal length of your value for Pi and see if you can get rid of this sudden change. You reach this point WAY before 1.2 trillion decimal places.

That is true. But you're defining one abstract idea with another abstract idea. Ending numbers (like 0.12 or 15) are concrete. Pi is an abstract idea because it doesn't have an ending number. If you define one abstract idea with another one, the former isn't proven to be concrete.

You are confusing mathematics and physics. The "proof" of something being concrete is if the series which defines it converges. There are many ways to test for convergence, and many ways to define various types of converges. If something converges, then it is concrete.

Check my gallery. There is an equation for Pi in there which is an expression involving 4 fractions. That is an expression for Pi in Base 16, as opposed to our Base 10. If you give me ANY "decimal" place for you want, I can tell you what it is in base 16. You want the 5th place? No problem. You want the billionth place, again, no problem. As you can see, that formula works for ANY n, there is no sudden "It doesn't work", so therefore the value of Pi must be a well defined on.

If you don't like Base 16 (mmm..hexidecimal) then numerous tests exist to prove Pi has a unique concrete value. Unfortunately, the requirements to show you rigirously are at least 1st year university mathematics, and some notation these forums don't suppose. If you are truely interested, and have a passing knowledge in mathematics (so it doesn't sail over your head) I can knock something up for you.

Suffice to say, there is a precise value for Pi.

If you define one abstract idea with another one, the former isn't proven to be concrete.

It is, provided your proved the concreteness of the previous step. This works bakcwards, again and again and again till you reach the axioms of mathematics. As few as possible statements taken to be "self-evident". I'm sure I can dredge up what they are if you want.

Suffice to say that "decimal expansions" are built up over hundreds of logical arguments from these axioms and contrary to what most people think 1+1=2 is not "self evident". The arguments which get from the axioms of mathematics to these results have been analyised, reanalyises, checked and rechecked by the best logisticians ever, the logic is flawless.

Except to David, who one day plans to flick through the 2000 pages of Principia Mathematica and pick out all the flaws 8) Despite it being quite clear his own logic leaves a lot to be desired.

That is true. But you're defining one abstract idea with another abstract idea. Ending numbers (like 0.12 or 15) are concrete. Pi is an abstract idea because it doesn't have an ending number. If you define one abstract idea with another one, the former isn't proven to be concrete.

You're defining the definition of a number with an abstract concept too.

What is wrong with 1/3? I have 3 apples, I take away 1, I've got 2 left. The total number has decreased by 1/3. Now, by your logic, that isn't right, there is an error, because 1/3 = 0.33333......, which I therefore use exactly. Is there an error in my calculations? Is taking 1 apple from 3 not removing 1/3 the total?

Similarly, What number do I multiply 7 by to get 1? I define it to be "1/7", so by definition "7*1/7" = 1. A computer might do it via a decimal version and get 1.00000000000000000000000000000001192. Infact, if you get C code to print out 300 decimal places for just the number "1" after about 100 it goes into random digits. Now, via your logic, its the mathematics saying 7*1/7 = 1.0000000000000000000000000000000000001192. Is it? No, its technical limitations within the computers memory and random errors within the CPU causes by imperfections (and increasingly so, quantum effects).

In the "mathematical universe" 7*1/7 == 1, its absolute. Do you deny that this is right? If so, please point out where the error is.

Similarly, lets consider 2Pi. Its the circumference of a unit circle. Now, I do not know the decimal expansion for Pi to infinite accuracy. Does this mean any calculation I do with it is therefore in error in some way? In a computer it will be, but real mathematicians don't use calculators and anyone who things mathematics is defined by what Microsoft Calculator says needs help. (2Pi)/Pi = 2. No error. Did I need to know Pi's decimal expansion? No, That wuld have been just as valid if I'd done "2X/X = 2".

Do I need to know the decimal expansion for a number if I am to use it in mathematics? Of course not, the equations which define a number tell me EVERYTHING I need to know about the number. I can derive its decimal expansion if I so wish, I can check to see if its rational, imaginary, etc.

You're defining it. What's the numerical value of sqrt(2)?

In mathematics, you do not need to know the decimal expansion of a number to use it. Since I know x^2-2=0 for "root2" if I ever get (root2)^2-2, I know I can instantly just write "0" down instead. Have I made an error because I don't know the decimal expansion? Of course not.

But isn't it all relative? On a smaller scale, wouldn't that difference be a big one? And even if it isn't a big difference, doesn't that show its imperfection?

If someone asks you what time it is, do you just say "Half past 3". You could say "3.27pm", or "3.27 and 32 seconds". If you had a fancy atomic clock you could give me to 9 decimal places of a second the "exact" time (though by the time you said it, it would be wrong ). Technology (and ultimately quantum mechanics) is a limit on our ability to measure things. You cannot tell me to time to better than 10^-43s, a "Planck Time". In only 49 order of magnitude you go from 1 year to the smallest time which has any meaning.
What about Pi? We know 1.2 TRILLION orders of magnitude in its decimal expansion, since each new place is an order of magnitude smaller than the last.

If you took a quantum fluctuation in a single atom, and blew it up to the size of the visible universe, you'd make it 40 orders of magnitude bigger (10^-14m to 10^26m). Hence, if you were measuring the size of the visible universe, and you wanted to take quantum fluctuations into account, you'd have to measure to 40 decimal places. Pi's decimal expansion we know to not 40, not 4000, not 1 billion but over 1 trillion places!! That is enough to go from the shortest meaningful length in the universe (10^-33m or so) to the size of the entire visible universe (10^26m) over 20 BILLION times. The vastness in the difference in size is beyond our ability to grasp.

If David is truely worried about the next calculated decimal value of Pi suddenly tipping the scales (which it can be easily checked, as I mentioned), then he might want to be more worried that we don't know the size of the universe to within 10^-33m!!

and even the thoughts of gravitation are up for grabs

I thought you said we understood black holes perfectly, and since black holes are very much gravity based, surely that means our gravity knowledge is perfect? Or do you now think that our knowledge of black holes is less than perfect?

You've never seen a real physics debate, have you? It's worst than that.

I would wager neither have you. If you call your claims and us constantly shotting them down with obvious errors "a debate", then you might want to get a new dictionary (though that was true after your "perfect" definition of a black hole).

or I can cut 6.15 mm out of my ruler.

Follwoing your own logic no you can't. If you think that "1/3" doesn't exist then you are not cutting off 6.15cm from your ruler. Are you sure its exactly 6.15cm? What if its 6.1500001cm?

The "error" goes deeper than that. I define a new length. I've never liked metres, so I define "1 AlphaNumeric", a new unit of length which has the incredible coincidence of being 3 times the size of a metre. Now by your logic, I can cut 0.5 "ANs" (for short ) off a ruler. I can cut 0.25AN's off a ruler, but I cannot cut 1/3 AN's off a ruler. But 1/3 AN is a metre. So by your logic, a metre is not exist, because a metre is 1/3 of some larger distance.

There is nothing "special about a metre or a mile. They are lengths we have picked up during our history. IIRC 1 metre of the distance from the N Pole to the Equator through Paris, divided by 10million. Doesn't sound a particularly well defined distance. I define a "Bob" to the be distance from the N Pole, to the equator, via Paris divided by 30 million.

I now have 1 Bob = 1/3 metre. Do you deny the existance of my "Bob"?

You cannot claim that "Our current method of measuring is find, so long as its a length with terminating decimal expansion" because what is so great about our units of length? Our unit length is 1/3 of some other length, does that suddenly make our unit of length wrong?

This is where the problem in conception lies. If you start claiming "Pi will tip the scales" or "1/3 of a metre doesn't exist", then you rapidly develop numerous other more stricking problems. If you step back and realise that 1/3 and Pi are simply mental constructs to what are in reality "imperfect entities" then the problems do not arise. A computer cannot do 3*1/3, it cannot give the every decimal place of Pi, or even 1/7 for that matter, but then it can't do it for 0.5. To a computer, 0.5 = 0.500000000000000000000001 or 0.4999999999999999999999999999999. You can reduce this by increasing memory size or comuting power, but "integers" to computers are just values extremely close to certain other values.

When I program in C I can't say "If ( k=1 )" when k is a double, I have to say "If (fabs(k-1) < 1E-20), because the computer doesn't realise k should be integer (if its defined as a double), because numerous roundoff errors during computation have created these slight discrepencies.

In mathematics, every number can, and is, defined by the equations it solves. To deny that is either because you have insufficent schooling in mathematics (which is not a crime, and so asking for clarification is fine ) or a result of ignorance. Since David claims to be well versed in areas such as primes, it would be a logical conclusion he says what he says from ignorance.

In reality, there are ALWAYS errors, but not from mathematics. You want Pi to 1 billion places? No problem, maths will tell you. 1000 trillion places? No problem, maths will tell you. 10^1000000000 places? No problem, maths will tell you. You want the radius of the universe to 100 places? Tough, can't be done. The errors in the universe from uncertainty prevent it.

David seems to fail to realise this, despite being "well versed" in both basic number theory (primes) and having sufficent cosmology knowledge to have "solved relativity".

As AN said - math isn't based on reality. Now if math isn't based on reality, then why would you "want to represent reality with it?"

Why do you represent reality using words? If I say a word like "Tree" to you, you think of an object which is a plant, tall, with leaves, a trunk etc. How the word "tree" is not based in reality, there is nothing special about the word "tree", any more so than the french "arbre", yet because you have made the mental connection between the symbols on this screen "tree" and the living thing, you consider "tree" to describe a...well, a tree.

Now if I say "The derivative" I think of a mathematical operation. But what happens if I make the additional connection and say "The derivative of the potential", and I have a description of what is otherwise known as "force".

Mathematics is a language of a mental construction whose development is not shaped by the world around us. However, does this prevent us giving additional meanings to some of it, like "If m is mass, and F is force, then whats this a?" then its found that its excellent for describing things in quantative ways.

The errors in peoples understanding seems to be that they think the errors in physics are from errors in the contstruction of the very mathematics behind it. The error is in the connections we make between the mathematical symbols and the physical quantities. Noone will come along and prove diffrentiation and integration wrong tomorrow (if you consider that statement wrong, you have a poor understanding of logic), but they are not the errors in physics, their application is. Sometimes, you don't need to take the derivative, or sometimes applying a certain idea to a problem is the wrong way to approach it. That is what problems arise in physics. Much of theoretical physics research at the moment is trying to find the right mathematical tools to apply to current problems. Previous tools were not "wrong", but just inappropriate.

Wow, one of my longest posts ever. Not bad for 10.15am on a Saturday morning

 

[Cex]

Do you guys think that the decimal expansion of a number somehow is that number? It's not. To take sexyanon's example of 1/3, for example, consider working in base three instead of base ten.

Then 1/3 (which would actually be 1/10 in base three) has the decimal expansion 0.1. This is undoubtedly a terminating sequence of digits, and so you would consider this to be a 'real' number. However, in base ten, it is an unending sequence of digits, so you would consider it to be 'unreal'. You've hit a contradiction there tiger - your number can't be both real and not-real. That's one of the founding principles of logic. You seem to be left with a choice:

(i) Admit that you're wrong.
(ii) Claim that logic is wrong.

Ball's in your court.

 

[Cex]

When I program in C I can't say "If ( k=1 )"

The real reason you can't say this is because it's incorrect syntax, and would make your program throw a hissy fit

 

[PGTips]

Then 1/3 (which would actually be 1/10 in base three) has the decimal expansion 0.1. This is undoubtedly a terminating sequence of digits, and so you would consider this to be a 'real' number. However, in base ten, it is an unending sequence of digits, so you would consider it to be 'unreal'. You've hit a contradiction there tiger -

Good example. I'd forgotten about that one.

The real reason you can't say this is because it's incorrect syntax, and would make your program throw a hissy fit

Notch it up to shitty coding ability and also the imprecsions in C. If k was exactly 1 then it would work. The very fact you need to use slightly diferent syntax, shows that programmers have developed a way to slightly side step the inherent problems in computing.