So we tend to "quantizise" time, thereby defining both past, present and future "as is".

Meaning with this that c (as in E=mc2) can not be a constant, but rather is a variable (expression).

You know, time flies.

With "quantize" or "quantification" we are AGAIN back to numbers and nunbers theory.

If we know the ("representative") numbers for energy and mass, we also should be able to compute the same or similar number for time itself.

Still, we are putting the notion of time in a separate context which differs or is different than the usual or ordinary definition for both energy and mass.

Still, mass is still easier to explain than energy and its behavioral charactericstics.

A formula is an expression, where each of the elements should be thought of as either being constants or variables on their own.

If c is not a constant, but rather is a variable, it means that it is possibly affected, or influenced by other factors.

How can c (or the representation of time) be affected or determined by "other factors"?

Energy and mass alone could still be thought of as being proportional to each other, however.

One constant (somewhere) tells me that there could be some 10^24 particles related to a (let's say) a drop of particle (Avogadro's constant). I guess a particle is only one upon many particles, regardless of water or liquid lead.

According to Google, the number for the Avogadro's constant is 6.0231367 * 10^23 .

Another constant, more famous, I believe, is the Planck's constant.

This number is sub-atomic, the exact number is according to Google,

6.626068 * 10-34 m2 kg / s .

If time is assumed to be a "constant", how can time be thought of as being running slow at times, but quick at other times?

Is it just a self determined or personal view or notion of time which is the determining factor in this process?

Take ageing as an example, it is constant, but very slow. It still happens with people. You don't live forever, you start developing gray hairs and your "promiscuity" steadlily declines.

You only get one chance in life.

So it goes.

Again, see you tomorrow for more on this.

Still, still.

Better to say, anyway, mass is still easier to explain than energy and its behavioral charactericstics.

Too late to edit.

You rounded off and you are only accurate to that level. You have no right to assume that the "last" digit at infinity would be any number other than 9. In fact there is no last infinite number.

William, i am surprised at you.
No rounding occurred.
This is something you quite likely saw in your own first semester of calculus.
And, I hope you read where I typed "(repeating)".

2/3 = 0.6 (repeating)

Let x = 0.6 (repeating).
Then 10x = 6.6 (repeating).

10x = 6.666666666666666666666666666666666666666666666666666666 (repeating)
-1x = 0.666666666666666666666666666666666666666666666666666666 (repeating)
==============================================================
9x = 6.0000000000000000000000000000000000000000000000000000000

In every single place, except for the ones place, the digits agree: they are sixes. So, in every spot except the ones place, the difference will be 0 (no borrowing/exchanging needed). (IE, the zeros repeat. There is no rounding!)

Now, since 9x = 6, x = 6/9, and of course, 6/9 reduces to 2/3.
Right back where I started.

Similarly, with no "tomfoolery", 0.9 (repeating) = 1, as stated.

3 times 1/3 equals 1

3 times .33333333...... equals .9999999999.......

So I conclude that our numbers are inadequate to correctly express 1/3 as a decimal even though it is a "rational" number.

Quantum mysteries in space and time may be nothing more than the fact that there are problems with our numbers and with the Calculus. These have served us well but things get weird in Physics at the very large and the very small.

Read a few articles on the Hyperreals and I think you will see what I am getting at in rejecting the popular proofs of .999999..... equal to 1.00000...... . A Hyperreal is a number that is smaller than any real number but greater than zero. It's inverse is larger than any real number . Sounds goofy doesn't it ; but dig into them and you will see what I am talking about.

There is a video explaining why the popular proofs are incorrect. I will try to find it again when I have more time.

This article appears to have something useful to say on the general topic of the OP.

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I think you'll find it's a bit more complicated than that ...

1/7=0,14285714285714285714285714285714 .

Truncate it and you are left with 0,1428571 .

But the ending 1 means rounding off downward (0-5 means rounding off downward, 6-9 means rounding down upward), still you get a 7 and not a 6.

Or maybe you are rounding off upward for 5 rather than 6, meaning 5-9?

You rounded off and you are only accurate to that level. You have no right to assume that the "last" digit at infinity would be any number other than 9. In fact there is no last infinite number.

William, i am surprised at you.
No rounding occurred.
This is something you quite likely saw in your own first semester of calculus.
And, I hope you read where I typed "(repeating)".

2/3 = 0.6 (repeating)

Let x = 0.6 (repeating).
Then 10x = 6.6 (repeating).

10x = 6.666666666666666666666666666666666666666666666666666666 (repeating)
-1x = 0.666666666666666666666666666666666666666666666666666666 (repeating)
==============================================================
9x = 6.0000000000000000000000000000000000000000000000000000000

In every single place, except for the ones place, the digits agree: they are sixes. So, in every spot except the ones place, the difference will be 0 (no borrowing/exchanging needed). (IE, the zeros repeat. There is no rounding!)

Now, since 9x = 6, x = 6/9, and of course, 6/9 reduces to 2/3.
Right back where I started.

Similarly, with no "tomfoolery", 0.9 (repeating) = 1, as stated.

and comparing those numbers using statistics shows that there is no significant difference in the numbers

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In a rich man's house there is no place to spit but his face.
Diogenes Of Sinope

Perhaps the difference can be called an infinitesimal. Perhaps that is why quantum effects seem so crazy.

Here is the proof that I promised earlier that .9999999........ does not equal 1.0000000.......

Watch it and let me have your comments.

Can you relate it to the reading assignment I gave you on the Hyper-reals

http://www.youtube.com/watch?v=wsOXvQn3JuE&feature=related

Here is the proof that I promised earlier that .9999999........ does not equal 1.0000000.......

Watch it and let me have your comments.

Can you relate it to the reading assignment I gave you on the Hyper-reals

http://www.youtube.com/watch?v=wsOXvQn3JuE&feature=related

The mathematicians will probably kill the presenter if she doesn't say "April Fools" at the end of a proof of .999... <> 1 released on 4/1/12.

Not sure the ending of the video supports what you're saying. Certainly some of the presentation does not.

x = .999...
10 * x = 10 * .999... (the presenter suggests that 10 has been added to both sides, clearly this is nonsense)
10x = 9.999...
10x - x = 9.999... - 0.999...
9x = 9
x = 9/9 = 1
thus .999... = 1

If there is a difference between 1 and .999... it is 1/∞, which is undefined in the system of real numbers, thus there's no defined difference between 1 and .999...

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I think you'll find it's a bit more complicated than that ...

You get an even bigger inaccuracy in the numbers by using 2/3 instead of 1/3.

You are supposed to end up with 0,66666666666666666666666666666667 using Windows Calculator, but in the end 6*3 (or 3*6) is only 18.

Where is the rest of the number?

I guess there may exist two or maybe three different words for the same thing, namely approximation, convergence and possibly probability which belongs to statistics.

The subject of probability is the way we think that a computation should be carried out on a number and what the end result might be supposed to be.

1, and you have something. 0, and you have a start of something. .99999999999, and you have less then something.

I see no problem with William Rothamel's logic, if indeed that is the point he is attempting to make. Looks that way to me anyhow with hyper-reals.

No problem with that.

Try dividing or splitting a cake into three pieces and give it to three different people.

In the end, one of them gets a little nudge more than the other two (the rest of the cake).

Perhaps the difference can be called an infinitesimal. Perhaps that is why quantum effects seem so crazy.

Planck distance is defined and thus > 1/∞.

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I think you'll find it's a bit more complicated than that ...

Perhaps I should restate that zero is but a place to start?

Yes, Intelligent Design, or if I may, I.D. for short, we take 0 for a start.

Because we are dealing with the subject of infinity ( ~ ) in relation with or when discussing the subject of "0".

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

But we do have both positive as well as relative numbers, meaning that -infinity is as far away from +infinity as you may get.

In the same way goes small numbers, both -10^-38 and 10^-38 are very small numbers, but the first one is a negative number slightly smaller than 0.

Indeed, both -10^-308 and 10^-308 are even smaller numbers.

We tend to omit the + where the number is generally assumed to be positive.

0 is supposed to mean "nothing" (of value).

Yes, Intelligent Design, or if I may, I.D. for short, we take 0 for a start.

Because we are dealing with the subject of infinity ( ~ ) in relation with or when discussing the subject of "0".

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

But we do have both positive as well as relative numbers, meaning that -infinity is as far away from +infinity as you may get.

In the same way goes small numbers, both -10^-38 and 10^-38 are very small numbers, but the first one is a negative number slightly smaller than 0.

Indeed, both -10^-308 and 10^-308 are even smaller numbers.

We tend to omit the + where the number is generally assumed to be positive.

0 is supposed to mean "nothing" (of value).

I.D. is fine.

Thank you, thought I was on the right track?

Please don't omit the +, Id rather not assume.

Then if Im following William Rothamel's logic [and I think I am] his problem with hyper-reals is that after so many places out from .9 that the number looks like it returned back to the start of zero?

It may seem we tend to agree a little more with each other when discussing the subject of mathematics.

Because we assume that mathematics is an "exact" science, regardless of whether numbers are "exact" (like 0 or 1), or 1/3, 2/3 or 1/7, which are supposed to be not so.

Is this because what we assume to be whole or exact numbers in the end also are complex or fractional number which possibly have been rounded or truncated off?

0 can be expressed as 0,00000000000000000000000000000000 .

1 can be expressed as 1,00000000000000000000000000000000 .

But if I ever was supposed to say:

"In the beginning the Devil (or Satan to be honest) created the Universe. He did so in seven days - in fact six days and took the seventh day off".

I guess this will go fine with you?

So what are "exact" numbers then?

Try to separate the reals into two sets by taking the Dedekind cut about a rational number, sat, 1/3. One set will contain the reals greater than the number and the other less than the number. But there are numbers in between as well as the rational number. There is a halo of hyperreals around each and every real number. rational or not.

Try to separate the reals into two sets by taking the Dedekind cut about a rational number, sat, 1/3. One set will contain the reals greater than the number and the other less than the number. But there are numbers in between as well as the rational number. There is a halo of hyperreals around each and every real number. rational or not.

That is what is postulated. I suspect at some point in the future some smarter mathematician is going to prove that the hyperreal set and the real set are an identity. Same for the surreal set.

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