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revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17281
revolution
You are avoiding the question. Show me 0.1 in this world.
08 Aug 2017, 08:07
Furs

Joined: 04 Mar 2016
Posts: 1471
Furs
YONG wrote:
Even a 4096-bit floating point number can't represent the EXACT value of 0.1.
There is no such thing as EXACT anything in quantum mechanics (or basically, any science), so I don't see how that means anything? Every measurement has an error tolerance way above that implied by a 512-bit float number. You're way too obsessed with "ideal math" when it was proven over and over again that the Universe does not follow "ideal math" equations, but it is in fact quantized. (the randomness could be just a source of "calculation errors" too)

In fact, people have calculated digits of PI to an insane amount that we will never ever find in the "real world physics" due to quantum mechanics effects. Just because you can express something -- like PI -- with mathematical logic, does not mean the world uses such ideal representation.
08 Aug 2017, 12:03
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
My original statement is

"Even a 4096-bit floating point number can't represent the EXACT value of 0.1."

which states a simple fact in computer science.

And then the focus just got shifted to something else. Sigh.

Anyway.

Furs wrote:
There is no such thing as EXACT anything in quantum mechanics (or basically, any science) ...
If that statement were made by revolution, I would not be surprised. Given that it was made by you -- a physics guru, I am quite disappointed.

Yes, such things can be easily found in science.

For example, the EXACT value of the resonant frequency of a simple harmonic oscillator can be found by graphical methods. Refer to:

Resonance
https://en.wikipedia.org/wiki/Resonance

Another example:

The EXACT value of the energy of a photon is given by the Planck–Einstein relation. Refer to:

Planck–Einstein relation
https://en.wikipedia.org/wiki/Planck%E2%80%93Einstein_relation

One more example:

The new definition of kg is EXACT. Refer to:

How We're Redefining the kg

Enough?

08 Aug 2017, 13:14
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17281
revolution
Frequencies (relying upon time), energies and mass are all human defined values. We can make them whatever we want. They show nothing about the underlying fabric of whatever it is that makes us up.
08 Aug 2017, 13:33
Furs

Joined: 04 Mar 2016
Posts: 1471
Furs
YONG wrote:
My original statement is

"Even a 4096-bit floating point number can't represent the EXACT value of 0.1."

which states a simple fact in computer science.
I have no idea what you're trying to say here. I mean yes, that's true, but 0.1 does not exist in the real world. What is 0.1 to you? "One tenth of something" is a concept. Real numbers are also a concept -- precision is definitely not infinite. There's a point where you can't split something when measuring, so 1/10 of it makes no sense in actual data, since it's indivisible as far as you know. Stop mixing human concepts (which are idealizations) with measurements.

For example your EXACT frequency formula relies on Planck's Constant, which is:
Quote:
The value of h – according to NIST’s new measurement – is 6.62606983x10-34 kg∙m2/s, with an uncertainty of plus or minus 22 in the last two digits.
Are you kidding or something? That's easily representable even with our current floating point formats, with such wide error. https://physics.stackexchange.com/questions/268064/can-the-accuracy-in-plancks-constant-ever-be-increased

Your redefinition of kg is pointless. kg is a human concept.

You can also say, PI is the exact value of "1 magic", with magic being a human-invented unit. This is perfectly adequate and you can use this unit for everything by converting it to others. It doesn't make PI any more "defined" than the infinite amount of precision it needs just because you changed units.
08 Aug 2017, 16:07
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17281
revolution
"Magic" is simply a number system using base Pi. We can define number bases as anything we like to suit our needs. Binary floats are just a convenience to us because we use binary computers. But it is by no means the only way it could be done. If we use base 10 floats suddenly 0.1 is easy to represent exactly. And as a bonus all fractions of powers of 2 and powers of 5 can be represented exactly. But none of this means anything outside of a mathematical construct.
08 Aug 2017, 16:37
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17281
revolution
Furs wrote:
Stop mixing human concepts (which are idealizations) with measurements.
This is the form/function confusion. It has been mentioned before.
08 Aug 2017, 19:20
Furs

Joined: 04 Mar 2016
Posts: 1471
Furs
revolution wrote:
"Magic" is simply a number system using base Pi. We can define number bases as anything we like to suit our needs. Binary floats are just a convenience to us because we use binary computers. But it is by no means the only way it could be done. If we use base 10 floats suddenly 0.1 is easy to represent exactly. And as a bonus all fractions of powers of 2 and powers of 5 can be represented exactly. But none of this means anything outside of a mathematical construct.
My point is that we have never measured something as being exactly 0.1 in size or whatever since it is literally impossible (due to quantum mechanics). Everytime we measure we get a different result because of the random movement and influence. Essentially, it is not possible to know that its size is exactly 0.1 (or any other), but only that it is +/- a small error around 0.1

Such error can easily be handled by a 512-bit float which was the main point. After all, even our own computer algorithms are based on ideal math, but the actual computations aren't infinitely precise. Same with the ideal math in the real world -- our actual measurements (which is our best knowledge of how the Universe works) aren't infinitely precise so we can't say that they are truly the same as our ideal math.

Just for reference (mostly to YONG ) 2^512 is on the order of 10^154 -- do you understand just how precise this is? have you ever seen anyone measure something with 154 digits of precision? Planck Length is "only" 10^-35 (yes I am aware not all 512 bits will be used for the significand, but whatever this is precision in full without even shifting with exponent)
08 Aug 2017, 19:58
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
revolution wrote:
Frequencies (relying upon time), energies and mass are all human defined values. We can make them whatever we want. They show nothing about the underlying fabric of whatever it is that makes us up.
Furs wrote:
Stop mixing human concepts (which are idealizations) with measurements.

It is one thing to change the subject of interest when the need arises. It is another when one just wants to shift the focus to something else in order to make room to defend oneself for his/her lousy statements and/or arguments.

Look at the facts.

The original focus was on simulation. So, we were talking about computers, or more precisely, supercomputers with the necessary processing power, speed, storage, and the like.

Thus, I pointed out the truth that the exact value of 0.1 cannot be represented by floating-point numbers no matter how many bits they have.

Then, Furs came along and argued -- by shifting the focus to something else -- that there was no such thing as EXACT anything in ... any science.

The keyword here is science, which is the study of nature by human. It is NOT nature itself.

So, I, once again, pointed out that lots of things in science were exact. Refer to my earlier post.

And then, revolution and Furs came along and blamed me for mixing up things.

Am I the one who mixed up "the study of nature" with "nature itself"?

Last edited by YONG on 09 Aug 2017, 04:44; edited 1 time in total
09 Aug 2017, 02:21
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
In science, which is the study of nature by human, we construct lots of concepts, models, theories, and the like to make it easier for us to understand nature. That is just how science works.

At the end of the day, science is simply the human interpretation of nature. It is not nature itself.

Hopefully, a couple of forum members now understand their errors, withdraw their lousy statements/accusations, and apologize to the forum member who has been always right. Well, I guess that I am asking for too much, especially from revolution and Furs.

Anyway.

Last edited by YONG on 09 Aug 2017, 12:28; edited 2 times in total
09 Aug 2017, 02:35
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17281
revolution
Your mention of 0.1 was completely irrelevant. It seems both myself and Furs were pointing that out. It has nothing to do with simulation or reality or any other topic that has been discussed so far. A concept that can't be represented by binary floating point values doesn't say anything about whether something is being simulated or not. Your request for any sort of apology is misplaced. Neither myself or Furs were attacking you. Instead we were correcting you. If you choose to view corrections as attacks then I am truly sorry for you. If you wish I could refrain from trying to correct you in the future.
09 Aug 2017, 03:06
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
revolution wrote:
Your mention of 0.1 was completely irrelevant.
So, the focus has been shifted again. It is no longer about "mixing up things"; it is about irrelevance.

See, this is how revolution conducts his/her arguments -- keeps shifting the focus to make room for himself/herself to defend his/her lousy arguments. Sigh!

Anyway.

First, let me make one thing absolutely clear. I am NOT the one who brought up the "simulation" discussions; you are.

Second, I am NOT the one who brought up the discussions on the enormous requirements, in terms of bandwidth and storage, that a supercomputer would need in order to create such simulations; you are.

Third, I am NOT the one who brought up the discussions on floating-point numbers; Furs is. (He said, "I'm fairly certain a 512-bit floating point number has enough precision for the entire Universe.")

So, I pointed out, as an example, that even a 4096-bit floating-number could not represent the exact value of 0.1. Thus, it was pointless for us to claim that we could create an exact simulation of the observable universe, let alone the entire universe.

Please, by all means, explain why my mention of 0.1 was completely irrelevant.

Hopefully, you are not going to shift the focus to something else, again.

09 Aug 2017, 04:35
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
revolution wrote:
If you wish I could refrain from trying to correct you in the future.
What an arrogant mod! That's why so many forum members have left this board.

09 Aug 2017, 04:39
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17281
revolution
The bandwidth and storage requirements was in response to your claim that everything is recorded. I was pointing out that it wouldn't be possible to record everything because the requirements would be too high. All we could have is the current state, past states are lost and unavailable.

Your response about 0.1 not being representable has nothing to do with 512-bit floats and how that somehow means we can use that knowledge to discount any such simulation. You are correct about that statement of 0.1 can't be represented by any length binary floats but it leads to no conclusion from there. I asked you to show where 0.1 is in our current reality. And the point being that it doesn't exist in our reality so there is not even a need to represent it. Note that the form of 0.1, i.e. the ASCII characters 0, dot and 1, is not the same as 0.1 the functional value, or as Furs explained the concept and the measurement. I did go further to show that other forms of representation can be used to give an exact 0.1 if one wanted to, although they are not needed actually. And even so there is no reason to suspect that all simulations will necessarily use binary, or for that matter even digital. So the 0.1 value doesn't prove anything, it doesn't give rise to any new insight, thus it is irrelevant. In a mathematical proof style it means: it is neither necessary or sufficient to show that 0.1 can't be represented.

The point where something like a limit comes up in detecting a simulation from the inside would be looking for capped or truncated responses. That is, looking for places where at an extreme the value tops-out or overflows. If we use the example of 512-bit floats as the base unit for the simulation then we'd have to look for extreme points where an anomaly shows up where strange or unexpected values occur. Perhaps in a super massive black hole where adding mass no longer gives an increase in gravity because the base unit value has reached its maximum value. Another possibility is for it to wrap around to zero and the SMBH suddenly has no event horizon. Or a third possibility is to look for stepped responses that show precision loss as higher extremes are encountered. All of these things would be impossible to detect with our current technology if 512-bit is the base unit.
09 Aug 2017, 05:14
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
revolution wrote:
The bandwidth and storage requirements was in response to your claim that everything is recorded.
Good. We are in business now. At least we are clear that when a forum member is responding to a claim made by another forum member, such a response will NOT be considered "irrelevant".

So, how come my response to Furs' claim was considered "irrelevant" by you?

See, double standard arises.

09 Aug 2017, 05:49
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
revolution wrote:
Your response about 0.1 not being representable has nothing to do with 512-bit floats and how that somehow means we can use that knowledge to discount any such simulation.
What a typical tactic employed by revolution: over-generalization!

Did I even say "any such simulation"?

Check my posts. I always wrote "an exact simulation of the observable universe / the entire universe"!

Last edited by YONG on 09 Aug 2017, 07:15; edited 1 time in total
09 Aug 2017, 05:56
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17281
revolution
Wot? The response itself is not irrelevant, the content (0.1) was the irrelevant part. I think you are confusing form with function again. The misunderstanding about representations (the form) and the things they represent (the function) is the key thing to realise. I think you have misunderstood a fundamental point here.
09 Aug 2017, 05:58
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17281
revolution
Any simulation would also include an exact simulation. So my statement still applies to an exact simulation, and all other simulations.
09 Aug 2017, 05:59
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
revolution wrote:
Wot? The response itself is not irrelevant, the content (0.1) was the irrelevant part.
Ah, I see. The focus has been shifted again. Now, in order to escape the double standard charge, you need to split the content from the container. So, the message carried by the response is not the response itself. Very clever.

09 Aug 2017, 06:09
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
revolution wrote:
Any simulation would also include an exact simulation.
True.

revolution wrote:
So my statement still applies to an exact simulation, and all other simulations.
revolution wrote:
Your response about 0.1 not being representable has nothing to do with 512-bit floats and how that somehow means we can use that knowledge to discount any such simulation.
You, by your statement, suggest that my mention of 0.1 can "somehow discount any such simulation", which -- based on your over-generalization tactic -- is plain WRONG.

09 Aug 2017, 06:19
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