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Author
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17287
revolution
l_inc wrote:
I don't have to prove it as long as I explicitly made it an assumption.
Alright, let's go with that assumption.
l_inc wrote:
Thus under the given assumption you have an example of an indescribable number.
But you described the process used to obtain the time period. Then you said the time period was unrepeatable. But just the same a PI, we can describe the process to obtain PI, and just because we can't write all the digits doesn't make it indescribable.
l_inc wrote:
Planck time by itself is inappropriate to mention here. It's just a value, not a time discontinuity hypothesis.
If time is discrete then all we need to state time intervals is a simple integer value. That would make it trivially describable. Whether or not Planck time is the base unit of time is not important, but I mentioned it to show that there is the possibility that time is discrete.
14 Aug 2015, 01:36
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
MHajduk wrote:
The fact that some numbers may not be expressed using the particular set of symbols and, at the same time, the same number may be expressed using another set of symbols is quite common and not especially interesting.
Thank you for your explanation. I am well aware of this fact.

MHajduk wrote:
As I understood this question, revolution referred here to the definition of an indescribable number as a number impossible to describe with any set of arbitrarily chosen symbols.
How many sets of such symbols are there?

These symbols are all man-made. We can always create a new set of symbols to describe any numbers that are indescribable by the existing sets.

Why would THAT be interesting to anyone?

What is really interesting is the latest rule set by revolution:

"Everything must be given in the chosen language."

If we can describe the number, it is not indescribable.

Yeah, I see the trick.

14 Aug 2015, 01:43
Tyler

Joined: 19 Nov 2009
Posts: 1216
Location: NC, USA
Tyler
revolution wrote:
Whether or not Planck time is the base unit of time is not important, but I mentioned it to show that there is the possibility that time is discrete.
I've been told before that discrete spacetime would violate Lorentz invariance. But I can't claim I understand it at more than a basic level. The idea is that orientation in space shouldn't change the outcome of an experiment, but this can't hold with any lattice. Discrete spacetime forms a lattice, so it would violate it. I'm betting MHajduk could provide more detail.
14 Aug 2015, 01:44
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
Tyler wrote:
The idea is that orientation in space shouldn't change the outcome of an experiment ...
I guess you are talking about physical invariance.

Tyler wrote:
I'm betting MHajduk could provide more detail.
I think so, too! MHajduk is an expert in theoretical physics & applied mathematics.

14 Aug 2015, 05:33
Tyler

Joined: 19 Nov 2009
Posts: 1216
Location: NC, USA
Tyler
YONG wrote:
Tyler wrote:
The idea is that orientation in space shouldn't change the outcome of an experiment ...
I guess you are talking about physical invariance.
Close. https://en.wikipedia.org/wiki/Lorentz_covariance . Specifically, see #2 on the list in the introductory section.

Last edited by Tyler on 14 Aug 2015, 06:54; edited 1 time in total
14 Aug 2015, 06:06
l_inc

Joined: 23 Oct 2009
Posts: 881
l_inc
revolution
Quote:
But you described the process used to obtain the time period

I described a process that does not uniquely identify the number. For that reason the description of the process is not a description of the number. Only the experiment is.
Quote:
But just the same a PI, we can describe the process to obtain PI, and just because we can't write all the digits doesn't make it indescribable

I find it strange that you initiated the discussion, but do not realize that possible representations are not limited solely by digits. As long as you can specify a function able to generate arbitrary precision of the number, you can write down its complete representation as a limit of that function.
Quote:
I mentioned it to show that there is the possibility that time is discrete

And my objection is that the term of Planck time does not indicate the time discontinuity in any way.

_________________
Faith is a superposition of knowledge and fallacy
14 Aug 2015, 14:14
MHajduk

Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk

You can watch it also in a form of presentation here: http://www.slideshare.net/fullscreen/mikhajduk/indescribable-numbers
14 Aug 2015, 15:21
MHajduk

Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
Tyler wrote:
I'm betting MHajduk could provide more detail.
YONG wrote:
I think so, too! MHajduk is an expert in theoretical physics & applied mathematics.
Hehe, I'm not an expert in theoretical physics and only striving to be a professional in applied mathematics but accordingly to the well known adage vox populi, vox Dei (i.e. "the voice of the people is the voice of the God") seems there is a need to synchronize my internal image with what others think about me.
14 Aug 2015, 17:40
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
@MHajduk:

Thank you very much for your detailed explanation. I really like the background color of your proof, which makes it less boring to read a couple of pages that are full of text.

However, I must point out that your proof does NOT address my question.

My question is NOT about whether or not indescribable numbers exist, which is what your proof correctly shows.

"As I understood this question, revolution referred here to the definition of an indescribable number as a number impossible to describe with any set of arbitrarily chosen symbols."

Assume that your interpretation is correct.

Here is my question for you:

If we don't even know how many sets of such symbols there are and what these symbols actually represent, how could we find an example of a number that is indescribable by any sets of such symbols?

See, your interpretation renders the challenge meaningless.

Hope that you now understand my question.

15 Aug 2015, 06:09
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
MHajduk wrote:
I'm not an expert in theoretical physics ...
Don't be too modest. You know a great deal of math that is used in theoretical physics.
15 Aug 2015, 06:13
MHajduk

Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
YONG wrote:
If we don't even know how many sets of such symbols there are and what these symbols actually represent, how could we find an example of a number that is indescribable by any sets of such symbols?

See, your interpretation renders the challenge meaningless.

Hope that you now understand my question.
But we perfectly know how many sets of such symbols there may be. Exactly, an upper bound of the number of all possible alphabets should have cardinality of the power set of the set of all natural numbers, i.e. c (cardinality of the continuum).

However, that has nothing to do with describability because we assumed that an arbitrarily chosen set of symbols (alphabet) should always have a finite number of elements, so as it has been shown in my article/paper/whatever-we-name-it the cardinality of any available language based on such finite alphabet is much smaller than cardinality of the set of real numbers. Hence we can't "name" all real numbers, the set of "names" in any possible language (build on a base of an arbitrarily chosen finite alphabet) is too scarce to make one-to-one correspondence with the set of all real numbers.

The set of indescribable numbers (a subset of the set of all real numbers) behaves like "dark matter", to use the physical analogy, we know that it should exist, but we can not "catch" it with any available tool.

Where do you see maninglessness?
15 Aug 2015, 08:18
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
MHajduk wrote:
The set of indescribable numbers (a subset of the set of all real numbers) behaves like "dark matter", to use the physical analogy, we know that it should exist, but we can not "catch" it with any available tool.
That may no longer be the case, as scientists have already identified neutrinos as a form of dark matter, specifically hot dark matter.

Refer to:
https://en.wikipedia.org/wiki/Neutrino
https://en.wikipedia.org/wiki/Hot_dark_matter

MHajduk wrote:
Where do you see maninglessness?
What is the point of having a challenge that can never be met?

15 Aug 2015, 09:56
MHajduk

Joined: 30 Mar 2006
Posts: 6034
Location: Poland
MHajduk
YONG wrote:
MHajduk wrote:
The set of indescribable numbers (a subset of the set of all real numbers) behaves like "dark matter", to use the physical analogy, we know that it should exist, but we can not "catch" it with any available tool.
That may no longer be the case, as scientists have already identified neutrinos as a form of dark matter, specifically hot dark matter.

Refer to:
https://en.wikipedia.org/wiki/Neutrino
https://en.wikipedia.org/wiki/Hot_dark_matter
That's interesting, I've never realized that neutrinos are considered a part of dark matter because it has been known for some time. Seems that analogy between dark matter and indescribable numbers is not so obvious as it seemed to me.
YONG wrote:
MHajduk wrote:
Where do you see maninglessness?
What is the point of having a challenge that can never be met?
Alchemists were the people who tried to find a way of creation of the philosopher's stone, an elixir of life and tried to perform transmutation of metals which goals were completely out of reach then and now (with a little exception if we assume that "transmutation" is an analogue of the nuclear reactions performed in accelerators). Of course, as a side effect of those experiments, they discovered a few chemical elements, synthesized new substances and developed a bunch of new methods used in analytical chemistry till this day.
16 Aug 2015, 16:38
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17287
revolution
Given that z is any value, show any/all values where the following is not true when using the x86 FPU for all operations (includes using the FPU for comparisons):

[1/sqrt(z)] >= 0

For simplicity assume z is limited to 32-bits. If you want a slightly more challenging problem assume z is any tword (10 byte) value.
04 Sep 2015, 05:23
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
revolution wrote:
Given that z is any value, show any/all values where the following is not true when using the x86 FPU for all operations (includes using the FPU for comparisons):

[1/sqrt(z)] >= 0

For simplicity assume z is limited to 32-bits. If you want a slightly more challenging problem assume z is any tword (10 byte) value.
When z is zero, "division by zero" occurs.

When z is negative, "taking square root of a negative number" occurs.

There could be other values that satisfy the requirement. But I have not touched FPU operations for a very long time -- I am not sure.

04 Sep 2015, 05:48
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17287
revolution
YONG wrote:
When z is zero, "division by zero" occurs.
Yes, but that doesn't invalidate the question. Will the outcome of the comparison be false or true?
04 Sep 2015, 06:00
YONG

Joined: 16 Mar 2005
Posts: 8000
Location: 22° 15' N | 114° 10' E
YONG
revolution wrote:
YONG wrote:
When z is zero, "division by zero" occurs.
Yes, but that doesn't invalidate the question. Will the outcome of the comparison be false or true?
I don't know. Someone should try it out in a debugger or something.
04 Sep 2015, 06:08
revolution
When all else fails, read the source

Joined: 24 Aug 2004
Posts: 17287
revolution
YONG wrote:
revolution wrote:
YONG wrote:
When z is zero, "division by zero" occurs.
Yes, but that doesn't invalidate the question. Will the outcome of the comparison be false or true?
I don't know. Someone should try it out in a debugger or something.
Or someone could write a simple little program to spin through all 32-bit values and report the results.

Note that the extra challenge for all 10-byte values requires more forward planning than a basic brute force for all possible 80-bit input values.
24 Dec 2015, 10:07
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