# Digital physics, 6

Many people interested in physics keep on believing all kinds of evidently incorrect mystifications related to the notion of a “minimal length” and its logical relationships with the Lorentz invariance. Let’s look at them.

— Myths about the minimal length

— Lubos Motl

2012.09.30 Sunday ACHK

= 因果鏈相交

= 共同問題

— Me 2011.11.11

.

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# Universal Grammar, 2

Predicate logics may be viewed syntactically as Chomsky grammars. As such, predicate logics (as well as modal logics and mixed modal predicate logics) may be viewed as context-sensitive, or more typically as context-free, grammars. As each one of the four Chomsky-type grammars have equivalent automata, these logics can be viewed as automata just as well.

— Wikipedia on Predicate logic

2012.09.29 Saturday ACHK

— Me@2012.09.29

# 西瓜 5

[physical geometry]

In so far as the statements of geometry speak about reality, they are not certain;

[mathematical geometry]

and in so far as they are certain, they do not speak about reality.

— Albert Einstein

Analytic statements are about the languages.

Synthetic statements are about the world.

Choosing the best language describing the world is itself a synthetic problem.

— Me@2012-03-24 12:02:44 AM

“Is logic empirical?” is not a valid question, because it does not specify the meaning of “logic”.

“Is logic empirical?” is due to the confusion of two different concepts.

If you have no such confusion, the answer to the question is trivial.

As systems of analytical statements, the different theories of logic are not empirical.

But choosing the best among the logic systems to describe the real world is itself empirical.

— Me@2012-09-23 05:10:23 PM

# 數學教育 5

You cannot teach. You can only accelerate other people’s self-learning.

If someone does not self-study, it is impossible for you to help.

— Me@2011.11.10

# Completeness theorem, 4

Why truth table is not used in logic?

— JiminP

… the difference between semantics and syntax. A syntactic proof is a finite formal derivation of a sentence from the axioms of a theory using the logical axioms and the rules of inference of a logic. A proof by a truth table is a semantic proof; in allowing truth tables you are tacitly assuming the completeness theorem of propositional logic. Essentially, a priori, we don’t know that everything we can prove by studying the models of a theory (i.e. truth tables, in the case of propositional logic) can be proven syntactically, or even for that matter vice versa. It’s a non-trivial result in logic, …

— Zhen Lin

— Mathematics – Stack Exchange

2012.09.27 Thursday ACHK

# Digital physics, 5

Part of our disagreement is a misunderstanding. I am not questioning that the usual notions of geometry break down at the Planck scale (or earlier).

But the reason in string theory is that it does not make sense to talk about shorter distances because the physics at “shorter” distances is not just normal geometry plus something else, but a stringy generalized fuzzy blah blah structure.

Loop quantum gravity, on the other hand, says that geometry is a good variable at all distance scales, and the areas etc. have discrete spectrum, which contradicts Lorentz invariance in any theory with local excitations.

— Lubos Motl

2012.09.26 Wednesday ACHK

# Punishment

Punishment is for avoiding further harm, not revenge, unless revenge has such an effect.

If no further harm is possible, no punishment needed.

— Me@2011.11.11

— Inspired by Bertrand Russell

— Me@2012-09-26 11:06:48 AM

— Me@2012.09.26

# Principia Mathematica, 3

Principia is nowadays only of historical interest, since the subject has developed in quite different directions from those initiated by Russell and Whitehead. The idea of basing mathematics (including the development of the usual integers, reals, function spaces) purely on “logic” has largely been abandoned in favour of set-theory based formulations. And Principia does not have a clear separation between syntax and semantics. Such a separation is essential to the development of Model Theory in the past 80 years.

— Mathematics – Stack Exchange

— Andre Nicolas

2012.09.25 Tuesday ACHK

# 三國演義

（安：你網誌的部分文章，雖然是改編自你我的對話，即是我親身和你討論過那些話題，但是現在看回，感覺十分奇怪，而又帶點震撼。）

— Me@2012.09.24

# Information lost, 4

Losing information is the same as generating entropy. And generating entropy means generating heat. The virtual black holes that Stephen had so blithely postulated would create heat in empty space.

— The Black Hole War, p.23

— Leonard Susskind

2012.09.23 Sunday ACHK

# Teaching is useless

Intellect is invisible to those have none.

– Arthur Schopenhauer

Teaching is useless. Information is useful. Although intelligence can seldom be increased, giving relevant information to a GOOD person so that he can fully realize his existing intelligence potential is always useful.

The intelligence-absorption principle should actually be called the information-absorption principle, because intelligence cannot be increased directly.

「智攝原則」應該改稱為「資攝原則」，因為你沒有可能，直接增加別人的智力。你可以做到的，就只有透過給予相關資料，去加快別人智力潛能的發展。換句話說，你只可以破除無知，而不可刪減愚蠢。

Information is just like technology: Intellectually challenging to create doesn’t mean intellectually challenging to use.

— Me@2011.11.10

You cannot teach a man anything, you can only help him to find it for himself.

– Galileo

— Me@2012.09.23

# Existential Import, 1

Universal claims about empty sets are all true, because there are no falsifying instances.

NOTE: Claims about empty sets are trivially true. Sure, “all irrational prime numbers are odd” because there are no irrational prime numbers, but it is equally true that “all irrational prime numbers are even”.

— Tutorials, PL 120 Symbolic Logic I, Fall 2011

— Professor H. Hamner Hill

2012.09.22 Saturday ACHK

# Result-oriented, 2

p. xii How can we discern whether NDErs are truly blessed by divine light or deceived by the Prince of Darkness? No less an authority than Jesus gave us the methodology when he said, “By their fruits ye shall know them” (Matthew 7:20).

— Lessons from the Light

— by Kenneth Ring

2012.09.22 Saturday ACHK