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• ### Tumbling Mill Critical Speed Mineral Processing &

2015-8-6 · Effect of Speed and Filling on Power. In this section, a 0.545-m x 0.304-m ball mill is simulated to study the combined effect of mill speed and filling on the power draft of the mill. Mill operating speed and filling, among other things, are known to affect the power draft. Mill

### critical speed of tumbling mill

Critical speed of tumbling mill arrowfactoryeu critical speed the critical speed for a grinding mill is defined as thethe basic formula for this is the bond formuladrive tumbling mills are most commonly rotated by a pinion meshing with a gi remove; What is the critical speed of a tumbling mill, [24/7 online] Tumbling mill Meaning YouTube.

### critical speed tumbling mill formula shibang-china

critical speed equation in a tumbling mill Grinding Mill China. Posted at: August 14, 2012. ball mill critical speed calculation OneMine Mining Analysis Of Power Draw In Tumbling

### Critical Speed Grinding Mill Equation logopedia

2020-12-20 · Critical speed of ball mill formula derivation. 3 apr 2018 semiautogenous grinding sag mill and a ball mill.Apply bonds equation to industrial mills, which differ from the standard, for each mill there is a critical speed that creates centrifuging figure 37c of the with the help of figure 38, the concepts used in derivation of tumbling mills critical.

### Equation Formula Critical Speed Of The Ball Mill 2cmuc

2020-11-16 · Derivation Of Critical Speed Of Ball Mill Machine Mining . Critical Speed Of Ball Mill Formula Derivation 3 Apr 2018 SemiAutogenous Grinding SAG mill and a ball mill apply Bonds equation to industrial mills which differ from the standard For each mill there is a critical speed that creates centrifuging Figure 37c of the With the help of Figure 38 the concepts used in derivation of tumbling

### derived equation for estimating the critical speed in a

Critical speed of ball mill formula derivation. 3 apr 2018 semiautogenous grinding sag mill and a ball mill.Apply bonds equation to industrial mills, which differ from the standard, for each mill there is a critical speed that creates centrifuging figure 37c of the with the help of figure 38, the concepts used in derivation of tumbling mills

### Mill Speed Critical Speed Paul O. Abbe

In most cases, the ideal mill speed will have the media tumbling from the top of the pile (the shoulder) to the bottom (the toe) with many impacts along the way. The ideal mill speed is usually somewhere between 55% to 75% of critical speed. Critical Mill Speed. Critical Speed (left) is the speed at which the outer layer of media centrifuges

### Ball Mill Critical Speed Mineral Processing &

2015-6-19 · A Ball Mill Critical Speed (actually ball, rod, AG or SAG) is the speed at which the centrifugal forces equal gravitational forces at the mill shell’s inside surface and no balls will fall from its position onto the shell. The imagery below helps explain what goes on inside a mill as speed varies. Use our online formula. The mill speed is typically defined as the percent of the Theoretical

### SAGMILLING.COM .:. Mill Critical Speed Determination

Mill Critical Speed Determination. The "Critical Speed" for a grinding mill is defined as the rotational speed where centrifugal forces equal gravitational forces at the mill shell's inside surface. This is the rotational speed where balls will not fall away from the mill's shell.

### Critical Speed Of Ball Mill Formula Derivation

Ball mill critical speed derivation . Ball Mills Mine EngineerCom ball mill critical speed derivation,If the peripheral speed of the mill is too great, it begins to act like a centrifuge and the balls do not fall back, but stay on the perimeter of the mill The point where the mill becomes a centrifuge is called the Critical Speed, and dragThe second is air drag, which.

### derived equation for estimating the critical speed in a

critical speed equation in a tumbling mill grinding mill china. Critical speed of tumbling mill.Critical speed equation in a tumbling mill processing industries are mostly of the tumbling mill the critical speed of the mill, c, is defined as the speed at which a single ball will just remain in equation 8 14, d is the diameter inside the mill liners and le.

### determine critical speed grinding mill in malaysia

2021-4-16 · Mill Speed Critical Speed Paul O Abbe. In most cases the ideal mill speed will have the media tumbling from the top of the pile the shoulder to the bottom the toe with many impacts along the way The ideal mill speed is usually somewhere between 55 to 75 of critical speed Critical Mill Speed Critical Speed left is the speed at which the outer layer of media centrifuges

### Mill Speed Critical Speed Paul O. Abbe

In most cases, the ideal mill speed will have the media tumbling from the top of the pile (the shoulder) to the bottom (the toe) with many impacts along the way. The ideal mill speed is usually somewhere between 55% to 75% of critical speed. Critical Mill Speed. Critical Speed (left) is the speed at which the outer layer of media centrifuges

### critical speed grinding mill equation kwaksmolle.nl

Critical Speed Grinding Mill Equation Libranhnl. 2020-4-26Ball mill operating speed mechanical operations solved problems sep 11 2014 in a ball mill of diameter 2000 mm 100 mm dia steel balls are being used for aug 18 2016 ball mill rpm calculation mtm crusher the critical speed of ball mill is a mill ball mill ceramic ball mill critical speed formula derivation ball.

### Critical Speed Equation Of A Ball Mill

The critical speed is calculated as under [5]. rR g. 2 standard equation used by them for the ball mill work index (Bond work index) is as follows. Read more Attritors and Ball Mills How They Work.pdf

### Critical Speed Calculation Formula Of Ball Mill

Ball mill critical speed calculation YouTube. Nov 18, 2013 formula for calculating the critical speed of a ball mill, ball mill speed? newbie questions 2 most if the actual speed of a 6 ft diameter ball mill

### Experimental Study of Operational Parameters on Product

The rotational speed of the mill motor can be adjusted continually to 100% of critical speed. The applied speeds of this study were 60%, 70%, 80% and 90% of the critical speed. In Table 1, the

### Critical Speed Of Ball Mill Formula Derivation

Ball mill critical speed derivation . Ball Mills Mine EngineerCom ball mill critical speed derivation,If the peripheral speed of the mill is too great, it begins to act like a centrifuge and the balls do not fall back, but stay on the perimeter of the mill The point where the mill becomes a centrifuge is called the Critical Speed, and dragThe second is air drag, which.

### Ball Mill Design/Power Calculation LinkedIn

2016-12-12 · The basic parameters used in ball mill design (power calculations), rod mill or any tumbling mill sizing are; material to be ground, characteristics, Bond Work Index, bulk density, specific

### Modelling SAG milling power and specific energy

2017-12-14 · the power equation is also function of all the operational variables selected for this study. The applied force is a function of the mass inside the mill and it is composed of balls, ore and water. The ball charge is a function of the bulk fraction of the SAG mill volume (Jb) occupied by balls; the ore retained in the mill is the result of the

### calculating critical speed of ball mills mining

calculating critical speed in a ball mill. critical speed ball mill calculation critical speed ball mill calculation The critical speed of the mill, ampc, is defined as the speed at which a single ball in equation,d is the diameter inside the mill liners and le is the rod and ball mills in mular al and bhappu r b editors mineral processing plant design MORE; critical speed ball mill

### formula for critical speed of ball mill rxd

Mill Critical Speed Calculation. Effect of Mill Speed on the Energy Input In this experiment the overall motion of the assembly of 62 balls of two different sizes was studied The mill was rotated at 50, 62, 75 and 90% of the critical speed Six lifter bars of rectangular crosssection were used at equal spacing The overall motion of the balls at the end of five revolutions is shown in Figure 4

### Critical Speed Of Ball Mill Calculation India

Critical Speed Calculation Of Ball Mill. How To Calculate Critical Speed Of Ball Mill The critical speed of the mill, c, is defined as the speed at which a single ballIn equation 814, d is the diameter inside the mill liners and le is theRod and ball mills in mular al and bhappu r b editors mineral Read Now. Live Chat

### Mill Critical Speed Formula For Excel

ball mill critical speed calculation xls BINQ Mining. ball mill formulas and calculations Gold Ore Crusher. Excel speed/feed calculators for Ball Nose Finishers,

### A mill power equation for SAG mills SpringerLink

1990-2-1 · Development of an equation for tumbling charge and balls plus comparison to plant data suggests that the net mill power for cylindrical semiautogenous mills can be calculated from {m_p} = 10.6{D^{2.5}}L\left( {1 1.03J} \right)\left[ {\left( {1 {\varepsilon _B}} \right)\left( {{\rho _s}/{w_o}} \right)J + 0.6{J_B}\left( {{\rho _b} {\rho _s}/{w_c}} \right)} \right]\left( {{\phi _c

### A positron emission particle tracking investigation of

2016-12-20 · But the measured volume fraction in the dense regime for tumbling mills is clearly shown in figure 4 to span for the of critical speed data. Clearly the three literature models (da Cruz et al 2005,Jop et al 2005,Lee and Huang 2012 ) do not span a wide enough range of the volume concentration for adequately addressing tumbling mill flows and

### TECHNICAL NOTES 8 GRINDING R. P. King

2009-7-30 · A simple equation for calculating net power draft is P 2.00 3 cD 2.5 m LKl kW (8.12) Kl is the loading factor which can be obtained from Figures 8.5 for the popular mill types. 3 c is the mill speed measured as a fraction of the critical speed. More reliable models for the prediction of the power drawn by ball, semi-autogenous and fully autogenous

### Modelling SAG milling power and specific energy

2017-12-14 · the power equation is also function of all the operational variables selected for this study. The applied force is a function of the mass inside the mill and it is composed of balls, ore and water. The ball charge is a function of the bulk fraction of the SAG mill volume (Jb) occupied by balls; the ore retained in the mill is the result of the

### Ball Mill Design/Power Calculation LinkedIn

2016-12-12 · The basic parameters used in ball mill design (power calculations), rod mill or any tumbling mill sizing are; material to be ground, characteristics, Bond Work Index, bulk density, specific

### Ball Mills an overview ScienceDirect Topics

Oleg D. Neikov, in Handbook of Non-Ferrous Metal Powders, 2009 Tumbling Ball Mills. Tumbling ball mills or ball mills are most widely used in both wet and dry systems, in batch and continuous operations, and on a small and large scale.. Grinding elements in ball mills travel at different velocities. Therefore, collision force, direction and kinetic energy between two or more elements vary


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# What is 7-3(-8-2) + 6 -:2?

40

#### Explanation:

We can use PEMDAS:

• $\textcolor{red}{P}$ - Parentheses (also known as Brackets)
• $\textcolor{b l u e}{E}$ - Exponents
• $\textcolor{g r e e n}{M}$ - Multiplication
• $\textcolor{g r e e n}{D}$ - Division (this has the same weight as M and so I gave it the same colour)
• $\textcolor{b r o w n}{A}$ - Addition
• $\textcolor{b r o w n}{S}$ - Subtraction - (again, same weight as A and so the same colour)

First we have a $\textcolor{red}{P}$:

$7 - 3 \textcolor{red}{\left(- 8 - 2\right)} + 6 \div 2$

$7 - 3 \textcolor{red}{\left(- 10\right)} + 6 \div 2$

Next we have an $\textcolor{g r e e n}{M}$ and a $\textcolor{g r e e n}{D}$

$7 \textcolor{g r e e n}{- 3 \left(- 10\right)} + \textcolor{g r e e n}{6 \div 2}$

$7 \textcolor{g r e e n}{+ 30} + \textcolor{g r e e n}{3}$

And now we have $\textcolor{b r o w n}{A}$

$\textcolor{b r o w n}{7 + 30 + 3} = 40$

format: plain


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# How does L1 regularization make low-value features more zero than L2?

Below formulas, L1 and L2 regularization

Many experts said that L1 regularization makes low-value features zero because of constant value. However, I think that L2 regularization could also make zero value. Could you please explain the reason why L1 has more tendency to make zero value? (It's gonna be great if you let me know this reason by using formula(like above equation)!

With L1, when a weight value comes closer to zero, it tends to get even closer, because of the $$\epsilon\lambda$$ penalty which stays constant.
With L2, the $$\epsilon\lambda w^{(t)}$$ term gets smaller, so the regularization gets smaller as a weight comes closer to zero, with the update depending only on $$\epsilon\Delta E(w)$$.
So the main argument for this to my knowledge is that $$\lim_{w\rightarrow0}\lambda = \lambda\\ \lim_{w\rightarrow0}\lambda w = 0$$


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# qz like function in Mathematica

MATLAB has the function qz() such that [AA, BB, Q, Z, V, W] = qz(A, B) produces matrices V and W whose columns are generalized eigenvectors. This function gives the right and left eigenvectors. I didn't find a similar function in Mathematica. Does it exist?

Thanks.

• I'm pretty sure the built-ins Eigensystem, Eigenvalues, or Eigenvectors can do this. See the documentation. – march Nov 29 '17 at 16:39
• This page has maping of some matlab functions to Mathematica, including qz. But Matlab qz returns number of values. So may be there is some functionality not there. But f you have specific example you want to see it in Matlab, you can provide one. – Nasser Nov 29 '17 at 17:01

As already hinted, Mathematica is perfectly capable of computing the eigensystem of a pencil. However, none of the commenters gave the function that is the closest to the functionality of MATLAB's qz(), and that is Mathematica's SchurDecomposition[].

Briefly put, when given a pencil (as a list of two square matrices of the same dimensions), SchurDecomposition[] will return the generalized Schur decomposition (apparently termed the "QZ decomposition" in some circles). More concretely, given a pencil $(\mathbf A,\mathbf B)$, SchurDecomposition[] will return a similar (i.e., same eigenvalues) pencil $(\mathbf T,\mathbf U)$, where $\mathbf T$ and $\mathbf U$ are quasitriangular matrices, and are related to $\mathbf A$ and $\mathbf B$ as $\mathbf Q\mathbf T\mathbf Z^\top=\mathbf A$, and $\mathbf Q\mathbf U\mathbf Z^\top=\mathbf B$, where $\mathbf Q$ and $\mathbf Z$ are orthogonal matrices. (For complex matrices, replace transpose with conjugate transpose, quasitriangular with triangular, and orthogonal with unitary.)

(If you are reading Golub and Van Loan, note that my convention is slightly different from theirs.)

If the resulting pencil is triangular, the eigenvalues of the pencil can be obtained as the ratio of the diagonal elements of $\mathbf T$ and $\mathbf U$. Zero diagonal elements in $\mathbf U$ correspond to infinite eigenvalues of the pencil.

Let's look first at what MATLAB does:

A = [3 2 1; 2 3 1; 5 1 2];

B = [1 2 3; 4 5 6; 7 8 9];

[at, bt, q, z] = qz(A, B)

at =

-2.1394    6.0702    2.8152
0    0.8982    1.8737
0         0   -2.0817

bt =

1.9287   14.3282    2.2505
0    8.2195    1.8326
0         0         0

q =

-0.6272   -0.5758   -0.5244
0.6633   -0.0420   -0.7472
0.4082   -0.8165    0.4082

z =

0.4729   -0.4012   -0.7845
0.3630   -0.7226    0.5883
-0.8029   -0.5630   -0.1961

Here is the Mathematica equivalent:

amat = N[{{3, 2, 1}, {2, 3, 1}, {5, 1, 2}}];
bmat = N[{{1, 2, 3}, {4, 5, 6}, {7, 8, 9}}];

MatrixForm /@ ({q, at, z, bt} = SchurDecomposition[{amat, bmat}])

$$\left\{\begin{pmatrix} -0.627226 & 0.663265 & 0.408248 \\ -0.575823 & -0.0419709 & -0.816497 \\ -0.524419 & -0.747207 & 0.408248 \\ \end{pmatrix}, \begin{pmatrix} -2.13941 & 6.07017 & -2.81516 \\ 0. & 0.898164 & -1.87371 \\ 0. & 0. & 2.08167 \\ \end{pmatrix}, \begin{pmatrix} 0.47294 & -0.401178 & 0.784465 \\ 0.362966 & -0.722566 & -0.588348 \\ -0.802859 & -0.562988 & 0.196116 \\ \end{pmatrix}, \begin{pmatrix} 1.92866 & 14.3282 & -2.25052 \\ 0. & 8.21954 & -1.83255 \\ 0. & 0. & 0. \\ \end{pmatrix}\right\}$$

Note the similarities and differences in the output. For MATLAB, we have the relations q.' * at * z.' == A and q.' * bt * z.' == B, while for Mathematica, we have q.at.Transpose[z] == amat and q.bt.Transpose[z] == bmat.

Additionally, MATLAB's qz() provides a form where the (right and left) eigenvectors of the given pencil are also produced. In Mathematica, Eigenvectors[] (and thus Eigensystem[] as well) can work on a pencil. Using the same matrices as above in both MATLAB and Mathematica:

[at, bt, q, z, vl, wl] = qz(A, B)

...

vl =

0.5891    0.2404   -0.5000
0.4521   -0.0128    1.0000
-1.0000   -1.0000   -0.5000

wl =

-1.0000    1.0000    0.5000
0.2915   -0.7044   -1.0000
0.1749   -0.4226    0.5000

where I had omitted the output of the other four matrices. In Mathematica, the equivalent for vl is

MatrixForm[vecs = Eigenvectors[{amat, bmat}]]

$$\begin{pmatrix} 0.408248 & -0.816497 & 0.408248 \\ 0.47294 & 0.362966 & -0.802859 \\ 0.233732 & -0.0124306 & -0.972221 \\ \end{pmatrix}$$

It looks a little different from what MATLAB produced, but we can verify that certain properties are satisfied. In MATLAB:

adi = diag(diag(at));
bdi = diag(diag(bt));

norm(A * vl * bdi - B * vl * adi)

ans =

1.3591e-14

and in Mathematica:

amat.Transpose[vecs[[{2, 3, 1}]]].DiagonalMatrix[Diagonal[bt]] -
bmat.Transpose[vecs[[{2, 3, 1}]]].DiagonalMatrix[Diagonal[at]]
7.65362*10^-15

(Note that I needed to permute the eigenvectors to agree with the order in the generalized Schur decomposition.)

As for wl, that is the set of left eigenvectors for the pencil. Unfortunately, in Mathematica, there is no convenient way to get the left eigenvectors, so you have to do a second computation:

MatrixForm[lvecs = Eigenvectors[Transpose /@ {amat, bmat}]]

$$\begin{pmatrix} 0.408248 & -0.816497 & 0.408248 \\ -0.946782 & 0.276006 & 0.165603 \\ -0.772724 & 0.544287 & 0.326572 \\ \end{pmatrix}$$

Check in MATLAB:

norm(bdi * wl.' * A - adi * wl.' * B)

ans =

1.0668e-14

and in Mathematica:

Norm[DiagonalMatrix[Diagonal[bt]].lvecs[[{2, 3, 1}]].amat -
DiagonalMatrix[Diagonal[at]].lvecs[[{2, 3, 1}]].bmat]
5.36595*10^-15

• Perhaps a naive question, but where does the term pencil come from here? – b3m2a1 Mar 21 '18 at 7:06
• "Pencil" is actually a more general term, but most conventionally applied to a pair of matrices. It comes from projective geometry; see this MO thread. – J. M.'s discontentment Mar 21 '18 at 7:11
• @J.M. Thanks for the sophisticated answer. – qahtah Mar 22 '18 at 16:49


text:
Newton's Laws of Motion Problem

Homework Statement

Mass of Block A = 1 kg
Mass of Wedge B = 2 kg
Inclination of Wedge is 37°
and Cos 37° = 4/5
The wedge is given an acceleration of 5 ms-2
Find -
1. Acceleration of Block wrt Wedge
2. Normal Force

Homework Equations

Newton's Law for a System (hereby referred as NLS)
∑fext = m1a1+m2a2......+mnan

The Attempt at a Solution

Let the Acceleration of Block wrt Wedge be λ along the inclination.
In Y axis, there is only one Ext force i.e. The gravity and ∑fnet in Y direction is m1g+ m2g = (m1+ m2)g
Therefore in Y axis using Newton's Law for a System,
mAaA + mBaB = (m1+ m2)g
but in Y axis , aA = 0
and ab in Y axis = λsinθ + aAcos 90
= λsinθ + 0
= λsinθ
Therefore, mBaB = (m1+ m2)g
1 (λsin(θ)) = (1 + 2)g
λ sin 37° = (3)10
λ(3/5) = 30
λ = 50
but using pseudo force, λ = 2 ms-2 which is correct answer in the Answer Key
Where am I going Wrong?

Attachments

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text:
Viser treff 1-1 av 1

• #### Kiln process impact of alternative solid fuel combustion in the cement kiln main burner - Mathematical modelling and full-scale experiment

(Journal article; Peer reviewed, 2014-02)
Increased use of alternative fuels in cement kilns is a trend in the world. However, replacing fossil fuels like coal with different alternative fuels will give various impacts on the overall kiln process due to the fuel ...


text:
This week in pre-calc 11 we learned how to subtract and add radicals
the first step is to simplify the radical like example $sqrt {4}$ would be 2
no matter if the radical is mixed or entire for radicand must be the same
Example: You can’t add $sqrt (2)$ and $sqrt (3)$
In this example I show how when the radicand is the same you can add them $sqrt (2)$ + $sqrt (2)$ = $sqrt (4)$ which equals 2

When the radicand is not the same you have to try to use prime factorization to give the radicand a coefficient which hopefully ends in a radical that has the same radicand


text:
# Domain of a Type-2 Computable Function

In Weihrauch's Type-2 computability theory, a string function $$f\colon\subseteq \Sigma^{\omega}\rightarrow \Sigma^{\omega}$$ (the $$\colon\subseteq$$ indicates that $$f$$ may be a partial function) is computable iff there exists a Type-2 Turing machine that exactly realizes $$f$$, which implies that the Turing machine must fail to produce an output on inputs that are not in the domain of $$f$$.

To extend this to functions between arbitrary domains $$D_1$$ and $$D_2$$, one specifies representations $$\gamma_i\colon\subseteq\Sigma^{\omega}\rightarrow D_i$$, and Weihrauch defines $$f\colon\subseteq D_1\rightarrow D_2$$ to be $$(\gamma_1,\gamma_2)$$-computable iff there exists a Type-2 computable string function $$g$$ such that $$f(\gamma_1(y)) = \gamma_2(g(y))$$ whenever $$f(\gamma_1(y))$$ is defined.

But $$\gamma_2(g(y))$$ is allowed to be defined even when $$f(\gamma_1(y))$$ is not.

Why is it defined this way? It seems to me more natural to require $$f\circ\gamma_1 = \gamma_2\circ g$$, i.e. the domain of the realization $$g$$ must match the domain of $$f$$. With Weihrauch's definition we have the odd condition that, for a string function $$f$$, the statements "$$f$$ is Type-2 computable" and "$$f$$ is $$(\mathrm{id},\mathrm{id})$$-computable" (where $$\mathrm{id}$$ is the identity function) are not equivalent.

Reference: Weihrauch, K. (2000), Computable Analysis: An Introduction, Springer.

• Are you looking for an explanation in terms of category theory or at an intuitive level? – Andrej Bauer May 18 '20 at 7:27
• Intuitive level. In particular, why does it make sense to define things in such a way that an uncomputable string function $f$ may nonetheless be considered computable if we regard $\Sigma^{\omega}$ as just another arbitrary domain and use the definition of computability for arbitrary domains? – Kevin S. Van Horn May 18 '20 at 23:54

The general philosophy in realizability theory (TTE is a special case of it) is that for a program $$p$$ realizes a map $$f : A \to B$$ then $$p$$, it should work correctly on realizers of arguments, i.e., if $$r$$ realizes $$x \in A$$ then $$p\,r$$ realizes $$f(x) \in B$$. It is quite unnatural to say anything about "non-realizers", for at least two reasons. First, it would break the categorical structure of the category of representations (exponentials break). Second, from the programming point of view you are asking that a program always produce garbage output when given garbage input. This is an unreasonable request: the behavior should be unspecified for garbage input, as a program may in fact be unable to tell that it was given garbage input.

We are in the realm of realizability theory, of which TTE is a special case. It is important to understand that, when working with representations, there are two notions of function:

1. The maps which take realizers to realizers, in the case of TTE these are the maps $$\Sigma^\omega \to \Sigma^\omega$$. Let us call these realizers.

2. The morphisms in the category of represented sets, which are maps between sets that are tracked by a realizers. In TTE these are also called $$(\gamma_1, \gamma_2)$$-computable maps, but we shall just call them morphisms.

Standard textbooks on computability theory almost alawys talk about the first notion. The question is asking about the relationship between the first and the second notion.

Typically realizers are not actually functions, but are elements of some model of computation, such as Turing machines (either type I or type II) or the closed terms of $$\lambda$$-calculus. In the case of Type Two Effectivity this becomes apparent once we try to compute the standard representation for the set of realized maps, because that is when we define what it means for an element of $$\Sigma^\omega$$ to implement a realizers $$\Sigma^\omega \to \Sigma^\omega$$.

Morphisms between represented sets are functions (which happen to be tracked by a realizer).

Let us consider the question "Is the restriction of a computable map also computable?" in both senses.

1. Is the restriction of a realizers (as a map) again a realizer? The answer is negative, for if $$f {:}{\subseteq} \Sigma^\omega \to \Sigma^\omega$$ is computed by a Turing machine, one can show that the domain of $$f$$ is a $$G_\delta$$-set. Therefore, if we restrict $$f$$ to a domain which is not a $$G_\delta$$-set there will be no Turing machine that computes the restriction.

2. Is the restriction of a morphism $$f : D_1 \to D_2$$ again a morpshism? Here we have to understand "restriction" in the sense of category theory, i.e., a precomposition with a (regular) mono. This amounts to restricting the representation $$\gamma_1 : \Sigma^\omega \to D_1$$ to a subset $$D \subseteq D_1$$. We could define the realizability model so that restrictions need not be realized, but that would be silly and useless. It is much better to make sure that the resulting category has good properties, because then we can actually do something with it. And so we define the notion of "tracked by a computable map" in the way we do and enjoy the resulting ambient.

• Minor comment: the second part of the answer is more interesting. The first part is rather counter-intuitive, since if an arbitrary restriction of a computable partial function does not have to be computable, in general. E.g. a set is RE iff its semi-characteristic function is partial computable. Any semi-char. is a restriction of the constant one function, but that doesn't make it computable (or every set would be RE). Hence, this computability notion ("we only care about realizers") seems to follow a slightly different intuition compared with the "basic" computability notion. – chi May 18 '20 at 22:52
• @Andrej, you say it's reasonable to expect the restriction of a computable map to be computable, but my textbook definition of (standard, Type-I) computability does not have this property for either string functions nor arbitrary domains, nor does Weihrauch's definition of Type-II computability for string functions. Why does your argument not apply in these cases? – Kevin S. Van Horn May 19 '20 at 0:04
• As @chi points out, there are two different things: computable functions as programs or realizers (which is what your textbook is talking about) and computable morphisms in a realizability model (which is what you are asking about). I'll amend my answer as this is not clearly pointed out. – Andrej Bauer May 19 '20 at 8:33

Andrej's answer raises some excellent points. I think we can gain some additional insight by looking at why we demand the computable partial functions come with their natural domain in classical computability theory.

One benefit we get from this is that in Type-1 computability a string function computation can only provide garbage in a very limited way: It either halts and provides an output, or it does not halt. Requiring that halting always indicates a valid input and subsequent valid computation means that we can trust any output we see. Already for a Type-2 computation on infinite sequences, invalid output can be more complicated, as we can see some finite prefix of an input before the computation stalls (the natural domain of a Type-1 computation is $$\Sigma^0_1$$, that of a Type-2 computation is $$\Pi^0_2$$). As soon as we move to more complicated represented spaces, garbage outputs can be arbitrarily hard to detect - so there is no gain in information coming from a requirement that garbage input must yield garbage output.

A second reason that we do want the set of computable partial functions to be countable, and in fact, want to have a standard enumeration of it. This motivation carries over to Type-2 computable partial functions of type $$\Sigma^\omega \to \Sigma^\omega$$, which we use as realizers. However, we (almost) never care about the set of partial computable functions from one represented space to another. We either speak about the set/space of computable total functions (which is countable without any garbage-in/garbage-out requirements, and in fact better behaved without); or we say that an individual partial function is computable. So this reason does not apply here, either.

• Thanks, this was quite useful. BTW, I'm currently looking at a case where we do care about partial computable functions $f\colon\subseteq\Sigma^{\omega}\rightarrow D$: random variate generators that map a random string of bits into a draw from some distribution on $D$. These functions can be partial, as long as the domain has measure 1. – Kevin S. Van Horn May 19 '20 at 13:58
• @KevinS.VanHorn I would tend to assume that you wouldnt actually work with the space of partial computable functions with full measure domain here, but rather with some quotient of it. But these are the kind of things that caused me to put the "almost" in there. – Arno May 19 '20 at 14:32


text:
]>

## STATISTICAL MECHANICS OF NEOCORTICAL INTERACTIONS:REACTION TIME CORRELATES OF THEFACTOR

Lester Ingber

Lester Ingber Research PO Box 06440 Wacker Dr PO Sears Tower Chicago, IL 60606 and DRW Investments LLC 311 S Wacker Dr Ste 900 Chicago, IL 60606 ingber@ingber.com, ingber@alumni.caltech.edu http://www.ingber.com/

Psycholoquy Commentary on The$g$ Factor: The Science of Mental Ability by Arthur Jensen

ABSTRACT: A statistical mechanics of neuronal interactions (SMNI) is explored as providing some substance to a physiological basis of the$g$ factor. Some specific elements of SMNI, previously used to develop a theory of short-term memory (STM) and a model of electroencephalography (EEG) are key to providing this basis. Specifically, Hick’s Law, an observed linear relationship between reaction time (RT) and the information storage of STM, in turn correlated to a RT-$g$ relationship, is derived.

KEYWORDS: short term memory; nonlinear; statistical

## 1. Introduction

### 1.1. Context of Review

My specific interest in taking on this review of “The$g$ Factor” by Arthur Jensen (AJ) is to see if some anatomical and/or physiological processes at the columnar level of neuronal interactions can account for the$g$ factor.

From circa 1978 through the present, a series of papers on the statistical mechanics of neocortical interactions (SMNI) has been developed to model columns and regions of neocortex, spanning mm to cm of tissue. Most of these papers have dealt explicitly with calculating properties of short-term memory (STM) and scalp EEG in order to test the basic formulation of this approach. SMNI derives aggregate behavior of experimentally observed columns of neurons from statistical electrical-chemical properties of synaptic interactions. While not useful to yield insights at the single neuron level, SMNI has demonstrated its capability in describing large-scale properties of short-term memory and electroencephalographic (EEG) systematics (Ingber, 1982; Ingber, 1983; Ingber, 1984; Ingber, 1991; Ingber, 1994; Ingber, 1995a; Ingber & Nunez, 1995; Ingber, 1996a; Ingber, 1997).

### 1.2. Errors In Simple Statistical Approaches

I must assume that AJ faced very difficult problems in choosing just how much technical details to give in his broad text, e.g., discussing the extent of expert statistical analyses that have been brought to bear upon the$g$ factor. However, I do see reason to criticize some general features of the simple statistical algorithms presented, especially those that overlap with my own mathematical and physics expertise.

The simple approach to factor analysis initiated on page 23,

 $X=t+e,$ (1) where$e$ is the residual “noise” of fitting the variable$X$ to the independent variable$t$ , has some serious flaws not addressed by additional material presented thereafter. For example, in this context, I find the arguments in the long footnote 16 on pages 101-103 unconvincing, but I agree with its conclusion: But the question is mainly of scientific interest, and a really satisfactory answer ... will become possible only as part and parcel of a comprehensive theory of the nature of$g$ obtained measurements should conform to the characteristics of the distribution dictated by theoretical considerations. I think it clear that any such “theoretical considerations” must themselves be well tested against experimental evidence at each spatial-temporal scale purported to be modeled. It must be understood that there is a quite explicit model being assumed here of the real world — that of a simple normal Gaussian process. The real issue in many physical/biological systems is that most often the real multivariable world is much more aptly described by something like
 $X={t}_{X}\left(X,Y\right)+{s}_{X}\left(X,Y\right)\text{ }{e}_{X}$ (2.a)
$Y={t}_{Y}\left(X,Y\right)+{s}_{Y}\left(X,Y\right)\text{ }{e}_{Y}.$

(2.b)

When the$t$$s$ determine their values and cross-correlations between the$s$

Simple statistical methods can even do OK if the$t$ simple quasi-linear parameterized functions. Such simple methods fail quite miserably if the$t$ nonlinear functions, especially if care is not taken to employ sophisticated optimization algorithms. The most terrible flaws often occur because, for the sake of making life easier for the analyst, any model faithful to the real system is butchered and sacrificed, and the$s$ In general, there can be a lot of “signal” in the (generally nonlinear) functionality of the “noise” terms. In general, no degree of fancy quasi-linear statistical analysis can substitute for a proper theory/model of the real system.

In general, the proper treatment of the problem is quite difficult, which is of course no excuse for poor treatment. The solution in many disciplines is to go a level or two deeper in some Reductionist sense, to develop plausible models at the top scale being analyzed. Indeed, this was the call I saw and responded to in the advertisement for reviewers of the work by AJ:

Commentary is invited from psychometricians, statisticians, geneticists, neuropsychologists, psychophysiologists, cognitive modellers, evolutionary psychologists and other specialties concerned with cognitive abilities, their measurement, and their cognitive and neurobiological basis.

In this context, the successes of SMNI and its agreement with general STM observations are due to processing stochastic nonlinearities of the forms described above. Attempts to avoid dealing with these nonlinearities, derived from lower-level synaptic and neuronal activity, have not been as successful as SMNI in detailing STM (Ingber, 1995b).

## 2. SMNI Description of Short-Term Memory (STM)

Since the early 1980’s, a series of papers on the statistical mechanics of neocortical interactions (SMNI) has been developed to model columns and regions of neocortex, spanning mm to cm of tissue. Most of these papers have dealt explicitly with calculating properties of short-term memory (STM) and scalp EEG in order to test the basic formulation of this approach (Ingber, 1981; Ingber, 1982; Ingber, 1983; Ingber, 1984; Ingber, 1985a; Ingber, 1985b; Ingber, 1986; Ingber & Nunez, 1990; Ingber, 1991; Ingber, 1992; Ingber, 1994; Ingber & Nunez, 1995; Ingber, 1995a; Ingber, 1995b; Ingber, 1996b; Ingber, 1997; Ingber, 1998). This model was the first physical application of a nonlinear multivariate calculus developed by other mathematical physicists in the late 1970’s (Graham, 1977; Langouche et al, 1982).

### 2.1. Statistical Aggregation

SMNI studies have detailed a physics of short-term memory and of (short-fiber contribution to) EEG phenomena (Ingber, 1984), in terms of${M}^{G}$ firings, where$G$ represents$E$ or$I$ ,${M}^{E}$ represents contributions to columnar firing from excitatory neurons, and${M}^{I}$ represents contributions to columnar firing from inhibitory neurons. About 100 neurons comprise a minicolumn (twice that number in visual cortex); about 1000 minicolumns comprise a macrocolumn. A mesocolumn is developed by SMNI to reflect the convergence of short-ranged (as well as long-ranged) interactions of macrocolumnar input on minicolumnar structures, in terms of synaptic interactions taking place among neurons (about 10,000 synapses per neuron). The SMNI papers give more details on this derivation.

In this SMNI development, a Lagrangian is explicitly defined from a derived probability distribution of mesocolumnar firings in terms of the${M}^{G}$ and electric potential variables,${\Phi }^{G}$ Several examples have been given to illustrate how the SMNI approach is complementary to other models. For example, a mechanical string model was first discussed as a simple analog of neocortical dynamics to illustrate the general ideas of top down and bottom up interactions (Nunez, 1989; Nunez & Srinivasan, 1993). SMNI was applied is to this simple mechanical system, illustrating how macroscopic variables are derived from small-scale variables (Ingber & Nunez, 1990).

### 2.2. STM Stability and Duration

SMNI has presented a model of STM, to the extent it offers stochastic bounds for this phenomena during focused selective attention. This$7±2$ “rule” is well verified by SMNI for acoustical STM (Ingber, 1984; Ingber, 1985b; Ingber, 1994), transpiring on the order of tenths of a second to seconds, limited to the retention of$7±2$ items (Miller, 1956). The$4±2$ “rule” also is well verified by SMNI for visual or semantic STM, which typically require longer times for rehearsal in an hypothesized articulatory loop of individual items, with a capacity that appears to be limited to$4±2$ (Zhang & Simon, 1985). SMNI has detailed these constraints in models of auditory and visual cortex (Ingber, 1984; Ingber, 1985b; Ingber, 1994; Ingber & Nunez, 1995).

Another interesting phenomenon of STM capacity explained by SMNI is the primacy versus recency effect in STM serial processing (Ingber, 1985b), wherein first-learned items are recalled most error-free, with last-learned items still more error-free than those in the middle (Murdock, 1983). The basic assumption is that a pattern of neuronal firing that persists for many$\tau$ cycles,$\tau$ on the order of 10 msec, is a candidate to store the “memory” of activity that gave rise to this pattern. If several firing patterns can simultaneously exist, then there is the capability of storing several memories. The short-time probability distribution derived for the neocortex is the primary tool to seek such firing patterns. The highest peaks of this probability distribution are more likely accessed than the others. They are more readily accessed and sustain their patterns against fluctuations more accurately than the others. The more recent memories or newer patterns may be presumed to be those having synaptic parameters more recently tuned and/or more actively rehearsed.

It has been noted that experimental data on velocities of propagation of long-ranged fibers (Nunez, 1981; Nunez, 1995) and derived velocities of propagation of information across local minicolumnar interactions (Ingber, 1982) yield comparable times scales of interactions across minicolumns of tenths of a second. Therefore, such phenomena as STM likely are inextricably dependent on interactions at local and global scales.

### 2.3. SMNI Correlates of STM and EEG

Previous SMNI studies have detailed that maximal numbers of attractors lie within the physical firing space of${M}^{G}$ , consistent with experimentally observed capacities of auditory and visual short-term memory (STM), when a “centering” mechanism is enforced by shifting background noise in synaptic interactions, consistent with experimental observations under conditions of selective attention (Mountcastle et al, 1981; Ingber, 1984; Ingber, 1985b; Ingber, 1994; Ingber & Nunez, 1995). This leads to all attractors of the short-time distribution lying along a diagonal line in${M}^{G}$ space, effectively defining a narrow parabolic trough containing these most likely firing states. This essentially collapses the 2 dimensional${M}^{G}$ space down to a 1 dimensional space of most importance. Thus, the predominant physics of short-term memory and of (short-fiber contribution to) EEG phenomena takes place in a narrow “parabolic trough” in${M}^{G}$ space, roughly along a diagonal line (Ingber, 1984).

Using the power of this formal structure, sets of EEG and evoked potential data were fit, collected to investigate genetic predispositions to alcoholism and to extract brain “signatures” of short-term memory (Ingber, 1997; Ingber, 1998). These results give strong quantitative support for an accurate intuitive picture, portraying neocortical interactions as having common algebraic or physics mechanisms that scale across quite disparate spatial scales and functional or behavioral phenomena, i.e., describing interactions among neurons, columns of neurons, and regional masses of neurons.

For future work, I have described how bottom-up neocortical models can be developed into eigenfunction expansions of probability distributions appropriate to describe short-term memory in the context of scalp EEG (Ingber, 2000). The mathematics of eigenfunctions are similar to the top-down eigenfunctions developed by some EEG analysts, albeit they have different physical manifestations. The bottom-up eigenfunctions are at the local mesocolumnar scale, whereas the top-down eigenfunctions are at the global regional scale. However, these approaches have regions of substantial overlap (Ingber & Nunez, 1990; Ingber, 1995a), and future studies may expand top-down eigenfunctions into the bottom-up eigenfunctions, yielding a model of scalp EEG that is ultimately expressed in terms of columnar states of neocortical processing of attention and short-term memory.

An optimistic outcome of future work might be that these EEG eigenfunctions, baselined to specific STM processes of individuals, could be a more direct correlate to estimates of$g$ factors.

### 2.4. Complexity in EEG

In Chapter 6, Biological Correlates of$g$ , AJ puts these issues in perspective:

First, psychometric tests were never intended or devised to measure anything other than behavioral variables. ... at this point most explanations are still conjectural.

However, most of the chapter falls back to similar too-simple statistical models of correlations between measured variables and behavioral characteristics.

The sections on Biological Correlates of$g$ dealing with EEG recordings are incomplete and at a level too superficial relative most of the other parts of the book. The introduction of “complexity” as a possible correlate to IQ is based on faddish studies that do not have any theoretical or experimental support (Nunez, 1995). If such support does transpire, most likely it will be developed on the shoulders of more complete stochastic models and much better EEG recordings.

## 3. SMNI STM Correlates of the Factor

### 3.1. High vs Low Categories

The outline of test categories giving rise to high versus low$g$ loadings on page 35 provides me with some immediate candidates for further investigations of a physiological basis for the$g$ factor. I think a good working hypothesis is that these two categories are marked by having the high$g$ loadings more correlated than the low$g$ loadings to statistical interactions among the peaks of the probability distributions described above in the context of SMNI’s theory of STM. The high$g$ categories clearly require relatively more processing of several items of information than do the low$g$ categories.

This seems to be a similar correlation as that drawn by Spearman, as described by AJ, in having “education of relations” and “education of correlates” more highly correlation with high$g$ categories than the “apprehension of experience.”

### 3.2. Mechanisms of High Categories

From the SMNI perspective, control of selective attention generally is highly correlated with high utilization of STM, e.g., to tune the “centering mechanism.” This seems similar to Spearman’s correlation of “mental energy” with high$g$ categories.

There are several mechanisms that might distinguish how well individuals might perform on high$g$ category tasks. The ability to control the “centering mechanism” is required to sustain a high degree of statistical processes of multiple most probable states of information. The particular balance of general chemical-electrical activity directly shapes the distribution of most probable states. For some tasks, processing across relatively more most probable states might be required; for other tasks processing among larger focussed peaks of most probable states might be more important.

### 3.3. Hick’s Law — Linearity of RT vs STM Information

Th SMNI approach to STM gives a reasonable foundation to discuss RT to items in STM storage. Previous calculations give detailed support to items in STM storage as being represented as peaks in the short-time (10 msec) (Ingber, 1984; Ingber, 1985b) as well as the long-time (several secs) (Ingber, 1994; Ingber & Nunez, 1995) conditional probability distribution of correlated mesocolumnar firings of columns of neurons, correlated to STM tasks also correlated to EEG observations of evoked potential activities (Ingber, 1997; Ingber, 1998). This distribution is explicitly calculated by respecting the nonlinear synaptic interactions among all possible combinatoric aggregates of columnar firing states (Ingber, 1982; Ingber, 1983).

The RT necessary to “visit” the states under control during the span of STM can be calculated as the mean time of “first passage” between multiple states of this distribution, in terms of the probability$P$ as an outer integral$\int \text{\hspace{0.17em}}dt$ (sum) over refraction times of synaptic interactions during STM time$t$ , and an inner integral$\int \text{\hspace{0.17em}}dM$ (sum) taken over the mesocolumnar firing states$M$ (Risken, 1989), which has been explicitly calculated to be within observed STM time scales (Ingber, 1984),

 $RT=-\int \text{\hspace{0.17em}}dt\text{ }t\text{ }\int \text{\hspace{0.17em}}dM\text{ }\frac{dP}{dt}\text{ }.$ (3) As demonstrated by previous SMNI STM calculations, within tenths of a second, the conditional probability of visiting one state from another$P$ , can be well approximated by a short-time probability distribution expressed in terms of the previously mentioned Lagrangian$L$ as
 $P=\frac{1}{\sqrt{\left(2\pi dtg\right)}}\text{exp}\left(-Ldt\right)\text{ },$ (4) where$g$ is the determinant of the covariance matrix of the distribution$P$ in the space of columnar firings. This expression for$RT$ can be approximately rewritten as
$RT\text{≈}K\int \text{\hspace{0.17em}}dt\text{\hspace{0.17em}}\int \text{\hspace{0.17em}}dM\text{ }P\text{ }\text{ln}P\text{ },$

(5)

where$K$ is a constant when the Lagrangian is approximately constant over the time scales observed. Since the peaks of the most likely$M$ states of$P$ are to a very good approximation well-separated Gaussian peaks (Ingber, 1984), these states by be treated as independent entities under the integral. This last expression is essentially the “information” content weighted by the time during which processing of information is observed.

The calculation of the heights of peaks corresponding to most likely states includes the combinatoric factors of their possible columnar manifestations as well as the dynamics of synaptic and columnar interactions. In the approximation that we only consider the combinatorics of items of STM as contributing to most likely states measured by$P$ , i.e., that$P$ measures the frequency of occurrences of all possible combinations of these items, we obtain Hick’s Law, the observed linear relationship of RT versus STM information storage, first discussed by AJ in Chapter 8. For example, when the bits of information are measured by the probability$P$ being the frequency of accessing a given number of items in STM, the bits of information in 2, 4 and 8 states are given as approximately multiples of$\text{ln}2$ of items, i.e.,$\text{ln}2$ ,$2\text{ln}2$ and$3\text{ln}2$ , resp. (The limit of taking the logarithm of all combinations of independent items yields a constant times the sum over${p}_{i}\text{ln}{p}_{i}$ , where${p}_{i}$ is the frequency of occurrence of item$i$

## 4. Conclusion

The book written by AJ provides motivation to explore a more fundamental basis of the$g$ factor. I have examined this work in the narrow focus of some specific elements of SMNI, previously used to develop a theory of STM and a model of EEG.

I have focussed on how bottom-up SMNI models can be developed into eigenfunction expansions of probability distributions appropriate to describe STM. This permits RT to be calculated as an expectation value over the STM probability distribution of stored states, and in the good approximation of such states being represented by well separated Gaussian peaks, this yield the observed linear relationship of RT versus STM information storage.

This SMNI STM approach also suggests several other studies that can be performed in the context of examining an underlying basis for the$g$ factor.

## REFERENCES

Graham, R. (1977) Covariant formulation of non-equilibrium statistical thermodynamics. Z. Physik B26:397-405.

Ingber, L. (1981) Towards a unified brain theory. J. Social Biol. Struct. 4:211-224.

Ingber, L. (1982) Statistical mechanics of neocortical interactions. I. Basic formulation. Physica D 5:83-107. [URL http://www.ingber.com/smni82_basic.ps.gz]

Ingber, L. (1983) Statistical mechanics of neocortical interactions. Dynamics of synaptic modification. Phys. Rev. A 28:395-416. [URL http://www.ingber.com/smni83_dynamics.ps.gz]

Ingber, L. (1984) Statistical mechanics of neocortical interactions. Derivation of short-term-memory capacity. Phys. Rev. A 29:3346-3358. [URL http://www.ingber.com/smni84_stm.ps.gz]

Ingber, L. (1985a) Statistical mechanics of neocortical interactions. EEG dispersion relations. IEEE Trans. Biomed. Eng. 32:91-94. [URL http://www.ingber.com/smni85_eeg.ps.gz]

Ingber, L. (1985b) Statistical mechanics of neocortical interactions: Stability and duration of the 7+−2 rule of short-term-memory capacity. Phys. Rev. A 31:1183-1186. [URL http://www.ingber.com/smni85_stm.ps.gz]

Ingber, L. (1986) Statistical mechanics of neocortical interactions. Bull. Am. Phys. Soc. 31:868.

Ingber, L. (1991) Statistical mechanics of neocortical interactions: A scaling paradigm applied to electroencephalography. Phys. Rev. A 44:4017-4060. [URL http://www.ingber.com/smni91_eeg.ps.gz]

Ingber, L. (1992) Generic mesoscopic neural networks based on statistical mechanics of neocortical interactions. Phys. Rev. A 45:R2183-R2186. [URL http://www.ingber.com/smni92_mnn.ps.gz]

Ingber, L. (1994) Statistical mechanics of neocortical interactions: Path-integral evolution of short-term memory. Phys. Rev. E 49:4652-4664. [URL http://www.ingber.com/smni94_stm.ps.gz]

Ingber, L. (1995a) Statistical mechanics of multiple scales of neocortical interactions, In: Neocortical Dynamics and Human EEG Rhythms, ed. P.L. Nunez. Oxford University Press, 628-681. [ISBN 0-19-505728-7. URL http://www.ingber.com/smni95_scales.ps.gz]

Ingber, L. (1995b) Statistical mechanics of neocortical interactions: Constraints on 40 Hz models of short-term memory. Phys. Rev. E 52:4561-4563. [URL http://www.ingber.com/smni95_stm40hz.ps.gz]

Ingber, L. (1996a) Nonlinear nonequilibrium nonquantum nonchaotic statistical mechanics of neocortical interactions. Behavioral and Brain Sci. 19:300-301. [Invited commentary on Dynamics of the brain at global and microscopic scales: Neural networks and the EEG, by J.J. Wright and D.T.J. Liley. URL http://www.ingber.com/smni96_nonlinear.ps.gz]

Ingber, L. (1996b) Statistical mechanics of neocortical interactions: Multiple scales of EEG, In: Frontier Science in EEG: Continuous Waveform Analysis (Electroencephal. clin. Neurophysiol. Suppl. 45), ed. R.M. Dasheiff & D.J. Vincent. Elsevier, 79-112. [Invited talk to Frontier Science in EEG Symposium, New Orleans, 9 Oct 1993. ISBN 0-444-82429-4. URL http://www.ingber.com/smni96_eeg.ps.gz]

Ingber, L. (1997) Statistical mechanics of neocortical interactions: Applications of canonical momenta indicators to electroencephalography. Phys. Rev. E 55:4578-4593. [URL http://www.ingber.com/smni97_cmi.ps.gz]

Ingber, L. (1998) Statistical mechanics of neocortical interactions: Training and testing canonical momenta indicators of EEG. Mathl. Computer Modelling 27:33-64. [URL http://www.ingber.com/smni98_cmi_test.ps.gz]

Ingber, L. (2000) Statistical mechanics of neocortical interactions: EEG eigenfunctions of short-term memory. Behavioral and Brain Sci. (to be published). [Invited commentary on Toward a Quantitative Description of Large-Scale Neo-Cortical Dynamic Function and EEG, by P.L. Nunez. URL http://www.ingber.com/smni00_eeg_stm.ps.gz]

Ingber, L. & Nunez, P.L. (1990) Multiple scales of statistical physics of neocortex: Application to electroencephalography. Mathl. Comput. Modelling 13:83-95.

Ingber, L. & Nunez, P.L. (1995) Statistical mechanics of neocortical interactions: High resolution path-integral calculation of short-term memory. Phys. Rev. E 51:5074-5083. [URL http://www.ingber.com/smni95_stm.ps.gz]

Langouche, F., Roekaerts, D. & Tirapegui, E. (1982) Functional Integration and Semiclassical Expansions. Reidel, Dordrecht, The Netherlands.

Miller, G.A. (1956) The magical number seven, plus or minus two. Psychol. Rev. 63:81-97.

Mountcastle, V.B., Andersen, R.A. & Motter, B.C. (1981) The influence of attentive fixation upon the excitability of the light-sensitive neurons of the posterior parietal cortex. J. Neurosci. 1:1218-1235.

Murdock, B.B., Jr. (1983) A distributed memory model for serial-order information. Psychol. Rev. 90:316-338.

Nunez, P.L. (1981) Electric Fields of the Brain: The Neurophysics of EEG. Oxford University Press, London.

Nunez, P.L. (1989) Towards a physics of neocortex, Vol. 2, In: Advanced Methods of Physiological System Modeling, ed. V.Z. Marmarelis. Plenum, 241-259.

Nunez, P.L. (1995) Neocortical Dynamics and Human EEG Rhythms. Oxford University Press, New York, NY.

Nunez, P.L. & Srinivasan, R. (1993) Implications of recording strategy for estimates of neocortical dynamics with electroencephalography. Chaos 3:257-266.

Risken, H. (1989) The Fokker-Planck Equation: Methods of Solution and Applications. Springer-Verlag, Berlin.

Zhang, G. & Simon, H.A. (1985) STM capacity for Chinese words and idioms: Chunking and acoustical loop hypotheses. Memory & Cognition 13:193-201.


text:
Resonance questions

1. Dec 1, 2012

Erbil

1. The problem statement, all variables and given/known data

1) The equation of the particle on one dimension given by;

d^2y/dt^2 + 2 dy/dt + 6y = 10sinωt

a) Find the displacement as a function of time.
b) find T= ? A=? (period,amplitude)

2) Show that the amplitude of the vibration damping halved on time 1,39/γ.
3)On one LC circuit;
C = 100mikroF and resonance frequency is 2MHz.Find the value of coil. (L)

2. Relevant equations

General form = d^2y/dt+γdy/dt+y=F0cosωt
And I don't know can we use this formula but maybe can help;
A=-F0/m /(ω^4+γ^2ω^2)^1/2

d^2θ/dt^2 = -W0^2q

3. The attempt at a solution

I just tried to use the formula for amplitude but there's no mass.And I don't have an idea about 2 and 3.

2. Dec 2, 2012

haruspex

Do you know how to solve the homogeneous equation y'' + ay' + by = 0?

3. Dec 2, 2012

Erbil

y=c1e^r1x+c2er^2x (distinct) if we have two root,
y= c1e^rx+c2xe^2x (repeated) if we have one root,
y= e^θx*(c1cos(Bx)+c2sin(Bx)

4. Dec 2, 2012

Erbil

d^2y/dt^2 + 2 dy/dt + 6y = 10sinωt

I found imaginer roots ;

r1 = (-1-10i)
r2 = (-1+10i)

But matlab says that roots are ;

-1.0000 + 2.2361i
-1.0000 - 2.2361i

So, what? is it a non-lineer homogenous dif eq.?

IF we use the general solution formula ;

y= e^θx*(c1cos(Bx)+c2sin(Bx)

where can we use our roots?

Edit : -1.0000 + 2.2361i
-1.0000 - 2.2361i are roots.I have forgot to take the square root of ∇

Last edited: Dec 2, 2012
5. Dec 2, 2012

Erbil

y'' + 2y' + 6y = 10sinωt

r1=(-1 + 2,236)i
r2=(-1-2,2236)I

Yp = Asinωt + Bcosωt
Y' = ωAcosωt -ωBsinωt
Y'' = -ω^2Asinωt - ω^2Bcosωt

(-ω^2Asinωt-ω^2Bcosωt)+2ωAcosωt-2ωBsinωt+6Asinω+6Bcosωt=10sinωt

-ω^2A-2ωB+6A=10
-ω^2B+2ωA+6B=0

A = 10/(-ω^2)+6b
B=0

Yp=10/(-ω^2)+6bsinωt

y= e^θx*(c1cos(Bx)+c2sin(Bx)+10/(-ω^2)+6bsinωt

Last edited: Dec 2, 2012
6. Dec 2, 2012

haruspex

So can you answer all the questions now?

7. Dec 2, 2012

Erbil

No.Because my expression is so complex :D

8. Dec 2, 2012

haruspex

Did you verify that it satisfies the equation?

9. Dec 2, 2012

Erbil

No? How can I do it? Where can I use roots.

10. Dec 2, 2012

haruspex

Your solution for the roots of the homogeneous equation was correct and leads to
y = Ae(-1+i√5)t+Be(-1-i√5)t
You can rewrite that as
y = e-t(C cos(αt) + D sin(αt)) where α=√5.
Don't confuse that α with the given ω.
Now we just have to find a particular solution for the inhomogeneous equation. Clearly this will be of the form A cos(ωt) + B sin(ωt) (different A and B from before).
you correctly obtained
2A-2ωB+6A=10
2B+2ωA+6B=0
but I don't understand where you went from there. How did you deduce B = 0?
Wrt q 2, what is γ in this context?

11. Dec 2, 2012

Erbil

2A-2ωB+6A=10
2B+2ωA+6B=0 I can't solve it.I had a mistakes.I just figure now.There's no γ in my context.

12. Dec 2, 2012

haruspex

You still can't solve it? ω is a given constant here. It's just a pair of linear simultaneous equations in A and B.
Q2 reads:
2) Show that the amplitude of the vibration damping halved on time 1,39/γ.

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text:
# Software Tools in Haskell: compare

## find the first position where two text streams differ

Posted on 2016-03-01 by nbloomf

This post is literate Haskell; you can load the source into GHCi and play along.

-- compare: find the first position where two text streams differ
module Main where

import System.Exit (exitSuccess, exitFailure)
import System.Environment (getArgs, getProgName)
import System.IO (hPutStrLn, stderr)
import Data.Maybe (maybeToList)
import Data.List (unfoldr)

import Lib.Backslash (bsUnEsc)

The purpose of compare is to detect whether or not two streams of text are byte-for-byte identical. This alone is simple enough, but the job is complicated by the fact that (1) there are a few useful places these text streams might come from and (2) in the (typical) case that the streams are not identical, we want to report the position of the first difference.

The diffList function takes two lists and returns the position of the earliest difference as well as the differing elements (if they exist).

diffList :: (Eq a) => [a] -> [a] -> (Maybe a, Maybe a, Integer)
diffList = comp 1
where
comp _ []     []     = (Nothing, Nothing, 0)
comp k []     (y:_)  = (Nothing, Just y, k)
comp k (x:_)  []     = (Just x, Nothing, k)
comp k (x:xs) (y:ys) = if x == y
then comp (k+1) xs ys
else (Just x, Just y, k)

This isn’t quite what we want, though. The problem is that word “position”. The most useful position information will depend on what kind of text is being compared. For instance, when comparing line text we’d like to report the line and column numbers of the earliest difference, rather than just the character index. The diffLists function does this.

diffLists :: (Eq a) => [[a]] -> [[a]]
-> (Maybe [a], Maybe [a], Integer, Integer)
diffLists = comp 1
where
comp _ []       []       = (Nothing, Nothing, 0, 0)
comp m []       (ys:yss) = (Nothing, Just ys, m, 1)
comp m (xs:xss) []       = (Just xs, Nothing, m, 1)
comp m (xs:xss) (ys:yss) = case diffList xs ys of
(Nothing, Nothing, _) -> comp (m+1) xss yss
(_,_,n) -> (Just xs, Just ys, m, n)

Like we did with echo, we’ll allow the user to specify which kind of position they mean with a --char option (default is line). Now the streams to be compared (of which we need two) can come from one of three places:

1. stdin,
2. a file (one or two), or
3. command line arguments (interpreted like echo).

The main program first reads the arguments and extracts (1) the mode (char or line) of text being compared, (2) the name and contents of the first stream to be compared, and (3) the name and contents of the second stream to be compared. Then we evaluate either diffList or diffLists and report the results.

data Mode = Chars | Lines

main :: IO ()
main = do
args <- getArgs

-- interpret arguments
(mode,(name1,stream1),(name2,stream2)) <- do
let
(flag,rest) = case args of
("--char":xss) -> (Chars,xss)
xss            -> (Lines,xss)

case rest of
("--to":ys) -> do
let
as = bsUnEsc $case flag of Chars -> concat ys Lines -> fromLines ys bs <- getContents return (flag,("args",as),("stdin",bs)) [xs] -> do as <- readFile xs bs <- getContents return (flag,(xs,as),("stdin",bs)) [xs,ys] -> do as <- readFile xs bs <- readFile ys return (flag,(xs,as),(ys,bs)) otherwise -> argError >> exitFailure -- Some helpers let (label1,label2) = padToLongerWith ' ' name1 name2 report label [] = putStrLn$ label ++ ": (empty)"
report label xs = putStrLn $label ++ ": " ++ xs case mode of Chars -> case diffList stream1 stream2 of (Nothing, Nothing, _) -> return () (x, y, t) -> do putStrLn$ "first differ at column " ++ show t
report label1 (maybeToList x)
report label2 (maybeToList y)

Lines -> case diffLists (getLines stream1) (getLines stream2) of
(Nothing, Nothing, _, _) -> return ()
(x, y, m, n) -> do
putStrLn $"first differ at line " ++ show m ++ ", column " ++ show n report label1 (concat$ maybeToList x)
report label2 (concat $maybeToList y) exitSuccess argError :: IO () argError = do reportErrorMsgs [ "usage:" , " compare FILE1 FILE2 -- find first discrepancy between FILE1 and FILE2" , " compare FILE -- find first discrepancy between FILE and stdin" , " compare --to STR ... -- find first discrepancy between STRs and stdin" , "options:" , " --char : compare as (unlined) character streams" ] padToLongerWith :: a -> [a] -> [a] -> ([a], [a]) padToLongerWith _ [] [] = ([],[]) padToLongerWith z [] ys = unzip$ zip (repeat z) ys
padToLongerWith z xs [] = unzip $zip xs (repeat z) padToLongerWith z (x:xs) (y:ys) = let (as,bs) = padToLongerWith z xs ys in (x:as, y:bs) fromLines :: [String] -> String fromLines xs = concat$ zipWith (++) xs (repeat "\n")

compare can be used to implement a very simple testing scheme by comparing the output of some program under development to its “expected” output. One improvement I can think of is to have compare optionally output delimited data, to make it easier to extract this information with other tools.

## Old Stuff

-- split on \n
getLines :: String -> [String]
getLines = unfoldr firstLine
where
firstLine :: String -> Maybe (String, String)
firstLine xs = case break (== '\n') xs of
("","")   -> Nothing
(as,"")   -> Just (as,"")
(as,b:bs) -> Just (as,bs)

-- write list of messages to stderr
reportErrorMsgs :: [String] -> IO ()
reportErrorMsgs errs = do
name <- getProgName
sequence_ $map (hPutStrLn stderr)$ ((name ++ " error"):errs)


text:
## Friday, June 24, 2016 ... /////

### An arrogant centralized EU is no longer sustainable

The English voters' (not so much Scottish voters') decision to leave the European Union has certain implications for the United Kingdom that has preserved its independence, sovereignty, and democracy in this way. I think that even the consequences for the U.K. are being overestimated – I do think that the departure from the EU is a smaller change than e.g. Slovakia's departure from Czechoslovakia because the latter was a real country while the EU is not. The EU began to influence many aspects of the Europeans' lives but it is still deciding about a few percent of the GDP only etc. (and about a small part of non-economic issues, too). So although I often say bad things about the EU, I think it's a smaller deal for the citizens of the U.K. than the dissolution of Czechoslovakia was for us.

Yes, the United Kingdom will liberate itself from some decisions done by Brussels bureaucrats. But in practice, the effect of this change on the life of almost everybody is very small because the bureaucrats and ideologues in London don't differ from their counterparts in Brussels too much. After all, Britain has sent many sons and daughters to the EU headquarters and they were stauncher Eurocrats than many others – such as their Czech counterparts.

Britain is also a key country whose climatological institutions were the template from which the IPCC was created, along with the climate hysteria. Britain is also a home to many multiculturalists. Like Germany, it's largely a welcoming country – one that had no problem to pick an ethnic Pakistani as the mayor of the capital (whether you think it's great or not so great).

My point is that the decisions will be done more locally and more democratically once the United Kingdom leaves the EU. This will improve the feedbacks and the accountability of the politicians and the voters' ability to correct mistakes. But the content of all these decisions won't differ much – and the differences from the EU decisions will fluctuate in "both directions", if you get my point.

### Central banks should intervene, push markets towards pre-Brexit levels

British voters have chosen to exit the European Union, 52-to-48 or so, which is the ethically correct decision. For example, the Klaus Institute praises Britain as a heroic essential country of Europe that decided to challenge the megalomaniac European plans for the third time – Napoleon, Hitler, Juncker ;-) and that created a wonderful opportunity for the Old Continent. However, the apparent costs are so intense that – I admit – I would have voted Bremain if I were a Briton yesterday.

PM David Cameron, the boss of the "Stay" camp, announced resignation later in the morning, saying that he isn't the right captain to steer the ships (British islands) now. Czech right-wing party chairman Prof Fiala says that the resignation of Tusks, Junckers, and Schulzes who have caused the problems would be more appropriate than Cameron's. Meanwhile, the world markets have kickstarted an absolute hysteria. This reaction could have been expected – we saw a small demo of that hysteria exactly 2 weeks earlier when polls indicated that the Leave side was ahead.

Within hours, the British pound lost some 8% on the dollar from $1.50 below$1.37 – low levels of the pound last seen in the 1980s. And the pound has seen the threshold \$1.32 for a while, too. The stock markets are typically losing up to 10%, too. I am convinced that this hysteria is absolutely insanely unjustifiable. It doesn't reflect any underlying reality. And if economic problems begin, they will be consequences of the irrational hysteria itself, not the underlying event – Brexit – that is claimed to "justify" the havoc.

Some decisions will be gradually moved from Brussels to London but there's no reason to expect that the new London decisions will be worse or that some important processes will completely stop working.

## Thursday, June 23, 2016 ... /////

### Leonard Susskind vs Donald Trump

A co-father of string theory and lots of other creative ideas in physics and my once co-author Lenny Susskind (he's been surely more important for me than the very modest paper indicates) is the current director of physics at Stanford and he wrote a "letter on the lunatic" which he agreed to turn into an open letter. Here it is:

Letter to My Friends, by Leonard Susskind

I’m watching this thing that’s happening with disbelief, dismay, and disgust. There is a lunatic loose—I’m sure we all agree about that—but I keep hearing people say that they can’t vote for Hillary. I heard it at my daughter’s birthday party Sunday. Boy oh boy, will these people be sorry if the lunatic gets his way. Personally I do not find it an excuse that “I live in California, which will go Democrat whatever I do.”

(C) LM

I strongly believe in all things Bernie, but Hillary is not the Anti-Bernie. There is much less difference between Clinton and Sanders than the distortions of the nominating process might lead people to think. She’s for health care, he’s for health care; he’s for increased minimum wage, she’s for increased minimum wage; she’s for immigrant rights, he’s for immigrant rights; and on and on it goes.

The lunatic may be just that—a lunatic—but he is also a master of smear and innuendo. He is a gigantic liar, and he knows that if you keep saying something over and over, it sticks in people’s minds. It’s called the Big Lie, and it works. Say it enough and it sows confusion and distrust, not only among the know-nothings, but even among those who know better.

The lunatic and his supporters are exceedingly dangerous. Tell your friends: don’t be fooled. The only thing between us and the lunatic is Hillary. Get off your ass and vote in Nov.

Leonard Susskind
Director, Stanford Institute for Theoretical Physics,
Stanford University
It's often being said that left-wing ideologies are unavoidably totalitarian in character and every leftist is a Stalin to the extent to which he is allowed to act as one. One's firm fist – either literally or metaphorically – is the only thing that protects tens of millions of lives from a leftist. It's hard to disagree when you read this Susskind's rant.

## Wednesday, June 22, 2016 ... /////

### Negative rumors haven't passed the TRF threshold

...yet?...

Several blogs and Twitter accounts have worked hard to distribute the opinion that the 2015 excess of diphoton events resembling a new $750\GeV$ particle at the LHC wasn't repeated in the 2016 data. No details are given but it is implicitly assumed that this result was shared with the members of ATLAS at a meeting on June 16 at 1pm and those of CMS on June 20 at 5pm.

In recent 5 years, my sources have informed me about all similar news rather quickly and all such "rumors about imminent announcements" you could have read here were always accurate. And I became confident whenever I had at least 2 sources that looked "probably more than 50% independent of one another".

Well, let me say that the number of such sources that are telling me about the disappearance of the cernette is zero as of today. It doesn't mean that those negative reports must be unsubstantiated or even that the particle exists – it is totally plausible that it doesn't exist – but there is a reason to think that the reports are unsubstantiated. The channels that I am seeing seem untrustworthy from my viewpoint.

### A fixed numerical value of $\hbar$ got a bit closer

The Parisian kilogram prototype should move to a museum in 2018

Yesterday, Phys.org published an interesting news report

Important milestone reached on road to a redefined kilogram
that explains some experiment that helps to realize my 2012 call to fix the numerical value of Planck's constant.

The experiment is described in "AIP Review of Scientific Instruments" article
Invited Article: A precise instrument to determine the Planck constant, and the future kilogram

## Tuesday, June 21, 2016 ... /////

### Václav Klaus' 75th birthday

On Sunday, I was honored to attend the magnificent birthday party of Václav Klaus, the second president of Czechia, which took place at the Štvanice [=Hunt or Exhaustive Effort] Island on the Moldau River in Prague. The island is named "Hunts" after dog hunts at animals (bears, bulls, deer, cows...) that have been organized on that island up to 1816 or so – this activity has been defunct for 200 years in this year. The ban of this entertainment was penned by Francis I of Austria in 1802 and after a delay, the island switched to more peaceful sports.

Lots of European politicians have sent him birthday wishes remotely (the video above was posted by AfD and is AfD+FPÖ-centered but if you're patient, Marine Le Pen sings) and lots of famous Czech politicians, economists, artists, and singers have attended. The party was located [bird's eye] in the real estate of the First Bohemian Lawn Tennis Club (founded 1893) which has owned it since 1901 but the current modern buildings were only opened in 1986.

## Monday, June 20, 2016 ... /////

### Formal string theory is physics, not mathematics

I was sent a book on string theory by Joseph Conlon and I pretty much hate it. However, it's the concise, frank comments such as his remark at 4gravitons that make it really transparent why I couldn't endorse almost anything that this Gentleman says.

I can’t agree on the sociology. Most of what goes under the name of ‘formal string theory’ (including the majority of what goes under the name of QFT) is far closer in spirit and motivation to what goes on in mathematics departments than in physics departments. While people working here like to call themselves ‘physicists’, in reality what is done has very little in common with what goes on with the rest of the physics department.
What? If you know the amusing quiz "Did Al Gore or Unabomber say it?", these sentences could be similarly used in the quiz "Did Conlon or Sm*lin say it?".

## Sunday, June 19, 2016 ... /////

### Ambulance chasing is a justifiable strategy to search for the truth

As Ben Allanach, a self-described occasional ambulance chaser, described in his 2014 TRF guest blog, ambulance chasers were originally lawyers with fast cars who were (or are) trying to catch an ambulance (or visit a disaster site) because the sick and injured people in them, potential clients who may have a pretty good reason to sue someone and win the lawsuit. For certain reasons, this practice is illegal in the U.S. and Australia.

Analogously, in particle physics, ambulance chasers are people who write many papers about a topic that is hot, especially one ignited by an excess in the experimental data. This activity is thankfully legal.

The phrase "ambulance chasing" is often used pejoratively. It's partly because the "ambulance chasers" may justifiably look a bit immoral and egotistically ambitious. However, most of the time, it is because the accusers are jealous and lazy losers. Needless to say, it often turns out that there are no patients capable of suing in the ambulance which the critics of ambulance chasing view as a vindication. However, this vindication is not a rule.

The probability to find clients is higher in the ambulances. It's similar as the reason why it's a better investment of money to make Arabs strip at the airport than to ask old white grandmothers to do the same – whether or not some politically correct ideologues want to deny this obvious point.

Is it sensible that we see examples of ambulance chasing such as the 400 or so papers about the $750\GeV$ cernette diphoton resonance?

It just happens that in recent 2 days, there were two places in the physics blogosphere that discussed a similar topic:

An exchange between 4gravitons and Giotis

Game of Thrones: 750 GeV edition (Resonaances)
It seems rather clear that much like your humble correspondent, the first page is much more sympathetic to the ambulance chasing episodes than the latter one.

## Saturday, June 18, 2016 ... /////

### Subdivisions of string theory are completely misunderstood by critics

Tetragraviton wrote an insightful blog post

Most of String Theory Is Not String Pheno
where he tries to clarify some brutal misconceptions believed by Backreaction – as well as most laymen who read similar "sources" – about "what various string theorists actually do". He points out that Hossenfelder pretends to be a hero fighting against a powerful community, the string theory community, but in reality, she is only waging jihad against a small minority of the string community that is actually less numerous than groups such as the "loop quantum gravity fans" and others.

I completely agree with his main point.

This is the key pie chart that Tetragraviton has created. The string theory research has some vaguely defined parts. And because Hossenfelder considered "the research of less understood aspects of quantum field theory using string theory ideas" to be OK or a success, and this branch is actually a majority of the research – e.g. according to the pie chart that categorizes talks at the Strings 2015 annual conference, Hossenfelder is actually trying to fight against string cosmology and string phenomenology only, something that is researched just by more than a hundred of people.

Tetragraviton believes and I do believe that these subfields of string theory are actually understudied Cinderellas. They should be much larger than they are!

## Friday, June 17, 2016 ... /////

### Universe may arise from nothing

Nothing means no spacetime and no information but it cannot mean no mathematics or no laws of physics

Two weeks ago, Inspiring Philosophy posted a YouTube video claiming "A Universe From Nothing, Therefore God Exists!"

It starts with a bizarre quote of Lee Smolin who said that the information is important – one could have achieved the same thing by quoting people like John Wheeler, you don't need to spend one of the most glorious crackpots in the present world. Then it criticizes Lawrence Krauss and sort of endorses William Lane Craig, an Evangelical ideologue.

## Thursday, June 16, 2016 ... /////

### Most scientific discoveries don't produce a technological gap

Various websites criticizing modern physics attract all sorts of individuals who really think that people shouldn't do science – in the sense of finding out how things work. A commenter at Backreaction named "akidbelle" believes that some amazing constraints should be imposed:

In my opinion, a successful theory leads to a technological gap. In this way, the sorcerer who could make fire was the scientist of the time - whatever the fairy tales he used to explain his doing. This is not a problem until a class of sorcerers emerges working not for the fire, but for the fairy-tales explanation that support their class.

What I learn from your list is that super-symmetry is not mentioned to lead to a technological gap (- in your list). What about string theory? [...]

Now if scientists ask the public to please give them money so they can write papers, make congresses, careers, receive prizes, and make experiments about topics they like and in which they have no hope to lead to a technological gap any time in the next 100 years, would that be true?... and what would happen?
In other words, akidbelle thinks that pure science should be completely eradicated while only applied science should be pursued by someone. Wow.

### Like Al Gore, the Orlando shooter was an anti-Big-Oil TV actor

Does it make sense to think about the characteristics of killers such as Omar Mateen? I am not sure. He may look like a generic Muslim or a generic Afghani American and all his idiosyncrasies could be accidents that don't teach us anything.

He may have been gay or partly gay – but that doesn't mean anything, either. Once we start to say that "straight according to the normal evidence" men are gay, then every man may be a gay. Or a gay "in some sense" or "to some extent". So we don't learn anything at all from such vague information about him. Quite generally, I think that some "defenders of gays" are extremely hypocritical. On one hand, they say that gays are great and should be proud; on the other hand, they demonstrably use the accusation "he is also gay" as the ultimate insult.

I found the finding of NY Daily News much more interesting. He has worked for G4S, the world's largest security company, since 2007 – for nine years. His pointing out that he worked for Al Qaeda or an investigation by the FBI clearly weren't a problem for his career of a security guard. (See also his more recent threats on FB.)

But the video I embedded is even more interesting.

## Wednesday, June 15, 2016 ... /////

### LIGO has announced the December 26th gravitational wave

Here, you could have learned the details in advance and watch the event live

Tonight, at 19:15-20:15 Prague Summer Time (or, locally, 10:15-11:15 am PDT), you could follow the webcast here (video) of the new findings by LIGO. Because the most recent detailed rumors I was spreading were absolutely accurate, it may be a good idea for the dear readers to trust the exciting report below (update: the data were accurate again). The paper was released while they were speaking, PDF.

Nine concentric curves indicate the 10%-90% confidence areas.

Ladies and Gentlemen, one additional gravitational wave has been discovered at the 5-sigma confidence level in the first observing run (O1) that ended on January 12th, 2016.

### Research into totally settled questions is meaningless

Yesterday, I mentioned the obsession of Marxist "critics of science" with the politicization of everything in science and with assorted sociological conspiracy theories that have nothing to do with proper scientific research and that no serious scientists spend any substantial amount of time with.

But that doesn't mean that the likes of Ms Hossenfelder understand some other basic principles of the scientific method. Another totally elementary issue she clearly misunderstands is the following:

Scientific research may only be valuable if it investigates questions that are not completely settled. A complete certainty about the answers makes any research meaningless and worthless.
Climate skeptics often like to point out that some climate alarmists love to say that "everything is settled" in their field but they still want to be getting funds for the research. The criticism of this inconsistency isn't just some malicious harassment. It's absolutely fundamental that in science, you can't have both. Either you're certain about something, or it makes sense to do further research on it.

For example, people are reasonably certain that the Earth is round ;-) so not too many people are receiving scientific grants to cover their journey around the world (although, I am sure, some of them do have sponsors like that – but I would simply never call it science in 2016). If and when we know what the outcome, why would someone pay for such a journey as if it were science? The knowledge won't evolve at all but some evolution of knowledge is really the point of research.

A libel lawsuit should be launched and starve the mayor

London's new mayor Sadiq Khan is said to be not so much a Pakistani Muslim but rather a social democrat. However, a new policy – thanks to Tony – raises some doubts about his true passions.

He already banned bikini ads on the London subway and he's in the process of banning them at all public spaces in London. Maybe he will fight to ban them in the private spaces, too. A not so new coalition of the Islamic terrorists and fat feminists supports him.

## Tuesday, June 14, 2016 ... /////

### One can't understand physics through sociology

Experimental news: Listen to a new report from LIGO tomorrow (on Wednesday) at 19:15 Prague Summer Time; new detected gravitational wave GW151226 will be announced, with a 10 times higher frequency than GW150914. Also, in 2016, the LHC has recorded 4/fb, pretty much matching all of 2015, and some articles and LHCnews Twitter indicate that they could have something new about the $750\GeV$ cernette soon, too. Results at $Z\gamma$ and $gg$ were null.
I have written numerous blog posts, e.g. this one in 2015, about this question but the question keeps on returning.

There exists a bunch of arrogant social scientists who believe or pretend to believe that they may reduce the wisdom about the world – including natural sciences – to their cheap ideological clichés about the society and discrimination and similar constructs. They think that when they observe how scientists dress or talk to each other, they may understand everything important about science, much like when they are observing dancing savages in the Pacific Ocean.

Famously, in 1996, Alan Sokal proved [PDF] that this postmodern filth belongs to a [beep] [beep] when he published a totally idiotic crackpot hoax article about quantum gravity that licked the rectums of these individuals, and that's why it was enthusiastically embraced by a would-be prestigious journal published by those hacks, Social Text, despite dozens of cute claims in the paper that the value of pi depends on the oppression of women and similar "gems".