text:
Pioneers

20/05/2009

Jeffrey Mandula is a well-knwon theoretical physicist whose main result, Coleman-Mandula theorem, opened the road to the discovery of supersymmetry. But Mandula is also known for his pioneering works on lattice QCD. Looking back to old papers on the question of the Yang-Mills propagators, I have found two beautiful papers by Mandula and Ogilvie (see here and here) published in the eighties, where they arrive to the following conclusion

From the behavior of the gluon propagator reported here, it appears that in pure Yang-Mills theory, a dynamical Higgs phenomenon occurs. Our best estimate of the effective gluon mass, as determined at large distances, is about 600 MeV, with finite size effects, possible scaling violations, and statistical uncertainties of at least $\pm 25\%$. In analogy with the concept of a constituent quark mass, it may be useful to think of the mass in the gluon propagator as a constituent gluon mass. The massiveness of the gluon may be connected to the apparent suppression of many-gluon intermediate states in $J/\psi$ decay, and the relative absence of the mixing between the lowest quark model states and those with gluonic excitations.

They used small lattices due to the computer limitations at that time and ideas about infrared behavior of Yang-Mills theory were just beginning to flourish. But, with our hindsight, we should emphasize the deep intuition that these authors put forward when such analysis were just starting. Besides, $\sigma$ resonance was not yet seen and their estimate of the gluon mass appears really good.

As you may know, after these works, things took a different turn and for a long time since now we have been coping with a different scenario from that devised by Mandula and Ogilvie that took the scenes and not yet left them. This scenario appears today to be in a serious difficulty against lattice computations but people do not generally agree about what the right view should be, making painfully slow truth achievement .

format: plain


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coshf Function

Calculates the hyperbolic cosine function of a single precision floating-point value.

Include

<math.h>

Prototype

float coshf(float x);

Argument

 x value for which to return the hyperbolic cosine

Return Value

Returns the hyperbolic cosine of x. It returns infinity if x is ±∞ .

Remarks

If the magnitude of x is too large, a range error occurs, and errno will be set to ERANGE.

Example

See the notes at the beginning of this chapter or section for information on using printf() or scanf() (and other functions reading and writing the stdin or stdout streams) in the example code.

#include <math.h>
#include <stdio.h>
#include <errno.h>

int main(void)
{
float x, y;

errno = 0;
x = -1.0F;
y = coshf (x);
if (errno)
perror("Error");
printf("The hyperbolic cosine of %f is %f\n", x, y);

errno = 0;
x = 0.0F;
y = coshf (x);
if (errno)
perror("Error");
printf("The hyperbolic cosine of %f is %f\n", x, y);

errno = 0;
x = 720.0F;
y = coshf (x);
if (errno)
perror("Error");
printf("The hyperbolic cosine of %f is %f\n", x, y);
}

Example Output

The hyperbolic cosine of -1.000000 is 1.543081
The hyperbolic cosine of 0.000000 is 1.000000
Error: range error
The hyperbolic cosine of 720.000000 is inf


text:
# Rationalize the denominator and express in simplest form?

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text:
# Henry's Law

## What is Henry’s Law?

Henry law explains the solubility of a gas in liquid solution by partial pressure and mole fraction of the gas in liquid.

Henry’s Law states that “the partial pressure applied by any gas on a liquid surface is directly proportional to its mole fraction present in liquid solvent.”

### The Mathematical Formula of Henry’s Law is as Follows –

P ∝  X

Where P = partial pressure applied by the gas on liquid in the solution

X = Mole fraction of gas in liquid

On Removing the Proportionality –

P = kH.X

Where kH is called Henry’s law constant.

### What is Mole Fraction?

Mole fraction can be defined as a unit of concentration which is equal to the number of moles of a solute divided by the total number of moles of a solution. It is also called amount fraction or molar fraction. Thus, mole fraction of a gas (solute) in a solution of gas in liquid can be written as follows –

Mole fraction of Gas in Liquid (X) = [Moles of gas (solute)] / [Total number of moles (solution)]

As mole fraction is a ratio, it is a unitless expression.

### When Pressure is Constant

When pressure remains constant, according to henry’s law henry constant will be inversely proportional to mole fraction of the gas. It can be represented as follows –

P ∝ X (Henry’s Law)

P = kHX

If P is constant, from above equation can be written as –

X ∝ $\frac{1}{k_{H}}$

It means if the value of Henry's law constant decreases, the value of mole fraction of gas in liquid increases. Mole fraction of the gas in liquid can be taken as solubility. Thus, as henry’s law constant decreases, solubility of the solute in solution increases.

### Relation of Henry’s Law Constant with Temperature

As we know, increasing the temperature solubility of the gas in liquid decreases. Thus, we can write a relation between temperature and solubility for a gas in liquid solution as follows –

T ∝ $\frac{1}{Solubility}$  - - - - - - (1)

According to henry’s law, we have explained above that if pressure is constant, as the value of henry’s law constant increases, solubility of gas in liquid decreases. It can also be expressed as follow –

$k_{H}$ ∝ $\frac{1}{Solubility}$ - - - - - - (2)

From equation (1) and (2), we can write –

T ∝ kH

### Factors affecting Henry’s Law Constant

Following Factors Affect the Henry’s Law of Constant of a Gas –

• Nature of the gas. This is the reason different gases have different henry’s law constants in the solvent.

• Nature of the solvent

• Temperature and Pressure of the system. This is the reason kH value is given differently for a gas at different temperatures.

### Graph Between Solubility and Pressure (for Gas in Liquid Solution) According to Henry’s Law

Mathematical Expression of Henry’s Law can be Written as Follows –

P = kH.X _ _ _ _ _(3)

Where,

P = Partial pressure of the gas

X= mole fraction of gas in liquid

kH = Henry’s law constant

Equation (3) is the same as Y = MX which is a straight-line equation. So, graph can be drawn as –

### Applications of Henry’s Law

• Production of carbonated beverages is based on Henry’s law.

• Hypoxia (concentration of oxygen is low in blood and tissues) can be explained by Henry’s law.

• It is applied in deep sea diving as well.

• We can understand by Henry’s law that aquatic life survives better in cold water.

### Limitations of Henry’s law

• It is applicable when the system is in equilibrium.

• It is applicable for those gases only which do not react with water(solvent).

• Gas shouldn’t cause any chemical change in the solution.

• Henry’s law is appropriate only when pressure is not high, temperature is not too low and gas is extremely soluble.

This was a brief of Henry’s Law, if you want to get solved numerically based on Henry's Law with detailed explanation then register yourself on Vedantu or download Vedantu learning app for class 6-10, IITJEE and NEET.


text:
# r^2-50r+200=0

## Simple and best practice solution for r^2-50r+200=0 equation. Check how easy it is, and learn it for the future. Our solution is simple, and easy to understand, so dont hesitate to use it as a solution of your homework.

If it's not what You are looking for type in the equation solver your own equation and let us solve it.

## Solution for r^2-50r+200=0 equation:

r^2-50r+200=0
a = 1; b = -50; c = +200;Δ = b2-4acΔ = -502-4·1·200Δ = 1700The delta value is higher than zero, so the equation has two solutionsWe use following formulas to calculate our solutions:$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$The end solution:
$\sqrt{\Delta}=\sqrt{1700}=\sqrt{100*17}=\sqrt{100}*\sqrt{17}=10\sqrt{17}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-10\sqrt{17}}{2*1}=\frac{50-10\sqrt{17}}{2}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+10\sqrt{17}}{2*1}=\frac{50+10\sqrt{17}}{2}$

`


text:
# [SOLVED]Difference between <= Relational operator and <= Non blocking assignment

Status
Not open for further replies.

#### debasish_deka

##### Newbie level 3
Hi All,
I am very new to verilog and got confused between the Relational operator <= (which is less than equal to) and the Non-blocking assignment operator <=.:bang:
I want to know how does the verilog compiler know that the variables on the either side of this operator means assignment operation not comparison or the vice versa.

#### TrickyDicky

It will depend on context. A simple

A <=b;

Is an assignment. But

If a <= b

Will be less than or equall

#### debasish_deka

##### Newbie level 3
Thanks Tricky Dicky,
Then how'll this code behave
Code:
if(a<=b)
d<=a;
Actually I am from microcontroller programming background. To me it seems like (a<=b) evaluates to TRUE always and finally the value of b goes to d.
Am I right?

#### rberek

##### Full Member level 6
No, you are not correct.

All that bit of code says is that "if a is greater than or equal to b, assign a to d." The value of b is not changed by the comparison, and nor would it be in the microcontroller world. There is also nothing in that code to indicate that a<=b would always evaluate to TRUE. You have given no values for any of a, b or d so no assumption can be made as to the result of that comparison.

r.b.

Last edited:

##### Super Moderator
Staff member
All that bit of code says is that "if a is greater than or equal to b, assign a to d." The value of b is not changed by the comparison, and nor would it be in the microcontroller world. There is also nothing in that code to indicate that a<=b would always evaluate to TRUE. You have given no values for any of a, b or d so no assumption can be made as to the result of that comparison.
rberek, you've missed the point the OP was making, the OP thinks the if (a<=b) is an assignment a gets assigned b and the if is checking the assignment operation which is always true as b did get assigned to a.

Code:
if(a<=b)
d<=a;
To me it seems like (a<=b) evaluates to TRUE always and finally the value of b goes to d.
Am I right?
Don't know how you would think this would be true for C, C++, Verilog, etc, Perl perhaps but certainly not Verilog or C.

To reiterate what Tricky posted:
It depends on the context.

a <= b; // assignment (notice it's on a line by itself with no "if" in front of it and it ends with a ";"), stick the value of b into a.

If (a <= b) // comparison of a less than or equal to b when true execute the next statement

assign c = (a <= b) ? d : e; // comparison of a less than or equal to b being true assigns c with d

debasish_deka said:
Actually I am from microcontroller programming background.
Then don't use for loops, while loops, tasks, and functions until you understand how to write simple Verilog RTL that describes hardware using standard coding templates. This will save you a lot of grief and hopefully keep you from making the same mistakes so many others with a software background make when they try to learn what they think is the Verilog "software" language.

Regards

Last edited:

#### rberek

##### Full Member level 6
To be honest I wasn't sure how/why the OP made those conclusions but I felt it made the best use of my time explaining the correct interpretation rather than fall down a rathole trying to figure out the incorrect one.

Also I misinterpreted the following sentence:

and finally the value of b goes to d

I now see they meant to say that d gets the value of b rather than the reverse.

r.b.

Last edited:

##### Super Moderator
Staff member
To be honest I wasn't sure how/why the OP made those conclusions
You haven't used Perl much ;-)

#### rberek

##### Full Member level 6
I've used it a fair bit, I must just never have been confused by that. I have, however, been confused in lots of other ways!

r.b.

#### dave_59

It's very simple: the compiler uses the BNF to parse text token by token and recognizes what are called productions . A good example of this is the text

Code:
A <= B <= C

If you were to send just this text through a Verilog compiler, you would get the following error:
** Error: abc.v(1): near "A": syntax error, unexpected IDENTIFIER
That's because at the top level of a Verilog source file, there are only three productions available
Code:
source_text ::= { description }
description ::=
module_declaration
| udp_declaration
| config_declaration
which basically means the first word in a Verilog source descriptions can only be one of module, primitive, or config. The compiler could not match any of the productions with the token "A", so it throws a syntax error.
Now lets send the following code to the compiler:
Code:
module test;
A <= B <= C
you would get the following error
** Error: abc.v(4): near "<=": syntax error, unexpected <=, expecting IDENTIFIER
Note the error is now on the "<=" token and not the "A". That's because inside a module_declaration, you are allowed any number of module_item productions, one of which could have been a module_instantiation like
Code:
A inst_name();
But there no module_item production that matches an identifier followed by '<='. So you get an error.

This process of parsing all your source text in productions keeps going until there is is no ambiguity left in what a token represents. Skipping ahead to a block of code that looks like
Code:
begin
A <= B <= C;
end
The compiler is parsing a set of procedural statements, or statement_item productions. One of the production choices is
Code:
nonblocking_assignment ::=
variable_lvalue <= [ delay_or_event_control ] expression
There is no expression production in a statement_itemso the first '<=' can only be matched as a nonblocking assignment construct. When the compiler parses the B <= C part of the statement, the only thing <= could match in an expression would be a less-than-or-equal operator.

Hope this helps.

Points: 2

Points: 2

### debasish_deka

Points: 2

#### mrflibble

Re: Difference between <= Relational operator and <= Non blocking assignment

Bonus points for having the patience to type what I thought. After 1 paragraph of typing I went "ah screw it, people just have to read the fine LRM" and pressed delete.

- - - Updated - - -

And speaking of reading the fine LRM ... just google "verilog 2001 lrm" to find the standard for verilog 2001. And you'll run into the SystemVerilog documentation as well that way. Or grab it here:

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Not open for further replies.


text:
## Jean-Paul CIPRIA

————— PHYSICS – SPACE – ALGORITHMICS ——-

## Algorithmics 03 – Signal by Fourier Transforms- FFT – 3

Written By: Jean-Paul Cipria - Mai• 10•17

FFT – Only One Partition – Execution Times Comparison – ©J.P. Cipria 2017.

How do a Fast Fourier Transform by Cooley and Tukey Algorithms ? Why High Potential with a high level QI don’t understand official physics memorization ? The answer is in the question : nobody ask you to … understand ! Then let’s read the original engineers experts ! Come Back to … 1964.

It is a simple demonstration in thesis annexis. Here is a resume. (Not so clear to read for you. We know it)

.

Created :2017-05-10 13:08:46. – Modified : 2018-04-14 19:14:44.

Difficult ! Master Level.

26 views on 10/05/17.
37 : 12/05/17

Experiment in Progress.

# How do evaluate number of FFT Calculations Efficiency ?

## Cooley and Tukey Number of Calculations Evaluation

If we perform a Fourier Transform from the original document [COOLEY-TUKEY-1964] we take all $N$ decomposition terms $A(k)$ then we multiply each $k$ order term by exponential $exp(2.i.\pi.\frac{k.j}{N})$. We get a « frequential » $X(j)$ term.

We changed notation to $X(k)$ time and $F(n)$ frequency signals to match with engineer’s needs and … then we change also sign and recalibrate to $\frac{1}{\pi.N}exp(-2.i.\pi.\frac{k.n}{N})$ for energy conservation !!!

That’s all folks ?

« What’s Up, Doc ? »  ©J.P. Cipria.

Of Course … Not !

Let’s read the original document [COOLEY-TUKEY-1964] : We decompose $A$ signal with $k$ index on any base, for example $r_1$ as well as the $X(j)$ results we decompose it on any base $r_2$ so that we have $N=r1*r2$. One of a trick is using $log_{r_1}$ or $log_{r_2}$ to symplify equations. After many times, more complicated than difficult, we estimate the $r/log(r)$ ratio when $r_1=r_2$. The smallest is it the more efficient for the number of calculations we got.

See one of demonstration [CIPRIA-2017] or the original. The result is :

• 2 ==> 2
• 3 (Let’s read e=2.718) ==> 1.88
• 4 ==> 2
• 5 ==> 2.15

The more efficient base is 3 as integer or e=2.718 in the continuous domain. Then 3 is the closer integer. The more adapted for calculator is 2. If we use QAM (4), old wireless transmission example (« air interface »), we should perform directly in 4 base more than 2 base !

## We traduct C. T . here to avoid some bad interpretation

• $r$ is the calculation base we search for.
• $RealCalculationNumber=N.log(N).\frac{r}{log(r)}$
• $N$ is a constant then $N.log(N)=C^{te}$ is also a constant for $r$ fixed.
• $RealCalculationNumber=C^{te}.\frac{r}{log(r)}$

## Key Resume

• Fast Fourier Transform (FFT).
• Cooley–Tukey FFT Algorithm (FTTCT).
• Discrete Fourier Transform (DFT).

## Let’s try to find the r right base with Matlab

In the following picture [CIPRIA-2017] we search $r$ as a possible base to made calculations. We need to know if 10 base, 16 hexadecimal base or other is the more efficient to tend from $N^2$ calculations to a PROPORTIONAL limit to $N.log_2(N)$.

Cooley Tukey Efficiency – r is the search Base the More Efficient Calculations Rate – ©J.P. Cipria 2017.

### Why is r = 2.718 = e the best efficiency for a calculation base ?

Cooley and Tukey didn’t answer this question but we need to understand to … anticipate. It is the aim of physics and sciences !

OR, very simple ? 😉 We decompose all $X(k)$ on a $e^{-2i\pi.k.n}$ objects when we do a Fourier Transform. Those objects are perpendicular when $k$ change. This decomposition permits to retreive all $F(n)$ possible in the frequencies domain. Then $e^{-2i\pi.k.n}$ objects form a mathematical base with dimension … ? $r=e=2.718$. CQFD.

OR, with other words, if you project $X(k)$ on other base than $2.718$ then the projections are not perpendicular or and then distances increase. CQFD

OR, the derivative function is nul for an extremum :

• $(\frac{r}{log_2(r})^{\prime}=(1-log(r))/log(r)^2 =0$ ==> $r=e=2.718$ CQFD

# Do we Play it with Matlab ?

## Let’s try three different algorithms

Let’s try input signal with two frequencies :

• $X(k) = sin(w1*k/N) + sin(w2*k/N)$

Let’s try Normal Fourier Transform :

• $F(n)=\sum\limits_{k=0}^{N-1} X(k)*exp(-2i\pi\frac{k.n}{N})$

Let’s try Matlab FFT :

• $F(n) =fft(X,N)$

Let’s try FFT with Only One Partition :

We just separate in two blocks all the $N$ $X(k)$ samples. Then we do calculation twice with $N/2$.

• $F(n)=\sum\limits_{k=0}^{N/2-1}Pair(X)+exp(-2i\pi.n/(N)).Impair(X)+\sum\limits_{k=N/2}^{N-1}Pair(X)-exp(-2i\pi.n/(N)).Impair(X)$
• A simple prove is on Wikipedia English. Students can follow the demonstration on the first order or read Cooley and Tukey [COOLEY-TUKEY-1964]. Don’t try French courses you will not understand anything .

## CT Algorithm by One Partition Comparisons

FFT – Only One Partition – Execution Times Comparison – ©J.P. Cipria 2017.

We divide calculation in only two parts. A duration for a Fourier transform lasted 3.22 seconds against 1.83 seconds for the FFT with one partition. Then the gain is 1.8. We remark Matlab FFT had  lasted 0.0012 seconds.

## Double Partition

FFT – Double-Partition – m11 – ©J.P. Cipria 2017.

We divide calculation in only four parts. A duration for a Fourier transform lasted 3.33 seconds against 0.73 seconds for the FFT with two partition. Then the gain is 4.5. We remark Matlab FFT had  lasted 0.0016 seconds.

## Rapidity Comparison ?

Cooley and Tukey runs about two more rapidly than normal Fourier Transform (1.7 to 2 when N increase) when you just divide algorithm in two parts with $N/2$.
CQFD by Measurements.

The Matlab function follows a $\frac{N^2}{log_2(N)}$ and not a $N.log_2(N)$. Then when you evaluate Cooley and Tukey you got $2.N.log_2(N)$ and not $N.log_2(N)$ written on every French and English courses. Why ? You must multiply by 2 because the efficiency coefficient $\frac{2}{log_2(2)}$ is 2 and not 1. (See first paraph).

That’s all , Folks ? Of Course … Not !

## Spectral Repliement ?

FFT – Simple and Double Partition Spectral Repetition – ©J.P. Cipria 2017.

# References

## Courses

### Wikipedia English Items

• Cooley–Tukey FFT algorithm – Wikipedia.

### C Language Programmation

.

Jean-Paul Cipria
26/06/2015

You can follow any responses to this entry through the RSS 2.0 feed. You can skip to the end and leave a response. Pinging is currently not allowed.


text:
Enter the standard deviation of a population and sample of two different sets of information into the calculator. The calculator will evaluate the f statistic, also known as the f value.

## F Statistic Formula

The following equation can be used to calculate the f-value of two sets of data.

f = [ s1212 ] / [ s2222 ]

• Where f is the f statistic (f value)
• S1 is the standard deviation of the sample of population 1
• σ1 is the standard deviation of population 1
• S2 is the standard deviation of the sample of population 2
• σ2 is the standard deviation of population 2

## F Statistic Definition

An f statistic is defined as the ratio between the standard deviations of both the population and samples of two different but connected sets of data.

## F Statistic Example

How to calculate an f statistic

1. First, determine the standard deviations of the populations

Calculate the standard deviations of both populations of data.

2. Next, determine the standard deviations of the samples

Take 1 sample set from each population and calculate their standard deviations.

3. Calculate the F Statistic

Enter the standard deviations from steps 1 and 2 into the equation presented above to calculate the f value.

## FAQ

What is an f statistic?

An f statistic, also known as an f value, is a ratio that compares the standard deviations of a sample and population of two separate but related pieces of data.

What is a standard deviation?

A standard deviation is the average deviation from the mean that a random value can be expected to have.


text:
# Hive Cheat Sheet

## 1. Hive options

Set execution engine

set hive.execution.engine=mr/spark/tez;

Set queuename

set mapreduce.job.queuename=default;

## 2. Hive optimizations

Vectorized execution

hive.vectorized.execution.enabled

https://cwiki.apache.org/confluence/display/Hive/Vectorized+Query+Execution

Map Joins

hive.auto.convert.join;

https://cwiki.apache.org/confluence/display/Hive/Vectorized+Query+Execution

When hive.auto.convert.join is activated, Hive will make a MAPJOIN in case the n-1 tables of the join are smaller or equal to the value of hive.auto.convert.join.noconditionaltask.size. But this paramter should also be lower than the heap size of the HiverServer or HiveCli (depending how you acess Hive). Thus, we need to lower the value of hive.auto.convert.join.noconditionaltask.size to avoid OOM errors.

Note that the ORC compression is not included in the hive.auto.convert.join.noconditionaltask.size. Which means a table of 1GB in ORC is actually 10 times bigger once uncompressed and it should fit into the heap memory.

Conclusion: With hive.auto.convert.join.noconditionaltask.size = 256MB, we may have in memory up to 10x more, i.e 2GB (which should correspond to the heap of the Hiveserver)

## 3. Hive queries

Deduplicate lines

select  <needed fields>
from
select *, row_number() over (partition by id order by tech_timestampchargement desc) as rank
from [database.table]
where rank = 1  // to keep only rhe first occurence

## 4. Hive procedures

Tranfert data between clusters If it’s an external table, you just need to execute a “show create table” from the source cluster and execute it on the new cluster. You just need to copy paste the content of the table folder from a ccuster to the other in the path specified in the create statement.

For internal tables, the process is the same but you may need to execute an “msck repar table” in order to update the tables pointers.


text:
# Thermal expansion of steel pipe

1. Feb 4, 2005

### rwh

The equatorial radius of the earth is about 6370km. Consider a 40,000 km long steel pipe that forms a giant ring that fits snugly around the equator of the earth. Suppose the temp. of the pipe is increases 1 degree C. The pipe gets longer. it is also no longer snug. How high does the pipe stand off the ground?

Assume that D L = L o x 1/100,000 x D T

. I came up with .07 km. The radius of the pipe is actually 6369.42 km. When the temperature of the pipe is increased 1 degree Celsius it will expand .4 km making the pipe 40000.4 km. 40000.4 / 3.14 = 12738.98. 12738.98 / 2 = 6369.49 (radius) 6369.49- 6369.42 is .07km.

Am I right?

2. Feb 4, 2005

### Pseudopod

yes, I believe so

3. Feb 4, 2005

### Gokul43201

Staff Emeritus
Simpler yet ... (with DT = 1)

$$\Delta L = \Delta 2 \pi R = 2 \pi \Delta R = \frac{L_o}{ 100,000} = \frac {2 \pi R}{100,000}$$

Canceling 2pi on both sides :

$$\Delta R = \frac {R}{100,000} = 0.06369 ~km$$

Your number is a little high because of round off error. If your first significant digit is in the second decimal place, you want to calculate with numbers written up to at least 3 decimal places.

4. Feb 4, 2005

Thank you!


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# In a quadrilateral ABCD, it is given that BD = 16 cm.

Question:

In a quadrilateral ABCD, it is given that BD = 16 cm. If AL ⊥ BD and CM ⊥ BD such that AL = 9 cm and CM = 7 cm, then ar(quad. ABCD) = ?

(a) $256 \mathrm{~cm}^{2}$

(b) $128 \mathrm{~cm}^{2}$

(c) $64 \mathrm{~cm}^{2}$

(d) $96 \mathrm{~cm}^{2}$

Solution:

(b) $128 \mathrm{~cm}^{2}$

ar(quad ABCD) = ar (∆ ABD) + ar (∆ DBC)

We have the following:

$\operatorname{ar}(\Delta A B D)=\frac{1}{2} \times$ base $\times$ height $=\frac{1}{2} \times 16 \times 9=72 \mathrm{~cm}^{2}$

$\operatorname{ar}(\Delta D B C)=\frac{1}{2} \times$ base $\times$ height $=\frac{1}{2} \times 16 \times 7=56 \mathrm{~cm}^{2}$

$\therefore \operatorname{ar}($ quad $A B C D)=72+56=128 \mathrm{~cm}^{2}$


text:
# CentOS / RedHat remove unused kernel versions

I notice many servers tend to have many kernels, alot of the time people do not clean these up, this can obviously lead to /boot becoming full, there are a few ways that the unused kernels can be removed, Remember you should be running the latest kernel when possible

The suggested method would be to use package-cleanup which is part of the yum-utils package.

yum install yum-utils

Once yum-utils is installed you can clean the unused kernels with the following command

package-cleanup --oldkernels --count=2

This command would keep 2 kernel versions, you can obviously change this to however many you would prefer to keep.

Another method which I would not suggest is to use something like the following to compare the running kernel against a rpm list and then remove the ones not in use.

rpm -qa | grep kernel | grep -v \$(uname -r) | xargs -i yum remove -y {}


text:
# Math Help - Finite set of integers closed under addition

1. ## Finite set of integers closed under addition

Can any finite set of integers be closed under addition? Prove your answer.

I kind of have an understanding of what this means but don't know how to prove this?

2. Originally Posted by acevipa
Can any finite set of integers be closed under addition? Prove your answer.

I kind of have an understanding of what this means but don't know how to prove this?
{0}

3. Hello, acevipa!

Can any finite set of integers be closed under addition? Prove your answer.

Suppose the set is: . $S \:=\:\{a,\:b,\:c,\:\hdots\:n\}$ . . . in increasing order.

. . $\text{If }n\text{ is positive: }\:n+n\;\notin S$

. . $\text{If }a\text{ is negative: }\:a+a\;\notin S$

The set is not closed under addition.

The only such set is a trivial one: . $\{0\}$

Edit: too slow . . . again !


text:
# How to position the origin of an object next to edges of another object with python

First I import a cone next to a box:

The cone has a good position in the X axis but not in the Y and Z axis.

So I translate it to this position :

Ideally, I want about 1 mm between the edges of the box and the center of the cone. I was wondering how can I translate the cone to that position (which is linked to the box) with a python script ?

• is the origin of the box at its center ? – Chebhou Mar 23 '15 at 14:53
• When I import the cone, both origins of the box and the cone are at the same position (0,0,0). – reflyon Mar 23 '15 at 15:01
• i mean at their geometry center – Chebhou Mar 23 '15 at 15:02
• No, they are not, but after playing a bit with your script I obtain what I want, thanks ! – reflyon Mar 23 '15 at 15:48

import bpy


text:
Category Theory for the Working non-Mathematician 2

Last time I talked about the very basics of Category Theory, objects and morphisms and what exactly a Category consisted of. If nothing else sticks just remember that categories consist things (objects) and ways to go between things (morphisms) where you always have the ability to go from something to itself by doing nothing and you can go from thing to thing to thing via arrows composed together having a common middle object. The next step is to figure out how to go between two different categories. At the moment our view of the world is like a human stuck on the earth. There are places on earth and there are ways that we can go from place to place (routes) and we can compose our traveling methods to get from one place to another and then to another. So a category is much like a planet. However humans are curious. We look up at the stars and we want to venture to other planets. We are also very fragile creatures and we can’t just go to to any planet all willy nilly, we have to go there in a very specific way so that we don’t die. Not only that but the planet we go to has to have similar features to earth, so that again we don’t die. I know how earth looks and so the best way to survive is to correspond this new planet to the one I already know. This very restrictive way of going from one planet to another is similar to the nature of going from one category to another.

Let’s think about what it would mean to go from a category C to a category D. We start out in C, and there is some set of objects. Well D also has objects so the most logical thing to do is to have something in D correspond to something in C. The mathy way to write this is that for any object X in C, there is an object F(X) in D. Simple, elegant, no restrictions. Now, there are also morphisms (ways to go between objects) living in the category C and D. Any morphism in C goes between two objects in C and I’ve already said that the objects in C MUST be associated to some objects in D. The most logical thing to do once again would be to associate a given morphism from X to Y in C to a morphism between F(X) and F(Y) over in the category D. This part is a bit trickier because I want the morphism in C to be associated to the morphism in D in a way that makes sense. If I have a way to go from California to New York and then I go to Earth 2.0 discover California 2.0 and New York 2.0 then I’m going to want the way to go between the originals to correspond to the way to go between the new ones rather than some completely different route.

How is this going to work? First of all we need better notation. We are going to start calling our space travel from Earth to Earth 2.0, a functor. A functor $F:C\rightarrow D$ is a map from the category C to the category D that does the following. For any object X in C, there is an object F(X) in D. For any morphism between objects X,Y in C, $f:X\rightarrow Y$ there is a corresponding morphism $F(f):F(X)\rightarrow F(Y)$ which obey some rules to be explained later. For now just see how this functor is taking objects to CORRESPONDING objects in D, and paths between objects to paths between CORRESPONDING objects in D. What other rules do I need? Well if you will recall from the previous article, a category is not just objects and morphisms. It had some special rules about these things. Remember that for any object X in a category C there has to be at least this one special morphism; the identity morphism $id_X : X\rightarrow X$ which was like taking the path from X to X by not moving. In the current analogy, I can go from California to California by doing nothing at all. Since C and D are both categories, they both have these special “do nothing” paths and so logically it would be best if we took the one from C and sent it to the one in D. So our first condition for the functor F is that $F(id_X) = id_{F(X)}$. This is merely saying that F takes in the identity morphism from X to X, and sends it to the identity morphism from F(X) to F(X), which is the object in D that corresponded to X in C via the functor.

The last condition we need involves the other property that was forced upon a category in the previous post. In any category we had to be able to put two morphisms together, i.e. compose two morphisms $f:X\rightarrow Y$ and $g:Y\rightarrow Z$ to make one longer morphism $g\circ f : X\rightarrow Z$. So let’s see how this works with our functor going from one category to another. First, this requires 3 objects in C. Call them X,Y, Z. If we go from X to Y via the morphism f we can use the functor to make a corresponding path from F(X) to F(Y) via F(f) and if we go from Y to Z via g we can make a corresponding path from F(Y) to F(Z) via F(g).

Over in the land of C we were able to put f and g together to make $g\circ f:X\rightarrow Z$ so what we really want is to be able to put the corresponding morphisms F(f) and F(g) together in a way that makes sense. Since $g\circ f:X\rightarrow Z$ is itself just a morphism in C we know that $F:C\rightarrow D$ can transfer it over to a corresponding morphism in D. The functor F takes a morphism between two objects to a morphism between the two corresponding objects. So F is going to take $g\circ f$ to a functor between F(X) and F(Z). We can then write that $F(g\circ f ): F(X) \rightarrow F(Y)$. But now think about what F does to f and g separately. We have $F(f):F(X)\rightarrow F(Y)$ and $F(g):F(Y)\rightarrow F(Z)$. These are two morphisms with a common middle object, F(Y), in the category D, so of course we are allowed to stick them together to get $F(g) \circ F(f) : F(X) \rightarrow F(Z)$. We now have two morphisms living in D that go from F(X) to F(Z). Would it make sense that they are secretly the same? Yes my dear Watson it would.

Consider the states (objects) California, Texas, and New York on Earth with a route to go from California to Texas then to New York. We can use our spaceship (functor) to go over to Earth 2.0 that has corresponding states and routes. Specifically we make corresponding states, California 2.0, Texas 2.0, and New York 2.0 with corresponding routes. You and I are very different people though. You prefer a bunch of information at once and hate wasting precious time so you write down the entire damn route in a little notebook. From California to Texas then to New York. You fly over to Earth 2.0 and then you draw the corresponding entire route on Earth 2.0. However I am a simple minded peasant and need bits and pieces at a time. So first I draw the route from California to Texas and fly (using my spaceship called functor) on over to Earth 2.0, then draw it there between the California 2.0 and Texas 2.0. Then I take another trip and functor over the route between Texas and New York. The first trip ended at Texas 2.0 and the second one began at Texas 2.0, so I decide I can just glue these two routes together in my notebook. Well what difference does it make if we do it my way or your way? If there is to be any sense in the universe these two routes will be the same.

That is my long winded explanation that a functor needs to “preserve” composition. We had composition in the category C and then functored it over to D in the only logical way to do it. First composing two morphisms, then sending the resulting morphism over through the functor is exactly the same as first sending each morphism through the functor and then composing them afterwards. The next step is to go very meta which I will probably not do for another month or so. This may seem very meta already, but it isn’t.

First we talked about objects and ways to go between objects. Then we talked about a way to go between two categories, which consist of objects and ways to go between objects. When it comes down to it though, categories are themselves still sort of object like (thus far) and so going from one to another isn’t too much trouble after a lot of practice. After we achieve space travel going from one planet to another won’t be that complicated. The point is that in real life it’s typically easy to go from point A to point B. But what if I have two ways to go from A to B and because going from A to B is so easy, I want to know what it means to go between the two paths? Going from a path to a path turns out to be a lot more difficult than going from a thing to a thing.


text:
## Philosophy of software engineering?

• 1.3k
When X is something people do, then sooner or later the "Philosophy of X" will arise. Nowadays a large number of people are involved in the world of software engineering.

Wikipedia has an interesting overview on the subject.

What strikes me, is that it seems to be quite divorced from the philosophy of mathematics, even though that is where it all originated. Alan Turing, Alonzo Church, Bertrand Russell, Stephen Kleene, and John Von Neumann, just to name a few, dreamed up abstract machines that were later painstakingly implemented. They were all mathematicians using pen and paper long before the first computer was actually built.

Is there more continuity in philosophy between the founders of the field and current practice than I suspect?
• 5.9k
The Wikipedia seems to be a listing of aspects of software engineering. Maybe therein a set of clues that a philosophy-of might organize somehow. As to your question, it seems to me that you're perched between thinkers(-doers) and practitioners. Folks can be in either or both camps, but they're two different camps.

Would it facilitate this discussion if you expanded on what your notion of what such a philosophy would or should be and be about?
• 4.5k
That wiki page is about workflow design and programming language styles in programming. Not anything about philosophy; it's philosophy in the sense of perspective rather than the topic of this site. You're looking for this kind of thing.
• 1.3k
it's philosophy in the sense of perspective rather than the topic of this site. You're looking for this kind of thing.

Yes, that is a better page. Unfortunately, all it really says, is:

There is still no common understanding of the content, aim, focus, or topic of the philosophy of computer science, despite some attempts to develop a philosophy of computer science like the philosophy of physics or the philosophy of mathematics.

That is exactly what I thought ...
• 1.3k
Maybe therein a set of clues that a philosophy-of might organize somehow.

Concerning "Software development philosophies", they tend to be epistemic considerations, but not very rigorous at that. Furthermore, their applicability is rather debatable. The "Rules of thumb" section actually looks like a better starting point.

By the way, I accidentally ended up drilling down into expensive consultancy practices: Rational Unified Process (RUP). Like all snake-oil style consulting, IBM's RUP has a rather poor reputation.

There is a nascent meta-level to these things, but it is rather poor. Epistemology would be a good starting point, and seems to have the largest number of contributions; but philosophy is more than only epistemology.
• 5.9k
but philosophy is more than only epistemology.
Maybe like Bacon we - you - need to put it to the question. Instead of asking what it is, telling it. If wrong, at least you'll know one thing it isn't.
• 62
The wikipedia article also has a lot of links to documents and not only the information you read.
• 1.8k
I accidentally ended up drilling down into expensive consultancy practices

Yes, there's a whole industry, supposedly based on 'teaching' the latest fads. Snake oil, mostly, as you suggest. Agile is one of the recent fads, and it has been changed from its original (worthwhile) intent to something that can be taught in a classroom, and produce Agile Managers. :scream: :rage: It makes actual practitioners wince and despair.

it seems to be quite divorced from the philosophy of mathematics, even though that is where it all originated. Alan Turing, Alonzo Church, Bertrand Russell, Stephen Kleene, and John Von Neumann, just to name a few, dreamed up abstract machines that were later painstakingly implemented.

Yes, and then other people learned to program them. Programming is a separate discipline. And it is divorced from mathematics, as you observe. But the names we give our discipline don't help. "Programming" and "software engineering" do not offer the right tone/view, in my opinion. They neglect the heart of our discipline: design. I always called myself a "software designer". Just as there is art at the heart of science, so also is there art in software. And science too; quite a lot of it! And this is but the start.

Some years ago, there was an "Iron Man" version of a definition of software engineering, and the list of associated disciplines, that the successful candidate should master was extensive. It included psychology and an understanding of how humans think and work together. And loads more.

As for the philosophy of programming, well philosophy is about thinking, so thinking about software engineering is presumably practicing the philosophy of programming? If this is a good definition, I think all capable software practitioners are also philosophers (of programming, if nothing else). :chin:
• 1.8k
As to your question, it seems to me that you're perched between thinkers(-doers) and practitioners. Folks can be in either or both camps, but they're two different camps.

Disclaimer: I'm writing here as an experienced software designer, not as an expert in the "philosophy of programming".

There are not two camps; there is only one. No programming project can succeed without both thinking and doing being present in the appropriate combination. All successful practitioners know this so deeply they wouldn't even think of expressing it, like we don't notice we're breathing (most of the time).

Those who reside in only one 'camp' are not capable of successfully practicing 'programming'. They might be former practitioners who are thinking about how their discipline might move forward, or they might have some other aim. They just aren't software designers.
• 1.8k
Some years ago, there was an "Iron Man" version of a definition of software engineering

I tracked some of this stuff down. Here's what I found.

In order to propose Knowledge Areas and Related Disciplines for “generally accepted” knowledge and to do so based on recognized, public and verifiable sources of information, it was decided that the tables of contents of general software engineering textbooks, the curricula of undergraduate and graduate programs in software engineering, and the admission criteria for graduate programs would constitute the input to our analysis. A total of 24 textbooks and 29 programs were examined.For the purposes of this Straw Man version, a potential knowledge area had to be mentioned in the table of contents of at least one quarter of the textbooks sampled to qualify as a proposed Knowledge Area.The ISO/IEC 12207 standard on Software Life Cycle Processes is used as the basis and vocabulary for the classification of the different topics related to the life cycle. A number of other topics not related to the life-cycle were also considered.

The list of proposed Knowledge Areas based on ISO/IEC 12207 is:
— SWEBOK
• Development Process
• Requirements Analysis
• Detailed Design
• Coding
• Testing
• Maintenance Process
• Configuration Management
• Quality Assurance
• Verification and Validation
• Improvement Process

The list of proposed Knowledge Areas that do not converge well with ISO/IEC 12207 is:
• Software Development Methods−Object Oriented−Formal Methods−Prototyping
• Software Development Environments
• Software Engineering Overview & DefinitionüMeasurement/Metrics
• Software Reliability

The list of proposed Related Disciplines is:
• Computer Science
• Project Management
• Electrical Engineering
• Mathematics
• Telecommunications/NetworksüManagement
• Science
• Other Engineering Disciplines
• Cognitive Sciences

Sorry about the text layout, it was originally laid out as a bulleted and tabbed list, but it seems I can't embed lists into quotes. :fear: The original is here.
• 1.8k
Thanks for creating this topic! It's a bit weird though, commenting on something I actually know something about! :rofl:
• 1.3k
Agile is one of the recent fads, and it has been changed from its original (worthwhile) intent to something that can be taught in a classroom, and produce Agile Managers.

In my opinion, "agile" is epistemically worthless. If knowledge is a justified belief, then the very last industry that feels the need to come up with reasonable justification, are the consultancy snake-oil factories. It is incredible how intellectually poor their conjectures are. The more money floats around in flogging the nonsense, the more nonsensical it tends to be.
• 4.2k
In my opinion, "agile" is epistemically worthless.

The motivation isn't. The reason agile became a thing is because often it's the case that during a software project the requirements change as the customer comes to realize what they really want which they were unable to specify at the outset. This is particularly true for web and app software.

I was just in a meeting today where with a deadline a couple weeks away where the customer once again is changing the requirements. And this customer is state funded.

That's part of the reason why programming isn't math. In a platonic software world, you would know the exact requirements before starting. But in the real world it's often the case that the process is one of discovery and negotiation. Agile is meant to address that reality. But whatever you call it, software engineering needs to take into account changing requirements when you can't nail them down before starting the project.

And sometimes you just have to ship it to meet a deadline, even if it's hacked together. The whole "real developers ship" is contrasted against having mathematically rigorous software specifications nailed down first where shipping less than perfect code is financially prudent.

Now it's a bit different if safety is the number one requirement, say for flying a plane or autonomous cars.
• 1.3k
But whatever you call it, software engineering needs to take into account changing requirements when you can't nail them down before starting the project.

Well, the very concept of "project" is a problem. In a successful "project", 80+% of the cost will be incurred during later maintenance. Of course, most "projects" will never reach that stage.

In other words, setting a project goal to be achieved, and associating a budget for it, tends to fail. Successful software rarely emerges out of that kind of context. I am surprised that even civil service bureaucracies begin to understand the fundamental problem:

www.csc.gov.sg The Civil Service College (CSC) was established as a statutory board under the Public Service Division in 2001. As the heart of learning for the Singapore Public Service, we deliver an innovative, inspiring and impactful learning experience for public officers.

How to Build Good Software
Software has characteristics that make it hard to build with traditional management techniques; effective development requires a different, more exploratory and iterative approach.

It is the very notion of "project" with "start" date, "delivery" date, and definitive "budget" that is the problem. The larger the distance between what you want to achieve versus what you can download verbatim from github, the more costly the failure will be.
• 107
Well, To comment on the thread start, software and mathematics maybe have some general differences. And some similarities. Both are kind of logic based activites, there isnt on the lower levels anything fuzzy about it, its not in the humanities. And both can be considered as tools to enhance life for people by solving problems. Computer guys are most often good at maths as well.

But the computer programs have a different kind of complexity, in that the problem really isnt the complexity of the problem to be solved, but in the communications. What is it we want done, how shall the different persons realizing the programming project work together, how shall the programming parts communicate with each other, how can we use already delivered program code.

Programming has, since I studied computer engineering in the 80´s exploded to be a massive activity, and all of us use the results of endless efforts all the time. So computer programming have more in common with house construction work or something like that than with maths.

One problem here is that I dont really know much about the philosophy of maths. What is that all about?
• 1.3k
So computer programming have more in common with house construction work or something like that than with maths.

House construction work is relatively well manageable as projects. You start, you build, and you finish within a particular time frame and budget. Corporations have attempted to to manage software development in the same way, and have failed for decades now to do exactly that. That does not mean that it is necessarily more related to doing original math work either. Still, viewing software as projects, is a failing proposition.

One problem here is that I dont really know much about the philosophy of maths. What is that all about?

Philosophy of mathematics

The Platonic, formalist, and structuralist views certainly ring a bell with me. In fact, even the fictionalist take on mathematics makes sense to me. In my opinion, the different schools of thought do not necessarily exclude each other, even though my own opinion is certainly incompatible with the constructivist view. I cannot reconcile myself with people like Brouwer.
• 526
the philosophically enlightening thing about the craft of software engineering is it's cut-throat pragmatism that makes explicit what mathematics and logic are really about, such that the disease of philosophical speculation cannot take hold. There aren't any software engineers debating whether an infinite loop really runs forever, unlike a significant proportion of set-theorists, who as a result of refusing to get their hands dirty in practical application, end up associating mathematical infinity with the religious idea of eternity.
• 1.3k
unlike a significant proportion of set-theorists, who as a result of refusing to get their hands dirty in practical application, end up associating mathematical infinity with the religious idea of eternity.sime

According to Cantor's theory, the infinities (Beth numbers) (or Aleph numbers) are a series of successive numbers, with the smallest one being countable infinite, the next one uncountable infinite, and each successive infinity, inf[n] = 2^inf[n-1], the cardinality of the power set of the previous one. Such sequence of infinities is not particularly compatible with the idea of one God, which would correspond to one infinity.

According to Cantor's diagonal argument, it is absolutely excluded that countable infinite would be the same number/cardinality as uncountable infinite.
• 1.7k
According to Cantor's theory, the infinities (Beth numbers) (or Aleph numbers) are a series of successive numbers, with the smallest one being countable infinite, the next one uncountable infinite, and each successive infinity, inf[n] = 2^inf[n-1], the cardinality of the power set of the previous one. Such sequence of infinities is not particularly compatible with the idea of one God, which would correspond to one infinity.

Cantor thought that the limit of that process, essentially the union of all the infinite cardinals, was God. God is the absolute infinity. Cantor's theology is forgotten today but it was important to him. This would be relevant if you're trying to use set theory to make a theological argument.

In any event, there are many uncountable cardinals. All the cardinals other than the countable one Aleph-0 are uncountable. The Beth numbers are the Alephs in the presence of the continuum hypothesis; they're distinct in its absence.
• 3.1k

I work in the software industry. Software development is a subset of computer science, however in practice it is more like a trade. When entering the trade, one begins as an apprentice, before advancing to journeyman and finally master. Sometimes this involves a university degree.

There are guild-like organizations and communities that are built around "philosophies" of software engineering. These philosophies are different ways of developing software.

What is interesting is how closely tied mainstream software development practices are to capitalism. I was taught and currently work in a development environment called Agile, which is meant to facilitate pipelined production of software in iterations. The cycle of production never ends - as soon as one checkpoint is reached, the next checkpoint is immediately placed. Programmers are told what the customer wants, and they have to negotiate with their boss about the workload. Every day there is a check-up to see what progress has been made and what set backs have been encountered - this peer pressure acts as incentive to work.

With web development, which is one area I work in, the name of the game is efficiency. Everything must continuously be quicker and easier. This is mostly because anything less will lose the short attention span of potential customers. There are lots of gimmicky widgets, like pop ups, infinite scrolls, silent collection of user data, etc that are all meant to help lure customers into spending money, or giving up their privacy (I do not code this kind of stuff).

Computers are like crack to capitalism. They make everything more efficient, more automated, more blind. I think perhaps in the next few decades, programmers will put themselves out of a job by developing an artificial intelligence that can do their jobs.

There are tons of nauseating self-help books for programmers that are written by self-absorbed assholes who think their way is the right way. Often there are pretentious quotes from Lao Tzu or some other sage in the beginning of each chapter. Super cringey.

So my point is that, from an industry perspective, software development is intimately tied to capitalism. But there are other ways of developing software that are less tied to economics - open source software is a great example.

On the other end of the spectrum of computer science is the actual science. This is less tied to capitalism, partly because it is usually limited to universities. And it is close to philosophy as well. This is where you will find philosophical concepts like Turing machines, finite state machines, semantics of programming languages, algorithms, etc.

I think probably the most ubiquitous philosophical mindset of computer science must be a certain reductionism. Abstraction is a fundamental concept to computer science, but nevertheless these abstractions could not function unless the underlying substrate is also functional. High-level applications do not function unless the operation system does, and the operation system does not function unless the low-level firmware does, and the low-level firmware does not function unless the hardware does. The Unix "philosophy" could be described as reductionistic too, because it emphasizes making larger things out of smaller, basic modules.

I think it's safe to say that if you ever hear someone on the internet proclaiming that some difficult philosophical issue "is just" something, this person might be a computer science undergraduate.
• 1.3k
The Beth numbers are the Alephs in the presence of the continuum hypothesis; they're distinct in its absence.

Finite fields (in which arithmetic is permitted) must have a prime-power size. Therefore, there tend to be gaps between permissible calculation field sizes. E.g. a size of 13 is allowed, but 14,15 are not; 16=2⁴ is a prime power and is again allowed, and so on. So, in a way, we could wonder why it would be any different -- the fact that there are gaps -- in between infinite field sizes in which arithmetic is permitted? Of course, this kind of pattern is not a proof, but it seems to point in a particular direction.

But then again, since CH is provably not provable/disprovable from ZFC, proving CH from any alternative set of axioms, that is not just itself, may not be particularly "simple". It would require a meaningful distance, i.e. a meaningful number of non-trivial derivation steps from these axioms to CH, while these axioms would also have to be provably independent of ZFC. I do not see how else anybody could make progress in CH?
• 1.3k
What is interesting is how closely tied mainstream software development practices are to capitalism.

But there are other ways of developing software that are less tied to economics - open source software is a great example.

The first problem is, of course: What is the definition of "capitalism"? It is often confused with (free) trade, commerce, and the resulting trend to specialization:

Modern capitalist societies—marked by a universalization of money-based social relations, a consistently large and system-wide class of workers who must work for wages, and a capitalist class which owns the means of production—developed in Western Europe in a process that led to the Industrial Revolution.

So, modern capitalism may revolve around the existence of a capitalist class which owns the means of production.

So, is this the case in software? What are the means of production and who owns them?

To produce software, you need relatively inexpensive computer equipment, owned by the public at large. So, the hardware part is not capitalistic.

You also need other software such as operating systems, compilers, basic libraries, and so on. You do have two large, proprietary owners of their version of basic software, i.e. IBM and Microsoft, but nowadays most software is built using free software, especially if you consider that most software runs on mobile phones, and that Android is (or is based on) free software.

Hence, even though there are noticeable elements of capitalism that operate in the realm of software, i.e. a few large capitalist players, they do not generally own the means of production. In other words, there is no (dominant) capitalist class which owns the means of production in software.
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The reason agile became a thing is because often it's the case that during a software project the requirements change as the customer comes to realize what they really want which they were unable to specify at the outset.

It is the very notion of "project" with "start" date, "delivery" date, and definitive "budget" that is the problem. The larger the distance between what you want to achieve versus what you can download verbatim from github, the more costly the failure will be.

[C]omputer programs have a different kind of complexity, in that the problem really isnt the complexity of the problem to be solved, but in the communications. What is it we want done, how shall the different persons realizing the programming project work together, how shall the programming parts communicate with each other, how can we use already delivered program code.

It's a joy to see posts based on real knowledge and understanding! @Ansiktsburk, aren't you wandering around the word "design" in what you wrote? :wink: To successfully design a program (or anything else, come to that), we need to understand all the contributing forces, as @Ansiktsburk describes. The need for understanding is paramount. This being the case, I wonder what the role of the philosophy of SE is?

Philosophy most often tries to lead us in the direction of understanding. In other areas, say X, the philosophy of X is an investigation into background issues, those that are rarely scrutinised. But in SE, understanding of roughly that sort is necessary for its practitioners. So where is the space for the philosophy of SE? I'm not sure. But I'm sure someone here will offer suggestions? :wink:
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the philosophically enlightening thing about the craft of software engineering is its cut-throat pragmatism...sime

...unexpectedly coupled with its need to satisfy human-based desires (requirements), which move well away from "pragmatism". Many of them are only distantly connected to logic or reason; ask any working software designer! :smile:
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I think perhaps in the next few decades, programmers will put themselves out of a job by developing an artificial intelligence that can do their jobs.

I see from your post that you're a relatively recent recruit to our ranks, as you mention web development, and starting with Agile. Nevertheless, you seem to have developed quite an eye for our industry! :wink: As to AIs replacing us, I've read the same thing twice a year since I started, in the (very) late 70s. I don't think our replacement is likely, because of the strong and central core of creativity in our work. We are not artists like Emin or Monet, but we could not do our jobs without the creativity that gets us from a whole host of requirements (from the customer; technical requirements from the engineering side; commercial requirements from the managerial side; and so on) to a solution acceptable to all.
• 1.7k
Finite fields (in which arithmetic is permitted) must have a prime-power size. Therefore, there tend to be gaps between permissible calculation field sizes. E.g. a size of 13 is allowed, but 14,15 are not; 16=2⁴ is a prime power and is again allowed, and so on. So, in a way, we could wonder why it would be any different -- the fact that there are gaps -- in between infinite field sizes in which arithmetic is permitted? Of course, this kind of pattern is not a proof, but it seems to point in a particular direction.

The Alephs aren't fields. Finite fields have absolutely nothing at all to do with this. They're apples and rutabagas.

But then again, since CH is provably not provable/disprovable from ZFC, proving CH from any alternative set of axioms, that is not just itself, may not be particularly "simple". It would require a meaningful distance, i.e. a meaningful number of non-trivial derivation steps from these axioms to CH, while these axioms would also have to be provably independent of ZFC. I do not see how else anybody could make progress in CH?

One can Google around. A lot of work has been done by Woodin, Hamkins, and other contemporary set theorists. Work on CH has been ongoing for decades. It just doesn't make the mainstream news.

One big new idea is Woodin's Ultimate-L. It's so new and so technical it doesn't have a Wikipedia entry. This MathOverflow thread has some references. Nothing in this topic is comprehensible to laymen, just mentioning it since it's the state of the CH art.

https://mathoverflow.net/questions/269780/the-ultimate-l-in-a-nutshell-on-descriptive-articles

Another idea is Hamkins's set-theoretic multiverse.

http://jdh.hamkins.org/themultiverse/

Here's an accessible article that surveys the modern developments.

https://www.ias.edu/ideas/2011/kennedy-continuum-hypothesis
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The Alephs aren't fields. Finite fields have absolutely nothing at all to do with this. They're apples and rutabagas.

The cardinality of an infinite set ("aleph") is indeed formally not a Galois field. What I was saying, isn't a formal argument. I was just pointing out an uncanny similarity, i.e. just some kind of pattern:

[1] arithmetic is allowed in finite fields of prime powers only. This rule creates gaps between the field sizes.

At the same time, arithmetic is allowed in the integers (or rationals), i.e. a set with cardinality of aleph-0, and is also allowed in the reals (or computable numbers or similar), i.e. a set with cardinality of aleph-1.

[2] Continuum hypothesis. There is an insurmountable gap between aleph-0 and aleph-1. There are no infinite cardinalities in between.

As far as I am concerned, there is an uncanny similarity between the gaps in between finite calculation fields and the gaps between infinite calculation fields. Furthermore, with aleph[k]=2^aleph[k-1], the aleph[k] cardinalities are also prime powers; which is another uncanny similarity.

Of course, formally proving the link between both phenomena, is something else altogether. That is obviously another exercise.

One can Google around. A lot of work has been done by Woodin, Hamkins, and other contemporary set theorists. Work on CH has been ongoing for decades. It just doesn't make the mainstream news.

Well, of course, people are still working on CH. I was just pointing out how "rigged" the game is. The context to work in, is really difficult. The proof that any axiomatization of CH is independent of ZFC, makes doing something meaningful, really hard. The structure required is incredibly annoying. You need other axioms, but which must still have a real provability distance from CH, because otherwise you would just be axiomatizing the final result itself ... Well ...

One big new idea is Woodin's Ultimate-L. It's so new and so technical it doesn't have a Wikipedia entry. This MathOverflow thread has some references. Nothing in this topic is comprehensible to laymen, just mentioning it since it's the state of the CH art.

Apparently, the current status is: How Woodin changed his mind: new thoughts on the Continuum Hypothesis.

This paper illustrates Woodin’s solutions to the problem, starting in Sect. 3 with his 1999–2004 argument that Cantor’s hypothesis about the continuum was incorrect. From 2010 onwards, Woodin presents a very different argument, an argument that Cantor’s hypothesis is in fact true.

Well, yeah. My own intuition is in favour of CH. So, I obviously like Woodin's new approach better.

This argument is still incomplete, but according to Woodin, some of the philosophical issues surrounding the Continuum Problem have been reduced to precise mathematical questions, questions that are, unlike Cantor’s hypothesis, solvable from our current theory of sets.

That explains why there is no Wikipedia entry for Woodin's work yet. They are not supposed to report on proofs that still have gaps in them. A proof with existing remaining gaps is a research hypothesis and not something to be propagated as "finished work" in places like Wikipedia.

If you look at the subtleties he needs in order to make his point:

[1] A Reinhardt cardinal, [2] An n-huge cardinal, [3] A huge cardinal, [4] An extendible cardinal, [5] A supercompact cardinal, [6] A superstrong cardinal, [7] A Woodin cardinal, [8] A measurable cardinal, [9] A (strongly) inaccessible cardinal.

The complexity proposed is substantially beyond what is done in existing, established theories. Therefore, what he is doing, looks quite ... ambitious.

Then, he writes:

As mentioned in the article, too much would have to be said to give an argument as to why the Axiom of Projective Determinacy, PD, should be accepted.

There, he is hitting the core of the problem. In fact, there should be no argument as to why axiom PD is accepted. If he does that, it is not an axiom. So no, all he needs to do, is to prove that there is a real distance, a serious series of transformative derivation steps from PD to CH.

There is no such thing as the quality of an axiom, because that implies "justification" of an axiom, which is exactly what is not allowed. All we need to see, is that CH is not trivial from PD. That would be enough.

I think that Woodin's work is interesting, but before further digging into the nitty-gritty details of the pyramid of vocabulary on which his work rests, I will just let him first complete the gaps in his argument! ;-)

Another idea is Hamkins's set-theoretic multiverse.
http://jdh.hamkins.org/themultiverse/

The multiverse view in set theory, introduced and argued for in this article, is the view that there are many distinct concepts of set, each instantiated in a corresponding set-theoretic universe. The universe view, in contrast, asserts that there is an absolute background set concept, with a corresponding absolute set-theoretic universe in which every set-theoretic question has a definite answer.

In my opinion, Hamkins' work sounds less promising than Woodin's work, with which I can somehow identify. Hamkins does not talk about juxtaposing a set of axioms provably independent from ZFC from which there exists a noticeable derivation distance from CH, but from which he successfully derives CH. Therefore, I cannot identify with Hamkins work.

Here's an accessible article that surveys the modern developments.
https://www.ias.edu/ideas/2011/kennedy-continuum-hypothesis

He writes:

How ironic then that the continuum hypothesis is unsolvable—indeed, “provably unsolvable,” as we say.

Well, CH is not unsolvable. It is just unsolvable from ZFC. That does not mean that it would be unsolvable from anything else. For example, it is trivially solvable from itself. However, that is not what we want. We want some larger distance between CH and the X someone would solve it from. This X needs to be independent from ZFC, and that is a problem, because ZFC is extremely powerful. So, finding such X is not easy.

Gödel, however, [...] taking the view that his incompleteness theorems, though they show that some provably undecidable statements do exist, have nothing to do with whether the continuum hypothesis is solvable or not.

Yes, of course!

what would it be like to go beyond set-theoretic methods and suggest something new? Still, this is exactly what is needed to solve the continuum hypothesis.

Yes, X needs to be independent from ZFC (not easy to achieve) and still have a real distance from CH. Next, CH needs to be proven from X. That is what needs to happen, but as I argued before, that is clearly not easy. Furthermore, it is also a very counter-intuitive procedure to follow.
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[2] Continuum hypothesis. There is an insurmountable gap between aleph-0 and aleph-1. There are no infinite cardinalities in between.

This is true by the definition of the Aleph numbers. It's not a statement of the continuum hypothesis. I hope we can clarify this if we're going to talk about CH.

There is no transfinite cardinal between $\aleph_0$ and $\aleph_1$, period. It's a matter of definitions within ZF, Zermelo-Fraenkel set theory without the axiom of choice.

$\aleph_0$ is by definition the cardinality of the set of natural numbers.

$\aleph_1$, by definition, is the cardinality of the set of all distinct well-order types of countable sets. $\aleph_2$ is the cardinality of the set of all distinct well-order types of sets of cardinality $\aleph_1$, and so forth. If you don't know what that means that's ok, I don't want to get sidetracked by technical detail. All that's important at the moment is that each Aleph number has a specific technical definition such that the they form a sequence of discrete cardinalities, one after the other. There can be no Alephs strictly between two Alephs simply by virtue of their definitional construction. That's the key point. They're defined such that there are no "in-between" Alephs.

Now consider the real numbers. We can code each real number (between 0 and 1 for simplicity and without loss of generality) as an infinite binary sequenc; a bitstring with an implied binary point in front. It's clear that a real number is essentially a function from the set of natural numbers to a set with two elements (zero and one). Such a set (again omitting technical details) has cardinality $2^{\aleph_0}$, which is defined as the cardinality of the set of all functions from the natural numbers to a two-element set.

So $2^{\aleph_0}$ is SOME cardinal; and if we assume that every cardinal is an aleph (this actually depends on the axiom of choice) then there must be some ordinal number $x$ such that $2^{\aleph_0} = \aleph_x$. Which $x$ could that be?

The continuum hypothesis is the claim that $2^{\aleph_0} = \aleph_1$,

The generalized continuum hypothesis, GCH, is the claim that $2^{\aleph_\alpha} = \aleph_{\alpha + 1}$ for every ordinal $\alpha$.

[If you've never seen the ordinals they're the coolest thing ever. They show up in logic and sometimes computer science, especially in the theory of hypercomputation].

As far as anyone knows, $2^{\aleph_0}$ could be huge -- it could be $\aleph_{100000}$ or worse. Gödel thought that it was $\aleph_2$. Cohen thought it could be much larger. Or ... and there's a lot of support for this position ... the question could be entirely meaningless.

Your idea isn't entirely without merit. Cohen wrote that intuitively, exponentiation is a much more powerful operation than taking successors. For example going from $2^4$ to $2^5$ is a much larger jump than going from $2^4$ to $2^4 + 1$. (My example, not Cohen's). By that analogy, CH would be false. That's essentially your argument I think. You're analogizing with the permissible cardinalities of finite fields. It's not a bad idea as far as it goes if you find it helpful.

Some of what you wrote is a little off the mark IMO but I wanted to nail down the definition and meaning of CH first. What you call uncanny I call "a stretch" not justified by the math. I accept your analogy only insofar as it's helpful to you personally.

ps ... this also really jumped out at me.

[1] A Reinhardt cardinal, [2] An n-huge cardinal, [3] A huge cardinal, [4] An extendible cardinal, [5] A supercompact cardinal, [6] A superstrong cardinal, [7] A Woodin cardinal, [8] A measurable cardinal, [9] A (strongly) inaccessible cardinal.

The complexity proposed is substantially beyond what is done in existing, established theories. Therefore, what he is doing, looks quite ... ambitious.

Those technical terms are the meat and potatoes of 20th century set theory, especially of the last thirty or forty years. They're not "beyond existing theories." They're just beyond what you've heard about. Measurable cardinals for example were studied in 1930 by Stefan Banach. An inaccessible cardinal was implicitly used by Wiles in his proof of Fermat's last theorem, though specialists believe his proof could be done without it. Advanced set theory doesn't make the TED talks and math blogs but it's out there. And it's really "out there."
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hose technical terms are the meat and potatoes of 20th century set theory, especially of the last thirty or forty years. They're not "beyond existing theories."

Sure.

I just somehow hope that the nitty-gritty distinctions between "extremely large", "super huge", and "incredibly out-sized" cardinals won't be needed.

Furthermore, I was more interested in the remark by/on Woodin, "why the Axiom of Projective Determinacy, PD, should be accepted". I do not think it matters "why". What matters is that If PD is provably independent from ZFC, and that Woodin also manages to prove CH from PD, because then Woodin will have managed to finish the job. The real problem is what he writes at "the argument is still incomplete ...". That is why I said that I am waiting for him to complete the argument. Unfortunately, we cannot do particularly much with just half the argument ...
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I just somehow hope that the nitty-gritty distinctions between "extremely large", "super huge", and "incredibly out-sized" cardinals won't be needed.

Why not? May I ask if these are technical terms with which you're familar? You mis-stated CH in such a way as to give me the impression you haven't studied much set theory beyond the basics. If you're a specialist in advanced set theory who made an elementary error then you have my apologies. It's just that I don't understand why you are trying to discuss or comment on things that are far outside of your (and my) competence. If I've got this all wrong just tell me.

I
Furthermore, I was more interested in the remark by/on Woodin, "why the Axiom of Projective Determinacy, PD, should be accepted". I do not think it matters "why". What matters is that If PD is provably independent from ZFC, and that Woodin also manages to prove CH from PD. Then, Woodin will have finished the job. The real problem is what he writes at "the argument is still incomplete ...". That is why I said that I am waiting for him to complete the argument. Unfortunately, we cannot do particularly much with just half the argument ...

Do you know what PD is? Do you have an opinion on its truth or falsity, and knowledge of how it relates to other candidate axioms floating about? Do you know a lot about infinite games and projective sets? I saw a lecture on AD once, the axiom of determinacy. That says that EVERY set of reals is determined. PD says that every projective set is determined, which is weaker.

I
That is why I said that I am waiting for him to complete the argument. Unfortunately, we cannot do particularly much with just half the argument ...

My point is that neither of us is remotely qualified to discuss Woodin's work at all, unless you have set-theoretic knowledge far in excess of what you have demonstrated so far. Nor is his argument incomplete. Google for "extender models" and you'll probably find some papers.

I'm honestly having trouble here. By your comments I've placed you at a certain level in set theory. And you seem perfectly confident of your ability to understand what Woodin is talking about. There's a massive disconnect. He's one of the world's leading set theorists. This is bleeding edge theoretical work. It's not absent from Wiki because it's "not complete." It's absent because there are as yet no humans who can understand his work and translate it for the public; even that segment of the public with a technical degree or two. There are one or two popular articles on the subject that are no help at all. You wouldn't expect to jump into the latest bleeding edge research in biology or physics.

I had a professor once, Fields medalist, very famous guy. In grad-level real analysis he forgot the wording of Zorn's lemma and asked for help, Which I, bright-eyed young genius that I was at the time, quoted for him perfectly. That was the high point of my math career. Point being that you misconstrued CH either because: (a) you haven't studied much set theory; or (b) you are so advanced you can no longer be bothered with the basics. There's a disconnect and it's bothering me.
• 1.3k
You mis-stated CH in such a way as to give me the impression you haven't studied much set theory beyond the basics.
About CH, I just said in my own words what you can find in Wikipedia too. Maybe it is a mis-statement. I don't particularly care, actually. CH is not "critically" important to me. I do not research it. It is not my job. I do other stuff. So, yes, just like Wikipedia (as an earlier remark), I am not much interested in going particularly much beyond what is provable already, and therefore, what are merely "the basics".

My point is that neither of us is remotely qualified to discuss Woodin's work at all, unless you have set-theoretic knowledge far in excess of what you have demonstrated so far. Nor is his argument incomplete.

Well, Woodin literally says that his argument is incomplete. (Read the original paper. I literally quoted what it said.)

Furthermore, If it weren't incomplete, Woodin would simply provide us with the proof, instead of saying that his argument is incomplete.

By the way, if you look at the problem, you can see that the only workable proof strategy is exactly about avoiding set-theoretic knowledge. It is a hard requirement to stay clear of ZFC, because if you don't, the proof will automatically be wrong. That is probably what makes the proof strategy so hard for people who are too deeply steeped in set-theoretic knowledge. They simply won't be able to do it.

As I said, Woodin's strategy to prove CH from PD -- while staying clear of ZFC in any form or shape -- sounds really interesting, but he has also clearly said that he still hasn't managed to do it. I am just repeating Woodin's own words.
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# Monte Carlo Integration on the Real Line

Suppose that we want to compute $$\int_{\mathbb{R}} f(x) dx$$ using monte carlo integration so that we can normalize $f(x)$ and make it a pdf. The examples you typically see involve integrals over a finite domain such as $[a,b]$. In such cases we can sample from the uniform distribution on $[a,b]$. In the case we integrate over $\mathbb{R}$ we need to sample from a pdf whose support is $\mathbb{R}$, say the standard normal pdf which we represent as $p(x)$. We can then compute $$\frac{1}{n} \sum_{i=1}^{n} \frac{f(x_i)}{p(x_i)}$$ as our unbiased estimate of $$\int_{\mathbb{R}}f(x)dx=\int_{\mathbb{R}}\frac{f(x)}{p(x)}p(x)dx=\mathbb{E}\left[\frac{f(x)}{p(x)}\right]$$ so long as $$(1)\;\;\;\;\int_{\mathbb{R}}\frac{f(x)^2}{p(x)}dx < \infty$$ We can also rely on estimates of the variance of the estimator as well as employ the central limit theorem to construct confidence intervals so long as $$(2)\;\;\;\;\int_{\mathbb{R}}\frac{f(x)^4}{p(x)^3}dx < \infty$$ My problem is that I struggle to construct and example where (1) and (2) hold. Can someone give examples of monte carlo integration techniques used to normalize a function over $\mathbb{R}$ which satisfy the necessary assumptions so that the estimate is reliable?

• @Tim: I am afraid I do not see your point. If one seeks an approximation to $\int_a^b f(x(\text{d}x$, it can be interpreted as a uniform integral, no matter what the original problem is. Importance sampling shows us that the reference probability measure is arbitrary. Aug 26, 2016 at 1:04
• @Wintermute: It is possible to use a first importance sampler to estimate the integral and a second one to estimate the variance term. The condition (2) is thus not necessary for estimating $\int f(x)\text{d}x$. Note also that the distinction between a support of $[1,b]$ and $\mathbb{R}$ is not connected with the existence of a second or a fourth moment. Take for instance $f(x)=1/sqrt{x}$ and$[a,b]=[0,1]$. Aug 26, 2016 at 1:08
• @Xi'an ok, I may have misunderstood something.
– Tim
Aug 26, 2016 at 7:32
• @Xi'an Condition (2) is necessary to get a reliable estimate of the error of your estimator. I would think that using a different sampler to estimate the variance will not give you a reliable notion of the error of your estimator. Condition (2) just ensures that your estimator has enough moments to get a reliable estimate of the error. Aug 26, 2016 at 15:28
• The variance is another integral that can be estimated separately based on the same sample or another sample. Aug 27, 2016 at 0:04

Extreme example: $f$ a standard normal distribution, and $p$ a Cauchy distribution (just remove a constant from $f$ to make it more similar to your context). Then,

$$\frac{f(x)^2}{p(x)} = \dfrac{\pi(1+x^2)}{(2\pi)}\exp(-x^2),$$

and

$$\frac{f(x)^4}{p(x)^3} = \dfrac{\pi^3(1+x^2)^3}{(2\pi)^2}\exp(-2x^2),$$

which are clearly integrable since they are related to the moments of normal distributions, which always exist.

• Your formulas do not seem to agree with your descriptions. For instance, if $p$ is a Cauchy density, then $1/p(x)$ is proportional to $1+x^2$, not $1/(1+x^2)$.
– whuber
Aug 25, 2016 at 16:36
• @whuber well spotted, I have corrected the expressions and the argument. Thanks.
– Eso
Aug 25, 2016 at 16:40
• So is the kurtosis playing a role here? Should the pdf sampled from have a higher kurtosis than the one we are trying to normalize? Aug 25, 2016 at 16:42
• @Wintermute It has to do with the tails. The variance of this estimator exists when the tails of the denominator are heavier. That's the rule of thumb when constructing importance sampling estimators.
– Eso
Aug 25, 2016 at 16:44


text:
no effect of \baselinestretch

I'm probably doing something wrong, but i can't see any effect of the command \baselinestretch, which should modify the vspace between lines. I read somewhere, that i should add \selectfont after it, but i can't see any effect either:

\documentclass[12pt]{article}
\begin{document}

{\renewcommand{\baselinestretch}{2}\selectfont coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou coucou }

\end{document}

-
You're issuing \par when the setting of \baselinestretch has been forgotten because the group has ended. Put \par before the closing brace. –  egreg Mar 27 '12 at 7:59
May be tex.stackexchange.com/questions/48741/… is of some help? –  Harish Kumar Mar 27 '12 at 8:14
ok, thanks a lot. –  nicolas roy Mar 27 '12 at 8:15

This problem is similar to when one writes

{\Large some long text
that will span two or
more lines}

and the line spacing comes out wrong.

TeX uses one baseline skip for all lines in a paragraph, using the value in force when it scans the end of paragraph. In the example and also in your code the \par (or equivalent blank line) is found when the group where the change has been issued has already been closed and its effect canceled. The following code

\documentclass[12pt]{article}
\begin{document}

won't have the problem. Notice the \linespread{2} command, which is handier than \renewcommand{\baselinestretch}{2} and has the same effect.


text:
• 研究论文 •

### 灰飞虱长、短翅型品系对高、低温的适应能力差异

1.  (南京农业大学植物保护学院昆虫学系, 南京 210095)
• 出版日期:2019-07-20 发布日期:2019-07-09

### Difference in the adaptability of the long- and short-winged strains of Laodelphax striatellus (Hemiptera: Delphacidae) to high and low temperatures

TIAN Xin-Xin, ZHANG Chao, LIU Xiang-Dong*

1. (Department of Entomology, College of Plant Protection, Nanjing Agricultural University, Nanjing 210095, China)
• Online:2019-07-20 Published:2019-07-09

【目的】灰飞虱Laodelphax striatellus种群存在长翅和短翅个体，其翅型分化受遗传和环境条件的影响。本研究旨在明确经连续定向选育的灰飞虱长、短翅型品系对高、低温的适应能力差异。【方法】在室内分别长期定向筛选63和65代建立灰飞虱长、短翅型品系，并在南京田间采集灰飞虱自然种群；分别在25℃, 30℃和35℃恒温条件下测定上述灰飞虱长、短翅型品系和自然种群的繁殖力、存活率和发育历期，测定若虫在5℃和-20℃下的存活率以及若虫和成虫的过冷却点，通过品系间存活率、发育历期、生殖力和过冷却点的比较分析，确定灰飞虱长、短翅型品系对高温和低温的耐受能力。【结果】在25℃, 30℃和35℃下，灰飞虱自然种群雌成虫的繁殖力均显著高于室内筛选后的长、短翅型品系，而长、短翅型品系雌成虫之间的繁殖力均无显著差异；长、短翅型品系的繁殖力在25℃和30℃之间均无显著差异，但自然种群在25℃下的繁殖力显著高于30℃条件下的繁殖力；35℃下长、短翅型品系基本无若虫产生。25℃下长翅型品系、短翅型品系和自然种群若虫的存活率无显著差异，但在30℃下，短翅型品系若虫的存活率显著低于自然种群，而与长翅型品系差异不显著；35℃下长、短翅型品系的若虫最长只能存活到3龄，且两品系间无显著差异，而自然种群可存活到5龄。25℃下，短翅型品系若虫的发育历期显著短于自然种群，而与长翅型品系无差异；但是在30℃下，短翅型品系若虫历期显著长于长翅型品系和自然种群。长翅型品系、短翅型品系和自然种群灰飞虱3-4龄若虫在5℃低温下的存活天数无显著差异，并且长翅和短翅型品系在-20℃极端低温下暴露10 min后其死亡率也无显著差异且均显著高于自然种群。3个品系(种群)成虫的过冷却点无显著差异，但5龄若虫的过冷却点表现为短翅型品系显著高于自然种群，而与长翅型品系无显著差异。【结论】经连续定向选育的灰飞虱长、短翅型品系对低温和高温的适应力基本相当，且低于自然种群。在高温条件下灰飞虱短翅型品系的发育速率低于长翅型品系。

Abstract: 【Aim】 There are long-winged and short-winged morphs in populations of the small brown planthopper (SBPH), Laodelphax striatellus. The wing morphs of SBPHs are affected by the genetic and environmental factors. The aim of this study is to illustrate the adaptability of the long-winged and short-winged strains of SBPHs to high and low temperatures. 【Methods】 The selection of long-winged and short-winged strains in SBPHs was performed under a constant condition, and the strains with long and short wings were set up after 63 and 65 generations of selection, respectively. The fecundity, survival rates and developmental duration of populations of the long-winged and short-winged strains and a wild population collected from rice filed in Nanjing were measured at 25, 30 and 35℃. The survival rates of nymphs of these three populations were measured after exposure to 5℃ and -20℃. The supercooling points of nymphs and adults of these three populations were also measured. The adaptability of long-winged and short-winged strains to high and low temperatures was analyzed by comparing the survival rate, developmental duration, fecundity and supercooling point. 【Results】 The fecundity of the female adults of the long-winged and short-winged strains of SBPH was significantly lower than that of the wild population at 25, 30 and 35℃, and there was no significant difference in the fecundity between the short-winged and long-winged strains. The fecundity of the female adults of the short-winged or long-winged strain at 25℃ was not significantly different than that at 30℃, but the fecundity of the female adults of the wild population at 25℃ was significantly higher than that at 30℃. At 35℃, the short-winged and long-winged strains hardly produce nymphs. The nymphal survival rate at 25℃ was similar among the short-winged strain, long-winged strain and wild population. But at 30℃, the nymphal survival rate of the short-winged strain was significantly lower than that of the wild population, and there was no significant difference in the nymphal survival rate between the short-winged and long-winged strains. At 35℃, the nymphs of the short-winged and long-winged strains only survived to the 3rd instar, but the nymphs of the wild population could survive to the 5th instar. The nymphal duration of the short-winged strain at 25℃ was significantly shorter than that of the wild population, but did not differ from that of the long-winged strain. At 30℃, however, the nymphal duration of the short-winged strain was significantly longer than those of the long-winged strain and the wild population. The survival days of the 3rd-4th instar nymphs of the long-winged strain were not different from those of the short-winged strain and the wild population at 5℃. The mortality rates of nymphs of the long-winged strain and the short-winged strain after exposure to -20℃ for 10 min showed no significant difference, but were significantly higher than that of the wild population. The supercooling points of adults were not significantly different among the short-winged strain, long-winged strain and wild population. However, the supercooling point of the 5th instar nymphs of the short-winged strain was significantly higher than that of the wild population, but showed no significant difference from that of the long-winged strain. 【Conclusion】 The adaptability of the long-winged and short-winged strains of SBPH to high and low temperatures is similar but lower than that of the wild population. The nymphal development of the short-winged strain of SBPH is slower than that of the long-winged strain under conditions of high temperature.