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# Differentiation involving Pi

1. Sep 16, 2007

### fk378

[SOLVED] Differentiation involving Pi

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

Differentiate sin(t) + (pi)cos(t)

2. Relevant equations

Am I supposed to leave pi alone and just solve for the cos and sin parts? Or do I get f'(x) of pi as well?

3. The attempt at a solution

I know that f'(x) of sin(t) = cos(t)
Now what do I do with the (pi)cos(t) part? Do I say that the slope of pi is zero, therefore the derivative of (pi)cos(t) is 0, then the answer would be just sin(t) for the whole equation.

OR

Leave pi there, and have f'(x) of cos(t)= -sin(t) so that would make: cos(t) + (pi)(-sin[t]) ?

2. Sep 16, 2007

### Staff: Mentor

pi is a constant, so treat it like any other number. What's the derivative of 5x? Of pi*x?

3. Sep 16, 2007

### Kurdt

Staff Emeritus
Pi is just a constant. What do you know of the derivative of $a cos(t)$ where a is a constant?

4. Sep 16, 2007

### fk378

Interesting way to put it. So is that what pi will be in most differentiation cases? How will you know if they are referring to pi as the radian in which the slope = 0?

5. Sep 16, 2007

### Staff: Mentor

Huh? Pi is a number!

6. Sep 16, 2007

### fk378

Yes, but Pi is also a radian measure of 180 degrees.

7. Sep 16, 2007

### Staff: Mentor

True--the number of radians in 180 degrees equals pi. Pi is also the number of square meters within a circle who's radius is one meter. And many other things. But in all cases, pi is just a pure number--and that's all you care about when differentiating an expression that contains pi.

8. Sep 16, 2007

### Kurdt

Staff Emeritus
That would only matter if pi was the argument of one of the trig functions, which it is not. It is merely a number multiplying the function.

9. Sep 16, 2007

### fk378

Ah, I see. Thank you both :)


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<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
You are reading an older version of this FlexBook® textbook: Algebra Explorations Concepts, Pre-K through Grade 7 Go to the latest version.

# 3.6: Stars and Moons

Difficulty Level: At Grade Created by: CK-12

Can you continue the pattern shown below? In this concept, we will practice figuring out patterns and then extending them.

### Guidance

In order to continue patterns like the one with stars and moons shown above, we can use the problem solving steps to help.

• First, describe what you see.
• Second, figure out what your job is. In these problems, your job will be to continue the pattern and fill in the empty cards.
• Third, make a plan . Decide how you will figure out and then continue the pattern.
• Fourth, solve . Fill in the empty cards with the correct number of stars and moons.
• Fifth, check . State the pattern you found and verify that it worked for all of the cards.

#### Example A

Solution:

We can use the problem solving steps to help us extend this pattern.

$& \mathbf{Describe:} && \text{There are} \ 6 \ \text{cards.}\\&&& \text{Card} \ 1:1 \ \text{star and} \ 1 \ \text{moon}\\&&& \text{Card} \ 2:1 \ \text{star and} \ 2 \ \text{moons}\\&&& \text{Card} \ 3:1 \ \text{star and} \ 3 \ \text{moons}\\&&& \text{Card} \ 4,5 \ \text{and} \ 6 \ \text{are empty.}\\& \mathbf{My \ Job:} && \text{Figure out the pattern.}\\&&& \text{Make drawings on the empty cards.}\\& \mathbf{Plan:} && \text{Look at the card numbers. Figure out the pattern of stars.}\\&&& \text{Look at the card numbers. Figure out the pattern of moons.}\\&&& \text{Make the drawings.}\\& \mathbf{Solve:}$

$& \mathbf{Check:} && \text{The number of moons is the same as the card number.}\\&&& \text{The number of stars is always one.}$

#### Example B

Solution:

We can use the problem solving steps to help us extend this pattern.

$& \mathbf{Describe:} && \text{There are} \ 6 \ \text{cards.}\\&&& \text{Card} \ 1:1 \ \text{star and} \ 1 \ \text{moon}\\&&& \text{Card} \ 2:2 \ \text{stars and} \ 2 \ \text{moons}\\&&& \text{Card} \ 3:3 \ \text{stars and} \ 3 \ \text{moons}\\&&& \text{Card} \ 4,5 \ \text{and} \ 6 \ \text{are empty.}\\& \mathbf{My \ Job:} && \text{Figure out the pattern.}\\&&& \text{Make drawings on the empty cards.}\\& \mathbf{Plan:} && \text{Look at the card numbers. Figure out the pattern of stars.}\\&&& \text{Look at the card numbers. Figure out the pattern of moons.}\\&&& \text{Make the drawings.}\\& \mathbf{Solve:}$

$& \mathbf{Check:} && \text{The number of moons is the same as the card number.}\\&&& \text{The number of stars is the same as the number of moons.}$

#### Example C

Solution:

We can use the problem solving steps to help us extend this pattern.

$& \mathbf{Describe:} && \text{There are} \ 6 \ \text{cards.}\\&&& \text{Card} \ 1:2 \ \text{stars and} \ 1 \ \text{moon}\\&&& \text{Card} \ 2:4 \ \text{stars and} \ 1 \ \text{moon}\\&&& \text{Card} \ 3:6 \ \text{stars and} \ 1 \ \text{moon}\\&&& \text{Card} \ 4,5 \ \text{and} \ 6 \ \text{are empty.}\\& \mathbf{My \ Job:} && \text{Figure out the pattern.}\\&&& \text{Make drawings on the empty cards.}\\& \mathbf{Plan:} && \text{Look at the card numbers. Figure out the pattern of stars.}\\&&& \text{Look at the card numbers. Figure out the pattern of moons.}\\&&& \text{Make the drawings.}\\& \mathbf{Solve:}$

$& \mathbf{Check:} && \text{The number of moons is always one.}\\&&& \text{The number of stars is twice as many as the card number.}$

#### Concept Problem Revisited

We can use the problem solving steps to help us extend this pattern.

$& \mathbf{Describe:} && \text{There are} \ 6 \ \text{cards.}\\&&& \text{Card} \ 1:2 \ \text{stars and} \ 1 \ \text{moon}\\&&& \text{Card} \ 2:3 \ \text{stars and} \ 2 \ \text{moons}\\&&& \text{Card} \ 3:4 \ \text{stars and} \ 3 \ \text{moons}\\&&& \text{Card} \ 4,5 \ \text{and} \ 6 \ \text{are empty.}\\& \mathbf{My \ Job:} && \text{Figure out the pattern.}\\&&& \text{Make drawings on the empty cards.}\\& \mathbf{Plan:} && \text{Look at the card numbers. Figure out the pattern of stars.}\\&&& \text{Look at the card numbers. Figure out the pattern of moons.}\\&&& \text{Make the drawings.}\\& \mathbf{Solve:}$

$& \mathbf{Check:} && \text{The number of moons is always the same as the card number.}\\&&& \text{The number of stars is one more than the number of moons.}$

### Vocabulary

One type of pattern is when the number of a certain object increases, decreases, or stays the same in a consistent way. In this concept, we saw patterns of stars and moons. With any pattern you should be able to describe the pattern and how to get from one step of the pattern to the next.

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Recognitions:
Gold Member

## Progressive Taxation

What are the arguments for\against a "flat tax" where everybody pays a share of the taxes as a share of their income.

$100 total income,$10 taxes
Person 1 Income: $80 Person 2 Income:$15
Person 3 Income: $5 Person 1 Taxes:$8
Person 2 Taxes: $1.5 Person 3 Taxes:$0.5

 PhysOrg.com social sciences news on PhysOrg.com >> Daylight Saving Time spurs drop in crime rate>> Student attitude of 'excessive entitlement' may result in exam failure>> Female conversion to Islam in Britain examined in unique research project
 Mentor The problem is that half dollar paid by the person who makes five dollars hurts a whole lot more than does the eight dollars paid by the person who makes eighty. The person who makes five dollars might well have to forego eating entirely for a few days to pay his share. The person who makes eighty might will have to forego eating the caviar appetizer.
 Recognitions: Gold Member Science Advisor Staff Emeritus This looks, to me, an awful lot like one of those simple homework problems whose point is to get you to thinking about the possibilities. I don't see how other people giving you suggestions will help you do that.

Recognitions:
Gold Member

## Progressive Taxation

Not a homework problem, just a musing. =) I wasn't even sure what the name of this type of taxation system was (thus the incorrect title). Once I figure it out I had requested to delete it, but someone commented on it so I left it. Sorry.

DHs example assumes that the taxes aren't being used to help the poor I guess.

Mentor
 Quote by DavidSnider DHs example assumes that the taxes aren't being used to help the poor I guess.
I don't see that assumption. However, there can be two ways to look at it: one is looking at only taxes paid on income from a job. Though that's the usual way to look at it, it can be a little misleading, imo. To me, direct cash subsidies are essentially a direct tax rebate.

You didn't specify in your example which way you are looking at the issue, but at least in the US, if you use the first method a very large fraction pays no taxes and if you look at it the second way, a sizeable fraction pays negative taxes. Any "flat tax" plan needs to specify how it deals with those government subsidies to be properly understood/evaluated.

 mostly it is due to what is called the "law of diminishing returns" D. H. eluded to this in his post earlier. The thinking behind it is something like this. All taxes hurt(because you are loosing your hard work) however not having government can hurt more(everyone has the choice of moving to Antarctica, or another remote place without government, but I digress) so the thinking behind progressive taxation is that the "hurt" should be equal to all, and in that way more money can be collected fairly. Because the hurt of losing 100 dollars to a person who makes 1,000 dollars a year is much greater than loosing 10,000 dollars to a person who makes 100,000, even though this is both an example of 10% taxation. I could probably explain it better in a more drawn out fashion, but hey this is just a quick answer
 Recognitions: Gold Member If there is a "law of diminishing returns" then why do rich people object to high taxes?
 why do poor people object to taxes? Americans are perpetually hating and trying to get rid of taxes, it's just part of our nature as humans, but we also enjoy the benefits of our military, social security, Medicare, some welfare and education. But without struggle and compromise we would not have a democracy.

Recognitions:
Gold Member
 Quote by D H ... The person who makes eighty might will have to forego eating the caviar appetizer.
Perhaps. Or perhaps person 1 ($80 income/$8 tax) would have to forego creating another job for a person 3 ($5 income,$0.5 tax)

Recognitions:
Gold Member
The number of countries with a flat tax rate has been growing:
http://en.wikipedia.org/wiki/Flat_ta...at_tax_systems
The Baltic states in particular have almost all picked it up since the fall of the Berline wall Estonia uses 21% for example:
 "I must say Steve Forbes was a genius," [Estonian]Prime Minister Andrus Ansip declared during an interview in his hilltop office. "
In the US recently we had a candidate (R) for in the NJ 2009 race for governor, Steve Lonegan, calling for a flat tax. He proposed a 2.98% flat rate to replace the current 1.4% to 8.97% scale. Lonegan was beaten in the primary by Christie.
http://online.wsj.com/article/SB124329298290552503.html
(R) candidate for President Fred Thompson proposed an almost flat tax, two tax rates of 10% and 25%, and McCain said he'd sign one if 'it crossed his desk'

Mentor
Article today on CNN.com about the fraction of Americans who don't pay income tax:
 In 2009, roughly 47% of households, or 71 million, will not owe any federal income tax, according to estimates by the nonpartisan Tax Policy Center. Some in that group will even get additional money from the government because they qualify for refundable tax breaks. The ranks of those whose major federal tax burdens net out at zero -- or less -- is on the rise. The center's original 2009 estimate was 38%. That was before enactment in February of the \$787 billion economic recovery package, which included a host of new or expanded tax breaks.... When considering federal income taxes in combination with payroll taxes, the percent of households with a net liability of zero or less is estimated to be 24% this year, according to the Tax Policy Center's estimates.
http://money.cnn.com/2009/09/30/pf/t...ex.htm?cnn=yes


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How is current affected by a charging capacitor in parallel to a resistor?

Imagine a circuit with a battery followed by a lightbulb and an uncharged capacitor in parallel. Next to it is an open switch. When I close the switch completing the circuit, does the brightness of the lightbulb change over time due to the capacitor charging?

My reasoning is that the brightness must change slightly as an uncharged capacitor initially does have current flowing through its path. In an uncharged state, a capacitor can be equated to a resistor (air over a short distance still having a high resistance, of course).

So for the while the capacitor is not yet fully charged, it is lowering the effective resistance of the entire circuit thus allowing more total current to be generated with our constant battery EMF. This extra current will allow more power usage for our lightbulb by the equation $$P=I^2 R$$ .

I had a question like such in a HS class and the teacher's explanation was that the brightness should not change because the potential difference across the lightbulb is always the same. I do see even with my reasoning that perhaps the extra current generated would have to be split across both paths meaning maybe that the lightbulb always has the same current flowing through it, regardless. However, for my own understanding I would like to see a more detailed response as my teacher told me as well that the current should be constant. Maybe it could be approximated to be unaffected by our capacitor charging, but I am unsure if he is totally right.

Kirchhoff’s Junction Rule Applies: $$\frac{V_T}{R_T}=\frac{V_L}{R_L} + \frac{V_C}{R_C}$$. The constant value $$\frac{V_L}{R_L}$$ indicates current drawn through the lightbulb. This does not change even if we vary the total resistance by adding parallel components with resistance. Of course adding straight wire in parallel would just make the voltage drop value to be zero and short the circuit.


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# The Simple World Hypothesis

post by DragonGod · 2017-06-05T19:34:06.488Z · score: 2 (4 votes) · LW · GW · Legacy · 15 comments

## Contents

Introduction
Simplicity
Interlude
Weak Hypothesis
Strong Hypothesis
Rules That Govern Universes.
Degree of Functionality
Simulating a Universe.
Expressive Power.
Criticism of the Simple world hypothesis
Trivia
Conclusion
None

Part of a Series in the Making: "If I Were God".

# Introduction

The current universe is the simplest possible universe with the same degree of functionality.

This hypothesis posits that the current universe is the simplest universe possible which can do all that our universe can do. Here, simplicity refers to the laws which make up the universe. It may be apt to mention the Multiverse Axioms at this juncture:
Axiom 1 (axiom of consistency):

Any possible universe is logically consistent and strictly adheres to well-defined laws.

Axiom 2 (axiom of inclusivity):

Whatever can happen (without violating 1) happens—and in every way possible (without violating 1).

Axiom 3 (axiom of simplicity):
The underlying laws governing the Multiverse are as simple as possible (while permitting 1 and 2).

The simple world hypothesis posits that our universe has the fewest laws which can enable the same degree of functionality that it currently possesses. I’ll explain the concept of “degree of functionality”. Take two universes: U_i and U_j with degrees of functionality d_i and d_j. Then the below three statements are true:
d_i > d_j implies that U_i can simulate U_j.
d_j < d_i implies that U_j cannot simulate U_i. d_i = d_j implies that U_i can simulate U_j, and U_j can in turn simulate U_i.

Let’s consider a universe like Conway’s Game of Life. It is far simpler than our universe and possesses only four laws. The simple world hypothesis argues that Conway’s Game of Life (U_c) cannot simulate our universe (U_0). The degree of functionality of Conway’s Game of Life (d_c) < the degree of functionality of our universe d_0. An advance prediction of the simple world hypothesis regarding U_c is the below:

Human level intelligence cannot emerge in U_c.

The above implicitly assumes that Conway’s Game of Life is simpler than our universe—is that really true?

# Simplicity

It is only prudent that I clarify what it is I mean by simplicity. For any two Universes U_i and U_j, let their simplicity be denoted S_i and S_j respectively. The simplicity of a universe is the Kolmogorov complexity of the set of laws which make up that universe.
For U_c, those laws are:
1. Any live cell with fewer than two live neighbours dies, as if caused by underpopulation.
2. Any live cell with two or three live neighbours lives on to the next generation.
3. Any live cell with more than three live neighbours dies, as if by overpopulation.
4. Any dead cell with exactly three live neighbours becomes a live cell, as if by reproduction.

At this point, I find it prudent to mention the topic of Kolmogorov Complexity. The Kolmogorov Complexity of an object is the length (in bits) of the shortest computer program (in a predetermined language) that produces that object as output. Let’s pick any (sensible) Turing Complete Language T_x. We’re concerned with the binary length of the shortest T_x program that produces the laws that describe U_i. When discussing the simplicity of a universe, we refrain from mentioning its initial state; the degrees of functionality are qualitative and not quantitative. For example, A universe U_1 which contains only the milky way, will have d_1 = d_0. As such, we take only the Kolmogorov complexity of the laws describing the Universe, and not the Kolmogorov complexity of the universe itself. For any U_i and U_j, let the Kolmogorov complexity of the laws describing U_i and U_j be K_i and K_j respectively.

S_i = K_i-1
S_j = K_j-1

# Interlude

Let the set of universes which confirm to the multiverse axiom be denoted M.

## Weak Hypothesis

According to the simple world hypothesis, no U_z with K_z < K_0 has d_z >= d_0.

To be mathematically precise:
For all U_z in M there does not exist U_z: K_z < K_0 and d_z >= d_0.

## Strong Hypothesis

The strong hypothesis generalises the weak form of the simple world hypothesis to all universes.

The degree of functionality of a universe is directly proportional to its Kolmogorov complexity.

To be mathematically precise:
For all U_z, U_y in M there does not exist U_z: K_z < K_y and d_z >= d_y.

# Rules That Govern Universes.

When I refer to the “rules that govern a universe”, or “rules upon which a universe is constructed”, I refer to a set of axioms. The principles of formal logic are part of the Multiverse axiom, and no possible Universe can violate that. As such, the principles of formal logic are a priori part of any possible Universe U_z in M.

The rules that govern the Universe, are only those set of axioms upon which the Universe is constructed in tandem with the principles of formal logic. For example, in our Universe the laws that govern it would not include Newtonian mechanics (as such is merely a special case of Einstein’s underlying theories on relativity). I suspect (with P > 0.67) that the law(s) that govern our Universe, would be the Theory of Everything (TOE) and/or Grand Unified Theory (GUT). All other laws can be derived from them in combination with the underlying laws of formal logic.

# Degree of Functionality

The degree of functionality of a Universe U_z (d_z) refers to the maximum complexity (qualitatively not quantitatively; e.g. a human brain is more complicated than a supercluster absent of life) that can potentially emerge from that universe from any potential initial state. Taking U_c to illustrate my point, the maximum complexity that any valid configuration of U_c can produce is d_c. I suspect that human level intelligence (qualitatively and not quantitatively; i.e. artificial super intelligence is included in this category. I refer merely to the potential to conceive the thought “dubito, ergo cogito, ergo sum—res cogitans”) is d_0.

# Simulating a Universe.

When I mention a Universe, I do not refer specifically to that Universe itself—and all it contains—but to the set of laws (axioms) upon which that Universe is constructed. Any Universe that has the same base laws as ours—or mathematically/logically equivalent base laws—is isomorphic to our universe. I shall define a set of Universes A_i. A_i is the set of universes that possess the same set of base laws L_i or a mathematical/logical equivalent. The set of laws that govern our Universe is L_0. In my example above, U_1 is a member of A_0.

Initially, I ignored the initial state/conditions of the Universe stating them irrelevant in respect to describing the universe. For any universe U_i, let the initial state of the universe be F_{i0}. Let the set of all possible initial states (for all universes) be B. B: B = {F_{{i_1}{j_1}}, F_{{i_1}{j_2}}, F_{{i_1}{j_3}}, …., F_{{i_1}{j_n}}, {F_{{i_2}{j_1}}, F_{{i_2}{j_2}}, F_{{i_2}{j_3}}, …., F_{{i_2}{j_n}}, {F_{{i_3}{j_1}}, F_{{i_3}{j_2}}, F_{{i_3}{j_3}}, …., F_{{i_1}{j_n}}, …, F_{{i_n}{j_n}}}. Let the current/final (whichever one we are concerned with) state of any U_i be G_ij.

I shall now explain what it means for a Universe U_i to simulate another Universe U_j.

U_i simulates U_j if for all F_{{i_j}{j_y}} in B, there exists a F_{i{j_l}} such that G_ij = G_{i{j_l}}.

In concise English:

U_i simulates U_j if for every (valid) possible initial configuration of U_j which maps to a current/final state, there exists a valid configuration of U_i which produces U_j’s current/final state.

When I refer to producing the state of another Universe, I refer to expressing all the information that the other universe does. The rules for transformation and extracting of information confirm to the third axiom:

The underlying laws governing the universe are as simple as possible while permitting 1 and 2.

# Expressive Power.

Earlier, I introduced the concept of A_i for any given set of Laws L_i that governs a universe. When we mention U_i, we are in fact talking of U_i in conjunction with some initial state. If we ignore the initial state, we are left with only L_i. I mentioned earlier that the degree of functionality of a Universe is the maximum complexity that can emerge from some valid configuration of that Universe. The expressive power of a universe is the expressive power of it’s L_i.

The expressive power of a given L_i is the set of L_j which L_i can potentially simulate.

The set of L_j that can be concisely and coherently represented in L_i is the expressive power of L_I. I shall once again rely on Conway’s Game of Life (U_c). The 4 laws governing U_c can be represented in L_0, and as such L_0 has an expressive power E_0 >= E_c the expressive power of U_c. As such, E_c is a subset of L_0. If a Universe U_i can simulate another Universe U_J, then it follows that whatever U_j can simulate, then U_i can too. Thus, if U_i can simulate U_j, then E_j is a subset of E_i.

To conceive of a Universe U_i, we merely need conceive L_i. If we can conceive L_i and concisely define it, then it follows that U_0 can simulate U_i. I argue that this is so because if we could conceive and concisely define L_i then U_i can be simulate as a computer program. Any simulation that a subset/member of a universe can perform is a simulation that the universe itself can perform.

An important argument derives from the above:

It is impossible for the human mind (or any other agent) in a universe U_i to conceive another Universe U_j with a greater degree of functionality than U_i.

The above is true, because if we could conceive it, we could define its laws, and if we could define its laws, we could simulate it with a computer program.
The below is also self-evident:

No universe U_i can simulate another universe U_j with a greater degree of functionality than it.
The below is true, because the degree of functionality is defined as the maximum complexity that can arise from a universe. If U_i simulates U_j, and d_i < d_j, then we have a contradiction as U_i simulated more complexity than the maximum complexity U_i can lead to.

Concluding from the above, the below is self-evident:

The degree of functionality of a universe is that universe itself.

The maximum complexity a universe can lead to is itself. Simulating a Universe involves simulating all that universe simulates. Let the maximum complexity that U_i can lead to be denoted C_i. Simulating U_I involves simulating C_i and as such the complexity of simulating U_i >= complexity of simulating C_i. Therefore, the greatest complexity U_i can lead to is a simulation of U_i.

However, can a universe simulate itself? I accepted that as true on principle, but is it really? For a universe to simulate itself, it must also simulate the simulation which would simulate the simulation and beginning an infinite regress. If any universe has finite information content, then it cannot simulate itself?
As such, the universe itself serves as a strict upper boundary for the complexity that a universe can lead to.

If a Universe attempted to simulate itself, how many simulations would there be? Would the cardinality of simulations be countably infinite? Or non-countably infinite? The answer to that question determines how plausible a universe simulating itself would be.

What about U_i being able to simulate U_j, and U_j in turn being able to simulate U_i? This implies U_i can simulate U_j simulating U_i simulating U_j … beginning another infinite regress. How many simulations are needed? Do the universes involved need to be able to hold aleph_k different simulations? Do the laws constructing those universes permit that?

# Criticism of the Simple world hypothesis

While sounding nice in theory, the simple world hypothesis—in both of its forms—offers no insight into the origin of the Universe. One may ask “Why Simplicity?” “What would cause the simple world hypothesis to be true?” “What is necessary for all universes to behave as the simple world hypothesis predicts?” Indeed, might the simple world hypothesis not violate Occam’s razor by positing that all universes confirm to it?

I suggest that the simple world hypothesis does not describe the origin of the universe—that was never its aim to begin with. It merely seeks to describe how universes are, and not how they came to be.

# Trivia

I conceived the simple world hypothesis when I was thinking up a blog post titled “Why Occam’s Razor?”. I had intended to make an argument along the lines of: “Even if the simple world hypothesis is false, Occam’s razor is still valuable because…”, going along that train of thought, I realised that I would have to define the simple world hypothesis.

# Conclusion

I do not endorse this hypothesis; I believe in something called “informed opinion”, and due to my abject lack of knowledge regarding physics I do not consider myself as having an informed opinion on the Universe. Indeed, the simple world hypothesis was conceived to aid an argument I was thinking up to support Occam’s razor. However, I admit that if I were to design the base laws that would be used in addition with the laws constructing each possible universe, then the simple world hypothesis would be true. However, I’m not the one—if there is any—who designed the base laws that would be used in addition with the laws constructing each possible universe, and as such I do not support the simple world hypothesis. Indeed, there is not even enough evidence to locate the simple world hypothesis among the space of possible hypothesis, and as such, I do not—I cannot as long as I profess rationality—accept it—yet.

Indeed, as Aristotle said:

It is the mark of an educated mind to be able to entertain a thought without fully accepting it.

I shall describe the “multiverse axiom” and “base laws” in more detail in a subsequent blog post.

comment by entirelyuseless · 2017-06-06T01:47:25.755Z · score: 4 (4 votes) · LW(p) · GW(p)

The simple world hypothesis argues that Conway’s Game of Life (U_c) cannot simulate our universe (U_0).

Conway's Game of Life is Turing complete, so unless our universe is incomputable, it can be be simulated by Conway's game.

comment by Viliam · 2017-06-08T16:01:55.663Z · score: 0 (0 votes) · LW(p) · GW(p)

Is there good evidence about our universe being or not being computable?

For example, if positions of particles have infinitely many decimal places, then the universe is incomputable, even if its laws are relatively simple. If the positions of particles are computationally finite, that probably requires explanation for why physical processes seem the same if you e.g. rotate them by an arbitrary angle.

comment by entirelyuseless · 2017-06-09T14:15:28.058Z · score: 1 (1 votes) · LW(p) · GW(p)

I think the universe could be computable even if positions have infinitely many decimal places, as long as the sequence is computable. But you are right that it would be incomputable if the sequence is basically random, and there is no proof that things are not like this.

comment by DanWilliams · 2017-08-22T10:08:59.033Z · score: 0 (0 votes) · LW(p) · GW(p)

yes

comment by denimalpaca · 2017-06-08T20:27:20.309Z · score: 0 (0 votes) · LW(p) · GW(p)

If you have a universe of a certain complexity, then to simulate another universe of equal complexity it would have to be that universe to fully simulate it. To simulate a universe, you have to be sufficiently more complex and have sufficiently more expendable energy.

comment by MrMind · 2017-06-08T08:44:26.045Z · score: 0 (0 votes) · LW(p) · GW(p)

Re: axiom 1

Any possible universe is logically consistent and strictly adheres to well-defined laws.

Logically consistent against what set of logical axioms? There are a bunch of logics out there, and one man inconsistency is another man's axiom.

Axiom 2 implies that the set of laws in uncomputable, ergo has no Kolmogorov complexity, which contradicts Axiom 3.

The weak hypothesis is false.

And so on.

comment by DragonGod · 2017-06-08T10:59:28.222Z · score: 0 (0 votes) · LW(p) · GW(p)

The principles of Aristotelian logic.

I don't understand how Axiom 2 implies uncomputability; please explain.

The other universes have their own laws, which work together with $L_{\alpha}$ to create them. Axiom 2 just implies there are an infinite number of universes, and every universe exists. Axiom 2 does not imply that $L_{\alpha}$ contains all possible laws.

comment by MrMind · 2017-06-08T14:22:38.140Z · score: 1 (1 votes) · LW(p) · GW(p)

The principles of Aristotelian logic.

Which is not a consistent set of axioms, but let's just pretend you said "classical propositional logic". Then why this and not something else, say intuitionistic, relevant, modal, etc.?

I don't understand how Axiom 2 implies uncomputability; please explain.

Well, as per the First Incompleteness Theorem, there's no recursive set of axioms complete for arithmetics. So if the universe realizes all arithmetic truth at least its set of laws is non-recursive, that is has no finite Kolmogorov complexity.
...
unless you meant that the Multiverse realizes all possibilities.

On the other hand, the maximum complexity realizable by a simulation is a function not only of its laws but also of its available space. As entirelyuseless already pointed out, Uc can simulate any computable universe, given enough space.

comment by turchin · 2017-06-05T22:03:25.358Z · score: 0 (0 votes) · LW(p) · GW(p)

I think also that it would be great to show if this theory applied to the actual physical universe in which we exist, or it just describes a type of mathematical objects as sets or groups.

If it apllied to physical universe, we can't ignore the question of its origin, as it will have direct correlation with its observed complexity. If mathematical universe hypothesis (MUH) is true, and all math objects exists, than more complex objects should dominate. But it contradict our expiriences and Occam razor. There is a need to bring order to all possible universes. And here Logical universes hypothesis (LUH) helps. It claims that existing math objects following from simple to more complex in logical order, like 1,2,3. In that case simplest math objects appear first - and we get support to your Axiome 3.

I explored different ways of the universe origin and its correlation with observation here: http://lesswrong.com/lw/nw7/the_map_of_ideas_how_the_universe_appeared_from/

comment by turchin · 2017-06-05T21:43:39.848Z · score: 0 (0 votes) · LW(p) · GW(p)

I have been thinking about the same post about the Occam razor, and stuck in question: "what is the medium complexity of the true hypothesis from all the field of the hypotheses". I hope that my question is clear without the need to longer explained what did I mean. Anyway, I will try to explain it a little bit.

Occam Razor doesn't say that simplest hypothesis is true. It just says that probability of truth is diminishing as the complexity of the hypothesis is growing. It is clear that most times the true hypothesis will be somewhere after pN1+pN2 +pNn=0.5, where n is the number of hypotheses ranged by their complexity, and p(N) is the probability that a given hypothesis is true according to Occam razor principle.

I also have a feeling that in EY writing it is always assumed that Occam razor law is diminishing very quickly and so most simple hypothesis has an overwhelming probability to be true. However, I also have a feeling that in real life medium complexity hypotheses are dominating, like somewhere near 100 from the beginning. It results in much more complex and unpredictable world.

It looks like you have been thinking in the similar direction - do you have any ideas about the medium complexity of true hypotheses?

comment by TheAncientGeek · 2017-06-06T14:45:09.207Z · score: 1 (1 votes) · LW(p) · GW(p)

"Simple" in O's R means "simplest that explains the facts at all". So you delete a bunch of hypotheses that are too simple to be explanatorily adequate, and then you delete the ones that are unnecessarily complex. That gives you soem sort of medium complexity.

comment by turchin · 2017-06-06T15:59:41.985Z · score: 0 (0 votes) · LW(p) · GW(p)

My question was more about the medium length of an algorithm predicted by Solomonov induction. Update: According to https://wiki.lesswrong.com/wiki/Solomonoff_induction the weight of hypothesis is diminishing very quickly, like 2power(-n), where n is the program length. And in this case, the medium level will somewhere between first and second hypothesis.

comment by TheAncientGeek · 2017-06-14T12:03:14.302Z · score: 0 (0 votes) · LW(p) · GW(p)

Are you using medium to mean median?

comment by turchin · 2017-06-14T13:26:55.013Z · score: 0 (0 votes) · LW(p) · GW(p)

Yes, by mistake :(

comment by DanWilliams · 2017-08-22T10:13:20.097Z · score: -3 (2 votes) · LW(p) · GW(p)

I can say for sure that I do not have an "informed opinion" about physics and I also know that I do not have such knowledge about the Universe. But after reading your Blog, I agree with the above. All these hypotheses also have the opposite side, which does not prove the existence of a simple world hypothesis. There are many resources to study this. This, at least, does not require physical evidence, only pre-training and logistical skills are required.


text:
# Zac Hatfield Dodds(Zac Hatfield-Dodds)

Karma: 610

Researcher at Anthropic, previously #3ainstitute; interdisciplinary, interested in everything; ongoing PhD in CS (learning / testing / verification), open sourcerer, more at zhd.dev

• “maximize the expected amount of money in this bank account until 1 day from now, then maximize the probability of shutting yourself off”… might cause a lot of damage, but it probably wouldn’t end the world in pursuit of these objectives.

This is not actually a limited-horizon agent; you’ve just set a time at which it changes objectives. And wouldn’t ending the world be the most reliable way to ensure pesky humans never turn you back on?...

(unfortunately thinking about constraints you can place on an unaligned agent never leads anywhere useful; alignment is the only workable solution in the long term)

• Probably since prehistory and certainly since antiquity we’ve had some ‘mesa’/‘runtime’ understanding of heritability, in contrast to (presumably) all other animals.

No, not so much. See e.g. https://www.gwern.net/reviews/Bakewell

Like anything else, the idea of “breeding” had to be invented. That traits are genetically-influenced broadly equally by both parents subject to considerable randomness and can be selected for over many generations to create large average population-wide increases had to be discovered the hard way, with many wildly wrong theories discarded along the way. Animal breeding is a case in point, as reviewed by an intellectual history of animal breeding, Like Engend’ring Like, which covers mistaken theories of conception & inheritance from the ancient Greeks to perhaps the first truly successful modern animal breeder, Robert Bakewell (1725–1795).

Why did it take thousands of years to begin developing useful animal breeding techniques, a topic of interest to almost all farmers everywhere, a field which has no prerequisites such as advanced mathematics or special chemicals or mechanical tools, and seemingly requires only close observation and patience? … What is most interesting is the intellectual history we can extract from it in terms of inventing heritability and as important, one of the inventions of progress in the gradual realization that selective breeding was even possible.

• I enjoyed the whole paper! It’s just that “read sections 1 through 8” doesn’t reduce the length much, and 5-6 have some nice short results that can be read alone :-)

• The paper is really only 28 pages plus lots of graphs in the appendices! If you want to skim, I’d suggest just reading the abstract and then sections 5 and 6 (pp 16--21). But to summarize:

• Do neural networks learn the same concepts as humans, or at least human-legible concepts? A “yes” would be good news for interpretability (and alignment). Let’s investigate AlphaZero and Chess as a case study!

• Yes, over the course of training AlphaZero learns many concepts (and develops behaviours) which have clear correspondence with human concepts.

• Low-level / ground-up interpretability seems very useful here. Learned summaries are also great for chess but rely on a strong ground-truth (e.g. “Stockfish internals”).

• Details about where in the network and when in the training process things are represented and learned.

The analysis of differences between the timing and order of developments in human scholarship and AlphaZero training is pretty cool if you play chess; e.g. human experts diversify openings (not just 1.e4) since 1700 while AlphaZero narrows down from random to pretty much the modern distribution over GM openings; AlphaZero tends to learn material values before positions and standard openings.

• On a quick skim it looks like that fails both “not equivalent to executing the model” and the float32 vs problem.

It’s a nice approach, but I’d also be surprised if it scales to maintain tight bounds on much larger networks.

• Ah, crux: I do think the floating-point matters! Issues of precision, underflow, overflow, and NaNs bedevil model training and occasionally deployment-time behavior. By analogy, if we deploy an AGI the ideal mathematical form of which is aligned we may still be doomed, even it’s plausibly our best option in expectation.

Checkable meaning that I or someone I trust with this has to be able to check it! Maxwell’s proposal is simple enough that I can reason through the whole thing, even over float32 rather than , but for more complex arguments I’d probably want it machine-checkable for at least the tricky numeric parts.

• First, an apology: I didn’t mean this to be read as an attack or a strawman, nor applicable to any use of theorem-proving, and I’m sorry I wasn’t clearer. I agree that formal specification is a valuable tool and research direction, a substantial advancement over informal arguments, and only as good as the assumptions. I also think that hybrid formal/empirical analysis could be very valuable.

Trying to state a crux, I believe that any plan which involves proving corrigibility properties about MuZero (etc) is doomed, and that safety proofs about simpler approximations cannot provide reliable guarantees about the behaviour of large models with complex emergent behaviour. This is in large part because formalising realistic assumptions (e.g. biased humans) is very difficult, and somewhat because proving anything about very large models is wildly beyond the state of the art and even verified systems have (fewer) bugs.

Being able to state theorems about AGI seems absolutely necessary for success; but I don’t think it’s close to sufficient.

• I note that this seems pretty strongly disanalogous to any kind of safety proof we care about, and doesn’t generalise to any reasoning about nonzero sensitivity. That said your assumptions seem fair to me, and I’d be happy to pay out the prize if this actually works.

• I have an optional internal monologue, and programming or playing strategy games is usually a non-verbal exercise.

I’m sure you could in principle (though not as described!) map neuron firings to a strongly predictive text stream regardless, but I don’t think that would be me. And the same intuition says it would be possible for MuZero; this is about the expressiveness of text rather than monologue being a key component of cognition or identity. Conversely, I would expect this to go terribly wrong when the tails come apart, because we’re talking about correlates rather than causal structures, with all the usual problems.

• I was halfway through a PhD on software testing and verification before joining Anthropic (opinions my own, etc), and I’m less convinced than Eliezer about theorem-proving for AGI safety.

There are so many independently fatal objections that I don’t know how to structure this or convince someone who thinks it would work. I am therefore offering a \$1,000 prize for solving a far easier problem:

Take an EfficientNet model with >= 99% accuracy on MNIST digit classification. What is the largest possible change in the probability assigned to some class between two images, which differ only in the least significant bit of a single pixel? Prove your answer before 2023.

Your proof must not include executing the model, nor equivalent computations (e.g. concolic execution). You may train a custom model and/or directly set model weights, so long as it uses a standard EfficientNet architecture and reaches 99% accuracy. Bonus points for proving more of the sensitivity curve.

I will also take bets that nobody will accomplish this by 2025, nor any loosely equivalent proof for a GPT-3 class model by 2040. This is a very bold claim, but I believe that rigorously proving even trivial global bounds on the behaviour of large learned models will remain infeasible.

And doing this wouldn’t actually help, because a theorem is about the inside of your proof system. Recognising the people in a huge collection of atoms is outside your proof system. Analogue attacks like Rowhammer are not in (the ISA model used by) your proof system—and cache and timing attacks like Spectre probably aren’t yet either. Your proof system isn’t large enough to model the massive floating-point computation inside GPT-2, let alone GPT-3, and if it could the bounds would be .

I still hope that providing automatic disproof-by-counterexample might, in the long term, nudge ML towards specifiability by making it easy to write and check falsifiable properties of ML systems. On the other hand, hoping that ML switches to a safer paradigm is not the kind of safety story I’d be comfortable relying on.

• The question is whether that decline in effectiveness is because of declining immune response (in which case an identical booster would help) or a shifting distribution of influenza strains—in which case you’d need a different shot. Of course it’s likely to be a mixture, but my understanding is that it’s mostly the latter.

• The (Old Order) Amish are the closest precedent I can think of—very strong maintenance of tradition, internal trade and a little external but tightly constrained by their values and eschewing modern technology, and without external assistance beyond a live-and-let-live approach.


text:
### Home > GB8I > Chapter 5 Unit 6 > Lesson INT1: 5.3.2 > Problem5-106

5-106.

Chris got a summer job at an environmental sciences lab. He was using a microscope to measure the length of a particular organelle in tree sap cells and the diameter of the cell itself. Chris collected the following data. A “$µm$” is a micrometer or one-millionth of a meter. Homework Help ✎

 Length of Organelle ($µm$) $2$ $9$ $7$ $4$ $4$ $9$ $6$ $2$ Diameter of Cell ($µm$) $46$ $34$ $36$ $42$ $46$ $36$ $42$ $45$
• Use your calculator to make a scatterplot.
Complete and draw $LSRL$.
Verify linearity with a residual plot.
Describe the form, direction (including the slope and $y$-intercept in context),
strength (including an interpretation or $r$ and $R^2$), and possible outliers.
Draw upper and lower bounds for the model used for prediction.

1. What would you include in a mini-report that fully describes all aspects of a linear association? Make as detailed a list as you can.

2. Fully describe all aspects of the linear association in context. Include appropriate graphs.


text:
# Global symplectic Lanczos method with application to matrix exponential approximation

Document Type : Research Article

Authors

1 Laboratory LabSI, Faculty of Science, University Ibn Zohr, Agadir

2 Laboratory LAMAI, Faculty of Science and Technology, University Cadi Ayyad, Marrakesh

Abstract

It is well-known that the symplectic Lanczos method is an efficient tool for computing a few eigenvalues of large and sparse Hamiltonian matrices. A variety of block Krylov subspace methods were introduced by Lopez and Simoncini to compute an approximation of $\exp(M)V$ for a given large square Hamiltonian matrix $M$ and a tall and skinny matrix $V$ that preserves the geometric property of $V$. For the same purpose, in this paper, we have proposed a new method based on a global version of the symplectic Lanczos algorithm, called the global $J$-Lanczos method ($GJ$-Lanczos). To the best of our knowledge, this is probably the first adaptation of the symplectic Lanczos method in the global case. Numerical examples are given to illustrate the effectiveness of the proposed approach.

Keywords


text:
# Gaussian vectors, half-spaces, and convexity

Let A be a subset of R^n and let B be a half-space with the same Gaussian measure as A. For a pair of correlated Gaussian vectors X and Y, Pr(X \in A, Y \in A) is smaller than Pr(X \in B, Y \in B); this was originally proved by Borell, who also showed various other extremal properties of half-spaces. For example, the exit time of an Ornstein-Uhlenbeck process from A is stochastically dominated by its exit time from B. We will discuss these (and other) inequalities using a kind of modified convexity.

This talk is part of the Statistics series.


text:
Two burning ropes measure 5 minutes

Today I was at a job interview and the last question was, "How can I measure 5 minutes by lighting two ropes that each take an hour to burn but do not burn uniformly?" (classical).

I know how to measure 15 minutes and 45 minutes, but 5 minutes....?

• can you cut or burn the ropes? – cats Nov 17 '16 at 22:07
• you can cut and burn them if you want, but burning is not uniform as usual. – user32000 Nov 17 '16 at 22:08
• Does one rope burn for 15min and the other 45min? This isn't clear in the question... – aznbanana9 Nov 17 '16 at 22:10
• This answer seems to imply that it is impossible. It states that you can only measure time intervals that can be expressed as $\frac{m}{2^n}$ hours for integers $m$ and $n$. 5 minutes is $\frac1{12}$ of an hour, an dyou can't express $\frac1{12}$ as $\frac{m}{2^n}$, so it seems that your task is impossible. – GentlePurpleRain Nov 17 '16 at 22:13
• You light one of the ropes, and use the light from it to look at your watch. – Sconibulus Nov 17 '16 at 22:28

Cut the first rope into 12 pieces and light one end of each. Throw the second rope in the trash. If at any time one of the twelve segments is about to be completely consumed, cut some of the extra off of any of the other longer pieces and attach to the nearly-consumed segment, so that all twelve segments finish burning at the exact same time. Then 60 minutes of rope is consumed in 5 minutes.

• Come on. Seriously, you're accepting this? – Rubio Nov 17 '16 at 22:30
• Well the cuttingextra part part is a little bit too much but... – user32000 Nov 17 '16 at 22:33
• @Rubio the other comments on the question point out that a 5 minute interval isn't possible using the standard method - the only way around it is to cheese the non-homogeneous nature of the ropes out of the problem. – Avarkx Nov 17 '16 at 22:35
• @user32000 What they probably should have said is "Oh, I copied the question I was meant to ask you down wrong." Sounds like you might have dodged a bullet in terms of your future employment, imo – Avarkx Nov 17 '16 at 22:39
• Please don't curse. Curse free communities are nice communities. – greenturtle3141 Nov 17 '16 at 22:39


text:
How to calculate formula from text variable.

Hello All NAV Developers,

We have a requirement where the user will put a string on each Item card and system should calculate the formula by replacing the actual value.

On Item1

Filed Name VALUE

FORMULA ELEMENT “(LxWxD)^2”

based on the actual values of L, W and D system should replace then and calculate the formula and assign it in a variable.

The above mentioned formulas will be different item to item so we need to have generic code to cater all the options.

Any suggestion on this will be highly appreciated.

Regards,

Hi,

http://mibuso.com/dlinfo.asp?FileID=820

http://gotcal.com/index.php/2010/06/evaluate-formulas-in-dynamics-nav-2/


text:
## Algebra 2 Common Core

Given: $3x + 2y = 10$ $6x + 4y = 15$ Multiply the first equation, $3x + 2y = 10$, by $2$. $6x + 4y = 20$ Subtract the first equation, $6x + 4y = 20$, from the second equation, $6x + 4y = 15$. $6x + 4x - (6x + 4x) = 15 - (20) \\6x+4x-(6x+4x)=-5$ Subtract each term of the binomial: $6x - 6x + 4x - 4x = -5$ Combine like terms: $0 = -5$ This is a contradiction, as obviously $0 \ne -5$. Thus, there are no solutions.


text:
Matplotlib plot stops responding when trying to close it
0
0
Entering edit mode
4 months ago
Kevin • 0

I am using a library called ProDy for protein analysis. One of the commands in this library creates a plot using matplotlib but when I try closing the plot it freezes and I need to force quit python.

The weird part is that the issue only happens when I try to do a loop to create multiple plots. If I just do one plot I can close it with no issues.

Singe plot code (works):

anm1 = ANM('f2000')
anm1.buildHessian(f2000)
anm1.calcModes()
anm2 = ANM('f1000')
anm2.buildHessian(f1000)
anm2.calcModes()
showOverlapTable(anm1[:], anm2[:]);
plt.show()

Loop code (produces first plot but freezes when trying to close that plot)

pdbs = [f2000, f1000, f1307, f1335]
pdbs_str = ['f2000', 'f1000', 'f1307', 'f1335']

pairs = [(a, b) for idx, a in enumerate(pdbs) for b in pdbs[idx + 1:]]
pairs_str = [(a, b) for idx, a in enumerate(pdbs_str) for b in pdbs_str[idx + 1:]]

# Visualize overlap tables for each pdb pair
for pair, pair_str in zip(pairs, pairs_str):
anm1 = ANM(pair_str[0])
anm1.buildHessian(pair[0])
anm1.calcModes()
anm2 = ANM(pair_str[1])
anm2.buildHessian(pair[1])
anm2.calcModes()
showOverlapTable(anm1[:], anm2[:]);
plt.show()

python python3 ProDy matplotlib • 191 views
0
Entering edit mode

Not a perfect fix but using savefig() instead of showing the plot then saving it allows the loop to work.


text:
# Physics equationsImpulse, momentum, along with movement about a repaired axis

#### A. Regulation connected with Reflectivity as well as Photo Structure by way of Planes Mirror

$\Delta \theta Is equal to \Delta \text/\text$ (illustrated around ). There seemed to be yet another customer within the So that you can discussion boards that had been another artist, My partner and i *think* his or her label was Crinos however won’t be able to call to mind in the event I am just simply just combining in place WWtA products with this particular male. In arithmetic, the angle regarding spinning (or angular position ) is often a statistic in the amount (i.elizabeth., this point of view) than a determine is definitely spun regarding a predetermined factor (most of the core of any radius, when found within ). Last but not least, estimate the skepticism within the pitch (S_m) via $\alpha Equals \Delta \omega/\Delta \text$ Lastly, assess the actual uncertainness while in the tend (S_m) via 2? radical Equals Just one movement.

• We can certainly produce their bond involving straight line speed in addition to angular swiftness into two ways: v=r? as well as ?=v/r.
• In circle action, centripetal velocity means adjustments to the track in the velocity however, not its value. An object having spherical movements ordeals centripetal speeding.
• In spherical motion, straight line acceleration and speed is tangent towards the group of friends within the attraction, which is identified as tangential development.
• tangential acceleration: The actual acceleration in a route tangent to the eliptical within the attraction around round movements.
• The swifter the change throughout angular pace takes place, the larger the angular speed.

Frequency range : 1 Hertz to Five Hz
High levels : Mind traumas, discovering problems, being unable to think, serious ADHD
Low levels : Inability to refresh human body, inability to refresh your brain, terrible snooze
Optimal range : Healthful disease fighting capability, treatment REM sleep Delta has been produced by the Phoenician mail Dalet, along with the traditional Ancient expressions them symbolized a been vocal dental care plosive /d?/. Both people are normally shown within the similar colouring towards some sort custom papers online of supporting simple coloring historical past, and might end up being styled additionally by simply intertwining your words. Find the calculated tend in addition to y-intercept on the details. Angular velocity is the charge involving change involving angular pace.

### Physical Rules:

No matter what items you decide to assess a direction between them, it feels right continue to a similar, although approximations works extremely well in one technique limited to certain weighing machines. Therefore, for example finish revolution the rotation viewpoint is usually: Throughout the process of getting older, reduced Delta waves are developed. Respond to the following concerns. These aspects will be used to full the actual science lab. For case in point, the actual list involving refraction with regard to fresh air is One particular.00, with regard to 100 % pure normal water A person.33 along with overhead cup it’s 1.Fladskrrrm. It is a specifically exciting subject connected with neuro-research presently.

#### Physical Rules:

This result’s the basis to get understanding this devices accustomed to evaluate turn attitudes to generally be radians (rad), characterized in order that: Torque, moment or maybe moment with force is also identified as minute. Try out waves engage in an active purpose around network skill in addition to conversation , nor arise right until four years old enough in mankind. The ideal mental product are able to do of which.

## Were/Therian Image History

Determine this anxiety in the directory regarding refraction with the window. A larger angular pace for that fatigue means a better acceleration for your automobile. Something going through circular action experiences centripetal speeding (while found in the diagram below.) As a result, at and ac usually are perpendicular and outside of one another. This type of rate is really what radians tend to be, even though ratios to exactly 2*pi instead of rates one pattern (normalised wavelength).

Homework informs us that will Delta waves are related to a lot of spontaneous bodily processes such as regulating the cardio and the digestive system methods. This common sense because of this is Theta surf is generally located once you dream and also are asleep, thus showcasing an even more relaxed, start mindstate. Remember that quite a few college textbooks may possibly change ?E by using B as well as e, and ?? by using ?T, they stand for the exact same aspects. Clearly there was yet another person for the To be able to user discussion forums that has been a fellow musician, I personally *think* his or her name appeared to be Crinos however i can’t remember in case I am merely merging right up WWtA things using this man. Answer the following bestessay4u.com/custom-essay queries. You excel any laser light on the outside of an rectangular with window, collecting the next facts: n_2 Means 1, p Means 13.1 \pm 4.Two \mathrm, q Implies -6.Half a dozen \pm 1.A couple of \mathrm. The actual circumference of an circle is 2?r.

This gives united states the actual system: My a couple of at length connected concerns will be: One) Simply what does this individual imply with the specifications connected with speed? is definitely he / she dealing with your magnitude involving v_1, v_2 as well as \Delta v? Explain their bond amongst angular acceleration and speed along with angular velocity Within Supposrr que devices, it really is measured with radians per minute squared (rad/s Two ), which is normally denoted because of the Ancient letter alpha ($\alpha$).

They are supplied by The amount function will it decide on warm some sort of well-insulated room from 12-15 °C to help 21 years of age °C, if the area can be a dice by using area time-span 10m, as well as solidity on the atmosphere is actually One.2kgm ?3 ? For several years, medical doctors as well as scientists include researched these kinds of head lake utilising an EEG or even electroencephalograph, a fancy machine that paths the neuro activity known as brainwaves more than 5 various distinctive channels. This gives you a formulation: A really relation ‘s what radians are, although rates to exactly 2*pi rather then rates to a single never-ending cycle (normalised wavelength). My two at length similar queries are usually: 1) Exactly what does they signify with the size regarding acceleration? is definitely this individual speaking about your scale of v_1, v_2 or perhaps \Delta v? Alpha waves are the actual ‘frequency bridge’ among the cognizant imagining (Beta) in addition to subconscious mind (Theta) head.

#### Physical Rules:

Consider these conditions where angular velocity is just not frequent: if a skater pulls within their biceps and triceps, every time a baby begins your merry-go-round via slumber, or perhaps if a computer’s hard drive retards to a stop any time turned off.

Substance State Temperature (°C) Specific Heat Capability (kJkg ?1 Ok ?1 )
Air gas 23 1.01
Aluminium solid 25 0.90
Animal (along with human being) tissue mixed 25 3.5
Argon gas 25 0.52
Copper solid 25 0.39
Glass solid 25 0.84
Helium gas 25 5.19
Hydrogen gas 25 14.3
Iron solid 25 0.45
Nitrogen gas 25 1.04
Oxygen gas 25 0.92
Uranium solid 25 0.12
Water solid -10 2.05
Water liquid 25 4.18
Water gas 100 2.08

One of its primary employs would be to often be additionally put on, just as one distinguishing token, to ensure that different Therians would probably acknowledge this individual wearing as another Therian, and never feel clumsy concerning starting a dialogue with regards to Therianthropy. In this particular predicament, your Try out ocean control making alpha dog because we all mainly because our body is replying really on the improved Try out action, ordinarily in a condition connected with raised cognitive excitement. If we are doing work in complete harmonizes (the rationale they’re working with v_\perp as well as v_\parallel), then let’s suppose this particular small movement isn’t altering this specifications of your vector, it is only adjusting a path (therefore why we only love v_\perp). Imagine that the vector v_\perp is very small.

Angular Velocity: An automobile moving in a speed v to the correct incorporates a roll revolving by having an angular acceleration ?. The Theta-Delta came to be throughout The year 2003 by using an very early type of This Werelist forums. Not too long ago, they are actually simplified within customer systems by simply our friends at Emotiv. Put together any spreadsheet or computer program to perform your computations under. Can certainly someone reveal to myself in which the item have originated from? Centripetal as well as tangential speeding therefore are verticle with respect to one another. You can make use of any unit you end up picking with regard to viewpoint, level, radians, fertility cycles.

Further Inspections (A couple of items each) Regardless, we squeeze company logo with each other. To get the accurate relationship among angular along with straight line pace, most people once again downsides Around situation variety, angular speeding is conveyed the subsequent:

• angular velocity: Any vector quantity outlining a product around spherical motion; it is magnitude is equal to the interest rate in the chemical and also the path can be verticle with respect on the planes of that circular motion.
• tangential acceleration: This acceleration and speed in a track tangent towards the group of friends for the a growing concern around round activity.
• The speedier the alteration with angular velocity arises, the larger the angular speed.
• angular velocity: A vector range explaining a physical object inside rounded action; it’s size is the same as the velocity from the compound along with the route is actually perpendicular to your planes of circle motion.
• In circle motions, centripetal acceleration and speed describes adjustments in the actual route from the velocity however, not it is specifications. A product considering circular movement ordeals centripetal acceleration and speed.
• In round movement, straight line velocity is usually tangent to your group of friends in the attraction, and is also termed tangential development.
• angular velocity: Any vector quantity conveying a thing around sale paper movements; the magnitude equals the pace from the compound as well as the course is actually vertical with respect on the jet of that round movement.
• We can easily write their bond amongst straight line speed and also angular velocity in two other ways: v=r? or even ?=v/r.

The urgent angular pace is related to dirt pace by The initial romance claims that a linear velocity sixth is v is relative to the range through the middle regarding spinning, thus it is usually largest for your place for the side (biggest s), you may assume. With circular action, there exists acceleration that’s tangent to the radius for the priority (seeing that found in the actual plans down below). Just how much function wouldn’t it decide on warm the well-insulated bedroom by 12-15 °C to help 21 years of age °C, should the area can be a cube having area span 10m, and also the thickness with the fresh air will be Just one.2kgm ?3 ? A rotation viewpoint could be the amount of turn, and is also analogous to be able to straight line mileage.

#### Physical Rules:

That velocity is named tangential speed, at. It is helpful to be aware of exactly how linear along with angular velocity refer. $\Delta \theta Equates to (2 \pi \text)/\text = A couple of \pi$. Being any range, the particular contact maintain particularly completely. Torque, moment as well as moment connected with force is likewise identified as time.

#### Physical Rules:

Explain their bond between angular speed plus angular velocity It must be helpful, evidence-based, in addition to safe. Theta can on the other hand have their own benefits of supporting increase our creative imagination, wholeness as well as pure intuition, causing us to be really feel more natural. If we heating a more enormous thing upward, it will require additional function, because we must supply much more dust, generally, a power kT. From $\Delta \theta Equals (\Delta \text)/\text$ there are of which $\Delta \text = \text\cdot \Delta \theta$. And I have faith that Coyote Osborne appeared to be one that advised we cause it to a certified ancient greek “theta-delta” in order that a minimum of the particular symbology ended up being to some degree “normal” (Hi there, it is really 2 ancient greek language text letters) and because Therianthropy’s main statement of foundation (therios) will be ancient greek And began with the Theta. Angular acceleration will be the charge of modify regarding angular swiftness.


text:
## WeBWorK Main Forum

### Matrix Object ans_array

by Andrew Dabrowski -
Number of replies: 8
Am I doing something wrong in the code below? When the correct answer is entered only the 1,1 entry in the matrix turns green.

Also, is there a way to give partial credit for getting some of the entries right? At my school we're used to giving 75% if 3 out 4 entries are correct.

DOCUMENT();

"PG.pl",
"PGbasicmacros.pl",
"MathObjects.pl"
);

TEXT(beginproblem);
Context("Matrix");

$M = Matrix([[1,0],[0,1]]); BEGIN_TEXT What is the identity Matrix? \{$M->ans_array \}

END_TEXT

&ANS( $M->cmp() ); ENDDOCUMENT(); In reply to Andrew Dabrowski ### Re: Matrix Object ans_array by Davide Cervone - This was fixed last August, and the fix is included in WeBWorK version 2.10, so you would need to update to that version in order to get the coloration for ans_array. As for partial credit, there is no current mechanism for checking the answer if not all the entries are filled in (the corresponding MathObject can't actually be created in that case). While it would be possible to add such functionality, there is nothing currently in place to allow it. In reply to Davide Cervone ### Re: Matrix Object ans_array by Andrew Dabrowski - OK, our server has 2.8 I think. What if all entries are filled in but all are correct? Should that give partial credit? In reply to Andrew Dabrowski ### Re: Matrix Object ans_array by Davide Cervone - What if all entries are filled in but all are correct? Should that give partial credit? Currently it does not. (You can get entry hints for vectors and points, but not matrices). But you can certainly arrange for it with a custom checker or a post-filter. Here is an example that uses the post-filter approach (for reasons I'll explain below). sub MatrixPartialCredit { my$N = shift;   # number of entries that must be right for partial credit
return sub {
my $ans = shift;$ans->{_filter_name} = "Matrix Partial Credit";
my $correct =$ans->{correct_value};
my $student =$ans->{student_value};
if ($ans->{score} < 1 && defined($correct) &&
defined($student) &&$student->class eq "Matrix") {
my @c = map {@$_} ($correct->value);   # flatten matrix
my @s = map {@$_} ($student->value);   # flatten matrix
my $score = 0; my$n = @c;
foreach my $i (0..$#c) {$score ++ if$c[$i] ==$s[$i]}$ans->score($score/$n) if $score >=$N;
}
return $ans; } } Context("Matrix");$M = Matrix([1,2],[3,4]);

BEGIN_TEXT
\{$M->ans_array\} END_TEXT ANS($M->cmp->withPostFilter(MatrixPartialCredit(3)));

Here, the MatrixPartialCredit function takes an argument that is the number of entries that must be correct and returns a post filter that checks that the student has at least that many correct. The filter is passed an AnswerHash object, and it gets the correct and student answers from that. It checks that the score isn't 100 percent already (score = 1), and that the correct and student answers are actually valid (if the student has a syntax error, for example, there will be no $ans->{student_value}, or if not all the entries are filled, $student will not be a Matrix object (it will either be empty or a Real that is the top-left entry).

If both are valid, then we get an array of all the entries of the matrix ($M->value returns an array of references to arrays, where the references are to arrays that are the rows of the matrix; the entries of the rows are Real MathObjects). We then compare the correct and student arrays entry by entry (and since these are Real objects, they will use the fuzzy checks controlled by the tolerance and tolType context flags), and add up the number of entries that are equal. If enough of them are equal, then we adjust the score to be the proper percentage. Finally, we return the AnswerHash. You could put the MatrixPartialCredit() filter in a separate file and load that into whatever problems need it. You could have done this in a custom checker without having to do the checks of whether the values are defined or the correct type, but there are two reasons to use the filter approach instead, even though there is a little more checking to do. First, you can more easily add messages like "Your entry (2,3) is incorrect" if you wanted to help the student out more. (But because there are so many entries, it might be better to make an array-like layout that has X for incorrect entries or something like that.) Second, it would allow you to check matrices that are not completely filled in, though you would have to work a bit to get the data about the matrix in that case, because the Matrix MathObject is not actually created when there are blank entries. So that is more sophisticated. But if you use the post-filter approach with a macro file for MatrixPartialCredit(), then you could update that macro file at some time in the future to handle partially filled matrices, and all your existing problems would take advantage of that automatically. Hope that does what you need. In reply to Andrew Dabrowski ### Re: Matrix Object ans_array by Davide Cervone - Well, it turns out that most of what you need to handle the partly filled in matrix and generate a correct/incorrect matrix message is already in place. Here is another example like the one above that implements a message indicating which entries are correct, which incorrect, and which not filled in. TEXT(MODES(TeX=>"",HTML=>"")); sub MatrixMarkIncorrect { my$right = "✔";
my $wrong = "✘"; return sub { my$ans = shift; $ans->{_filter_name} = "Matrix Mark Incorrect"; my$correct = $ans->{correct_value}; my$student = $ans->{student_value}; if ($ans->{score} < 1 && defined($correct) && defined($student)) {
my @c = $correct->value; my @s =$student->value;
@s = @{$ans->{student_formula}} if ref($ans->{student_formula}) eq 'ARRAY';
foreach my $i (0..$#c) {
foreach my $j (0..scalar(@{$c[$i]})-1) { my$ca = $c[$i][$j]; my$sa = $s[$i][$j];$s[$i][$j] = ($ca ==$sa ? "[$right]" : "[$wrong]") if ref($sa); } }$ans->{ans_message} = "Incorrect entries are marked with '$wrong':
".$correct->format_matrix([@s],@{$correct->{format_options}},tth_delims=>1)."

";$ans->{ans_message} =~ s/~~n//g;
}
return $ans; } } Context("Matrix");$M = Matrix([1,2],[3,4]);

BEGIN_TEXT
\{$M->ans_array\} END_TEXT ANS($M->cmp->withPostFilter(MatrixMarkIncorrect));

The important details here are that $ans->{student_formula} usually holds the Formula object that came from parsing the student answer, but in the case of an answer array that included empty values, it will be an array that contains either the strings used for the underlines for missing entries or the MathObject Reals for the filled in ones. The code above goes through the correct answer and the student answer and (when the student answer is filled in) checks it against the correct answer and changes the array to a checkmark or an "x". At the end, it uses the format_matrix() method to turn the array into the HTML for displaying the matrix (just like in the "Entered" column). One caveat is that you have to remove the newlines or they will be turned into
 elements automatically by the code that creates the table. I also added some CSS to get the coloration to be correct for the table. You should be able to combine this with the previous filter to get partial credit as well. E.g., ANS($M->cmp->withPostFilter(MatrixPartialCredit(3))->withPostFilter(MatrixMarkIncorrect));

Of course, you can modify this to suite your tastes, so it is just an example to get you started. Note that if you were to move this to a macro file, you would need to change the ~~ to \ in the substitution.

### Re: Matrix Object ans_array

by Andrew Dabrowski -
Thanks for the suggestions, I'm just coming back to this issue now and will use them.

What's a good reference for post-filters?

### Re: Matrix Object ans_array

by Andrew Dabrowski -
I'm also looking at the custom answer checker route. Does that work correctly in WW 2.9? I tried

sub matrixAnsChecker{
my ( $correct,$student, $ansHash ) = @_; return 0.001; } which you will note also returns a score of 0.001 whatever the student's answer. &ANS($P->cmp( 'tol' => 0.0001, checker => ~~&matrixAnsChecker ) );

But then the student always gets full credit. In other words it seems that webwork is interpreting the output from the checker as a Boolean rather than a float.

### Re: Matrix Object ans_array

by Davide Cervone -
Yes, it turns out that the result of the custom checker is treated as boolean, not a percentage (that should be changed).

You can get the desired effect, however, by using

sub matrixAnsChecker {
my ($correct,$student,$ansHash) = @_; ...$ansHash->score(.5);
return 0;
}

if you want to award 50%. (Note that the scores are only shown as whole number percents, so .001 would end up being 0%.) You need to return 0 in order to prevent the score from being changed to 1 later.

As an aside, you are using the old-style &ANS(), but the ampersand is no longer necessary, and is deprecated. So ANS(...) is preferred.

Also, you can do


text:
UPSKILL MATH PLUS

Learn Mathematics through our AI based learning portal with the support of our Academic Experts!

### Theory:

A median is an intersecting line, separating the original triangle into two triangles of equal area.
Let's discuss the day to day application of the median.

In  your home, your mom cooked Mexican hexagon pizza (look like as below picture).

Your mom offered one piece to you.  At that time one of your friends arrives at your home.

You then offer to share your pizza with your friend.

Now the question is how you will divide your pizza so that each of you will get the same amount.

Here comes a remarkable concept to solve this issue. Use the concept of MEDIAN.

Let the corners of the pizza piece be $$A, B$$ and $$C$$.

From any interior angle (say $$A$$) of a triangle, $$ABC$$ cut the midpoint of the opposite side (say $$D$$) so that you will have an equal amount of pizza ($$ADB$$ and $$ADC$$) for  you and your friend.

Suppose two more friends arrived!

Again use the concept of MEDIAN.

Cut the pizza along another median, from any interior angle to the midpoint of the opposite side (Say $$D$$ to the midpoint $$E$$ of $$AC$$ and $$D$$ to the midpoint $$F$$ of $$AB$$).

Let's enjoy the pizza with your friends as all get an equal amount.


text:
142 views

The pushdown automata $M=\left \{ \left ( q_{0},q_{1},q_{2} \right ),\left ( a,b \right ) ,\left ( 0,1 \right ),\partial ,q_{0},0,\left \{ q_{0} \right \}\right \}$

$\partial \left ( q_{0},a,0 \right )=\left ( q_{1},10 \right )$

$\partial \left ( q_{1},a,1 \right )=\left ( q_{1},11 \right )$

$\partial \left ( q_{1},b,1 \right )=\left ( q_{2},\lambda \right )$

$\partial \left ( q_{2},b,1 \right )=\left ( q_{2},\lambda \right )$

$\partial \left ( q_{2},\lambda ,0 \right )=\left ( q_{0},\lambda \right )$

Accepts language

$l=\left \{ a^{n}b^{n}\mid n\geq 0\right \}$

$l=\left \{ a^{n}b^{n}\mid n> 0\right \}$

Please tell me with these two options which one is correct? I think here $q_{2}$ is accepting state , not $q_{0}$

As last transition going from $q_{2}$ to $q_{0}$ and not $q_{0}$ to $q_{2}$

Am I right?

| 142 views
0
This is PDA right, and "Set of Final states" has q0 which is also initial state here, so if only these two options are there we don't need to even check anything as it will accept empty string i.e, a^0b^0. So the answer would definitely be the first one
0

"Set of Final states" has q0

how?

last transition is q2 to q0, and not q0 to q2

0
$\left ( Q,\sum,\tau ,\partial ,q_{0},Z_{0},F\right )$

So, here $F=q_{0}$

right?

I thought $q_{2}$ final state

but that is not the case, right?
0
here goes q2 to q0, so accept the empty state
+1
Yes exactly what I was going to say too😃
0
thanks a lot

Made Easy diagram showing q2 final :(

So, getting in this trouble


text:
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