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# Non-unital ring contains a unital ring as a subring?

It is well known that every non-unital ring can be embedded into a unital ring (e.g., Dorroh's adjunction). I am curious about the converse: every unital ring can be viewed as a subring of a non-unital ring?

If this converse is not correct, will this be still partially true? I am looking for a non-trivial example. One trivial example would be that $\{0\}$ as a subring of $2\mathbb{Z}$.

PS: by a ring here I mean a set that is an additive abelian group and a multiplicative semigroup, and satisfies the distributive laws.

• What do you mean by embedded? Do you mean that there is an injective ring homomorphism? Because any unital ring would have no homomorphism to a non-unital ring if morphisms must preserve $1.$ – Chickenmancer Aug 15 '18 at 4:49
• @Chickenmancer You may have a look at here for what I mean:math.stackexchange.com/questions/1113097/… – Easy Aug 15 '18 at 5:10
• @Chickenmancer I think we should note that a ring and its subring do not share the same "1" in general. – Easy Aug 15 '18 at 5:14
• math.stackexchange.com/questions/170953/… They do share the same 1 in general. – Chickenmancer Aug 15 '18 at 6:32
• @Chickenmancer Can you tell what are the "1"s in $\{0\}$ and $\mathbb{Z}$ respectively? – Easy Aug 15 '18 at 7:31

Take any ring $S$ without identity. If $R$ is any ring with identity, then $R\times S$ does not have identity. Is this what you seek?

format: plain


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# What does it mean (how is it visualized) for a particle to act as a wave?

I have no background in physics. This isn't for homework, just for interest.

In quantum physics, it's described that a particle can act as both a particle and a wave.

Quoted from HowStuffWorks "Wave-Particle Duality"

Today, physicists accept the dual nature of light. In this modern view, they define light as a collection of one or more photons propagating through space as electromagnetic waves. This definition, which combines light's wave and particle nature, makes it possible to rethink Thomas Young's double-slit experiment in this way: Light travels away from a source as an electromagnetic wave. When it encounters the slits, it passes through and divides into two wave fronts. These wave fronts overlap and approach the screen. At the moment of impact, however, the entire wave field disappears and a photon appears. Quantum physicists often describe this by saying the spread-out wave "collapses" into a small point.

I have trouble visualizing a particle transforming into a wave and vice-versa. The quote says that light travels away from a source as an electromagnetic wave. What does that even look like? How can I visualize "a wave"? Is that supposed to look like some thin wall of advancing light? And then, the quote says, at the moment of impact, the wave disappears and a photon appears. So, a ball of light appears? Something that resembles a sphere? How does a sphere become something like an ocean wave? What does that look like?

My (completely uneducated) guess is, by a particle becoming a wave, does that mean that this expansive wave is filled with tons of ghost copies of itself, like the one electron exists everywhere in this expansive area of the wave, and then when it hits the wall, that property suddenly disappears and you're left with just one particle. So, this "wave", is really tons of identical copies of the same photon in the shape and form and with the same properties of, a wave? My guess comes from reading about how shooting just one photon still passes through two slits in the double-slit experiment. So the photon actually duplicated itself?

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Possible duplicate: physics.stackexchange.com/q/33333/2451 –  Qmechanic Nov 6 '12 at 22:13
The wave nature is what evolves with time and the particle nature is what is observed. This link may help: upload.wikimedia.org/wikipedia/commons/e/e7/… –  Dimensio1n0 Jun 18 '13 at 9:41

What we observe in nature exists in several scales. From the distances of stars and galaxies and clusters of galaxies to the sizes of atoms and elementary particles.

Now we have to define "observe".

Observing in human size scale means what our ears hear, what our eyes see, what our hands feel, our nose smells , our mouth tastes. That was the first classification and the level of "proxy", i.e. intermediate between fact and our understanding and classification, which is biological. (the term proxy is widely used in climate researches)

A second level of observing comes when we use proxies, like meters, thermometers, telescopes and microscopes etc. which register on our biological proxies and we accumulate knowledge. At this level we can overcome the limits of the human scale and find and study the enormous scales of the galaxies and the tiny scales of the bacteria and microbes. A level of microns and milimeters. We observe waves in liquids with such size wavelengths

Visible light is of the order of Angstroms, 10^-10 meters. As science progressed the idea of light being corpuscles ( Newton) became overcome by the observation of interference phenomena which definitely said "waves".

Then came the quantum revolution, the photoelectric effect (Particle), the double slit experiments( wave) that showed light had aspects of a corpuscle and aspects of a wave. We our now in a final level of use of proxy, called mathematics

The wave particle duality was understood in the theory of quantum mechanics. In this theory depending on the observation a particle will either react as a "particle" i.e. have a momentum and location defined , or as a wave, i.e. have a frequency/wavelength and geometry defining its presence BUT, and it is a huge but, this wavelength is not in the matter/energy itself that is defining the particle , but in the probability of finding that particle in a specific (x,y,z,t) location. If there is no experiment looking for the particle at specific locations its form is unknown and bounded by the Heisenberg Uncertainty Principle.

What is described with words in the last paragraph is rigorously set out in mathematical equations and it is not possible to understand really what is going on if one does not acquire the mathematical tools, as a native on a primitive island could not understand airplanes. Mathematics is the ultimate proxy for understanding quantum phenomena.

Now light is special in the sense that collectively it displays the wave properties macroscopically, and the specialness comes from the Maxwell Equations which work as well in both systems, the classical and the quantum mechanical, but this also needs mathematics to be comprehended.

So a visualization is misleading in the sense that the mathematical wave function coming from the quantum mechanical equations is like a "statistical" tool whose square gives us the probability of observing the particle at (x,y,z,t). Suppose that I have a statistical probability function for you, that you may be in New York on 17/10/2012 and probabilities spread all over the east coast of the US. Does that mean that you are nowhere? does that mean that you are everywhere? Equally with the photons and the elementary particles. It is just a mathematical probability coming out of the inherent quantum mechanical nature of the cosmos.

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Thanks for the really detailed post and the concept of proxies. Surely mathematics isn't "the final" proxy to observe and learn? There may be others? –  Jason Oct 17 '12 at 7:38
Mathematics itself has several levels used in physics, and those are continually expanding as research progresses. The question becomes esoteric to mathematics, imo. –  anna v Oct 17 '12 at 10:35

At the moment of impact, however, the entire wave field disappears and a photon appears.

Any source that is content to describe scientific theories in terms of black magic is worse than useless.

How can I visualize "a wave"?

You can visualize it as y=sin(x). The wave's strength oscillates both over time (if you stand in one place and watch it pass), and space (if you "freeze" it in time). Light is more complex than more familiar waves (eg, waves in water), in that it's made up of oscillating electrical and magnetic waves.

So the photon actually duplicated itself?

No, it hasn't duplicated itself, just spread itself out so that it can pass through two slits simultaneously (just like a wave in water would do). The "collapsing" occurs due to the quantization of light, which is evident when the light gets absorbed by matter.

Realize that trying to visualize is a very limited vehicle for understanding quantum-scale physics. Since such tiny scales are out the domain of our ordinary sense perception, all we have available is hypothesis based on experiments. So, to understand a theory is to understand the paradoxes and experiments that gave rise to it; in the case of the wave-particle duality, that would be (among others) the double slit experiment, as you mentioned. On the quantization of light, a good class of experiments to ponder is those of emission/absorption spectra of elements.

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Visualization is difficult since, for example, the 'waves' that we're talking about a probability amplitude density waves. (In fact, we (teachers) should probably discourage initiates into the subject from trying to do this outright.)

One thing that has always helped when I describe this to folks is something I got from Paul Tipler's undergrad book (!) a long time ago when I was a teaching assistant. He makes a very useful distinction: when an electron (as a canonical example of a quantum 'particle') propagates it behaves in a wavelike fashion; when it exchanges energy with other systems, it does so discretely, like a particle.

In this sense then the 'duality' of quantum mechanics is less paradoxical and perhaps less seemingly contradictory. Electrons behave as waves and particles but never 'at the same time.'

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Particles in quantum mechanics are always particles and act as particles. E.g. an electron or a photon are always defined as particles according to the Standard Model and Wigner representation. E.g. an electron is defined as a particle with mass $m_e$, spin 1/2 and charge e and always behaves as a particle, never as a wave. As emphasized in CERN website "everything in the Universe is found to be made from twelve basic building blocks called fundamental particles".

There is not need for a wave-particle duality in modern interpretations of quantum mechanics (in fact quantum mechanics can be formulated without wavefunctions) and the wave-particle duality term is often considered a "myth", Klein prefers the term "misnomer". The historical roots of the wave-particle duality myth are explained in Ballentine's celebrated textbook Quantum Mechanics: A Modern Mechanics Development:

"Are ”particles” really ”waves”? In the early experiments, the diffraction patterns were detected holistically by means of a photographic plate, which could not detect individual particles. As a result, the notion grew that particle and wave properties were mutually incompatible, or complementary, in the sense that different measurement apparatuses would be required to observe them. That idea, however, was only an unfortunate generalization from a technological limitation. Today it is possible to detect the arrival of individual electrons, and to see the diffraction pattern emerge as a statistical pattern made up of many small spots (Tonomura et al., 1989)."

As stated by Klein:

"The miraculous "wave-particle duality" continues to flourish in popular texts and elementary text books. However, the rate of appearance of this term in scientific works has been decreasing in recent years."

Look Akira Tonomura’s video clip .wmv .mpeg for a beautiful demonstration of the appearance of statistical wave pattern on a double-slit interference experiment when a large number of independent single particles (electrons) impact the detector.

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In advanced formulations of QM, wavefunctions are substituted by kets, density matrices, Wigner distributions... Have you heard of some ket-particle, matrix-particle, or distribution-particle duality? No, because there is none. Moreover, wavefunctions are not waves, are functions. –  juanrga Oct 21 '12 at 11:07
Thank you! It was -4 some days ago. I would like to know two things: (i) why do they appeal to a hypothetical wave-particle duality, when $\Psi$ is not a physical wave but a mathematical function? and (ii) what term would they use in those advanced formulations of QM, where there is no wavefunction $\Psi$? E.g. in the Wigner-Moyal formulation of QM the state of the system is given by the Wigner distribution W and the evolution equation is not the Schrödinger equation but the Moyal equation $\dot{W} = \{H, W\}_{M}$. –  juanrga Oct 22 '12 at 14:59
I really think, this answer is spot on. –  Iota Mar 12 '14 at 21:04


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# How can I check if one expression implies another?

Say I have one expression, for example $x^3-3 + c = y$, and I want to check if it implies another with some set of explicitly stated assumptions. With the previous example, assuming all variables are positive real numbers, we might ask if $x^3-3 + c = y$ implies $c = -x^3 + y$. This example is trivial, but I'd like to do the same where, perhaps, choices can be made about the use of various special functions or identities and there can also be inequalities.

Is there something like ImpliesQ[{exp1,exp2}]?

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Implies[x^3 - 3 + c == y, c == y - x^3] // Reduce –  ciao Feb 16 '14 at 3:45
@rasher Wham. :) –  user12404 Feb 16 '14 at 5:55
@Nasser The example I choose was a poor one... I was thinking more along the lines of there being some choice for special functions / etc. in one derivation vs. another, and then making sure that the results are the same. –  user12404 Feb 16 '14 at 5:56

Simplify[c == y - x^3, Assumptions -> x^3 - 3 + c == y]

Simplify[c == y - x^3 + 3, Assumptions -> x^3 - 3 + c == y]


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# Stokes parameters

The Stokes parameters are a set of values that describe the polarization state of electromagnetic radiation. They were defined by George Gabriel Stokes in 1852,[1] as a mathematically convenient alternative to the more common description of incoherent or partially polarized radiation in terms of its total intensity (I), (fractional) degree of polarization (p), and the shape parameters of the polarization ellipse. The effect of an optical system on the polarization of light can be determined by constructing the Stokes vector for the input light and applying Mueller calculus, to obtain the Stokes vector of the light leaving the system.

## Definitions

The Poincaré sphere is the parametrisation of the last three Stokes' parameters in spherical coordinates

The relationship of the Stokes parameters S1, S2, S3, S4 to intensity and polarization ellipse parameters is shown in the equations below and the figure at right.

\begin{align} S_0 &= I \\ S_1 &= I p \cos 2\psi \cos 2\chi \\ S_2 &= I p \sin 2\psi \cos 2\chi \\ S_3 &= I p \sin 2\chi \end{align}

Here $I$$p$, $2\psi$ and $2\chi$ are the spherical coordinates of the three-dimensional vector of cartesian coordinates $(S_1, S_2, S_3)$. $I$ is the total intensity of the beam, and $p$ is the degree of polarization, constrained by 0 ≤ p ≤ 1. The factor of two before $\psi$ represents the fact that any polarization ellipse is indistinguishable from one rotated by 180°, while the factor of two before $\chi$ indicates that an ellipse is indistinguishable from one with the semi-axis lengths swapped accompanied by a 90° rotation. The phase information of the polarized light is not recorded in the stokes parameters. The four Stokes parameters are sometimes denoted I, Q, U and V, respectively.

If given the Stokes parameters one can solve for the spherical coordinates with the following equations:

\begin{align} I &= S_0 \\ p &= \frac{\sqrt{S_1^2 + S_2^2 + S_3^2}}{S_0} \\ 2\psi &= \mathrm{atan} \frac{S_2}{S_1}\\ 2\chi &= \mathrm{atan} \frac{S_3}{\sqrt{S_1^2+S_2^2}}\\ \end{align}

### Stokes vectors

The Stokes parameters are often combined into a vector, known as the Stokes vector:

$\vec S \ = \begin{pmatrix} S_0 \\ S_1 \\ S_2 \\ S_3\end{pmatrix} = \begin{pmatrix} I \\ Q \\ U \\ V\end{pmatrix}$

The Stokes vector spans the space of unpolarized, partially polarized, and fully polarized light. For comparison, the Jones vector only spans the space of fully polarized light, but is more useful for problems involving coherent light. The four Stokes parameters are not a preferred coordinate system of the space, but rather were chosen because they can be easily measured or calculated.

#### Examples

Below are shown some Stokes vectors for common states of polarization of light.

 $\begin{pmatrix} 1 \\ 1 \\ 0 \\ 0\end{pmatrix}$ Linearly polarized (horizontal) $\begin{pmatrix} 1 \\ -1 \\ 0 \\ 0\end{pmatrix}$ Linearly polarized (vertical) $\begin{pmatrix} 1 \\ 0 \\ 1 \\ 0\end{pmatrix}$ Linearly polarized (+45°) $\begin{pmatrix} 1 \\ 0 \\ -1 \\ 0\end{pmatrix}$ Linearly polarized (−45°) $\begin{pmatrix} 1 \\ 0 \\ 0 \\ 1\end{pmatrix}$ Right-hand circularly polarized $\begin{pmatrix} 1 \\ 0 \\ 0 \\ -1\end{pmatrix}$ Left-hand circularly polarized $\begin{pmatrix} 1 \\ 0 \\ 0 \\ 0\end{pmatrix}$ Unpolarized

## Alternate explanation

A monochromatic plane wave is specified by its propagation vector, $\vec{k}$, and the complex amplitudes of the electric field, $E_1$ and $E_2$, in a basis $(\hat{\epsilon}_1,\hat{\epsilon}_2)$. The pair $(E_1, E_2)$ is called a Jones vector. Alternatively, one may specify the propagation vector, the phase, $\phi$, and the polarization state, $\Psi$, where $\Psi$ is the curve traced out by the electric field as a function of time in a fixed plane. The most familiar polarization states are linear and circular, which are degenerate cases of the most general state, an ellipse.

One way to describe polarization is by giving the semi-major and semi-minor axes of the polarization ellipse, its orientation, and the sense of rotation (See the above figure). The Stokes parameters $I$, $Q$, $U$, and $V$, provide an alternative description of the polarization state which is experimentally convenient because each parameter corresponds to a sum or difference of measurable intensities. The next figure shows examples of the Stokes parameters in degenerate states.

### Definitions

The Stokes parameters are defined by

$\begin{matrix} I & \equiv & \langle E_x^{2} \rangle + \langle E_y^{2} \rangle \\ ~ & = & \langle E_a^{2} \rangle + \langle E_b^{2} \rangle \\ ~ & = & \langle E_l^{2} \rangle + \langle E_r^{2} \rangle, \\ Q & \equiv & \langle E_x^{2} \rangle - \langle E_y^{2} \rangle, \\ U & \equiv & \langle E_a^{2} \rangle - \langle E_b^{2} \rangle, \\ V & \equiv & \langle E_l^{2} \rangle - \langle E_r^{2} \rangle. \end{matrix}$

where the subscripts refer to three different bases of the space of Jones vectors: the standard Cartesian basis ($\hat{x},\hat{y}$), a Cartesian basis rotated by 45° ($\hat{a},\hat{b}$), and a circular basis ($\hat{l},\hat{r}$). The circular basis is defined so that $\hat{l} = (\hat{x}+i\hat{y})/\sqrt{2}$.

The symbols ⟨⋅,⋅⟩ represent expectation values. The light can be viewed as a random variable taking values in the space C2 of Jones vectors (E_1, E_2). Any given measurement yields a specific wave (with a specific phase, polarization ellipse, and magnitude), but it keeps flickering and wobbling between different outcomes. The expectation values are various averages of these outcomes. Intense, but unpolarized light will have I > 0 but P = U = V = 0, reflecting that no polarization type predominates. A convincing waveform is depicted at the article on coherence.

The opposite would be perfectly polarized light which, in addition, has a fixed, nonvarying amplitude -- a pure sine curve. This is represented by a random variable with only a single possible value, say (E_1, E_2). In this case one may replace the brackets by absolute value bars, obtaining a well-defined quadratic map

$\begin{matrix} I \equiv |E_x|^{2} + |E_y|^{2} = |E_a|^{2} + |E_b|^{2} = |E_l|^{2} + |E_r|^{2} \\ Q \equiv |E_x|^{2} - |E_y|^{2}, \\ U \equiv |E_a|^{2} - |E_b|^{2}, \\ V \equiv |E_l|^{2} - |E_r|^{2}. \end{matrix}$

from the Jones vectors to the corresponding Stokes vectors; more convenient forms are given below. The map takes its image in the cone defined by |I |2 = |Q |2 + |U |2 + |V |2, where the purity of the state satisfies p = 1 (see below).

The next figure shows how the signs of the Stokes parameters are determined by the helicity and the orientation of the semi-major axis of the polarization ellipse.

### Representations in fixed bases

In a fixed ($\hat{x},\hat{y}$) basis, the Stokes parameters when using an increasing phase convention are

$\begin{matrix} I&=&|E_x|^2+|E_y|^2, \\ Q&=&|E_x|^2-|E_y|^2, \\ U&=&2\mbox{Re}(E_xE_y^*), \\ V&=&-2\mbox{Im}(E_xE_y^*), \\ \end{matrix}$

while for $(\hat{a},\hat{b})$, they are

$\begin{matrix} I&=&|E_a|^2+|E_b|^2, \\ Q&=&-2\mbox{Re}(E_a^{*}E_b), \\ U&=&|E_a|^{2}-|E_b|^{2}, \\ V&=&2\mbox{Im}(E_a^{*}E_b). \\ \end{matrix}$

and for $(\hat{l},\hat{r})$, they are

$\begin{matrix} I &=&|E_l|^2+|E_r|^2, \\ Q &=&2\mbox{Re}(E_l^*E_r), \\ U & = &-2\mbox{Im}(E_l^*E_r), \\ V & =&|E_r|^2-|E_l|^2. \\ \end{matrix}$

## Properties

For purely monochromatic coherent radiation, it follows from the above equations that

$\begin{matrix} Q^2+U^2+V^2 = I^2, \end{matrix}$

whereas for the whole (non-coherent) beam radiation, the Stokes parameters are defined as averaged quantities, and the previous equation becomes an inequality:[2]

$\begin{matrix} Q^2+U^2+V^2 \le I^2. \end{matrix}$

However, we can define a total polarization intensity $I_p$, so that

$\begin{matrix} Q^{2} + U^2 +V^2 = I_p^2, \end{matrix}$

where $I_p/I$ is the total polarization fraction.

Let us define the complex intensity of linear polarization to be

$\begin{matrix} L & \equiv & |L|e^{i2\theta} \\ & \equiv & Q +iU. \\ \end{matrix}$

Under a rotation $\theta \rightarrow \theta+\theta'$ of the polarization ellipse, it can be shown that $I$ and $V$ are invariant, but

$\begin{matrix} L & \rightarrow & e^{i2\theta'}L, \\ Q & \rightarrow & \mbox{Re}\left(e^{i2\theta'}L\right), \\ U & \rightarrow & \mbox{Im}\left(e^{i2\theta'}L\right).\\ \end{matrix}$

With these properties, the Stokes parameters may be thought of as constituting three generalized intensities:

$\begin{matrix} I & \ge & 0, \\ V & \in & \mathbb{R}, \\ L & \in & \mathbb{C}, \\ \end{matrix}$

where $I$ is the total intensity, $|V|$ is the intensity of circular polarization, and $|L|$ is the intensity of linear polarization. The total intensity of polarization is $I_p=\sqrt{|L|^2+|V|^2}$, and the orientation and sense of rotation are given by

$\begin{matrix} \theta &=& \frac{1}{2}\arg(L), \\ h &=& \sgn(V). \\ \end{matrix}$

Since $Q=\mbox{Re}(L)$ and $U=\mbox{Im}(L)$, we have

$\begin{matrix} |L| &=& \sqrt{Q^2+U^2}, \\ \theta &=& \frac{1}{2}\tan^{-1}(U/Q). \\ \end{matrix}$

## Relation to the polarization ellipse

In terms of the parameters of the polarization ellipse, the Stokes parameters are

$\begin{matrix} I_p & = & A^2 + B^2, \\ Q & = & (A^2-B^2)\cos(2\theta), \\ U & = & (A^2-B^2)\sin(2\theta), \\ V & = & 2ABh. \\ \end{matrix}$

Inverting the previous equation gives

$\begin{matrix} A & = & \sqrt{\frac{1}{2}(I_p+|L|)} \\ B & = & \sqrt{\frac{1}{2}(I_p-|L|)} \\ \theta & = & \frac{1}{2}\arg(L)\\ h & = & \sgn(V). \\ \end{matrix}$

## Relationship to Hermitian operators and quantum mixed states

From a geometric and algebraic point of view, the Stokes parameters stand in one-to-one correspondence with the closed, convex, 4-real-dimensional cone of nonnegative Hermitian operators on the Hilbert space C2. The parameter I serves as the trace of the operator, whereas the entries of the matrix of the operator are simple linear functions of the four parameters I, Q, U, V, serving as coefficients in a linear combination of the Stokes operators. The eigenvalues and eigenvectors of the operator can be calculated from the polarization ellipse parameters I, p, ψ, χ.

The Stokes parameters with I set equal to 1 (i.e. the trace 1 operators) are in one-to-one correspondence with the closed unit 3-dimensional ball of mixed states (or density operators) of the quantum space C2, whose boundary is the Bloch sphere. The Jones vectors correspond to the underlying space C2, that is, the (unnormalized) pure states of the same system. Note that phase information is lost when passing from a pure state |φ⟩ to the corresponding mixed state |φ⟩⟨φ|, just as it is lost when passing from a Jones vector to the corresponding Stokes vector.


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## Chemistry: Principles and Practice (3rd Edition)

Wavelength = $\frac{Speed}{Frequency}$ = $\frac{344ms^{-1}}{512s^{-1}}$ = 0.672 m


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×

# Integrals!

$\large \int_0^\infty \dfrac{x e^{-11x}}{\sqrt{e^{2x} -1}} \, dx = - \dfrac{10!!}{11!!} \left( \ln 2 + \sum_{n=1}^{11} \dfrac{(-1)^n}n \right)$

Prove the equation above.

Clarification: $$!!$$ denotes the double factorial notation.

Note by Hummus A
1 year, 7 months ago

Sort by:

$$\frac { 10! }{ 11! } =\frac { 1 }{ 11 }$$ · 1 year, 6 months ago

it was supposed to be a double factorial · 1 year, 6 months ago

Nowhere double factorial notation is used . hahaha · 1 year, 7 months ago


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# Math Expressions Grade 3 Student Activity Book Unit 3 Review/Test Answer Key

This handy Math Expressions Grade 3 Student Activity Book Answer Key Unit 3 Review/Test provides detailed solutions for the textbook questions.

## Math Expressions Grade 3 Student Activity Book Unit 3 Review/Test Answer Key

Vocabulary

Choose the best word from the box.

elapsed time
liquid volume
mass
bar graph
line plot

Question 1.
You can use a ____ to show data on a number line. (Lesson 3-1)
line plot
Explanation:
A Line plot can be defined as a graph that displays data as points or check marks above a number line, showing the frequency of each value.

Question 2.
The amount of water in a bottle can be measured with a unit of _____ (Lesson 3-2)
liquid volume.
Explanation:
Liquid volume is a way to measure an amount of liquid by describing,
it how much 3-D space it occupies.

Question 3.
The time that passes between the beginning and the end of an activity is ____ (Lesson 3-8)
elapsed time.
Explanation:
Elapsed time is the amount of time that passes from the start of an event to its finish.
In simplest terms, elapsed time is how much time goes by from one time to another.

Concepts and Skills

Question 4.
If the hour hand is half-way between the 3 and 4 on a clock in the afternoon, what time is it? Explain. (Lesson 3-6)
3:30
Explanation:
In a complete hour, hour hand moves 5 minutes and minute hand moves 60 minutes.
If the hour hand is half-way between the 3 and 4 on a clock in the afternoon,

Question 5.
When would you use kilograms to measure something. (Lesson 3-4)
We use kilograms to measure the mass of heavier objects.
Explanation:
Kilogram is a unit of measurement used to measure much heavier objects.
The standard unit of kilogram is kg.
For example,
Fruits such as small watermelons and pineapples also have a mass of around 1 kilogram.

Question 6.
Estimate the length of the marker in inches. Then measure it to the nearest $$\frac{1}{4}$$ inch. (Lesson 3-1)

Estimate: _____
Actual: _____
Estimate: 5.0 inches
Actual: 5 $$\frac{1}{4}$$

Explanation:
Estimation uses round numbers in a calculation to make it quicker or easier to get an approximate answer.

Write each time on the digital clock. Then write how to say the time. (Lessons 3-6, 3-7)

Question 7.

7 hours and 13 minutes.
Explanation:

Explanation:
Hours hand is on 7 and minutes hand is between the two consecutive numbers 2 and 3.
So, to find the minutes count by ones till you reach the minutes.
The time shown in the above clock is 7:13

Question 8.

09:32
9 hours and 32 minutes

Explanation:
Hours hand is on 9 and minutes hand is between the two consecutive numbers 6 and 7.
So, to find the minutes count by ones till you reach the minutes.
The time shown in the above clock is 9:32

Circle the better estimate. (Lesson 3-2, Lesson 3-3, Lesson 3-4)

Question 9.

2 gallons
2 cups

2 cups

Explanation:
16 cups makes one gallon.
Measurement of 1 gallon is more than 1 cup.
So, the tetra pack of orange juice is hardly 2 cups.

Question 10.

3 milliliters
3 liters

3 liters

Explanation:
Milliliter is used to measure a small amount of liquid.
For a larger quantity of liquid.
1 liter = 1000 milliliters or 1 ml = 0.001 l.

Question 11.

2 kilograms
2 grams

2 kilograms

Explanation:
A gram (g) is a metric unit for a small amount of mass or weight.
A kilogram (kg) is a metric unit for a larger of amount of mass or weight.
1kg = 1000gm
So, weight of watermelon is measured in kilograms.

Use the table for Exercises 12 and 13. (Lessons 3-11, 3-12)

Question 12.
Use the data in the table to complete the pictograph.

Explanation:
A pictograph uses picture symbols to illustrate statistical information.
While making a pictograph, use two columns that represent the category and data.
Finally, draw the pictograph using symbols/images, which represents the frequency.

Question 13.
Use the data in the table to complete the bar graph.

Explanation:
A bar graph must have a tittle written above the bar graph as shown.
The information in a bar graph is represented along the horizontal and vertical axis.
The horizontal axis generally represents the periods or intervals and vertical axis represents the quantity and each axis has a label.

Problem Solving

Use the bar graph below to solve problems 14 and 15. (Lessons 3-11, 3-12)

Question 14.
How many more tickets were sold for the roller coaster than bumper cars?
15 tickets.
Explanation:
With reference to the above bar graph,
Number of tickets sold of Roller Costa = 80
Number of tickets sold of Bumper Cars = 65
The difference of tickets sold between roller coaster and the bumper cars,
80 – 65 = 15 tickets.

Question 15.
How many tickets were sold altogether?
185 tickets.
Explanation:
With reference to the above bar graph,
Number of tickets sold of Roller Costa = 80
Number of tickets sold of Bumper Cars = 65
Number of tickets sold of Ferris Wheel = 40
Number of tickets sold altogether,
80 + 65 + 40 = 185 tickets.

Solve.

Question 16.
Kyle started his homework at 6:30 P.M. He spent 35 minutes on math and 40 minutes on a science report. What time did he finish his homework? How long did he spend doing homework? (Lessons 3-9, 3-10)

7:45 he finished his work.
Time spent on homework 1 hour 15 minutes.

Explanation:
Kyle started his homework at 6:30 P.M.
He spent 35 minutes on math and 40 minutes on a science report.
The time he finish his homework,
6:30 + 1:15 = 7:45
Total time spend doing homework,
35 + 40 = 75 minutes or 1hr 15min.

Question 17.
At 6:45 Rico went to basketball practice. His practice lasted 1 hour and 20 minutes. What time did he finish practice? (Lesson 3-8)

8:05 P.M.
Explanation:

Starting Time = 6:45 P.M
Elapsed Time = 1 hour and 20 minutes
End time = 8:05 P.M.

Problem Solving

Use the drawing to represent and solve the problem.

Question 18.
Ariel picked some peaches. A peach has a mass of about 150 grams. If the peaches she picked had a total mass of 600 grams, how many peaches did she pick? (Lessons 3-4, 3-5)

4 peaches picked
Explanation:
Each peach has a mass of about 150 grams.
Total mass is 600 grams.
Number of peaches = 600/ 150 = 4

Question 19.
Sue needs 100 milliliters of juice to make a batch of a juice drink. How many milliliters does she need to make 5 batches? (Lessons 3-3, 3-5)

500 milliliters.
Explanation:
Sue needs 100 milliliters of juice to make a batch of a juice drink.
Number of milliliters she need to make 5 batches,
100 x 5 = 500 milliliters.

Question 20.
Extended Response A high school student measured the length of third graders’ feet for a science project. The results are in the frequency table below. Use the frequency table to complete the line plot.
(Lessons 3-1, 3-3, 3-13, 3-14, 3-15)
What is the length of a typical third grader’s foot in this survey? Explain why you chose that length.
______________________
______________________


text:
# Guidelines

### NOTE: Submission guidelines and templates updated 2018/3/25.

CHI PLAY 2018 had planned to transition to the new 2017 ACM Master Article Template but due to difficulties reported, we are reverting to the previous submission format. Apologies for any confusion caused, we hope that the templates below will ensure a simpler submission process. Your paper will not be rejected if it is in the wrong format but this will be something that would need to be fixed after acceptance and before the final camera-ready deadline.

### Guidelines

CHI PLAY 2018 uses two formats for submissions: “Proceedings” (for full papers) and “Extended Abstracts” (all other tracks e.g. Works-in-Progress, Doctoral Consortium, Spotlight). In addition, because CHI PLAY deals with games, we provide express advice on how to cite games as scholarly resources.

### Quick Overview

Submissions should be made to CHI PLAY 2018 via Precision Conference 2.0.

We will be using the SIGCHI proceedings template, which you can download below.

### Proceedings Format

CHI PLAY full papers use the following SIGCHI templates. Submissions can be up to 10 pages long. Note that references do not count toward page limits. Please note that the classification system has changed and you are now required to use the ACM 2012 classifiers. See instructions here.

Proceedings Word Template

Proceedings Latex Template

### Extended Abstracts Format

CHI PLAY venues other than full papers (e.g., Works-in-Progress, Doctoral Consortium, Spotlight) are extended abstracts. Please check the page length for your associated track. Note that references do not count toward page limits.

Extended Abstracts Word Template

Extended Abstracts Latex Template

### Citing Games

As games figure prominently in CHI PLAY research, we provide advice on how to cite them as scholarly sources. Authors are encouraged to use this new format in their papers. Word users can follow the guidelines; LaTeX users should use the BibTeX information below. An example of the game reference format follows:

Sample: Nintendo R&D1 and Intelligent Systems. 1994. Super Metroid. Game [SNES]. (18 April 1994). Nintendo, Kyoto, Japan. Last played August 2011.

General Pattern (note that for each entry, you should cite a specific version (e.g., platform) for a game): <developer>. <release year>. <game title in italics>. Game [<platform>]. (<game release date in <day> <month> <year> formats>). <publisher name>, <publisher address> (optional) Last played <last played date>.

LaTeX / BibTeX users should use the @misc entry type; the data fields should be filled as follows (the running example is at the end):
Author: Use the developer or developers of the version being cited. To avoid having the system treat the developer(s) as a first and last name, use curly braces around each developer.
Year: The release year for the version being cited.
Title: The game title, which has to be manually italicized (using \emph).
Howpublished: The word “Game” followed by the platform in square brackets.
Day: The release day, if known, for the version being cited.
Month: The release month, if known, for the version being cited.
Note: The publisher’s name and location, followed by, optionally “Last played” and the date last played.
Publisher and Address: The template will not read these (hence the need to enter them as a note).

Example:

@misc{SM,
Year = {1994}}


text:
# Raised Dot Computing Newsletter: Exploring Microcomputer Applications for the Visually Impaired October 1986 -- Volume 5, Number 46

Published Monthly by Raised Dot Computing, Inc., 408 South Baldwin Street, Madison WI 53703. General phone: 608-257-9595. Technical Hotline: 608-257-8833.

Subscriptions: $18/year Print,$20/year Audio Tape, $30/year Disk. (Kindly add$20/year for postage outside N. America.)

Submissions are always welcome, particularly those on diskette. All are subject to editing for style and clarity. All opinions expressed are those of the author.

Table of Contents: the all-uppercase words name the disk chapters; the words after the equals sign are the actual article titles.

• BRL BEX DOX = Braille BEX Dox Finally Available
• VERSAPOINT ANNOUNCE = RDC is Now Selling the TSI VersaPoint Embosser
• TRANSCRIBEX ANNOUNCE = Computer-Assisted Braille Production with TranscriBEX
• WORDTALK REVIEW = WORD-TALK: A Word Processing Program with a Different Look by Neal Ewers
• SENSIBLE UPDATE = Talking Sensible Speller Gets TEXTALKER
• AAAS WANTS YOU = AAAS Compiling Directory of Scientists and Engineers with Disabilities
• CTEC CLOSES = C-TEC Closes Doors After Three Years
• KOOKY KURZWEIL = Kurzweil's Kooky Korporate Kulture by Lee Kamentsky
• HISTORY PT2 = A History of Raised Dot Computing by David Holladay, Founder, President, and Janitor
• MASTHEAD & TMS = Who's Who at Raised Dot Computing, Inc. -- Copyright and Trademark Information

Yes friends, it's finally true. The braille BEX Dox have been expeditiously reprinted by National Braille Press and speedily shipped to our door by the US Mail. Five volume set of Learner User and Master Levels costs $50, shipped UPS. We deeply appreciate the patience you've shown with the delays! ## RDC is Now Selling the TSI VersaPoint Embosser We're pleased to announce that we are now selling the VersaPoint continuous-form embosser manufactured by TSI. We feel the VersaPoint is a well-designed and rugged machine; we're selling it for$3,595.

Since we have a strong interest in increasing the availability of braille, RDC makes a point to contact companies in the process of brailler design and offer them assistance and testing. TSI took us up on our offer: since February they've been picking our brains about embosser design. We had the opportunity to thoroughly test a number of prototypes and make suggestions. We're delighted that, at our urging, a number of useful features were added and some undesirable features changed. We're convinced that TSI is seriously committed to producing and supporting an excellent, medium-cost braille embosser.

### Facts and Figures

The VersaPoint's stated embossing rate is 20 characters per second. In real-life tests, we've found that it embosses between 16 cps and 24 cps, depending on the length and format of the document. One of the VersaPoint's best features is its huge buffer, which holds 30,000 characters--around 32 braille pages. The large buffer frees your computer for other tasks: it takes around 1 minute to print a 6-page Zippy chapter to the VersaPoint. During embossing, you can pause and restart the VersaPoint at a flick of the on-line switch.

### The 60-Second Summary

RDC feels keenly our responsibilities to our customers; we thought long and hard about whether the VersaPoint was the embosser we wanted to sell. We wanted a unit that was well-designed, sturdy, and easy to interface. We know that our customers need a full braille line (the VersaPoint can emboss 42 cells) and strong, thermoform-able dots. We understand the crucial importance of reliability and good, dependable service. We feel the VersaPoint fits the bill.

The VersaPoint costs $3595 from RDC, including shipping within the continental US. (Our arrangement with TSI states that we only sell VersaPoints within the 50 United States. Canadians and others outside the US should contact TSI directly.) To connect the VersaPoint to your computer, you need an appropriate cable. For an Apple Super Serial Card, it's the 9M; for an Apple 2c, it's the 10M, and for an IBM-PC serial port, it's an 8M. Each of these cables costs$35.

For those just starting out, we have two VersaPoint packages that bundle software and hardware. The BEX & VersaPoint package costs $4195, and it includes the VersaPoint, BEX, a Super Serial Card and 9M cable, and an Echo Plus. The TranscriBEX & VersaPoint adds the TranscriBEX module to those items; it costs$4295.

## Computer-Assisted Braille Production with TranscriBEX

[Editor's Note: Way back in May 1985, we announced a program called "BETTE-BEX." Since then, there's been nothing but loud silence on the topic. That's because we learned our lesson the hard way with BEX: never announce a program before it's ready to ship out the door! Well, we may have been quiet, but we've not been idle. And so without further ado ... JK]

RDC is proud to announce that we're now shipping TranscriBEX Version 2.0. The TranscriBEX module consists of a detailed manual and a disk of transformation chapters and sample data. Adding the TranscriBEX module turns BEX into a high-quality braille transcription system, that allows individuals with widely varying skills to contribute to the task of braille production.

### Meeting the Standards for Braille

Over the years those interested in braille have adopted detailed braille format standards. English Braille--American Edition, 1969 defines the complex rules by which print is contracted into Grade 2 braille, as well as providing formatting standards for general text material. More rigorous formatting standards have been developed for braille textbooks, where the braille reader must be able to relate the braille text to the pagination of the print original. The Code of Braille Textbook Formats and Techniques, 1977, establishes set routines for representing inkprint texts in a consistent, readable, and efficient manner. The standards set by the Code and English Braille free the individual transcriber from the responsibility of redesigning braille format with every transcription.

TranscriBEX supports the vast majority of the standards established by these two books, including:

• Textbook format prose (with print page indicators), with or without runninghead
• Literary format prose (without print page indicators), with or without runninghead
• Preliminary and supplemental material such as dedications, prefaces, forewords, tables of contents, indexes, and outlines
• Poems: as verse or as prose, with or without numbered lines, with or without multiple levels of indentation
• Plays: as verse or as prose, with or without numbered lines
• Tables and columnar material: when transcribed line-for-line with guide dots between the columns; when transcribed in "stair-step" fashion; when transcribed as paragraphs
• Foreign languages: both occasional foreign words with "generic" dot 4 accents and large passages of grade 1 text with unique braille cells for each accented letter
• Questions and exercises: both simple lists and hierarchical lists, with or without answer choices

As you can see from this list, TranscriBEX is designed for rigorous transcription of already-published print materials. Not every person producing braille documents needs TranscriBEX's power. BEX alone suffices when you're only producing "casual" braille. By "casual" we mean short worksheets, simple tests, papers, and reports. Especially when you're creating print and braille editions of the same document, BEX alone is fine.

### Note to BETTE Users

As you can see from the list of supported formats, TranscriBEX can do a lot more than BETTE. And TranscriBEX's base program, BEX, is much easier to use than BRAILLE-EDIT. TranscriBEX is so much better than BETTE, in fact, that we've stopped selling BETTE. We're offering real bargains to encourage existing BETTE users to convert to TranscriBEX. We've prepared a 13-page "Difference Manual" that explains the nitty-gritty details of TranscriBEX and BETTE. This week we sent out letters to all the BETTE users for whom we have addresses. If you have not yet received a letter, please give us a call today!

### Elements of the TranscriBEX System

TranscriBEX is a transcribing-specific way of using BEX. You enter and correct text and store it on disk using BEX's Editor. (BEX can also read the textfiles that most Apple word processors create, so it's possible to do data entry in another editor, if your prefer.) Experienced transcribers can enter data directly in braille using the Apple keyboard as a braillewriter. People who know nothing about braille, however, can do all their data entry in print, because BEX's braille translator changes regular inkprint text into Grade 1 or 2 braille appropriate for transmission to a computer-driven braille device. TranscriBEX supplies a set of transformation rules for use with BEX's file-driven Replace characters. This serves as an automatic link between the mnemonic TranscriBEX commands and the complex instructions that control the formatter. BEX's formatter generates the appropriate page format in accordance with the Code and English Braille.

BEX's formatter supports every brailler on the market. In addition, BEX's braille previewer allows you to proofread format and braille translation on the computer screen before committing anything to paper. Thanks to the braille previewer, every TranscriBEX user doesn't need to own a computer-driven braille embosser. You can confidently perform the first four steps of the braille transcription process and then send the final disks to a brailling center for actual embossing.

The TranscriBEX Manual is aimed at both novices and experts. It provides basic background information on braille translation and format, as well as specific references to the Code and English Braille where needed. In addition to reference material on specific page formats, the TranscriBEX Manual and disk contain a step-by-step tutorial. Combining the BEX Dox, the TranscriBEX Manual, and occasional consultation with an experienced transcriber, someone knowing nothing about computers or braille transcription can produce many types of braille.

### Braille Translation

While no micro-computer-based braille translator can be 100% perfect, our translator comes very close. Even if you know absolutely nothing about braille, you can enter print and quickly generate highly readable braille. The TranscriBEX Manual explains how you can slightly modify your print data entry to create truly perfect braille. A logical system of special symbols let you force or suppress placement of the braille letter sign, show braille italics and boldface, distinguish between the braille apostrophe and opening and closing single quotes, and more. You can switch between Grade 1 and Grade 2 translation, and you can transcribe non-English languages like French and Spanish, complete with all diacritic marks. We supply a list of transformation rules that automatically fix any obscure braille translation errors that may occur, and tell you how to add to that list.

### A Sample of TranscriBEX Commands

The TranscriBEX commands don't require that you remember the particular page layout that the rule books mandate. Instead, the commands are named after the type of format you want to create. Each TranscriBEX command begins with two backslashes. Following the \\, there is an English-like word or words.

Suppose you're transcribing a poem with three levels of indentation; the print original numbers every fifth line in the left margin. The Code requires three different indents: the first-level lines to cell 1, the second-level lines to cell 3, and the third-level lines to cell 5. All levels runover to cell 7. The last six cells of each line are reserved for the line numbers, which must appear (without the number sign), on the same braille line where the poetic line begins. Manually keeping track of the varying indent and runover can be a real chore: TranscriBEX simplifies the process considerably.

The TranscriBEX commands are patterned after what you see in print. In this case, you enter \\poem \\3level \\numberedlines to establish the appropriate framework. Each poetic line is preceded with \\1p, \\2p, or \\3p, depending on how it's indented in print. To place a line number over on the right hand side, you enter \\ln 5, \\ln 10, etc.

The TranscriBEX Manual thoroughly explains the hundred-odd \\ commands, as well as providing references to the relevant portions of the Code and English Braille.

### The Advantages of the TranscriBEX Approach

Because BEX's formatter creates the proper braille format as it is printing, the text itself is very easy to change. Inserting or deleting characters, words, or paragraphs does not affect the page format, because the text on disk is not page-oriented. The transcription of a single book can be divided among several transcribers. Each can independently proofread their portion for typographical errors, braille translation, and appropriate print page indicators. One individual then collates the various disks into a single document. To facilitate this division of labor, we've developed special package prices for transcribing groups--contact us for more information.

The TranscriBEX system allows individuals with a wide variety of transcribing skills to contribute to the job of getting a braille translation finished. Because BEX lets you use DOS 3.3 and ProDOS textfiles from other Apple word processors, data entry volunteers don't need to own BEX or TranscriBEX. "Braille-naive" users can do print data entry using the widely-available AppleWorks software, for example. As they become more familiar with braille format, they could also enter some of the simpler TranscriBEX commands, like the print page indicators.

Slightly more experienced TranscriBEX users then convert the data from the AppleWorks file structure to BEX's "chapters"--full details on this are supplied in the TranscriBEX Manual. They "massage" the data, entering transcriber's notes and establishing the appropriate braille formats with TranscriBEX commands.

Skilled braillists can do data entry directly in braille, using six keys on the Apple's keyboard as an electronic braillewriter. It's also possible to print the braille text as braille dot patterns on the computer screen, which allows skilled braillists to read braille in a familiar way.

The TranscriBEX system is in no way an attempt to obsolete the skilled transcriber. Just the opposite: by automating the more routine aspects of braille transcription, it frees the skilled braillist for more challenging work. By serving as a resource for the data entry team, one skilled transcriber can help create many accurate and well-formatted documents quickly.

### TranscriBEX's History and Future

TranscriBEX replaces BETTE, the first Apple program to support the Code of Braille Textbook Formats and Techniques, 1977. TranscriBEX incorporates many suggestions from the more-than-150 BETTE users around the country. Suggestions from seven "beta testers" helped us to make BETTE and TranscriBEX better programs; for all their work and insights, we thank: David Barnett and associates at the Prose & Cons Braille Unit; Bill Davis and associates at the New Mexico School for the Visually Impaired; Conchita Gilbertson of Virginia; Rebecca Keenan of the Virginia IMRC; Bettye Krolick of Colorado; Daveed Mandell of San Francisco; and William Peary of Baha'i Service for the Blind.

RDC is committed to supporting TranscriBEX users, because we are committed to increasing braille availability in general and braille literacy in the schools in particular. We're very excited about TranscriBEX: we feel the quality of its output compares favorably with any other microcomputer-based braille translation system.

### Ordering Information

A complete package of BEX plus the TranscriBEX module costs $500. This includes the BEX program disk and documentation in large print and audio tape; the TranscriBEX module disk with transformation chapters and sample data in every stage of the TranscriBEX process; and the TranscriBEX Reference Card and Manual in large print. (The TranscriBEX Manual and Reference Card are also available in braille upon request.) For individuals who already own BEX, the TranscriBEX module alone costs$100. We urge transcribing groups interested in multiple copies of TranscriBEX to contact us for special group prices.

## WORD-TALK: A Word Processing Program with a Different Look by Neal Ewers

WORD-TALK is a talking, ProDOS-based word processor for the Apple and Echo from Computer Aids Corporation. Unlike BEX and ProWORDS, WORD-TALK is a "what you see is what you get" (WYSWYG) program. The editor screen always resembles the currently formatted printed page. There are no embedded print format commands to learn. To indent a paragraph or create several columns of words or numbers, simply press the tab key and the cursor will go to the preset positions called up by the program. (You can change these positions to your liking.) To center a line, simply press control-W at the end of the text you want centered. The appropriate number of spaces are inserted in the beginning of the line so it's moved over to the correct position.

Additional format options are supplied in the format menu. Here you can set margins, single sheet or continuous feed, page numbering, running headers and footers, or decide the specific page or pages of a multiple page document you wish to have printed. And when you have finished formatting, you can simply return to the editor to check out your new parameters.

Place the cursor where ever you wish, and press control-A. The column, line, and page location of the cursor will immediately be spoken. Or you can press control-G, and direct the cursor to "Go" to whatever column, line, or page you desire.

By placing the printed page at the tips of the user's fingers, WORD-TALK allows those of us who cannot see to more easily accomplish a variety of tasks. Anyone who spends more than a few minutes a day writing or proofreading forms which contain information in specific column and line locations probably doesn't need to be convinced of the merits of this program. Except for the absence of a command designed to right justify the text on a particular line, WORD-TALK seems to have all the formats and flexibility required for form-filling applications. Or, you may need to check the exact word placement of a complicated brochure you will be sending your customers. Understanding how the page appears to people who can see may help you more confidently determine the shape of the final product.

Add to all this the fact that the WORD-TALK manual, free from the necessity of explaining a complex variety of embedded commands, is short, well written and easily understood, and you're on your way.

### Limitations of the Program

This particular "what you see is what you get" program can be a mixed blessing, especially for those who write long documents. The absence of embedded commands can make locating text difficult. Consider, for example, searching for titles and paragraphs in a 15 page document. A blind user can't just arrow the cursor to these boundaries when they only appear on the screen.

I started by searching for the returns that most often mark paragraphs. But WORD-TALK does not place searchable <CR>s in the text. The return key simply causes the cursor to go to the next line, so that strategy won't work. Searching for multiple spaces finds the spaces at the ends of lines as well as at the beginnings. I contacted the folks at Computer Aids Corp for guidance, and they suggested two approaches. Use the "Go To" command, mentioned above, to move to the line number that contains the title, or, simply search for the words that begin the title or paragraph in question. But I find it all but impossible to recall that information from among the hundreds of words and lines in a 15 page document, especially one I may have written several months ago.

They did supply me with an undocumented trick. You can set up your own "tokens" by pressing Open-Apple-Number. For example, for the start of each paragraph, enter Open-Apple-1. These tokens show as inverse characters on the screen and can be searched for, but they do not appear in the printout. This trick works, but not perfectly. The tokens take up space on the line. When your paragraphs indent five spaces, a token at position four is no problem, but when you have block style paragraphs, your line lengths will be off by one. Also the numbered tokens are recognized as real characters by other programs that can read the WORD-TALK textfile which contains them. Thus, they are faithfully printed out by both ProWORDS and BEX.

But even with these user tokens to mark title and paragraph boundaries, I still had problems. WORD-TALK can only search forwards. As a result, if you're currently at paragraph 12 and you want to go back to paragraph nine, you either return to the beginning of the document and attempt to find paragraph 9 by starting the search procedure all over again, or you spend a fair amount of time running the cursor up the left hand margin in search of the desired boundary. When you do, the Echo pronounces the first letter of each word passed over. Eventually you come to a space that signifies either a blank or indented line. But this is a very slow process for a blind user.

### Formatting the Print Page

WORD-TALK provides a distinctive beep that marks the transition between print pages. But, unlike BEX and ProWORDS, WORD-TALK has no way of preventing the very bottom line on that print page from containing the title of a major section of the document. The only way around this dilemma is to insert a blank line before the title, thus forcing that title to appear on the next page. So I used WORD-TALK's "Go To" command to call up the last line of each page of the document and insert a blank line where ever needed.

Unfortunately, you could have the same problem I had. When I arrived at the final page of my document I realized that there was only one line of print on that page. "Easy!" I said, entering the format menu and making my right margin a little narrower. "Let's hear it for the magic of computers." Oh for some magic indeed, for now my 14-page document had added lines that all were in the wrong place. And, for all I knew, the bottom line of any page could still contain a title.

There was nothing to do but begin this procedure all over again, and then I discovered another problem. My centered titles were the same number of spaces from the left margin they had been before I reformatted the document by adding 3 spaces to each line. In other words, my titles were no longer centered. Since WORD-TALK does not make use of embedded commands, I was forced to once again search for all 13 titles and perform the control-W centering operation on each of them in turn. If WORD-TALK had the ability to search for format information as well as characters, it would be a lot more flexible.

### Miscellaneous Problems

Computer Aids has modified a very early version of the TEXTALKER program which, among other things, mispronounces a far greater number of words than some of the later versions. Three speech speeds are available, and the punctuation parameters can be controlled separately in both the keyboard or typing mode and in the review or listening mode. But the pitch and delay defaults of the voice output cannot be adjusted. The absence of the TEXTALKER screen review mode makes it difficult to spell out catalog entries and other relevant information.

Like ProWORDS, WORD-TALK saves information to disk as a ProDOS sequential textfile. It will also read textfiles written by other programs. But there is no way to search for and delete the numerous undesired returns that might be scattered throughout the file. Those returns simply show up as new lines on the WORD-TALK screen, and each unwanted line break must be reformatted by hand.

WORD-TALK provides only limited DOS utilities--you must leave WORD-TALK to format or copy disks, copy files, or convert information between DOS 3.3 and ProDOS. It does allow you to delete and rename files as well as create additional ProDOS sub-directories. When loading or saving a document, it is always necessary to include the name of the volume you are accessing, since WORD-TALK always defaults to the volume which contains the program. The WORD-TALK manual makes almost no attempt to explain even the limited ProDOS utilities it provides, and it does even less to help the beginning ProDOS user cope with the concept of volumes, subdirectories, pathnames, etc.

### Summary

There are some definite advantages to a "what you see is what you get" program. WORD-TALK provides that certain sense of security in always knowing exactly what your printed page will look like. For people writing short memos and letters or filling out forms, WORD-TALK is an easily-navigated and easy-to-use program. However, for people writing longer documents, the price paid for WYSWYG security may be too high. Without embedded commands that control page formatting, margins, paragraph indents, centering, etc., one must constantly reformat the text by hand, much as you would on a very good talking typewriter.

### An Act of Desperation

January of 1983 was a month of many changes: Apple was switching from the Apple two plus to the Apple 2e; TSI was switching from the VersaBraille P2B to the P2C; Street Electronics was switching to a new speech chip that required a new TEXTALKER; and I was trying to switch from exclusively supporting the CCS 7710 card to also supporting the Super Serial Card. Keeping in touch with all my customers about these issues by phone was overwhelming.

Besides, it seemed that I was on the phone 20 hours a day. On several occasions I moved the telephone into the bathroom and conducted business from the bathtub. I'm sure that the folks on the other end of the wire were a little surprised to hear the sloshing when I got up to get names and addresses.

In an attempt to keep customers up-to-date with all the changes, the first issue of the Raised Dot Computing Newsletter was published in February, 1983. I just wrote a BRAILLE-EDIT chapter and used "Multi-copy print" to produce 40 copies on my dot matrix printer. [If anyone has one of these originals, I would appreciate a copy for the archives.] For the March issue, I got a tape duplicator.

The Newsletter was useful in cutting down on phone time, but it also complicated my life. Very soon, I realized that I was spending about half my time doing the Newsletter. The other half of my time was spent opening mail, writing letters, and answering the phone. A third half of my time was spent trying to write programs. I was quickly running out of halves!

Next Month: Raised Dot Hires Someone & The Last Year in Lewisburg