[BlindMath] discussion about making tactile images

[John]


>> Hello,
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>> Are you a blind or low vision person with a fascination about science, technology, engineering, and math?
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>> Are you a sighted person who wishes to help the blind in these areas or learn along side us?
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>> I am asking for input and discussion about 2-dimensional tactile images.
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>> I am particularly interested in what is a meaningful text-based description of such images.
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>> In addition, I have developed example images that can be viewed with a 40-cell refreshable braille display.
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>> If you are interested in this discussion please contact me at johnmillerphd at hotmail.com.
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>>  
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>> I was reviewing the concepts of concave up and concave down on Khan Academy.
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>> The youtube video said a function is concave up if it forms a shape like a cup.
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>> It is concave down if it forms a shape like a cap.
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>> I remember learning in school that concave up forms a shape like a bowl that holds water.
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>> A blind friend said for speech output he would prefer the word dome rather than cap since cup and dome sound very distinct.
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>> By the way concave down is a cap or a dome such as an architectural feature in some buildings like the U.S. Capitol.
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>>  
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>> The youtube video then presented a graphic of the cubic polynomial f(x) = x^3-x.
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>> It plotted the function for x ranging from -5 to 5.
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>> I was curious to know where did the function cross the x-axis.
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>> I immediately knew it crossed the x-axis at the origin since the y value is 0 for 0^3-0.
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>> But I had to think about where else the function crosses the x axis.
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>> And what is the general shape of the 2-D plot anyway?
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>> Once you know its shape you can get at which ranges of x it is concave up and which it is concave down.
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>> The designer of the youtube video selected the x range from -5 to 5 for this function because it looks good for the resolution and size of typical video displays.
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>> Here I mention that a video display is a device for sighted users.
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>> For this range of x the y value ranges from -120 to 120.
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>> I have studied this function and now have answered all my questions about it.
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>> It turns out all 3 zero-crossings happen between x with a value of -1.5 and x with a value of 1.5.
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>> For a zoomed in tactile image with x from -1.5 to 1.5, the y value ranges from -1.875 to 1.875.
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>> The graph has a local minimum and maximum with magnitude of approximately 0.384.
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>> The tactile image with the above x range and y range displays the local minimum and maximum sufficiently far away from the x-axis that it looks good in braille.
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>> When I say "looks good" in braille I mean that its y value is observable from the tactile image as nonzero.
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>> This tactile image sent to a braille graphic embosser, sent to a braille embosser as a text file, or raised up on swell touch paper would look good.
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>> Recall that a braille graphic embosser takes about a minute to form a paper-based tactile image.
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>> Viewing a tactile image on a refreshable braille display can be somewhat disappointing.
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>> It requires arrowing down the image to explore it from top to bottom.
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>> Its resolution is rather low compared to typical resolutions for plots made for viewing by sighted individuals.
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>> Its resolution is lower than that for that of a tactile braille embosser.
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>> The area of the graphic that can be viewed at once is not very much; it is just 3 braille dots tall by 80 dots wide.
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>> For primary viewing I would recommend paper tactile graphics, those from a Columbia braille embosser by View Plus, or using a graphiti.
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>>  
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>> And yet many blind individuals have a 40-cell refreshable braille display next to a laptop all the time.
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>> And any time the laptop is powered on.
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>> So for ease of access, cost, portability, and quietness, sometimes viewing a tactile graphic with a refreshable braille display is quite helpful.
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>> You might want a quick review of a tactile image to make sure the plot is not blank before you paste it in a powerpoint and share it with a professor or a colleague.
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>>  
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>> For an audio description of a mathematical function, one might ask where are local maxima and minima?
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>> As you progress across the x-axis, how is the function behaving in each segment?
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>> For example, is it increasing, decreasing, or holding steady?
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>> Are there things you can say about 2-D scatter plots in a text description that provide meaning as a stand alone description or that complement a tactile image?
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>> Would you like to view or generate a tactile image of a mathematical function by yourself?
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>> If you are a programmer and would like to volunteer to help the blind community, there is an opportunity here.
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>> But again if you are just a hobbyist who likes to think about what 2-D images or graphs look like, this discussion is also for you.
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>> Best Regards,
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>> John
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