<div dir="ltr">From tally marks as numbers are real things to modern mathematics<br><br>Tally marks were the first way people counted things. They were good for simple counting and helped people think of better ways to count. As societies grew and needed to count more things, they needed better methods. Tally marks were not good for big numbers or doing math, so people made symbols for numbers.<br><br>This change from tally marks to number symbols happened in places like ancient Sumer, Egypt, and China. These cultures moved from using tally marks to using better and easier ways to write numbers.<br><br>Skipping some important steps, in the 1600s, some crucial things happened to go from simple tally marks as numbers are real things to the math we use today.<br><br>René Descartes was a French mathematician. In 1637, he introduced the Cartesian coordinate system. This system helps us connect algebra and geometry. We use it to plot points on a graph with an x-axis and a y-axis. It makes it easier to see how numbers and shapes work together.<br><br>Isaac Newton from England and Gottfried Wilhelm Leibniz from Germany were two other important mathematicians. In the 17th century, both of them independently developed calculus. Calculus is a branch of math that helps us understand change and motion. It’s very important for studying things like physics, engineering, and economics.<br><br>These developments were big steps forward in math. The Cartesian coordinate system made it easier to work with shapes and numbers together. Calculus helped us study changes and solve complex problems. Together, these ideas helped make modern math more powerful and useful for many different fields. <div><br></div><div>All from the humble beginnings of tally marks as numbers are real things.<br></div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Tue, 23 Jul 2024 at 06:02, Frank Wimberly <<a href="mailto:wimberly3@gmail.com">wimberly3@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex"><div dir="auto"><div><br></div><div><br></div><div>---<br>Frank C. Wimberly<br>140 Calle Ojo Feliz, <br>Santa Fe, NM 87505<br><br>505 670-9918<br>Santa Fe, NM</div></div><br><div class="gmail_quote"><div dir="ltr" class="gmail_attr">On Mon, Jul 22, 2024, 9:33 PM Nicholas Thompson <<a href="mailto:thompnickson2@gmail.com" target="_blank">thompnickson2@gmail.com</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0px 0px 0px 0.8ex;border-left:1px solid rgb(204,204,204);padding-left:1ex">
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Hi Jon,</div>
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As a Peircean, I neverdoubted it for a minute. A true ;roposition is one upon which we will agree in the very long run. A real thing is any concept about which a true proposition can be uttered. I think that makes numbers, and right triangles real given
that 3^2 + 4^2 = 5^2 and that the squire upon the hippopotamus is equal to the son of the squires on the other two hides. So they are real even though we will neverever touch one. </div>
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Weird.</div>
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Nick</div>
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<div id="m_3502097204972111906m_-5322341746943037662divRplyFwdMsg" dir="ltr"><font face="Calibri, sans-serif" style="font-size:11pt" color="#000000"><b>From:</b> Friam <<a href="mailto:friam-bounces@redfish.com" rel="noreferrer" target="_blank">friam-bounces@redfish.com</a>> on behalf of Jon Zingale <<a href="mailto:jonzingale@gmail.com" rel="noreferrer" target="_blank">jonzingale@gmail.com</a>><br>
<b>Sent:</b> Monday, July 22, 2024 6:22 PM<br>
<b>To:</b> <a href="mailto:friam@redfish.com" rel="noreferrer" target="_blank">friam@redfish.com</a> <<a href="mailto:friam@redfish.com" rel="noreferrer" target="_blank">friam@redfish.com</a>><br>
<b>Subject:</b> Re: [FRIAM] New Mexican's Sunday's story on education proficiency</font>
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Numbers are real things. The more one explores them, the more experiences one has of them, the more confidently one comes to rely on them.</div>
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