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Discussion and Debate
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Physical & Life Sciences
What “is” a radio signal-?
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<blockquote data-quote="sjastro" data-source="post: 73129948" data-attributes="member: 352921"><p>A Mathematical Universe does raise some interesting philosophical questions as highlighted in <a href="https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences" target="_blank">Wigner's article</a> published in 1960 which leads to the ultimate question is mathematics invented or discovered?</p><p>The history of science would suggest the answer is both.</p><p>As an example in the late 19th century the formula for the <a href="https://en.wikipedia.org/wiki/Balmer_series" target="_blank">Balmer series</a> for the emission lines of the hydrogen atom was devised in an <strong>ad hoc</strong> manner.</p><p>As to why the formula worked was largely a mystery in which the case the formula can be considered an example of mathematics being "invented" to show an empirical relationship.</p><p>With the advent of quantum mechanics in the early 20th century it was found a much deeper level of mathematics involving <a href="https://en.wikipedia.org/wiki/Laguerre_polynomials" target="_blank">Laguerre polynomials</a> led to the <strong>derivation</strong> of Balmer series.</p><p>In this case the mathematics was a "discovery" which also explained why the formula works.</p><p>It is cases like this which is the motivation behind Wigner's article and probably an influence on Tegmark.</p></blockquote><p></p>
[QUOTE="sjastro, post: 73129948, member: 352921"] A Mathematical Universe does raise some interesting philosophical questions as highlighted in [URL='https://en.wikipedia.org/wiki/The_Unreasonable_Effectiveness_of_Mathematics_in_the_Natural_Sciences']Wigner's article[/URL] published in 1960 which leads to the ultimate question is mathematics invented or discovered? The history of science would suggest the answer is both. As an example in the late 19th century the formula for the [URL='https://en.wikipedia.org/wiki/Balmer_series']Balmer series[/URL] for the emission lines of the hydrogen atom was devised in an [B]ad hoc[/B] manner. As to why the formula worked was largely a mystery in which the case the formula can be considered an example of mathematics being "invented" to show an empirical relationship. With the advent of quantum mechanics in the early 20th century it was found a much deeper level of mathematics involving [URL='https://en.wikipedia.org/wiki/Laguerre_polynomials']Laguerre polynomials[/URL] led to the [B]derivation[/B] of Balmer series. In this case the mathematics was a "discovery" which also explained why the formula works. It is cases like this which is the motivation behind Wigner's article and probably an influence on Tegmark. [/QUOTE]
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