an autodidact meets a dilettante…

‘Rise above yourself and grasp the world’ Archimedes – attribution

Posts Tagged ‘maths

algorithms, logarithms and biorhythms

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Wilhelm Fliess with Sigmund Freud (you guess)

In a recent conversation I was talking about the algorithms used by organisations like Facebook and Google to get people hooked into reading or listening to or otherwise attending to a whole host of stuff related to what they attended to yesterday. My interlocutor continued the conversation, but inadvertantly replaced the word ‘algorithm’ with ‘logarithm’ throughout, which I didn’t correct, perhaps not so much out of politeness but because, though I knew enough about the difference to use the right word, I would have difficulty in defining either term, in case he asked. As for biorhythms, I threw them in just for fun.

Mathematics is probably my weakest subject, and for that reason I’ve often been drawn to it in my dilettantish fashion, as to a kind of secret society I’ve been excluded from due to lack of the requisite. So I’ll start with my extremely limited and probably wrong working understanding of algos and logos (and bios), then provide a more informed account through a bit of research.

An algorithm, I think, is a largely computer-generated aggregate of a person’s data-gathering which provides some predictive power about their future data-gathering, or future interest, so that the data can be presented to them for gathering. Or something like that. A logarithm, I think, has something to do with exponentials. So that if something increases exponentially, it also increases logarithmically. Or logarithmickly? Or maybe a logarithm is some mathematical relation between a number and its exponent. Or something like that. A biorhythm is something to do with your supposed natural cycle of activity/inactivity throughout the day. It was new age stuff of the seventies, my early teen years. It seems to have died the death.

So now for the details and correctives.

An algorithm is indeed most associated with computing and data processing, though it may be used in a broader sense, mathematically or not. In fact it can be used to describe the process to get any result. In that sense a cookbook is a set of algorithms. But even in computing, the term is broader than my working understanding of it implied. I was thinking of particular algorithms, the ones used by certain web presences like Google, Facebook and Netflix to get you hooked into continuing to use them. To get you addicted, in a sense. So that’s all that needs to be said here about algorithms in general. In another post I’ll look at those particular algorithms that have worked so well for their creators (or the hirers of those creators) that they’ve become some of the richest folk in the world. That should be much more interesting. 

A logarithm is also something like what I thought it was, but of course my understanding was very vague. It’s described as the inverse function to exponentiation – just as I sort of thought. For example, take the number 64, and think of it as 2 x 2 x 2 x 2 x 2 x 2, or 2. The 6 here is the exponent (n), while the 2 is the base (b), so the general formulation is bn. The exponent (n) is also called the power, as in two to the sixth power, 26. Now, say that you want to know what power to raise the number two to get 256. That’s to say, 2n = 256, find n. This number that we want to find is the logarithm. So the question or equation can be restated thus:

log2(256) = n , find n

and the answer is n = 8. So the logarithm is the power that we have to raise a specified (base) number to, in order to get to another specified number. That’s all we need to know as a beginning. Obviously it gets more complicated with higher powers – but then, with higher powers, anything’s possible.

A biorhythm chart is a development of ideas concocted by one Wilhelm Fliess, a good mate of the only slightly less eccentric Sigmund Freud, back in the late 19th century. I well remember this fad gaining super-popularity in the seventies, with a paperback on the topic floating around our household. That and ‘speed reading’ were all the go. The basic hypothesis was that our lives – presumably in terms of energy, ‘clarity’ and competence – go in cycles, which can be charted as sinusoidal waves. The standard model argued for a 23-day physical cycle, a 28-day emotional cycle and a 33-day intellectual cycle. I’ve actually met someone who drew up these charts for herself back in the day. You live and learn. Needless to say, there’s no evidence whatever to back these ideas up, but they’re claimed often as ancient learning which has been eclipsed by the monstrous juggernaut of modern science, much like that other font of cyclical predictive wisdom, astrology…..


Khan academy video: intro to logarithms

Written by stewart henderson

June 6, 2019 at 9:55 am

how to debate William Lane Craig, or not – part 4, on mathematics and gods

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Now we come to the argument that God is the best explanation of the applicability of mathematics to the physical world. My intuitive response to this – and of course I’m not a mathematician – is that mathematics appears to me to be be a kind of abstraction from, that’s to say a manipulation of, a play on and further development of, the regularities that exist in the world, and that if no such regularities existed, the world wouldn’t exist. Or at least would not be in any sense describable. For example, the most basic form of regularity required would be a binary contrast, describable in mathematical or logical terms as x and not x.  The real world, though , offers far more opportunities for playing on and manipulating regularities than this. So many opportunities have been found in fact, and so many beautiful theorems have been developed from them over the centuries that mathematics has often been given a mystical, miraculous status. One thinks of the Pythagoreans in ancient times, and the mathematically-obsessed philosophers of the seventeenth century, such as Descartes, Spinoza and Leibniz. However, I think it’s fair to say that, historically, when mathematics has been raised to mystical heights, great problems have ensued. So I don’t see anything particularly miraculous in the fact that a tool for understanding the regularities of the world can be developed and manipulated to underpin theories which further deepen or extend that understanding.

Eugene Wigner’s 1960 essay, ‘The unreasonable effectiveness of mathematics in the natural sciences’ is available online, and everyone should be encouraged to read it – though it doesn’t make for easy reading. I think it’s a little unfortunate that Wigner uses the word ‘miracle’ a number of times in the essay, but he certainly doesn’t refer at any time to a god. And while I would hesitate to interpret Wigner from my lay background, I’m not sure I agree with his view in the essay that, while elementary mathematical concepts derive directly from the perceived regularities of the actual world, more complex and abstract mathematical concepts don’t so derive, and yet can be applied with uncanny reliability, or if you like profitability, from our perspective, to that world, as is the case with much modern physics. If that were so, if the mathematical abstractions our minds create were completely removed from the world’s actual regularities, and yet just happened to apply to them to provide us with a richer and more developed view of our universe, then that would indeed be a ‘happy coincidence’. But abstraction doesn’t occur in a vacuum. Just as non-Euclidian geometry derives from the regularities of nature that Euclid strove to axiomise in a set of rules, and just as multi-dimensionality derives from the standard three-dimensional world of our experience, mathematical abstraction is always tied to some underlying actual regularity, however obscured by its overlay. The applicability of maths is not a happy coincidence (which isn’t to say all mathematical abstractions are applicable of course), but that is just because the world has regularity. Thus when we look at Dr Craig’s formal argument:

1. If God did not exist, the applicability of mathematics would be a happy coincidence.

2. The applicability of mathematics is not a happy coincidence.

3. Therefore God exists.

we see once again that the problem lies in the conditional statement – this time statement one. Our world has regularities, without which not. Mathematics is all about the play of regularities, so it isn’t coincidental that some mathematics has applicability. This is not mysterious, and it doesn’t imply anything about supernatural agency. Thus it isn’t reasonable to infer the existence of any god, let alone the human-obsessed, son-begetting god adhered to by Dr Craig.

Written by stewart henderson

March 17, 2013 at 12:14 pm