Yes, the "Men What Do Rock" are back purveying "Rock-Based Music of Exceptional Quality". But how good is their second effort? The artefactory investigates.
First, the reviews.
Kerrang say it's the most massive sounding rock album since Def Leppard's "Hysteria", giving it a KKKKK rating.
Classic Rock say it makes Def Leppard's "Hysteria" look like a four-track demo and call it album of the year.
Rolling Stone say that, on the title track, the bravado is unmistakable -- a chorus with the sold-out-arena kick of Def Leppard's "Rock Rock ('Til You Drop)" - the words of David Fricke who wrote the Leppard biography, Animal Instinct.
As with Hysteria, this album was a bit of a long struggle. The Darkness were trying to follow up their previous enormously success, Permission to Land.
And as Leppard did, The Darkness seem to have done some shopping around for a producer. Leppard first went with Jim Steinman (Meat Loaf, Bonnie Tyler) as producer before returning to the legendary Mutt Lange. The Darkness couldn't agree terms with Lange and went with Roy Thomas Baker (Queen, Foreigner, The Cars).
The new album... the sound is much better than before, sacrificing the hard edged crunch from the first record for a more rounded sound. Some of it is overblown with strings and bagpipes and sitars and pan-pipes. The harmonies, swirling strings etc are all generally very Queen-like.
Bald is easily the most interesting track here, who the heck thinks of rhyming "follicle" with "diabolical"! The song opens with a sort ofdoom-laden intro with church bells, but then goes off into the sort ofZeppelin-esque epic that powered Pyromania. It's never so dark as to be serious so they get away with it.
One Way Ticket lifts both form and riff from AC/DC's "Highway to Hell" but then AC/DC would regard cowbells, harmonies, sitars, and the coke-snorting that opens the song as incredibly effete. Only a master producer like RTB could make this sort of mess sound good, and his Queen-like flourishes make this an instant classic. Not sure if the coke-snorting intro is lifted from Rammstein's Kokain.
Dinner Lady Arms the most Leppardesque song here, with a beautifulintro that reminds me of Animal and Stand Up (Kick Love Into Motion). The chorus is all Queen for variation. I wish Mutt Lange had produced this but it's very good anyway.B
Is It Just Me to me sounds lifted from AC/DC's Big Gun (riff) and Shoot to Thrill (form) but then takes on a life of its own. Very catchy.
Knockers as juvenile as the title suggests. Intro sounds like Leppard-lite. Insanely catchy.
Blind Man Queen-influenced dreamy-sounding closing track, very well done.
English Country Garden Perfect Queen pastiche with a Meat Loaf piano intro. Very English, very silly.
Hazel Eyes more English whimsy. Pretty silly too but will probably be a mass singalong with everyone jigging about when they do it live with all the bagpipes and marching-beat drums.
Seemed Like A Good Idea At The Time starts out as a crap ballad laden with strings but then gets Queen-like and more interesting. Rips off their own Love Is Only A Feeling.
Girlfriend Status Quo with some very camp disco flourishes, almost sound Abba-esque.
So the verdict? Some misses but enough hit to make it all well worth it.It's short at 35 minutes so the bad bits pass by quickly.
History tells us that two of RTB's later bands, namely Foreigner and the Cars, went on to do great work with Mutt Lange. With Foreigner we got Waiting For A Girl Like You, Urgent, Juke Box Hero. With the Cars, it was Drive, Magic, You Might Think... so who knows?
Interestingly, other reviewers seem to have seen every band in here from Aerosmith to Bachman-Turner Overdrive to everybody I have mentioned up above. It's almost as if every rock fan listener is reading into this record their own favourites, whatever it is they are most familiar with. Perhaps we ought to see this as an indicator of just how well the Darkness have been able to distill and incorporate all these pretty disparate influences.
Top effort!
December 18, 2005
December 14, 2005
Zero
The concept of zero was absolutely crucial in the development of mathematics, enabling the development of algebra and latterly, calculus.
It was in India that the notion of zero as representing nothingness first took root.
The Indians were not the first to employ a place value system like the decimal number system we use today. The Babylonians employed such a system and the Mayans independently used one too, and each realised that a marker of some sort needs to be used in such a system to prevent errors. So in a crude sense, you had an idea of a zero as a marker of an empty place, with a very definite and resticted technical meaning. But this would not be the result of, say, subtracting 1 from 1. That result, i.e "nothing", was something the Babylonians and the Greeks who followed them had great trouble with.
The key leap in thought that occurred to ancient Indian mathematicians here was to recognise that this zero could also be used to represent "nothingness". Brahmagupta was the first to hit upon a deep - and unique - insight, that the arithmetical number line could be extended to yield zero and negative integers.
It's only abstractly that one can conceive of speaking of "one apple", "two apples" and consider "no apples" as inhabiting the same thought-space. We take this for granted now but at the time, this was a revolutionary achievement.
It was in India that the notion of zero as representing nothingness first took root.
The Indians were not the first to employ a place value system like the decimal number system we use today. The Babylonians employed such a system and the Mayans independently used one too, and each realised that a marker of some sort needs to be used in such a system to prevent errors. So in a crude sense, you had an idea of a zero as a marker of an empty place, with a very definite and resticted technical meaning. But this would not be the result of, say, subtracting 1 from 1. That result, i.e "nothing", was something the Babylonians and the Greeks who followed them had great trouble with.
The key leap in thought that occurred to ancient Indian mathematicians here was to recognise that this zero could also be used to represent "nothingness". Brahmagupta was the first to hit upon a deep - and unique - insight, that the arithmetical number line could be extended to yield zero and negative integers.
It's only abstractly that one can conceive of speaking of "one apple", "two apples" and consider "no apples" as inhabiting the same thought-space. We take this for granted now but at the time, this was a revolutionary achievement.
Mathematics: what India contributed to the ancient world
My previous post touched on the knowledge ancient Indian astronomers gleaned from the ancients.
Here, however, I'd like to highlight what they contributed to mathematicians at large. I exclude techniques they uncovered which were either independently used elsewhere or which generally never came into use, there being alternatives.
India's big contribution was in the development of techniques and tools.
A major practical trigonometric contribution the Indians made was the development of sines. This was to replace the tables of "chords" of angles first used for calculations by Hipparchus: the half-chord of double an angle corresponds to its sine, the chord of an angle being 120 times the sine of half the angle. Aryabhatta, in particular, seems to have realised that this value came up more frequently in trigonometric calculations than the more unwieldy chord. He even detailed the construction of the first sine table: for angles from 0 to 90 degrees in steps of 3.75 (i.e pi/48 radians).
Brahmagupta developed a numerical interpolation technique which we now know as the method of second-order differences.
And of course, the decimal place value number system as we know it, and the use of zero are Indian in origin. More on this in a later post.
Incidentally, the calculation of the sine of pi/48 is reasonably straigjtforward if you know basic trig identities. pi/24 = pi/6 - pi/8. pi/6 has standard sine and cosine values that can be read off an equilateral triangle. Those for pi/8 can be worked out using the half-angle formulae for pi/4, corresponding to an isosceles right triangle. Then use the difference formula to obtain the values for pi/24, and the half-angle formulae again to get the desired answer.
Aryabhatta might have missed a trick, though: calculating these values in steps of 3 or 1.5 degrees (pi/60 or pi/120) would have been a bit more effort but could still have been managed with the techniques of his day.
The trick is to obtain trig values for pi/5: this can be done from similar triangles obtained by drawing diagonals in a regular pentagon, making use of the golden ratio to obtain these values in terms of the square root of 5. One you have this, use pi/30 = pi/5 - pi/6, and the half-angle formulae then for pi/60 and again for pi/120.
Why not at intervals of 1 degree (pi/180) then? Well, the issue here is that you would need to solve a cubic equation to obtain this value from that of pi/60. The techniques for solving these analytically were not available until Cardano came along centuries later, they certainly cannot be solved geometrically. Moreover, attempting to solve the cubic for this case leads to an answer in terms of complex numbers, though the value is demonstrably real! The way out is to use approximations, but that theory would be more fully developed much later.
Here, however, I'd like to highlight what they contributed to mathematicians at large. I exclude techniques they uncovered which were either independently used elsewhere or which generally never came into use, there being alternatives.
India's big contribution was in the development of techniques and tools.
A major practical trigonometric contribution the Indians made was the development of sines. This was to replace the tables of "chords" of angles first used for calculations by Hipparchus: the half-chord of double an angle corresponds to its sine, the chord of an angle being 120 times the sine of half the angle. Aryabhatta, in particular, seems to have realised that this value came up more frequently in trigonometric calculations than the more unwieldy chord. He even detailed the construction of the first sine table: for angles from 0 to 90 degrees in steps of 3.75 (i.e pi/48 radians).
Brahmagupta developed a numerical interpolation technique which we now know as the method of second-order differences.
And of course, the decimal place value number system as we know it, and the use of zero are Indian in origin. More on this in a later post.
Incidentally, the calculation of the sine of pi/48 is reasonably straigjtforward if you know basic trig identities. pi/24 = pi/6 - pi/8. pi/6 has standard sine and cosine values that can be read off an equilateral triangle. Those for pi/8 can be worked out using the half-angle formulae for pi/4, corresponding to an isosceles right triangle. Then use the difference formula to obtain the values for pi/24, and the half-angle formulae again to get the desired answer.
Aryabhatta might have missed a trick, though: calculating these values in steps of 3 or 1.5 degrees (pi/60 or pi/120) would have been a bit more effort but could still have been managed with the techniques of his day.
The trick is to obtain trig values for pi/5: this can be done from similar triangles obtained by drawing diagonals in a regular pentagon, making use of the golden ratio to obtain these values in terms of the square root of 5. One you have this, use pi/30 = pi/5 - pi/6, and the half-angle formulae then for pi/60 and again for pi/120.
Why not at intervals of 1 degree (pi/180) then? Well, the issue here is that you would need to solve a cubic equation to obtain this value from that of pi/60. The techniques for solving these analytically were not available until Cardano came along centuries later, they certainly cannot be solved geometrically. Moreover, attempting to solve the cubic for this case leads to an answer in terms of complex numbers, though the value is demonstrably real! The way out is to use approximations, but that theory would be more fully developed much later.
December 13, 2005
Astronomy: what Indians picked up from the ancients
One thing Indians quickly come to realise is how central astrology is to how many people choose to order their lives.
Astrology is of course for the most part bunkum. But the ancient Indians included among their number some decent world-class astronomers whose contributions were significant, and had a major impact on how modern mathematics and physics developed in the West.
This is sometimes taken much too far. Some ill-informed Indians occasionally speak as if ancient Indian knowledge has informed this native tradition all along. In their reading, the absence of any firm historical records means nothing and Indians independently discovered all the glories the ancient world had to offer.
The reality is different.
Indian astronomers must have been in contact with Babylonians (before 500 BC). We know this since Babylonian astronomers are known to have calculated various numerical time periods, e.g to do with the period of the moon's revolution round the earth, and the methods they used have survived. The Indians later developed their own mathematical models of moon behaviour and other phenomena but made use of these exact same figures.
Other data from Babylonian observations would prove to be crucial for the later development of Greek astronomy. The concept of the zodiac was theirs, the division of the circle into 360 degrees (for days of the year) too.
We also know that Indian astronomers must have been in contact with the Greeks.
Celestial bodies could, according to the Platonic dictates of Greek aesthetics, not move in anything other than circular paths. Yet there is no way the orbits of the planets as observed from earth can be made to fit circular paths with the earth at their centre. The particular problem lay in the need to explain the apparent retrograde motion of planets, where they appear to double back on themselves in the sky
Hipparchus (2nc entury BC) proposed an ingenious explanations for this, with more complex orbits composed of epicycles. The idea was that here you would have the planet in question travelling in a circlular orbit, still, except that the centre of this circle would itself travel along a circle centred at the earth.
Aryabhatta (5th century) is known to have used such a model, so it is fair to say he and Indian astronomers picked up this idea from the Greeks and were bound by such thinking, at least in this matter.
Ptolemy (2nd century) would go on to refine this model further, introducing epicycles of epicycles and so on. This complicated approach held sway across the Arab and Western worlds until Copernicus and Kepler came along.
However, Aryabhatta and his immediate successors had no inclination of this model, which would only reach India via Arab influences much later.
Interestingly, only in this century was it finally realised that Ptolemy might have been onto something. Apparently the circle and epicycle form the first and second approximations respectively, if you were to consider Fourier series expansiona of the mathematical expressions for the orbits.
It's not clear if Ptolemy had the mathematical nous or tools to take the calculations those extra steps further, though!
My source for all this is the fabulous From Eudoxus to Einstein: A History of Mathematical Astronomy by C M Linton, an outstanding volume. This fabulous book covers many of the gaps popular-science books have when it comes to explaining just how and why particular theories of the celestial skies were developed.
Astrology is of course for the most part bunkum. But the ancient Indians included among their number some decent world-class astronomers whose contributions were significant, and had a major impact on how modern mathematics and physics developed in the West.
This is sometimes taken much too far. Some ill-informed Indians occasionally speak as if ancient Indian knowledge has informed this native tradition all along. In their reading, the absence of any firm historical records means nothing and Indians independently discovered all the glories the ancient world had to offer.
The reality is different.
Indian astronomers must have been in contact with Babylonians (before 500 BC). We know this since Babylonian astronomers are known to have calculated various numerical time periods, e.g to do with the period of the moon's revolution round the earth, and the methods they used have survived. The Indians later developed their own mathematical models of moon behaviour and other phenomena but made use of these exact same figures.
Other data from Babylonian observations would prove to be crucial for the later development of Greek astronomy. The concept of the zodiac was theirs, the division of the circle into 360 degrees (for days of the year) too.
We also know that Indian astronomers must have been in contact with the Greeks.
Celestial bodies could, according to the Platonic dictates of Greek aesthetics, not move in anything other than circular paths. Yet there is no way the orbits of the planets as observed from earth can be made to fit circular paths with the earth at their centre. The particular problem lay in the need to explain the apparent retrograde motion of planets, where they appear to double back on themselves in the sky
Hipparchus (2nc entury BC) proposed an ingenious explanations for this, with more complex orbits composed of epicycles. The idea was that here you would have the planet in question travelling in a circlular orbit, still, except that the centre of this circle would itself travel along a circle centred at the earth.
Aryabhatta (5th century) is known to have used such a model, so it is fair to say he and Indian astronomers picked up this idea from the Greeks and were bound by such thinking, at least in this matter.
Ptolemy (2nd century) would go on to refine this model further, introducing epicycles of epicycles and so on. This complicated approach held sway across the Arab and Western worlds until Copernicus and Kepler came along.
However, Aryabhatta and his immediate successors had no inclination of this model, which would only reach India via Arab influences much later.
Interestingly, only in this century was it finally realised that Ptolemy might have been onto something. Apparently the circle and epicycle form the first and second approximations respectively, if you were to consider Fourier series expansiona of the mathematical expressions for the orbits.
It's not clear if Ptolemy had the mathematical nous or tools to take the calculations those extra steps further, though!
My source for all this is the fabulous From Eudoxus to Einstein: A History of Mathematical Astronomy by C M Linton, an outstanding volume. This fabulous book covers many of the gaps popular-science books have when it comes to explaining just how and why particular theories of the celestial skies were developed.
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