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ArishMell · 70-79, M
Sorry - it is not possible to type algebra and formulae correctly in SW's basic text-editor but I'll risk these copying properly from writing them in 'Word', and edit as necessary:
18. The Period, T, in seconds of a Simple Pendulum of length L.
[i]T = 2π √(L/g)[/i].
If not attributed directly to Galileo Galilei, it does formalise his observations.
.
19 Geometrical Progression from first term [i]a[/i] and common ratio [i]r[/i]; the [i]n[/i]th value =
[i]a.r^(n-1)[/i] NB: the index is on the ratio alone, not the product.
One practical application is in designing gear-boxes.
'
20 . Spherical-spreading attenuation of amplitude with distance D from source, of a radiated sound or other signal:
[i]Attenuation = 20Log(D)[/i] , in deciBels.
It is the familiar inverse-square law, but in logarithmic rather than linear terms. The logarithm is to base-10 but that is not possible to type properly here.
.
21. Conversion of Sound Pressure-Level from linear units to dB:
[i]SPL in dB = 20Log(measured / reference)[/i] , dB; where the measured and reference pressures are in µPa and again, base-10 logs.
The 0db level of the familiar noise-measuring deciBel scale is the lowest SPL discernable by the fully-healthy human ear. If you analyse human hearing in linear and dB terms, what you learn about the ear's sensitivity is awe-inspiring......
18. The Period, T, in seconds of a Simple Pendulum of length L.
[i]T = 2π √(L/g)[/i].
If not attributed directly to Galileo Galilei, it does formalise his observations.
.
19 Geometrical Progression from first term [i]a[/i] and common ratio [i]r[/i]; the [i]n[/i]th value =
[i]a.r^(n-1)[/i] NB: the index is on the ratio alone, not the product.
One practical application is in designing gear-boxes.
'
20 . Spherical-spreading attenuation of amplitude with distance D from source, of a radiated sound or other signal:
[i]Attenuation = 20Log(D)[/i] , in deciBels.
It is the familiar inverse-square law, but in logarithmic rather than linear terms. The logarithm is to base-10 but that is not possible to type properly here.
.
21. Conversion of Sound Pressure-Level from linear units to dB:
[i]SPL in dB = 20Log(measured / reference)[/i] , dB; where the measured and reference pressures are in µPa and again, base-10 logs.
The 0db level of the familiar noise-measuring deciBel scale is the lowest SPL discernable by the fully-healthy human ear. If you analyse human hearing in linear and dB terms, what you learn about the ear's sensitivity is awe-inspiring......
Sazzio · 31-35, M
@ArishMell Would you say we use these equation on a daily basis without realising? Like judging when to slow down a car (speed) when approaching (time) a narrow gap (size)? Ok it's just speed, time and length I know... but still?
Judging things by mental equations we never realise? Maybe we even use Algorithm, Pie spherical without knowing? 🤔
Judging things by mental equations we never realise? Maybe we even use Algorithm, Pie spherical without knowing? 🤔
ArishMell · 70-79, M
@Sazzio [i]Interesting question.....[/i]
Speed, time and distance are hardly "just", and yes, whatever our brains are doing to make the necessary judgements must be extremely subtle and complicated, far beyond the simple algebra of D = ST.
To a large extent we do this instinctively too, although we need learn to judge them for artificial contexts like driving a car.
I don't think we use the circular formulae and similar laws not directly applicable biologically, by instinct though. We need to learn them.
.
Your question ties in with my last 2 examples, relating to sound. I took an interest in wondering what bats might possibly image in their minds when hunting for insects in a wood at night; or navigating through a cave in which the darkness is absolute.
To help me I set out to understand sound and hearing at a basic level, using our own sense as an example because it is so easy to find texts for, anchored in our own experience. The biological principles are much the same.
What I realised is that in the little animal just a very few grammes of brain is carrying out some extraordinarily complex, rapid and responsive signal-processing to control its flying, breathing, calling and (hopefully for a hungry bat) prey-catching; while still leaving enough brain simply keeping the animal alive!
Further, if its roost is in a cave, the same physically-little brain has to deal with very peculiar acoustics without any help from sight, and remember them enough to find the way in and out safely.
The corollary is that of our brains, many, many times larger than a bat's; how much is busy with our primary animal physiology; compared to how much is handling our far greater speech, dexterity, intellectual and emotional capacities?
'
So if the human - or any animal - brain is "doing maths" instinctively and behind the scenes as it were, [i]just what sort of maths is it[/i]?
Speed, time and distance are hardly "just", and yes, whatever our brains are doing to make the necessary judgements must be extremely subtle and complicated, far beyond the simple algebra of D = ST.
To a large extent we do this instinctively too, although we need learn to judge them for artificial contexts like driving a car.
I don't think we use the circular formulae and similar laws not directly applicable biologically, by instinct though. We need to learn them.
.
Your question ties in with my last 2 examples, relating to sound. I took an interest in wondering what bats might possibly image in their minds when hunting for insects in a wood at night; or navigating through a cave in which the darkness is absolute.
To help me I set out to understand sound and hearing at a basic level, using our own sense as an example because it is so easy to find texts for, anchored in our own experience. The biological principles are much the same.
What I realised is that in the little animal just a very few grammes of brain is carrying out some extraordinarily complex, rapid and responsive signal-processing to control its flying, breathing, calling and (hopefully for a hungry bat) prey-catching; while still leaving enough brain simply keeping the animal alive!
Further, if its roost is in a cave, the same physically-little brain has to deal with very peculiar acoustics without any help from sight, and remember them enough to find the way in and out safely.
The corollary is that of our brains, many, many times larger than a bat's; how much is busy with our primary animal physiology; compared to how much is handling our far greater speech, dexterity, intellectual and emotional capacities?
'
So if the human - or any animal - brain is "doing maths" instinctively and behind the scenes as it were, [i]just what sort of maths is it[/i]?