I tried looking up how Justin actually catches objects but it drew a blank on the www. However, I'm somewhat confident that Justin's catching ability involves actual mathematical calculations of a thrown object's trajectory and velocity and its own movements. — TheMadFool
Justin suggests that we actually do perform mathematical calculations but are just unaware of it; it happens subconsciously so to speak. — TheMadFool
Recent research suggests that a more computationally efficient strategy is to simply run so that the acceleration of the tangent of elevation of gaze from fielder to ball is kept at zero. — StreetlightX
humans don't do mathematical calculations when we play throw and catch, at least not consciously. — TheMadFool
Roboticists need to rethink their approach to the subject in a fundamental way. — TheMadFool
Recent research suggests that a more computationally efficient strategy is to simply run so that the acceleration of the tangent of elevation of gaze from fielder to ball is kept at zero. Do this and you will intercept the ball before it hits the ground. — StreetlightX
Russell said 'Physics is mathematical, not because we know so much about the physical world, but because we know so little — Wayfarer
I see that StreetlightX made much the same point with a quote. — fdrake
By analogy, hopefully not a poor one, the processes that confer the catching ability should also be similar if not identical. — TheMadFool
Sounds very mathematical — TheMadFool
Ergo, it seems probable that our brains actually do the math when catching thrown objects and by extension, when doing other physical activities. — TheMadFool
Why would you ever conclude that? If a group of people show up at work in the morning do you conclude that they took similar, if not identical modes of transportation, just because they demonstrate that they have the capacity to get to work? — Metaphysician Undercover
Excellent post. But I've seen some of those spooky Boston Dynamics robot videos, and they're pretty darn good at freestyle running! — Wayfarer
I don't see how the body's physical abilities are quantifiable mathematically and yet the brain controls it non-mathematically — TheMadFool
I don't think it's that hard to see. Remember the mathematization process is a method - that's why I mentioned its history. I mean, before Descartes came along nobody had ever thought of modelling three dimensional space as geometrical co-ordinates. (This is one of the discoveries that qualifies Descartes for the title of genius.)
Almost anything physical is quantifiable using that method insofar as it has mass, velocity, and other attributes that can be quantified. That methodology was very much the consequence of the discoveries of Newton, Galileo and Descartes, among a few others - crucial to modern science. Nobody from before their time thought about things that way. And that methodology is universal in scope - you can use it to model almost anything from the atomic to galactic scales (with the caveat that the discovery of relativity and quantum theory have shown that Newtonian physics is only universal within certain scales.)
So, that methodology is what is used in robotics, artificial intelligence, and so on - it all relies on the computation of quantifiable attributes. It's not that there's something intrinsically mathematical about what's being modeled (in this case, although there might be in other subjects). It's simply that mathematical modelling is what is behind all such technologies.
The whole question of 'what is maths' and 'what is number' is also a really interesting one, but it's not actually connected with the question of how 'Justin' does its stuff. — Wayfarer
Do you have any idea what such a system of non-numerical determinants of motion that makes predictions possible would look like? — TheMadFool
Textbook example of putting the cart before the horse. — Wayfarer
1. Either catching involves math or catching doesn't involve math
2. If catching doesn't involve math then changing mathematical parameters (like mass) shouldn't affect catching ability — TheMadFool
But you're not comparing like with like. When a human catches, then the action consists of muscular reflexes, hand-eye co-ordination, and on a micro-cellular level, the exchanges of ions across membranes, and so forth and so on.
Those actions can be modelled by machines, but that modelling relies on maths.
When a machine performs an action, then you have motors which position instruments controlled by binary code. This is reliant on mathematics, in a way which is completely different to the way in which organic performance is.
If you can't see that, I give up. (But then, this should have been obvious from the way the thread was named, as nothing about what 'Justin' can do, connotes 'insight', and indeed the word is not to be found in the linked Wikipedia page.) — Wayfarer
n my robot-human analogy, not only is the ability to catch near-identical when observed but the methods employed seem to be similar in terms of needing quantification (math). — TheMadFool
So, there's something non-mathematical in human and animal physics? If that's true then how come mathematical physics is applicable to kinesiology and biomechanics; after all human limbs are essentially mechanical levers and the amount of force muscles can exert can be quantified. I don't see how the body's physical abilities are quantifiable mathematically and yet the brain controls it non-mathematically. At the very least the applicability of physics, a mathematical enterprise, to our bodies indicates that somewhere along the chain from intending a movement to the actual movement itself there is some math involved. — TheMadFool
Well, to be fair, there is no reason why there shouldn't be non-mathematical determinants of motion. However, given that we can model motion based on only math it seems either these non-numerical determinants of motion are superfluous or operate in parallel to the mathematical ones. Do you have any idea what such a system of non-numerical determinants of motion that makes predictions possible would look like? — TheMadFool
Ergo, given what practice is and how my story reveals that changing the key physical quantity involved in a sport can turn you from a pro to a beginner, it must be that our brains do math — TheMadFool
This doesn't follow at all. Just more idiotic reasoning, as with all of your posts. — StreetlightX
1. It's impossible for Justin to possess an ability to catch thrown objects without actually performing some mathematical calculations.
2. Humans possess the ability to catch thrown objects and we, unlike Justin, routinely catch objects without even thinking of mathematics let alone doing any actual calculations. — TheMadFool
What about brains? Are brains programmed? The model is just as much part of reality as what is being modeled. The model has causal relationship with what is being modeled and has causal power itself (it changes your behavior based on the model and what is being modeled).Not at all. It's the requirement of computers - they process binary code, and anything they're programmed to do must be coded. But it's a way of modelling reality, not reality itself. — Wayfarer
Looks like you are being run by an IF-THEN program. A high-level language is a representation of the machine language that computers understand. So is your mind a representation of what is going on at the neurological level. You're not aware of the mathematical calculations your neurons are performing. You mind's mental imagery is a representation of what is going on at the neurological level, just as you aren't aware of what is going on inside the computer by just looking at the screen, but the screen is a representation of what is happening inside the computer.Thing move, I move, must make it so that one thing move in certain way in relation to other thing; if move good, catch ball. — StreetlightX
Mathematics is part of our birthright. One-week-old babies perk up when a scene changes from two to three items or vice versa. Infants in their first ten months notice how many items (up to four) are in a display, and it doesn't matter whether the items are homogeneous or heterogeneous, bunched together or spread out, dots or household objects, even
whether they are objects or sounds. According to recent experiments by the psychologist Karen Wynn, five-month-old infants even do simple arithmetic. They are shown Mickey Mouse, a screen covers him up, and a second Mickey is placed behind it. The babies expect to see two Mickeys when the screen falls and are surprised if it reveals only one. Other babies are shown two Mickeys and one is removed from behind the screen. These babies expect to see one Mickey and are surprised to find two. By eighteen months children know that numbers not only differ but fall into an order; for example, the children can be taught to choose the picture with fewer dots. Some of these abilities are found in, or can be taught to, some kinds of animals.
Can infants and animals really count? The question may sound absurd because these creatures have no words. But registering quantities does not depend on language. Imagine opening a faucet for one second every time you hear a drumbeat. The amount of water in the glass would represent the number of beats. The brain might have a similar mechanism, which would accumulate not water but neural pulses or the number of active neurons. Infants and many animals appear to be equipped with this simple kind of counter. It would have many potential selective advantages, which depend on the animal's niche. They range from estimating the rate of return of foraging in different patches to solving problems such as "Three bears went into the cave; two came out. Should I go in?"
Human adults use several mental representations of quantity. One is analogue—a sense of "how much"—which can be translated into mental images such as an image of a number line. But we also assign number words to quantities and use the words and the concepts to measure, to count more accurately, and to count, add, and subtract larger numbers. All cultures have words for numbers, though sometimes only "one," "two," and "many." Before you snicker, remember that the concept of number has nothing to do with the size of a number vocabulary. Whether or not people know words for big numbers (like "four" or "quintillion"), they can know that if two sets are the same, and you add 1 to one of them, that set is now larger. That is true whether the sets have four items or a quintillion items. People know that they can compare the size of two sets by pairing off their members and checking for leftovers; even mathematicians are forced to that technique when they make strange claims about the relative sizes of infinite sets. Cultures without words for big numbers often use tricks like holding up fingers, pointing to parts of the body in sequence, or grabbing or lining up objects in twos and threes.
Children as young as two enjoy counting, lining up sets, and other activities guided by a sense of number. Preschoolers count small sets, even when they have to mix kinds of objects, or have to mix objects, actions, and sounds. Before they really get the hang of counting and measuring, they appreciate much of its logic. For example, they will try to distribute a hot dog equitably by cutting it up and giving everyone two pieces (though the pieces may be of different sizes), and they yell at a counting puppet who misses an item or counts it twice, though their own counting is riddled with the same kinds of errors.
Formal mathematics is an extension of our mathematical intuitions. Arithmetic obviously grew out of our sense of number, and geometry out of our sense of shape and space. The eminent mathematician Saunders Mac Lane speculated that basic human activities were the inspiration for every branch of mathematics:
Counting -» arithmetic and number theory
Measuring —> real numbers, calculus, analysis
Shaping —> geometry, topology
Forming (as in architecture) —> symmetry, group theory
Estimating —> probability, measure theory, statistics
Moving —> mechanics, calculus, dynamics
Calculating —> algebra, numerical analysis
Proving —> logic
Puzzling —» combinatorics, number theory
Grouping —> set theory, combinatorics
Mac Lane suggests that "mathematics starts from a variety of human activities, disentangles from them a number of notions which are generic and not arbitrary, then formalizes these notions and their manifold interrelations." The power of mathematics is that the formal rule systems can then "codify deeper and non-obvious properties of the various originating human activities." Everyone—even a blind toddler—instinctively knows that the path from A straight ahead to B and then right to C is longer than the shortcut from A to C. Everyone also visualizes how a line can define the edge of a square and how shapes can be abutted to form bigger shapes. But it takes a mathematician to show that the square on the hypotenuse is equal to the sum of the squares on the other two sides, so one can calculate the savings of the shortcut without traversing it.
Consider this request: Visualize a lemon and a banana next to each other, but don't imagine the lemon either to the right or to the left, just next to the banana. You will protest that the request is impossible; if the lemon and banana are next to each other in an image, one or the other has to be on the left. The contrast between a proposition and an array is stark. Propositions can represent cats without grins, grins without cats, or any other disembodied abstraction: squares of no particular size, symmetry with no
particular shape, attachment with no particular place, and so on. That is the beauty of a proposition: it is an austere statement of some abstract fact, uncluttered with irrelevant details. Spatial arrays, because they consist only of filled and unfilled patches, commit one to a concrete arrangement of matter in space. And so do mental images: forming an image of "symmetry," without imagining a something or other that is symmetrical, can't be done.
The concreteness of mental images allows them to be co-opted as a handy analogue computer. Amy is richer than Abigail; Alicia is not as rich as Abigail; who's the richest? Many people solve these syllogisms by lining up the characters in a mental image from least rich to richest. Why should this work? The medium underlying imagery comes with cells dedicated to each location, fixed in a two-dimensional arrangement. That supplies many truths of geometry for free. For example, left-to-right arrangement in space is transitive: if A is to the left of B, and B is to the left of C, then A is to the left of C. Any lookup mechanism that finds the locations of shapes in the array will automatically respect transitivity; the architecture of the medium leaves it no choice.
Suppose the reasoning centers of the brain can get their hands on the mechanisms that plop shapes into the array and that read their locations out of it. Those reasoning demons can exploit the geometry of the array as a surrogate for keeping certain logical constraints in mind. Wealth, like location on a line, is transitive: if A is richer than B, and B is richer than C, then A is richer than C. By using location in an image to symbolize wealth, the thinker takes advantage of the transitivity of location built into the array, and does not have to enter it into a chain of deductive steps. The problem becomes a matter of plop down and look up. It is a fine example of how the form of a mental representation determines what is easy or hard to think. — Steven Pinker
You seem to be conflating "performing" with "thinking". Does Justin "think", or "perform"? Is there a difference between "performing" mathematical calculations as opposed to "thinking" of mathematical calculations? — Harry Hindu
Get involved in philosophical discussions about knowledge, truth, language, consciousness, science, politics, religion, logic and mathematics, art, history, and lots more. No ads, no clutter, and very little agreement — just fascinating conversations.