Explain how math is not a universal logic

[Ouroboros]

Reading the original paper, it doesn't seem like the bees visit all the flowers. They only optimize between the flowers they visit. That's not the same as the Traveling Salesman Problem. TSP is the graph problem of finding the optimal path for visiting all cities (flowers), not just the ones they happen to land on. It sounds to me like the reporting on this research was simplified and exaggerated to make headlines rather than accurate descriptions.

 

[Enai de a lukal]

Honey Bees have been studied for thousands of years. So you aren't the only one that questions their abilities. I just accept the fact they are capable of creating honeycomb structures in hexagonal patterns. However, since this is still being debated ...

Einstein seemed to think geometry was a natural science. I will quote a reference I made to one of his theories (relativity), in a previous thread I made from his lecture on Geometry and Experience. Where he said his theory would not have been possible without it.

“Yet on the other hand it is certain that mathematics generally, and particularly geometry, owes its existence to the need which was felt of learning something about the relations of real things to one another. The very word geometry, which, of course, means earth-measuring, proves this. For earth-measuring has to do with the possibilities of the disposition of certain natural objects with respect to one another, namely, with parts of the earth, measuring-lines, measuring-wands, etc. It is clear that the system of concepts of axiomatic geometry alone cannot make any assertions as to the relations of real objects of this kind, which we will call practically-rigid bodies. To be able to make such assertions, geometry must be stripped of its merely logical-formal character by the geometry. To accomplish this, we need only add the proposition:- Solid bodies are related, with respect to their possible dispositions, as are bodies in Euclidean geometry of three dimensions. Then the propositions of Euclid contain affirmations as to the relations of practically-rigid bodies.

Geometry thus completed is evidently a natural science; we may in fact regard it as the most ancient branch of physics. Its affirmations rest essentially on induction from experience, but not on logical inferences only.”

Honey Bees can solve the traveling salesman problem faster than super computers. They can create honeycombs with hexagonal structures. I don’t see why they would not be capable of knowing some type of math, or even geometry if they are capable of things like this. Either these Bees know their bees knees (their stuff or what the hell they are doing) or they are just creating siphons for no real apparent reason and it is sheer coincidence.

I think they know are a lot more intelligent than we give them credit for and are natures little helpers.

Either Einstein was wrong about general relativity or Bees are smarter than Einstein. They were capable of flight long before we ever were so they might even know a little thing or two about physics too.

I'm not disputing that bees create honeycombs with hexagonal shapes- maybe they do. But even if they do, this does not entail that they understand geometry or math, just as bees flying doesn't entail that they understand physics. This is a rather large non-sequitur; doing something doesn't require understanding the physics or mathematical concepts involved. When a baby takes her first steps, she doesn't understand the physics involved. When I use a computer, I don't understand computer design or programming. When I ride on an airplane, I don't understand the physics of flying or of airplane engineering. Similarly with bees. An animal may do something without understanding how/what they did- just like the dog crossing the street doesn't understand traffic laws. For a bee to understand geometry, it must be able to do more than create geometric shapes out of honeycomb- there must be some awareness or consciousness of these geometric shapes as geometric shapes. In other words, they must understand what they are doing (creating geometric patterns in honeycomb) in terms of mathematics, for them to "understand math".

 

[Ouroboros]

The hexagonal shape of the honeycomb can be explained by simple mechanics: Honeycombs' Surprising Secret Revealed | LiveScience

They start as circles. The bees heat up the wax. And simply by all the circles pressure on each other, a hexagonal shape happens naturally.

 

[Enai de a lukal]

And I suspect there's some economy to the way they do it such that it was selected for. In other words, they do it that way because it works, not because they're thinking about math.

 

[Ouroboros]

And I suspect there's some economy to the way they do it such that it was selected for. In other words, they do it that way because it works, not because they're thinking about math.

Agree.

I suspect it's a matter of the most efficient use of space, and it creates a very solid and sturdy structure. You can build a grid using squares or hexagons, but hexagons have 6 corners and 6 sides instead of the 4/4 square.

If anyone has played with those tiny magnetic buckyballs he/she will see that hexagon shapes are very easy to make.

 

[Skwim]

And I suspect there's some economy to the way they do it such that it was selected for. In other words, they do it that way because it works, not because they're thinking about math.

Agree.

I suspect it's a matter of the most efficient use of space, and it creates a very solid and sturdy structure. You can build a grid using squares or hexagons, but hexagons have 6 corners and 6 sides instead of the 4/4 square.

If anyone has played with those tiny magnetic buckyballs he/she will see that hexagon shapes are very easy to make.

As I related in post 27, along with the accompanying illustration below:

"As Sunstone points out, the hexagonal shape of a cell is merely a result of the squeezing effect of the surrounding cells. Moreover, lone individual cells are rarely hexagonal."
​

​

To impute a reasoning purpose behind the geometry is not only unnecessary, but ludicrous. It's on the order of claiming that a dog who poops at three different spots in the back yard is purposely creating a triangle because if one connects the three spots that's exactly the resultant shape. A honey bee cell is six-sided because exactly six---no more, no less---cells of the same size can completely encompass it. My suspicion is that Slapstick may be identifying with John Belushi

​

Or perhaps IS John Belushi. This ↑ you, Slappy?

 

[Slapstick]

A lot of words in what you say---and not all that intelligible, but nothing to refute the article.

Interesting, and your supporting evidence that bees have more gray matter than any other animal is . . . . . . .? (A link will be sufficient)

The Traveling Salesman Problem isn’t some easy task to accomplish for people or even computers. Computers have to compute every possible route to determine the shortest. Yet Bees are capable of finding the shortest, most efficient route to hit all of their objectives and to consume the least amount of energy and find their way back to their nest without determining every possible route to find the most efficient.

“The traveling salesman problem is easy to state, and — in theory at least — it can be easily solved by checking every round-trip route to find the shortest one. The trouble with this brute force approach is that as the number of cities grows, the corresponding number of round-trips to check quickly outstrips the capabilities of the fastest computers. With 10 cities, there are more than 300,000 different round-trips. With 15 cities, the number of possibilities balloons to more than 87 billion.” https://www.simonsfoundation.org/quanta/20130129-computer-scientists-take-road-less-traveled/

That is a lot of possibilities for so few cities. A computer has to run every route before it can calculate the shortest most efficient distance or solution. A Bee does not. “After trying about “20 of the 120 possible routes, the bees were able to select the most efficient path to visit the flowers,” Lihoreau says. “They did not need to compute all the possibilities.” A naïve bee traveled almost 2,000 meters on its first foraging bout among the pentagonal array; by her final trip, she’d reduced that distance to a mere 458 meters.” Flying Math: Bees Solve Traveling Salesman Problem - Wired Science

“Professor Lars Chittka from Queen Mary's School of Biological and Chemical Sciences said: ‘In nature, bees have to link hundreds of flowers in a way that minimises travel distance, and then reliably find their way home - not a trivial feat if you have a brain the size of a pinhead! Indeed such travelling salesmen problems keep supercomputers busy for days. Studying how bee brains solve such challenging tasks might allow us to identify the minimal neural circuitry required for complex problem solving.’” Tiny brained bees solve a complex mathematical problem

As you might expect, not all of us, or even many of us, read all the links a person posts. Just which one debunks the evidence?

So what that they're filled with honey? Is this really relevant? As for my argument being junk science, this is something you've yet to establish. But I await a cogent argument with proof..

This is from post #28.

"The nests of European honeybees ([FONT=&quot]Apis mellifera[/FONT]) are organised into wax combs that contain many cells with a hexagonal structure. Many previous studies on comb-building behaviour have been made in order to understand how bees produce this geometrical structure; however, it still remains a mystery. Direct construction of hexagons by bees was suggested previously, while a recent hypothesis postulated the self-organised construction of hexagonal comb cell arrays; however, infrared and thermographic video observations of comb building in the present study failed to support the self-organisation hypothesis because bees were shown to be engaged in direct construction. Bees used their antennae, mandibles and legs in a regular sequence to manipulate the wax, while some bees supported their work by actively warming the wax. During the construction of hexagonal cells, the wax temperature was between 33.6 and 37.6 °C. This is well below 40 °C, i.e. the temperature at which wax is assumed to exist in the liquid equilibrium that is essential for self-organised building." From: Hexagonal comb cells of honeybees are not produced via a liquid equilibrium process - Springer

They used heat image recordings and displayed the photographs that was used to record the process. They even cut out a cell and the Bees quickly repaired it into a hexagonal shape and this wasn’t due to physics or any natural forces or “self-organized building” as the article states. The honeybees were directly involved in the building process. If a cell were cut out after the structure had already formed then the Bees would have replaced that cell and created a circle cell shape. They did not. They created a hexagonal shape which not only included repairing that single cell, but also its adjacent cells.

 

[Skwim]

The Traveling Salesman Problem isn’t some easy task to accomplish for people or even computers. Computers have to compute every possible route to determine the shortest. Yet Bees are capable of finding the shortest, most efficient route to hit all of their objectives and to consume the least amount of energy and find their way back to their nest without determining every possible route to find the most efficient.

“The traveling salesman problem is easy to state, and — in theory at least — it can be easily solved by checking every round-trip route to find the shortest one. The trouble with this brute force approach is that as the number of cities grows, the corresponding number of round-trips to check quickly outstrips the capabilities of the fastest computers. With 10 cities, there are more than 300,000 different round-trips. With 15 cities, the number of possibilities balloons to more than 87 billion.” https://www.simonsfoundation.org/quanta/20130129-computer-scientists-take-road-less-traveled/

That is a lot of possibilities for so few cities. A computer has to run every route before it can calculate the shortest most efficient distance or solution. A Bee does not. “After trying about “20 of the 120 possible routes, the bees were able to select the most efficient path to visit the flowers,” Lihoreau says. “They did not need to compute all the possibilities.” A naïve bee traveled almost 2,000 meters on its first foraging bout among the pentagonal array; by her final trip, she’d reduced that distance to a mere 458 meters.” Flying Math: Bees Solve Traveling Salesman Problem - Wired Science

“Professor Lars Chittka from Queen Mary's School of Biological and Chemical Sciences said: ‘In nature, bees have to link hundreds of flowers in a way that minimises travel distance, and then reliably find their way home - not a trivial feat if you have a brain the size of a pinhead! Indeed such travelling salesmen problems keep supercomputers busy for days. Studying how bee brains solve such challenging tasks might allow us to identify the minimal neural circuitry required for complex problem solving.’” Tiny brained bees solve a complex mathematical problem

As the article I linked to observed:

"Even if we had exceptionally tireless bees map a route between a million flowers, would we be able to say that we found a general solution for this? How would we know that they had really found the shortest possible route between flowers and not merely an approximation of the shortest route? Why, we’d have to mathematically set up a Traveling Salesman problem and sic supercomputers on it for days. Even if the supercomputer’s solution and the bees’ solution wound up syncing up perfectly, how would we know that the bees’ solution would be optimal if it was a million and one flowers instead of a million? And so on. It should be clear that the practical application is not and cannot be a mathematical solution.

" There’s a key difference, though, between what the bees did — finding the shortest distance between a set of flowers — and producing a general solution for the mathematical problem known as the Traveling Salesman Problem. To wit: The formal definition of the TSP is, “We are given a complete undirected graph G that has a nonnegative integer cost (weight) associated with each edge, and we must find a hamiltonian cycle (a tour that passes through all the vertices) of G with minimum cost.”​

So while bees do indeed continue to improve their foraging efficiency, even to an amazing degree, it's a fallacy to claim they have "effectively solv(ed) the "travelling salesman problem."

This is from post #28.

"The nests of European honeybees ([FONT=&quot]Apis mellifera[/FONT]) are organised into wax combs that contain many cells with a hexagonal structure. Many previous studies on comb-building behaviour have been made in order to understand how bees produce this geometrical structure; however, it still remains a mystery. Direct construction of hexagons by bees was suggested previously, while a recent hypothesis postulated the self-organised construction of hexagonal comb cell arrays; however, infrared and thermographic video observations of comb building in the present study failed to support the self-organisation hypothesis because bees were shown to be engaged in direct construction. Bees used their antennae, mandibles and legs in a regular sequence to manipulate the wax, while some bees supported their work by actively warming the wax. During the construction of hexagonal cells, the wax temperature was between 33.6 and 37.6 °C. This is well below 40 °C, i.e. the temperature at which wax is assumed to exist in the liquid equilibrium that is essential for self-organised building." From: Hexagonal comb cells of honeybees are not produced via a liquid equilibrium process - Springer

They used heat image recordings and displayed the photographs that was used to record the process. They even cut out a cell and the Bees quickly repaired it into a hexagonal shape and this wasn’t due to physics or any natural forces or “self-organized building” as the article states. The honeybees were directly involved in the building process. If a cell were cut out after the structure had already formed then the Bees would have replaced that cell and created a circle cell shape. They did not. They created a hexagonal shape which not only included repairing that single cell, but also its adjacent cells.

Now this is interesting, and it would be nice to read the full paper. So, although this lack of information (not about to pay to download it) prevents me from changing my belief, it has put me on the fence. Thanks for the information.

 

[Slapstick]

As the article I linked to observed:

"Even if we had exceptionally tireless bees map a route between a million flowers, would we be able to say that we found a general solution for this? How would we know that they had really found the shortest possible route between flowers and not merely an approximation of the shortest route? Why, we’d have to mathematically set up a Traveling Salesman problem and sic supercomputers on it for days. Even if the supercomputer’s solution and the bees’ solution wound up syncing up perfectly, how would we know that the bees’ solution would be optimal if it was a million and one flowers instead of a million? And so on. It should be clear that the practical application is not and cannot be a mathematical solution.

" There’s a key difference, though, between what the bees did — finding the shortest distance between a set of flowers — and producing a general solution for the mathematical problem known as the Traveling Salesman Problem. To wit: The formal definition of the TSP is, “We are given a complete undirected graph G that has a nonnegative integer cost (weight) associated with each edge, and we must find a hamiltonian cycle (a tour that passes through all the vertices) of G with minimum cost.”​

So while bees do indeed continue to improve their foraging efficiency, even to an amazing degree, it's a fallacy to claim they have "effectively solv(ed) the "travelling salesman problem."

It isn’t a fallacy when they can solve it for themselves and not for us. We, people, mathematicians or scientists are the ones responsible for finding better solutions to the problem, not bees. Yet, studying bees may lead to a finding a better solution to complex problem solving. That is why research is done on these animals (and insects) so we can better understand things, such as TSP, how they create their honeycombs and bio-mechanics of flight to create robotics or even nano bots.

“Although the issue is not as profound as how the universe began or what kick-started life on earth, the physics of bee flight has perplexed scientists for more than 70 years. In 1934, in fact, French entomologist August Magnan and his assistant André Sainte-Lague calculated that bee flight was aerodynamically impossible. The haphazard flapping of their wings simply shouldn't keep the hefty bugs aloft.
And yet, bees most certainly fly, and the dichotomy between prediction and reality has been used for decades to needle scientists and engineers about their inability to explain complex biological processes.” From: Deciphering the Mystery of Bee Flight | Caltech

Although when it comes to biomechanics I am more fascinated by other animal’s flight mechanics, such as the hummingbird than Bees and I’m not trying to be sarcastic when I say this, but a Bee isn’t going to get a pencil and piece of paper to write down how it came to its conclusion for us on TSP. That is what science is for. It helps us discover that our methods are not always the best, and this is already known when it comes to TSP. If there is a simpler solution then one is possible and it has been proven by Bees being able to route their shortest distances for foraging.

Now this is interesting, and it would be nice to read the full paper. So, although this lack of information (not about to pay to download it) prevents me from changing my belief, it has put me on the fence. Thanks for the information.

I would send it to you, but doubt I can.

 

[Skwim]

It isn’t a fallacy when they can solve it for themselves and not for us.

The fallacy I was talking about was the remark from the article in The Guardian to which my linked article was referring:

"The insects learn to fly the shortest route between flowers discovered in random order, effectively solving the 'travelling salesman problem'" , said scientists at Royal Holloway, University of London.

'Despite their tiny brains bees are capable of extraordinary feats of behaviour,' said Raine. 'We need to understand how they can solve the travelling salesman problem without a computer.' "
source
​

I would send it to you, but doubt I can.

Thanks for the thought.

 

[LegionOnomaMoi]

The Traveling Salesman Problem isn’t some easy task to accomplish for people or even computers. Computers have to compute every possible route to determine the shortest.

1) It's impossible for computers to accomplish
2) It's often incredibly easy to solve the Traveling Salesman Problem. The problem isn't that we don't have known methods to solve it, the problem is that it represents a class of problems that do not have any singular solution method (it is an optimization problem that ranges from a simplistic path minimization algorithm to a directed graph with weighted edges.
3) Bees are not capable of solving this problem. That is because they can only solve a single instantiation of it, and the only reason it is a difficult problem is because it does not exist as any single instantiation.

Yet Bees are capable of finding the shortest, most efficient route to hit all of their objectives

And I can give you two or three algorithms off of the top of my head that will do this but work for many more instances than the kind of routes bees minimize.

That is a lot of possibilities for so few cities

Let me know when bees come up with solutions for minimizing routes between cities.

It's incredibly difficult to factor large numbers (by large, I mean the kind of numbers so large they are why we have googol). It's simplicity itself to factor 10, or 100, or 149, or a million. You are equating the difficulties that result from a lack of any specific algorithm that applies equally well to any and all instances of any problem that can be formulated as the traveling salesman problem with the difficulty of one, specific instance. If it mattered in the slightest that bees were capable of path minimization, than the traveling salesman problem wouldn't be a problem it would be a button on a graphing calculator.

 

[Slapstick]

And I can give you two or three algorithms off of the top of my head that will do this but work for many more instances than the kind of routes bees minimize.

... and? So what. The point is they do this nature with many hundreds of flowers. Not just this single instance with how the researchers setup their experiment.

Let me know when bees come up with solutions for minimizing routes between cities.

You are making the same mistake that others have made by thinking Bees are to provide some sort of all-purpose solution to TSP.

 

[LegionOnomaMoi]

... and? So what. The point is they do this nature with many hundreds of flowers. Not just this single instance with how the researchers setup their experiment.

The point is directly related to this:

You are making the same mistake that others have made by thinking Bees are to provide some sort of all-purpose solution to TSP.

I'm not making that mistake. The reason that the Traveling Salesman Problem is worthy of note is precisely because there is no all-purpose solution, and thus every class of problems to which solution algorithms are supplied is distinct from every other. Adaptive mechanisms are fairly general (e.g., not bee hive depends on any single configuration of flowers, but rather employs mechanisms which yield optimal or near-optimal routes through path minimization over successive navigations). However, generalization take us only so far. Bees rely on a particular "algorithm' (procedure) that works for particular "classes" of environments. This is as much a solution to the Traveling Salesman Problem as is one's route to get to common locations regularly visited (work, home, bars, friends' houses, grocery store, etc.).