Is Mathematics Alone a safe medium for exploring the frontiers of Science. Or should Observation and Hypothesis lead in front ?

[studiot]

 

Strange

You have answered the question. The purpose of a model in science is to derive precise results. Either to test the theory or to produce useful results. That means it must be mathematical.

 

So offer me a mathematical model of the output of a 74C126.

Edited April 2, 2015 by studiot

[Strange]

However that does not cover up the fact that a mathematical model must contain mathematical axioms and at least one unprovable mathematical deduction.

 

It will implicitly contain mathematical axioms, as all mathematics does. It may contain unprovable results but that is extremely unlikely. Are there examples of theories which choose on one or other possible results of an undecidable proposition? I'm not aware of any (obviously there are in pure maths - new axioms are added and new areas of maths explored).

 

Maybe the maths based on non-Euclidean geometry? Euclid's fifth postulate is unprovable based on the others and you can choose different versions to derive different geometries. And hence GR. Maybe ...

 

So offer me a mathematical model of the output of a 74C126.

 

1. That is not science.

 

2. Which aspect? The logical function? The gain? The drive strength? The semiconductor physics of the manufacturing process? The thermal model of the packaging?

 

Do you think it was designed by chance, or trial and error? No. It was designed using mathematical models for every aspect.

[ajb]

So offer me a mathematical model of the output of a 74C126.

I am a little confused. This chip takes inputs and gives three outputs 'yes', 'no' and 'indeterminate'. If I cannot know what happens when I feed a specific input in, then how is this chip useful? There are various logic tables for different kinds of three state logic. Or am I missing something?

[studiot]

 

strange

Do you think it was designed by chance, or trial and error? No. It was designed using mathematical models for every aspect.

 

 

You are wriggling

 

 

The above is in direct opposition to your other statment in the same post.

 

 

Strange

1. That is not science.

[Strange]

I chose that chip because there is no calculation or observation that can be performed which can unambigouusly answer the question

 

What is the output state of the chip?

 

Nonsense. Your computer wouldn't work if that was true. We model all aspects of the behaviour of circuits like that, at many different levels of detail, to be sure the circuit will work. Do you really think I would sign off a design to a manufacturing process that can cost hundreds of thousands of dollars if I wasn't sure it would work?

You are wriggling

 

No. I am pointing out that there are mathematical models for every aspect of the device.

 

 

The above is in direct opposition to your other statment in the same post.

 

No. I am pointing out that your are dragging engineering into a discussion of science. As it happens, the same is largely true of engineering but that is not the topic of this thread.

I am a little confused. This chip takes inputs and gives three outputs 'yes', 'no' and 'indeterminate'. If I cannot know what happens when I feed a specific input in, then how is this chip useful? There are various logic tables for different kinds of three state logic. Or am I missing something?

 

There are, of course, ways of modelling the behaviour of the device. Otherwise, as you say, it would be of no value.

[John Cuthber]

re. the 74126:

The output isn't indeterminate, it's a high impedance state.

The point is that it makes some sorts of interfacing easier.

these chips are only used when all the outputs of several chips are directly connected together and where the logic ensures that one of the outputs will be driven.

So the output of what actually gets used is determined by the inputs.

 

In fact there is a model of the output; it's disconnected in the 3rd state and drifts with whatever else drives it.

A very simple model compared to the output impedance when it's in one of the other two states where you have to worry about things like fan out.

[studiot]

I am a little confused. This chip takes inputs and gives three outputs 'yes', 'no' and 'indeterminate'. If I cannot know what happens when I feed a specific input in, then how is this chip useful? There are various logic tables for different kinds of three state logic. Or am I missing something?

 

In much of electronics it is bad practice and sometimes dangerous to connect two outputs together, as each device tries to assert its own output.

 

Tristate was invented to cope with this so that two outputs could be connected in opposition without damage by putting one into a don't care (indeterminate is actually a bit of a misnomer) state. Other parts of the circuitry will then determine when the tristate chip output is active or valid, or not.

 

 

If you like it's the Engineer's answer to how to apply an irresistable force to an immovable object.

 

Edit I see I xposted with John Cuthber.

 

Thank you JC, I note you are using an admittedly incorrect model to cope with the inadequacies of the mathematical modle here.

 

The device is not physically disconnected.

 

If it weere there would be no need for tristate devices.

 

So your model is inadequate in that it cannot distinguish between disconnected and tristate.

 

Edit2

It is ironic that as we chat here I am fixing a Hewlett Packard PC that looks like its ethernet connection has suffered physical damage from the recent electrical storm on Exmoor.

Tristate rules OK.

Edited April 2, 2015 by studiot

[Mike Smith Cosmos]

 

Yes indeed, I am not talking about circuit failure or incorrect circuit action.

 

There is a family of logic chips that can be deliberately put into an indeterminate state.

This is known as Tri state logic.

 

http://en.wikipedia.org/wiki/Three-state_logic

. Just saying 'increase' or 'decrease' is not really a prediction. It maybe what one is looking for in an experiment and this could then be used to rule out certain classes of theories.

Well I can not really agree with that .

 

Prof Lee Smolin of the Perimeter Institute in Canada. Came up with an Hypothesis that the universe is constantly changing ( increasing and decreasing . Going through a sort of ' natural selection process' from galaxies, to solar systems to black holes. Constant change and adaption . I am sure his hypothesis has led others in to producing more refined hypothesis , including all sorts of later computer models of exactly what happens where . But it was led by him , with his original proposition and Hypothesis with more global models and reasoning .

 

Mike

Edited April 2, 2015 by Mike Smith Cosmos

[swansont]

.

This juncture is the ' fork in the road' or ' the division in the river tributary ,up stream ' .

 

Going up the Nile , looking for its source , was going to lead Livingstone to Lake Victoria Or a dead end. If figuratively the one leading to the dead end was solely maths ( in its present state of understanding ) , and the one leading to Lake Victoria was figuratively the tributary like some modest amount of maths conjoined with a high percentage of Analogy taken from a direct view of nature with ALL her mysterious, yet undiscovered features . Then success , we would have gained access to waters ,unimaginable , analogous to Lake Victoria in all her depth ,opportunity and glory. Wa hey !

 

Mike

 

image.jpg Analogies + Maths

.

image.jpg. Maths ONLY

 

Q.E.D. .....WA hey !

 

Q.E.D.? Assertions aren't proofs, and for the umpteenth time, absolutely nobody is saying that "maths only" is the exclusive path of discovery. Except you, in the straw man that you have built.

[studiot]

 

Strange

It will implicitly contain mathematical axioms, as all mathematics does. It may contain unprovable results but that is extremely unlikely. Are there examples of theories which choose on one or other possible results of an undecidable proposition? I'm not aware of any (obviously there are in pure maths - new axioms are added and new areas of maths explored).

 

Maybe the maths based on non-Euclidean geometry? Euclid's fifth postulate is unprovable based on the others and you can choose different versions to derive different geometries. And hence GR. Maybe ...

 

 

 

Yes there are things in Mathematics that are not in Physics and vice versa.

 

That was partly why I recently started a thread on that very subject, though not many answered.

We are not supposed to advertise our own threads so no link I'm afraid, but it was in Mathematics.

 

Engineering is the application of Science and a valid and respectable part of this website.

 

I recently had cause to note there the difference in handling of the word 'Field' in Mathematics and Physics.

 

Elsewhere we had a question posed

 

Why do energy bands form in semiconductors?

There are many presentations of this subject online and elsewhere, but they generally seem to state that they do form bands, without explanation.

 

Interestingly the explanation is mathematical, but the also demonstrates a difference between the handling of complex numbers in Mathematics and Physics.

Edited April 2, 2015 by studiot

[Strange]

It is ironic that as we chat here I am fixing a Hewlett Packard PC that looks like its ethernet connection has suffered physical damage from the recent electrical storm on Exmoor.

 

It is worrying that someone who appears not to know how electronic circuits are designed is attempting to fix something. Hopefully it is only a matter of replacing complete sub-systems (which have already been design by engineers with a firm grasp of the mathematics required).

[studiot]

Strange, please compare your directly personal approach here to that of ajb and note the difference in the level, quality and progress of the conversation.

Edited April 2, 2015 by studiot

[Mike Smith Cosmos]

Q.E.D.? Assertions aren't proofs, and for the umpteenth time, absolutely nobody is saying that "maths only" is the exclusive path of discovery. Except you, in the straw man that you have built.

I appreciate that , believe me.

 

But what I am saying there is a good case, when we are trying to search out new ideas , because we have a crop of mysteries outstanding.

 

THEN it is wise to let Observation and Hypothesis lead at the frontiers .

 

As was the case with Livingston I presume.

 

. No doubt the cumbersome , ridged, heavy boats got snarled up in the rapids and swamps. ( like a unsuitable ridged mathematical approach )

 

. Whereas the light ,flexible, craft, could be easily ' portaged ' across or around the swamps and rapids to make it to lake Victoria and the discovery of source of the Nile later. ( like the loose, flexible , lightweight , Observation and Hypothesis approach )

 

Later to meet up with Stanley I presume with his exploits on the Congo river. Africa navigated.

 

Mike

Edited April 2, 2015 by Mike Smith Cosmos

[Strange]

Strange, please compare your directly personal approach here to that of ajb and note the difference in the level, quality and progress of the conversation.

 

Sorry, it was intended as friendly joke, not an attack. I forgot the " :-)"

(And it probably isn't funny, in hindsight. )

Edited April 2, 2015 by Strange

[swansont]

 

 

 

Elsewhere we had a question posed

 

Why do energy bands form in semiconductors?

There are many presentations of this subject online and elsewhere, but they generally seem to state that they do form bands, without explanation.

 

From what I've read, it's the uncertainty principle, same as the level widths in atoms. When you make a hole in a band, it takes a characteristic time to fill it. That determines the energy width of the band, according to ∆E∆t > hbar

 

I'll see if I can dig up a link for that.

[studiot]

I am always happy to appreciate jokes made at my expense, so long as it is clear they are jokes.

 

I like a good joke.

 

Any good Engineer will tell you that the first question to resolve is Hardware or Software?

Mindless changing of boards will not resolve the latter.

But enough of this off topic.

 

Mathematical models and physical reality are not identical.

I have offered some thoughts on their differences.

Please continue to comment technically on them.

[swansont]

I appreciate that , believe me.

 

But what I am saying there is a good case, when we are trying to search out new ideas , because we have a crop of mysteries outstanding.

 

THEN it is wise to let Observation and Hypothesis lead at the frontiers .

 

 

And I believe it is wiser to let the scientists involved make this decision. And given that there are a lot of theoretical physicists (and theoreticians in other disciplines) out there who actually lead with the maths, I believe it is a mistake to insinuate that they are being foolish (i.e. unwise)

[studiot]

 

From what I've read, it's the uncertainty principle, same as the level widths in atoms. When you make a hole in a band, it takes a characteristic time to fill it. That determines the energy width of the band, according to ∆E∆t > hbar

 

I'll see if I can dig up a link for that.

 

Look up the Kronig-Penny model.

[Mike Smith Cosmos]

And I believe it is wiser to let the scientists involved make this decision. And given that there are a lot of theoretical physicists (and theoreticians in other disciplines) out there who actually lead with the maths, I believe it is a mistake to insinuate that they are being foolish (i.e. unwise)

No , I certainly would not want to infer, or want to suggest that .

 

My motive for my pushing this idea of ..(Observation and hypothesis should lead,). is to a very specific end .

 

I am worried that there might well be a whole raft of maths that has yet remained undiscovered. Maths , we would be hard to recognise as maths .

Similarly ,that there might well be a whole other raft of a view of reality ,that has yet remained , unnoticed, not thought about, not speculated upon, and thus no serious observation or hypothesis has as yet not been formed. Because of fear of thinking and speaking about something that sounds ' far fetched'

 

So if it was compulsory ,that we have to use maths , as is, to model reality, for it to be considered science , If we as yet, and maybe never develop the new necessary maths . Then we may be inclined to ignore certain observations , and / or dismiss certain speculations and the following hypothesis , as it does not have a ' current maths ' model .

 

So I am not saying ALL research should not use maths, far from it. But I am suggesting we should allow scientists to observe obscure patterns, hunches, and sometime ideas that sound conflicting with the current model of the cosmos. And to make hypothesis sometimes where as yet, and maybe never( because it is not possible to develop a mathematical model ) . To make hypothesis that can be checked by another method ( say , because it WORKS , or for some other reason )

 

Mike

Edited April 3, 2015 by Mike Smith Cosmos

[swansont]

I am suggesting we should allow scientists to observe obscure patterns, hunches, and sometime ideas that sound conflicting with the current model of the cosmos.

 

Consider it done. In fact, I'll travel back in time and fix things to ensure that this will have happened all along.

 

And to make hypothesis sometimes where as yet, and maybe never( because it is not possible to develop a mathematical model ) . To make hypothesis that can be checked by another method ( say , because it WORKS , or for some other reason )

 

That's more of a problem, because how do you check to see if it works unless you make specific predictions and compare them with experiment?

[Mike Smith Cosmos]

That's more of a problem, because how do you check to see if it works unless you make specific predictions and compare them with experiment?

.

 

. That rather raises a different issue! Or set of issues .

 

Does ' everything ' ...Have to be predictable ? ....eg living things or something else ... Other entities ..? Even other purely ' material phenomenon invisible to us ' but if we want a correct scientific view of things , we surely must take these things into account if we want a ' whole ' scientific view of things ?

 

True most animals are predictable by their instincts , but even then because of complexity issues , individual animals , would not always be predictable .

 

Humans can be pretty unpredictable , sometimes, ... And both animals and humans are considered science based ...and perhaps there is a whole raft of other things yet unidentified , going about their existence in an other unpredictable way !

 

Yet these things might need to be recognised for us to understand ,( scientifically or as necessary for a complete and correct view , scientific view ) how the universe works . That is . If all these wooly issues are not a conflict in terms?

 

Mike

Edited April 4, 2015 by Mike Smith Cosmos

[ajb]

I am worried that there might well be a whole raft of maths that has yet remained undiscovered.

There almost certainty is and for sure there are lots of things we don't know in already established branches of mathematics. If not, I would be out of a job.

 

Maths , we would be hard to recognise as maths.

I am not sure about this. Humans seem to recognise mathematics even if we can't properly define it.

 

 

So if it was compulsory ,that we have to use maths , as is, to model reality, for it to be considered science , If we as yet, and maybe never develop the new necessary maths . Then we may be inclined to ignore certain observations , and / or dismiss certain speculations and the following hypothesis , as it does not have a ' current maths ' model .

Well, I understand where you are coming from here. However, my reply is that physics offers great motivation to understand mathematics, to discover new mathematics and to develop further tools. We have seen this in practice over hundreds of years now and it is still happening today. Things that don't quite fit can be great sources of ideas.

 

But I am suggesting we should allow scientists to observe obscure patterns, hunches, and sometime ideas that sound conflicting with the current model of the cosmos. And to make hypothesis sometimes where as yet, and maybe never( because it is not possible to develop a mathematical model ) . To make hypothesis that can be checked by another method ( say , because it WORKS , or for some other reason )

To some extent this does happen. I have said it all along the way; experiments/observations do throw up surprises. But we have these surprises because of deviations from what was expected and these come from the theory. We need some 'theoretical background' to compare our finding against. These finding will either support the theory or will help find a better theory.

 

True most animals are predictable by their instincts , but even then because of complexity issues , individual animals , would not always be predictable .

This is a good point, but physicists developed statistical methods for this sort of thing. You may not be able to make great predictions of the individuals, but you maybe able to make sense of what happens on average or what happens collectively for groups of such individuals. Again mathematics is vital here.

Edited April 4, 2015 by ajb

[swansont]

.

 

. That rather raises a different issue! Or set of issues .

 

Does ' everything ' ...Have to be predictable ?

If you want it to be called a scientific theory, yes.

 

....eg living things or something else ... Other entities ..? Even other purely ' material phenomenon invisible to us ' but if we want a correct scientific view of things , we surely must take these things into account if we want a ' whole ' scientific view of things ?

 

True most animals are predictable by their instincts , but even then because of complexity issues , individual animals , would not always be predictable .

 

Humans can be pretty unpredictable , sometimes, ... And both animals and humans are considered science based ...and perhaps there is a whole raft of other things yet unidentified , going about their existence in an other unpredictable way !

 

Yet these things might need to be recognised for us to understand ,( scientifically or as necessary for a complete and correct view , scientific view ) how the universe works . That is . If all these wooly issues are not a conflict in terms?

 

Mike

Do we have theories of individual behavior (e.g. is there a "theory of how Chuck behaves" that's science), or is it more group behavior, where we can use statistical analysis (i.e. math)?

[Mike Smith Cosmos]

If you want it to be called a scientific theory, yes. Do we have theories of individual behavior (e.g. is there a "theory of how Chuck behaves" that's science), or is it more group behavior, where we can use statistical analysis (i.e. math)?

I do see what you are getting at . But I wonder if by trying to insist on predictability as a pre requisite for every single corner of science, you might be ' missing a trick '

 

I know I am just about 'to walk out on thin ice ' . But if I have got it right , and that is most unlikely , Women , do NOT Generally like to be thought of as predictable. Men like to be though of as dependable. Anyway the ice is creaking .

 

..........'Knowing ' .... about nature, I would have thought could be counted as scientific , even if we could not predict something about the behaviour of a something. I appreciate this is considerably looser than predicting the angle of a trajectory after a collision. That is fine rigorous and very useful . But as regards a new as yet unknown area of knowledge , surely just discovering that it exists, knowing that some 'thing' is actually there, with a few vague descriptions , is still conducting science and discovery , even though at this stage we can make NO predictions , as to its behaviour

 

Mike .

Edited April 4, 2015 by Mike Smith Cosmos

[swansont]

I do see what you are getting at . But I wonder if by trying to insist on predictability as a pre requisite for every single corner of science, you might be ' missing a trick '

 

I know I am just about 'to walk out on thin ice ' . But if I have got it right , and that is most unlikely , Women , do NOT Generally like to be thought of as predictable. Men like to be though of as dependable. Anyway the ice is creaking .

And what does this have to do with whether something is considered science?