Maths Uni Chat Watch

v-zero
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#741
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#741
(Original post by CHEM1STRY)
Which area of maths would you people say will advance most in the next century? Which has the most room for 'expansion' if you get what I am saying?
Probably computational, with the advent of quantum computing and improvements in massively parallel programming...
If we can reach the point wherein we can take infinite calculations in finite time, then we can prove/disprove a lot of things computationally...
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Oh I Really Don't Care
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#742
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#742
(Original post by v-zero)
Probably computational, with the advent of quantum computing and improvements in massively parallel programming...
If we can reach the point wherein we can take infinite calculations in finite time, then we can prove/disprove a lot of things computationally...
Yes - but in theory that could be done now. The only problem with perfomring an infinte number of calculations is the time taken at each step - for instance if the first step took 1 unit time, and each step after required 1/3 as much time then the total time required would be;

1 + 1/3 + 1/9 + ...

3/2 units - which sounds all well and peachy but note that in physical reality there is a limit to processing time - say when the components start to approach the speed of light - but we can clearly find that for some Nth step, all steps greater than n require less processing time than this physical cap that we cannot make smaller.

Even with quantum computing things would be bad.

(Original post by CHEM1STRY)
Which area of maths would you people say will advance most in the next century? Which has the most room for 'expansion' if you get what I am saying?
In stark contrast to the above I would also say that computational mathematics has a lot to look forward to.
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MrShifty
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#743
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#743
(Original post by Simplicity)
Wait a minute, would you class yourself as a mathematician that doesn't care about the foundation? as yeah one of my lecturer said he doesn't worry about it. Its a bit of a weird philosophy
Pretty much, though it's not so much a philosophy as it is a preference. Having said that, the truth is that most of us use categories without really thinking about it, either in the guise of homology, representations, homomorphism spaces or what have you, so it's not like people are ignoring category theory, more it's just not as high on the list of priorities for some people.

And it really is a question of personal priorities. Mathematics is such a vast and diverse field today, much more so than it was even in the twenties or thirties, that it's largely impractical for someone to have a specialist knowledge in more than a couple of areas. So, if you want to work in some particular area, you're better served by getting a grip on those areas that are most relevant to your interests. In some cases this will indeed include an in depth knowlege of category theory, and in others you can get on just fine only knowing the basics and treating it more as a useful tool.
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v-zero
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#744
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#744
(Original post by DeanK22)
Yes - but in theory that could be done now. The only problem with perfomring an infinte number of calculations is the time taken at each step - for instance if the first step took 1 unit time, and each step after required 1/3 as much time then the total time required would be;

1 + 1/3 + 1/9 + ...

3/2 units - which sounds all well and peachy but note that in physical reality there is a limit to processing time - say when the components start to approach the speed of light - but we can clearly find that for some Nth step, all steps greater than n require less processing time than this physical cap that we cannot make smaller.

Even with quantum computing things would be bad.
That is only one of many suggestions though...
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Oh I Really Don't Care
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#745
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#745
(Original post by v-zero)
That is only one of many suggestions though...
I'm pretty sure that is the only method for computing an infinte amount of steps in a finite time - even with quantum computers the processing time of each step must be such that the sum of the time required for all processing steps is finte.
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v-zero
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#746
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#746
(Original post by DeanK22)
I'm pretty sure that is the only method for computing an infinte amount of steps in a finite time - even with quantum computers the processing time of each step must be such that the sum of the time required for all processing steps is finte.
I'm pretty sure you're wrong, however I'm too tired to bother to look it up, and so I will instead hit the sack.
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Totally Tom
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#747
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#747
fight!
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Simplicity
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#748
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#748
(Original post by v-zero)
I'm pretty sure you're wrong, however I'm too tired to bother to look it up, and so I will instead hit the sack.
I don't like to take sides. But, I think DeanK22 is right.
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v-zero
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#749
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#749
(Original post by Simplicity)
I don't like to take sides. But, I think DeanK22 is right.
Then I disagree with you both..
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CHEM1STRY
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#750
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#750
To reach 3/2 units time you would need to perform infinite calculations surely? If it requires 1/3 of the previous time only via infinite calculations can we reach 3/2 units, the finite time?! This is confusing
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Hathlan
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#751
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#751
(Original post by Totally Tom)
fight!
fail tom is fail
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Totally Tom
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#752
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#752
(Original post by Hathlan)
fail tom is fail
shut up Kathleen.
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The Muon
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#753
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#753
(Original post by Totally Tom)
shut up Kathleen.
ouch, thats gonna hurt
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Oh I Really Don't Care
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#754
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#754
(Original post by CHEM1STRY)
To reach 3/2 units time you would need to perform infinite calculations surely? If it requires 1/3 of the previous time only via infinite calculations can we reach 3/2 units, the finite time?! This is confusing
The principle behind the idea is that of a convergent series (more specifically the geometric series in the example given.). In theory if you could continue the process of reducing the calculation time of each step (in such a way you satisfy certain conditions) you could do infintely many calculations in finte time.
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CHEM1STRY
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#755
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#755
(Original post by DeanK22)
The principle behind the idea is that of a convergent series (more specifically the geometric series in the example given.). In theory if you could continue the process of reducing the calculation time of each step (in such a way you satisfy certain conditions) you could do infintely many calculations in finte time.
Ah, I see. The limitations are the hardware?
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Oh I Really Don't Care
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#756
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#756
(Original post by CHEM1STRY)
Ah, I see. The limitations are the hardware?
Yeah - because at some point your hardware could have the best possible scenario of moving basically at the speed of light (lets pretend it can even though this would require infinte energy). When the hardware reaches this maximum speed a calculation takes 1/e unit time (e > 0). The hardware can't go any faster so all steps thereafer take a time of 1/e units at best and so if we perfome ne steps after this point we take at least n unit time to do so - and we can make n arbitarly large.
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DFranklin
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#757
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#757
(Original post by DeanK22)
Yeah - because at some point your hardware could have the best possible scenario of moving basically at the speed of light (lets pretend it can even though this would require infinte energy).
Couple of points: photons manage to travel quite well at the speed of light without using infinite energy.

But more importantly, the whole point of a quantum computer is that it can do many calculations simultaneously. If you consider that a quantum computer can have an infinite number of eigenstates, it is not impossible to imagine scenarios where you could effectively do an infinite number of calculations (with the "best" result emerging as a single eigenstate).

Now I'm pretty sure that isn't possible in practice (and it's *very* not-possible in terms of what we actually know how to do) but it's for reasons quite a bit more involved than simply "the speed of light".
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Swayum
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#758
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#758
I now officially use Maple. I feel so grown up :proud:

In other news, things are going pretty well I think. Need to focus more on the social aspect though but a lot of economics has piled up somehow
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Oh I Really Don't Care
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#759
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#759
(Original post by DFranklin)
Couple of points: photons manage to travel quite well at the speed of light without using infinite energy.
I think it is quite obvious I wasn't talking about every type of particle in the universe but the actual hardware of the machine we are using.

(Original post by DFranklin)
But more importantly, the whole point of a quantum computer is that it can do many calculations simultaneously. If you consider that a quantum computer can have an infinite number of eigenstates, it is not impossible to imagine scenarios where you could effectively do an infinite number of calculations (with the "best" result emerging as a single eigenstate).

Now I'm pretty sure that isn't possible in practice (and it's *very* not-possible in terms of what we actually know how to do) but it's for reasons quite a bit more involved than simply "the speed of light".
There surely would be some hardware that would limit the machine during the process?
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DFranklin
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#760
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#760
(Original post by DeanK22)
I think it is quite obvious I wasn't talking about every type of particle in the universe but the actual hardware of the machine we are using.
Actual hardware that uses photons already exists. Although as I said, it's a minor issue - speed of light is still finite, so it doesn't affect your point.

There surely would be some hardware that would limit the machine during the process?
Surely. But that's more of a statement of faith than of calculation, unless you've actually done the math. I know I don't know enough to do so, which as I say, puts it a fair way beyond the trivial "things can't move faster than light" observation.
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